. Graph the equation y = 49x, where y
represents the distance traveled over time,
x, in hours. Is the relationship proportional?
How many miles from home is the family
after 5 hours?
Distance from Home (miles)
441
392
343
294
245
196
ty
147
98
49
0
Vacation Driving
0123456789
Time (hours)
X

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

1 value

Step-by-step explanation:

spicifically 5/3

The x satisfy only 1 value and x is  \(\frac{5}{3}\)   .

The modulus function, which is also called the absolute value function gives the magnitude or absolute value of a number irrespective of the number being positive or negative. It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

According to the question

-2|3x-5|=0  

Step1: Dividing -2 both side

|3x-5|=0  

Step 2: Open modulus

3x-5=0      and        - 3x+5=0

3x=5         and         - 3x = - 5

x = \(\frac{5}{3}\)    

Hence, the x satisfy only 1 value and x is  \(\frac{5}{3}\)   .

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Answer:

Sample means and the grand mean

Step-by-step explanation:

The total sum of squares present in the sample can be partitioned into two parts.

1) Within sum of squares ( also called error sum of squares)

2) Between sum of squares

The first part is the sum of squares of deviations of the observations from the sample mean and is called the within sum of squares ( also called error sum of squares).

The second part is the weighted sum of the square of deviations of the sample means from the grand mean and is called between sum of squares.

Thus symbolically

Totastal SS = Within SS + Between SS

The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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The value of x with the given condition is 10

From the question, we have the following parameters that can be used in our computation:

D(7,2), E(1, 9), F(4,8), and G(x, 1),

Also, we have

DE || FG

This means that the lines DE and FG are parallel lines and they have equal slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(9 - 2)/(1 - 7) = (1 - 8)/(x - 4)

Evaluate the difference

-7/6 = -7/(x - 4)

So. we have

x - 4 = 6

Evaluate

x = 10

Hence. the value of x is 10

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Answer:

1,000,000

Step-by-step explanation:

Answer:

Step-by-step explanation:original quantity = $30

New quantity = $39

increase amount = 39-30 = 9

Percent change:

30 x = 9

x = 9/30

x = 0.3

0.3x 100 = 30%

Since the quantity grows, it's a percent increase.

Answer:

The Taylor series of f(x) around the point a, can be written as:

\(f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....\)

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

\(fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}\)

In this exercise we must calculate the Taylor series for the given function in this way;

\(f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}\)

The Taylor series of f(x) around the point a, can be written as:

\(f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....\)

Here we have:

\(f(x) = 4cos(x)\\a = 7\pi\)

Then, let's calculate each part:

\(f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4\)

Here we already can see two things:

1) The odd derivatives will have a sin(x) function that is zero when evaluated in \(x=7\pi\).

2) We also can see that the sign will alternate between consecutive terms.

So we only will work with the even powers of the series:

\(f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....\)

So we can write it as:

\(f(x)=\sum f_n\)

Such that the n-th term can written as:

\(f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}\)

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Using the Central Limit Theorem, it is found that these conditions are required to avoid the high variability associated with small samples.

\(s=\sqrt{p(1-p)/n}\)

\(p v=2*p(z < -0.531)=0.595\)

1) Data given and notation

n=500 represent the random sample taken

X=380 represent the number of people with some characteristic

estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

3) Calculate the statistic  

\(z=\frac{0.76 - 0.77}{\sqrt{\frac{0.77(1-77)}{500} } =0.531}\)

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \(\alpha =0.05\)The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

\(pv=2*p(z < -0.0531)=0.595\)

If we compare the p value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.  

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The monthly cost for 17 hundred of cubic feet is $52.13.

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Let y represent the bill paid for x HCF of water.

The slope is 1.45, hence m = 1.45.

The monthly cost for 13 HCF is $46.33, hence:

46.33 = 1.45(13) + b

b = 27.48

y = 1.45x + 27.48

For 17 HCF:

y = 1.45(17) + 27.48 = 52.13

The monthly cost for 17 hundred of cubic feet is $52.13.

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Answer:

Y: 0, x:0

Y:1, x: 3

Y: 2, x: 6

Y: 3, x:9

Step-by-step explanation:

Plug in the x to get the y

3 is the digit in the ten places of 33,300.

