functions s(10)=??
need help

Functions S(10)=??need Help

Answers

Answer 1

Answer:

We're required to find s(10).

therefore , the polynomial applicable will be

[tex]s(x) = - 5{x}^{2} + x - 8 \: \\ \: ( \: since \: x > - 1)[/tex]

[tex]\therefore \: s(10) = - 5( {10}^{2}) + 10 - 8 \\ \dashrightarrow \: s(10) = - 5(100) + 2 \\ \dashrightarrow \: s(10) = - 500 + 2 \\ \dashrightarrow \: \boxed{ \: s(10) = - 498}[/tex]

hope helpful! :)


Related Questions

5, 6, and -2 are zeros of f(x). Find its three factors.

Answers

Since 5, 6, and -2 are zeros of f(x), they must divide the polynomial f(x) completely.

Let's call the polynomial f(x) as "p(x)". Then, the three factors can be expressed as:

p(x) = (x - 5)(x - 6)(x + 2)

So, the polynomial f(x) has three factors: (x - 5), (x - 6), and (x + 2).

in a city, 80% of people like watching basketball, 70% like watching football, and 30% enjoy watching both sports. what percentage of the people neither like watching football, nor basketball?

Answers

In this city, the percentage of people who neither like watching football nor basketball is 20%.

This is calculated by subtracting the total percentage of people who like watching either football or basketball (80% + 70% - 30% = 120%) from the total population (100%).

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign (%). For example, 45% means 45 out of 100, or simply 0.45. To calculate the percentage of a number, divide the number by the total and multiply by 100. For example, to find the percentage of 12 out of 50, divide 12 by 50 and then multiply by 100, which equals 24%.

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Two trucks leave a warehouse at the same time. One travels due south at an average speed of 49 miles per hour, and the other travels due north at
an average speed of 62 miles per hour. After how many hours will the two trucks be 277.5 miles apart

Answers

Answer:

2.5hrs

Step-by-step explanation:

We can start solving the problem by using the formula: distance = rate x time. If we call the time t in hours, we can write two equations:

49t = distance for the truck going south

62t = distance for the truck going north

We also know that the distance between the two trucks is the sum of the distances they have traveled, so:

distance = 49t + 62t = 111t

Now we can use the given information that the distance between the two trucks is 277.5 miles to find the value of t:

277.5 = 111t

t = 277.5 / 111

So the two trucks will be 277.5 miles apart after t = 2.5 hours.

Which graph shows the solution to this system of equations? x/2 - 3 = y 3+y/2 = x

Answers

The equation of the red line will be y = 5/3 x - 3 and The equation of the green line will be y = 0x + 1 i.e y = 1 .

What is Equation of a Straight line ?

Equation of a straight line as follows : y = mx + c

where m is the slope of line.

Start by seeing where the lines go. They cross (intersect) at (1, -1). We can use this to check later.

Now for slope: green is -4/2 = -2

pink is 4/2 = 2

Now we can create the equations

Let's make green = g(x) and pink = p(x)

if we use y = mx + b, then the green has a y-intercept (b) of +1

So g(x) = -2x + 1

pink has a y-intercept of -3, so p(x) = 2x - 3

Now let's plug n play: put our solutions x into each equation and confirm that it makes the y = -1

g(x) = -2x + 1 = -2(1) + 1 = -2+1 = -1

p(x) = 2x - 3 = 2(1) - 3 = 2-3 = -1

Therefore, The equation of the red line will be y = 5/3 x - 3 and The equation of the green line will be y = 0x + 1 i.e y = 1 .

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[BRAINLIEST] The election board’s voter registration list is
not a census of the adult population. Explain why.

Answers

The election board’s voter registration list is not a census because the eligibility to vote may affect some persons not to be counted also the body organizing the activities are not same

How is census different from voter registration count?

A census,, is a comprehensive count of the population that is conducted by the government. It is used to gather information about the size, distribution, and characteristics of the population for a variety of purposes, including apportioning congressional seats, drawing electoral districts, and allocating federal funds to states and localities.

