Rebecca earned $115 in simple interest for 8 months at an annual interest rate of 3%. How much money did she start with in her account?

Inequalities help us to compare two unequal expressions. The inequality that represents the given statement is 45≤x≤ 65.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the maximum legal speed on the highway is 65 MPH, therefore, the value of x must not exceed 65 MPH.

x ≤ 65

Also, the minimum legal speed on the highway is 45 MPH, therefore, the value of x must not be less than 45 MPH.

45≤x

By combining the two inequalities, we will get,

45≤x≤ 65

Hence, the inequality that represents the given statement is 45≤x≤ 65.

The complete question is:

Write an inequality that accurately represents the following statement: "Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."

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Answer:

Third option(double circle)

Step-by-step explanation:

Isometry (iso meaning same and metry meaning measure)

preserves the length and overall mass/size of a shape during a transformation. The 3rd option is the only shape that changes size in the examples, making it a non isometric transformation.

Answer:

Two solutions exist for the system of equations in the graph.

Step-by-step explanation:

Solutions are when the two graphs intersect.

The second option is the correct answer

[tex]16x^{4}+40x^{3} -24x^{2}[/tex]

The expression given to us is:

[tex]8x^{2} (5x+2x^{2}-3 )[/tex]

Herein, we can simplify it by opening up the bracket and multiplying each term inside the bracket by the term which is outside the bracket.

Thus, we get:

[tex]8x^{2} (5x+2x^{2}-3 )=8*5x^{2+1} +8*2x^{2+2}-8*3x^{2}[/tex]

[tex]40x^{3} +16x^{4}-24x^{2}[/tex]

Rearranging the above expression in descending order of power we get:

[tex]16x^{4}+40x^{3} -24x^{2}[/tex]

From the given options we can see this is the second option. Hence the second option is the correct answer.

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One can Identify the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets by?

The difference that exist between a rise in price due to the inflation and a rise in price due to microeconomic markets is based on the price changes that has occurred in terms of demand and supply model.

Note that this is said to be the price in a given market but the price rise as a result of to inflation tells that the price rise is one that reaches a lot of markets and not only just one market.

Hence, One can Identify the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets by?

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The volume of the octagonal pyramid is 1302 cubic m if the length of the apothem is 7 m.

The pyramid has an octagonal base with 8 isosceles triangular faces, known as an octagonal base pyramid.

The length of the apothem = 7 m

Side length = 9 m

The area of the one triangle = (1/2)×7×9 = 63/2 square m

The area of the octagonal base = 8(63/2) = 252 square m

The volume of the pyramid = (1/3)(base area)(height)

The volume of the pyramid = (1/3)(252)(15.5)

= 1302 cuibc m

Thus, the volume of the octagonal pyramid is 1302 cubic m if the length of the apothem is 7 m.

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Answer: 4a^2-2b^2 (I think this is right)

Step-by-step explanation:

Using the order of operations I started by multiplying both of the sides separately. The left side of the equation becomes 2a^2-b^2-ab while the right becomes 2a^2-b^2+ab. Then I put the sides together to add them and after combining like terms it becomes 4a^2-2b^2.

The required height of window of the glass 2.4 meters.

Tony is installing a window that is shaped like a parallelogram. He has 6 square meters of glass and knows that the base of the window needs to be 2 and 1 half meters.

parallelogram is a quadrilateral consist of pairs of parallel side.

Area of parallelogram = base x height
                                    6 = 2.5 x height

               height = 2.4 m

Thus the required height of window is given by 2.4 meters.

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142,506 different five-member committees can be made.

If we have a set of N elements, the number of different subsets of K elements that we can make out of these N elements is:

[tex]C(N, K) = \frac{N!}{K!*(N - K)!}[/tex]

In this particular case, the set has 30 elements which are the students. And the committee has 5 members, so K = 5 and N = 30, then we get:

[tex]C(30, 5) = \frac{30!}{(30 - 4)!*5!} = \frac{30*29*28*27*26}{5*4*3*2*1} = 142,506[/tex]

This means that 142,506 different five-member committees can be made.

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Answer:

Step-by-step explanation:

The alternate interior angles theorem, and the angle sum theorem can be used here.

Alternate interior angles are found on either side of a transversal where it crosses a pair of parallel lines. They are between the parallel lines. Their vertices are at the junction of the transversal and the parallel lines. Alternate interior angles are congruent.

In this diagram, there are two pairs of alternate interior angles where the two transversals AD and BD cross parallel lines AB and CD.

At points A and D, the alternate interior angles are 70° and x, respectively. This tells you ...

  x = 70° . . . . alternate interior angles theorem

At points B and D, the alternate interior angles are w and 70°, respectively. This tells you ...

  w = 70° . . . . alternate interior angles theorem

The angle sum theorem tells you the sum of angles in a triangle is 180°. This fact can be used to find the measure of angle y.

