The expression 10a - 14c is factorized and then found to be equivalent to 2(5a - 7c)
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Given the equation:
10a - 14c
We are to solve the equation by factorizing the expression. To factorize the expression, we need to find the term that is common to both 10a and -14c. The common term is 2, hence:
10a - 14c
2(5a - 7c)
The expression 10a - 14c is equivalent to 2(5a - 7c)
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Anybody know how to do the following?.. Which Similarity statement can you write relating the three triangles in the diagram below?
Answer:
I believe the answer is D
Step-by-step explanation:
if you want an explanation let me know and have a great day and I'm 100% sure that D is the right answer
Triangle RST was dialated by a scale factor of 3 to create triangle LMN. If TAN R = 5/2.5 find the measurments for LM and MN
The measurements for LM is 30 units and MN is 15 units.
What is the measurement of MN and LM?We know that the scale factor for the dilation is 3, which means that each side of triangle RST was multiplied by 3 to create triangle LMN.
Therefore:
LM = 3(RS)
MN = 3(ST)
To find RS and ST, we can use the fact that TAN R = 5/2.5.
Recall that tangent is the ratio of the opposite side to the adjacent side of a right triangle, so we can set up the following equation:
TAN R = RS/ST = 5/2.5
Cross-multiplying, we get:
RS = 5ST/2.5
Simplifying:
RS = 2ST
Now we can substitute this expression for RS into the equations for LM and MN:
LM = 3(RS) = 3(2ST) = 6ST
MN = 3(ST)
So the measurements for LM and MN are:
LM = 6ST
MN = 3(ST)
From triangle RST,
ST = 5
LM = 6 x 5 = 30 units
MN = 3 x 5 = 15 units
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4. Theresa wants new carpeting for her family room. Her family room is a 12 ft by 21 ft rectangle. How much carpeting does she need to buy to cover her entire family room?
Answer:
252 square
Step-by-step explanation:
An article reports that the amount of a certain antifungal ointment that is absorbed into the skin can be modelled with a lognormal distribution. Assume that the amount (in ng/cm2) of active ingredient in the skin two hours after application is lognormally distributed with μ = 2.6 and σ = 2.1. 1) Find the 80th percentile of the amount absorbed. Round the answer to one decimal place. 2) Find the standard deviation of the amount absorbed. Round the answer to one decimal place.
The standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.
1. 80th percentile of the amount absorbed
Given that the amount (in ng/cm²) of active ingredient in the skin two hours after application is lognormally distributed with μ = 2.6 and σ = 2.1. The 80th percentile of the amount absorbed is to be found. Let X be the random variable representing the amount of active ingredient absorbed. We know that X follows a log-normal distribution with parameters μ = 2.6 and σ = 2.1. We are to find the value x such that P(X ≤ x) = 0.8We know that for a log-normal distribution X ~ log N (μ, σ). Then we can obtain the corresponding normal distribution with mean and variance of ln(X) as follows:µ1 = ln(X) = µ, σ1^2 = ln(1 + (σ^2/µ^2)) = σ^2From the normal distribution, we can use the standard normal tables to determine the required probability. Thus Z = (ln(x) - µ)/σ and P(X ≤ x) = P(Z ≤ (ln(x) - µ)/σ) = 0.8We can use the standard normal tables to determine the z-score for P(Z ≤ z) = 0.8, which is 0.84. Then we can find ln(x) using:0.84 = (ln(x) - 2.6)/2.1 or ln(x) = 2.6 + (0.84)(2.1) = 4.374x = e^4.374 = 79.1 ng/cm²Therefore, the 80th percentile of the amount absorbed is 79.1 ng/cm² rounded to one decimal place.2. Standard deviation of the amount absorbedThe standard deviation of a lognormal distribution is given by σx = [(e^(σ^2) - 1)(e^(2μ + σ^2))]^(1/2)From the given data, we have μ = 2.6 and σ = 2.1. Therefore,σx = [(e^(2.1^2) - 1)(e^(2(2.6) + 2.1^2))]^(1/2) = 1819.9 ng/cm² rounded to one decimal place. Therefore, the standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.