Because voter registration and census are two different processes with different goals, they may not capture the same individuals. For example, not all adults are eligible to vote, such as non-citizens, felons, and those under the age of 18. Additionally, some eligible voters may choose not to register, while others may be missed by registration efforts. Therefore, the voter registration list may not be a complete or accurate representation of the adult population.

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How many 2in x 2in square tiles will fit along the edge of a square mosaic that has an area of 196in2

Answers

Answer:

it should be 24

Step-by-step explanation:

QUESTION 7
Use the following table relating the the population in millions and median age for a variety of American cities.
New
Philadelphia Phoenix
Los
Angeles York
3.849 8.214
31.6 34.2
City
Population
(millions)
Median Age
Chicago Dallas
2.833 1.233
31.5 30.5
Houston
2.144
30.9
1.448
34.2
1.513
30.7
San
Antonio
1.297
31.7
San
Diego
1.257 0.930
32.5 32.6
San
Jose
Find and interpret the correlation coefficient.
The correlation coefficient is 0.2722. This means that there is a very weak positive correlation between population and median age.
The correlation coefficient is 0.2722. This means that 27.22% of the variation in the median age can be explained by the population of the given city.
The correlation coefficient is 0.2040. This means that there is a very weak positive correlation between population and median age.
The correlation coefficient is 0.2040. This means that 20.4% of the variation in the median age can be explained by the population of the given city.
The correlation coefficient is 0.4517. This means that there is a weak positive correlation between population and median age.
The correlation coefficient is 0.4517. This means that 45.17% of the variation in the median age can be explained by the population of the given city.

Answers

5 points? Really? Like? I should be given 5 points just to read 1/4 of the question

for what values of k does the quadratic equation (k 4)x -3kx-4(k -2) = 0 have two roots which differ by 1?

Answers

According to the quadratic equation the solution of k is 48 ± 8√26.

In math the term called quadratic equation is known as the polynomial equation whose highest degree is two

As we all know that the value of the quadratic equation is written as,

=> (k - 4)x² - 3kx - 4(k -2) = 0.

Now we have identified that the given equation is in the form of ax² + bx + c = 0.

Here we have also identified the value of a = k - 4, b = -3k and c = 4(k-2)

And then we have to use the quadratic formula to identify the value of k,

Here it can be written as.

=> (-3k)² - (4 x (k - 4) x 4(k-2))

When we expand the term then we get,

=> 9k² - (16k² - 32k - 64k + 128)

When we simplify this one then  we get

=> -5k² + 96k - 128 = 0

Here we have to factorize the expression then we get the value of k as 48 ± 8√26.

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Create an example of a relation that is a function and an example of a relation that is not a function. Use two different forms of representation. Upload an image for the graph or the mapping example. Post your examples to the discussion board without revealing which relation is a function and which relation is not a function.

Answers

An example of a relation that is a function is {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Relations and functions define a mapping between two sets (Inputs and Outputs) such that they have ordered pairs of the form (Input, Output).

An example of a relation that is a function:

{(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}

It is a function as every input has a single output.

So, 2,5,8,11,14 and 17 are the elements of the domain of the given relation.

Here domain ={2,5,8,11,14,17} and range ={1}

An example of a relation that is not a function

{(1,3),(1,5),(2,5)}

Since the element  1 corresponds to two different images i.e., 3 and 5 . So, this relation is not a function.

Therefore, an example of a relation that is a function is {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}.

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if a system of linear equations has two different solutions, it must have infinitely many solutions. true or false? select all that apply

Answers

This statement is true. If a system of linear equations has two different solutions, it must have infinitely many solutions.

Linear equations are equations that involve only linear functions, or functions of the form f(x) = mx + b. These equations can be used to describe a variety of real-world phenomena, such as the motion of a particle along a straight line. Linear equations are generally solved by using the linear equation solving methods, such as substitution, elimination, and graphing. The solutions to a linear equation are the values of the variables that make the equation true.

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a purse contains $2.20 in dimes and quarters. if the number of dimes is 1/4 the nuber of quarters, how many dimes are there?

Answers

There are 2 dimes in the purse that contains $2.20

What is an equation?

