12 shirts cost $59.36. Find the unit rate.

The length of the median of the trapezoid is 12 units.

What is trapezoid?

Let the parallel sides be  x and x+4

The area of a trapezium is  the average or the parallel sides multiplied by the height

Area = [(x + x+ 4)/2 ] *h

= [ (2x+4)/2] * 5

= [2(x+2)/2] * 5

Area = 5(x+2)

60 = 5(x+2)

60/5 = x+2

12 = x+2

x = 12 - 2

x = 10

The parallel sides are 10 and 14 units.

Now the median length is the average of the parallel side lengths

Length of median = (10+14)/2

Length of median = 12 units

Hence, the length of the median of the trapezoid is 12 units.

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As per the unitary method, the number of students in the auditorium is 108

Unitary method.

In algebra, the process of finding the value of a single unit, and based on this value is known as unitary method.

Given,

Students filled 6 rows in Level 1 of Section A and 3 rows in Level 3 of Section B.

Here we need to find the number of  students were seated in the auditorium.

As per the given table, in level 1, the total number of rows in A section is 9.

So, the number of students is

=> 9 x 6

=> 54

Similarly, there are 3 rows in Level 3 of Section B.

So, the number of students in the level 2,

=> 3 x 18

=> 54

Therefore, the total number of students is,

=> 54 + 54 = 108

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The required reasons statements to prove the congruency of the angles  the value of x, and the measures of ∠2 and ∠4 are as follows;

Problem 1

The question and the diagram indicates that ∠1 and ∠3 are vertical angles formed by two lines, therefore, ∠1 and ∠3 are both a linear pair and therefore supplementary to ∠2, indicating that m∠1 = m∠3, therefore;

∠1 ≅ ∠3

Problem 2

Supplementary angles are angles that have a sum of 180°

The reasons for the statements in the completed table of the two column method used to prove ∠1 ≅ ∠3 are as follows;

Statement         [tex]{}[/tex]                                      Reasons

1. ∠1 and ∠3 are vertical angles [tex]{}[/tex]       1. Given

2. ∠1 and ∠2 form a linear pair [tex]{}[/tex]        2. Definition of linear pair

∠2 and ∠3 form a linear pair

3. ∠1 and ∠2 are supplementary [tex]{}[/tex]     3. Linear pair ∠s are supplementary

∠2 and ∠3 are supplementary

4. m∠1 + m∠2 = 180°        [tex]{}[/tex]                 4. Definition of supplementary ∠s

m∠2 + m∠3 = 180°

5. m∠1 + m∠2 = m∠2 + m∠3        [tex]{}[/tex]    5. Substitution property

6. m∠1 = m∠3        [tex]{}[/tex]                            6. Subtraction property      

7. ∠1 ≅ ∠3        [tex]{}[/tex]                                  7. Definition of congruency

Problem 2

∠2 = 4·x - 4

∠4 = x + 50

∠2 and ∠4 are vertical angles, therefore;

∠2 ≅ ∠4 (Vertical angle theorem)

m∠2 = m∠4 (definition of congruency)

4·x - 4 = x + 50 (substitution property)

4·x - x = 4 + 50 = 54

3·x = 54

x = 54 ÷ 3 = 18

x = 18°

m∠2 = (4 × 18 - 4)° = 68°

m∠3 = (18 + 50)° = 68°

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The probability of having L greater than Shelia's mean glucose level is 0.03 for L = 144.48.

Sheila's glucose level is shown to have a normal distribution, with a mean of 128 mg/dl and a standard deviation of 8 mg/dl.

L represents the patient's blood test level.

The probability that the mean glucose level, 128 mg/dl, is greater than L is given as 0.03.

To find L,

P(128>L) = 0.03

= 1 - P(128 ≤ L) = 0.03

=P(128 ≤ L) = 0.98

We know that we can find the probability of any normal distribution by converting it to standard form and then checking the p-value.

P(X < x) = Φ[(x - μ)/σ]

μ = mean

σ = standard deviation

=Φ[(L - 128)/8] = 0.98

Therefore ,

(L - 128)/8 = 2.06

= L - 128 = 16.48

= L = 128 + 16.48

= 144.48

= L

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R(t)=6.6 for t, 5 minutes, the domain of R relative to this context [0, 65 ÷ 6], the range of R related to this context, the domain of R relative to this context, [0, 12], and the range of R relative to this context.

