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Explanation

Part 1: tan 226

Angle 226 lies in the third quadrant. This can be seen below.

In the above, the principal angle is 226, therefore, the acute angle becomes,

Since tan is positive in the third quadrant, therefore

Answer: tan 46

Part B: Sin-46.6

In trigonomtery,

Therefore;

Answer: -sin 46.6

Answer:

125 boxes

Step-by-step explanation:

6,000/48 = 125

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Step-by-step explanation:

6. 7x + 7y = -11

7. -1x + 8y = 12

8. 9x + 11y = -7

A 14.2 million donation was made to a charity. The overall amount of the charity's contributed funds is 34 million if which amounts to 42% of those monies.

Let x represent the total amount of donations received by the charity.

According to the problem, 14.2 million represents 42% of the charity's donated funds:

14.2 million = 0.42x

We must isolate x on one side of the equation in order to find it. We can do this by dividing both sides of the equation by 0.42:

x = 14.2 million / 0.42

x = 33.80952381 million

Rounding this answer to the nearest million gives:

x ≈ 34 million

Therefore, the total amount of the charity's donated funds is approximately 34 million.

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Step-by-step explanation:

To find the quartile, decile, and percentile for the given dataset, we need to first organize the data in ascending order:

63.0, 63.4, 63.7, 64.2, 64.3, 69.1, 75.3, 81.6, 82.2, 82.9, 83.4, 84.2, 84.6, 84.6, 87.0

Now, we can use the following formulas to find the quartile, decile, and percentile:

Quartile: A quartile is a type of quantile that divides the dataset into four equal parts. To find the quartile, we can use the following formulas:

Q1 (first quartile): (n+1)/4th term

Q2 (second quartile or median): (n+1)/2nd term

Q3 (third quartile): 3(n+1)/4th term

Using the above formulas and the given data, we get:

Q1 = (15+1)/4 = 4th term = 64.3

Q2 = (15+1)/2 = 8th term = 81.6

Q3 = 3(15+1)/4 = 12th term = 84.2

Decile: A decile is a type of quantile that divides the dataset into ten equal parts. To find the decile, we can use the following formula:

D(n) = (n+1)/10th term, where n = 1, 2, ..., 9

Using the above formula and the given data, we get:

D1 = (15+1)/10 = 1.6th term = 63.4

D2 = 3.6th term = 64.2

D3 = 5.6th term = 69.1

D4 = 7.6th term = 81.6

D5 = 9.6th term = 82.9

D6 = 11.6th term = 84.2

D7 = 13.6th term = 84.6

D8 = 15.6th term = 87.0

Answer:

x = -12

m∠FCD = 29°

Step-by-step explanation:

Finding x:

Since m∠BCD = 95°, we can find x by the sum of the measures of angles BCF and FCD equal to 95:

m∠BCF + m∠FCD = m∠BCD

x + 78 + x + 41 = 95

(2x + 119 = 95) - 119

(2x = -24) / 2

x = -12

Thus, x = -12

Finding m∠FCD:

Now, we can find m∠FCD by plugging in -12 for x in x + 41:

m∠FCD = x + 41

m∠FCD = -12 + 41

m∠FCD = 29

Thus, m∠FCD = 29°

The final answer for the surface area of the prism is 32 m^2 + 16h m^2.

To find the surface area of the prism, we need to calculate the area of each face and sum them up.

The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:

Area of square face = side length^2 = 4^2 = 16 m^2

Since there are two square faces, the total area of the square faces is:

Total area of square faces = \(2 * 16 = 32 m^2\)

The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:

Area of rectangular face = length * width = \(4 * h = 4h m^2\)

Since there are four rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = \(4 * 4h = 16h m^2\)

Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:

Surface area of prism = Total area of square faces + Total area of rectangular faces

                          = \(32 m^2 + 16h m^2\)

                          = \(32 m^2 + 16h m^2\)

The answer for the surface area of the prism is 32 m^2 + 16h m^2.

