Answer:
From the information given, we can draw the following diagram:
S ------- P
/ \ / \
/ \ QR / \
/ \ / / \
/ Q \
R-----------------P
MN
Here, SP || QR, so we have ∠QSP = ∠PQR and ∠SPQ = ∠QRP.
Since m∠QRS = 120, we have m∠QRP = 360 - m∠QRS = 360 - 120 = 240.
Since m∠QPS = 135 and ∠QSP = ∠PQR, we have m∠PQR = 360 - m∠QPS = 360 - 135 = 225.
Let x = MN. Since MN is the median of the trapezoid, we have MP = NR = x.
Now, consider the triangles SPQ and RPQ. We have:
tan(∠SPQ) = x/12 (using the tangent ratio in triangle SPQ)
tan(∠RPQ) = x/12 (using the tangent ratio in triangle RPQ)
Since ∠SPQ = ∠RPQ (as they are corresponding angles), we have:
x/12 = x/12
x = 12
Therefore, MN = x = 12.
Which is the following not true?
For every pound of warming gas produced by agriculture, how many pounds of gas are produced by transportation?
1.0
1.3
2.0
2.7
3.0
Function or not a function answers
Answer:
Only the set of ordered pairs is one-to-one
Step-by-step explanation:
You have three right
The last one:
A function is one-to-one if and only if, for every value of y there is only one value of x
The mapping diagram is not one-to-one since for two values of x, x = -3 and x = 5 we get the same y value of 6
The set of ordered pairs is a one-to=-one since for every value of y there is a unique value for x
Find m1 if m5 =142 and m4=65
The value of m∠1 is 103°. The solution has been obtained by using the angle sum property.
What is the angle sum property?
The angle sum property of a triangle states that the sum of the three internal angles of a triangle is 180 degrees.
We are given that m∠5 = 142° and m∠4 = 65°.
Since m∠5 and m∠2 lie on a straight line so, they form a linear pair.
So,
⇒ m∠5 + m∠2 = 180°
⇒ 142° + m∠2 = 180°
⇒ m∠2 = 38°
We know that sum of angles of a triangle is 180°.
So,
⇒ m∠3 + m∠4 + m∠2 = 180°
⇒ m∠3 + 65° + 38° = 180°
⇒ m∠3 + 103° = 180°
⇒ m∠3 = 77°
Now, since m∠3 and m∠1 lie on a straight line so, they form a linear pair.
So,
⇒ m∠3 + m∠1 = 180°
⇒ 77° + m∠1 = 180°
⇒ m∠1 = 103°
Hence, the value of m∠1 is 103°.
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The complete question and the figure has been attached below.
Question: Find m∠1 if m∠5 = 142° and m∠4 = 65°.
Find the value of x. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
9. sin 18 = x/21
x = 21* sin 18
x = 6.5
10. tan 55 = 29/x
x* tan 55 = 29
x = 29/tan 55
x = 20.3
11. sin 23 = x/25
x = 25 * sin 23
x = 9.8
12. sin 47 = 33/x
x * sin 47 = 33
x = 33/sin 47
x = 45.1
A hardware store sells nylon rope for $0.89/yd. A lumber yard sells the same rope for $0.94/m.
a) Which store sells the rope for a lower price? Explain your answer.
b) How much money would Jim save if he purchased 650 ft. of the less expensive rope, before taxes?
pls complete a and b!!
Therefore , the solution of the given problem of unitary method comes out to be 14.7 dollars before taxation, assuming he bought 650 feet of the cheaper rope.
What is an unitary method?The job can be completed by bringing together what was learned and applying this variable technique, that also includes all supplementary data from two people that utilized a specific tactic. To put it another way, if the desired outcome materialises, either the entity stated in the calculation will be recognised, or both expression essential processes will truly skip the colour. For forty pencils, a refundable charge of Rupees ($1.01) might be required.
Here,
To evaluate the prices, we need to use the same units.
Since 0.9144 metres make up one yard, we can convert the cost of the rope at the hardware shop to dollars per metre as follows:
=> 0.89 dollars/yard * 1 yard/0.9144 meters = 0.97 dollars/meter
b) We must change the units to yards or metres in order to evaluate the costs of 650 feet of rope. 650 feet is equivalent to 3 yards, which is:
=> 650 feet x 3 feet per yard = 216.67 yards
The hardware store's price for the cord is:
=> 192.5 dollars ($0.89/yard x 216.67 yards)
At the timber yard, the price of the rope is:
=> (216.67 yards * 0.9144 meters/yard) * 0.94 dollars/meter = 177.8 dollars.
