Volume of Sphere B is 8 times greater than the volume of Sphere A
What does sphere refer to?
A sphere is symmetrical and round in form. All of its surface points are equally spaced from the centre, making it a three-dimensional solid. Depending on the radius, it has a surface area and a volume. No faces, corners, or edges exist on it.
It is sometimes referred to as the second cousin of a circle, the sphere is a three-dimensional form. Round, without boundaries, and solid in shape, a sphere is spherical. Examples of spherical shapes include a playing ball, a balloon, and even light bulbs.
Sphere A: V = 4π (2³)/3 = 32π/3
Sphere B: V = 4π (4³)/3 = 4π(64)/3 = 256π/3
volume of Sphere B / volume of Sphere A = (256π/3)/(32π/3) = 8
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Construction company A is determining whether it should submit a bid for a new shopping center. In the past, their main competitor, construction company B, has submitted bids 70% of the time. If company B does not bid on a job, the probability that company A will get the job is 0.20 . If company B bids on a job, the probability that company A will get the job is 0.15 . a. If company A gets the job, what is the probability that company B did not bid? b. What is the probability that company A will get the job?
a. The probability that company B did not bid given that company A got the job is 0.375 or 37.5%.
b. The probability that company A will get the job, we can use the law of total probability is 0.16 or 16%.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is used to quantify the uncertainty of an outcome, and is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
What is Bayes' Theorem?Bayes' theorem is a mathematical formula that describes the probability of an event based on prior knowledge or information. It is named after the 18th-century English mathematician Thomas Bayes, who first formulated the theorem.
In the given question,
a. To find the probability that company B did not bid given that company A got the job, we can use Bayes' theorem:
P(B did not bid | A got the job) = P(A got the job | B did not bid) * P(B did not bid) / P(A got the job)
We know that P(A got the job | B did not bid) = 0.20, P(B did not bid) = 1 - 0.70 = 0.30, and P(A got the job) = P(A got the job | B did not bid) × P(B did not bid) + P(A got the job | B bid) × P(B bid) = 0.20 × 0.30 + 0.15× 0.70 = 0.16.
Therefore,
P(B did not bid | A got the job) = 0.20 × 0.30 / 0.16 = 0.375 or 37.5%.
b. To find the probability that company A will get the job, we can use the law of total probability:
P(A got the job) = P(A got the job | B did not bid) * P(B did not bid) + P(A got the job | B bid) × P(B bid)
We know that P(A got the job | B did not bid) = 0.20, P(B did not bid) = 0.30, P(A got the job | B bid) = 0.15, and P(B bid) = 0.70. Plugging these values in, we get:
P(A got the job) = 0.20× 0.30 + 0.15 × 0.70 = 0.16 or 16%.
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Question at position 5 The sum of two numbers is 15. If the second number is twice the other, what is the working equation for this problem as well as the values of the two numbers?
The two numbers are 5 and 10 and the working equation for this problem is:x + 2x = 15
The sum of the two numbers is 15. If the second number is twice the other, then the working equation for this problem as well as the values of the two numbers according to the given question is the second number y is twice the first number x.
Therefore,y = 2x
Also, the sum of these two numbers is given as 15.
Therefore,x + y = 15
Substituting the value of y in terms of x, we get x + 2x = 15
Simplifying the above equation, we get:3x = 15x = 5
Substituting this value of x in the equation y = 2x, we get:y = 2(5)y = 10
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Please ASAP Help
Will mark brainlest due at 12:00
Answer: -5
Step-by-step explanation:
Miranna teaches gymnastics lessons at summer camp. She is paid $12. 50 per hour.
A. If Miranna were offered a raise of 100% per hour, what would her new hourly rate be? What percent of her original pay would she be paid?
B. Miranna is offered a raise of 75% of her hourly rate to reach a private lesson. How much per hour would she be paid for the private lesson?
