Area of a triangle with base, b, and height, h:
A = 1/2 bh = 1/(____)(____) =
Area of a rectangle with length, e, and width, w:
A = lw= (______)(______) = .
square feet
Area of base of prism
=
square feet
+
square feet

Step-by-step explanation:

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

Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.

1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).

Step 1: Set up the equation using the given information.

One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:

Reciprocal of the original number + 1 = $\frac{7}{3}$

Step 2: Solve for the reciprocal of the original number.

Reciprocal of the original number = $\frac{7}{3}$ - 1

Step 3: Simplify the equation.

Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$

Reciprocal of the original number = $\frac{4}{3}$

Step 4: Find the original number.

Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:

Original number = $\frac{1}{(\frac{4}{3})}$

Step 5: Simplify the expression.

Original number = $\frac{1}{1} \times \frac{3}{4}$

Original number = $\frac{3}{4}$

The original number expressed as a common fraction is $\frac{3}{4}$.

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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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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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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:

y=-1/12x+61/12

Step-by-step explanation:

y=-1/12x+61/12

Answer: 64 sqaure centimetres.

Step-by-step explanation:

- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.

Top and Bottom

4 x 4 = 16

16 x 2 = 32

Both faces are the same so once we find the area of one, we can just double it.

North, South, East and West Side

4 x 2 = 8

8 x 4 = 32

All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.

To find the overall surface area add all the areas you have.

32 + 32 = 64

or

16 +_16 + 8 + 8 + 8 + 8 = 64

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 probability that a student who did not complete the homework passed the test is 0.25.

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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Answer:

Step-by-step explanation:

Answer:

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

3(n + 6) = 3n + 18

Answer:

50 meters/21.91 seconds = 2.282 m/sec

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 score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.

Let us consider the score that Tim needs to get on his fourth quiz be x.

Score he needs to get in order to have a mean quiz score of 90,

Set up an equation using the formula for the mean ,

(mean score) = (sum of scores) / (number of scores)

If Tim wants his mean quiz score to be 90, then we have,

⇒ 90 = (86 + 92 + 94 + x) / 4

Multiplying both sides by 4, we get,

⇒360 = 86 + 92 + 94 + x

Simplifying this equation, we get,

⇒ x = 360 - 272

⇒ x = 88

Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.

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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:

Total=$90

Used=$40

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

1 carton = $4.49

$50÷$4.49

=11.135857 ≈ $11 10¢

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 you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.

Explain month

A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.

According to the given information

If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:

$2299.99 * (1 + 0.020825)²⁴ = $3,637.16

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Answer: y=1/2x-3

Step-by-step explanation:

I'm assuming you're trying to find it in slope intercept form!

y=mx+b

y=1/2x-3

easy

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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Answer:About 1,012 Inches

Step-by-step explanation:

Duri can make 72 cupcakes on his own and Habib can make 36 cupcakes on her own, assuming they have enough of all the other ingredients.

To determine how many cupcakes each person can make on their own, we need to check if they have enough of all the other ingredients required to make 12 cupcakes.

Terrance has 1 cup of flour and 6 eggs, which is not enough to make 12 cupcakes.

Duri has 12 cups of flour and 1000 grams of butter, which is more than enough to make 12 cupcakes. However, the recipe requires 3/4 cup of sugar, 2 eggs, and 3/4 cup of milk, which we do not know if Duri has enough of.

Habib has 3 cups of milk and 6 cups of sugar, which is enough to make 12 cupcakes.

Anika has 1 cup of sugar and 4 cups of milk, which is not enough to make 12 cupcakes.

Therefore, only Duri and Habib have enough ingredients to make 12 cupcakes on their own.

To determine how many cupcakes they can make, we need to calculate how much of each ingredient is required for one cupcake and then divide the available ingredients by that amount.

For one cupcake, we need:

1/6 cups of flour

1/16 cup of sugar

1/6 eggs

1/16 cups of milk

125/12 grams of butter

Duri has 12 cups of flour and 1000 grams of butter, which is enough to make 72 cupcakes. Habib has 6 cups of sugar and 3 cups of milk, which is enough to make 36 cupcakes.

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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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Answer:

f(x + 1) + 2

Step-by-step explanation:

All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.

P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.

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:

(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)