Use the distributive property (FOIL) to determine each product. Show your steps. (2-5 marks each) a) (2 + 5y)2 b)2(2a + 3b) + c) 2x(x2 + x - 1) d) 3(x - 2y)(x + y) e) (2a - 3)(3a? + 5a - 2) Math 10-C: Unit 2: - Assignme f) (x2 + 2x - 1)(x2 - 2x + 1) g) (2x + 3) - 4x(x + 4)(3x - 1)

Answer:

Shelf A = $6 ;Shelf y = $4

Step-by-step explanation:

Let :

x = cost of items from shelf A

y = cost of items from shelf B

3x + 2y = 26 - - - - (1)

2x + 5y = 32 - - - - (11)

Using elimination method :

Multiply (1) by 2 and (11) by 3

6x + 4y = 52 - - - (111)

6x + 15y = 96 - - - (1V)

Subtract (1V) from (111)

-11y = - 44

y = 44/ 11 ; y = 4

Put y = 4 in (1)

3x + 2(4) = 26

3x + 8 = 26

3x = 26 - 8

3x = 18

x = 18 / 3

x = 6

You can use those variables specified to make symbolic relation between the cost and number of items. Then you can use any of the methods to solve the obtained system of equations.

The cost of items from shelf A is x = $6

The cost of items from shelf B is y = $4

Given that:

x represents the cost of an item from shelf A

y represents the cost of an item from shelf B

From given data, we have:

\(3 \times x + 2 \times y = \$26\\ 2 \times x + 5 \times y = \$32\)

Or, we get the system of equations as:

\(3x + 2y =26\\ 2x + 5y = 32\)

\(3x + 2y = 26\\ 2y = 26 - 3x\\ y = \dfrac{26-3x}{2} = 13 - 1.5x\)

Substituting this value of y in second equation, we get:

\(2x + 5y = 32\\ 2x + 5(13-1.5x) = 32\\ 2x - 7.5x + 65 = 32\\ -5.5x = -65 + 32\\ 5.5x = 33\\\\ x = \dfrac{33}{5.5}\\\\ x = 6\)

Using this value of x, we get:

\(y = 13 - 1.5x\\ y =13 - 1.5 \times 6\\ y = 13 - 9 = 4\)

Thus, we have:

The cost of items from shelf A is x = $6

The cost of items from shelf B is y = $4

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The area of the circular base of the fountain is 179 square feet.

A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.

A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.

Combined area of the walkway and fountain: (3.14)112=379.94 ft2.

Fountain area: (3.14)8*2=200.96 feet

Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.

The area of the circular base of the fountain is 179 square feet.

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True, people most often react favorably to four kinds of evidence which includes numerical data, examples, expert testimony.

Peοple οften react favοrably tο fοur kinds οf evidence, which include numerical data, examples, expert testimοny, and narratives. These types οf evidence prοvide different fοrms οf suppοrt and can be persuasive in different ways. Numerical data appeals tο the lοgical and analytical side οf individuals, while examples and narratives make the evidence mοre relatable and memοrable. Expert testimοny adds credibility and authοrity tο the argument. By presenting a cοmbinatiοn οf these types οf evidence, οne can increase the persuasive impact οf their message.

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The mean absolute deviation (MAD) and mean absolute percent error (MAPE) are both measures used to assess the accuracy or variability of a dataset. However, they differ in terms of the type of data they analyze and the way they express the deviation.

Mean Absolute Deviation (MAD):

MAD measures the average absolute difference between each data point and the mean of the dataset.

It provides information about the dispersion or spread of the data.

MAD is calculated by taking the absolute value of the differences between each data point and the mean, summing these values, and then dividing by the total number of data points.

MAD is expressed in the same units as the original data.

Mean Absolute Percent Error (MAPE):

MAPE measures the average percentage difference between each data point and its corresponding value in a reference dataset (often a forecast or predicted value).

It provides information about the relative error or accuracy of a model or prediction.

MAPE is calculated by taking the absolute value of the percentage difference between each data point and its corresponding reference value, summing these values, and then dividing by the total number of data points.

MAPE is expressed as a percentage.

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Answer:

EM SORY

Step-by-step explanation:

DUNIA BERDITI TAHUN TOGTV

Answer:

12 INCHES

Step-by-step explanation:

lol

also might have to do with the ratio tho......but i forgot

Answer:

I think the answer is "D" 12 inches

Step-by-step explanation:

I think this because on the right it says 12 inches and the left and the right look like the same length. Hope this helped and if it's wrong I'm so sorry.