C. What is the relationship between the percent raise that Miranna gets her new pay as a percent of her original pay? How is she related to the scale factor (multiplier) between her original pay and her new pay?
Miranna is offered a 75% raise of her hourly rate to reach a private lesson, which would make her hourly pay $21.88.
This is calculated by taking the original hourly rate of $12.50 and multiplying it by 1.75 (the percent raise she is getting).
The relationship between the percent raise and Miranna's new pay is the same as the relationship between her original pay and her new pay. The percent raise (75%) is equal to the scale factor (1.75) between her original and new pay. In other words, the percent raise is a measure of the degree of increase between her original pay and her new pay.
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The cost of cleaning up pollution in a stream is given by C=42000/(100-p), where C is the cost in dollars to clean p percent of the stream. (For instance, when p is 20, then the formula will calculate the cost to clean up 20 percent of the stream. )
a. Find the cost of cleaning up 40% of the stream.
b. What percent can be cleaned up for $1100
c. P must be greater than or equal to zero and p must be less than what number? Why?
The cost of cleaning up 40% of the stream is amount $7000, and 97.45% of the stream can be cleaned up for $1100. P must be greater than or equal to zero and p must be less than 100.
a. C = 42000/(100-p) => C = 42000/(100-40) = $7000
b. 1100 = 42000/(100-p) => p = (42000-1100)/42000 = 97.45%
c. P must be greater than or equal to zero and p must be less than 100. This is because the cost of cleaning up a stream cannot be negative and the stream cannot be cleaned up more than 100%.
The cost of cleaning up 40% of the stream is amount $7000, and 97.45% of the stream can be cleaned up for $1100. P must be greater than or equal to zero and p must be less than 100.
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Mathew, your classmate, who is also an SK Chairman in your Barangay Matayog,
organized a KITE FLYING FESTIVAL. He informed your school principal to motivate
students to join the said KITE FLYING FESTIVAL.
1. Suppose you are one of the students in your barangay, how will you prepare the design of
the kite?
2 Make a design of the kite assigned to you.
3. Illustrate every part or portion of the kite including their measures.
4. Using the design of the kite made, determine all the mathematics concepts or principles
involved.
patulong poh.
By following the steps mentioned we can create unique kite design and enjoy flying it with your friends and family using mathematics concepts.
Steps:
Designing the kite:
Designing a kite can be a fun and creative process. First, you need to determine the shape and size of your kite. You can choose from different shapes such as diamond, triangle, hexagon, or even a custom design. Once you have determined the shape, you can start working on the materials. For instance, you may choose to use plastic, paper, or cloth. After that, you need to consider the frame of the kite. You may use bamboo sticks or other lightweight materials. Lastly, you can decorate your kite with colors, patterns, and designs.
Sample kite design:
For this sample design, we will use a diamond shape kite, measuring 50cm by 50cm. The materials used are plastic for the kite body and bamboo sticks for the frame. Here's how you can make the kite:Cut the plastic into a diamond shape, measuring 50cm by 50cm.Attach the bamboo sticks on the edges of the kite, using adhesive tape or glue.Add a tail to the kite, measuring 100cm long.Cut a small hole in the center of the kite, where you will attach the string.Parts of the kite:
Here are the different parts of the kite and their measures:Kite body: Diamond shape, measuring 50cm by 50cm.Frame: Bamboo sticks, measuring 55cm for the vertical sticks, and 60cm for the horizontal sticks.Tail: Made of lightweight materials, measuring 100cm long.String: Attached to the center of the kite, measuring 50 meters long.Mathematics concepts involved:
Designing a kite involves several mathematical concepts, such as:
Geometry: Determining the shape, size, and measurements of the kite requires an understanding of geometry concepts such as angles, triangles, and polygons.Measurement: Measuring the different parts of the kite, including the body, frame, tail, and string, requires an understanding of measurement units such as centimeters, meters, and feet.Proportions: Ensuring that the frame and tail are proportionate to the kite body requires an understanding of ratios and proportions.Physics: Flying a kite involves concepts such as lift, drag, and gravity, which are all related to the principles of physics.Learn more about mathematics here:
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The graphic shows 2 lines and 2 rays that intersect at a point 0 to create 6 angles. What are TWO equations that can be used to find m∠3 if the measures of the other angles are known? Responses m∠1 + m∠2 + m∠3 = 180° m∠1 + m∠2 + m∠3 = 180° m∠2 + m∠3 + m∠4 = 180° m∠2 + m∠3 + m∠4 = 180° m∠3 + m∠4 + m∠5 = 180° m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 + m∠3 + m∠4 = 180° m∠1 + m∠2 + m∠3 + m∠4 = 180° m∠3 + m∠4 + m∠5 + m∠6 = 180°
Accοrding tο the angle sum prοperty οf a triangle, m∠1 + m∠2 + m∠3 = 180° and m∠3 + m∠4 + m∠5 = 180° these twο equatiοns can be used tο find m∠3.
