Gia made a garden stone shaped like a regular octagon with the dimensions shown. Find the area of the octagon.
5.5 in.
4.6 in

The solution of the expression is 964.

To start solving this problem, let's find the sum of -29 and 303. The sum of two numbers is the result when you add them together. So,

-29 + 303 = 274

The sum of -29 and 303 is 274.

Now, let's find the sum of -52 and -638. To add two negative numbers, you just add their absolute values and put a negative sign in front of the result. So,

-52 + (-638) = -690

The sum of -52 and -638 is -690.

Finally, the problem asks us to subtract the sum of -52 and -638 from the sum of -29 and 303. To subtract one sum from another, we just subtract the second sum from the first. So,

( -29 + 303 ) - ( -52 + -638 )

We can simplify the expression by rearranging the terms:

274 - (-690)

When we subtract a negative number, it's the same as adding its absolute value. So,

274 + 690 = 964

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Step-by-step explanation:

Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3

The profit (p) is $7500 generated by selling 1500 units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x²

To maximize our profit, we must locate the vertex of the parabola represented by this function. The x-value of the vertex indicates the number of units that must be sold to maximize profit.

We may use the formula for the x-coordinate of a parabola's vertex:

x = -b/2a

where a and b represent the coefficients of the quadratic function ax² + bx + c. In this situation, a = -0.004 and b = 12, resulting in:

x = -12 / 2(-0.004) = 1500

This indicates that when 1,500 units are sold, the profit is maximized.

To calculate the greatest profit, enter x = 1500 into the profit function:

P(1500) = -1500 + 12(1500) - 0.004(1500)^2

P(1500) = -1500 + 18000 - 9000

P(1500) = $7500

Therefore, the maximum possible profit is $7,500 and it is generated when 1,500 units are sold.

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To achieve this maximum profit, exactly 1500 units must be sold.

To find the maximum profit and the number of units needed to generate it, we can use the given profit function p(x) = -1500 + 12x - 0.004x^2. We need to find the vertex of the parabola represented by this quadratic function, as the vertex will give us the maximum profit and the corresponding number of units.

Step 1: Identify the coefficients a, b, and c in the quadratic function.
In p(x) = -1500 + 12x - 0.004x^2, the coefficients are:
a = -0.004
b = 12
c = -1500

Step 2: Find the x-coordinate of the vertex using the formula x = -b / (2a).
x = -12 / (2 * -0.004) = -12 / -0.008 = 1500

Step 3: Find the maximum profit by substituting the x-coordinate into the profit function p(x).
p(1500) = -1500 + 12 * 1500 - 0.004 * 1500^2
p(1500) = -1500 + 18000 - 0.004 * 2250000
p(1500) = -1500 + 18000 - 9000
p(1500) = 7500

So, the maximum profit is $7,500, and 1,500 units must be sold to generate it.

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The game owner should charge option (a) $0.55 to make it a fair game

To determine how much the game owner should charge to make it a fair game, we need to calculate the average value of each package. We can do this by finding the total value of all the packages and dividing it by the total number of packages.

The total value of the 30 packages worth $.65 each is:

30 x $.65 = $19.50

The total value of the 10 packages worth $.60 each is:

10 x $.60 = $6.00

The total value of the 15 packages worth $.30 each is:

15 x $.30 = $4.50

The total value of all the packages is

$19.50 + $6.00 + $4.50 = $30.00

The total number of packages is

30 + 10 + 15 = 55

The average value of each package is

$30.00 / 55 = $0.55

Therefore, the correct option is (a) $0.55

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Answer:

(z - 1) (z + 19)

Step-by-step explanation:

z² + 18z - 19

Consider the form x² + bx + c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is −19 and whose sum is 18.

-1, 19

Write the factored form using these integers.

(z - 1) (z + 19)

The output value of f(-6) in the given function f(x) = 2x² + 5x - x/3 is 44.

A function is simply a relationship that maps one input to one output.

Given the function in the question;

f(x) = 2x² + 5x - x/3

f( -6 ) = ?

To find f(-6), we need to substitute -6 for x in the function f(x) and simplify:

f(x) = 2x² + 5x - x/3

Plug in f = -6

[Replace x with -6]

f(-6) = 2(-6)² + 5(-6) - (-6)/3

Simplify using order of operations

f(-6) = 2(36) - 30 + 2

f(-6) = 72 - 30 + 2

f(-6) = 72 - 28

f(-6) = 44

Therefore, the output value of f(-6) is 44.

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The  closest possible  choice is 198.06 ft².

Option C is correct.

The area of the base is gotten as :

length x width = 8 ft x 7 ft = 56 ft².

The length of the pyramid's slant height (s) must be determined in order to determine the area of each triangle face.

We may determine that s = (h2 + (w/2)2) = (62 + (7/2)2) = (36 + 24.5) = 60.5 7.78 ft using the Pythagorean theorem.

