vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?

Step-by-step explanation:

some to check if it correct

The length of the  line segment AB is 8.48 unit.

The term used for identifying the size of an object or the distance from one point to another is known as length.

The length of the line segment having endpoints A (x1, y1) and B (x2, y2) can be determined using the formula,

\(AB=\sqrt{(x_{2} ^{2} -x_{1} ^{2} )+(y_{2} ^{2} - y_{1} ^{2} )}\)

Given that x1 = -1, x2= 11, y1= 7, and y2= -1.

Substituting the given values in the above equation

\(AB=\sqrt{(11^{2}-(-1)^2 )+((-1)^2-7^2)}\)

\(AB=\sqrt{72} = 8.48\)

Hence, 8.48 unit is the length of line segment AB.

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The value of the function at x = 4 is 8.79.

Tangent line approximation is the approximation of any function using a linear function. It is also called as linear approximation.

It allows us to approximate the value of a general function with a more simpler linear function.

Given that,

f(1) = 2

f'(x) = \(\sqrt{x^{2} +2cos x + 3}\)

We have the formula for linear approximation as,

f(x) = f(a) + f'(a) (x - a)

Here x = 4 and a = 1

f(a) = f(1) = 2

f'(a) = f'(1) = \(\sqrt{1^{2} +2cos 1 + 3}\) = 2.254

Substituting,

f(4) = 2 + (2.254) (4 - 1)

     = 8.762 ≈ 8.79

Hence the value of f(4) is 8.79.

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Answer:

Step-by-step explanation:

y=mx+b is the general equation of a line, where

m= slope = (y2-y1)/(x2-x1)= (6-2)/(0- -3)= 4/3

b= y intercept

for point (0,6)

y=(4/3)x+b will become 6=(4/3)*0 +b, so b=6

the equation of the line that passes trough the given points is

y= (4/3) x +6

Answer:

y = 4/3 x + 6

Step-by-step explanation:

M = -4/-3 = 2/3

y = 4/3 X + B

6 = 4/3(0) + B

B=6

Answer:

There is 2121.80 in the account after 2 years.

Step-by-step explanation:

Use the formula A = P(1 + r)^t  where P = initial amount, A = amount after t years and r = the rate (as a decimal).

So, for this problem:

Amount after 2 years = 2000(1 + 0.03)^2

= £2121.80

Cathy and Iris have 259,459,200 ways to skip countries.

Data;

To solve this problem, we would have to use a mathematical procedure known as combination.

Let us calculate the number of countries that would have to skip.

\(13 - 9 = 4\)

To decide which country they have to skip, it would be 4 out of 13.

\(x = ^1^3C_4 = \frac{13!}{4!}\)

Let's solve this

\(\frac{13!}{4!} = \frac{13*12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\ \frac{13!}{4!} = 13*12*11*10*9*8*7*6*5 = 259459200 ways\)

Cathy and Iris have 259,459,200 ways to skip countries.

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Answer:

Yes it is

Step-by-step explanation:

Each x value is represented by exactly one y value.

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

Expand the left side and solve the resulting 2-step linear equation.

  x^2 -(4 -4x +x^2) = 8

  x^2 -4 +4x -x^2 = 8 . . . . . eliminate parentheses

  -4 +4x = 8 . . . . . . . . . . . . . collect terms

  -1 +x = 2 . . . . . . divide by 4

  x = 3 . . . . . . . . . add 1

Answer:

(x + 3)

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

if four people dont want it and there are 14 people total, then it would be (14-4). The photos cost $3 so it would be 3(14-4)=$30

Answer:

C

Step-by-step explanation:

from 14 friends you have to take away the 4 that do not want a photo

(14- 4 ) is the number of kids Charlie will have to pay for

and will pay $3 for each (14-4) kids

3(14-4)  is the cost

3(14-4) = 3*10 = is $30

Given

The degree of a polynomial is the greatest exponent of x. In this case, the greatest exponent of x is 2.

Answer: false

Answer:

✔️Length of the space Mr. Hamilton wants to fill with pictures = 4 ft long

✔️8 pictures can be fit on this wall by Mr. Hamilton

Step-by-step explanation:

The wall = 9.75 ft long

Window = 5¾ ft long = 5.75 ft

Each President's picture = 6 in. wide = 0.5 ft wide (note: 1 ft = 12 in.)

✍️Length of the space Mr. Hamilton wants to fill with pictures = 9.75 ft - 5.75 ft = 4 ft

✍️ Numbers of pictures that can fit on this wall = the space Mr. Hamilton wants to fill ÷ the width of each picture

= 4 ft ÷ 0.5 ft

= 8.

8 pictures will can be fit on the wall.

Answer: x = 5 2/3 - 3 1/3

Step-by-step explanation:

From the question, we are informed that Shelly has a beaker which contains 5 2/3 fluid ounces of water and that she pours out 3 1/3 fluid ounces of water. The expression that an be used to find the number of fluid ounces of water which remain in the beaker goes thus:

Let's represent the remaining water in the beaker as x.

