Points are: A= (-2,7)B= (3,5)C= (1,0) To show that the triangle is a right triangle, show that the sum of the squares of the lengths of two sides (the legs) equals the square length of the third side (hypotenuse). What is the sum of the squares of the lengths if the legs?What is the square of length of the hypotenuse of the triangle?

According to the given information, 10 grey wolf pups will survive to adulthood.

What is a fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another.

Yellowstone National Park is home to a variety of wildlife, including the grey wolf. A survey conducted in the park recorded the birth of 25 grey wolf pups. However, it is estimated that only 2/5 of these pups will survive to adulthood.

To estimate the number of grey wolf pups that will survive to adulthood, we can use a simple mathematical formula. We multiply the total number of grey wolf pups by the estimated survival rate:

Survivors = (2/5) x 25

Therefore, we can estimate that 10 grey wolf pups will survive to adulthood.

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The product of the two matrices is  [2 - 3]    x  [1  -  4]

                                                            [ 3   2]       [4     1]

option B.

A product matrix is also known as matrix multiplication, which involves the multiplication of two matrices, to get or simply to a single matrix.

For example, if P and Q are the two matrices, then the product of the two matrices P and Q are denoted by:

Y = PQ.

For the given question; we have the first matrix as; (2 - 3i) and the second matrix as (1 - 4i).

Matrix (2 - 3i) is transformed to [2 - 3]

                                                   [ 3   2]

Matrix (1 - 4i) is transformed to [1  -  4]

                                                  [4     1]

The product of the two matrices =  [2 - 3]    x  [1  -  4]

                                                          [ 3   2]       [4     1]

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Answer:

Tran's hamster is faster as it took his hamster 19 seconds which is 4 seconds faster than Maria's hamster. I know this because the data shows Maria's hamster took 19 second and Tran's took 15 seconds to run through the maze hence Maria's hamster was slower and Tran's won. You can  use the calculation 19-15=4 so the difference is 4.

A subscript n baseline refers to the placement of a subscript, typically a letter or number, at a lowered position relative to the baseline of the surrounding text. It is commonly used in mathematical and scientific notation to denote a specific element or variable in a sequence or series.

To determine which choices describe a subscript n baseline = 4 (0.9) superscript n, we need to substitute the values of n into the equation and check if the given sequences match.

Let's substitute n = 1 into the equation:
s1 = 4 * (0.9)^1 = 3.6

Now, let's substitute n = 2 into the equation:
s2 = 4 * (0.9)^2 = 3.24

Finally, let's substitute n = 3 into the equation:
s3 = 4 * (0.9)^3 = 2.916

Comparing the given sequence values to the values we calculated, we can see that none of the choices match the sequence. Therefore, none of the choices describe a subscript n baseline = 4 (0.9) superscript n. Additionally, since the sequence values do not match any of the given choices, we cannot determine if the sequence diverges based on the information provided.

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Step-by-step explanation:

"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)

"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)

Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:

(3C + 2) + C = 90

4C + 2 = 90

4C = 88

C = 22

Plugging C = 22 back into either equation (1) or (2) gives us

B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)

Thus, ∠B = 68º; ∠C = 22º

Step-by-step explanation:

1) solution

Hypotenous(h)=?

perpendicular(p)=16

base(b)=12

By using formula

h^2 = p^2 + b^2

h^2 = 16^2 + 12^2

h^2 = 256 + 144

h^2 = 400

h^2 = 20^2

h = 20

therefore hypotenous (h) is 20

2) solution

hypotenous = (?)

perpendicular=(77)

base=(36)

by using formula

h^2 =p^2 + b^2

h^2=77^2+ 36^2

h^2=5929+1296

h^2=7225

h^2=85^2

h=85

therefore hypotenous (h) is 85

Answer:

49.7 \(cm^{2}\)

Step-by-step explanation:

Although it is hidden a bit, we are actually given the circumference of the circle, which is 25 cm.

We know that C = 2πr, so we can substitute variables to find the radius (r).