The values of variables, domain, and range:

a) 12 - 1.2t, Using the build equation.

b) Least length = 0 mm.

max time = 12 - 1.2t = 0

t = 65 ÷ 6 minutes.

domain t ∈ [0, 65 ÷ 6]

c) range, R ∈ [0, 12]

d) domain of [tex]R^{-1}[/tex] [0, 12]

e) domain of [tex]R^{-1}[/tex] [0, 65 ÷ 6]

f) 12 - 1.2t = 7

1.2t = 7

t = 5

R(t)=6.6 for t, 5 minutes.

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The statement: transformations are mathematical operations that map 3d space to 2d space and so mathematics has standard ways to represent them is false.

What is 3D to 2D projection?

A three-dimensional (3D) object is displayed on a two-dimensional (2D) surface using a 3D projection, also known as a graphic projection. In order to project a complex object for viewing capability on a simpler plane, these projections rely on visual perspective and aspect analysis.

The fundamental method is: u = x / z; v = y / z; if you're converting from world-space (x, y, z) coordinates to screen-space (u, v) coordinates. Before applying the projection matrix, transform (x, y, z) by the view matrix if the camera is not positioned at the origin.

Hence, the statement transformations are mathematical operations that map 3d space to 2d space and so mathematics has standard ways to represent them is false.

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Answer: 5%

Step-by-step explanation:

To find the percentage you put the part over the whole so in this case it would be 6/120 or 6÷120

pop that into a calculator and you get 0.05  or    [tex]\frac{5}{100}[/tex] or 5%

Hope that helps

No as their no difference in Mr. Goodman's evaluation and the History department

What is Statistics ?

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

descriptive statistics types in mathematics The data in this type of statistics is summarized using the provided observations. Statistics that are inferential. To interpret the meaning of descriptive statistics, this kind of statistics is employed. Example of Statistics.

Seeing the data we can conclude that their no difference in Mr. Goodman's evaluation and the History department

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To compare the weight of a flea and an ant, we first need to convert the weight of the flea and the ant to the same units. Since the weight of the flea is given in decigrams and the weight of the ant is given in milligrams, we can convert the weight of the flea to milligrams by multiplying it by 10.

We can use the following equation to calculate the weight of the flea in milligrams:

weight of flea in milligrams = 8 decigrams * 10 = 80 milligrams

Once we have the weight of the flea and the ant in the same units (milligrams), we can subtract the weight of the ant from the weight of the flea to find the difference in their weights.

We can use the following equation to calculate the difference in weight between the flea and the ant:

difference in weight = weight of flea - weight of ant

difference in weight = 80 milligrams - 3 milligrams

difference in weight = 77 milligrams

Therefore, a flea weighs 77 milligrams more than an ant.

When bananas cost 75 cents per pound over the previous month, the increase was 8%. Today, we notice that the price per pound has increased to 81 cents.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Here,

The solution is attached in image.

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Answer:

  100°

Step-by-step explanation:

You have two supplementary angles in the ratio 7:2, and you want the measure of their positive difference.

The sum of supplementary angles is 180°. The sum of the ratio units in the ratio 7:2 is 7+2 = 9, so each ratio unit must stand for 180°/9 = 20°.

The difference in ratio units is 7 -2 = 5, so the difference in the angles will be 5·20° = 100°.

The measure of their difference is 100°.

__

Additional comment

The two angles are 7·20° = 140°, and 2·20° = 40°. The difference is 140° -40° = 100°.

The completing the square leads to the equivalent equation of (x +5)² = -2.

The given quadratic equation is-

 x² + 10x = -27

Now, add a square of 1/2 of  coefficient of 'x':

x² + 10x + 5² = -27 + 5²

x² + 10x + 5² = -27 + 25

Write this equation in the form of perfect square as;

(x +5)² = -2

Thus, the completing square leads to the equivalent equation of (x +5)² = -2.

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Answer:

it is actually 35

Step-by-step explanation:

This is because the plot is accelerating not decreasing also like if you think peter griffin is in! EPIC

We get

(A) The probability that her winnings will exceed zero is 0.50.