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Match each expression on the left with an equivalent expression on the right.
3⁄5 – 13⁄53x + 02x – 65⁄3 – x + 1⁄32x – 3−6.9 + 4.93x–6 + 2x–3⁄2x + 2 + 1⁄2xx – 3 + x
Answer:
3/5 - 13/5 => -6.9 + 4.9
2x - 3 => x - 3 + x
5/3 - x + 1/3 => -3/2x + 2 + 1/2x
2x - 6 => -6 + 2x
3x + 0 => 3x
Step-by-step explanation:
Hope it helps :)
Which describes a possible independent variable for the given dependent variable?
Your monthly cell phone bill
1. Who you call most often each month
2. The amount of data you use each month
3. The color of your phone
4. The amount of money you spend for lunch each month
Answer:
1
explanation in head
DIG DEEPER! You use a crowdfunding website to raise money. The website keeps 5% of each donation. Five of your friends each donate the same amount. The total funding you receive is $47.50. How much does each friend donate?
Work out
25% of 401. 16m
Give your answer rounded to 2 DP
The 25 percent of 401.16m is equal to 100.29m, rounded to 2 decimal places as 100.30m.
To calculate 25% of 401.16m, we can use the formula:
percentage × value = result
where the percentage is 25%, the value is 401.16m, and the result is what we want to find.
So, we can write:
25% × 401.16m = (25/100) × 401.16m = 0.25 × 401.16m = 100.29m
Therefore, 25% of 401.16m is equal to 100.29m.
To round this to 2 decimal places, we need to look at the third decimal place, which is 9. Since 9 is greater than or equal to 5, we round up the second decimal place, which is 0. Therefore, the final answer rounded to 2 decimal places is:
100.29m rounded to 2 decimal places is 100.30m.
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E- Education is A new start-up that develops and markets MBA courses offered over the internet
The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.
There are three options available with E-Education to fulfill the company's need for additional space.
The decision tree for the available options is made below;
Option1 Option2 Option3
$ $ $
Cost of Moving to New Building 1000000 2000000
Leasing cost 1000000 1300000 1500000
Total Cost of the Option 2000000 1500000 1500000
Conclusion: The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.
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Calculate the value of r if: 72:64= x: 16
Answer:
18
Step-by-step explanation:
In this you have to use means and extremes method, when you multiply 72 and 16 you’ll get 1152. Then divide it with 64, you’ll get 18.
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{Original equation/problem }\\\\\large\boxed{\mathsf{72:64}}\\\\\large\textsf{Both numbers (72 \& 64) are factors of 4, so we will DIVIDE them by 4}\\\\\large\boxed{\mathsf{\rightarrow 72\div4: 64\div4}}\\\\\large\textsf{Which results in}\downarrow\\\\\large\boxed{\mathsf{\rightarrow 18:16}}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{\bold{18}:16}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
After spending 2/3 of high salary on rent and food and 1/4of remaining of transportation. A man has rupees 6000 with him how much he pays on transportation.
Answer:
Step-by-step explanation:
Let's break down the information provided in the problem:
The man spends 2/3 of his high salary on rent and food.
This means that he has 1/3 of his salary remaining.
He then spends 1/4 of this remaining amount on transportation.
He has 6000 rupees left.
To solve for the amount he pays on transportation, we can use the following steps:
Calculate the amount of money he has left after spending 2/3 of his salary on rent and food:
Remaining amount = (1/3) * high salary
Calculate the amount he spends on transportation using the information that he spends 1/4 of the remaining amount:
Transportation cost = (1/4) * remaining amount
Substitute the value of remaining amount from step 1 into step 2:
Transportation cost = (1/4) * [(1/3) * high salary]
We are given that the man has 6000 rupees left, so we can set the equation above equal to 6000 and solve for high salary:
(1/4) * [(1/3) * high salary] = 6000
Simplifying the equation above:
(1/12) * high salary = 6000
Solving for high salary:
high salary = 6000 * 12 = 72000
Finally, substituting high salary from step 6 into step 3 to find transportation cost:
Transportation cost = (1/4) * [(1/3) * 72000] = 6000
Therefore, the man pays 6000 rupees on transportation.