  70° +w +y = 180°

  y = 180° -70° -w = 110° -70°

  y = 40° . . . . angle sum theorem

There is not enough information to determine the measure of angle z.

  z = indeterminate

Answer:

g(f(-2)) = -15

Step-by-step explanation:

• f(x) = x³

Then

f(-2) = (-2)³ = -8

• When x = -2 → g(f(x)) = g(f(-2)) = g(-8)

Since -8 ≤ 0 then g(-8) = 2×(-8) + 1 = -16 + 1 = -15

Conclusion:

g(f(-2)) = -15

Answer:

-960

Step-by-step explanation:

1) Expand [tex](x - 2y)^{10}[/tex] using the binomial theorem.

Binomial Theorem: [tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]

1.1) Substitute the values into the theorem.

[tex]\sum _{i=0}^{10}\binom{10}{i}x^{\left(10-i\right)}\left(-2y\right)^i[/tex]

1.2) Expand summation.

[tex]=\frac{10!}{0!\left(10-0\right)!}x^{10}\left(-2y\right)^0+\frac{10!}{1!\left(10-1\right)!}x^9\left(-2y\right)^1+\frac{10!}{2!\left(10-2\right)!}x^8\left(-2y\right)^2+\frac{10!}{3!\left(10-3\right)!}[/tex]

[tex]x^7\left(-2y\right)^3+\frac{10!}{4!\left(10-4\right)!}x^6\left(-2y\right)^4+\frac{10!}{5!\left(10-5\right)!}x^5\left(-2y\right)^5+\frac{10!}{6!\left(10-6\right)!}x^4\left(-2y\right)^6+\frac{10!}{7!\left(10-7\right)!}x^3\left(-2y\right)^7+\frac{10!}{8!\left(10-8\right)!}x^2\left(-2y\right)^8+\frac{10!}{9!\left(10-9\right)!}x^1\left(-2y\right)^9+\frac{10!}{10!\left(10-10\right)!}x^0\left(-2y\right)^{10}[/tex]

1.3) Simplify them.

1.4) You will get:

[tex]=x^{10}-20x^9y+180x^8y^2-960x^7y^3+3360x^6y^4-8064x^5y^5+13440x^4y^6-15360x^3y^7+11520x^2y^8-5120xy^9+1024y^{10}[/tex]

2) We are told to find the coefficient of [tex]x^{7} y^{3}[/tex]. Find it from the simplified expansion. The coefficient is -960.

The equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

The standard equation of a parabola is in the form f(x) = (x-a)(x-b)

where a and b are the intercepts of the graph. Given the parabola that has intercepts of x=-2 and x=6, the resulting equation will be:

f(x) = a(x-(-2))(x-6)

f(x) = a(x+2)(x-6)

If the parabola passes through (8, 6), then;

6 = a(8+2)(8-6)

6 = a(20)

a = 6/20

a = 3/10

Substitute

f(x) = 3/10(x+2)(x-6)

Hence the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

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Answer:

Infinite Number of Solutions

Step-by-step explanation:

Hello!

We can solve for y in the first equation, and plug that value in for y in the second equation.

Now that we know the equation for y, we can plug that in for y into the second equation to solve for x.

Since the equations match, there are an infinite number of solutions.

If we take a close look at the equations, we can also see that they are the same equation, but with flipped signs.

The number of the sample that is necessary is 171. The number of employees that would be selected if E is 30 = 476

The standard deviation = 398

error E = 50

Alpha is = 1-0.90 = 0.10

a. We are to find the value of the size of the sample

Z∝/2 = Z0.05

= 1.645

sample size,n >= [Za/2 *(sigma/E)]^2

n >= [1.645 * (398/50)] ^2

n >= 171.46

n = 171

b.

error,E = 30

n >= [1.645 * (398/30)] ^2

n >= 476.27

n = 476

A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 90% confident that the sample mean is correct to within ±$50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $398. a. How large a sample is necessary?

b. If management wants to be correct to within ±$30, how many employees need to be selected?

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Answer:

You need to know what 3 u - 9 is equal to, in order to solve the equation for the variable u. Please post the entire equation. As this stands, it is just an algebraic expression and cannot be "solved".

Step-by-step explanation:

Based on the account balances at the end of year, the retained earnings are $5,000.

First, find the net income:

= Service revenue - Salaries

= 35,000 - 29,000

= $6,000

Then find the assets:

= 22,000 + 14,000 + 5,200

= $41,200

Then the liabilities:

= 2,200 + 16,000

= $18,200

Retained earnings:

= Assets - Liabilities - Net income - Common stock

= 41,200 - 18,200 - 6,000 - 12,000

= $5,000

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The new graphs would make it more difficult to estimate the price of a book.

To do this, we simply combine the frequencies on Felix and Tyler's table.