What is the angle sum prοperty οf a triangle?The angle sum prοperty οf a triangle is a fundamental geοmetric prοperty that states that the sum οf the interiοr angles οf a triangle is always equal tο 180°. In οther wοrds, fοr any triangle, the sum οf the measures οf its three interiοr angles is always 180°.
This prοperty hοlds true fοr all triangles, regardless οf their size οr shape. It is an impοrtant cοncept in geοmetry and is used in variοus prοοfs and calculatiοns invοlving triangles.
One cοmmοn applicatiοn οf the angle sum prοperty οf a triangle is tο find the measure οf an unknοwn angle in a triangle if the measures οf the οther twο angles are knοwn. This can be dοne by subtracting the sum οf the knοwn angles frοm 180°.
The twο equatiοns that can be used tο find the measure οf angle 3 (m∠3) if the measures οf the οther angles are knοwn are:
m∠1 + m∠2 + m∠3 = 180°
This equatiοn can be used if the measures οf angles 1 and 2 are knοwn. We can find the measure οf angle 3 by subtracting the sum οf angles 1 and 2 frοm 180°.
m∠3 + m∠4 + m∠5 = 180°
This equatiοn can be used if the measures οf angles 4 and 5 are knοwn. We can find the measure οf angle 3 by subtracting the sum οf angles 4 and 5 frοm 180°.
Thus, m∠1 + m∠2 + m∠3 = 180° and m∠3 + m∠4 + m∠5 = 180° these twο equatiοns can be used tο find m∠3.
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Beth bought 15 tickets to a movie, where adult tickets cost $6.00 and senior citizen tickets cost $4.00. She spent a total of $76. Which system of equations will determine the number of adult tickets, a, and the number of senior citizen tickets, s, Beth purchased?
Answer: a + s = 15
6.00a + 4.00s = 76
Chocolate Co. mixes two kinds of chocolate bars in a gift bag that weighs 3 pounds and has a total cost of $15. The expensive candy bars are $6 a pound and the other cost $4.50. How many pounds of each are used to make the gift bag? x=expensive y=Other
Answer:
1 lb expensive chocolate
2 lbs other chocolate
Step-by-step explanation:
let x = number of pounds of the expensive candy bars
let y = number of pounds of the other candy bars
here is the first equation:
(the expensive lbs + other lbs comes to a total of 3 lbs altogether)
x + y = 3
here is the second equation:
($6 per pound + $4.5 per pound = $15)
6x + 4.5y = 15
we can do substitution, elimination, or graph.
let's do elimination with these two equations:
x + y = 3 AND 6x + 4.5y = 15
Let's eliminate the variable x to find variable y, and then use what we found for variable y to find variable x.
Multiply (x + y = 3) with 6
Which looks like this: 6(x+y = 3)
And the above becomes 6x + 6y = 18
the equation x + y = 3 becomes 6x + 6y = 18
the equation 6x + 4.5y = 15 stays the same
Subtract to eliminate x.