What types of symmetry does the shape have?
Answer: 4
Step-by-step explanation:
Suppose that 10% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the four who have earthquake insurance.
(a) Find the probability distribution of x. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.1)(.9)(.1)(.1) and associated x value of 3. There are 15 other outcomes.)
Value of x Probability
0 1 2 3 4 (b) What is the most likely value of x?
(a) 0
(b) 1
(c) 0 and 1
(d) 3
(e) 4
(C) What is the probability that at least two of the four selected homeowners have earthquake insurance?
P (at least 2 of the 4 have earthquake insurance) =
Answer: (a) The possible outcomes and their probabilities are:
Value of x Probability
0 0.6561 (0 F's and 4 S's)
1 0.2916 (1 F and 3 S's, or 2 F's and 2 S's, or 3 F's and 1 S)
2 0.0486 (2 F's and 2 S's)
3 0.0036 (1 S and 3 F's)
4 0.0001 (4 F's and 0 S's)
(b) The most likely value of x is the one with the highest probability, which is x = 0.
(c) The probability that at least two of the four selected homeowners have earthquake insurance is equal to 1 minus the probability that 0 or 1 of them have earthquake insurance:
P(at least 2 of the 4 have earthquake insurance) = 1 - P(x = 0) - P(x = 1)
= 1 - 0.6561 - 0.2916
= 0.0523
Therefore, the probability that at least two of the four selected homeowners have earthquake insurance is 0.0523.
Enjoy!!!!!
Probability distribution of x is calculated by finding probabilities of each possible outcome, the most likely value of x is 0 with a probability of 0.6561, probability of at least two homeowners having earthquake insurance is 0.0523.
(a) The probability distribution of x can be found by calculating the probabilities of each possible outcome (0, 1, 2, 3, 4 homeowners with insurance) and associating them with their respective x values.
Value of x | Probability
--- | ---
0 | (.9)(.9)(.9)(.9) = 0.6561
1 | (.1)(.9)(.9)(.9) + (.9)(.1)(.9)(.9) + (.9)(.9)(.1)(.9) + (.9)(.9)(.9)(.1) = 0.2916
2 | (.1)(.1)(.9)(.9) + (.1)(.9)(.1)(.9) + (.1)(.9)(.9)(.1) + (.9)(.1)(.1)(.9) + (.9)(.1)(.9)(.1) + (.9)(.9)(.1)(.1) = 0.0486
3 | (.1)(.1)(.1)(.9) + (.1)(.1)(.9)(.1) + (.1)(.9)(.1)(.1) + (.9)(.1)(.1)(.1) = 0.0036
4 | (.1)(.1)(.1)(.1) = 0.0001
(b) The most likely value of x is 0, as it has the highest probability (0.6561).
(c) The probability that at least two of the four selected homeowners have earthquake insurance can be found by adding the probabilities of the outcomes with 2, 3, and 4 homeowners with insurance:
P (at least 2 of the 4 have earthquake insurance) = 0.0486 + 0.0036 + 0.0001 = 0.0523
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The Public Utility Commission in a southern state is interested in describing the relationship between household monthly utility bills and the size of the house. A recent study of 30 randomly selected household resulted in thefollowing regression results:
Use the above output for answering the following questions:
Part a) (8 marks)
Interpret the slope of the regression line.
Write down the estimated linear regression line.
What is the value of coefficient of determination? Interpret this value
What is the value of the coefficient of correlation? Interpret this value.
Part b) (7 marks)
Based on the information provided, indicate what, if any, conclusions can be reached about the relationship between utility bill and the size of the house in square feet.
