For a printing company, the cost of printing business cards is a linear function, C(x) = 0. 05x + 20, where x is the number of cards printed. What is the cost of printing 950 business cards? 15 points

Answer:

STEP

1

:

Equation at the end of step 1

 ((15 • (y3)) +  (2•3y2)) -  21y

STEP

2

:

Equation at the end of step

2

:

 ((3•5y3) +  (2•3y2)) -  21y

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  15y3 + 6y2 - 21y  =   3y • (5y2 + 2y - 7)

Trying to factor by splitting the middle term

4.2     Factoring  5y2 + 2y - 7

The first term is,  5y2  its coefficient is  5 .

The middle term is,  +2y  its coefficient is  2 .

The last term, "the constant", is  -7

Step-1 : Multiply the coefficient of the first term by the constant   5 • -7 = -35

Step-2 : Find two factors of  -35  whose sum equals the coefficient of the middle term, which is   2 .

     -35    +    1    =    -34

     -7    +    5    =    -2

     -5    +    7    =    2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  7

                    5y2 - 5y + 7y - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

                   5y • (y-1)

             Add up the last 2 terms, pulling out common factors :

                   7 • (y-1)

Step-5 : Add up the four terms of step 4 :

                   (5y+7)  •  (y-1)

            Which is the desired factorization

Final result :

 3y • (y - 1) • (5y + 7)

Step-by-step explanation:

Answer:

It is ( D )

Step-by-step explanation:

Have a good day

Answer:

N = 5/6

Step-by-step explanation:

4/5 N= 2/3.  Find N (solve for N).  

Isolate N.  To do this, multiply both sides of the equation by (5/4):

(5/4)(4/5)N= (5/4)(2/3)

becomes N = 10/12, or N = 5/6.

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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The model of the height the ride given by the sine function indicates that

the motion is periodical.

Reasons:

Time at which the power failure occur = 6 minutes after the ride started

The given sine function model for the height of the height of the last passenger above the ground is given by the formula;

h = -82.5·cos(3·π·(t)) + 97.5

Where;

h = The height of the last passenger above the ground in feet

t = The time of operation of the ride

Required:

Height of the last passenger the moment the power failure occurs.

Solution:

At t = 6 minutes, the height of the last passenger is given as follows;

h = -82.5·cos(3·π·(6)) + 97.5 = 15

Therefore;

(b) The lowest position = h = -82.5·cos(3·π·(0)) + 97.5 = 15

Given that the height of the last passenger is 15 feet above the ground at

the time the time the power failure occurs, the last passenger is at the

lowest position and therefore, does not have to wait to exit the ride.

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Answer:

(1,4)

Step-by-step explanation:

take 2 minus 1 then nine minus 5

The mean μ=9 is the setting so that an 8 ounce cup will overflow when only 0.5% of the time.

A Z-score indicates how far a given value is from a standard deviation. A Z-score (standard value) is the number of standard deviations that a particular data point is above or below the mean. Standard deviation essentially reflects the amount of variability within a given data set.

The average is calculated as: From the Z-score formula:

z=(x-μ)/σ

Z-score associated with 0.5% is 0

(8μ)/0.4=0

Solving for x gives:

μ=9

For μ=9, an intermediate setting such that the 8 ounce cup overflows 0.5% of the time.

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The number of voters that should be sampled for a confidence interval depends on the desired level of confidence and the margin of error.

A larger sample size generally leads to a smaller margin of error and a higher level of confidence in the accuracy of the results. However, the relationship between sample size and margin of error is not linear, meaning that doubling the sample size will not necessarily halve the margin of error.
To calculate the required sample size, a formula can be used that takes into account the margin of error, level of confidence, and population size.
the number of voters that should be sampled for a confidence interval depends on several factors and cannot be determined without more information.
To determine the required sample size, you can use the following formula:
n = (Z^2 * p * (1-p)) / E^2

Where:
- n is the sample size
- Z is the Z-score (usually 1.96 for a 95% confidence interval)
- p is the estimated proportion of the population (usually 0.5 for the worst-case scenario)
- E is the margin of error (in decimal form)

Hence, without the specific margin of error, we cannot provide the exact sample size needed.

