A 9-pack of popsicles costs $4.77. What is the unit price?

One statement that is necessarily true when a quadrilateral is inscribed in a circle is that the opposite angles of the quadrilateral are supplementary. In other words, the sum of the measures of two opposite angles is always 180 degrees.

To understand why this is true, let's consider a specific example. Imagine a quadrilateral PQRS inscribed in circle A. Let's say angle PQR measures 80 degrees. Since angle PQR is an inscribed angle that intercepts arc PS, it is equal in measure to half the measure of arc PS. Therefore, arc PS measures 160 degrees.

Now, let's focus on angle PSR. Angle PSR also intercepts arc PS, so it has the same measure as half the measure of arc PS, which is 160 degrees. Therefore, angle PSR measures 160 degrees as well.

If we add the measures of angles PQR and PSR, we get 80 + 160 = 240 degrees. This violates the fact that the sum of the measures of angles in a quadrilateral is always 360 degrees. Thus, it is clear that angles PQR and PSR cannot both measure 80 degrees.

Based on this example, we can conclude that the opposite angles of a quadrilateral inscribed in a circle are supplementary. This means that their sum is always 180 degrees.

To Know more about  quadrilateral Visit:

https://brainly.com/question/31266965

#SPJ11

Answer:

y= -2/3x-3

Step-by-step explanation:

The independent samples t-test is the appropriate statistic to use when comparing the mean number of hours worked per week for males and females.

To compare the mean number of hours worked per week for males and females, you would use the independent samples t-test. The independent samples t-test is a statistical test used to determine if there is a significant difference between the means of two independent groups. In this case, the independent groups are males and females.

The t-test allows you to compare the means of the two groups and determine if any observed difference is statistically significant or simply due to chance. It takes into account the sample means, sample sizes, and sample variances of both groups.

By conducting the independent samples t-test, you can assess whether there is evidence to suggest that the mean number of hours worked per week differs significantly between males and females. If the p-value associated with the t-test is below a predetermined significance level (commonly 0.05), it suggests that there is a statistically significant difference in the mean number of hours worked per week between the two groups.

To learn more about the mean;

brainly.com/question/13451489

#SPJ1

Answer:

Largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.

Step-by-step explanation:

Design of a mural is 16 in. wide and 9 in. high.

Dimensions of the wall are 24 ft by 14 ft.

If we enlarge the size of the design along the width the wall, scale factor to be used,

Scale factor = \(\frac{\text{Width of the wall}}{\text{Width of the design}}\)

                    = \(\frac{24}{16}\)

                    = \(\frac{3}{2}\)

With the same scale factor, height of the design will be,

\(\frac{3}{2}=\frac{\text{Height of the wall used}}{\text{Height of the design}}\)

\(\frac{3}{2}=\frac{\text{Height of the wall used}}{9}\)

Width of the wall used = \(\frac{3\times 9}{2}\)

                                     = 13.5 ft

Therefore, largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.  

\(6a = 4.54 - 5b \\ a = \frac{227}{300} - \frac{5}{6} b \\ 6a = 4.54 - 5b \\ a = \frac{227}{300} - \frac{5}{6} \\ 3( \frac{227}{300} - \frac{5}{6} b) + 7b = 3.17 \)

\( 3( \frac{227}{300} - \frac{5}{6} b) + 7b = 3.17 \\ \frac{227}{100} - \frac{5}{2}b + 7b = 3.17 \\ \frac{9}{2}b = 0.9 \\ b = 0.2 \\ a = 0.59\)

\(~~~~~~~~\text{Perimeter of square} = 144\\\\\implies 4 \times \text{Side} = 144\\\\\implies \text{Side} = \dfrac{144}4\\\\\implies \text{Side} = 36\\\\\text{Hence the length of each side is 36 units.}\)

Answer:

36

Step-by-step explanation:

In a Square,

perimeter (p) = 144

Length of side (L) = ?

we know,

p=4*L

144 = 4 *L

L = 144/4

L = 36

Since, All side of Square are equal . so,the length of each side is 36.