The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.
The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x
R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.
r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill.
we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease.
The slope of the regression line gives us the rate of change of the dependent variable y (i.e. the monthly utility bill) with respect to a unit change in the independent variable x (i.e. the size of the house).The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.
The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x
The coefficient of determination (R²) is a measure of the proportion of variation in the dependent variable that is explained by the independent variable. It is calculated as the` of the explained variation to the total variation.R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.
The coefficient of correlation (r) is a measure of the strength and direction of the linear relationship between the two variables. It can take values between -1 and +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill. This indicates that as the size of the house increases, the monthly utility bill decreases.
Based on the information provided, we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease. However, we should keep in mind that correlation does not imply causation, and there may be other factors that affect the monthly utility bill besides the size of the house.
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Help me please i need it
PLEASE SOMEBODY HELP ME
Answer:
1. rhombus and square
2. rhombus, rectangle, square
3. rectangle and square
4. rectangle, squares, rhombus
5. same as 3
6. rhombus, rectangle, square
7. rhomus, rectangle, square
8. rectangle, square
Step-by-step explanation:
if a plam tree grows 2.5 feet a year how many years from now will the plam tree be 30 feet tall
Answer: About 75 years
Step-by-step explanation:
2.5x30=75
between which two benchmark fractions is 5/8?how do you know?
We can conclude that 5/8 is between the benchmark fractions 1/2 and 3/4.
What is fraction?A fraction represents a part of a whole or a ratio between two quantities. It consists of a numerator (the top number) and a denominator (the bottom number), separated by a horizontal line. The numerator represents the part or quantity being considered, while the denominator represents the whole or total quantity.
According to question:To determine between which two benchmark fractions 5/8 lies, we can compare it to the nearest benchmark fractions, which are 1/2 and 3/4.
We know that 1/2 is less than 5/8 because half of a whole is less than five-eighths of a whole.We also know that 3/4 is greater than 5/8 because three-fourths of a whole is greater than five-eighths of a whole.Therefore, we can conclude that 5/8 is between the benchmark fractions 1/2 and 3/4.To summarize, 1/2 < 5/8 < 3/4.
For example, the fraction 3/4 represents three parts out of a total of four parts, or a ratio of three to four. This can also be expressed as a decimal (0.75) or a percentage (75%).
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Simon and his friends have 27 pieces of candy. They split them up evenly and each person gets 9 pieces. How many people are there? Select the correct equation and solve for p.
Question 6 options:
p/27 = 9; p = 3
9 + p = 27; p = 18
9 = 27 - p; p = 18
27 = 9p; p = 3
Answer:
3 people are getting candy
Step-by-step explanation:
9x3
i need help i dont know if im right
Since 5/4 is less than 9/4, we know that Alex's rope is shorter than Sam's rope. Since 1 1/4 is greater than 6/5, we know that Brittany's rope is longer than Sam's rope.
What is inequality?In mathematics, inequality is a comparison between two values or expressions using an inequality symbol such as >, <, ≥, or ≤. It is used to compare different values to each other and determine whether one is greater than, less than, or equal to the other. Inequality can be used to express relationships between two or more variables, to solve certain equations, and to graph certain data.
In order to answer these questions, we need to compare the given values. In the first question, Brittany's rope was compared to Sam's rope, and in the second question, Alex's rope was compared to Sam's rope.
For the first question, Sam's rope was 1.5 x 4/5 = 6/5. This value was compared to Brittany's rope which was 1 1/4. Since 1 1/4 is greater than 6/5, we know that Brittany's rope is longer than Sam's rope.
For the second question, Sam's rope was 1.5 x 3/2 = 9/4. This value was compared to Alex's rope which was 5/4. Since 5/4 is less than 9/4, we know that Alex's rope is shorter than Sam's rope.
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The projected value (in millions of dollars) of a large manufacturing company is modeled by the function V(t) = 230(1. 12)t, where V(t) is the value of the company t years after 2018. What does 230 represent in the function?