(B) The probability that her winnings will be less than zero is 0.25.

(c) Her winnings' estimated worth is 0.

Given that,

A player engages in a game where the odds of winning or losing one dollar are equal. The games are stand-alone. The game will be played until the first win occurs, at which point the player will instantly stop.

We have to find

(A) determine the probability that her winnings will exceed zero.

(B) calculate the probability that her winnings will be less than zero.

(c) calculate her winnings' estimated worth.

We know that,

a) probability that her winnings are greater than zero =P(wins 1st game) =1/2 =

b) probability that her winnings are less than zero =P(lose 1st 2 games) =(1/2)×(1/2 )=1/4 =0.25

c) below is pmf of X (gain from the game)

P(X=1)=P(win 1st game) =1/2

P(X=0)=P(lose 1st and win 2nd) =(1/2)×(1/2) =1/4

P(X=-1)=P(lose 1st two and wins 3rd)=(1/2)×(1/2)×(1/2) =1/8

P(X=-2)=1/16

therefore expected value E(X )=ΣxP(x) =1×1/2+0×1/4-1×1/8-2×1/16........

= (1/2)+0-(1×1/8+2×1/16+3×1/32+4×1/64+...)

=(1/2)-(1/4)×(1/(1/2))

=(1/2)-(1/2)

=0

Therefore,

(A) The probability that her winnings will exceed zero is 0.50.

(B) The probability that her winnings will be less than zero is 0.25.

(c) Her winnings' estimated worth is 0.

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Answer:

b. 8.33

Step-by-step explanation:

"mean" is the math word for what non-math people call average. This is where you add up all the numbers and divide by however many there are.

3+5+8+11+11+12 is 50

There are 6 numbers in the data set. So 50/6 is 8.3333...

b. 8.33 is the correct answer.

Mean means add and divide.

The slope of a line perpendicular to the given equation of line is 6.

For the stated question, the equation of the line is given as;

3x + 18y = 10

This can be written as;

y = -3/18 x  + 10/18

y = -1/6 x + 5/9

Comparing with general equation of line in slope intercept form.

y = mx + c

slope m = -1/6

The relation of slope for the two perpendicular lines are-

m x m1 = -1

m1 = -1/(-1/6)

m1 = 6

Thus, the slope of a line perpendicular to the given equation of line is 6.

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the null and alternative hypotheses for the above scenario This is a left failed test.

What is confidence interval?

In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. Although 95% is the most common confidence level, confidence intervals can also be calculated at other levels, such 90% or 99%. The confidence level is the proportion of linked CIs over the long run which really contain the true value of the parameter. The breadth of the CI may be influenced by a number of variables, including sample size, sample variability, and degree of confidence. If all other factors were same, a larger sample would lead to a narrower confidence interval. A sample with greater variability would result in a broader confidence interval and a higher level of confidence.

a newsletter publisher believes that less than 46% of their readers own a rolls Royce.

there is sufficient evidence at the 0.01 level to substantiate the publisher's claim

The null hypothesis (Mo) in this case has a P value of 0.46. P 0.46 Alternative Hypothesis (Ha) (claim)

The left test failed here.

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Yes, the given data provide convincing evidence that the Nuthatches prefer particular types of trees while searching for seeds and insects.

A statistical hypothesis test used to examine if a variable is likely to come from a given distribution is the Chi-square goodness of fit test. It is frequently used to assess how well sampling data represents the entire population.

Given that the number of red-breasted nuthatches (n) is 156. By convention, the significance level is α=0.05.

First, let's state the null hypothesis and alternate hypothesis.

Null hypothesis H₀: Nuthatches don't prefer particular types of trees while searching for seeds and insects.

Alternate hypothesis H₁: Nuthatches prefer particular types of trees while searching for seeds and insects.

Given: p₁=54%=0.54, p₂=40%=0.40, p₃=6%=0.06

The expected frequency (E) for each probability is:

[tex]\begin{aligned}E_1&=np_{1}\\&=156\times0.54\\&=84.24\\E_2&=np_{2}\\&=156\times0.40\\&=62.4\\E_3&=np_{3}\\&=156\times0.06\\&=9.36\end{aligned}[/tex]

The observed values (O) are given as 70, 79, and 7. Calculating chi-square, we get,

[tex]\begin{aligned}\chi^{2}&=\sum\frac{(O-E)^2}{E}\\&=\frac{(70-84.24)^2}{84.24}+\frac{(79-62.4)^2}{62.4}+\frac{(7-9.36)^2}{9.36}\\&=7.4182\end{aligned}[/tex]

And the degree of freedom is given by df = n-1, where, n is the sample size. Here, the sample size is 3.

