2. What type of Triangle is it?​

Let

S = 1 + 2 + 3 + … + (n - 2) + (n - 1) + n

Reversing the order of terms, we have

S = n + (n - 1) + (n - 2) + … + 3 + 2 + 1

and we observe that terms in the same position on the right side add up to n + 1.

2S = (1 + n) + (2 + (n - 1)) + (3 + (n - 2)) + … + (n + 1)

There are n terms in the sum, so each the right side is simply n copies of n + 1, and

2S = n (n + 1)

S = n (n + 1)/2

Now,

17 + 18 + 19 + … + 41 + 42 + 43

= (1 + 2 + 3 + … + 41 + 42 + 43) - (1 + 2 + 3 + … + 14 + 15 + 16)

= (S with 43 terms) - (S with 16 terms)

= 43 (43 + 1)/2 - 16 (16 + 1)/2

= 810

Answer:

(a) 0.1414

(b) 0.1010

Step-by-step explanation:

(a)

The density curve is rectangular in shape.

This implies that the distribution of donations is Uniform.

(b)

Compute the probability of donations at least 85 cents as follows:

\(P(X\geq 85)=\int\limits^{99}_{85} {\frac{1}{99-0} \, dx\)

                 \(=\frac{1}{99}\times [x]^{99}_{85}\\\\=\frac{99-85}{99}\\\\=0.1414\\\\\)

Thus, the proportion of donations that are at least 85 cents is 0.1414.

(b)

Compute the probability of donations between 30 and 40 cents as follows:

\(P(30\leq X\leq 40)=\int\limits^{40}_{30} {\frac{1}{99-0}} \, dx\)

                         \(=\frac{1}{99}\times [x]^{40}_{30}\\\\=\frac{40-30}{99}\\\\=0.1010\)

Thus, the probability of donations between 30 and 40 cents is 0.1010.

**Kind note:

Since there are two variables in one equation, it is impossible to determine a specific value for x and y. (Unless the trial-and-error method is used).

How to determine the value of x using the equation (16x - 8y = 72)?

To determine the value of "x", we need to isolate the x-variable on one side. The value (or expression) obtained on the opposite side of the x-variable will be the value of x.

How to determine the value of y using the equation (16x - 8y = 72)?

To determine the value of "y", we need to isolate the y-variable on one side. The value (or expression) obtained on the opposite side of the y-variable will be the value of y.

Determining the x-variable:

⇒ 16x - 8y = 72

⇒ 16x = 72 + 8y                            [Adding 8y to both sides of the equation]

⇒ 16x/16 = (72 + 8y)/16                [Dividing 16 to both sides of the equation]

⇒ x = 9/2 + y/2                               [Simplifying both sides of the equation]

⇒ x = (9 + y)/2                                     [Combining the denominators]

Determining the y-variable:

⇒ 16x - 8y = 72

⇒ 16x - 8y - 16x = 72 - 16x         [Subtracting 16x both sides of the equation]

⇒ -8y = 72 - 16x                              [Simplifying both sides of the equation]

⇒ -8y/-8 = (72 - 16x)/-8                [Dividing -8 to both sides of the equation]

⇒ -8y/-8 = 72/-8 - 16x/-8

⇒ -8y/-8 = -72/8 + 16x/8

⇒ y = -9 + 2x                                  [Simplifying both sides of the equation]

First simplify it to suitable form of slope intercept then you can get values

The pairs are

And so on

Valid Null Hypothesis: 02 = 49.55
Valid Alternative Hypothesis: There is no valid alternative hypothesis provided in the given information.

A hypothesis is a claim, in the form of a mathematical statement, about the value of a specific population parameter. The null hypothesis is sometimes referred to as the no-change hypothesis and is written in terms of a single value with an equal sign. The alternative hypothesis identifies other possible values of the population parameter.

Based on the given information, the following can be concluded:

The valid Null Hypothesis is 02 = 49.55 This is a valid null hypothesis.

Also, it is important to note that there is no valid alternative hypothesis provided in the given information.

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The limit of 8x³ as x approaches infinity, divided by \(e^(^5^x^)\), can be evaluated using L'Hopital's rule.

To evaluate the given limit using L'Hopital's rule, we differentiate the numerator and the denominator separately. Let's begin by differentiating the numerator:

Differentiating the numerator, we obtain d/dx (8x³) = 24x².

Next, we differentiate the denominator: d/dx (\(e^(^5^x^)\)) = \(5e^(^5^x^)\).

Now, we take the limit of the differentiated numerator and denominator as x approaches infinity. As x becomes larger and larger, the term 24x² grows significantly faster than the term \(5e^(^5^x^)\). Thus, the limit of 24x²/\(5e^(^5^x^)\) as x approaches infinity will approach infinity.

Using L'Hopital's rule, we find that the limit of 8x³ divided by \(e^(^5^x^)\) as x approaches infinity is infinity.

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Answer:

equal because by adding them u get equal numbers 36 and Bob aquarium is high while Terry aquarium is long and wide.

Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

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Answer:300,000

Step-by-step explanation:

Ap3x

The total initial deposit of the bank is $ 300000.

Percentages, one of the most frequent ways to show the statistics is by percentage. Percent simply means "per hundred" and the symbol used to express percentage is %.

Here, Let the total initial deposit be x

         Bank receives amount = $ 30,000

         Bank reserve requirement = 10 %

Now, 10% of total = 30,000

    x = 30000 /0.1

  x = 300000

Thus, he total initial deposit of the bank is $ 300000.

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If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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Answer:

22.12feet

Step-by-step explanation:

the ladder becomes your hypotenuse,the wall is the height,this forms a right angled triangle and the angle of elevation forms at the base,use sine which is opposite over hypotenuse to get your answer

The standard deviation of the sum of the 4 random variables is 10.23

The question is incomplete the complete question is  

For each of the 4 stroke categories 2,4,6,8 consider a random variable representing the time of a randomly selected swimmer in that category is 0.6,0.8,0.2,0.7. What is the standard deviation of the sum of the 4 random variables?.

To calculate the Expected Value, we need to multiply each value by its probability and then sum the products up.

μ = E(x) = ∑xp(x)

That is, (0.6x2) + (0.8x4) + (0.2x6) + (0.7x8) = 1.2 + 3.2 + 1.2 + 5.6 = 11.2

Mean = 11.2

Now we take the first and second steps,

(2- 11.2)² x 0.6 = 84.64 x 0.6 = 50.78

(4 - 11.2)² x 0.8 = 51.84 x 0.8 = 41.47

(6 - 11.2)² x 0.2 = 27.04 x 0.2 = 5.4

(8 - 11.2)² x 0.7 = 10.24 x 0.7 = 7.16

Now we take the the third step and add our products together to get the variance V,

V = σ2 = ∑(x−μ)2P(x)

V = 50.78 + 41.47 + 5.4+ 7.16 = 104.81

Now we take the last step by taking the square root of the variance to get the standard deviation SD,

SD = σ = √σ2

Standard Deviation SD = √104.81 = 10.23

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See below for the proof that the areas of the lune and the isosceles triangle are equal

The area of the isosceles triangle is:

\(A_1 = \frac 12r^2\sin(\theta)\)

Where r represents the radius.

From the figure, we have:

\(\theta = 90\)

So, the equation becomes

\(A_1 = \frac 12r^2\sin(90)\)

Evaluate

\(A_1 = \frac 12r^2\)

Next, we calculate the length (L) of the chord as follows:

\(\sin(45) = \frac{\frac 12L}{r}\)

Multiply both sides by r

\(r\sin(45) = \frac 12L\)

Multiply by 2

\(L = 2r\sin(45)\)

This gives

\(L = 2r\times \frac{\sqrt 2}{2}\)

\(L = r\sqrt 2\)

The area of the semicircle is then calculated as:

\(A_2 = \frac 12 \pi (\frac{L}{2})^2\)

This gives

\(A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2\)

Evaluate the square

\(A_2 = \frac 12 \pi (\frac{2r^2}{4})\)

Divide

\(A_2 = \frac{\pi r^2}{4}\)

Next, calculate the area of the chord using

\(A_3 = \frac 12r^2(\theta - \sin(\theta))\)

Recall that:

\(\theta = 90\)

Convert to radians

\(\theta = \frac{\pi}{2}\)

So, we have:

\(A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))\)

This gives

\(A_3 = \frac 12r^2(\frac{\pi}{2} - 1)\)

The area of the lune is then calculated as:

\(A = A_2 - A_3\)

This gives

\(A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)\)

Expand

\(A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2\)

Evaluate the difference

\(A = \frac 12r^2\)

Recall that the area of the isosceles triangle is

\(A_1 = \frac 12r^2\)

By comparison, we have:

\(A = A_1 = \frac 12r^2\)

This means that the areas of the lune and the isosceles triangle are equal

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Answer:

A

Step-by-step explanation:

These are cross angles

Answer:

I'm pretty sure slope is 4/1 and y-intercept is 3

Answer:

Slope: 4/1

Y-Intercept: (0,3)

Step-by-step explanation:

This should be the correct answer if the graph is in increments of one.

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Answer:

15.38

Step-by-step explanation:

two angles are equal

3.25x=50

x= 15.38461538461

Answer:

it's is the answer is 4 and r 2

Answer:

Step-by-step explanation:

a

Homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The homogeneity of variance assumption assumes that the two populations have equal variances. Therefore, the correct answer is option c, "The two populations have equal variances."

This assumption is often made in statistical tests that compare the means of two groups, such as the t-test.

When the variances of the two populations are equal, it allows for more precise estimates of the standard error and can improve the accuracy of the test results.

However, if the variances are not equal, it can lead to biased and unreliable results.

In such cases, alternative methods, such as Welch's t-test or the Brown-Forsythe test, can be used to adjust for unequal variances.

Hence, homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

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The differentiable function the value of f(4) is(d: 7.9541).

To find the value of f(4), integrate the given derivative of f(x). Let's integrate √(x²) + 2cos(x)/3 with respect to x.

∫√(x²) + 2cos(x)/3 dx

The integral of √(x²) simplified as follows:

∫√(x²) dx = ∫|x| dx = (1/2)(x |x|) + C

integrate 2cos(x)/3:

∫2cos(x)/3 dx = (2/3) ∫cos(x) dx = (2/3) sin(x) + C

∫(√(x²) + 2cos(x)/3) dx = (1/2)(x |x|) + (2/3) sin(x) + C

that f(1) = 2. So, this information to find the constant C.

f(1) = (1/2)(1 |1|) + (2/3) sin(1) + C

2 = (1/2)(1) + (2/3) sin(1) + C

2 = 1/2 + (2/3) sin(1) + C

C = 2 - 1/2 - (2/3) sin(1)

the constant C, f(4):

f(4) = (1/2)(4 |4|) + (2/3) sin(4) + C

f(4) = 2(4) + (2/3) sin(4) + (2 - 1/2 - (2/3) sin(1))

f(4) = 8 + (2/3) sin(4) + (2 - 1/2 - (2/3) sin(1))

To determine the exact value of f(4), the values of sin(4) and sin(1). sin(4) = -0.7568 and sin(1) =0.8415.

Substituting these values,

f(4) = 8 + (2/3)(-0.7568) + (2 - 1/2 - (2/3)(0.8415))

f(4) =8 - 1.511 + 1.666 - 0.5609

f(4) = 8 - 0.0459

f(4) = 7.9541

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Complete question:

let f be a differentiable function such that f(1)=2 and f′(x)=√x2 2cosx 3. what is the value of f(4) ?

a. 10.790

b. 8.790

c. 12.996

d. 7.9541.

e. -6.79

Answer:

Student B

Step-by-step explanation:

You know because:

The common factor between 3 and 6 is 3.

You can factor 2 x's from both parts and 2 y's.

Therefore, it would be

3x^2y^2.

The best pricing would be determined by a number of criteria, including slope the cost of ingredients, labour, and overhead expenditures, as well as market competitiveness.

The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7)

The slope of the line of fit is 3/5, which indicates the business will earn $0.60 for each additional doughnut sold. In other words, if the quantity of donuts sold grows, so does the overall cost of the doughnuts by $0.60 each donut sold.

It is crucial to note that, based on the data supplied, the slope of the line of fit shows the average link between the number of donuts sold and the overall cost. That might not always show the best pricing for the doughnuts. The best pricing would be determined by a number of criteria, including the cost of ingredients, labour, and overhead expenditures, as well as market competitiveness.

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the volume of the solid is \(V = π r2 (sqrt(3/4)r) / 3 = π r3 sqrt(3/4) / 3.\)

Plugging in the given values, we get\(V = π (3)3 sqrt(3/4) / 3 = 27π/4.\)

The volume of a solid with a circular base and cross sections taken parallel to one of the diameters that are equilateral triangles can be found using the slicing method. The formula for the volume of such a solid is:\(V = π r2 h/3,\)where π is the constant pi, r is the radius of the circular base, and h is the height of the solid.

In this case, the radius of the circular base is 3 and the height is equal to the length of the sides of the

equilateral triangles. To find the height, we can use the Pythagorean Theorem. The hypotenuse of the triangle is 2r, so the length of the sides is sqrt(r2 - (r/2)2), which simplifies to sqrt(3/4)r.

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The regression function given is a log-log model where the natural logarithm of the dependent variable is a linear function of the natural logarithm of the independent variables. Test the significance of the coefficients and the overall goodness of fit of the model using appropriate statistical tests.

The regression function given is a log-log model where the natural logarithm of the dependent variable is a linear function of the natural logarithm of the independent variables. The model has three independent variables, X1, X2, and X3, and the coefficients B1, B2, and B3 represent the percentage change in Y for a 1% change in X1, (140-X2), and X3, respectively. The coefficient B0 is the intercept.

To fit the regression function based on theoretical considerations, we need to use the principles of economic theory or other relevant theory to derive the functional form of the model. Once the theoretical model is derived, we can estimate the coefficients using regression analysis. In this case, the theoretical argument suggests a log-log model, and we can use the method of ordinary least squares (OLS) to estimate the coefficients.

To estimate the coefficients, we need a dataset with observations on the dependent variable Y and the independent variables X1, X2, and X3. Once we have the data, we can use a statistical software package to perform the regression analysis and obtain the estimates of the coefficients. We can also test the significance of the coefficients and the overall goodness of fit of the model using appropriate statistical tests.

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Answer:

slopes is 1/4

y intercept is 3 i think the inequality would be y=mx+b so it would be y=1/4x+3

Step-by-step explanation:

Answer:

D) 122

E) 30

F) 28

Step-by-step explanation:

Angle D:

value of angle across is equal to angle D = 122

Angle E:

value of angle across is equal to angle E = 30

Angle F:

180 - 122-30

Answer:

D) 122

E) 30

F) 28

Step-by-step explanation:

When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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The index variable for the element at the last row and last column in the array x is B. x[4][6].

In Java, arrays are zero-indexed, which means the first element of an array is at index 0. The given array x is a 2D boolean array with dimensions 5x7 (5 rows and 7 columns). To access the last row and last column, we need to subtract 1 from each dimension:

- For the last row, the index is 5 - 1 = 4.
- For the last column, the index is 7 - 1 = 6.

So, the correct index variable to access the last row and last column is x[4][6]. The other options provided are incorrect as they do not accurately represent the index of the last element:

- a. x[4][5] refers to the second to last element in the last row.
- c. x[5][6] would be out of bounds, as the maximum row index is 4.
- d. x[5][7] would also be out of bounds, as both the row and column indices are too large.

Therefore, the correct option is B.

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