I need help finding the equation and what it illustrates!!!

The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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When we reflect a point across the x-axis,

When we reflect a point across the y-axis,

The coordinates of B are (-3,-4).

Therefore, the coordinates of B' would be (-3,4)

(-3,4)

Answer:

Excluded values are any given number(s) that can make an expression's denominator zero.

First you set the denominator equal to zero, like so:

(x-1)(x+7) = 0

Now you can see if you make each (x-1) and (x+7) equal to zero:

x-1=0 x=1

x+7= x=-7

Excluded values:

From my understanding 1 and -7 would be the excluded values.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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We can be 99% confident that the true difference between the proportion of men and women who favor Mr. Singleton as a candidate is between 0.059 and 0.219.

Step 1: Determine the values of the \(\mathrm{\hat p_1}\) and \(\mathrm{\hat p_2}\) sample proportions.

The percentage of men who, on average, support Mr. Singleton is:

\(\mathrm{\hat p_1}\)  = \(\dfrac{282}{659}\), or around 0.428

The percentage of women who favour Mr. Singleton, as a sample, is:

\(\mathrm{\hat p_2}\) = \(\dfrac{182}{629}\), or around 0.289

Locate the critical value that must be utilised to build the confidence interval in step 2.

The level of significance is \(\alpha\) = 0.01/2 = 0.005 (divided by 2 because it's a two-tailed test) because we want to determine a 99% confidence interval. The critical value for a z-score with  \(\alpha\) = 0.005 is roughly 2.576 when using a table or calculator.

Step 3: Determine the standard error's value.

The standard error of the difference between two sample proportions is calculated as follows:

\(\mathrm{(\Hat p 2-\Hat p 2) + n_1 + \frac {\hat p_2}{1}}\)

When we enter the values from the issue, we obtain:

\(\mathrm{SE = \sqrt{\dfrac{\hatp_1}{SE}} = (\hat p_1 - \hat p_2) (\hat p_1 - \hat p_1) }\)

Create the 99% confidence interval in step four.

We may create the confidence interval using the sample proportions, critical value, and standard error:

\(\mathrm{SE(\hat p_1 - \hat p_2) 1:00 \ p.m. \ to \ 2:00 \ p.m. \ z \ \alpha \ 2}\)

When we change the values, we obtain:

2.576, × 0.031, = (0.428 - 0.289).

If we simplify, we get:

\($$0.139 \pm \ 0.08$$\).

3. Find the value of the standard error.

The following formula is used to compute the standard error of the difference between two sample proportions:

\(\mathrm{SE = \sqrt{\dfrac{\hatp_1}{SE}} = (\hat p_1 - \hat p_2) (\hat p_1 - \hat p_1) }\)

\(\mathrm{(\Hat p 2-\Hat p 2) + n_1 + \frac {\hat p_2}{1}}\)

When we type in the issue's values, we get:

\($ \mathrm{\sqrt{(\frac{1-0.428}{0.659}) + \frac{1-0.288}{0.629}) }= about \ 0.031 \ for \ SE (\hat p_1 - \hat p_2)}\)

In step four, calculate the 99% confidence interval.

With the sample proportions, critical value, and standard error, we can calculate the confidence interval:

\(\mathrm{SE(\hat p_1 - \hat p_2) 1:00 \ p.m. \ to \ 2:00 \ p.m. \ z \ \alpha \ 2}\)

When the values are changed, we get the following result: \($2.576 \times 0.031 = (0.428 - 0.289)$$\)

Simplifying, we obtain: \($$0.139 \pm \ 0.08$$\).

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Answer:

The new coordinates of point C after reflection and translation are (-2, -2).

Step-by-step explanation:

I hope it helps:)

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

Check the picture below.

recall, the bearing is always starting from the North line clockwise.

Answer:

f¹(x) = x - 3

To find the inverse of a function, just "trade" and y and solve for the "new" y. The graph of the inverse is the reflection of the original function over the line y = x.

Rewrite the function f(x) = x + 3

as the equation y = x + 3

Trade x and y.

x = y + 3

Solve for the "new" y.

= y + 3

3 - 3

Subtract 3 from both sides

y = x= 3

The symbol for the inverse is f-¹(x)

f¹(x) = x - 3

Step-by-step explanation:

brainlies me plss

\(f(x) = x -3 \\\\\text{Write f(x) as}~ y = x -3}\\\\\text{Now replace x and y,}\\\\x = y-3\\\\\text{Solve for y:}\\\\y = x+3 \\\\\implies f^{-1}(x) = x +3 ,~ \text{This is the inverse of given function.}\)

Answer:

1370754

Step-by-step explanation:

From what I can see, you are probably studying combinations and permutations at the moment. Since this is a question about how many groups of five can be produced from a sample size of 46, the groups are random and not in order, which may rule for us to use the combination formula.