[tex]\begin{aligned}df&=n-1\\&=3-1\\&=2\end{aligned}[/tex]

Then, the P-value from the table is given by, [tex]P(\chi^{2} > 7.4182) = 0.0245[/tex].

This value is less than the significance level.  Therefore, the null hypothesis is rejected. So, an alternate hypothesis is accepted.

Therefore,  nuthatches prefer particular types of trees while searching for seeds and insects.

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Answer:

Explanation: The idea is to draw a Venn Diagram and find the intersection. We have one circle of 70 and another with 40. When we add the two circles plus the 10 students who joined neither, we should get 100 students.

Step-by-step explanation:

Answer:

it is 5 you don't add the 3 in it

The total number of tests they can grade in 3 hours are 90.

What is graded test?

Your grade in an exam or written assignment is the letter or number you receive as a mark that represents your level of proficiency.

A graded exercise test (GXT) is a screening tool for determining a person's level of fitness. The test measures the cardiovascular response to exercise in order to assess the participant's capacity for exercise.

Since, the number of minutes in 3 hours is:

= 3 x 60 minutes per hour

= 3 x 60

= 180 minutes

The number of tests that Sam can grade in these 3 hours is therefore:

= ( Number of total minutes / Minutes taken by Sam for 6 tests) x 6 tests

= ( 180 / 24) x 6

= 45 tests

The number of tests that Ben can grade are:

= ( Number of total minutes / Minutes taken by Ben for 5 tests) x 5 tests

= ( 180 / 20 ) x 5

= 45 tests

So, the total number of tests they can grade in 3 hours is:

= 45 + 45

= 90 tests

Hence, the total number of tests they can grade in 3 hours are 90.

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After solving, the observed statistic for this study is 2.5.

In the given question, a professor collected data.

After fishing a test, the 27 students in the class wrote their pedicted scores on their tests and these were compared with the actual scores after they were graded.

The mean predicted score was 83.7. So SD = 83.7.

The mean actual score was 81.2. So SD = 15.6

the aen of the difference was 2.5. So SD = 8.6

Null: The average difference in test score (predicted-actual) is 0. μ = 0

Alternative: The average difference in test score (predicted-actual) is greater than 0. μ > 0

We have to find the observed statistic for this study.

predict mean = 83.7   S.D = 8.6

actual mean = 81.2    S.D = 15.6

n = 27

x = (predict mean - actual mean )

x = 83.7 - 81.2

x = 2.5

Hence, the observed statistic for this study is 2.5.

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The right question is given below:

Answer:D

Step-by-step explanation:D

Answer:

c

Step-by-step explanatio

Answer:

Step-by-step explanation:

The line has a slope with a measure of 8 / 5.

According to Euclidean geometry, lines can be constructed by knowing the location of two distinct points on a plane. By analytic geometry we can determined the slope of the line by knowing these two points and using the secant line formula:

m = Δy / Δx

Where:

If we know that (x₁, y₁) = (- 2, - 5) and (x₂, y₂) = (2, 3), then the slope of the line shown in the picture is:

m = [3 - (- 5)] / [3 - (- 2)]

m = 8 / 5

The slope of the line is equal of 8 / 5.

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Orion Flour Mills will initially report the $590 insurance amount as prepaid insurance and expense over the first year of coverage is $72120.

Given that,

Lapeer Flour Mills spent money on the following items in addition to buying new machinery: $64,00 in purchase price, plus sales tax 5,450 equipment shipments, 890 equipment insurance for the first year, and 590 equipment installations 1,780

We have to find the above expenditures for the new machines.

We know that,

Total cost of new machine = Purchase price + Sales tax+ Shipment of machine+ Installation of machine

= $64000+$5450+$890+$1780

= $72120

Therefore, Orion Flour Mills will initially report the $590 insurance amount as prepaid insurance and expense over the first year of coverage is $72120.

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