Using the distributive property, Marta multiplied the binomial (2x 3) by the trinomial (x2 x – 2) and got the expression below. (2x)(x2) (2x)(x) (2x)(–2) (3)(x2) (3)(x) (3)(–2) Which is the simplified product?.

Given the sales tax rate of 6.25% and the total cost of the items purchased at Walmart as $35.02, we can calculate the total cost including tax. To do this, we first need to find the tax amount on the purchase.

Tax amount = (Tax rate * Total cost of items) / 100
Tax amount = (6.25 * $35.02) / 100
Tax amount = $2.18875

Now, round the tax amount to the nearest cent:
Tax Amount ≈ $2.19

Next, add the tax amount to the total cost of the items to find the total cost including tax:
Total cost including tax = Total cost of items + Tax amount
Total cost including tax = $35.02 + $2.19
Total cost including tax ≈ $37.21

So, the total cost of the items purchased at Walmart, including the 6.25% sales tax, is approximately $37.21.

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Answer:

133.3m³

Step-by-step explanation:

Volume of pyramid=lwh/3

=10×8×5/3

=400/3

=133.3m³

Hopefully this helped :D

To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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The future value of the annuity is $11,200. $30,000 was invested, and the interest earned is -$18,800.

To find the future value of an annuity using the simple interest formula, we can use the following formula:

FV = P × (1 + r × n)

where:

FV is the future value of the annuity,

P is the annual payment,

r is the annual interest rate, and

n is the number of years.

In this case, the annual payment (P) is $10,000, the annual interest rate (r) is 4%, and the number of years (n) is 3. Let's calculate the future value.

FV = $10,000 × (1 + 0.04 × 3)

FV = $10,000 × (1 + 0.12)

FV = $10,000 × 1.12

FV = $11,200

Therefore, the future value of the annuity is $11,200.

To determine the amount invested, we need to multiply the annual payment by the number of years.

Amount Invested = P × n

Amount Invested = $10,000 × 3

Amount Invested = $30,000

So, $30,000 was invested.

To calculate the interest earned, we subtract the amount invested from the future value.

Interest Earned = FV - Amount Invested

Interest Earned = $11,200 - $30,000

Interest Earned = -$18,800

The negative value indicates that the annuity has not earned interest but has incurred a loss. However, it's worth noting that the simple interest formula assumes that the interest earned is proportional to the initial investment and does not account for compounding. If you're looking for a more accurate calculation of interest earned, it's advisable to use a compound interest formula.

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To find the coordinates of the centroid for the region bounded by the curves y=16x, y=9/x, y=0, and x=10, we need to calculate the x-coordinate and y-coordinate of the centroid separately. First, let's find the x-coordinate of the centroid.

We can use the formula: x-bar = (1/A) ∫[a,b] xf(x) dx, where A is the area of the region. The intersection points of the curves y=16x and y=9/x can be found by setting the equations equal to each other: 16x=9/x.

Solving this equation, we get x=±√(9/16)=±3/4. Since the region is bounded by x=10, we take the positive value x=3/4. To find the area A, we integrate the difference between the curves: A=∫[3/4,10] (16x-9/x) dx. Evaluating this integral, we find A=400-9ln(10).

Now we can calculate the x-coordinate of the centroid: x-bar=(1/A) ∫[3/4,10] x(16x-9/x) dx. Simplifying the integral and evaluating it, we get x-bar=(8160-36ln(10))/(400-9ln(10)). Next, let's find the y-coordinate of the centroid.

Since the region is symmetric about the x-axis, the y-coordinate of the centroid will be y-bar=0. Therefore, the exact coordinates of the centroid for the given region are: (x-bar, y-bar)=((8160-36ln(10))/(400-9ln(10)), 0).

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The area and perimeter of the composite figure are 576 square centimeters and 24 · (π + 2) centimeters.

In this problem we have the representation of a composite figure that is equivalent to a square with side length 24 centimeters, whose area is described by the following formula:

A = l²

Where:

If we know that l = 24 cm, then the area of the composite figure is:

A = (24 cm)²

A = 576 cm²

In addition, the perimeter (s), in centimeters, is found by the following expression:

s = 2π · R + 2 · l

Where R is the radius, in centimeters.

If we know that R = 12 cm and l = 24 cm, then the perimeter of the composite figure is:

s = 24π + 48 cm

s = 24 · (π + 2) cm

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Answer:

Step-by-step explanation:

Answer:6 times

Step-by-step explanation:12/7 divide 1/4

Answer:  6  times

Step-by-step explanation:  

Answer:

89.6994g

Step-by-step explanation:

M = DV

   = 11.34g/cm^3 * 7.91cm^3

   = 89.6994g

Hope this helps!