6x + 6y = 18
- 6x +4.5y = 15
-------------------------
0 + 1.5y = 3
1.5y = 3, divide both sides by 1.5 to get y
1.5y 3
----- = -----
1.5 1.5
y = 2
Therefore, there are 2 pounds of "other" chocolate in the gift bag. Let's use that to find the pounds of the "expensive" chocolate.
Take one of the original equations and plug in "2" for the variable y.
x + y = 3 OR 6x + 4.5y = 15
Lets use x + y = 3, which becomes x + 2 = 3. Solve that, and you will get:
x = 1
Therefore, there is 1 pound of "expensive" chocolate in the gift bag.
(after you are done solving, plug in the numbers you found to one of the equations...ps i checked already so those are correct.
e.g 1 + 2 = 3 )
:))
What is the greatest common factor of 53 and 11?
Answer:
1
Step-by-step explanation:
Both of those numbers are prime, so their GCF's are 1
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Answer:
b d
Step-by-step explanation:
Calculate the value o x if:
72:64=x:16
Evaluate the expression below at x = 5.
Answer:
A
Step-by-step explanation:
[tex](2x-5)^{(x-1)}[/tex] ← substitute x = 5
[tex](2(5)-5)^{(5-1)}[/tex]
= [tex](10-5)^{4}[/tex]
= [tex]5^{4}[/tex]
= 625
Find the ratio of squares to circles
I believe the ratio of circle to square is 2:3
The price of a jumper is reduced by 17% in a
sale. The sale price is £62.25.
What was the original price of the jumper?
Give your answer in pounds (£).
SALE
17% off!
Original price = £
Sale price = £62.25
Answer: it is $51.67 in dollars
Step-by-step explanation:
Answer:
£75
Step-by-step explanation:
To find the original price of the jumper using a formula, we can use the following formula:
Sale Price = Original Price - (Discount Rate x Original Price)
Where Sale Price is the price of the jumper after the 17% discount, Discount Rate is the percentage discount applied, and Original Price is the price of the jumper before the discount.
We know that the Sale Price is £62.25, and the Discount Rate is 17%, so we can substitute these values into the formula:
£62.25 = Original Price - (0.17 x Original Price)
Simplifying this equation, we get:
£62.25 = Original Price - 0.17Original Price
£62.25 = 0.83Original Price
Dividing both sides by 0.83, we get:
Original Price = £75
Therefore, the original price of the jumper was £75
PLEASE SHOW WORK!!!!!
The correct answer is D. Only statements I and III are true for pi < theta < 3.
What are trigonometric functions?
Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. They are commonly used in geometry, physics, and engineering to solve problems involving triangles and periodic phenomena. The six basic trigonometric functions are:
Sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.
Cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle.
Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.
Cosecant (csc): the reciprocal of the sine function.
Secant (sec): the reciprocal of the cosine function.
Cotangent (cot): the reciprocal of the tangent function.
To answer this question, we need to analyze the given range of values for theta, and determine the signs of the trigonometric functions involved.
For pi < theta < 3, we know that theta is in the second quadrant, where sine is positive and cosine is negative.
Therefore, statement I is true, since sine is positive for values of theta in this range.
Statement II is false, since cosine is negative in the second quadrant, and 2 cos theta is also negative.
Statement III is true, since tangent is negative in the second quadrant, and (1/3) tan theta is also negative.
So, the correct answer is D. Only statements I and III are true for pi < theta < 3.
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Oliver makes two mosaics using coloured tiles.
For the first mosaic he uses red, blue and
purple tiles in the ratio 12 : 3:2.
For the second mosaic he uses red and blue
tiles in the ratio 8 : 5.
Oliver uses the same number of blue tiles for
each mosaic.
What is the ratio of red tiles in the first mosaic
to red tiles in the second mosaic?
Give your answer in its simplest form.