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Answer:

Step-by-step explanation:

x= cost per gallon

10x=23

x=2.3

2.3*15= 34.5

the quotient of 5 and y:   5÷y

added to 3:   3 + 5÷y

is at least (AKA is greater than or equal to) 5:  3 + 5÷y  ≥ 5

Answer:   3 + 5÷y ≥ 5

Answer:

12

Step-by-step explanation:

(5/3)y-8 = (7/3)y-16

(5/3)y- (7/3)y = 8 -16

(-2/3) y = -8

y = 3*8/2

y=24/2

y=12

The values of the trigonometric ratios sec θ and cot θ are:

sec θ = -13/12

cot θ = 12/5

There are three main trigonometric ratios which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are told that sin θ = -5/13

Using Pythagoras theorem, we have that:

Adjacent side = √(13² - 5²)

Adjacent side = √144 = 12

Thus:

cos θ = -12/13

sec θ = 1/cos θ

Thus:

sec θ = 1/(-12/13)

sec θ = -13/12

1/ tan θ = cot θ

tan θ = sin θ/cos θ

tan θ = (-5/13)/(-12/13) = 5/12

cot θ = 1/(5/12) = 12/5

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Answer:

$ 11

Step-by-step explanation:

A game costs $ x.

Two games costs 2x.

50 + 2x = 72

2x = 72 - 50

2x = 22

x = 11

Given :

Two pyramid with same volume .

To Find :

If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B .

Solution :

\(V_a=V_b\)

Volume of pyramid is given by :

\(V=\dfrac{\text{Area of base}\times height}{3}\\\\V=\dfrac{Ah}{3}\)

Now , h'=3h

\(V'_b=\dfrac{Ah'}{3}\\\\V'_b=3\dfrac{Ah}{3}\\\\V'_b=3V_a\)

Therefore , new volume of pyramid B is 3 times the value of pyramid A .

Hence , this is the required solution .

The sum of an arithmetic sequence given a partial sum is 35532.

Firstly, we need to identify the common difference of the arithmetic sequence. This can be done by finding the difference between any two consecutive terms. In this case, subtracting 9 from 3 gives us a common difference of 6.

Next, we determine the number of terms in the sequence. To do this, subtract the first term from the given partial sum and divide the result by the common difference. In this case, subtracting 3 from 639 and dividing by 6 gives us 106 terms.

Finally, we can calculate the sum using the arithmetic series formula: Sn = (n/2)(2a + (n-1)d), where Sn represents the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we have Sn = (106/2)(2*3 + (106-1)*6). Simplifying this expression, we find that the sum of the arithmetic sequence is 35532.

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Answer:

A

Step-by-step explanation:

as one number being added on both sides

Answer:

C

Step-by-step explanation:

From the given table, we can calculate the earnings of Melissa.

4 hours' work makes 36 dollars

1 hour work makes=36×1/4=9 dollars

Melissa makes 9 dollars per hour.

Holli makes 8.25 dollars per hour.

So, Melissa makes more money.

9-8.25=0.75

Melissa earns 0.75 dollars more than Holli.

So, the answer is C.

Answer:

1 United States Dollar equals 6.85 Chinese Yuan

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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The angle that a side of 15 inches makes with the 6-inch side is approximately 78.46 degrees.

c²= a² + b² - 2ab cos(C)

In this case, we know that the lengths of the two congruent sides are both 15 inches, and the length of the remaining side is 6 inches. So we have:

15² = 6² + 15² - 2(6)(15)cos(x)

225 = 261 - 180cos(x)

180cos(x) = 36

cos(x) =\(\frac{36}{180}\)

cos(x) = 0.2

Now we can use the inverse cosine function (\(cos^{-1}\)) to find the value of "x" in degrees:

x = \(cos^{-1}\)(0.2)

x ≈ 78.46 degrees

An angle is a geometric figure formed by two rays with a common endpoint, called the vertex. The rays are known as the sides of the angle. The measure of an angle is usually expressed in degrees, and it represents the amount of rotation needed to rotate one of the sides of the angle onto the other. A full rotation around a point is 360 degrees, so an angle measuring 180 degrees is called a straight angle.