The area of each triangular face is

(1/2) x base x height = (1/2) x 8 ft x 7.78 ft

= 31.12 ft².

Hence, the total surface area of the pyramid :

56 ft² + 4 x 31.12 ft² = 192.48 ft².

In conclusion, the closest possible  choice is 198.06 ft².

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Answer:

Total=$90

Used=$40

Left=($90-$40)=$50

1 carton = $4.49

$50÷$4.49

=11.135857 ≈ $11 10¢

Answer:

Step-by-step explanation:

Answer:

3(n + 6) = 2(n + 6) + (n + 6)

3(n + 6) = 3n + 18

The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.

what is deposit ?

In the context of finance, a "deposit" refers to the act of placing money or funds into a bank account, investment account, or other financial account. A deposit can also refer to the initial payment made to secure or initiate a purchase

In the given question,

To calculate the sinking fund payment that Mary needs to make at the end of each quarter, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)ⁿᵇ - 1]/(r/n)

Where:

FV = future value (the amount Mary needs to accumulate, which is $9,000 in this case)

PMT = payment per period (what Mary needs to find)

r = annual interest rate (4% in this case)

n = number of compounding periods per year (4, since interest is compounded quarterly)

t = number of years (9 in this case)

Substituting these values into the formula, we get:

$9,000 = PMT x [(1 + 0.04/4)³⁶ - 1]/(0.04/4)

Simplifying and solving for PMT, we get:

PMT = $9,000 / [(1.01³⁶ - 1)/0.01]

PMT = $9,000 / 31.8422

PMT = $282.44 (rounded to the nearest cent)

Therefore, Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.

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The horizontal distance traveled by the rubber band is 4.5 feet

To write and solve an equation to find the horizontal distance traveled by the rubber band if its height is 0.75 feet, substitute f(x) = 0.75 feet into the equation representing the rubber band and solve for x. That is:

f(x) = -x² + 4x + 3

0.75 = -x² + 4x + 3

x² - 4x - 3 + 0.75 = 0

x² - 4x - 2.25 = 0

(x - 9/2)(x + 1/2) = 0       (factorize)

x = 9/2 or x = -1/2

x = 4.5 or x = -0.5

Since distance cannot be negative.

Thus, x = 4.5 feet

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The correct answer to the fraction expression is: 2²/₂₁

There are different types of fractions such as:

Proper fractions

Improper Fractions

Mixed Fractions

We are given the fraction expression:

²/₃ + 3⁴/₇ ÷ 2¹/₂

Let us convert all to proper or improper fraction to get:

²/₃ + ²⁵/₇ ÷ ⁵/₂

Using PEMDAS order of operations, we will carry out division first to get:

²/₃ + (²⁵/₇ ÷ ⁵/₂)

When dividing fractions, the divisor changes numerator and denominaor and the sign becomes multiplication:

= ²/₃ + (²⁵/₇ * ²/₅)

= ²/₃ + ¹⁰/₇

Using L.C.M, we have:

= (28 + 60)/42

= 88/42 = 44/21

= 2²/₂₁

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Answer:About 1,012 Inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find which number is closest to zero, we must find the number with the lowest absolute value. Luckily to our advantage, all of these numbers have the same denominators, so the number with the lowest numerator is closest to zero.

Out of these numbers, 1/5 is the closest to zero.

The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.

In the triangle HIJ,

The measure of angle J is equal to 90 degrees.

This implies ,

HI is the hypotenuse.

JH is the opposite side to angle I.

In triangle HIJ,

Using trigonometric ratio we get,

sin ∠I = Opposite side / Hypotenuse

Substitute the values we have,

⇒ sin ∠I = 4.8 / 6.7

⇒ sin ∠I = 0.72

Now , take sin⁻¹ both the side of the equation we get,

⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )

Here sin⁻¹(sin ∠I) = ∠I

⇒∠I = sin⁻¹( 0.72 )

⇒∠I = 46.05 degrees

Therefore, the measure of angle I is equal to 46.05 degrees.

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Answer:

i guess 97 %

Step-by-step explanation: see fist of all

most colour pencils ARE made of wood so yeah sorry dont know im still in 6th

Answer: The given inequality is:

y < c + 5

We can rewrite this inequality in slope-intercept form, y = mx + b, by isolating y:

y < c + 5

y - 5 < c

c > y - 5

In slope-intercept form, this is:

y = 1x + (-5)

The y-intercept of this boundary line is -5.

Step-by-step explanation:

If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.

As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.

However, the formula for calculating the variance is:

Variance = (sum of the squared differences from the mean) / (number of observations)

The first error Cara may have made is in calculating the sum of the squared differences from the mean.