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Let quarters be = x

The dimes be = 1/4 * x

25x+10x/4 = 220

(100x + 10x) /4 = 220

110x/4 = 220

110x = 220*4

110x = 880

x = 880/110

x = 8

The dimes be = 1/4 * x

The dimes be = 1/4 * 8

The dimes be = 2

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Is [tex]\frac{log11}{log5} = \frac{ln11}{ln5}[/tex] ? Why or why not?

Answers

[tex]\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(11)\implies \cfrac{\log_{10}(11)}{\log_{10}(5)}\implies \stackrel{\textit{\Large both are equal}}{\boxed{\cfrac{\log(11)}{\log(5)}}\implies \cfrac{\log_{e}(11)}{\log_{e}(5)}\implies \boxed{\cfrac{\ln(11)}{\ln(5)}}}[/tex]

Determine which fraction is larger: 6/7 or 4/5

Answers

Answer:

6/7

Step-by-step explanation:

find the least common multiple of 7 and 5:

7,14,21,28,(35)

5,10,15,20,25,30,(35)

7x5=35 and 5x7=35

So multiply the denominator and numerator of 6/7 by 5, so 30/35

and multiply the denominator and numerator of 4/5 by 7, so 28/35.

30 is bigger than 28, so 30/35 is greater than 28/35.

Therefore, 6/7 is greater than 4/5

N microeconomic, price help determine both quantity upplied and quantity demanded. Which other factor can impact each by cauing a hift to occur?

Quantity upplied i determined by production cot, and quantity demanded i determined by deire for the product. Quantity upplied i determined by production cot, and quantity demanded i determined by producer behavior. Quantity upplied i determined by conumer behavior, and quantity demanded i determined by aggregate demand. Quantity upplied i determined by producer behavior, and quantity demanded i determined by deire for the product

Answers

The quantity supplied is determined by production costs, and the quantity demanded is determined by the desire for the product

The quantity demanded is a term that is used in economics to describe the total amount of a good or service that consumers demand over a given interval of time

When the production increase, fewer people could afford to put up the capital to do it, which reduce the quantity supplied to the market.

When the desire for a product increased, the amount of demand for a product will be the same since there is a larger amount of consumers who might be willing to obtain the product even at a higher price.

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A sample of 21 of 30 students has a test score average above a b fine the critical value for a 95% confidence

Answers

Answer:

The critical value for a 95% confidence level is 1.711.

Step-by-step explanation:

a=0.05

1-a=0.95

Degrees of freedom df =21-1=20

using the t-distribution table, the critical value for a 95% confidence level and df=20 is 1.711

a merchant bought an item for $30 and sold it for 50% more for what price did the merchants sell the item

Answers

Answer:

$45

Step-by-step explanation:

We know

A merchant bought an item for $30 and sold it for 50% more.

50% of $30 = $15

What price did the merchants sell the item?

$30 + $15 = $45

So, the merchants sell the item for $45

let a=(−2,8,3) and b=(−3,−10,5) be vectors. (a) find the scalar projection of b onto a

Answers

The scalar projection of b onto a is -7.33.

The scalar projection of a vector b onto a vector a is the magnitude of the component of b that is parallel to a. It is calculated by taking the dot product of the two vectors, and dividing it by the magnitude of a. Mathematically, this is represented by the equation:

(a⋅b)/|a|

In this example, the dot product of vectors a and b is equal to -66, and the magnitude of vector a is equal to 9. Therefore, the scalar projection of b onto a is equal to -7.33.

To calculate the scalar projection, we first need to calculate the dot product of a and b. To do this, we take the components of each vector and multiply them together. For vector a, this is done by taking -2 multiplied by -3, 8 multiplied by -10, and 3 multiplied by 5. We then add all of these products together to get the dot product of a and b, which is equal to -66.

Next, we calculate the magnitude of vector a, which is done by taking the square root of the sum of the squares of its components. For vector a, this is equal to the square root of (-2)^2 + (8)^2 + (3)^2, which is equal to 9.

Finally, we divide the dot product of a and b by the magnitude of a, which is -66 divided by 9, which is equal to -7.33. Therefore, the scalar projection of b onto a is -7.33.

