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18. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. (IMAGE BELOW)

Given: ∠A is congruent to ∠B
Prove: ∠B is congruent to ∠A
Plan: Show that ∠A and ∠B have the same measure, thus ∠B and ∠A have the same measure under symmetry for equality. Conclude with ∠B being congruent to ∠A.

Answer:

3. 72.9%

Step-by-step explanation:

Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.

So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:

P(M∪C) = P(M) + P(C) - P(M∩C)

Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:

P(M) = 145/317 = 0.4574

There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:

P(C) = 167/317 = 0.5268

Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate  chip scones is:

P(M∩C) = 81/317 = 0.2555

Therefore,  P(M∪C) is equal to:

P(M∪C) = 0.4574 + 0.5268 - 0.2555

P(M∪C) = 0.7287

P(M∪C) = 72.9%

Answer:

3. 72.9%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.

There are 172 female customers and 317-172 = 145 male customers.

150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.

81 of those are male, so 167 - 81 = 86 are female.

So the total of desired outcomes is 86 + 145 = 231

Total outcomes:

317 total customers.

Probability:

231/317 = 0.729

So the correct answer is:

3. 72.9%

Answer:

A whole number that can be made by multiplying other whole numbers.

Example: 18 can be made by 3 × 6 so is a composite number.

16 can be made by 4 x 4 so it is a square root and a composite number

14 can be made by 2 x 7 so is is a composite number.

It is not a prime number as all Composite Number have factors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16,

Answer:

We need to examine the natural numbers.

The natural numbers are the counting numbers,

1, 2, 3, 4, 5, 6, ...

The number 1 is neither prime nor composite.

All natural numbers greater than 1 are either prime or composite.

A prime number is a number that has exactly two factors, itself and 1.

A composite number has more than 2 factors.

A composite number is a natural number greater than 2 that is not a prime number.

Examples:

Prime: 2, 3, 5, 7, 11, ...

Composite: 4, 6, 8, 9, 10, 12, ...

Answer:

The nearest time is 15 years or 180 months

Answer:

Average waiting time = 4 minutes

Step-by-step explanation:

From this question, we are told that the sky train is supposed to arrive every 8 minutes.

Thus, the waiting time of the passengers for the train = 8 minutes.

Then, the average waiting time is simply the mean or 50th percentile of the total waiting time.

So, average waiting time = 50% × 8

Average waiting time = 4 minutes

Answer:

5

Step-by-step explanation:

3(14+x) = 57

42 +3x = 57

3x = 15

x = 5

Answer:

  the least common denominator

Step-by-step explanation:

The least common denominator is that number. It is the least common multiple of the denominator values.

__

Simply multiplying by the product of the denominators will eliminate fractions, but may require reduction of fractions in the answer. If the "fractions" are rational expressions, extraneous solutions may be introduced.

Answer:

40°

Step-by-step explanation:

2x = 3x - 20 add like terms

x = 20 and angle l is equal to 3x minus 20 so 3 × 20 - 20 = 40°

Answer:

Step-by-step explanation:

Corresponding net sales before 1 month and after 1 month form matched pairs.

The data for the test are the differences between the net sales before and after 1 month.

μd = the​ net sales before 1 month minus the​ net sales after 1 month.

Before after diff

57.1 63.5 - 6.4

94.6 101.8 - 7.2

49.2 57.8 - 8.6

77.4 81.2 - 3.8

43.2 41.9 1.3

Sample mean, xd

= (- 6.4 - 7.2 - 8.6 - 3.8 + 1.3)/5 = - 4.94

xd = - 4.94

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (- 6.4 + 4.94)^2 + (- 7.2 + 4.94)^2 + (- 8.6 + 4.94)^2+ (- 3.8 + 4.94)^2 + (1.3 + 4.94)^2 = 60.872

Standard deviation = √(60.872/5

sd = 3.49

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (- 4.94 - 0)/(3.49/√5)

t = - 3.17

We would determine the probability value by using the t test calculator.

p = 0.017

Since alpha, 0.05 > than the p value, 0.017, then we would reject the null hypothesis. Therefore, at 5% significance level, the data indicate that the average net sales improved.

Answer:

The minimum score required for an A grade is 77.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 67.7, \sigma = 7.8[/tex]

Find the minimum score required for an A grade.

Top 12% of scores get an A.

100-12 = 88th percentile.

The 88th percentile of scores is the minimum required for an A grade. This score is X when Z has a pvalue of 0.88. So X when Z = 1.175.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.175 = \frac{X - 67.7}{7.8}[/tex]

[tex]X - 67.7 = 7.8*1.175[/tex]

[tex]X = 76.865[/tex]

Rounding to the nearest whole number:

The minimum score required for an A grade is 77.

Answer:

Jaleel is correct because 2 (x + 2) = 2x - 4

Step-by-step explanation:

To solve 2 (x - 2) + 2:

2 (x - 2) + 2

Distribute

2x - 4 + 2

Combine like terms

2x - 2

Lisa did not distribute correctly :)

Answer:

D

Step-by-step explanation:

Answer:

The velocity is v(t) = 2*t + a

a) we want to find the average velocity betwen t = 0 and t = 1.