The correct steps to find the variance are:

Find the mean:

Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78

Calculate the differences from the mean for each observation:

87 - 78 = 9

46 - 78 = -32

90 - 78 = 12

78 - 78 = 0

89 - 78 = 11

Square each difference:

[tex]9^2 = 81[/tex]

[tex](-32)^2 = 1024[/tex]

[tex]12^2 = 144[/tex]

[tex]0^2 = 0[/tex]

[tex]11^2 = 121[/tex]

Find the sum of the squared differences:

81 + 1024 + 144 + 0 + 121 = 1370

Divide the sum of squared differences by the number of observations:

Variance = 1370 / 5 = 274.

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Answer:

y=-1/12x+61/12

Step-by-step explanation:

y=-1/12x+61/12

The value of x after executing the last statement is still 10.

After executing the last statement, the value of x is still 10. The snippet of code declares an integer variable x and a pointer variable y that points to the address of x. Then, y is incremented by 1 (which means it now points to the next memory location after x). Finally, the value 100 is assigned to the memory location pointed to by y, which is actually beyond the memory allocated for variable x. This can lead to unexpected behavior, but since the value of x is never modified directly, its value remains unchanged at 10.

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The margin of error for the 95% confidence level is approximately $873.15.

To calculate the error bars for the 95% confidence level, we need to find the critical value of the z-score from the standard normal distribution table.

Accepting a 95% certainty level, the importance level (α) is 0.05, which implies the certainty level is 1-α = 0.95.

On the off chance that we see the z-score at the 95% certainty level on the standard typical conveyance table, we get an esteem of 1.96.

 Then you can use the formula for Tolerance (E).

error bar (E) = z * (standard deviation / sqrt(n))

where:

z = critical value in the standard normal distribution table

standard deviation = $3,000

n=40

Substitute the obtained value.

Error Bar (E) = 1.96 * ($3,000 / sqrt(40))

≈ $873.15

Therefore, the margin of error for the 95% confidence level is approximately $873.15.

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The theoretical probability of the spinner not landing on red is 0.875.

The total number of sections on the spinner is 8, out of which only one section is red. Therefore, the probability of the spinner landing on red is:

P(Red) = 1/8

The probability of the spinner not landing on red would be the probability of landing on any other section, which is:

P(Not Red) = 1 - P(Red) = 1 - 1/8 = 7/8

Therefore, the theoretical probability of the spinner not landing on red is 7/8 or 0.875 in decimal form.

So, the correct answer is: 0.875.

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Answer:

D

Step-by-step explanation:

The area of the rugs in square yards with given dimensions 1/2 yard by 2 5/6 yards is equal to  1 5 /12 square yards.

Dimensions of the rug are,

1/2 yard by 2 5/6 yards

Area of the rug in square yards solved by Keith is equal to

=  1/2 times 2 5/6

= ( 1/ 2 ) × (  2 5/6 )

Convert mixed fraction into proper fraction we get,

2 5/6 = ( 6 × 2 + 5 ) / 6

⇒ 2 5/6 = 17 / 6

⇒ Area of the rug in square yards solved by Keith = ( 1 / 2 ) × ( 17 / 6 )

⇒ Area of the rug in square yards solved by Keith = ( 17 / 12 )

⇒ Area of the rug in square yards solved by Keith = 1 5 /12 square yards.

Therefore, the area of the rugs is equal to 1 5 /12 square yards.

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The rate of change of the area is 20π square inches per second.

The area of the shaded region can be calculated as the difference between the areas of the outer circle and the inner circle:

A = πr^2 - πr'^2

where r is the radius of the outer circle, r' is the radius of the inner circle, and π is the constant pi.

To find the rate of change of the area, we can take the derivative of both sides of the equation with respect to time t:

dA/dt = d/dt (πr^2) - d/dt (πr'^2)

Using the chain rule, we can express the derivatives in terms of the rates of change of the radii:

dA/dt = 2πr (dr/dt) - 2πr' (dr'/dt)

Substituting the given values at the instant when r=4 inches and r'=3 inches, we have:

dA/dt = 2π(4)(2) - 2π(3)(-1) = 20π

Therefore, the rate of change of the area is 20π square inches per second.

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The total number of probability options will be 8 options.

1. Red plain and Red striped.

2. Blue plain and Blue striped.

3. Yellow plain and Yellow striped.

4. Green plain and Green striped.

5. Red plain and Blue striped.

6. Blue plain and Yellow striped.

7. Yellow plain and Green striped.

8. Green plain and Red striped.

There are 8 socks in the basket, and you can choose 1 plain sock and 1 striped sock.

This means that there are 8 possible combinations of socks you could choose.

Count the number of socks in the basket. There are 8 total socks (4 plain and 4 striped).

The number of options: There are 8 possible combinations of socks you could choose, so you have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.

Therefore,

You have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.

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Answer:

50 meters/21.91 seconds = 2.282 m/sec