Once you compute this, this answer is basically saying that 1370754 groups of 5 can be created from a sample size of 46

Te ajut eu la dacă vrei la matematica

The error that the manager made was that B. The manager divided 5/4 by 16 instead of dividing 4/5 by 16.

The information illustrates that the project manager is calculating work forecasts and he manager's team completed 4/5 of a job in 16 days.

Therefore, the amount that was done each day will be:

= 4/5 ÷ 16

= 4/5 × 1/16

= 4/80

= 1/20

Therefore, the error that the manager made was that the manager divided 5/4 by 16 instead of dividing 4/5 by 16. This was the reason that he got 5/64.

Therefore, the correct option is B.

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Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Answer:

Linear function 2

Step-by-step explanation:

If Linear function 1 has an x-intercept of 4,0 and a y-intercept of 0,22

It's a negative equation, Its not increasing Its decreasing.

So it must be Linear function 2

The values of x and y are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for this problem are given as follows:

2 and x.

The altitude is given as follows:

6.

Hence the length x is given as follows:

2x = 6²

2x = 36

x = 18.

Applying the Pythagorean Theorem, the length y is given as follows:

y² = 18² + 6²

y² = 360

\(y = \sqrt{36 \times 10}\)

\(y = 6\sqrt{10}\)

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Answer:

7/4

Step-by-step explanation:

rise over run

7 up, 4 right

Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

\(x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}\)

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

\(x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72\)

The probability that you win first prize and your friend wins second prize is given as follows:

B. 9/990.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes is given as follows:

990.

The number of desired outcomes is of 9, as:

Hence:

1 x 1 x 9 = 9.

Meaning that the probability is of:

p = 9/990.

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Answer:

1 kg = 1000 grams

15,000 grams = 15kg

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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We are given the following salaries for the research and development department:

$48,397

$27,982

$42,591

$19,522

$32,400

$37,582

We are asked to find the mean, median, and mode of the given data set.

To find the mean, we will use the following formula:

So the mean is $34,746 calculated as follows:

To find the median, we will have to arrange the data set and find the middle value. Because we have 6 data, we will get the average of the two middle numbers.

$19,522 $27,982 $32,400 $37,582 $42,591 $48,397

The two middle values are $32,400 and $37,582. Their average, $34,991, is the median.

Finally, to find the mode, we will have to get the most frequently occurring value. In this data set, though, all elements are unique. So there is no mode.

In the given right angled trianged, the hypotenuse side is 6 and the adjacent side is x.

The angle formed by the hypotenuse and the adjacent side is 60 degree

The objective is to find the value of the adjacent side x.

SInce, we are provided with hypotenuse and adjacent, use cosine formula.

It is known that

So,

From the trignometric table the value of sin 30 is 1/2. Substitute the value in the above equation.

Hence, the length of the hypotenuse side x is 3.

The slope of the line is 1 / 2. The equation of the line is y = 1/ 2 x + 3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line passes through points (8, 7) and (4, 5). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 5 - 7 ) / ( 4 - 8 )

Slope = -2 / -4

Slope = 1 / 2

Calculate the y-intercept,

y = mx + c

5 = 1 / 2 x 4 + c

c = 5 - 2 = 3

The equation is written as,

y = mx + c

y = 1/2x + 3

Therefore, the slope of the line is 1 / 2. The equation of the line is y = 1/ 2 x + 3.

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Given:

I'm 3 times younger than my mom but 3 times older than my younger brother.

Mom is older than my younger brother by 40 years.

To find:

How old am I.

Solution:

Let x be the age of the younger brother.

I'm 3 times older than my younger brother. So, my age is 3x.

I'm 3 times younger than my mom. So, she is 3 times older than me and her are is 3(3x)=9x.

The difference between the age mother and younger brother is 40 years.

\(9x-x=40\)

\(8x=40\)

Divide both sides by 8.

\(x=\dfrac{40}{8}\)

\(x=5\)

Now,

My age \(=3x\)

            \(=3(5)\)

            \(=15\)

Therefore, I'm 15 years old.

Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

Answer:

5 + 8 × 4

Assuming "five and eight" means 5 + 8

Answer:

3*3*3=27 is the rights answer

3x6=18(move 1 to the left/replace the 0)

3x1=3

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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