Answer:

Step-by-step explanation:

What's your problem?

Her change in account is x - 75 dollars.

She makes 3 withdrawals of $25.

Her change in account can be calculated as follows:

Therefore, let's find her change in her account,

Let us say she had x dollars in her account.

She withdraws 25 dollars on three occasions.

Therefore,

total withdrawer = 25 × 3

total withdrawer = 75 dollars

Therefore,

Her change in account = x - 75

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Answer:

Step-by-step explanation:

1. 25x3

2.75

$173.68 is the total amount Julio and Marisol still need to sell

Given that Julio and Marisol are selling magazines for a band fundraiser

Julio has sold $150.67 worth, and Marisol has sold $175.65.

We have to find  the total amount they still need to sell to reach the goal of

$500.00

To find the total amount Julio and Marisol still need to sell

we subtract the amount they have already sold from their goal of $500.00.

Total amount they still need to sell = $500.00 - ($150.67 + $175.65)

= $500.00 - $326.32

= $173.68

Therefore, the total amount Julio and Marisol still need to sell is $173.68.

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Answer:

I got 45

Step-by-step explanation:

so I did the triangle first I did 5 times 6 divided by 2 and got 15 then I did 5 times 6 and got 30 then I added the 30 and 15 together.

Answer:

Formula of trapezoid:

B1(base 1) + B2(base 2) x Height(h) x 1/2

Area of Trapezoid:

10(base 1) + 6(base 2) = 16

16 x 5 = 80

80 x 1/2 = 40

Answer:

THE ANSWER TO YOUR QUESTION IS B or 28/35 and 10/35

Step-by-step explanation:

we are going to focus on the 2/7 and the 10/35.

2 goes into 10 5 times. so 5 times 7 is 35. So that is true, the rule is what you do to the top you do to the bottom.

so basiclly 5 times 2 is 10 and 5 times 7 (from 2/7) is 35. so we then get 10/35.

now we will move onto the 25/35 and 4/5.

again 5 goes into 35 7 times. so 5 times 7 is 35. so we figured out how many times 5 goes into the denominator.

Now we have to figure out how many times 4 goes into 28. We got the four from the 4/5. so 28 divided by 4 is 7!!!

let me know if you dont get it im am always bord and eager to help others!!

THANKS FOR LETTING ME ANSWER!!

Answer:

160 in^3

Step-by-step explanation:

To find the volume, you do the base x height. If the base if 20 in^2 and the altitude is 8 in, then the volume is 20 * 8 in^3

20 * 8  = 160

The need to survey 26,304 freshmen to cut the margin of error in half.

a) To cut the stated margin of error in half, the sample size must be quadrupled.

The formula for the margin of error in a proportion is:

Margin of error = z* (sqrt(p*q/n))

where z is the z-score corresponding to the desired level of confidence, p is the proportion of interest (74% in this case), q = 1-p, and n is the sample size.

If we want to cut the margin of error in half, we need to solve the equation above for n, keeping all other variables constant.

Assuming a 95% confidence level and the proportions observed in the original study, we have:

Margin of error = 1.96 * sqrt(0.74 * 0.26/n)

If we want to cut the margin of error in half, we need to solve for n in the following equation:

1.96 * sqrt(0.74 * 0.26/n) = 1.96 * sqrt(0.74 * 0.26/4n)

Simplifying this equation, we get:

n = 16*1644=26,304

Therefore, we would need to survey 26,304 freshmen to cut the margin of error in half.

b) Yes, there are some concerns about this sample. Quadrupling the sample size will increase the precision of the estimate, but it may also increase the cost and the potential for nonresponse bias or other sources of error. Moreover, the original study was already stratified by type of college, which suggests that ACT, Inc. may be interested in analyzing the data at this level of disaggregation. In that case, a sample of 26,304 students may not be feasible or necessary. Finally, it's important to consider the representativeness of the sample and potential sources of bias, such as the sampling method, the response rate, or the exclusion of certain types of colleges or students.

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Answer: -10 or 9

Step-by-step explanation:

Let the number be x. Then,

\(x^2 +x=90\\\\x^2 +x-90=0\\\\(x+10)(x-9)=0\\\\x=-10, 9\)

The probability that the next card Scarlett selects will have an anglerfish on it is 2/15, or approximately 0.1333.