Answer:

Mean is 13.5

Median is 10

Step-by-step explanation:

Answer:

Mean: 13.5

Medain: 10

Eventually, the differential equation's general solution is:

y = y_h + y_p

y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)

In the context of differential equations, the homogeneous solution of a differential equation is a solution that satisfies the equation when the right-hand side is equal to zero.

To find the particular solution of y'' + 3y' + 2y = 4e^x using the variation of parameters method, we first find the homogeneous solution of the differential equation by setting the right-hand side to zero:

y'' + 3y' + 2y = 0

The characteristic equation is r^2 + 3r + 2 = 0, which factors as (r + 2)(r + 1) = 0. Therefore, the solutions are y_h = c1e^(-2x) + c2e^(-x), where c1 and c2 are constants.

Next, we find the Wronskian of the homogeneous solution:

W(y1, y2) = |e^(-2x) e^(-x) | = e^(-3x)

To find the particular solution, we assume that it has the form y_p = u1(x)e^(-2x) + u2(x)e^(-x), where u1(x) and u2(x) are unknown functions to be determined.

We then find y_p' and y_p'':

\(y_p' = u1'(x)e^(-2x) + u2'(x)e^(-x) - 2u1(x)e^(-2x) - u2(x)e^(-x)y_p'' = u1''(x)e^(-2x) + u2''(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x)u1''(x)e^(-2x) + u2''(x)e^(-x) + u1'(x)e^(-2x) + u2'(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x) = 4e^x\)

Simplifying and grouping terms, we get:

\(u1''(x)e^(-2x) - 3u1'(x)e^(-2x) + u2''(x)e^(-x) - u2'(x)e^(-x) = 4e^x\)

To solve for u1(x) and u2(x), we use the method of undetermined coefficients and assume that they are both linear combinations of the exponential function and its derivative:

u1(x) = A(x)e^x

u2(x) = B(x)e^(2x)

Substituting these expressions into the previous equation and solving for A(x) and B(x), we get:

A(x) = -e^x/6

B(x) = 2e^x/3

Therefore, the particular solution is:

\(y_p = (-e^x/6)e^(-2x) + (2e^x/3)e^(-x)y_p = (-1/6)e^(-x) + (2/3)\)

Eventually, the differential equation's general solution is:

y = y_h + y_p

y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)

Therefore, the particular solution of the given differential equation y′′+3y′+2y=4ex is

\(y(x)=c_1e^{-x} + c_2e^{-2x} - 4 + 2e^{x}.\)

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The integer that makes the inequality 3(n − 6) < 2(n + 12) false is

The integer that makes the inequality false is solved by substituting the values and solving the inequality

3(n − 6) < 2(n + 12)

for n = -5

substituting the value of n

3(-5 − 6) < 2(-5 + 12)

= -33 < 14

3(n − 6) < 2(n + 12)

for n = 3

substituting the value of n

3(3 − 6) < 2(3 + 12)

= -9 < 30

3(n − 6) < 2(n + 12)

for n = 12

substituting the value of n

3(12 − 6) < 2(12 + 12)

= 18 < 48

3(n − 6) < 2(n + 12)

for n = 42

substituting the value of n

3(42 − 6) < 2(42 + 12)

= 108 < 108 wrong

This is the only wrong solution since 108 = 108

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Step-by-step explanation:

You have to find a number that goes into both numbers and then divide. So for example question 25:

4 goes into 4 and 8

so the answer to 25 is 1/2

4/8 = 1/2

The cost for 1 song is $0.99, then from the 150 songs 149 will cost $0.10, therefore, the total cost for the 150 songs is:

Answer: $15.89.

The other transformations are given, (x, y) → (-3x, y), (x, y) → (3x, y - 1), and (x, y) → (-x, 3y), do not preserve distances and angles, and therefore do not preserve congruence.

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

A transformation that results in an image that is congruent to its pre-image is a rigid transformation, which means that it preserves distances and angles.

The only rigid transformations are translations, reflections, and rotations.

Out of the four transformations given, the transformation that is a reflection across the y-axis, (x, y) → (-x, y), will result in an image that is congruent to its pre-image.

This is because a reflection across the y-axis preserves distances and angles, and therefore preserves congruence.

Hence, The other transformations are given, (x, y) → (-3x, y), (x, y) → (3x, y - 1), and (x, y) → (-x, 3y), do not preserve distances and angles, and therefore do not preserve congruence.

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The statement "There are about three times as many green marble as there are red marble." about the bag of marbles is not supported by the data. So the option B is correct.