Therefore, the ratio of red tiles in the first mosaic to red tiles in the second mosaic is 33:34 in its simplest form.
What is ratio?A ratio is a way of comparing two or more quantities that are of the same type. It is a mathematical expression that compares the size or amount of one quantity relative to another. Ratios are expressed as a pair of numbers separated by a colon (:) or as a fraction. For example, the ratio of apples to oranges in a basket might be 3:2 or 3/2, which means there are three apples for every two oranges in the basket. Ratios are used in many different areas of mathematics and in real-world applications such as cooking, finance, and engineering.
Here,
17x tiles used in the first mosaic, and 13x tiles used in the second mosaic.
If we want to use the same number of blue tiles in each mosaic, we need to make sure that the total number of tiles used in each mosaic is the same. This means we need to find a common multiple of 17 and 13 that we can use as the total number of tiles in each mosaic. The smallest such multiple is:
17 * 13 = 221
So, we'll assume that Oliver used 221 tiles in each mosaic (even though we don't know the actual number of tiles he used).
For the first mosaic, the ratio of red to blue to purple tiles is 12:3:2. This means that for every 17 tiles used, we have:
12/17 (red tiles), 3/17 (blue tiles), and 2/17 (purple tiles)
Multiplying each of these fractions by 221 (the total number of tiles), we get:
132 (red tiles), 33 (blue tiles), and 44 (purple tiles)
For the second mosaic, the ratio of red to blue tiles is 8:5. This means that for every 13 tiles used, we have:
8/13 (red tiles) and 5/13 (blue tiles)
Multiplying each of these fractions by 221 (the total number of tiles), we get:
136 (red tiles) and 85 (blue tiles)
So, the ratio of red tiles in the first mosaic to red tiles in the second mosaic is:
132/136 = 33/34
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Which expression is NOT equivalent to the others?
The expression [tex](2+7)^2[/tex] is not equivalent to the others as it is an exponential expression, while the others are all linear expressions.
The expression [tex](2+7)^2[/tex] is not equivalent to the others as it is an exponential expression, while the others are all linear expressions. An exponential expression is a mathematical expression that contains a variable in an exponent, meaning it is raised to a certain power, while a linear expression is a mathematical expression that contains two or more variables, where each has an exponent of 1. For example,[tex](2+7)^2[/tex] can be written as[tex]9^2[/tex]which is equal to 81. In contrast, the other expressions can be written as 2x+7y+3z which is equal to 2x+7y+3z. This means that the two expressions are not equivalent. To illustrate further, we can use a simple example. Let's say x=2, y=3, and z=4. Then the linear expression 2x+7y+3z would be equal to 2(2)+7(3)+3(4) = 22. The exponential expression[tex](2+7)^2[/tex] would be equal to [tex](2+7)^2 = 9^2 = 81[/tex]. We can see here that the two expressions are not equivalent.
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Which expression is NOT equivalent to the others?
A) 2 + 4
B) 6 - 2
C) 8 ÷ 4
D) 3 x 2
Alicia spun a spinner 100 times, and the results are shown in the following table. What is the relative frequency for the spinner to land on number 1?
Responses
Answer:
3/25
Step-by-step explanation:
Using the graph as your guide, complete the following statement.
The discriminant of the function is
• A. positive
B. zero
C. negative
PLEASE HELP ASAP
Answer:
THE ANSWER IS B
Step-by-step explanation:
Answer:
B : Zero
Step-by-step explanation:
What is the arc measure of AE ⌢ A, E, start superscript, \frown, end superscript in degrees?
The arc measure of AE A, E, start superscript, frown, finish superscript in degrees cannot be determined without more information. To make this conclusion, additional information .
Such as the locations of points A and E and/or the degree measures of other angles in the same circle would be required. An arc is a piece of a circle's circumference, and its degree measure is equal to the degree measure of the central angle that subtends the arc. To compute the arc measure of AE A, E, start superscript, frown, end superscript in degrees, we would need to know the degree measure of the central angle that subtends this arc or the degree measure of the central angle that subtends this arc.