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Bob wants to catch an elevator before the door closes. He is 32ft
away when the door starts to close.
The door has to travel 4.3ft to fully close, and is closing at a rate of
1.2ft/s. Bob needs to get to the door while it is at least 0.6ft open.
How fast does he have to run in order to catch the elevator?
Give your answer in feet per second, and round to the nearest
hundredth.

Answers

Bob needs to run at a speed of at least 10.39 feet per second to catch the elevator.

How to calculate speed?

To catch the elevator, Bob needs to reach the door before it fully closes, which means he needs to cover the distance of 4.3 - 0.6 = 3.7 feet in the time it takes the door to close. We can use the formula:

distance = rate x time

to find the time it takes for the door to close, and then use this time to find the speed that Bob needs to run. Let's set up the equation:

3.7 = 1.2t

where t is the time it takes for the door to close.

Solving for t, we get:

t = 3.7/1.2 = 3.08 seconds

Now we can use the formula again to find the speed that Bob needs to run:

speed = distance / time

speed = 32/3.08

speed = 10.39 feet per second (rounded to the nearest hundredth)

Therefore, Bob needs to run at a speed of at least 10.39 feet per second to catch the elevator.

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such that f1(1) = f2(1) and f1(i) = f2(i), show that f1 = f2.

Answers

By the principle of mathematical induction, we can conclude that f1(x) = f2(x) ∀ x ∈ X. Hence, f1 = f2.

Let f1(x) and f2(x) be two functions such that f1(1)=f2(1). We can then say that f1(x)-f2(x) = 0 for x=1. Since f1(i)=f2(i) for all i, we can state that f1(x)-f2(x) = 0 for all x. Therefore, f1(x) = f2(x) for all x, and f1=f2.

Let f1 and f2 be two functions, f1:X→Y, f2:X→Y, where X and Y are two sets.

If we assume that f1(1) = f2(1) and f1(i) = f2(i) for all i ∈ X, then it follows that

f1(x)=f2(x) ∀ x ∈ X.

To prove this, we will use mathematical induction. We will assume that the statement is true for some k ∈ X and prove that it is true for k+1.

Let us assume that f1(k) = f2(k).

Then,

f1(k+1) = f2(k+1)

Since f1(k+1) = f1(k) and f2(k+1) = f2(k), we can say that

f1(k) = f2(k)

Therefore, by the principle of mathematical induction, we can conclude that f1(x) = f2(x) ∀ x ∈ X. Hence, f1 = f2.

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the investigators compared the change in calcium levels between the two groups and found a p-value of 0.026. they concluded that there was only a 2.6% chance that the two groups were the same and so rejected the null hypothesis and claimed a difference in change in calcium levels. a reviewer came back and said that this was incorrect. is their statement accurate? why or why not?

Answers

The statement that "there was only a 2.6% chance that the two groups were the same" is not accurate.

A p-value is a measure of the evidence against the null hypothesis, and represents the probability of observing a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

A low p-value (typically less than 0.05) is often taken as evidence against the null hypothesis, and in favor of the alternative hypothesis.

However, a p-value does not directly measure the probability that the null hypothesis is true. It only provides information about the evidence against the null hypothesis, and not about the probability of the difference between the two groups.

The conclusion that "there was only a 2.6% chance that the two groups were the same" is not a valid interpretation of the p-value.

It is also worth noting that p-values are not the only evidence to consider when making a decision about the null hypothesis. Other factors, such as the effect size, the sample size, and the quality of the study design, should also be taken into account.

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Goran the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other ( not both). On Wednesday there were 2 clients who did plan A and 5 who did plan B. On Thursday there were 8 clients who did plan A and 3 who did Plan B. Goran trained Wednesday clients for a total of 6 hours and his Thursday clients for a total of 7 hours. How long does each of the workout plan last ?

Answers

The 9-hour training schedule is broken up into his Wednesday clients' 6 hours and his Thursday clients' 7 hours.

what is equations ?

Its core idea is thought to represent number's greatest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and treble. A fractional number can be checked to discover if it is a prime number. A statement having two spherical geometry and an equal sign in the middle is referred to as a mathematical equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Neither conditional equation or identities are categories for equations.

given

Make a system of equations where A represents the length of a Plan A session and B represents a Plan B session.