We can do this as:

Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a

b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.

For this we can see the integral:

[tex]d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2[/tex]

Answer: 1/20

Step-by-step explanation:

Decimal Fraction Percentage

0.05 1/20          5%

Answer:

46.7%

Step-by-step explanation:

Given:

Total number of students in Mrs. Verner's class = 15

Number of girls = 8

To find: percentage are boys

Solution:

Percentage of boys = ( Number of boys / Total number of students ) × 100

Number of boys = Total number of students - Number of girls = 15 - 8 = 7

So,

Percentage of boys = [tex]\frac{7}{15}[/tex] × 100 = 46.7%

Answer:

I'm glad you asked!

Step-by-step explanation:

OK,let's simplify the number for a equivalent expression.

[tex]4+2(1+3x)[/tex]

Distribute:

[tex]=4+(2)(1)+(2)(3x)[/tex]

[tex]= 4+2+6x[/tex]

Combine Like Terms:

[tex]=4+2+6x[/tex]

[tex]=(6x)+(4+2)[/tex]

[tex]=6x+6[/tex]

The Final Answer is : [tex]6x+6[/tex]

The expression that is equivalent to 4+2(1+3x) is 6x+6.

Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.

Given, 4+2(1+3x)

Firstly distribute 2(1+3x) to get 2+6x then,

4+2(1+3x)

=4+2+6x

=6x+6

Thus, 4+2(1+3x)=6x+6

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Answer:

The expected value of profit is -$0.65.

Step-by-step explanation:

The rules of the lottery are as follows:

The probability of winning is, P (W) = 0.001.

Then the probability of losing will be,

P (L) = 1 - P (W)

       = 1 - 0.001

       = 0.999

Let the random variable X represent the amount of profit.

The probability distribution table of the lottery result is as follows:

Result      X        P (X)

Win      +349     0.001

Lose         -1       0.999

The formula to compute the expected value of X is:

[tex]E(X)=\sum X\cdot P(X)[/tex]

Compute the expected value of profit  as follows:

[tex]E(X)=\sum X\cdot P(X)[/tex]

         [tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]

Thus, the expected value of profit is -$0.65.

Answer:

15

Step-by-step explanation:

Because the two triangles are similar:

[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]

Hope this helps!

Answer:

[tex]= 8 \frac{27}{132} = 8\frac{9}{44}\\ [/tex]

Step-by-step explanation:

[tex]15 \frac{5}{11} - 7 \frac{3}{12} \\ \frac{170}{11} - \frac{87}{12} \\ \frac{2040 - 957}{132} \\ = \frac{1083}{132} \\ = 8 \frac{27}{132} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

8 9/44.

Step-by-step explanation:

15 5/11 - 7 3/12

= 15 - 7 + 5/11 - 1/4       The LCD of 4 and 11 is 44 so we have:

15 - 7 + 20/44 - 11/44

= 8 + 9/44

= 8 9/44.

Answer:

Thats not possible

Step-by-step explanation:

There is no:

Answer:

a. SST = 1816

SSR = 1511.804

SSE = 465.804

b. Coefficient of determination, R² = 0.832491079

c. The correlation coefficient r = 0.8636

Step-by-step explanation:

y = 23.194 + 0.318·x

Where:

x = Price

y = Overall score

The observed data are given as follows;

Brand                Price  Score

Bose                 180     76

Scullcandy       150      71

Koss                 95       62

Phillips/O'Neill 70       57

Denon              70       30

JVC                   35       34

[tex]SST = \sum \left (y - \bar{y} \right )^{2}[/tex]= 1816

[tex]SSR = \sum \left ({y}'-\bar{y{}'} \right )^{2}[/tex] = 1511.804

[tex]SSE = \sum \left (y - {y}' \right )^{2}[/tex] = 465.804

Coefficient of determination

[tex]Coefficient \, of \, determination = \dfrac{SSR}{SST}[/tex]= 0.832

Coefficient of correlation =

[tex]r = \dfrac{n\left (\sum xy \right )-\left (\sum x \right )\left (\sum y \right )}{\sqrt{\left [n\sum x^{2}-\left (\sum x \right )^{2} \right ]\left [n\sum y^{2}-\left (\sum y \right )^{2} \right ]}}[/tex]

Ʃxy  = 37500

Ʃx =600

Ʃy = 330

Ʃx² = 74950

Ʃy²  = 19966

[tex]r = \dfrac{6 \left (37500 \right )-\left (600 \right )\left (330 \right )}{\sqrt{\left [6\times 74950-\left (600 \right )^{2} \right ]\left [6 \times 19966-\left (330 \right )^{2} \right ]}} = 0.8636[/tex]

[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]

[tex]z_1z_2=12+8i+9i+6i^2[/tex]

[tex]i^2=-1[/tex], so

[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]

Answer:

a. In the explanation.

b. The point estimate of the difference can be calculated as the difference between the sample mean and the population mean:

[tex]d=M-\mu=24.95-23.8=1.15[/tex]

c. Test statistic t = 0.90

P-value = 0.1932

The null hypothesis failed to be rejected.