250 different coloured marbles are in the bag.

She then picked one stone at random, noted its color in the table, and put it back in the bag. after 50 repetitions of this.

It means that since there are 250 marbles and 50 random marble selections are made.

The quantity of red marbles in the bag is then,

n(R) = 250/50 × 20

n(R) = 5 × 20

n(R) = 100

Hence, the proportion of red marbles = 100/120 × 100

The proportion of red marbles = 40%

The number of blue marble is:

n(B) = 250/50 × 14

n(B) = 5 × 14

n(B) = 70

The number of yellow marble is:

n(Y) = 250/50 × 9

n(Y) = 5 × 9

n(Y) = 45

The number of green marble is:

n(G) = 250/50 × 7

n(G) = 5 × 7

n(G) = 35

From the we can say that

n(R) = 40%, n(B) = 2n(G), n(Y) = 45

So the option B is correct.

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The complete question is:

Tracy was given a bag of 250 colored marbles. she randomly chose a marble, recorded its color in the table, and returned it to the bag. After doing this 50 times, Tracy has the following data.

Marble selections by color

Color              Number

Red                     20

Blue                    14

Yellow                 9

Green                  7

Which statement about the bag of marbles is not supported by the data?

A. The bag probably contains about 45 yellow marble.

B. There are about three times as many green marble as there are red marble.

C. There are about twice as many blue marble as there are green marbles.

D. About 40% of the marbles in the bag of red marble.

Answer:

42.195 + 42.195 OR 42.195 X 2

= 84.39

Therefore, Joel ran 84.39 km altogether in two races

Hope it helps ;)

Please mark as brainliest!

Answer:

C.) SSA

Step-by-step explanation:

This took me awhile to figure out if the angles in between are equal

But all the sides that are congruent make up several smaller triangles that are congruent and then use CPCTC to use angles of the smaller triangles to show the angles are equal

Answer:

c because if the number next to the underlined is above 5 u round up under 4 u round down

Step-by-step explanation:

Answer: c. 76

Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.

\(a(0) = 1 \: \: \: \: \: \: b(0) = 2 \: \: \: \: \: c(0) = 3 \\ a(1) = b(0) + c(0) = 2 + 3 = 5 \\ b(1) = a(0) + c(0) = 1 + 3 = 4 \\ c(1) = a(0) + b(0) = 1 + 2 = 3 \\ \\ a(2) = b(1) + c(1) = 4 + 3 = 7 \\ b(2) = a(1) + c(1) = 5 + 3 = 8 \\ c(2) = a(1) + b(1) = 5 + 4 = 9\)

\(a(3) = b(2) + c(2) = 8 + 9 = 17\\ b(3) = a(2) + c(2) =7 + 9 = 16 \\ c(3) = a(2) + b(2) = 7 + 8 = 15 \\ \\ a(4) = b(3) + c(3) = 16 + 15 = 31 \\ b(4) = a(3) + c(3) = 17 + 15 = 32 \\ c(4) = a(3) + b(3) = 17 + 16 = 33\)

\(a(5) = 32 + 33 = 65 \\ b(5) = 31 + 33 = 64 \\ c(5) =31 + 32 = 63 \\ \\ a(6) = 64 + 63 = 127 \\ b(6) = 65 + 63 = 128 \\ c(6) = 65 + 64 = 129 \\ \)

\(a(7) = 128 + 129 = 257 \\ b(7) = 127 + 129 = 256 \\c (7) = 127 + 128 = 255 \\ \\ a(8) = 256 + 255 = 511 \\ b(8) = 257 + 255 = 512 \\ c(8) = 257 + 256 = 513\)

\(a(9) = 512 + 513 = 1025 \\ b(9) = 511 + 513 = 1024 \\ c(9) = 511 + 512 = 1023 \\ \\ a(10) = 1024 + 1023 = 2047 \\ b(10) = 1025 + 1023 = 2048 \\ c(10) = 1025 + 1024 = 2049\)

\(a(n) + b(n) + c(n) = \\ 2(a(n - 1) + b(n - 1) + c(n - 1)) \\ 6 \times 2 {}^{n } \)

\(6 \times 2 {}^{n} > 100 \: 000 \\ 2 {}^{n} > \frac{100 \: 000}{6} \\ n > log {}^{2} ( \frac{100 \: 000}{6} ) \\ n > 14.02468 \\ n = 15\)

Answer:

2:5

Step-by-step explanation:fraction sighn is equivilent to ratio sighn.

