In 1990, the cost of tuition at a large Midwestern university was $94 per credit hour. In 2004, tuition had risen to $290 per credit hour.
Determine a linear function
C
(
x
)
to represent the cost of tuition as a function of
x
, the number of years since 1990.

By using circle model the images are attached below:

A circle with a diameter of one has n firms distributed uniformly around it. In light of this, every company's distance from each of its closest neighbors is 1/n.

We must first create two circles in order to compare the ratios of 2 to 7 and 5:7 using a circle model.

Then, we must divide each circle into seven pieces.

We must shade 2 of the circle's total 7 portions in order to maintain the 2:7 ratio.

We must shade 5 of the circle's total 7 portions in order to maintain the 5:7 ratio.

As a result, the first circle symbolizes a 2:7 ratio, while the second circle a 5:7 ratio.

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Answer: using circles to model the ratios, divide both circles into

7

equal parts.

For the ratio 2 to 7,

2

parts should be shaded.

For the ratio 5:7,

5

parts should be shaded.

The ratio 2 to 7 is

less than

the ratio 5:7

The number line that shows approximately the location of √5 would the number line in option D.

A number line is defined as the expression that can be used to illustrate the position of a given number which show either it is a positive or a negative number with one at the middle.

The given value is thus;

= √5 = 2.236067977 = 2.2

From the chosen number line, the dark dot is just few points after 2.

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The result can be shown in multiple forms.

Exact Form:

15/7

Decimal Form:

2.142857

Mixed Number Form:

2   1/7

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Usually I try to explain what to do, but it's been a hot second from when I learned this. I uploaded a picture that might help.
This is a free tool for solving math problems if you ever need help: (no spaces or exclamation point) mat h way . co!m

------------------------

much love <333 good bye!!

The probability that calls last between 4.0 and 4.6 minutes will be around 0.4332.

we have to standardize the values and utilize the standard typical dispersion table or calculator.

To discover the z-scores for 4.0 and 6.0  minutes:

z1 = (4.0 - 6.0  ) / 0.70 = 2.8

z2 = (4.5 - 6.0  ) / 0.70= 2.1

Since Employing a standard ordinary conveyance table, we are able to discover the likelihood of the calls enduring between 4.0 and 4.6 minutes:

P(0 ≤ Z ≤ 2.1) = 0.4332

However the likelihood that calls final between 4.0 and 4.6 minutes is 0.4332, or around 0.4332.

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Answer:

Y = 5/2 X

Step-by-step explanation:

Number of Sculptures: 2, 8, 20

Number of paintings: 5, 20, 50

8 * 5/2 = 8 * 5/2

= 40/2

= 20

50 * 2/5 = 10 * 2

= 20

Assume X represents the number of sculptures

Y represents the number of paintings

Y = 5/2 X

Hope this helps!

To answer this, you use the formula \(I = Prt\) where

    \(I\) is the simple interest that builds

    \(P\) is the principal (AKA the amount invested/borrowed)

    \(r\) is the interest rate per year

    \(t\) is the lenght of the loan, in years.

In your situation:

    \(\begin{aligned}I &= (\$3000)(5 \%/\text{year})(3 \text{ years})\\[0.5em]&= (3000)(0.05)(3)\\[0.5em]&= 450\end{aligned}\)

This means there'd be $450 of simple interest due at the end of 3 years.

Answer:

$450

Step-by-step explanation:

Interest= 3000(5%)(3)= $450

Common mistake: Do not use 36 as the time period. Only use the number of years, it the number of months.

Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

:)

Answer:

149 more people.

Step-by-step explanation:

1. Subtract 2003 by 1854 and get 149

Answer:

the answer is

y=3/2+4

Step-by-step explanation:

4 is found on the y-axis and 3/2 is 1,5 and it looks like its going 1,5 steps up

Step-by-step explanation:

I think so the question is incorrect or I can't solve it.

Answer:

Step-by-step explanation:

If you would like to know how much water did Elena drink each practice if she drank the same amount each time, you can calculate this using the following steps:

5 bottles of water ... 7 practices

x bottles of water = ? ... 1 practice

5 * 1 = 7 * x

5 = 7 * x /7

x = 5/7 bottle of water

The correct result would be 5/7 bottle of water.

Answer:

  2x² +5

Step-by-step explanation:

You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.

The area is the product of length and width, so the width will be ...

  A = LW

  W = A/L = (2x³ +6x² +5x +15)/(x +3)

The cubic expression can be factored by grouping, so we have ...

  Area = (2x³ +6x²) +(5x +15)

  = 2x²(x +3) +5(x +3)

  = (2x² +5)(x +3)

Then the width is ...

  \(\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}\)

The width of the rectangle is 2x² +5.

