1) Find the total area of each figure. *10 points35533839Ο Ο Ο Ο4041

The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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The percent of students that preferred alternative ​music is 23.7%

The music type and the preference are given as:

Music Preferences

Rap            945

Alternative 462

Rock and Roll 275

Country         168

Jazz              15

Other          85

From the above table, we have:

Alternative = 462

Total = 945 + 462 + 275 + 168 + 15 + 85

Total = 1950

The percentage is then calculated as:

Percentage = Alternative/Total * 100%

This gives

Percentage = 462/1950 * 100%

Evaluate

Percentage = 23.7%

Hence, the percent of students that preferred alternative ​music is 23.7%

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Answer:

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form:

\(y=mx+b\)

Perpendicular lines have slopes that are negative reciprocals.

We're given:

1) Determine the slope

Let's first rearrange this equation into slope-intercept form:

\(4x-5y=-10\\-5y=-4x-10\\\\y=\dfrac{4}{5}x+2\)

Notice how \(\dfrac{4}{5}\) is in the place of m in y = mx + b. This is the slope of the give line.

Since perpendicular lines are negative reciprocals, we know the slope of the other line is \(-\dfrac{5}{4}\). Plug this into y = mx + b:

\(y=-\dfrac{5}{4}x+b\)

2) Determine the y-intercept

We're also given that the line passes through (6,3). Plug this point into our equation and solve for b:

\(y=-\dfrac{5}{4}x+b\\\\3=-\dfrac{5}{4}(6)+b\\\\b=3+\dfrac{5}{4}(6)\\\\b=\dfrac{21}{2}\)

Plug this back into our original equation:

\(y=-\dfrac{5}{4}x+\dfrac{21}{2}\)

\(y=-\dfrac{5}{4}x+\dfrac{21}{2}\)

Answer:

YU = 4.82.  angle STR = 23°

Step-by-step explanation:

7) Angle between U and V = 72°, since angles on a straight line add up to 180°. so angle UV = 180 - 108 = 72°.

similarly, angle YU = 180 - 85 - 72 = 23°.

length of circumference of full circle = π X diameter = π (2r)

= 2πr (radius = half of diameter).

circumference = 2π(12) = 24π.

there are 360° in full circle.

remember that angle YU = 23°.

length YU = (23/360) X 24π

= (23π)/15

= 4.817

= 4.82 to nearest one hundredth.

8) triangle RST sits inside of half the circle, ie in the semicircle.

angle RST = 90° because the angle in a semicircle =  90°.

there are 180° in a full triangle.

since angle RST = 90°, angle STR must be less than 180 - 90.

angle STR < 90°. so STR must be 23°.

The Alpha product is $1,836,000, and the Beta product, is $816,000 and the total amount of traceable fixed manufacturing overhead.

To determine the total amount of traceable fixed manufacturing overhead for each of the two products, we need to refer to the given information.

For the Alpha product:

The direct materials cost per unit is $25.

The direct labor cost per unit is $22.

The variable manufacturing overhead cost per unit is $17.

The traceable fixed manufacturing overhead cost per unit is $18.

To calculate the total amount of traceable fixed manufacturing overhead for Alpha, we multiply the traceable fixed manufacturing overhead cost per unit ($18) by the annual production capacity (102,000 units):

Total traceable fixed manufacturing overhead for Alpha = $18 * 102,000 = $1,836,000.

Similarly, for the Beta product:

The direct materials cost per unit is $10.

The direct labor cost per unit is $21.

The variable manufacturing overhead cost per unit is $12.

The traceable fixed manufacturing overhead cost per unit is $8.

To calculate the total amount of traceable fixed manufacturing overhead for Beta, we multiply the traceable fixed manufacturing overhead cost per unit ($8) by the annual production capacity (102,000 units):

Total traceable fixed manufacturing overhead for Beta = $8 * 102,000 = $816,000.

Therefore, the total amount of traceable fixed manufacturing overhead for the Alpha product is $1,836,000, and for the Beta product, it is $816,000.

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Answer:

57,000

Step-by-step explanation:

Answer:

Answer: 136.6 ft far apart are the cats

The value of distance between the cats are,

⇒ 136.6 feet

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Kristen stands in her backyard and watches two cats.

Here, First she looks to her cat, which is 100 feet away from her. She turns 115 degrees and views her neighbor's cat.

And, The neighbor's cat is 60 feet away from her.

Hence, We can formulate;

⇒ c² = 100² + 60² - 2×100×60 × cos 115°

⇒ c² = 10000 + 3600 - 12000 × - 0.422

⇒ c² = 18671.2

⇒ c = 136.6 feet

Thus, The value of distance between the cats are,

⇒ 136.6 feet

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Answer:

A. 24

B. I don't think you can make any since you can't repeat numbers and there is only two even numbers

Also, if you use all six numbers, it's 120 combos

The equation is  \(g(x) = -\frac{1}{16} (x - 1)^2 + 2\)  Graphing this equation below, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.