25 = 2πr

r = 25/(2π)

r = 3.9788... cm

The area of a circle is A = π\(r^{2}\), so:

A = π \(3.9788^{2}\)

A = 49.7359... \(cm^{2}\)

A ≈ 49.7 \(cm^{2}\)

The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

Step-by-step explanation:

1) Number of nickels = x

Number of quarter = y

x + y = 7   ----------------------(I)

x = 7 - y ------------------------(II)

0.05x + 0.25y = 0.55 -----------(III)

Substitute s = 7 - y in equation (III)

0.05*(7 - y)  + 0.25y = 0.55

0.05*7 - 0.05*y + 0.25y = 0.55

0.35 - 0.05y + 0.25y  = 0.55            {Combine like terms}

0.35  + 0.20y  = 0.55          {Subtract 0.35 from both sides}

  0.2y = 0.55 - 0.35

   0.2y = 0.2       {Divide both sides by 0.2}

        y = 0.2/0.2

y = 1

Substitute y =1 in equation (II)

x = 7 - 1

x = 6

Number of nickels = 6

Number of quarter = 1

2) Number of children tickets = x

Number of adult tickets = y

x + y = 40  -----------------(I)

     x = 40 - y  -----------------(II)

2x + 5y = 170 -----------------(III)

Substitute x = 40 - y in equation (III)

2*(40-y) + 5y = 170

2*40 - 2*y + 5y = 170

80 - 2y + 5y   = 170             {Combine like terms}

80 + 3y = 170                {Subtract 80 from both sides}

       3y = 170 - 80

       3y = 90       {Divide both sides by 3}

         y = 90/3

y = 30

Substitute y = 30 in equation (II)

x  = 40 - 30

x = 10

Number of children tickets = 10

Number of adult tickets =30

The ratio of the lengths of PR and QS is 1:1.

Given that, PQ is parallel to RS . PR and are perpendicular to PQ and RS.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

The slope of parallel lines is equal to each other.

If PQ is parallel to RS.

PR is perpendicular to PQ and RS.

QS is also perpendicular to PQ and RS.

The figure that will be formed using the two parallel lines, and the two perpendicular is a square.

When two lines are parallel to each other and the end points of the parallel lines are used to draw perpendiculars, then the line segments PQ and RS will be congruent.

By the property of Congruence, the ratio of the lengths PR and QS is equal to 1:1.

Therefore, the ratio of the lengths of PR and QS is 1:1.

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"Your question is incomplete, probably the complete question/missing part is:"

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

PQ is parallel to RS . PR and are perpendicular to PQ and RS .

The ratio of the lengths of PR and QS is __:__ .

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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Answer:

4

Step-by-step explanation:

To solve for x in the equation:

√(2x - 7) = 1

We can start by isolating the square root by squaring both sides of the equation:

(√(2x - 7))^2 = 1^2

2x - 7 = 1

Next, we can isolate the variable by adding 7 to both sides of the equation:

2x = 8

Finally, we can solve for x by dividing both sides by 2:

x = 4

Therefore, the solution to the equation √(2x - 7) = 1 is x = 4.

Answer:

Step-by-step explanation:

ruler

a. The probability is 4/10 or 0.4.

b. The combination formula: C(10, 5) = 252.

c. C(6, 3) = 20.

d. C(4, 2) = 6.

e. The probability is 120/252 ≈ 0.4762.

a. To calculate the probability that the person drawing the names is a Democrat, we divide the number of Democrats (4) by the total number of council members (10). Therefore, the probability is 4/10 or 0.4.

b. When there are no restrictions on the composition of the committee, we can calculate the number of ways it can be formed using combinations. Since there are 10 council members and we need to choose 5, the number of ways the committee can be formed is given by the combination formula: C(10, 5) = 252.

c. To determine the number of ways to choose 3 Republicans, we calculate the combination of 6 Republicans taken 3 at a time: C(6, 3) = 20.

d. Similarly, to calculate the number of ways to choose 2 Democrats, we use the combination formula with the 4 Democrats: C(4, 2) = 6.

e. To find the probability of selecting 3 Republicans and 2 Democrats, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes. The number of ways to select 3 Republicans from 6 and 2 Democrats from 4 is given by the product of their respective combinations: C(6, 3) * C(4, 2) = 20 * 6 = 120. The total number of possible outcomes is C(10, 5) = 252. Therefore, the probability is 120/252 ≈ 0.4762.

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In statistics the sampling method is collecting data based on sample of people who represent a population, whereas the census method involves studying each and every member of the population.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

The differences between census and sampling method is -

The investigator gathers data using the census method, which asks questions about every component of the population.

The investigator gathers data using the sampling method by selecting a sample of the objects that represent the entire population.

The Census Method of Collecting Data is appropriate when the area under inquiry is rather small. The sampling method is preferred when the investigation region is large.

The Census Method requires more time to gather data. The sampling method requires less time to gather data.

Generally speaking, the Census Method is more accurate than the Sampling Method. This accuracy can be attributed to the Census Method's inclusion of a study of every component of the population. The sampling approach has a lower level of accuracy because it examines a smaller sample of the population. However, since there are fewer elements in the sampling method, errors are simple to find and eliminate. Consequently, if that's the case, the sampling method gives more accuracy than census method.

Therefore, the differences for census and sampling method are pointed out.