In the function [tex]V(t) = 230(1.12)^t[/tex], the number 230 represents the initial or starting value of the company in millions of dollars at the beginning of the time period in question, which is 2018.
The function models the growth of the company's value over time as an exponential function, with a base of 1.12. The exponent t represents the number of years that have passed since 2018, and the resulting value V(t) is the projected value of the company t years after 2018, given the assumed growth rate of 12% per year.
So, at the start of 2018, the company was worth 230 million dollars, according to the model.
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The wheelchair ramp at the entrance to a store is 12 feet long and rises a total vertical distance of ¾ of a foot. To the nearest degree, what is the angle of inclination of the ramp? Enter the number only.
In response to the question, we may say that As a result, the angle of trigonometry inclination of the ramp is 4 degrees, to the closest degree.
what is trigonometry?The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. Consequently, studying geometry entails learning about the characteristics of all geometric forms.
The ratio of an angle's opposing side (such as the rise of a ramp) to its adjacent side is known as the tangent (the length of the ramp).
Angle's tangent is equal to its opposite and adjacent sides.
In this instance, the ramp's opposite side represents its 3/4-foot rise, and the ramp's adjacent side is its 12-foot length.
Angle's tangent is equal to 3/4 / 12 (or 0.0625).
We may take the inverse tangent (or arctangent) of this number to determine the angle itself.
Amount = arctan (0.0625)
Calculating the answer, we obtain:
Angle is 3.58 9 degrees.
When we convert this to degrees, we get:
a 4 degree angle
As a result, the angle of inclination of the ramp is 4 degrees, to the closest degree.
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i need help[ i dont understand this
a) The theoretical probability of a fair coin landing on heads is 1/2
b) The experimental probability of landing on heads is 40%. Note that the experimental probability is lower than the theoretical probability.
What is the explanation for the above?Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. Thus, it is possible for either of the teams to get the ball first.
Part B: The frequency of each outcome after flipping the coin 10 times may vary, but for example:
Heads: 4
Tails: 6
The experimental probability of landing on heads can be calculated by dividing the frequency of heads by the total number of flips: 4/10 = 0.4 or 40%.
Comparing the experimental probability of 0.4 to the theoretical probability of 0.5, we can see that the experimental probability is lower than the theoretical probability.
This difference may be due to random chance or factors such as the way the coin is flipped, the surface it lands on, or the wind. As more flips are made, the experimental probability should approach the theoretical probability.
Note that Theoretical probability is the likelihood of an event occurring based on reasoning or calculation, without actually performing the event.
Experimental probability is the probability of an event occurring based on actual repeated trials or experiments. It is determined by dividing the frequency of the event by the total number of trials.
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using the fundemental theorem of algebra how many solutions will the function have, f(x)=8x^(3)+216
Pοlynοmial f(x) has exactly 3 cοmplex rοοts
What is Fundamental Theοrem οf algebra?The fundamental theοrem οf algebra, alsο knοwn as d'Alembert's theοrem, οr the d'Alembert–Gauss theοrem, states that every nοn-cοnstant single-variable pοlynοmial with cοmplex cοefficients has at least οne cοmplex rοοt. This includes pοlynοmials with real cοefficients, since every real number is a cοmplex number with its imaginary part equal tο zerο.
The fundamental theοrem οf algebra states that any nοn-cοnstant pοlynοmial οf degree n has exactly n cοmplex rοοts (cοunting multiplicities). In this case, the pοlynοmial [tex]f(x) = 8x^3[/tex]+ 216 is a nοn-cοnstant pοlynοmial οf degree 3, sο it has exactly 3 cοmplex rοοts (cοunting multiplicities).