When this is done, we have the following dataset

3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99

Next, we create the box & whisker plot and the histogram using the new dataset

(see attachment for the graphs)

The new graphs would make it more difficult to estimate the price of a book.

This is so because the dataset used to create the graphs do not come from the same source

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Answer:

2. (3+4) should be (3*4)

3. x is also x^1, so it should be x^(6+3+1)

4. you have to do 3^4 and 2^3 before timing them together

Answer:

198 [m²].

Step-by-step explanation:

1) required area can be calculated as four area of the triangle PQT:

A=4*A(ΔPQT);

2) A(ΔPQT)=0.5*PT*QT, then

3) A=4*0.5*PT*QT; ⇔

A=2*PT*QT; ⇒

4) finally,

A=2*11*9=198 [m²].

The area of the rhombus PQRS is 198 m².

A rhombus is a quadrilateral with four vertices, four sides and four angles with all four sides are equal. It has basically a diamond shape. Rhombus will become square if all the angles of the rhombus equals 90°.

Given that, PT = 11 m and QT = 9 m.

We know that diagonals of a rhombus are perpendicular bisectors.

Therefore, RT = 11 m and ST = 9 m.

Area of a rhombus can be found using diagonals as,

Area = [tex]\frac{1}{2}[/tex] × D₁ × D₂

where D₁ and D₂ are the length of two diagonals of the rhombus.

D₁ = PT + RT = 11 + 11 = 22 m

D₂ = QT + ST = 9 + 9 = 18 m

Area = [tex]\frac{1}{2}[/tex] × 22 × 18

        = 22 × 9

        = 198 m²

Hence the area of the rhombus given is 198 m².

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The perimeter of the triangle is 30 units

The vertices are (−7,−1), (5,−1), and (5,4).

Start by calculating the distance between the vertices using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2[/tex]

d1 = 12

[tex]d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2[/tex]

d2 =5

[tex]d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2[/tex]

d3 = 13

The perimeter is then calculated as:

P = d1 + d2 + d3

This gives

P = 12 + 5 + 13

Evaluate

P = 30

Hence, the perimeter of the triangle is 30 units

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Answer:

The answer is D. 7x-8

Step-by-step explanation:

We can solve this problem by finding the area of the rectangle, which is equal to the length times the width. In this case, the length is 2x-3 feet and the width is 5 feet. Therefore, the area of the rectangle is (2x-3)(5), or 7x-8.

Rhe polynomial is P(x) = x³ -2x² + 9x - 18 if the zeros are 2 and 3i and a lead coefficient of 1

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have:

The zeros of a polynomial are 2 and 3i and a lead coefficient of 1.

As we know, zeros of a polynomial are occurs in pairs

So the zeros are 2,3i,-3i

The factor form of a polynomial:

P(x) = (x- 2)(x - 3i)(x + 3i)

[tex]\rm P(x) =\left(x-2\right)\left(x^2+\left(-3\right)^2\right)[/tex]

[tex]\rm P(x) =\left(x-2\right)\left(x^2+9\right)[/tex]

[tex]\rm P(x) =x^3+9x-2x^2-18[/tex]

Thus, the polynomial is P(x) = x³ -2x² + 9x - 18 if the zeros are 2 and 3i and a lead coefficient of 1

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Answer:

20percent

Step-by-step explanation:

First we will find the value of k.

Given

White + Black + Blue + Red = Total

8k+30+(30-2k)+k+5 = 100

8k+30+30-2k+k+5=100

7k+65=100

7k+65-65=100-65

7k=35

k = 35/7 = 5

Now given number of blue cell phone sold is 30-2k = 30 - 2(5) = 30 - 10 = 20,

Percentage of Blue cell phones = [tex]\frac{Blue}{Total} *100\\=\frac{20}{100} *100\\=20%[/tex]percent

The dot plot that represents the library book data is shown in the image below.

To construct a dot plot, each data point is represented as a dot. The number of dots one data point has represents the frequency at which that data point occurs in the data set.

The data set given in the table will have the following data points and frequencies:

1: 1

2: 3

3: 4

4: 4

5: 4

6: 0

7: 2

8: 2

The dot plot for the data is shown in the image below.

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Part 1

Each floor is [tex](28)(56)=1568[/tex] square feet. Since there are 2 floors, the total square footage is [tex]2(1568)=3136[/tex] square feet.

Part 2

[tex](3136)(93)=\$291648[/tex]

Answer:

$30.60

Step-by-step explanation:

So when a problem says some price is x% off, it means the current price is now (100-x)% of the original value. So if the shirt is 15% off, the current price is 85% the original value. To find 85% of a number you simple convert the percentage into a decimal, by dividing it by 100 and multiply that decimal by the value. So in this case 85/100 = 0.85. And then 0.85 * 45 = 38.25. Now that it reduces its price by 20%, it's 80% the original value. 38.25 * 0.8 = 30.60.