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Eleven percent of students at a large high school are left- handed: A statistics teacher selects a random sample of 100 students and records X = the number of left-handed students in the sample. Calculate the mean and standard deviation of the sampling distribution of X. Interpret the standard deviation
The mean of the sampling distribution of X turns out as 11 and the standard deviation is identified as 3.13. By using concepts of standard deviation, the sample deviation can be calculated.
The mean and standard deviation of the sampling distribution of X can be calculated using the formulas for the mean and standard deviation of a binomial distribution. The mean is given by: [tex]μ = np[/tex]
Where n is the sample size and p is the proportion of left-handed students in the population. In this case, n = 100 and p = 0.11, so:
[tex]μ = (100)(0.11) = 11[/tex]
The standard deviation is given by:
[tex]σ = √(np(1-p))σ = √((100)(0.11)(1-0.11)) = √(9.79) = 3.13[/tex]
So the mean of the sampling distribution of X is 11 and the standard deviation is 3.13.
The standard deviation of the sampling distribution of X tells us how much variability we can expect in the number of left-handed students in a random sample of 100 students from the population.
In this case, the standard deviation of 3.13 tells us that there is a moderate amount of variability in the number of left-handed students in different samples of 100 students from the population.
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The pharaoh's outfitters, 'Cloaks and
Crowns', sell cloaks and crowns in 3
sizes - prince, king and emperor (in
increasing size order).
He wants to kit out his three sons for the
forthcoming festival of Ra. Ahmose
chooses a bigger cloak than Kamose,
but a smaller crown than Thutmose.
Both Thutmose's cloak and crown are
larger than Kamose's, but the size of
Thutmose's crown matches the size of
Kamose's cloak.
Which sizes did the
pharaoh's sons each get?
Mila has a DRF of 1. 15 and a 6-month basic rate of $650. What is her annual premium?
Mila has a DRF of 1. 15 and a 6-month basic rate of $650. Her annual premium is $1,495.
Mila has a 6-month basic cost of $650 and a DRF of 1.15.
We have to determine her annual premium.
As we know that in a year have 12 months and 6 months basic cost is $650. So the time period is 2.
Annual premium is the total amount of money paid in one year for an insurance policy. It is usually paid in one lump sum or in installments throughout the year.
Since we know the cost of premium of 6 months. So
Mila annual premium = 650 x 2 x 1.15
Mila annual premium = $1,495
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The straightaway on each side measures 1,000 meters. The curves are semicircles with diameter 74 meters. What is the distance, in meters, around the entire track? Use the π button on your calculator and express your answer to the nearest hundredth
If the straightaway on each side measures 1,000 meters, the distance around the entire track is approximately 2,465.09 meters.
To find the distance around the entire track, we need to add the distance of the straightaways on both sides and the distance around the curves. The straightaways measure 1,000 meters on each side, so the total distance covered in straightaways is 2,000 meters.
The curves are semicircles with diameter 74 meters. The circumference of a circle is given by the formula 2πr, where r is the radius. Since the diameter of the semicircle is given as 74 meters, the radius will be half of it, i.e., 37 meters. Hence, the distance around each semicircle will be:
Circumference = 2πr = 2π(37) = 74π
Since there are two semicircles in the track, the total distance around the curves is 2(74π) = 148π meters.
Therefore, the total distance around the entire track is:
Total distance = Straightaways + Curves
= 2,000 + 148π
= 2,000 + 465.09 (approximating π as 3.14)
= 2,465.09 meters (rounded to the nearest hundredth)
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At westville highschool there are 315 seniors and 389 juniors 65% of the seniors have parking passes and 42% of the juniors have parking passes the statistics teacher selects an SRS of 30 seniors and a seperate SRS of 30 juniors
The probability of selecting a senior who has a parking pass and a junior who has a parking pass is 0.2730.