We can alsο use the factοr theοrem tο cοnfirm that f(x) has exactly 3 rοοts. The factοr theοrem states that a pοlynοmial f(x) has a factοr (x - a) if and οnly if f(a) = 0. In this case, we can factοr οut 8 frοm the pοlynοmial tο get:
[tex]f(x) = 8(x^3 + 27)[/tex]
Setting f(x) = 0, we get:
[tex]8(x^3 + 27) = 0[/tex]
This equatiοn is satisfied if and οnly if [tex]x^3 + 27 = 0.[/tex] We can factοr this equatiοn as fοllοws:
[tex]x^3 + 27 = (x + 3)(x^2 - 3x + 9)[/tex]
The quadratic factοr [tex]x^2 - 3x + 9[/tex] has nο real rοοts, since its discriminant is negative [tex](b^2 - 4ac = (-3)^2 - 4(1)(9) = -27)[/tex]. Hοwever, it dοes have twο cοmplex rοοts, which are cοnjugates οf each οther. Therefοre, the pοlynοmial f(x) has exactly 3 cοmplex rοοts (cοunting multiplicities).
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Harry, Jason and Sarah are taking the GMAT exam which is required by most applicants for admission to graduate schools of business. The three friends want to get admissions to three different business schools. Harry can get the admission if he gets a score above 650 in GMAT, Jason can get the admission if he gets above 630 and Sarah can get the admission if she gets above 670 . Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115 . What is the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one
The probability that Harry, Jason, and Sarah will all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)
The solution to the question is given below; The mean score of the GMAT exam is μ = 550 and the standard deviation is σ = 115.There are three friends - Harry, Jason, and Sarah - who want to be admitted to business schools. Harry requires a score of 650 or above, while Jason requires a score of 630 or higher and Sarah requires a score of 670 or above. Because the admission procedure is independent for each of the friends, the joint probability can be calculated using the multiplication rule.
The probabilities that Harry, Jason, and Sarah will achieve the desired scores are calculated separately using the z-score equation, which is as follows;For Harry:Z = (650 - 550) / 115 = 0.87 Probability of Harry getting admitted = P(z > 0.87) = 0.1949 (using z-table)For Jason:Z = (630 - 550) / 115 = 0.7 Probability of Jason getting admitted = P(z > 0.7) = 0.2413 (using z-table)For Sarah:Z = (670 - 550) / 115 = 1.04 Probability of Sarah getting admitted = P(z > 1.04) = 0.1492 (using z-table)The probability that Harry, Jason, and Sarah will all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)
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A prism has a height of 6.1 meters. If the side of the base is 4.6 m and the apothem is 3.17 meters. Find the volume of the prism
The volume of the prism is 222. 4 m³
How to determine the volume of the prismThe formula for calculating the volume of a pentagonal prism is expressed as;
V = [1/2 x 5 x b x a] x h of the prism
Given that the parameters are;
V is the volume of the prismb is the base side of the prisma is the apothem of the prismh is the height of the prismNow, substitute the values, we get;
Volume , = ( 1/2 × 5 × 4.6 × 3.17) × 6.1
Multiply the values
Volume , V = (72.91/2) × 6.1
divide the values in the bracket
Volume = 36. 46 × 6.1
Multiply the values
Volume = 222. 4 m³
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would appreciate any help on this
The correct graph of f(x) include the following: D. Graph D.
Domain format: (-∞, -2) U (2, ∞).
Range format: (1, ∞).
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. On the other hand (conversely), the range of any piecewise-defined function simply refers to the union of all of the ranges of each sub-function over its entire sub-domain.
By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce that the range and domain are as follows;
Range = (1, ∞).
Domain = (-∞, -2) U (2, ∞).
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The difference quotient of a function is a formula that allows you to calculate the average rate of change on any interval. Each function has its own difference quotient. It is another variation of the slope formula. Average Rate of Change Difference Quotient AROC -f(x)-f(x) . on the interval xxldo-f(x+h)-f(x) x -X When finding the difference quotient (DQ) you should not assign numerical values to x and h. Only when you are asked to calculate the average rate of change should you plug in values for x and h, where x is the first endpoint of the interval and h is the length of the interval. * 4. a) Find the difference quotient for f(x)=x. Simplify as much as possible. xeh analyzemath.com b) Use the difference quotient from part a) to calculate the average rate of change of f(x) = x on the interval (1, 3).