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Answer:

area=47cm²

Step-by-step explanation:

Answer:

D) 0.69

Step-by-step explanation:

Given :

5 × 2³ˣ = 21

Divide by 5 on each side :

Taking the cubic root :

Using logarithm values :

Answer:

D.  0.69

Step-by-step explanation:

Given equation:

\(5 \cdot 2^{3x}=21\)

Divide both sides by 5:

\(\implies \dfrac{5 \cdot 2^{3x}}{5}=\dfrac{21}{5}\)

\(\implies2^{3x}=4.2\)

\(\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:\)

\(\implies(2^3)^x=4.2\)

\(\implies8^x=4.2\)

Take natural logs of both sides:

\(\implies \ln 8^x=\ln 4.2\)

\(\textsf{Apply the log Power law} \quad \ln x^n=n\ln x :\)

\(\implies x \ln 8=\ln 4.2\)

Divide both sides by ln 8:

\(\implies \dfrac{x \ln 8}{\ln 8}=\dfrac{\ln 4.2}{\ln 8}\)

\(\implies x=\dfrac{\ln 4.2}{\ln 8}\)

\(\implies x=0.690129776...\)

\(\implies x=0.69 \: \sf (2\:dp)\)

Answer:

see explanation

Step-by-step explanation:

vertical angles are angles on the opposite side at a vertex of 2 lines.

1 and 6 , 2 and 5 , 3 and 8 , 4 and 7 are all vertical angles

supplementary angles sum to 180°

adjacent angles on a straight line sum to 180°

1 and 2 , 3 and 4 , 5 and 6 , 7 and 8 are examples of supplementary angles.

Answer:

it should be girls 12 to 18

Step-by-step explanation:

i just messed around with a calculator and found it.

Answer:

40 is the correct answer

Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-16\(x^{8}\) / -8\(x^{9}\)

= (-16/-8)\(x^{8 - 9}\)

= 2 \(x^{-1}\)

= 2/x

Thus,

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

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Answer:

2500

Step-by-step explanation:

Dimensions of first level

Length = Breadth = 75 ft (since it is a square)

It is assumed that a person will occupy \(2.25\ \text{ft}^2\)

Area of first level

\(75\times 75=5625\ \text{ft}^2\)

When the area of the level is divided by the area of one person then we will get the number of people that can occupy the room or the number of tickets that can be sold.

\(\dfrac{5625}{2.25}=2500\)

The number of tickets that can be sold for the first level is 2500.

Answer:

answer mga dalog points

Step-by-step explanation:

mga Gago mga mini o

unsa Pana dha

mga hangol og points answer na

The 12-ounce bottle has the lesser cost per ounce, at $0.67 per ounce, compared to the 8-ounce bottle, which has a cost per ounce of $0.75.

Ounces (oz) is a unit of measurement for weight or mass in the imperial system and U.S customary units. The term "ounce" is commonly used to describe the weight of food items, precious metals, and other objects. In the context of cooking and baking, ounces are used to measure ingredients and portion sizes.

To compare the cost per ounce of the two bottles of shampoo, we need to divide the cost of each bottle by its size in ounces.

For the 12-ounce bottle, the cost per ounce is $8 / 12 ounces = $0.67 per ounce.

For the 8-ounce bottle, the cost per ounce is $6 / 8 ounces = $0.75 per ounce.

Therefore, the 12-ounce bottle has the lesser cost per ounce, at $0.67 per ounce, compared to the 8-ounce bottle, which has a cost per ounce of $0.75.

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Answer:

Option: D. y= 545x + 80

Step-by-step explanation:

Linear Modeling

The initial amount in the bank is $545. Each week an amount of $80 is earned. In x weeks, Zoe will have earned 80x.

Thus, the total savings in x weeks are:

y = 545 + 80x

Option: D. y= 545x + 80

False, because the determinant of a triangular matrix is the product of the entries along the main diagonal.

What is cofactor expansion?

The Laplace expansion, also known as the cofactor expansion in linear algebra, expresses the determinant of a n n matrix B as a weighted sum of minors. It is named after Pierre-Simon Laplace.

a. The correct answer is A: True, because cofactor expansion across a row adds each of the cofactors together. Cofactor expansion down a column subtracts each cofactor from one another. This causes the two cofactor expansions to have opposite signs.

To see why this is true, let's consider an example.

Let A be the 3x3 matrix:

   \(size(8cm); \\real\ ticklen=3;\\ pen\ axispen=black+1.3bp; \\pen \ gridpen=gray(0.22);\\ pen\ tickpen=black+0.8bp;\\ pen \ ticklabelpen=black;\\ pen\ vectorpen=black;\\ x\ axis(extend)=true\)

The determinant of A can be computed using cofactor expansion along the first row:

det A = 2 * C_{12} - 3 * C_{13} + 4 * C_{14}

= 2 * (-6) - 3 * (5) + 4 * (-4)

= -12 - 15 + 16

= -11

Alternatively, we can compute the determinant using cofactor expansion down the first column:

det A = 8 * C_{21} - 5 * C_{31} + 2 * C_{41}

= 8 * (-6) - 5 * (5) + 2 * (-4)

= -48 + 25 -8

= -31

b. For part b,

The correct answer is C: False, because the determinant of a triangular matrix is the product of the entries along the main diagonal.