Jim would therefore save:
=> 192.5 dollars - 177.8 dollars = 14.7 dollars.
before taxation, assuming he bought 650 feet of the cheaper rope.
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A plane can fly 420 miles in the same time as it takes a car to go 150 miles. If the car travels 90 mph slower than the plane, find the speed of the plane. Using r as your variable to represent the speed of the plane in miles per hour, write an equation using the information above that can be solved to find the answer to this problem.
Answer:
Step-by-step explanation:
rate of the plane be x
distance traveled by plane = 420 miles
time taken by plane = 420/x
distance traveled by car =120 miles
rate of car = x-120
time taken by car = 120 / x-100
the time taken by both are same
420/x = 120/ x-100
420(x-100)=120x
420x-42000 = 120x
420x-120x=42000
300x= 42000
x=42000/300
x=140 mph the speed of the plane
solve for x. Round your answer to the nearest tenth.
The length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.
Describe Triangle?The angles of a triangle are the angles formed by its sides. The sum of the angles of a triangle is always 180 degrees, which is a fundamental property of this shape. There are different types of triangles, based on their side lengths and angle measures. For example:
A scalene triangle has three sides of different lengths and three different angles.
An isosceles triangle has two sides of equal length and two equal angles.
An equilateral triangle has three sides of equal length and three equal angles.
A right triangle has one angle that measures 90 degrees (a right angle), and the side opposite to it is called the hypotenuse.
Triangles have many important properties and applications in mathematics, physics, and engineering. They can be used to calculate distances, angles, areas, volumes, and many other quantities. Triangles are also used in the construction of buildings, bridges, and other structures, as well as in art, design, and other fields.
We can use the trigonometric ratio of sine to solve for x:
sin(42) = opposite/hypotenuse
sin(42) = x/5
To solve for x, we can multiply both sides by 5 and simplify:
x = 5*sin(42)
x ≈ 3.4 (rounded to the nearest tenth)
Therefore, the length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.
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x+y=20 and x-y=4 what is the smaller of these two numbers?
Answer:
y = 8 is the smaller number.
Step-by-step explanation:
Sove the system by adding the two equations together, one on top of the other. Add from the top, down.
x + y = 20
x - y = 4
________
2x = 24
Divide by 2.
x = 12
Put this back into either original equation.
x + y = 20
12 + y = 20
Subtract 12.
y = 8
The numbers are 12 and 8.
8 is the smaller number.
I WILL GIVE BRANLIST ONLYNOF YOUR RIGHT
Determine the scale factor used to create the image
A 1/2
B 2
C 1/4
D 4
Answer:
Step-by-step explanation:
b
Identify the discriminant value of the quadratic equation m² + 18m + 17 = 0.
Answer:
Step-by-step explanation:
The discriminant value (denoted by Δ) of a quadratic equation in the form of ax² + bx + c = 0 is given by the expression b² - 4ac.
For the quadratic equation m² + 18m + 17 = 0, a = 1, b = 18, and c = 17. Substituting these values into the expression for the discriminant, we get:
Δ = b² - 4ac
Δ = (18)² - 4(1)(17)
Δ = 324 - 68
Δ = 256
Therefore, the discriminant value of the quadratic equation m² + 18m + 17 = 0 is 256.
Iti...
00
t
Get ready
and
Evaluate.
Hint: Use the image to help break 9 x 4 up into two expressions.
9x4
5 fours +
fours
Based on the image, we can break 9 × 4 into two expressions as 4 groups of 9 or 9 groups of 4. This equals 36.
How to explain the expressionIt should be noted that to break 9 x 4 up into two expressions, you can use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.
So, we can rewrite 9 x 4 as:
9 x 4 = 9 x (3 + 1)
Using the distributive property, we can expand this expression as:
9 x (3 + 1) = (9 x 3) + (9 x 1)
Simplifying, we get:
9 x 4 = 27 + 9
Therefore, we have broken up 9 x 4 into two expressions: 27 and 9. This will give 36.
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G
Which inequality has a dashed boundary line when graphed?
3
oy²x+1
O y²-3x+1
2
Oy> 3x+1
O y≤7x-1
The inequality that has a dashed boundary line when graphed is:
y > 3x + 1
What is inequality?In mathematics, an inequality is a statement that two quantities are not equal or do not have the same value. In other words, it is a statement that compares two values, expressing that one value is greater than, less than, or not equal to the other value. An inequality is denoted by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
What is Dashed boundary?In mathematics, a dashed boundary refers to a boundary line that is graphed as a dashed line rather than a solid line. The use of a dashed line is typically used to indicate that the boundary itself is not included in the set of solutions of an inequality or equation.