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What is the difference between census method and sampling method in statistics?

Answer:

x = -2

Step-by-step explanation:

\(8^{x}\) = \(\frac{1}{64}\)

So to solve exponent.

8x=  1 /64

log(8x)=log( 1/ 64 ) (Take log of both sides)

x*(log(8))=log( 1 /64 )

x= log( 1 /64 ) /  log(8)

x=−2

Hope this helps!

Answer:

its b i took the test

Step-by-step explanation:

its b

The researcher wants to determine if the number of calories burned during an hour is the same for running and walking. To conduct this investigation, the researcher would measure continuous scale data.

Continuous scale data is quantitative data that can take any numerical value within a certain range.

In this case, the researcher would measure the number of calories burned, which is a continuous variable that can have various values within a specific range (e.g., 0, 100, 200, etc.).

By measuring the calories burned for both running and walking, the researcher can compare and analyze the numerical data to determine if there is a significant difference between the two activities.

It is important to note that the type of statistical analysis required to evaluate the data would depend on the specific research design and the number of groups involved.

If the researcher is comparing only two groups (running and walking), an independent t-test may be appropriate.

On the other hand, if there are more than two groups or additional factors being considered, an analysis of variance (ANOVA) might be more suitable.

The choice of statistical analysis method would depend on the specific research question and study design.

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The company's revenue at the break-even point is:

Total Revenue = Price per Table x Number of Tables Sold Total Revenue = 166 x 50 = $8,300

1a. In order to earn revenue of $7,104, the number of tables that the company must sell is 216.

We can find the solution through the following steps:

Let x be the number of tables that the company must sell to earn the revenue of $7,104.

Total Revenue = Total Cost + Total Profit64x = 49x + 2700 + 710464x - 49x = 9814x = 216

1b. In order to earn a profit of $6,000, the number of tables that the company must produce and sell is 60.

We can find the solution through the following steps:

Let x be the number of tables that the company must produce and sell to earn a profit of $6,000.

Total Profit = Total Revenue - Total Cost6,000 = (182x - 32x) - 1500(182 - 32)x = 7,500x = 60

The company must produce and sell 60 tables to earn a profit of $6,000.

1c. To find the company's revenue at the break-even point, we need to first find the number of tables at the break-even point using the formula:

Total Revenue = Total Cost64x = 34x + 150064x - 34x = 150030x = 1500x = 50 tables

The company's revenue at the break-even point is:

Total Revenue = Price per Table x Number of Tables Sold Total Revenue = 166 x 50 = $8,300

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We can draw the conclusion that there is insufficient evidence to support the idea that the model explains the relationship between the independent  variable and dependent variables if the global test of statistical significance for a regression model does not reject the null hypothesis.

The global test of statistical significance for a regression model is used to assess the overall explanatory power of the model. If the global test of statistical significance does not reject the null hypothesis, this indicates that the model does not explain the relationship between the  independent variable and dependent variables as expected. This could be due to a lack of sufficient data, a poorly constructed model, or simply a lack of correlation between the variables. In any case, the results of the test should be interpreted with caution, and further investigation into the model and data may be necessary.

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Answer:

212.8

Step-by-step explanation:

add the decimals

Answer:

N=+24,-24

Step-by-step explanation:

Well this is a quadratic equation and we can make further deductions using it's discriminant

b²-4ac=0

N²-4(1×144)=0

N²-576=0

N²=576

N=√576

N=+24,-24

The possible values of N are +24, and -24 if both roots of x² + Nx + 144 are equal to each other.

Any equation of the form \(\rm ax^2+bx+c=0\)  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

x² + Nx + 144 = 0

Discriminant will be zero:

D = 0

b²-4ac=0

N²-4(1×144)=0

N²=576

N=√576

N=+24,-24

Thus, the possible values of N are +24, and -24 if both roots of x² + Nx + 144 are equal to each other.

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Answer: i think it's y=10+1 maybe?

Step-by-step explanation:

Answer: Switch x and y

A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

To find the inverse of f(x) = 3x - 10, Jenna begins by replacing f(x) with y. The next step is to Switch x and y. And further, solve the equation for x.

Hence, the correct option is C.

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Answer:

-10

Step-by-step explanation:

h(-2) = 4(-2) -2

h(-2) = -8 -2 = -10

Answer:

y intercept = (0,7) , it is the weight of a newborn at birth/ before any months have passed

Step-by-step explanation:

in this equation:

weight= t(months) + 7

this is an equation written as y=mx +b

in a line equation like this b is the y intercept , or the y value when x=0

in this problem when x=0 it means that 0 months have passed , i.e. the baby is a newborn

merry Christmas to you!