Apply the Laws of Exponents to write an equivalent expression for the given expression.
(-9-4)7
(-9-4)² =
(Simplify your answer. Type your answer using exponential notation.)

Answer:

116 / 45

Step-by-step explanation:

To add fractions with unlike denominators, we need to find their common denominator.

One way to do this is by finding the least common multiple (LCM) of the denominators.

The LCM of 3, 5, 9 and 15 is 45.

We then convert each fraction so that its denominator is 45:

1/3 = 15/45

3/5 = 27/45

7/9 = 35/45

13/15 = 39/45

Now we can add the fractions:

15/45 + 27/45 + 35/45 + 39/45

To simplify, we can add the numerators and keep the common denominator:

(15 + 27 + 35 + 39) / 45

Which gives us:

116 / 45

Therefore, the sum of the fractions 1/3 + 3/5 + 7/9 + 13/15 is, 116 / 45.

Answer:

x = 9

Step-by-step explanation:

To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:

Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:

2x + 3x - 4x = 2 + 7

Simplifying the left side: x = 9

Simplify the right side of the equation:

x = 9

Therefore, the solution to the equation is x = 9.

Step-by-step explanation:

This is a geometric series where our common ratio is -1/2, and a is -4

Since r is less than -1, this series converges so

The sun is

\( \frac{ - 4}{1 + 0.5} \)

\( \frac{ - 4}{1.5} = - \frac{8}{3} \)

The sum is -8)3

Answer:

62 in

Step-by-step explanation:

5 x 2 = 10

5 x 3 = 15

2 x 3 = 6

2 x 3 = 6

2 x 5 = 10

3 x 5 = 15

Answer:

x= 5 , y = 34

Step-by-step explanation:

8x-6=5x+9

3x-6=9

3x=15

x=5

-

8(x5) - 6 =

34

25(x5) +9 =

34

Answer:

x = 5 and y = 34

Step-by-step explanation:

I used substitution method and did this ;

8x - 6 = 5x + 9 .....put like terms together

8x - 5x = 9 + 6

3x = 15

x = 5

y = 8 (5) - 6

y = 40 - 6

y = 34

Answer:

14

Step-by-step explanation:

hi! so the question is asking what h is when you input -18 for x, right?

inputing in this question means to substitute, meaning that in this equation, -18 will take the place of x!

now let's do the math :)

we can change that to --> h = 17 - 3

h = 14

let me know if you're still confused!

yuh the answers: a, d, d, for anyone who didnt understand

Answer:

A.D.D

Step-by-step explanation:

On Edge 2022

HOPED THIS HELPED YOU OUT

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

Step-by-step explanation:

To estimate the original volume of the pyramid in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.

The formula for the volume of a frustum of a pyramid is:

V = (1/3) * h * (A + sqrt(A * B) + B)

Where:

V = Volume of the frustum

h = Height of the frustum (vertical distance between the top and bottom)

A = Area of the top base

B = Area of the bottom base

Given the dimensions provided, we can calculate the areas of the bases:

Area of the top base (A) = 4 m * 4 m = 16 m²

Area of the bottom base (B) = 20 m * 20 m = 400 m²

The height of the frustum (h) is given as 12 m.

Now we can plug these values into the formula:

V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)

Calculating the square root and simplifying:

V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)

V = (1/3) * 12 m * (436 m²)

V = 1744 m³

Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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Answer:

Hope This Helps

Step-by-step explanation:

S=450 + 30W

Plugging 14 into W, we get:  S= 450 +30(14)= $870.

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Using the basic rational function, f(x) = 1/x, a rational inverse function with the given transformations is:

h(x) = g(x) + k = (1/2) / (x - h) + k

From the question, we are to create a rational inverse function that the given transformations

Let's start with a basic rational function:

f(x) = 1/x

To obtain a vertical compression of factor a, we need to multiply the function by a constant less than 1. Let's choose a = 1/2:

g(x) = (1/2) f(x) = (1/2) / x

To shift the function horizontally to the right by h units, we need to replace x with x - h:

g(x) = (1/2) / (x - h)

Finally, to shift the function vertically up by k units, we need to add k to the whole function:

h(x) = g(x) + k = (1/2) / (x - h) + k

Hence, a rational inverse function with the given transformations is:

h(x) = g(x) + k = (1/2) / (x - h) + k

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1. About 144 scoops of ice cream were served last Thursday.