In the given question,
The inequality that has a dashed boundary line when graphed is:
y > 3x + 1
The reason for this is that when graphed, the boundary line of the inequality y > 3x + 1 is a straight line, but it is dashed instead of solid. This is because the inequality is strict, meaning that the boundary line itself is not included in the set of solutions. On the other hand, if the inequality had been y ≥ 3x + 1, the boundary line would have been a solid line because the inequality is non-strict and includes the boundary line itself as a solution.
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WRITING EXAMPLE: EMAIL Compare both texts. Which one do you think is better written? 1. Hi Usma. I like blue colour. Because blue is the best color please when can you come and painting my room. If u coming tomorrow reply me back, dont worry about mony. I whant tell you my room. My room is white colour and I have one shair. Tell me about you rom. Maria 2. My favourite colour is pink, but for my bedroom I prefer white because it's the best colour for my room. My bedroom is big. It is white. There are 2 beds. There is one desk. There are 2 windos. There is one armchair. Bye, Maria
Answer:
Second one
Step-by-step explanation:
It is observed that 3 out of every 5 drills made at an oil-drilling site strike oil. The results from 50-simulation trials of the model showed 1 out of 5 drills
are guaranteed to strike oil. What is the hypothesis, and based on the results from the simulation trials, what should be concluded about the
hypothesis?
A. The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.
B. The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, it can be concluded that the hypothesis is
correct.
C. The hypothesis is that at least 3 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.
D. The hypothesis is that at least 3 out of 5 drills will strike oil. Based on the results from the simulation trials, it can be concluded that the hypothesis is
correct.
The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.
Blood pressure readings are normally distributed. The mean systolic blood pressure is 120 and the standard deviation is 8. If a medical researcher randomly selects a sample of 20 people, what is the probability that the mean blood pressure for this sample will be greater than 123?
Answer:
To solve this problem, we can use the central limit theorem and the standard normal distribution.
The central limit theorem states that the distribution of sample means is approximately normal, with a mean equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Let X be the systolic blood pressure of an individual in the population. We know that X is normally distributed with a mean of 120 and a standard deviation of 8.
Let Y be the sample mean blood pressure of a sample of 20 individuals. Then Y is also normally distributed, with a mean of 120 and a standard deviation of 8 / sqrt(20) = 1.7889.
We want to find the probability that the sample mean blood pressure is greater than 123. We can standardize this value using the standard normal distribution as follows:
Z = (Y - 120) / (8 / sqrt(20))
P(Y > 123) = P(Z > (123 - 120) / (8 / sqrt(20)))
= P(Z > 1.3363)
Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 1.3363 is approximately 0.0918.
Therefore, the probability that the mean blood pressure for a sample of 20 people will be greater than 123 is approximately 0.0918.
How much is 1/12 in milliters?
The conversion of 1/12in to milliters can be expressed as 2.117mm
How can the conversion be done?Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. As an illustration, if you had 1,000 interactions and 50 conversions, your conversion rate would be 5% because 50 x 1,000 = 5%.
The proportion of users who perform the intended action is known as the conversion rate. The proportion of website visitors who make a purchase there serves as the prototypical illustration of conversion rate.
We can 1/12in to milliters by using the conversion rate, which 1inch = 25.4mm,and this can be used to make the conversion as:
If 1inch = 25.4mm
1/12 = X mm
Xmm = (1/12 *25.4mm)/ 1inch
=2.117mm
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complete question:
How much is 1/12in to milliters?
Please help will get max points + brainliest!
Answer:
a) Area of inner square = 58 cm²
b) Area of inner square = (2x² - 2xy + y²) cm²
Step-by-step explanation:
To calculate the area of a square, multiply the length of one of its sides by itself. This can be expressed as A = s², where A is the area and s is the side length of the square.
To calculate the area of a triangle, halve the product of its base and height. This can be expressed as A = (1/2)bh, where A is the area, b is the base and h is the height of the triangle.
The easiest way to calculate the area of the inner square is to subtract the areas of the 4 congruent triangles from the area of the outer square.
[tex]\hrulefill[/tex]
Part a)The outer square has a side length of 10 cm. Therefore its area is:
[tex]\implies \sf A_{outer\;square} = 10^2 = 100 \; cm^2[/tex]
Each corner triangle has a height of 3 cm and a length of (10 - 3) cm.