This Wednesday: 2A + 12B = 9 hours.

Thursday: 5A + 3B = 9 hours

Using addition, multiply the Thursday equation by -4 to find the solution:

2A + 12B = 9

(5A + 3B = 9) * -4

2A + 12B = 9

-20A -12B

= -36

The B's disappear if you combine the two equations:

1.5 hours from -18A to -27A.

the following into one of the initial equations:

12B = 6 B = 0.5 hours + 2(1.5) = 9

The 9-hour training schedule is broken up into his Wednesday clients' 6 hours and his Thursday clients' 7 hours.

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Find the x-intercepts of the function f(x)=x^2-4x-2. Round to the nearest tenth if necessary.

Answers

The x- intercept of  y = x²-4x-2 is 4.44949 and −0.44949.

What is Intercept?

The line's point of intersection with the coordinate axes is known as an intercept. The y coordinate of the intersection point is zero if the line contacts the X axis, and the intercept is known as the x intercept.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given:

To find the x-intercepts of the function, y = x²-4x-2, we need to make the y-value of the function equal to zero,

So, x²-4x-2 = 0

Now, solving the above Quadratic Equation

x²-4x-2 = 0

D = √(-4)² - 4(1)(-2)

D = √16 + 8

D = √24

D = 2√6

So, x= 4 ±  2√6/ 2

x = 4 +  2√6/2  or x = 4-  2√6/2

x = 2 + √6 or x = 2- √6

x = 4.44949 or x = −0.44949

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Annual sales for a local restaurant are $650,000 and are increasing at a rate of 4
percent each year. Find the annual sales after 7 years. Round to the nearest dollar.
4

Answers

The annual sales after the 7th year is 855,355.65

What is an exponential functions?

An exponential function is a type of function in math that involves exponents. A basic exponential function is of the form f(x) = bx, where b > 0 and b ≠ 1.

The standard expression for an exponential function is expressed as: y=a(1+r)^t

From the parameters in the question

Given the following parameters

a = 650000

r = 4% = 0.04

t = 7

Substitute the given parameters into the formula:

y=a(1+r)^t

y = 650000(1+0.04)^7

y= 650000(1.04)^7

y=855,355.65

Hence, the annual sales for the local restaurant after 7 years is 855,355.65

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neil is analyzing a quadratic function f(x) and a linear function g(x). will they intersect? f(x) graph of the function f of x equals x squared plus 2 g(x) x g(x) 1 3 2 5 3 7 (1 point) yes, at a point with a positive x-coordinate yes, at a point with a negative x-coordinate yes, at a point where x is zero no, they will not intersect

Answers

Yes, the quadratic function f(x) and the linear function g(x) will intersect. The x-coordinate of the point of intersection could be positive, negative or zero, depending on the specific functions.

From the data given, it's not possible to determine the x-coordinate of the point of intersection.

A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.

Linear functions are usually written as y = mx + b and graphed as straight lines.

Begin with the y-intercept or b value, then use the slope to identify a second point on the graph. Quadratic functions are graphed as curved parabolas and have the formula y = ax2 + bx + c.

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(1 point) evaluate the integral by reversing the order of integration. ∫10∫55yex2dxdy

Answers

The solution to the given integral is 5ye10 - 5ye5 + c(y10 - y5).

To evaluate the given integral, we must first reverse the order of integration. This is done by switching the limits of integration for the two variables. In this case, the limits for the y variable are 10 and 5, and the limits for the x variable are 5 and 5. Thus, the integral can be rewritten as:

∫5∫10yex2dxdy

To evaluate this integral, we can use the following formula:

∫a∫bf(x,y)dxdy = ∫a∫bf(y,x)dydx

Using this formula, we can rewrite the integral as:

∫5∫10yex2dydx

We can now use the product rule to separate the integral into two separate integrals. First, we can integrate with respect to x:

∫5yex2dx

This integral can be solved using the fundamental theorem of calculus:

∫5yex2dx = 5ye5 - 5ye5 + c

Next, we can integrate with respect to y:

∫10(5ye5 - 5ye5 + c)dy

This integral can be solved by simply integrating the constants and the exponential:

∫10(5ye5 - 5ye5 + c)dy = 5ye10 - 5ye5 + c(y10 - y5)

Combining the two solutions, we get the following:

∫5∫10yex2dxdy = 5ye10 - 5ye5 + c(y10 - y5)

Therefore, the solution to the given integral is 5ye10 - 5ye5 + c(y10 - y5).