Angles can be classified according to their measure. An acute angle is an angle measuring less than 90 degrees. A right angle is an angle measuring exactly 90 degrees. An obtuse angle measures more than 90 degrees but less than 180 degrees. A reflex angle measures more than 180 degrees but less than 360 degrees.

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SOLUTION

We want to find the interquartile range of the box and whisker plot in the picture.

Interquartile range is calculated as

In the box and whisker plot

Hence the answer is 6

Answer:

x = -1

Step-by-step explanation:

5 less than a number is equivalent to 1 more than three times the number

number = x

x - 5 = 3x + 1

now im going to get the numbers and variable on different sides

x - 5 + 5 = x

3x + 1 - 3x = 1

x + 3x = 4x

1 - 5 = -4

4x = -4

lastly im going to divide each side by 4

4x / 4 = x

-4 / 4 = -1

x = -1

Value of side CD = x=3

When two triangles are  are referred to as similar figures when they share the same shape but different  in size.

given that CB and ED are perpendicular to AD,

in triangle ABC and ADE

∠A=∠A (common angle )

∠B=∠D (both are 90 degree)

ΔABC≈ ΔADE by angle-angle similarity .

and we know that when two triangle are similar then their corresponding sides are with in the same ratio or proportional.

so ,here we proved that triangle ABC and ADE are similar,

then ,

\(\frac{BC}{ED}=\frac{AB}{AD}\)

\(\frac{x}{5}=\frac{9}{9+6}\)

\(\frac{x}{5} =\frac{9}{15}\\ X=3\)

x=3

from above result ,value of side CB =x=3

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Answer:

8*12=96

Step-by-step explanation:

Answer:

8 newspapers in one pile

Step-by-step explanation:

\(\frac{96}{12} = \frac{8}{x} \\\\96x=8*12\\\\96x=96\\x=1\)

approximately 68 percent of the parts are predicted to wear out between 1,017 and 1,183 hours of operation.

To determine the range of hours within which approximately 68 percent of the parts are predicted to wear out, we can use the concept of the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:

- Approximately 68 percent of the data falls within one standard deviation of the mean.

- Approximately 95 percent falls within two standard deviations.

- Approximately 99.7 percent falls within three standard deviations.

In this case, we have a normal distribution with a mean of 1,100 hours and a standard deviation of 83 hours.

To find the range within which approximately 68 percent of the parts are predicted to wear out, we calculate one standard deviation above and below the mean:

Lower bound: Mean - 1 * Standard Deviation = 1,100 - 83 = 1,017 hours

Upper bound: Mean + 1 * Standard Deviation = 1,100 + 83 = 1,183 hours

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The magnitude of the vector sum of the four vectors = 278.158M

What is Magnitude?

The magnitude or size of a mathematical item defines whether it is larger or smaller than other objects of the same kind in mathematics. Formally speaking, the size of an object is the displayed outcome of an ordering—of the class of objects to which it belongs.

A = 82(cos 64 degree x +sin 64 degree y )

= 35.946 x +73.701y

B = 82 X

C= 82 Xx

D= 82 x (cos 64 degree x +sin 64 degree y)

= 35.946 x +73.701y

net = A+B+C+D

= X (35.946+82+82+35.946) + (2*73.701)

=235.892 X + 147.402Y

Magnitute = 278.158m

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The method that he chooses to select his sample is Stratified Sampling.

In Stratified, the population is divided into subpopulations and then the same sampling is applied to each region or subpopulation.

The ability to obtain a sample population that most accurately represents the overall population being investigated while ensuring that each subgroup of interest is represented makes stratified random sampling one popular technique employed by researchers. Researchers use stratified sampling to ensure that specific subgroups are represented in the sample. It also helps in the precise evaluation of each group's characteristics. This technique is often used in surveys to better understand disparities between subpopulations.

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Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7