2.Doris has 5 quarters, 10 dimes, and 5 nickels, and 4 pennies.

1. There are 16 ounces in a pound, so 18 pounds of ice cream weigh:

18 pounds * 16 ounces/pound = 288 ounces

Since one scoop of ice cream weighs 2 ounces, the number of scoops served is:

288 ounces / 2 ounces/scoop = 144 scoops

Therefore, about 144 scoops of ice cream were served last Thursday.

2. Let's use "q", "d", "n", and "p" to represent the number of quarters, dimes, nickels, and pennies that Doris has, respectively.

From the problem statement, we know that:

n = q (the number of nickels equals the number of quarters)

d = 2q (the number of dimes is twice the number of quarters)

n = 5 (she has 5 nickels)

We can use this information to write an equation for the total value of Doris's coins:

0.25q + 0.10d + 0.05n + 0.01p = 2.54

Substituting the values for n and d in terms of q, we get:

0.25q + 0.10(2q) + 0.05(5) + 0.01p = 2.54

Simplifying and solving for q, we get:

0.45q + 0.05 + 0.01p = 2.54

0.45q + 0.01p = 2.49

45q + p = 249

Since Doris has a total of 24 coins, we can write another equation:

q + d + n + p = 24

Substituting the values for n and d in terms of q, we get:

q + 2q + q + p = 24

4q + p = 24

We now have two equations with two unknowns:

45q + p = 249

4q + p = 24

Subtracting the second equation from the first, we get:

41q = 225

Solving for q, we get:

q = 225/41 ≈ 5.49

Since q must be a whole number, the closest integer value is 5. Substituting this value back into the equations for n and d, we get:

n = q = 5

d = 2q = 10

Finally, we can use the equation for the total number of coins to find the value of p:

q + d + n + p = 24

5 + 10 + 5 + p = 24

p = 4

Therefore, Doris has 5 quarters, 10 dimes, and 5 nickels, and 4 pennies.

Quarters are a type of coin used in the United States currency system. A quarter is worth 25 cents or 1/4 of a dollar. It has a diameter of 0.955 inches (24.26 mm) and a thickness of 0.069 inches (1.75 mm). The front side of the coin features a portrait of George Washington, the first president of the United States, and the back side features an eagle. Quarters are commonly used in daily transactions to make small purchases or provide change.

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Answer:

72

Step-by-step explanation:

circumference = 20

arc = 4

4/20 =1/5

a circle = 360°

1/5 * 360 = 72

The first step would take to solve the equation 1 1/2x 2 1/3 is to convert the mixed fraction to improper fraction

Fractions are defined as the expressions that involves the part of a whole number or the part of a variable.

There are different types of fractions in mathematics. These fractions are namely;

Also, in converting mixed fractions to improper fractions, we have to multiply the denominator of the fraction by the whole number, then, add the value of the product to the numerator.

We have that;

1 1/2x 2 1/3

convert to improper fractions

3/2 × 7/3

Multiply

7/2

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Answer:

it would be around 3 i think

Step-by-step explanation:

Answer:

12j + 6

Step-by-step explanation:

You have to multiplied this polynomial expression in order to expand it:

2(6j + 3)

12j + 6

Answer:

12j + 6

a(b+c) = ab + bc

2(6j+3)

2*6 = 12

12j

2*3 = 6

12j + 6

Answer:

The 80% confidence interval for the average net change in a student's score after completing the course is (15.4, 26.3).

Step-by-step explanation:

The net change in 7 students' scores on the exam after completing the course are:

S = {37 ,12 ,12 ,17 ,13 ,32 ,23}

Compute the sample mean and sample standard deviation as follows:

\(\bar x=\frac{1}{n}\sum x=\frac{1}{7}\times 146=20.857\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}}=\sqrt{\frac{1}{7}\times 622.8571}=10.189\)

As the population standard deviation is not known, a t-interval will be formed.