The ten-place digit is the second digit from the right in a whole number.

To find the digit in the ten places of 33,300, we need to divide the number by 10 and then take the remainder when divided by 10.

33,300 divided by 10 is 3,330 with a remainder of 0.

So the digit in the ten places of 33,300 is 3.

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Answer:

PEMDAS you have to simplify the exponent first

Step-by-step explanation:

copy and paste on edge its correct

Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.

We suppose a general triangle, for which:

The lengths and the sine of the angles are proportionally related as follows:

\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)

The segments in this problem are given as follows:

Hence it can be affirmed that:

BC > AB.

As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.

As for segment AC, we need the measure of angle B, hence nothing can be affirmed.

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The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Answer:

Step-by-step explanation:

CASNT HELP

Answer:

The height is about 5 inches.

Step-by-step explanation:

The volume for a cone is \(\frac{1}{3}\) × π × r² × h

The radius of the cone is 1.5

12= \(\frac{1}{3}\) × π × 1.5² × h

12= \(\frac{1}{3}\) × π × 2.25 × h

12=0.75×π×h

Divide both sides by 0.75

16=π×h

Divide both sides by π

5≈h

The height is about 5 inches.

Answer:

umm sorry but i think it going to need a picture to see the problem

Step-by-step explanation:

The corresponding element in the range of the function F when 7 is in the domain is 4.6.

The expression for the given function F following as:

F(x) = 6(x) - 19 / 5

The corresponding element in the range of the function F is the output of the function when 7 is input into the function.

To find this output, we can substitute 7 for X in the expression for the function F:

F(7) = 6(7) - 19 / 5

F(7) = 42 - 19 / 5

F(7) = 23 / 5

F(7) = 4.6

Thus, when 7 is in the domain, the equivalent element in the range of the function F is 4.6.

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Answer:

(x-8)(x+8)

Step-by-step explanation:

Answer:

(x + 8)(x − 8)

Step-by-step explanation:

Answer:

13.5 %

Step-by-step explanation:

For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)

To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean

= 95-68 = 27 %

Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5

The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

Given that, average age managers = 52 years standard deviation = 2.5 years.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Considering the equation Z =  (X−μ)/σ

Where, X is the lower or higher value, as the case may be μ  is the average σ  is standard deviation

Now, z1= (54.5 - 52)/2.5

= 1

z2= (57 - 52)/2.5

= 2

Now, z2-z1= 2-1

= 1

P(54.5>Z<57)= 0.8413

Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

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Answer:

30°

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.

In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:

short leglong leg​=13​​

short leg93​​=13​​

Cross-multiplying and solving for the short leg, we get:

short leg=3​93​×1​=9

Similarly, we can use another proportion to find the hypotenuse:

long leghypotenuse​=3​2​

93​hypotenuse​=3​2​

Cross-multiplying and solving for the hypotenuse, we get:

hypotenuse=3​2×93​​=18

Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.

it does not show the question

Answer:

x-60

Step-by-step explanation:

because x is the degree it started with, and it was less 60 degrees everyday

Answer:

She should win approximately 30 times.

Step-by-step explanation:

Since the probability of winning is 3/8, we multiply 3/8 with 80 to get 30.

It is given that you have invested $50 a month in an annuity that earns 48% APR compounded monthly. We can conclude that after 2 years you will have $1954.13 in your account.

To solve this we are going to use the formula for the future value of an ordinary annuity:

\(P[(\frac{(1+(r/n)^{nt}-1)}{(r/n)}]\)

where

FV is the future value

P is the periodic payment

r is the interest rate in decimal form

n is the number of times the interest is compounded per year

t is the number of years

It is given that you have invested $50 a month in an annuity that earns 48% APR compounded monthly. we need to find how much money you have in this account after 2 years.

Since the interest is compounded monthly, it is compounded 12 times per year; therefore,

r = 48% = 0.48

n = 12

Let's put the values in our formula:

\(P[(\frac{(1+(r/n)^{nt}-1)}{(r/n)}]\\\\50[(\frac{(1+(0.48/12)^{12\times 3}-1)}{(0.48/3)}]\\\\$1954.13\)

Thus, We can conclude that after 2 years you will have $1954.13 in your account.

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