To graph function g, we need to find its equation that satisfies the given properties. We know that the y-intercept of g is less than that of f, so we can choose it to be 1. Also, the parabola of g opens downwards and its vertex is between the two x-intercepts, which are at x = -2 and x = 4. We can use these points to find the equation of the parabola in the standard form: g(x) = a(x - h)² + k. Using the fact that g(0) = 1 and the x-intercepts, we can solve for a, h, and k. The resulting equation is:

\(g(x) = -\frac{1}{16} (x - 1)^2 + 2\)

Graphing this equation, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

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Answer:

the answer would be 10

Step-by-step explanation:

Using the given frequencies, the probabilities for the next color chosen is:

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

There were 50 markers, of which 12 were yellow, 37 blue and 1 red, hence the probabilities for each are given as follows:

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Step-by-step explanation:

30/6+3 = 5+3 = 8

hope this helps you.

Answer:

The answer is 48 :)

Answer:18

Step-by-step explanation: 19-7=12 bolts and 7+7=14 so 12-14=18

If a sample of 7 bolts is selected, then the probability that all in the sample are defective = \(\frac{7}{50388}\)

If a sample of 7 bolts is selected, then the probability that none in the sample are defective = \(\frac{66}{4199}\)

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

\(^nC_r=\frac{n!}{r!(n-r)!}\)

For given question,

Out of 19 bolts, 7 bolts are defective.

So 19 - 7 = 12 bolts are non-defective.

If sample of 7 bolts is selected.

The total number of ways of selecting 7 bolts from the 19 bolts.

Using combination formula,

\(^{19}C_7\\\\=\frac{19!}{7!(19-7)!} \\\\=50388\)

Let event A:  all bolts in the sample are defective

n(A) = 7

So the probability that all in the sample are defective would be,

\(P(A)=\frac{7}{50388}\)

Let event B: no bolt in the sample are defective

This means the sample of 7 bolts has non-defective.

The total number of ways of selecting 7 bolts from the 12 non-defective bolts.

Using combination formula,

\(^{12}C_7\\=\frac{12!}{7!(12-7)!}\\\\ =792\)

son n(B) = 792

So, the probability that none in the sample are defective would be,

\(P(B)=\frac{792}{50388} \\\\P(B)=\frac{66}{4199}\)

Therefore,  If a sample of 7 bolts is selected, then the probability that all bolts in the sample are defective = \(\frac{7}{50388}\)

If a sample of 7 bolts is selected, then the probability that none in the sample are defective = \(\frac{66}{4199}\)

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let x = the number of 2-point baskets Anya made

y = the number of 3-point baskets Anya made

Equations:

x + y = 14

2x + 3y =

Multiply the 1st equation by 3 to get:

3x + 3y = 42

Subtract above equation by 2nd equation to get:

(3x-2x) + (3y - 3y) = 42 -30

x = 12

Anya made 12 2-point baskets.

The article shows that it may make it easier for the government to have access to a person's private information and to conduct unwarranted searches and seizures.

A person's Fourth Amendment rights is related to the right of an individual to be protected from unwarranted searches and seizures by the government.

According to the articles, Goo_gle's mission is to give

everyone access to as much information as possible.

This however would make it easier for a person's personal belongings or private information to be a target of government officials.

Therefore, Goo_gle's mission may make it easier for the government to have access to a person's private information making it easier to conduct unwarranted searches and seizures.

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The methods would best describe the study above is: controlled experiment or letter C.

In this study described that factory wants to increase productivity by changing the working environment and specifically decreasing the temperature by 10 degrees.

In this case the controlled experiment is the most possible to be. Because is a manipulating one or more variables while keeping other variables constant. When controlling other factors and only manipulating the temperature, they can assess the specific impact of temperature on productivity.

In this case, the correct answer is C.

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Answer:

7.5

Step-by-step explanation:

The perimeter of the regular pentagon will be 7.5 units.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The sides of the regular polygon are 3(x - 1) and (5x - 6). Then the value of the variable x will be

3(x - 1) = 5x - 6

3x - 3 = 5x - 6

2x = 3

x = 1.5

Then the side length of the regular pentagon will be

Side = 3(1.5 - 3)

Side = 3 (0.5)

Side = 1.5

Then the perimeter of the regular pentagon will be

P = 5 x 1.5

P = 7.5 units

The perimeter of the regular pentagon will be 7.5 units.