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Kayla walks into her favorite store at the mall and sees a sign: All jeans and skirts 25% off! How much will she spend if she buys one pair of $49 jeans and one $19 skirt? Show work

Answers

Based on the information, it can be inferred that Kayla would spend $51 buying a pair of jeans and a skirt.

How to find the final value that I paid Kayla?

To find the final value that Kayla paid we must carry out the following procedure:

We must find the equivalent of 25% of the total value of your purchase. Then we must add the value of both products and find the discount.

$49 + $19 = $86$68 / 100 = $0.68$0.68 * 25% = $17$68 - $17 = $51

Based on the above, Kayla would pay $51 for both products and the discount would be $17.

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the density of copper is 9.86 g/cm3 work out the mass in kg

Answers

Answer: Thus the mass of copper in solid form is m = 9860 kg / m^3.

Step-by-step explanation: solve it step by step

the average ( ) gmat for students entering graduate school of business at ucla is 630. assume gmat scores are normally distributed with a standard deviation of 80. a)* the standardized z score for a student scoring 595 on their gmat is . write answers up to four decimal places b)* a student scoring 670 is standard deviations from the mean. c)* a score of corresponds to a z-score of 1.25. d)* a gmat score of is one standard deviations below the mean.

Answers

A:  The z-score is -0.9375; B:  a z-score of 1.25 corresponds to a score of 750; C: a score of 550 is one standard deviation below the mean.

a) To find the standardized z-score for a student scoring 595 on their GMAT, we use the formula:

z = (x - mu) / sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

z = (595 - 630) / 80 = -0.9375

Therefore, the z-score is -0.9375.

b) To find the number of standard deviations a student scoring 670 is from the mean, we use the formula:

z = (x - mu) / sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

z = (670 - 630) / 80 = 0.75

Therefore, the student scoring 670 is 0.75 standard deviations from the mean.

c) To find the score that corresponds to a z-score of 1.25, we use the formula:

x = mu + z * sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

x = 630 + 1.25 * 80 = 750

Therefore, a z-score of 1.25 corresponds to a score of 750.

d) To find the score that is one standard deviation below the mean, we use the formula:

x = mu - sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

x = 630 - 80 = 550

Therefore, a score of 550 is one standard deviation below the mean.

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After the last snowstorm, the snow in my backyard was 15 inches deep! The depth of the
snow decreased by 20% every day after the storm.

Write an equation to model the depth (d) of the snow n days after the storm.

Answers

The equation model the depth (d) of the snow n days after the storm is d(n) = 15 * (0.8)^n

How the equation was derived?

Let's call the initial depth of the snow (n = 0) as d0. d0 = 15 inches.

Every day, the snow depth decreases by 20%. So, the rate of change of the snow depth is -0.2.

Using this information, we can use the formula for exponential decay to find the depth of the snow (d) after n days:

d(n) = d0 * (1 - 0.2)^n

Substituting d0 = 15, we get:

d(n) = 15 * (0.8)^n

Therefore, the correct answer is as given above

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How much alcohol must a pharmacist add to 10 cm to the power of 3 of a 10% alcohol solution to strengthen it to a 70% solution

Answers

20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a pharmacist add to 10 cm³ of a 10% alcohol solution to strengthen it to a 70% solution.

Let x be the volume of pure alcohol (100%) in cm³ needed to be added.

x × 100% + 10 cm³ × 10% = 70% × (x + 10 cm³)

x × 1 + 10 × 0.1 = 0.7 × (x + 10)

x + 1 = 0.7x + 7

x - 0.7x = 7 - 1

0.3x = 6

x = 20 cm³

Therefore, 20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.

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