Step-by-step explanation:

We have a sample, wich mean and standard deviation are calculated as:

[tex]M=\dfrac{1}{14}\sum_{i=1}^{14}(27.8+23.84+25.25+21+17.52+19.61+...+26.94+27.24)\\\\\\ M=\dfrac{349.34}{14}=24.95[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{14}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(27.8-(24.95))^2+(23.84-(24.95))^2+...+(27.24-(24.95))^2]}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(8.106)+(1.238)+...+(5.23)]}\\\\\\ s=\sqrt{\dfrac{304.036}{13}}=\sqrt{23.39}\\\\\\s=4.8[/tex]

This is a hypothesis test for the population mean.

The claim is that the consumption of milk in the Midwest is significantly higher than the national average.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=23.8\\\\H_a:\mu> 23.8[/tex]

The significance level is 0.01.

The sample has a size n=14.

The sample mean is M=24.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.8.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.8}{\sqrt{14}}=1.28[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{24.95-23.8}{1.28}=\dfrac{1.15}{1.28}=0.9[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=14-1=13[/tex]

This test is a right-tailed test, with 13 degrees of freedom and t=0.9, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>0.9)=0.1932[/tex]

As the P-value (0.1932) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the consumption of milk in the Midwest is significantly higher than the national average.

The transformation matrix for the mapping T is the matrix T such that

[tex]\mathbf T(\vec x)=T\,\vec x[/tex]

where

[tex]T=\begin{bmatrix}1&4&0&0\\0&0&0&0\\0&3&0&1\\0&1&0&-1\end{bmatrix}[/tex]

The correct matrix A is

[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]

To find the matrix A that represents the linear transformation T, we need to determine the coefficients that map the input vector (X₁, X₂, X₃, X₄) to the output vector (x₁ +4x₂, 0, 3x₂ +x₄, x₂ -x₄)

By comparing the corresponding entries in the input and output vectors, we can determine the coefficients of the matrix A.

The first row of A will have the coefficients for X₁ and X₂, which are 1 and 4 respectively. The second row will have all zeros since the output vector has a zero in the second position. The third row will have the coefficient 3 for X₂ and 1 for X₄. Finally, the fourth row will have the coefficient 1 for X₂ and -1 for X₄.

Thus, the matrix A that implements the mapping T is:

[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]

Learn more about linear transformation here:

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We have a right triangle and we're given the leg lengths.  

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

tan X = YZ / XZ = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

Answer:

b. 4.9 × 1011

Step-by-step explanation:

Using scientific notation is similar to expressing in standard form. Given that (7 × 105)2

We open the parenthesis. This may first be expressed as

7² × 10⁽⁵⁾²

Then expand,

= 49 × 10¹⁰

To put in scientific notation, 49 = 4.9 × 10

Hence the expression becomes

= 4.9 × 10 × 10¹⁰

Using the laws of indices

= 4.9 ×  10¹¹ in scientific notation

Answer:

4.9 × 1011

Step-by-step explanation:

I did it in grandpoint

Answer:

36π

Step-by-step explanation:

area=πr²

=πx6x6

6x6=36

area = 36π

Answer:

[tex]47\frac{5}{8}[/tex]

Step-by-step explanation:

Weight from before + Weight gained

[tex]46\frac{3}{8} +1\frac{1}{4}[/tex]

Convert to improper fractions.

[tex]371/8 + 5/4[/tex]

Find the common denominator.

[tex]371/8 + 10/8[/tex]

Add.

[tex]381/8[/tex]

Convert to a mixed fraction.

[tex]47\frac{5}{8}[/tex]

Answer:

47 5/8 kg

Step-by-step explanation:

Ealier weight + gained weight = Monday's weight

46 3/8 + 1 1/4

= 371/8 + 5/4

= 371/8 + 10/8

= 381/8

= 47 5/8 kg

Answer:

64

Step-by-step explanation:

If the mean is 15, the sum of 5 numbers is:

Minimum value for the first four numbers would be:

Then the fifth number is:

So the maximum difference is:

Answer: 5x-3

Step-by-step explanation:

(f+g)(x) means f(x)+g(x). Knowing this, we add the 2 functions together.

2x-6+3x+9

5x-3

Answer:

7x+6 = 6x-3

Step-by-step explanation:

2 (x + 3) + 5 x = 3 (2 x - 1)

Distribute

2x+6+5x = 6x-3

Combine like terms

7x+6 = 6x-3

Answer:

7x + 6 = 6x - 3                                  Option A

Step-by-step explanation:

Now Jalesa wants to simplify this equation.

Firstly applying the distributive property

Distribute the 2 over the parenthesis and distribute the over the parenthesis

that is,

2*x + 2*3 + 5x = 3*2x - 3*1

2x + 6 + 5x = 6x - 3

After that combine like terms

2x + 5x + 6 = 6x - 3

7x + 6 = 6x - 3

Result is:

7x + 6 = 6x - 3

That's the final answer.