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The data on the attempts and distances of the science experiment on the launch of a ball by a catapult, presented in a tabular form gives the following;

a. The five attempts have an average distance of 50.58

b. The distance the sixth ball has to travel so as to give an average distance traveled of 50.9 meters is 52.5 meters

An average is a descriptive statistics that tends to describe the values in a dataset. An average or the mean of a dataset is obtained by summing the data values and dividing the result by the number of data points

Please find attached, the Attempt to Distance table obtained from a similar question online

a. The formula for average, \( \bar{x} \) of a set of data or observations is presented as follows;

\( \displaystyle{\bar x = \frac{Sum \: of \: observations}{Number \: of \: observations}} \)

Mathematically, we have;

\( \displaystyle{\bar x = \frac{\sum x}{N}} \)

Which gives from the attached table;

\(\displaystyle{\sum {x} =50.7+49.4 +52.3 + 48.9 + 51.6 = 252.9}\)

N = 5

Which gives;

\( \displaystyle{\bar x = \frac{252.9}{5} = 50.58}\)

b. The distance, d, the ball has to travel on the sixth attempt to get an average of 50.9 meters is found as follows;

The new total number of attempts, N = 6

Which gives;

\( \displaystyle{\bar x = 50.9 = \frac{d + 252.9}{6} }\)

6 × 50.9 = d + 252.9

Therefore;

d = 6 × 50.9 - 252.9 = 52.5

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The requried, Multiplies(with switching factors.) area given below,

a.

693 x 83 = 57489

83 x 693 = 57489

The answer is 57489.

b.

910 x 45 = 40950

45 x 910 = 40950

The answer is 40950.

c.

38 x 84 = 3192

84 x 38 = 3192

The answer is 3192.

d.

409 x 89 = 36401

89 x 409 = 36401

The answer is 36401.

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Answer:

C

Step-by-step explanation:

there would have to be one more zero between 0 and 8 for both of them

Answer:

C, 9+ the square root of 41

Step-by-step explanation:

got it right on edge :)

We can see here that the correct option will likely be option D.

None of the statements provided by Shelby, Tatyana, and Mauricio correctly describe the steps to simplifying the expression 17.62+(24-12). The correct steps would be:

Subtract 12 from 24 to get 12

Add 12 to 17.62 to get 29.62

Simplify the expression to 29.62

Simplification is the process of making an expression simpler, without changing its value. This can involve combining like terms, removing unnecessary operations or terms, and applying the order of operations. The goal of simplification is to make an expression easier to understand, read, and work with.

We see that the above steps given tells us how to simplify the given expression.

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Answer:

Step-by-step explanation:

Answer options, incorrect statements are underlined below:

1. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly two elements of the range.

2. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.

3. By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly two elements of the range.

4. By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range.

Answer:

2. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.

Step-by-step explanation:

A relation is a function only if it relates each element in its domain to only one element in the range. When you graph a function, a vertical line will intersect it at only one point.

Answer:

a) The third quartile Q₃ = 56.45

b) Variance \(\mathbf{ \sigma^2 =2633.31}\)

Step-by-step explanation:

Given that :

\(Q_1\)  =  30.8

Median \(Q_2\) =  48.5

Mean  = 42

a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :

\(SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}\)

\(-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}\)

\(-0.38Q_3 + 11.704 = Q_3 +30.8 - 97\)

\(1.38Q_3 = 77.904\)

Divide both sides by 1.38

\(Q_3 = 56.45\)

b) The objective here is to determine the approximate value of the variance;

Using the relation

\(SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}\)

\(-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}\)

\(-0.38= \dfrac{(-19.5) }{\sigma}\)

\(-0.38* \sigma = {(-19.5) }{}\)

\(\sigma =\dfrac {(-19.5) }{-0.38 }\)

\(\sigma =51.32\)

Variance =  \(\sigma^2 =51.32^2\)

\(\mathbf{ \sigma^2 =2633.31}\)