Note : you hadn't give unit in your question .

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

To learn more on logarithms: https://brainly.com/question/30226560

#SPJ1

Answer:

x = y = -2

Step-by-step explanation:

Hope this helps

Answer:

\(y = - 2 \\ x = - 2\)

Step-by-step explanation:

\( - 5x - 3y = 16 \: \: = > 1 \\ y = x = > 2\)

Now you can write the 1st equation like this.

\( - 5x - 3y = 16 \\ x = y \\ so \: \: you \: \: \: can \: \: write \\ - 5y - 3y = 16 \: \: \: = > 3\)

Now simply Solve the 3rd equation

\( - 5y - 3y = 16 \\ - 8y = 16 \\ \frac{ - 8y}{ - 8} = \frac{16}{ - 8} \\ y = - 2\)

Now replace y as 2 in the 2nd equation like this

\(y = x \\ - 2 = - 2\)

Now let's check whether the answer correct or wrong

\( - 5x - 3y = 16 \\ - 5 \times - 2 - 3 \times - 2 = 16 \\ 10 + 6 = 16 \\ 16 = 16\)

Yes, the answer is correct

hope this helps you !!

Answer:

Part A:  \(\frac{1}{2}\)

Part B: \(\frac{10}{9}\)

Step-by-step explanation:

Part A: What is the reciprocal of 2.

2 is just \(\frac{2}{1}\) in fraction terms. To find the reciprocal, you just have to flip it over. That would get to \(\frac{1}{2}\). Therefore, the reciprocal is \(\frac{1}{2}\).

Part B: What is the reciprocal of 9 over 10?

9 over 10 in numerical terms is just \(\frac{9}{10}\). o find the reciprocal, you just have to flip it over. That would get to \(\frac{10}{9}\). Therefore, the reciprocal is \(\frac{10}{9}\).

Hope this helped! If not, please let me know! <3

Answer:

10/29

Step-by-step explanation:

\(2\frac{9}{10}=\frac{29}{10}\)

Reciprocal of \(\frac{29}{10}= \frac{10}{29}\)

The standard deviation of the sampling distribution of the sample mean is 0.02.

The standard deviation of the sampling distribution of the sample mean can be calculated using the formula:

σ/√n

Where σ is the population standard deviation and n is the sample size.

In this case, the population standard deviation (σ) is 0.2 and the sample size (n) is 100. Substituting these values in the formula gives:

0.2/√100

Simplifying, we get:

0.2/10 = 0.02

This means that if we were to take multiple random samples of size 100 from the population, the mean of each sample would vary around the population mean of 3.2, with a standard deviation of 0.02.

This is because the standard deviation of the sampling distribution represents the amount of variation in sample means around the population mean.

To learn more about sample click on,

https://brainly.com/question/13931800

#SPJ4

There is not sufficient evidence to conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.

To determine if there is sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased, we can use a hypothesis test.

Let p be the true proportion of families who eat dinner together seven nights a week. Our null hypothesis is that there has been no decrease in the proportion of families who eat dinner together seven nights a week:

H0: p = 0.32

Our alternative hypothesis is that the proportion has decreased:

Ha: p < 0.32

We will use a one-tailed z-test with an alpha level of 0.01.

First, we need to calculate the sample proportion, P:

P = 325/1089 ≈ 0.298

Next, we can calculate the test statistic, z0:

z0 = (P - p) / sqrt(p(1-p)/n)

where n is the sample size.

z0 = (0.298 - 0.32) / sqrt(0.32(1-0.32)/1089) ≈ -2.32

Finally, we can compare the test statistic to the critical value for a one-tailed z-test at an alpha level of 0.01. The critical value is -2.33. Since -2.32 is greater than -2.33, we fail to reject the null hypothesis.

Therefore, there is not sufficient evidence to conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.