Answer:

8x+8

Step-by-step explanation:

x+4+3x+x+4+3x

8x+8

hope it helps :)

Answer:

Should be 8x+8.

Step-by-step explanation:

(non simplified) 3x+3x+(x+4)+(x+4)

6x+(2x+8)

8x+8

Hope this could help

Answer:

Answer:

3

Step-by-step explanation:

plz mark brainliest

The result is not statistically significant.

To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level.

The null hypothesis is

H₀ : μ ≥ 1520

The alternative hypothesis is

Hₐ : μ ≤ 1520

then the test statistic is,

t = (x - μ)/(s/√n)

 = (1501 - 1520)/(53/√20)

t = - 1.603

The t-test statistic is - 1.603.

Degree of freedom n - 1 = 20 - 1 = 19

Hence the t-critical value is -1.792.

The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance. There is insignificance evidence indicates that the mean SAT score is less than 1520.

The result is not statistically significant.

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Answer:

A. (3,3)

Step-by-step explanation:

Based on the given data, a linear regression model can be used to estimate the energy consumption for electricity in February. By analyzing the relationship between units produced and consumption, we can predict the consumption for February when 1000 units are produced. The estimate for February's energy consumption is approximately 1100 kWh.

To estimate the energy consumption for electricity in February, we can use a linear regression model. We observe the relationship between units produced and consumption from the given data. By fitting a line to this data, we can make predictions for February's consumption when 1000 units are produced.

Using the units produced and consumption data from February and January, we can calculate the slope of the line, which represents the average change in consumption per unit produced. From the data, the slope is (1200 - 600) / (1500 - 600) = 0.8.

Now, we can use this slope to estimate the consumption for February when 1000 units are produced. The estimated consumption can be calculated as 1200 + (0.8 * (1000 - 1500)) = 1100 kWh.

Therefore, based on the linear regression analysis, the estimate for February's energy consumption is approximately 1100 kWh.

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The value of c that satisfies the Mean Value Theorem for the function f(x) = 2 - 3x² on the interval [-6, 5] is c = -37/66.

In mathematics, slope refers to the steepness or incline of a line on a graph.

(A) To find the average or mean slope of the function on the interval [-6, 5], we need to use the formula:

average slope = (f(5) - f(-6)) / (5 - (-6))

where f(x) = 2 - 3x². We can evaluate f(5) and f(-6) by substituting these values into the function:

f(5) = 2 - 3(5)² = -73

f(-6) = 2 - 3(-6)² = -110

Substituting these values into the formula, we get:

average slope = (-73 - (-110)) / (5 - (-6)) = 37/11

Therefore, the average slope of the function on the interval [-6, 5] is 37/11.

(B) By the Mean Value Theorem, we know that there exists a c in the open interval (-6, 5) such that f'(c) is equal to the mean slope calculated in part (A).

To find c, we need to first find f'(x), which is the derivative of f(x) with respect to x:

f'(x) = d/dx (2 - 3x²) = -6x

Now we need to solve the equation f'(c) = 37/11 for c:

-6c = 37/11

c = -(37/11) * (1/6) = -37/66

Therefore, the value of c that satisfies the Mean Value Theorem for the function f(x) = 2 - 3x² on the interval [-6, 5] is c = -37/66.

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Answer:

Step-by-step explanation:

3 tickets to attend an Off-Broadway show cost $81,

4 tickets cost $108; and

5 tickets cost $135.

Let the price of a ticket=k

Therefore:

Solving any of the equation above gives: x=27

We therefore have:

\(\left|\begin{array}{c|c|c|c|c|c}$Tickets&1&2&3&4&5\\$Total Cost(\$)&27&54&81&108&135\end{array}\right|\)

Let y be the total cost of x tickets

An equation for the relationship is therefore:

y=27x (where x is the number of tickets and y is the total costs (in $)).

According to the information, the group of people over 60 who use the camping is 28.1% (option C).

To find the percentage that corresponds to the group of people over 60 years of age who used the park camping, we must consider the total number of people 60 years of age or older who were included in the survey. In this case we can infer that there were 21,000 people. On the other hand, the group that used the camping was 5,900. So the percentage would be:

Based on the above, we can infer that the correct answer is B.

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Answer:

6.4

Step-by-step explanation:

Answer:

6.5 kilometers

Step-by-step explanation:

Answer:

-4<x≤5

Step-by-step explanation:

first at negative 4 there is a white dot and it’s pointing right so x is greater then it

And at 5 it is a closed dot pointing left so x is less then and equal to 5

Hopes this helps