Therefore, the area of one triangle is:
[tex]\implies \sf A_{triangle}=\dfrac{1}{2} \cdot 7 \cdot 3=10.5\;cm^2[/tex]
Therefore, the area of the inner square is:
[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=\sf 100-(4 \cdot 10.5)\\&=\sf 100-42\\&=\sf 58\; cm^2\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Part b)The outer square has a side length of y cm. Therefore its area is:
[tex]\implies \textsf{A$_{\sf outer\;square}$} = y^2 \; \sf cm^2[/tex]
Each corner triangle has a height of x cm and a length of (y - x) cm.
Therefore, the area of one triangle is:
[tex]\begin{aligned}\implies \sf A_{triangle}&=\dfrac{1}{2} \cdot (y-x) \cdot x\\\\&=\dfrac{1}{2}x(y-x)\;\sf cm^2\end{aligned}[/tex]
Therefore, the area of the inner square is:
[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=y^2-4\left(\dfrac{1}{2}x(y-x)\right)\\\\&=y^2-2x(y-x)\\\\&=y^2-2xy+2x^2\\\\&=(2x^2-2xy+y^2)\; \sf cm^2\end{aligned}[/tex]
Confidence intervals are constructed to estimate the population parameter (like the mean) a specified proportion of the time. The upper and lower interval estimates are often described as the
The upper and lower interval estimate are often describe as associated with a specific level of confidence.
What is Interval Estimate?In statistics, interval estimate is the process of determining the interval, or range of values, within which a parameter—such as the mean (average) of a population—is most likely to fall.
The interval encompassing a population parameter is determined by computing the statistic from values obtained from a random sample chosen from the population and by using the understanding (derived from probability theory) of how accurately sample properties reflect those of the full population.
The possibility that the estimated confidence interval estimate will include the genuine population parameter is frequently referred to as the confidence level.
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Help!!
Question
Callie is buying fence for two triangular sections of her garden.
How much fence would she need for triangle DFG ?
Enter your answer in the box.
ft
Callie will need a total of 112 feet of fence for the triangle DFG.
How to find the amount of fence needed.We can find the amount of fence needed by finding the relationship between both triangles and find the missing side.
The sum of all the sides of the triangle will be known as the perimeter of the triangle. we can use this knowledge to find the amount of fence needed.
Both triangles are similar and are in the ratio of 1:7To find the missing side of triangle DFG, we multiply the corresponding side of triangle BAC by 7 to find the missing side.
This will give us 7 x 7 = 49ft
To find the amount of fence needed for triangle DFG we add all the sides of triangle DFG which will be 49 + 35 + 28.
The total will be 112ft.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 4 people took the trip. She was able to purchase coach tickets for $140 and first class tickets for $1000. She used her total budget for airfare for the trip, which was $2280. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought = ___
The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.
Let us assume the number of coach tickets purchased is x.
And the number of first-class tickets purchased is y.
Now,
Including Sarah, a total of 11 people took the trip.
Thus,
[tex]x + y = 11 [/tex]
The cost of coach tickets and first-class tickets are $210 and $1200 respectively.
The total budget for airfare for the trip is $10,230.
Therefore,
210x + 1200y = 102309
21x + 120y = 1023
Solving both the equations, we get.
x=3
y=8
Thus, The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.
Two step equations that equal 23
Line AB intersects line CD at point F. If m<AFC=(7x-8)° and m<BFD=(5x+6)°, what is m<BFD?
82°
48°
41°
7°
76 is m<BFD in linear equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.
m<AFC + m<BFD = 180°
(7x-8)° + m<AFC = 180°
(5x+6)° + m<BFD = 180°
(7x-8)° = (5x+6)
2x = 12
x = 14
m<BFD=(5x+6)°
= 5 * 14 + 6
= 70 + 6
= 76
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Consider the following function.
p(x)=2−29x
Step 1 of 2 : Find the slope and the y-intercept. Express the intercept as an ordered pair. Simplify your answer.
The slope of the function is -29 and the y-intercept is the point (0, 2).
What is function ?
In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range).
To find the slope and y-intercept of the function p(x) = 2 - 29x, we can write it in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
So, by comparing p(x) = 2 - 29x with y = mx + b, we can see that:
m = -29 (the coefficient of x)
b = 2 (the constant term)
Therefore, the slope of the function is -29 and the y-intercept is the point (0, 2).
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What are the x- and y-intercepts of f(x) - 3x - 4?