Since 3 1/3 fluid ounces of water has been poured our from 5 2/3 fluid ounces of water. The expression will be:

x = 5 2/3 - 3 1/3

Answer:

A

Step-by-step explanation:

It's A on edge

Answer:

This graph shows a function because no vertical line passes through more than one point on the graph.

Step-by-step explanation:

Answer:

12 1/6

It wants me to add more but there's nothing to add

Answer:

option B

Step-by-step explanation:

7 sq rt 3 cannot be simplified

4 sq rt 6 cannot be simplified

sq rt 48 = (sq rt 12 · sq rt 4) = (sq rt 4 · sq rt 4 · sq rt 3) = 4 sq rt 3

sq rt 54 =  (sq rt 9 · sq rt 6) = 3 · sq rt 6

combine each pair of like terms:  (7 sq rt 3 + 4 sq rt 3) =  11 sq rt 3

                                                        (-4 sq rt 6 - 3 · sq rt 6) = -7 sq rt 6

the claim aligns with the null hypothesis, as both assert the absence of an effect, difference, or relationship between variables.

The claim and the null hypothesis are the same when the claim being made is that there is no significant difference or relationship between variables or that there is no effect or impact of a particular factor. In other words, the claim asserts that the null hypothesis is true.

For example, if the null hypothesis (H₀) states that there is no difference between the means of two groups, the corresponding claim would be that the means are indeed equal. Similarly, if the null hypothesis states that there is no correlation between two variables, the claim would be that there is indeed no significant correlation.

In such cases, the claim aligns with the null hypothesis, as both assert the absence of an effect, difference, or relationship between variables.

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Answer:

Average rate of change for given function is: -2

Step-by-step explanation:

Given function is:

\(f(x)=x^2-6x+8\\x_12= 1\\x_1 = 3\)

In order to find the rate of change, we have to find the value of function on x1 and x2

So,

\(f(x_1) = (3)^2-6(3)+8 = 9-18+8 = -1\\f(x_2) = (1)^2-6(1)+8 = 1-6+8 = 3\)

The formula for finding the rate of change is:

\(Rate\ of\ change = \frac{f(x_2)-f(x_1)}{x_2-x_1}\)

Putting the values, we get

\(=\frac{3-(-1)}{1-3}\\=\frac{3+1}{-2}\\=\frac{4}{-2}\\= -2\)

Hence,

Average rate of change for given function is: -2

Answer:

Step-by-step explanation:

No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.

The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.

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the equation that describes the line that passes through point P(-2,2) and is perpendicular to the line on the graph is y = (-3/2)x - 1.

The coordinate plane below shows point P(-2,2) and the line y=2/3x-1.

In order to find out which equation describes the line that passes through point P and is perpendicular to the line on the graph, we need to find the slope of the given line equation y = (2/3)x - 1.

We know that slope of the line is given by y = mx+c, where m = slope of the line c = y-intercept of the line

The given line equation is y = (2/3)x - 1.

Therefore, m = 2/3. Now, let's find the slope of the line which is perpendicular to this line.

Since the line passes through the point P(-2,2) and is perpendicular to the line given by equation y = (2/3)x - 1. Therefore, the slope of the required line will be equal to the negative reciprocal of the slope of the given line equation. Thus, the slope of the required line is -3/2.

Using point-slope form, the equation of the line which is perpendicular to the given line equation and passes through point P(-2,2) is:

y - y1 = m(x - x1), where m = -3/2 and (x1, y1) = (-2, 2).y - 2 = (-3/2)(x - (-2))

Multiplying through the brackets, we get:

y - 2 = (-3/2)x - 3

Adding 3 to both sides, we get:

y - 2 + 3 = (-3/2)x

Simplifying, we get:

y + 1 = (-3/2)x

Rearranging, we get the equation:

y = (-3/2)x - 1.  

So, the equation that describes the line that passes through point P(-2,2) and is perpendicular to the line on the graph is y = (-3/2)x - 1.

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The probability (in percent form) of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 55%.

If 45% of Americans say they believe that statistics teachers know the true meaning of life, then 55% of Americans do not believe this. Therefore, the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 55%.

Percentage is referred to as the expression in which the number is written as multiple of 100 and the symbol to show percentage of a number is %. Now we need to express the value in percentage.

Expressing this as a percentage, we have:

55% = 55/100 * 100% = 0.55 * 100% = 55%

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the correct translation is ((∃x)E(x) → ((A(g) & ¬W(g)) ∨ (¬A(g) & W(g))))

The correct translation of the third premise "Evil can exist only if God is either able but unwilling or unable yet willing to prevent it" is:

((∃x)E(x) → ((A(g) & ¬W(g)) ∨ (¬A(g) & W(g))))

Explanation:

(∃x)E(x): There exists an x such that x is evil. This represents the existence of evil.

A(g): God is able to prevent evil.

¬W(g): God is unwilling to prevent evil.

¬A(g): God is unable to prevent evil.

W(g): God is willing to prevent evil.

The premise states that evil can exist only if one of two conditions is met:

God is able to prevent evil but unwilling to do so (A(g) & ¬W(g)).

God is unable to prevent evil yet willing to do so (¬A(g) & W(g)).