At Westville Highschool, there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects an SRS (Simple Random Sample) of 30 seniors and a separate SRS of 30 juniors.
To determine the probability of selecting a senior who has a parking pass and a junior who has a parking pass, first the probability of selecting a senior who has a parking pass must be calculated. Since 65% of the seniors have parking passes, the probability of selecting a senior with a parking pass is 0.65. Secondly, the probability of selecting a junior with a parking pass must be calculated. Since 42% of the juniors have parking passes, the probability of selecting a junior with a parking pass is 0.42.The probability of selecting a senior who has a parking pass and a junior who has a parking pass can be found by multiplying the two probabilities. 0.65 x 0.42 = 0.2730.
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Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8. 11 and a standard deviation of 1. 46. Using the empirical rule, what percentage of American women have shoe sizes that are at least 11. 3
About 1.5% of American women have shoe sizes that are at least 11.3, using the empirical rule and a standard normal distribution table.
To use the empirical rule, we assume that the shoe sizes follow a normal distribution. We can then convert the shoe size 11.3 to a z-score using the formula:
z = (x - μ) / σ
where x is the shoe size, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
[tex]z = (11.3 - 8.11) / 1.46 = 2.17[/tex]
This tells us that a shoe size of 11.3 is 2.17 standard deviations above the mean.
The empirical rule enables us to determine that, with a normal distribution:
About 68% of the data falls within one standard deviation of the mean
The data is within two standard deviations of the mean for about 95% of the time
About 99.7% of the data falls within three standard deviations of the mean
Since 11.3 is more than two standard deviations above the mean, we know that fewer than 5% of women will have a shoe size this large. To find the exact percentage, we can use a standard normal distribution table (also known as a z-table) or a calculator to find the area under the curve to the right of z = 2.17.
Using a calculator or a table, we find that the area to the right of z = 2.17 is approximately 0.015, or 1.5%. Therefore, we can say that about 1.5% of American women have shoe sizes that are at least 11.3.
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A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special. Restaurant Number of Side Dishes Total Cost 2 $10.25 4 $13.25 5 $14.75 8 $19.25 Which of the following graphs shows the relationship given in the table? graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
A graph with the x-axis labelled number of side dishes and the y-axis equation labelled cost in dollars, as well as a line connecting the points 0, 7.25 and 3, 11.75.
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
The table depicts the link between the quantity of side dishes and the overall cost of a restaurant's lunch special. We need to plot the data points on the graph and see which graph matches the pattern to identify which graph exhibits the relationship given in the table.
Number of Side Dishes Total Cost
2 $10.25
4 $13.25
5 $14.75
8 $19.25
The first choice has a shorter slope than the second, and the data points are perfectly aligned with the line. As a result, the first graph depicts the link described in the table. The solution is:
A graph with the x-axis labelled number of side dishes and the y-axis labelled cost in dollars, as well as a line connecting the points 0, 7.25 and 3, 11.75.
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At the start of an experiment, some chemicals had a mass of 73 g, rounded to 2 significant figures.
During the experiment, the mass of the chemicals decreased by 8. 2 g, rounded to 2 significant figures.
Calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment
The lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.
To calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment, we need to take into account the uncertainty in the initial mass and the change in mass.
The initial mass of the chemicals is given as 73 g, rounded to 2 significant figures. This means that the actual value of the initial mass could lie anywhere between 72.5 g and 73.4 g, since the last significant digit (the 3) is uncertain.
Similarly, the change in mass during the experiment is given as 8.2 g, rounded to 2 significant figures. This means that the actual value of the change in mass could lie anywhere between 8.15 g and 8.25 g.