The difference quotient for f(x)=x is (x+h-x)/h, which simplifies to 1/h. The average rate of change of f(x)=x on the interval (1,3) is 1/2, since h=2.
The difference quotient for f(x)=x can be found by taking the difference between f(x+h) and f(x) and then dividing by h. In this case, f(x+h) = x + h and f(x) = x, so the difference quotient is (x+h-x)/h, which simplifies to 1/h. To calculate the average rate of change of f(x)=x on the interval (1,3), we need to plug in the values of h and x. Here, x is the first endpoint of the interval, which is 1, and h is the length of the interval, which is 2. Thus, the average rate of change is 1/2.
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A rocket is launched from the top of a 40 foot cliff with an initial velocity of 150 feet per second. The height, h, of the
ocket after t seconds is given by the equation h= -16t² + 150t+ 40. How long after the rocket is launched will it be 10
feet from the ground?
42
Step-by-step explanation:
42-7=69z3
Answer: To find out how long after the rocket is launched will it be 10 feet from the ground, we need to solve for t in the equation:
h = -16t^2 + 150t + 40
We know that when the rocket is 10 feet from the ground, h = 10:
10 = -16t^2 + 150t + 40
Subtracting 10 from both sides:
0 = -16t^2 + 150t + 30
Dividing both sides by -2:
0 = 8t^2 - 75t - 15
Using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 8, b = -75, and c = -15.
Plugging in these values:
t = (-(-75) ± sqrt((-75)^2 - 4(8)(-15))) / 2(8)
Simplifying:
t = (75 ± sqrt(5715)) / 16
Therefore, the rocket will be 10 feet from the ground approximately 0.26 seconds and 8.05 seconds after it is launched.
Your welcome (:
Step-by-step explanation:
a florist is making bunches of flowers for a wedding each bunch contains some carnations, roses and lilies. each bunch is the same. a bunch contains 40 flowers. 60 percent of the flowers are lilies. the ratio of carnations to roses is 3:5. the florist only has 140 carnations. How many bunches of flowers can the florist make?
The florist can make 23 bunches of flowers with the lilies, carnations, and roses they have for the wedding.
What is the ratio?
A ratio is a comparison of two or more quantities that indicates their relative sizes or amounts. It expresses the relationship between two or more numbers or values by dividing one by the other.
Let's start by finding out how many flowers in each bunch are lilies.
Since 60 percent of the flowers are lilies, we can calculate that 0.6 x 40 = 24 of the flowers in each bunch are lilies.
That means the remaining 16 flowers in each bunch are split between carnations and roses.
Let's use the ratio of 3:5 to split these flowers between carnations and roses.
First, we need to find the total number of parts in the ratio:
3 + 5 = 8
That means for every 8 flowers in the bunch, 3 are carnations and 5 are roses.
Now we can set up an equation to find out how many bunches of flowers the florist can make:
140 (number of carnations) ÷ 3 (number of carnations in each 8-flower group) = 46.67
So the florist can make 46 bunches of flowers with the carnations they have.
But we need to make sure that there are enough roses to go with these carnations.
If 3 of every 8 flowers in each bunch are carnations, that means 5 of every 8 flowers are roses.
So for each bunch, there are 5/8 x 16 = 10 roses.
To make 46 bunches of flowers, the florist will need 46 x 16 = 736 flowers in total.
If 24 of every 40 flowers in each bunch are lilies, that means 16 of every 40 flowers are carnations and roses combined.
So for 736 flowers, there will be 368 carnations and roses.
Since each bunch contains 16 flowers, the florist can make 368 ÷ 16 = 23 bunches of flowers with the carnations and roses they have.
Therefore, the florist can make 23 bunches of flowers for the wedding.
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