<95141404393>

Answer:

By substituting the values of A, C, and D the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

Step-by-step explanation:

From the given information, we have;The vertical stretch of the sine function = 3 × The parent function∴ A = 3Given that the horizontal shift left = π/2 units, (from an online source with similar question)The vertical shift down = 4 unitsThe given function, g is g(x) = A·sin(x + C) + DWhere;A = The amplitude = The maximum displacement from the rest or equilibrium position = 3C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)Therefore, the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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FINDING THE SURFACE AREA OF A COMPOSITE SOLID

About "Finding the surface area of a composite solid"

Finding the surface area of a composite solid :

A composite solid is made up of two or more solid figures.

To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Finding the surface area of a composite solid - Examples

Example 1 :  

Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?

Solution :  

Step 1 :

Identify the important information.

• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.

• One face of each prism is not on the surface of the figure.

Step 2 :  

Find the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

Step 3 :  

Find the area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Step 4 :  

Find the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Step 5 :  

Add. Then subtract twice the areas of the parts not on the surface.

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

The surface area before the hole was drilled was 3,720 sq.cm.

The surface area before the hole was drilled was; 3,720 sq.cm.

A composite solid is made up of two or more solid figures.

To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

The bottom is a rectangular prism with h = 18 cm.

The base is a 30 cm x 24 cm rectangle.

One face of each prism is not on the surface of the figure.

Then the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

The area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Now the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Now,

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

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Answer: I believe

M = 80

Step-by-step explanation:

100 - 20 = 80

Answer:

.

Step-by-step explanation:

1.

Alpha = 0.05. alpha/2 = 0.025

Under the z table

Z 0.025 = 1.96

50+-1.96(2/√100)

= 50+-0.39

50+0.39 = 50.39

50-0.39 = 49.61

2.

At 99%

Alpha = 0.01

Alpha/2 = 0.005

In z table

= 2.58

50+-(2.58)(2√100)

= 50 +- 0.52

= 50+0.52 = 50.52

50 - 52 = 49.48

Please check attachment for answers 3 to 5. The test editor did not work properly. It kept flagging some of my typed content.

Using the z-distribution, it is found that:

a) The 95% confidence interval for the mean breaking strength of this type of wire, in kN, is (49.61, 50.39).

b) The 99% confidence interval for the mean breaking strength of this type of wire, in kN, is (49.49, 50.52).

c) The confidence level is of 86.64%.

d) 171 wires must be sampled.

e) 295 wires must be sampled.

We are given the standard deviation for the population, which is why the z-distribution is used to solve this question.

The information given is:

The confidence interval is:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

The margin of error is of:

\(M = z\frac{\sigma}{\sqrt{n}}\)

Item a:

The first step is finding the critical value, which is z with a p-value of \(\frac{1 + \alpha}{2}\), in which \(\alpha\) is the confidence level.

In this problem, \(\alpha = 0.95\), thus, z with a p-value of \(\frac{1 + 0.95}{2} = 0.975\), which means that it is z = 1.96.

Hence, the interval is:

\(\overline{x} - z\frac{\sigma}{\sqrt{n}} = 50 - 1.96\frac{2}{\sqrt{100}} = 49.61\)

\(\overline{x} + z\frac{\sigma}{\sqrt{n}} = 50 + 1.96\frac{2}{\sqrt{100}} = 50.39\)

The 95% confidence interval for the mean breaking strength of this type of wire, in kN, is (49.61, 50.39).

Item b:

\(\alpha = 0.99\), thus, z with a p-value of \(\frac{1 + 0.99}{2} = 0.995\), which means that it is z = 2.575.

\(\overline{x} - z\frac{\sigma}{\sqrt{n}} = 50 - 2.575\frac{2}{\sqrt{100}} = 49.49\)

\(\overline{x} + z\frac{\sigma}{\sqrt{n}} = 50 + 2.575\frac{2}{\sqrt{100}} = 50.52\)

The 99% confidence interval for the mean breaking strength of this type of wire, in kN, is (49.49, 50.52).

Item c:

The margin of error is:

\(M = \frac{50.3 - 49.7}{2} = 0.3\)

Hence:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.3 = z\frac{2}{\sqrt{100}}\)

\(0.2z = 0.3\)

\(z = 1.5\)

z = 1.5 has a p-value of 0.9332, hence:

\(\frac{1 + \alpha}{2} = 0.9332\)

\(1 + \alpha = 2(0.9332)\)

\(\alpha = 0.8664\)

The confidence level is of 86.64%.

Item d:

This is n for which M = 0.3, with z = 1.96, hence:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.3 = 1.96\frac{2}{\sqrt{n}}\)

\(0.3\sqrt{n} = 1.96(2)\)

\(\sqrt{n} = \frac{1.96(2)}{0.3}\)

\((\sqrt{n})^2 = \left(\frac{1.96(2)}{0.3}\right)^2\)

\(n = 170.7\)

Rounding up, 171 wires must be sampled.