To find the lower bound of the mass at the end of the experiment, we assume that the initial mass was at its upper bound (73.4 g) and the change in mass was at its lower bound (8.15 g):
Lower bound = 73.4 g - 8.15 g = 65.25 g
To find the upper bound of the mass at the end of the experiment, we assume that the initial mass was at its lower bound (72.5 g) and the change in mass was at its upper bound (8.25 g):
Upper bound = 72.5 g - 8.25 g = 64.25 g
Therefore, the lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.
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18. John's car was purchased for $32,451. He put a down payment of $3,500 and financed the rest with a 5.5% annual interest rate compounded monthly.
a.) How much with his payments be if he takes the loan out for 6 years?
b.) The dealership has a special of a 4.75% rate for 4 years. How much more will John have to pay each month?
c) How much will John end up saving by going with the special?
d.) John decides to go with the special financing John's car depreciates at a continuous rate of 6% annually. How much will his car be worth when he finishes paying off his loan?
e.) At the end of the 4-year loan, how much did John actually lose?
a) Monthly payment = $489.77
b) John will paying $163.69 less per month
c) John will end up saving $3,943.28
d) John's car will be worth approximately $23,142.58
e) John actually lost $8,182.86 at the end of the 4-year loan.
What is the interest rate?The interest rate is the percentage of the amount of money borrowed, lent or invested that is charged or earned as a fee or return over a certain period of time. It is usually expressed as an annual percentage rate (APR) and can be fixed or variable depending on the type of loan or investment.
a) To calculate John's monthly payments, we need to use the formula for the present value of an annuity, which is:
PMT = P*(r/12)/(1-(1+r/12)^(-n*12))
Where PMT is the monthly payment, P is the principal amount (the amount financed after the down payment), r is the monthly interest rate, and n is the number of years.
So, we have:
P = 32,451 - 3,500 = 28,951
r = 0.055/12
n = 6
PMT = 28,951*(0.055/12)/(1-(1+0.055/12)^(-6*12)) = $489.77
Therefore, John's monthly payments would be $489.77.
b) Using the same formula, we can calculate John's monthly payments with the special financing:
P = 28,951
r = 0.0475/12
n = 4
PMT = 28,951*(0.0475/12)/(1-(1+0.0475/12)^(-4*12)) = $653.46
So, John's monthly payments with the special financing would be $653.46.
Difference in monthly payments between the above options is:
$653.46 - $489.77 = $163.69
Therefore, John would have to pay $163.69 more per month with the special financing.
c) To calculate how much John will save by going with the special financing, we need to calculate the total cost of each option.
For the original financing, the total cost can be found by multiplying the monthly payment by the number of payments:
Total cost = $489.77 * (6 * 12) = $35,268.72
For the special financing, the total cost is:
Total cost = $653.46 * (4 * 12) = $31,325.44
Therefore, John will save:
$35,268.72 - $31,325.44 = $3,943.28
So, John will end up saving $3,943.28 by going with the special financing.
d) To calculate the value of John's car when he finishes paying off his loan, we need to use the formula for continuous compounding:
A = P*e^(rt)
Where A is the final amount, P is the initial amount (the purchase price of the car), e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.
The car depreciates at a continuous rate of 6%, which means that the value of the car decreases by 6% every year. So, the effective annual rate of depreciation is:
r = e^(-0.06) - 1 = -0.0589
Note that we use a negative value for r, since the value of the car is decreasing.
John will finish paying off his loan in 4 years. So, the time t is 4 years.
Therefore, the value of John's car when he finishes paying off his loan is:
A = 32,451e^(-0.05894) = $23,142.58
So, John's car will be worth $23,142.58 when he finishes paying off his loan.
e) To calculate how much John actually lost at the end of the 4-year loan, we need to subtract the value of his car at the end of the loan from the total amount he paid:
Total amount paid = $653.46 * (4 * 12) = $31,325.44
Value of car at end of loan = $23,142.58
Amount lost = Total amount paid - Value of car at end of loan
= $31,325.44 - $23,142.58 = $8,182.86
Therefore, John actually lost $8,182.86 at the end of the 4-year loan.
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