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Answer:

x = 6

Step-by-step explanation:

since the polygons are similar, then the ratios of corresponding sides are in proportion, that is

\(\frac{3x}{6}\) = \(\frac{12}{4}\) = 3 ( multiply both sides by 6 to clear the fraction )

3x = 18 ( divide both sides by 3 (

x = 6

Answer:

53.3333333%

Step-by-step explanation:

Given the following question:

14 desktops
16 laptops
14 + 16 = 30

To find the answer use the formula to calculate percentages.

\(\frac{16}{30}\times100\)
\(16\div30=0.533333333\)
\(0.533333333\times100=53.3333333\)
\(=53.3333333\)

16 of 30 as a percentage is "53.3333333%."

Hope this helps.

Answer:

first one is the right one

Step-by-step explanation:

The volume of a cube if the diagonal of one side is 50cm is approximately 48112.52 cubic centimeters.

Let s represent the width of the cube's sides, and d represent the width of one side's perpendicular. The Pythagorean formula can be used to connect s and d:

d**2 = s**2 + s**2 + s**2 = 3s**2

To solve for s, we obtain:

S = d/Sqrt(3)

Given a cube with edge lengths s, the volume V is equal to:

V = s**3

Inputting the word in place of s gives us:

V = (d / sqrt(3))**3 = d**3 / (3*sqrt(3))

Now we can change d to 50 centimetres to obtain the cube's volume:

V = 50**3 / (3*sqrt(3)) = 48112.52 cubic centimeters

As a result, the cube's capacity is roughly 48112.52 cubic centimetres.

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Answer:

\(\angle ABC=60\)

Step-by-step explanation:

\([Kindly\ refer\ the\ image\ attachment.]\\We\ are\ given\ that,\\AM\ is\ the\ Angle\ Bisector\ of\ \angle BAC.\\Hence,\\\angle BAM= \angle MAC\\CM\ is\ the\ Angle\ Bisector\ of\ \angle BCA.\\Hence,\\\angle BCM= \angle MCA.\\Also,\\\angle AMC=2 \angle ABC\)

\(Now,\\As\ we\ can\ observe\ that,\\\angle BCM + \angle MCA= \angle BCA\\\angle MCA+ \angle MCA= \angle BCA\ [\angle BCM = \angle MCA]\\Hence,\\2 \angle MCA= \angle BCA\\Or, \\\angle MCA=\frac{\angle BCA}{2} \\\\Similarly,\\\angle BAM + \angle MAC= \angle BAC\\\angle MAC + \angle MAC= \angle BAC\\2 \angle MAC = \angle BAC\\Or,\\\angle MAC=\frac{\angle BAC}{2}\)

\(Through\ the\ Angle\ Sum\ Property\ of\ a\ Triangle,\ we\ know\ that:\\'The\ Sum\ of\ all\ interior\ angles\ of\ a\ triangle\ is\ 180.'\\Hence,\\In\ \triangle BAC,\\\angle ABC + \angle BCA + \angle CAB=180\\In\ \triangle MAC,\\\angle MAC+ \angle ACM + \angle AMC=180\)

\(Hence,\\As\ \angle AMC= 2 \angle ABC, \angle MCA=\frac{\angle BCA}{2}, \angle MAC=\frac{\angle BAC}{2},\\2 \angle ABC+\frac{\angle BCA}{2}+\frac{\angle BAC}{2}=180\\By\ resolving\ the\ denominators,\\\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}=180\\\\By\ comparing\ the\ Sum\ of\ angles\ in\ both\ the\ triangles,\\We\ find\ that\ the\ RHS\ of\ both\ the\ equations\ are\ equal\ i.e.180,\\The\ LHS\ of\ the\ equations\ are\ equal\ too.\\\)

\(Hence,\\\angle ABC+ \angle BCA + \angle BAC=\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}\\Hence,\\2(\angle ABC+ \angle BCA + \angle BAC)=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle ABC+ 2 \angle BCA + 2 \angle BAC=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle BCA + 2 \angle BAC-\angle BCA- \angle BAC=4 \angle ABC- 2 \angle ABC\\Hence,\\\angle BCA+\angle BAC= 2\angle ABC\)

\(Lets\ get\ back\ to\ the\ Angle\ Sum\ of\ \triangle ABC,\\\angle ABC + \angle BAC + \angle ACB=180\\Hence,\\As\ \angle BCA + \angle BAC= 2 \angle ABC,\\\angle ABC + 2 \angle ABC=180\\Hence,\\3 \angle ABC=180\\\angle ABC=\frac{180}{3}=60\)

Answer:

not a hundred percent sure since there are no graphs attached but mine was Graph 1 to be the answer

After 2 years she will have earned $12 * 2*2.3% = $12* 4.6% = 55c interest (to the nearest cent). Therefore the balance will be $12.55

After 6 years she will have earned $12 * 6*2.3% = $12* 13.8% = $1.66 interest (to the nearest cent).  

Therefore the balance will be $13.66

After 10 years she will have earned $12 * 10*2.3% = $12* 23% = $2.76 interest (to the nearest cent).  

Therefore the balance will be $14.76

A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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