Compute the critical value of t for 80% confidence interval and 6 degrees of freedom as follows:

\(t_{\alpha/2, (n-1)}=t_{0.20/2, (7-1)}=t_{0.10,6}=1.415\)

*Use a t-table.

Compute the 80% confidence interval for the average net change in a student's score after completing the course as follows:

\(CI=\bar x\pm t_{\alpha/2, (n-1)}\times\frac{s}{\sqrt{n}}\)

     \(=20.857\pm 1.415\times\frac{10.189}{\sqrt{7}}\\\\ =20.857\pm 5.4493\\\\=(15.4077, 26.3063)\\\\\approx (15.4,26.3)\)

Thus, the 80% confidence interval for the average net change in a student's score after completing the course is (15.4, 26.3).

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Answer:

Step-by-step explanation:

A x + y = 5  1 + -4 = -3  Nope

B.X + y = 5  1 + -4 = -3  Nope  same as A unless X is somehow not equal to x,

C. xy = 5      1(-4) = -4    Nope and does not even qualify as a line.

D. x - y = .5​  1 - (-4) = 5 Nope unless you have a typo adding an unwanted decimal point

1. Drawn a straight line AB =7 cm with the help of ruler.

2. With the help of compass drawn an arc from A and at the point where it cuts AB from that point made another arc drawn an arc cutting the previous arc.

3. From A drawn a straight line joining the arc and extend it to M.

4. With the help of ruler measured 5 cm and mark it as AC.

5. Joined BC and we get the required triangle.

6. From C drawn an arc and make it cut on AC and BC and from the point it cuts AC and BC drawn arc cutting each other and extend a line from point C extend a line to the point point of intersection of two arc.

7. Similarly we do for A and the point where the two line intersect denoted as O.

8. Made a perpendicular from O on AB this perpendicular will be radius and taking O as centre we draw a circle this is our incircle.

9. And AN is our locus of points equidistant from two lines AB and AC.

We need to construct a circle inscribed in triangle that is incircle it can be done by making angle bisector of two sides the point where it intersect will be incentre. The centre of required circle.

The angle bisector is the locus where points are equidistant from two sides.

Answer:

Step-by-step explanation:

2(3x-1)+2(6)

6x-2+12

6x+10

Answer:

6x + 10mm

Step-by-step explanation:

first lets put all the sides into an equation

6mm + 6mm + (3x - 1mm) + (3x - 1mm)

then we simplify it

12mm + 6x -2mm

10mm + 6x

hope this helps <3

The volume of the cylindrical water cooler is 211.38 gallons. Therefore, option C is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall.

Now, radius = 3/2 =1.5 feet

We know that, the formula to find the volume of a cylinder is πr²h.

Here, 3.14×1.5²×4

= 28.26 cubic feet

In gallons = 28.26×7.48

= 211.38 gallons

Therefore, option C is the correct answer.

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The correct option is C, 211.38. Hope this helps :)

Answer and explanation:

1. Cost is response variable while file size is explanatory variable. Cost is response variable here because it is the dependent variable and the other is the independently variable that affects the dependent variable cost. The scatter plot will show how much cost increase with each change in file size. Scatter plot is in positive direction and strong

2. Time of delay of thunder is response variable while distance from lightning is explanatory variable. Time of delay is dependent variable while the other is independent variable which affects it. Scatter plot shows how much delay of thunder changes with change in distance from lightning. Positive scatter plot and strong

3. Your distance from it is explanatory variable while apparent brightness is response variable. Distance from it is independently variable while the the other is dependent variable. Scatter plot shows change of brightness with each change of distance. Negative direction as distance increase results in brightness decrease. It is strong.

4. weight of car is response variable while age of owner is explanatory variable. Weight of car is dependent variable while the other is independent variable. Scatter plot shows change of weight of car with change of age of owner. Positive direction as one increases the other increases. Strong

Answer:

a) 1/5

Step-by-step explanation:

There are 25 students total in the class.

If you look at the Venn Diagram, you can see that only 5 people have only "Fb" accounts.

Therefore, the probability that the person has a “Fb” account but not a “Snap” account is 5/25 or 1/5.

Answer:

94

Step-by-step explanation: