An angle measures 62° less than the measure of its supplementary angle. What is the measure of each angle?

Answer:

\(12 = n - 0.25(12 + 8n) \\ 12 = n - \frac{1}{4} (12 + 8n) \\ 12 = n - 3 - 2n \\ 12 + 3= n -2n \\ n = -15 \)

Answer:

KPL= 64 degrees JPL= 116 degrees

Step-by-step explanation:

2x+24+4x+36=180

combine like terms

6x+60=180

6x=120

x=20

2(20)+24=64

4(20)+36=116

Answer:12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Lambert's initial investment of $20,000 gave him a 1/3 interest in the partnership. Bonus is distributed, it would be added to the partnership's capital.

Here's a step-by-step explanation:

1. Determine the total capital before Lambert's investment: The other partners have a combined capital of $34,000.

2. Calculate the capital after Lambert's investment: Lambert invests $20,000, so the new total capital becomes $34,000 + $20,000 = $54,000.

3. Determine the value of 1/3 interest: Since Lambert has a 1/3 interest in the partnership, we need to find 1/3 of the total capital after his investment. (1/3) * $54,000 = $18,000.

4. Calculate the bonus: The difference between Lambert's initial investment ($20,000) and his 1/3 interest ($18,000) is the bonus. $20,000 - $18,000 = $2,000.

5. Determine Lambert's capital after the bonus distribution: Since the bonus is distributed, we subtract the bonus from Lambert's initial investment. $20,000 - $2,000 = $18,000.

So, after the distribution of the bonus, Lambert's capital in the partnership is $18,000.

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The central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

To find the central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

If you want the central angle in degrees, you can convert it using the fact that there are 2π radians in a full circle (360 degrees):

Central angle (in degrees) = (Arc length / Radius) * (180 / π)

Make sure to use consistent units for the arc length and radius, such as meters or centimeters, to obtain accurate results.

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Answer:

16

Step-by-step explanation:

27-11= rest of the length missing

There are 20/7 (or 2 and 6/7) 1/4-oz amounts in 5/7 oz of jam.

To find the number of 1/4-oz amounts in 5/7 oz of jam, we can use the division method.

The formula to calculate the number of 1/4 oz amounts in 5/7 oz of jam is:

Number of 1/4 oz amounts = 5/7 oz / 1/4 oz

Let's calculate: Number of 1/4 oz amounts = (5/7) ÷ (1/4)

First, we'll invert the divisor (1/4) to (4/1) and then multiply the dividend (5/7) with the inverted divisor (4/1).

Number of 1/4 oz amounts = (5/7) × (4/1)= 20/7

So, there are 20/7 (or 2 and 6/7) 1/4-oz amounts in 5/7 oz of jam.

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9514 1404 393

Answer:

  -2

Step-by-step explanation:

Let x represent the original number. Then the transformation Alex does is ...

  x/2 +5 = 4

  x/2 = -1 . . . . subtract 5

  x = -2 . . . . . multiply by 2

The original number was -2.

It is observed that males raise their hands more frequently than females for answering the question.

The mean difference is investigated to determine that whether values (directed toward that measure) of a two groups differ considerably or not, taking into account the equality in variance between given groups.

The Z test is employed based on the understanding about population data (here, standard deviation), while the t-test is used if sample values are utilized to estimate them.

Now, according to the question;

Then let population mean be the amount of men raising their hands \(\mu_{M}\)  as well as the population mean be the number of females raising their hands \(\mu_{F}\).

Then the hypothesis would be;

\(\begin{aligned}&H_{0}: \mu_{M} \leq \mu_{F} \\&H_{1}: \mu_{M} > \mu_{F}\end{aligned}\)

So, the test shows the result of right trailed.

Calculate the sample mean for the men;

\(\begin{aligned}\bar{x}_{M} &=\frac{\sum_{i=1}^{n} X_{i}}{n} \\&=\frac{9+8+4+9+3+8+10+8+9+8+10+7+6+12}{14} \\&=7.93\end{aligned}\)

Then, the standard deviation for males will become,

\(\begin{aligned}s_{M} &=\sqrt{\frac{\sum_{i=1}^{n}\left(X_{i}-\bar{x}_{M}\right)^{2}}{n-1}} \\&=\sqrt{\frac{(9-7.93)^{2}+(8-7.93)^{2}+(4-7.93)^{2}+\ldots+(7-7.93)^{2}+(6-7.93)^{2}+(12-7.93)^{2}}{14-1}} \\&=2.3685\end{aligned}\)

Now, calculate the mean for females;

\(\begin{aligned}\bar{x}_{F} &=\frac{\sum_{i=1}^{n} X_{i}}{n} \\&=\frac{3+5+1+2+6+4+3+6+7+9+7+3+7+6+8+8}{16} \\&=5.31\end{aligned}\)

Then, the standard deviation for female will become;

\(\begin{aligned}s_{F} &=\sqrt{\frac{\sum_{i=1}^{n}\left(X_{i}-\bar{x}_{F}\right)^{2}}{n-1}} \\&=\sqrt{\frac{(3-7.93)^{2}+(5-7.93)^{2}+(1-7.93)^{2}+\ldots+(6-7.93)^{2}+(8-7.93)^{2}+(8-7.93)^{2}}{16-1}} \\&=2.3866\end{aligned}\)

Assuming variance equality, a pooled variance is:

\(\begin{aligned}s_{p}^{2} &=\frac{\left(n_{M}-1\right) s_{M}^{2}+\left(n_{F}-1\right) s_{F}^{2}}{n_{M}+n_{F}-2} \\&=\frac{(14-1) 2.3685^{2}+(16-1) 2.3866^{2}}{14+16-2} \\&=5.6559\end{aligned}\)

The, the test statistics would be-

\(\begin{aligned}t &=\frac{\bar{x}_{M}-\bar{x}_{F}}{\sqrt{s_{p}^{2}\left(\frac{1}{n_{M}}+\frac{1}{n_{F}}\right)}} \\&=\frac{7.93-5.31}{\sqrt{5.6559\left(\frac{1}{14}+\frac{1}{16}\right)}} \\&=3.0103\end{aligned}\)

The degree of freedom will become-

\(\begin{aligned}d f &=n_{M}+n_{F}-2 \\&=14+16-2 \\&=28\end{aligned}\)

The critical value is 1.701 at 28 degrees of freedom & 0.05 level of significance.

As, \(t > t_{\text {critical }}\), the null hypothesis will be rejected.

As a result, males are more likely than females to raise their hands in response to the inquiry.

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The correct question-

Using the data set below, test the research hypothesis at the .05 level of significance that males raise their hands in class more often than females. Do this practice problem by hand using a calculator. What is your conclusion regarding the research hypothesis? Remember to first decide whether this is a one- or two-tailed test. (The table is attached)

Answer = 2

Step-by-step explanation:

3x + 2(5x) = 26

3x + 10x = 26

13x = 26

26 ÷ 13 = 2

The error is that ( − 2 , 52 ) (-2,52) (−2,52) is not on the graph of f ( x ) = − 13 x 2 f(x)=-13x^2 f(x)=−13x2.

The uncertainty or change of the corresponding coordinate of the point is shown by an error bar, which is a line drawn through a point on a graph that is parallel to one of the axes.

A graph is a visual representation of data that can be used to display values. The specific type of graph used to display values will depend on the type of data being represented and the purpose of the graph and thus some errors can be made.

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THE ANSWER IS

0.66

Or for fraction 6/10

Answer:

(ab-bc)²

Step-by-step explanation:

Answer:

(ab - bc)^2.

Step-by-step explanation:

ab(ab - bc) + bc(bc - ab)​

= ab(ab - bc) - bc(ab - bc)​

= (ab - bc)(ab - bc)

= (ab - bc)^2

Step-by-step explanation:

hope you can understand

The difference between the two investments after 35yrs is $4700 and  Bank of America is offering higher interest than 5/3rd banks.

Most interest is compounded semiannually, quarterly, or monthly. Continuous compounding assumes that interest is compounded indefinitely and reentered on the balance sheet. The continuous compounding formula takes into account four variables.

For the given question,

5/3rd bank offers continuous interest:

For continuous interest, A = P\(e^{rt}\)

where,

P = the initial amount

A = the final amount

r = the rate of interest

t = time

e is a mathematical constant where e ≈ 2.7183.

A = 10000 × \(2.71^{0.042*35}\)

A =  10000 × 4.04

A = $40400 approximately

Interest = Amount - Principle

Interest = 40400 - 10,000

Interest = $30400

Bank of America offers compound interest:

For compound interest:

\(A = P(1 + \frac{r}{n})^{nt}\)

A = 10000 × 4.51

A = $45100

Interest = Amount - Principle

Interest = 45100 - 10,000

Interest = $35100

The above calculation explains Bank of America is offering higher interest than 5/3rd bank by $35100 - $30400 = $4700

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The justification for the angle will be wrong because the angle does not depend on the radius of the circle.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Jaime makes the following claim. An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches.

The justification for the angle will be wrong because the angle does not depend on the radius of the circle.

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The correct answer is A histogram is the best way to summarize a large mass of data pictorially.

A histogram is an effective graphical representation for summarizing a large mass of data. It displays the distribution of values by dividing them into intervals or bins and showing the frequency or count of data points falling into each bin. The histogram provides a visual depiction of the data's range, central tendency, and variability. It allows for easy identification of patterns, outliers, and skewness in the data.

By observing the shape and characteristics of the histogram, such as the peaks, spreads, and gaps, one can gain insights into the underlying distribution and make comparisons between different data sets. Overall, a histogram provides a concise and informative summary of data in a visually appealing manner.

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The variance of cap beta_1 can be computed using the formula:

var(cap beta_1) = (var(u_i | X_1i, X_2i))/(n*var(X_1i))

When X_1i and X_2i are uncorrelated, we can plug in the given values to compute the variance of cap beta_1:

var(cap beta_1) = (6)/(300*2) = 0.01

When X_1i and X_2i are correlated with Corr(X_1i, X_2i) = 0.9, the variance of cap beta_1 will be larger. This is because the correlation between X_1i and X_2i will affect the variance of X_1i, making it larger. As a result, the denominator of the formula for var(cap beta_1) will be larger, leading to a smaller value for the variance of cap beta_1.

Therefore, the statement "When X_1i and X_2i are correlated, the variance of cap beta_1 is larger than it would be if X_1i and X_2i were uncorrelated. Thus, if you are interested in beta_1, it is best to leave X_2 out of the regression if it is correlated with X_1." is correct. By leaving X_2 out of the regression, we can avoid the issue of correlation between X_1i and X_2i affecting the variance of cap beta_1, leading to a more accurate estimate of beta_1.

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Answer:

$37.26

Explanation:

firstly, we find the total original price: $34 + $12 = $46.

next, we can multiply this by 100% - 25% = 75% to find the discounted price:

$46 × 75%

= $46 ÷ 100 × 75

= $34.50

finally, add on the sales tax which is 100% + 8% = 108%:

$34.50 × 108%

= $34.50 ÷ 100 × 108

= $37.26

i hope this helps! :D

The probability that the mean height of the sample is 0.6826. The correct answer is option c.

To solve this problem, we need to use the central limit theorem, which states that the sample means of a large enough sample size from a population with a known mean and standard deviation will be approximately normally distributed.

In this case, we are given that the heights of 18-year-old men are normally distributed with a mean of 67 inches and a standard deviation of 3 inches. We want to find the probability that the mean height of a random sample of nine 18-year-old men is between 66 and 68 inches.

First, we need to find the standard error of the mean, which is calculated by dividing the standard deviation by the square root of the sample size:

standard error of the mean = 3 / sqrt(9) = 1

Next, we need to standardize the sample mean using the z-score formula:

z = (sample mean - population mean) / standard error of the mean
z = (66 - 67) / 1 = -1
z = (68 - 67) / 1 = 1

We can now use a standard normal distribution table to find the area under the curve between z = -1 and z = 1. This area represents the probability that the sample mean falls between 66 and 68 inches.

Looking at the table, we find that the area between z = -1 and z = 1 is 0.6826. Therefore, the probability that the mean height of a random sample of nine 18-year-old men is between 66 and 68 inches tall is c. 0.6826.

Therefore the correct answer is option C.

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Answer:

(i) 12 = 2 x 2 x 3 => 2² x 3¹

(ii) 144 = 2 x 2 x 2 x 2 x 3 x 3 => 2⁴ x 3²

(iii) 5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 => 2⁴ x 3² x 5¹ x 7¹

Step-by-step explanation:

(a) Express each of these numbers as a

product of its prime factors in index

notation.

(i) 12 = 2 x 2 x 3 => 2² x 3¹

(ii) 144 = 2 x 2 x 2 x 2 x 3 x 3 => 2⁴ x 3²

(iii) 5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 => 2⁴ x 3² x 5¹ x 7¹

Answer:

4x + 4

Step-by-step explanation:

Answer:.83

Step-by-step explanation:

Khan academy

From the discrete distribution given, the standard deviation is of 0.83 children.

The distribution is:

\(P(X = 1) = 0.5\)

\(P(X = 2) = 0.25\)

\(P(X = 3) = 0.25\)

Hence:

\(\sqrt{V(X)} = \sqrt{0.5(1 - 1.75)^2 + 0.25(2 - 1.75)^2 + 0.25(3 - 1.75)^2} = 0.83\)

The standard deviation is of 0.83 children.

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Answer:

148

Step-by-step explanation:

Average = sum of numbers /total numbers

let x = 5th number

123.2 = (118+ 128 + 124,+ 98 + x) / 5

123.2 = (468 + x) / 5

Multiply both sides by 5

616 = 468 + x

x = 148

Answer:

Are you stuck step-sis?

Step-by-step explanation:

Answer:

$36

Step-by-step explanation:

.45 × 80 = 36

or

45/100 × 80 = 36

Answer:

$ 36

Step-by-step explanation:

hope it helps !

......

Answer: the four consecutive even integers are 12, 13, 14 and 15. To check the correctness of answer, let us take sum of these to confirm that these adds up to 54. Means the three consecutive numbers are correct. The product of two consecutive negative even integers is 24.

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