Item e:

Now z = 2.575, hence:

\((\sqrt{n})^2 = \left(\frac{2.575(2)}{0.3}\right)^2\)

\(n = 294.7\)

Rounding up, 295 wires must be sampled.

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The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.

The probability of getting exactly three robberies in a day is 0.1607.

The Poisson distribution is a discrete probability distribution used in probability theory and statistics to express the likelihood that a given number of events will occur within a specified time or space interval if they occur at a known constant mean rate and regardless of the interval since the last event.

The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.

In the poison distribution a discrete random variable X has the following probability mass function,

\($P(X=x)=\frac{e^{-\lambda} \cdot \lambda^x}{x !}$\), where \($\lambda$\) is the mean of the distribution and \($x=0,1,2,3 \ldots \ldots$\)

Given that \($\lambda=1.8$\)

The required probability, \($P(X=3)=\frac{e^{-1.8} .(1.8)^3}{3 !}=0.1607$\)

Therefore, the probability of getting exactly three robberies in a day is = 0.1607.

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Answer:

32

Step-by-step explanation:

The largest square possible is if the diagonal of the square = 8

The sides would \(8/\sqrt{2}\) or \(4\sqrt{2}\) because of 45 45 90 triangle

\(\frac{8}{\sqrt{2} } *\frac{8}{\sqrt{2} } = 64/2 = 32\)

Hope this helps :)

Have a great day!

Answer:

x intercept =(-5/3,0)

y intercept = (0,5)

Step-by-step explanation:

FOR THE X INTERCEPT:

-plug 0 in for the y value because the y value is 0 at the x intercept.

     * 3x-0=-5 ---> 3x=-5 -----> x=-5/3 while y = 0

FOR THE Y INTERCEPT

-do the same thing as the x intercept, but instead of making y 0, make x 0.

     * 3(0) -y=-5 ----> 0-y=-5 -----> -y=-5 ------->y=5 while x=0

Answer:

1.575 kg

Step-by-step explanation:

75g x 21

1575 g

convert to kg

1.575 kg

Brainliest Appreciated!

The two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

To determine which expressions are less than 7/8, we can compare them individually to 7/8 and evaluate their values.

Let's consider each expression one by one:

7/8 x 9/19:

To compare this expression to 7/8, we multiply the fractions:

(7/8) x (9/19) = 63/152.

Since 63/152 is less than 7/8, this expression is less than 7/8.

7/8 x 3/4:

Multiplying the fractions:

(7/8) x (3/4) = 21/32.

Since 21/32 is less than 7/8, this expression is less than 7/8.

7/8 x 9/9:

The fraction 9/9 simplifies to 1, so the expression becomes:

(7/8) x 1 = 7/8.

Since 7/8 is equal to 7/8 (not less than), this expression is not less than 7/8.

7/8 x 4/3:

Multiplying the fractions:

(7/8) x (4/3) = 28/24.

We can simplify 28/24 to 7/6.

Since 7/6 is greater than 7/8, this expression is not less than 7/8.

Therefore, the two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

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Answer:

Hello,

Step-by-step explanation:

P(n)=ax²+bx+c (quadratic sequence)

with a=1,b=1,c=13

\(\\\boxed{u_n=n^2+n+13}\\\)

Answer:

=============================

Given sequence:

We can see this not AP or GP as the difference or ratio of consecutive terms is not common.

But we can see the difference between terms has common difference of 2:

and

It means the sequence is of the second degree, in other words it is quadratic.

In general it is of the form:

Use the terms of the given sequence to work out unknown coefficients.

t₀ = 15 - (4 - 2) = 15 - 2 = 13

It gave us the value of c.

t₁ = 15

t₂ = 19

Compare the last two equations and solve for a and b:

Then

So we know the coefficients:

The nth term equation is:

Answer:

68

Step-by-step explanation:

4(4 + 1)²

4(16 + 1)

64 + 4

68

The rewritten fractions are 15/20 and 14/20. The correct answer is (a) 15/20 and 14/20.

To rewrite the fractions 3/4 and 7/10 with a least common denominator, follow these steps:
1. Find the least common multiple (LCM) of the denominators 4 and 10.

The LCM is the smallest number that both denominators can divide into.

In this case, the LCM is 20.
2. Rewrite each fraction with the new denominator (20) by multiplying the numerator and the denominator of each fraction by the necessary factor to reach the LCM.
For 3/4:
(3 * 5)/(4 * 5) = 15/20
For 7/10:
(7 * 2)/(10 * 2) = 14/20.

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

70

Step-by-step explanation:

100% means all of them.