To learn more about hypothesis visit:  https://brainly.com/question/29519577

#SPJ11

Answer:

probably 18

Step-by-step explanation:

144 divided by 8 is 18

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

To learn more about linear equations refer to:

https://brainly.com/question/2030026

#SPJ1

Answer:

x=53

y=26

H=106

G=93

Step-by-step explanation:

By the inscribed quadrilateral conjecture:

\(2x+(x+21)=180\\(3y+9)+(4y-11)=180\\3x+21=180\\3x=159\\x=53\\7y-2=180\\7y=182\\y=26\\H=2(53)=106\\G=(4(26)-11)=104-11=93\)

Hope this helps!

The category in the Excel Options dialog box that contains the option to change the user name is "General".

In the Excel Options dialog box, the category that contains the option to change the user name is the General category.

Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.

We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.

What are the primary three graphs?

How to Use Graphs in Science

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.

To know more about graph click here

brainly.com/question/30934484

#SPJ11

Answer:

<a and <d; <b and <c.

Step-by-step explanation:

When two triangles are said to be similar, the ratio of the corresponding sides of both triangles is always the same, also, their corresponding angles are congruent. That is, they are equal.

The 2 set of angles that are corresponding angles of the two similar triangles given in the question above are:

<a and <d; <b and <c.

Both set of angles are congruent to each other. In other words, they are equal.

Answer: yes

Step-by-step explanation:

yes

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Note that the Se and Sp of the screening test are 22.7 and  99.8 respectively.

SE and SP refer to  Sensitivity and Specificity.

The mathematical terms sensitivity and specificity indicate the accuracy of a test that reports the presence or absence of a disease. Individuals who have the ailment are called "positive," while those who do not are considered "negative."

Sensitivity is a measure of how effectively a test can detect genuine positives, while specificity is a measure of how well a test can identify real negatives:

Learn more about Sensitivity and Specificity at:

https://brainly.com/question/31606814

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

What are the Se and Sp of the screening test? (Report the answer as a percentage with one decimal place)

See attached image.

The five number summary and interquartile range for the data-set is given by:

In this problem, we have that:

More can be learned about five number summaries at brainly.com/question/17110151

#SPJ1

Answer:

20

Step-by-step explanation:

Divisors of 100

1, 2, 4, 5, 10, 20, 25, 50, 100

Step-by-step explanation:

the factor of 100 of this numbers is

20

Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

Writing linear equations given two points can be a useful skill when graphing linear equations.

To learn more about linear equation refer to:

https://brainly.com/question/2030026

#SPJ1

Answer:

$3624

Step-by-step explanation:

He earned $3624 because 3% of 120,800 is $3624

Answer:

You would have $25.20

if it was 25.02 the 0 would be included, money can be rounded like this too

Answer:

Yeah he/she is correct because I did that too.

Step-by-step explanation:

The experimental group is given the experimental treatment, and the comparison group is statistically significant.

To learn more about random sampling refer to :

https://brainly.com/question/24466382

#SPJ4

The formula E3 + E4 can b expressed in the form of absolute cell address, that is option (a) $E$3+$E$4

The given formula is

E3 + E4

In the absolute cell address the coordinates of the column and row will be constant while copying a formula from one cell to the other. Here we use the dollar sign "$" before the coordinates of the column and row to correct them.

The given formula is E3 + E4

The E is the name and 3 and 4 are the coordinates of the column and row

The absolute cell address =  $E$3+$E$4

Therefore, the absolute cell address of the given formula is $E$3+$E$4

Learn more about absolute cell address here

brainly.com/question/7541791

#SPJ4

Answer:

(1)C- Trapezoid

(2)D-20 square feet

Step-by-step explanation:

Question 1

A cross-section of a rectangular pyramid cut perpendicular to the base but not passing through the top will have two parallel sides where one of the sides will be longer. Therefore, the shape which describes the cross-section will be a trapezoid.

Question 2

The base of the Triangle = 5 feet

Height of the Triangle = 8 feet

\(\text{Area of a triangle}=\dfrac12 \times $Base \times Height\\=\dfrac12 \times 5 \times 8\\=20 ft^2\)

1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

Learn more about wavelength:

brainly.com/question/31143857

#SPJ4