The x- and y-intercepts as required to be determined in the task content are; (-4/3, 0) and (0, -4).
Which points represent the x- and y-intercepts of the function?As evident in the task content; the given function is; f(x) = - 3x - 4.
The x-intercept represents the value of x when f(x) = 0.
0 = -3x - 4
3x = -4
x = -4 / 3.
The y-intercept represents the value of f(0); hence, we have that;
f (x) = -3(0) - 4
f(0) = -4.
Ultimately, the points which correctly represents the x- and y-intercepts are; (-4/3, 0) and (0, -4).
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The histogram shows information about how 600 people travel to work.
40
35-
30-
25-
20-
15-
10-
5-
0
0 5 10 15 20 25 30 35 40 45 50 55 60
a) How many people travel more than 40 miles to work?
b) 225 of the 600 people travel further than Tim. Estimate how far Tim travels.
Frequency density
Distance (miles)
8
A
Answer:
A:0 Noone goes higher than 40. b: 5 miles
Weber Jewelry advertised a diamond necklace for $572.95 and a gold pendant for $113.76. The state tax is 6.5 percent and the city tax is 0.5 percent. What is the total purchase price?
Therefore, the total purchase price is $734.78.
What are profits?Profit is the financial gain obtained by subtracting the cost (or expenses) of producing and selling goods or services from the revenue generated from their sale. In other words, profit is the amount of money that is left over after all expenses have been paid, including the cost of goods sold, operating expenses, taxes, and any other costs associated with running a business.
Profit can be calculated using the following formula:
Profit = Revenue - Cost
by the question.
To calculate the total purchase price, we need to calculate the tax and add it to the sum of the prices of the diamond necklace and the gold pendant.
The tax on the diamond necklace is:
572.95 * 0.065 = 37.24
The tax on the gold pendant is:
113.76 * 0.065 = 7.40
The total tax is the sum of these two taxes:
37.24 + 7.40 = 44.64
We also need to add the city tax, which is 0.5 percent of the total price:
(572.95 + 113.76) * 0.005 = 3.43
The total purchase price is the sum of the prices of the diamond necklace and the gold pendant, the state tax, and the city tax:
572.95 + 113.76 + 44.64 + 3.43 = 734.78
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Gwen owes a total of $4,522.50 on revolving credit accounts that have total limits of $7,950.00. Calculate the amount she needs to pay on her debt to reduce her revolving credit accounts to reach a 25% debt-to-credit ratio.
The amount that she needs to pay on her debt to reach a 25% debt-to-credit ratio is given as follows:
$2,535.
How to obtain the amount that she needs to pay?The amount that she needs to pay on her debt reach a 25% debt-to-credit ratio is obtained applying the proportions in the context of the problem.
She has a credit limit of $7,950.00, hence 25% of her credit limit is obtained as follows:
0.25 x 7950 = $1987.5.
She current has $4,522.50 on debts, hence the amount that she needs to pay for the debts to be reduced to $1987.5 is given as follows:
4522.5 - 1987.5 = $2,535.
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A ball that is thrown upward follows the path h(t)=-t^2+8t+32, where h(t) represents the height of the ball above the ground at time t, and t represents the time since the ball was thrown. How high above the ground did the ball reach? show work
Answer:
Step-by-step explanation:
To find the maximum height of the ball, we need to find the vertex of the parabolic function h(t) = -t^2 + 8t + 32. The vertex represents the highest point of the parabolic curve.
The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = -1 and b = 8, so we have:
x = -b/2a = -8/(2(-1)) = 4
Therefore, the vertex occurs at time t = 4.
To find the y-coordinate of the vertex, we evaluate the function at t = 4:
h(4) = -4^2 + 8(4) + 32 = 16 + 32 = 48
Therefore, the ball reaches a maximum height of 48 feet above the ground.
Twenty percent of Americans ages 25 to 74 have high blood pressure. If 26 randomly selected Americans
ages 25 to 74 are selected, find the probability that one-half have high blood pressure.
Please write your answer as a decimal. Round your answer to seven decimal places.
The probability that one-half of the selected people will have high blood pressure is given as follows:
P(X = 13) = 0.0004684.
What is the binomial distribution formula?The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.
The mass probability formula is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters, along with their meaning, are listed as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 26, p = 0.2.
One-half of 26 is of 13, hence the probability is given as follows:
P(X = 13) = 26!/(13! x 13!) x (0.2)^13 x (0.8)^13
P(X = 13) = 0.0004684.
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