To find the probability of selecting an anglerfish on the next card, we need to calculate the ratio of the number of anglerfish cards to the total number of cards in the deck.

From the given information, Scarlett selected 2 anglerfish cards during her previous selections.

The total number of cards she selected is 2 + 3 + 1 + 4 + 5 = 15.

Therefore, the probability of selecting an anglerfish card on the next draw is 2/15.

Calculate the total number of cards Scarlett selected.

2 + 3 + 1 + 4 + 5 = 1

Calculate the number of anglerfish cards Scarlett selected.

Scarlett selected 2 anglerfish cards.

Calculate the probability of selecting an anglerfish card on the next draw.

Probability = Number of anglerfish cards / Total number of cards

Probability = 2 / 15

Probability ≈ 0.1333

Thus, the probability that the next card Scarlett selects will have an anglerfish on it is 2/15, or approximately 0.1333.

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The equation that can be used to determine the value of the car after 6 months is v(y) = 20,250(0.89)^6/12

Depreciation is the rate of decrease in value of an asset. When an asset depreciates, it declines in value with the passage of time.

The formula that can be used to represent depreciation is:

FV = P (1 + r)^n

v(y) = 20,250(1 - 0.11)^t

v(y) = 20,250(0.89)^6/12

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Answer: y=1/2x-3

Step-by-step explanation:

the y-intercept is negative so there's no need to put a plus sign.. feel free to let me know if im wrong

Answer:

You can regroup it 3 times and a remainder of 43. :) hope it helped!

Answer:

192.5 ft²

Step-by-step explanation:

Area of the shaded region (A) = Area of the major sector + Area of the triangle.

A = (πr²θ/360)+(r²sinα)/2............. Equation 1

From the diagram,

Given: r = 8.35 ft, α = 100°, θ = 360-100 = 260°

Substitute these values into equation 1

A = (3.14×8.35²×260/360)+(8.35²×sin100×1/2)

A = 158.16+34.33

A = 192.49 ft²

A  = 192.5 ft²

Hence the area of the shaded region = 192.5 ft²

Answer:  The correct answer is the first number = 10, the second number = 5

Step-by-step explanation:

x = the first number

y = the second number

What we know:

What we need to determine:

Solve using a system of equations:

The first equation (the first number subtracted from four times the second number equals ten):

4y - x = 10

Solve for x:

x = 4y - 10

The second equation (the first number is twice as large as the second):

x = 2y

Substitute the second equation in the first:

2y = 4y - 10

Solve for y:

y = 5

Substitute for y:

x = 2 (5)

x = 10

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The transformation of the graph f(x) = x² to the graph g(x) = -3(x+5)² + 12 involves a horizontal shift, a vertical stretch, and a vertical translation.

The graphs of f(x) = x² and g(x) = -3(x+5)² + 12 are the parabola.

The transformation of the graph is following as:

Firstly, the parabola has been shifted horizontally by 5 units to the left, which is reflected in the expression (x+5)².

Secondly, the parabola has been stretched vertically by a factor of -3, which is reflected in the coefficient in front of (x+5)².

Finally, the parabola has been raised up to 12 units. This means that the vertex of the parabola has been shifted upwards from the origin to the point (−5,12).

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Given:

Coordinates of point A are (2,8).

Point M(-2,2) is the midpoint of AC.

To find:

The coordinates of C.

Solution:

Let the coordinates of point C are (a,b).

Formula for midpoint:

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

Using the above formula, the midpoint of A(2,8) and C(a,b) is

\(M=\left(\dfrac{2+a}{2},\dfrac{8+b}{2}\right)\)

\((-2,2)=\left(\dfrac{2+a}{2},\dfrac{8+b}{2}\right)\)

On comparing both sides, we get

\(\dfrac{2+a}{2}=-2\)

\(2+a=-4\)

\(a=-4-2\)

\(a=-6\)

and,

\(\dfrac{8+b}{2}=2\)

\(8+b=4\)

\(b=4-8\)

\(b=-4\)

Therefore, the coordinates of point c are (-6,-4).

Answer:

1 and 1.50 or 1 and 2, but most likely the first one.

Step-by-step explanation:

Answer:

By translating the function cos(x) 90 degrees to the right.

Step-by-step explanation:

The sine function is just the cosine function translated 90 degrees to the right. You can see the visualization below. They overlap.

If you're wondering why the diagram shows a shift in

\(\pi / 2\)

That's just the equivalent to 90 degrees in radians.

Answer:

555/1000

Step-by-step explanation:

I guess it is the answer.

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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