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The diagonal matrix D has the eigenvalues 7, 2, and 3 along the diagonal.

To diagonalize matrix A, we first need to find the eigenvalues and eigenvectors.

The eigenvalues can be found by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue.

For the given matrix A, the characteristic equation is:

\(\begin{vmatrix}4 - \lambda & 1 & 2 \1 & 4 - \lambda & 2 \1 & 1 & 5 - \lambda\end{vmatrix} = 0\)

Expanding the determinant and solving for λ, we find the eigenvalues are λ = 7, 2, and 3.

Now, we find the corresponding eigenvectors by solving the equation Av = λv for each eigenvalue. For each eigenvalue, we can write the equation as (A - λI)v = 0 and solve for v.

For example, for λ = 7, we have:

\(\begin{bmatrix}-3 & 1 & 2 \1 & -3 & 2 \1 & 1 & -2\end{bmatrix}\begin{bmatrix}v_1 \v_2 \v_3\end{bmatrix} = \mathbf{0}\)

where the matrix on the left is (A - 7I) and the vector on the right is v.

Solving for v, we find that the eigenvector corresponding to λ = 7 is v = (1, 1, -2).

The diagonal matrix D can be written as:

\(\begin{bmatrix}7 & 0 & 0 \0 & 2 & 0 \0 & 0 & 3\end{bmatrix}\)

So, the diagonal matrix D has the eigenvalues 7, 2, and 3 along the diagonal.

The diagonalization of a matrix A is given by \(A = SD^{-1} S\), where D is a diagonal matrix with the eigenvalues along the diagonal, and S is the matrix of eigenvectors with the columns being the corresponding eigenvectors. \(S^ {-1}\) is the inverse of S.

Did you mean Diagonalize the matrix \(A = \left[\begin{array}{ccc}4&1&2\\1&4&2\\1&1&5\end{array}\right]\)  by finding the eigenvalues of A listed in increasing order, the corresponding eigenvectors, a diagonal matrix D, and a matrix S such that \(A = SD^{-1} S\).

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Answer:

b) no

Step-by-step explanation:

The regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, the relationship is determined to identify the relationship between density of seed planted and quality of lawn. The significance level is 1% which means strength of evidence is not strong enough to support the test.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

We know that,

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

a_n = a_1 + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.

When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.

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complete question:

what is the difference between the explicit formula and recursive formula for sequences when would you use one over the other​

We will use sine function, and length of the opposite side is \(\frac{25\sqrt{3}}{2}$\) feet.

To solve for the opposite side of the right triangle, we would use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

In this problem, we are given that one angle of the right triangle is 60 degrees and the hypotenuse is 25 feet. Let's label the opposite side as x and the adjacent side as y. Then we can use the sine function:

\($\sin 60^\circ = \frac{x}{25}$\)

Simplifying the left side, we have:

\($\frac{\sqrt{3}}{2} = \frac{x}{25}$\)

Multiplying both sides by 25, we get:

\($x = \frac{25\sqrt{3}}{2}$\)

Therefore, the length of the opposite side is \(\frac{25\sqrt{3}}{2}$\) feet.

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The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..

A vending machine automatically pours soft drinks into cups.

The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and a standard deviation of 0.4oz.

Examine figure 7.- and answer the following questions.

a) estimate the probability that the machine will overflow an 8oz cup.

Procedure:

Determine the z-score for 8

z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1

P(x>8) = P(z>1) = 0.1587..

-----------------------

b) Estimate the probability that the machine will not overflow an 8oz cup.

P(z<1) = 1 - 0.1587 = 0.8413..

-----------------

c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..; Rounded down you get 134 cups

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Answer:

2x-3 =  29

8x = 128

x+7 =  23

Step-by-step explanation:

The sum of the angles of a triangle is 180

2x-3 + 8x+ x+7 = 180

Combine like terms

11x+4 = 180

Subtract 4 from each side

11x+4-4= 180-4

11x = 176

Divide by 11

11x/11 =176/11

x =16

2x-3 = 2*16-3 =32-3 = 29

8x = 8*16 =128

x+7 = 16+7 = 23

Answer:

From Thursday to Friday, the change in the depth was 19/16 inches

or as a mixed number, 1 3/16 inches

Step-by-step explanation:

From Monday to Thursday, the depth of a snowdrift changed by 2 3/8 inches

now, 2 3/8 = 2(8/8)+(3/8) = 16/8 + 3/8 = (16+3)/8

so, 2 3/8 = 19/8 inches = depth change from monday to thursday

From Thursday to Friday, the depth changed by half as much,

so,

depth change from Thursday to Friday = 1/2(depth change from Monday to Thursday)

depth change from thursday to friday = 1/2(19/8) = 19/16 inches