In ΔUVW, the measure of ∠W=90°, UW = 39, WV = 80, and VU = 89. What is the value of the sine of ∠V to the nearest hundredth?

We would need approximately 112 square feet of carpet to cover the floor of the triangular room.

What is area ?

Area is a measure of the size of a two-dimensional surface or shape, such as a square, rectangle, triangle, circle, or any other shape with length and width. It is usually measured in square units, such as square feet, square meters, or square centimeters.

To find the amount of carpet needed to cover the triangular room, we need to first calculate the area of the triangle.

We can use the formula for the area of a triangle, which is:

Area = (base * height) / 2

In this case, we can choose one of the sides of the triangle as the base and draw an altitude (a perpendicular line) from the opposite vertex to that side, which will be the height.

Let's choose the side of length 20 ft as the base. To find the height, we need to draw an altitude from the opposite vertex that intersects the base. This altitude splits the triangle into two smaller right triangles, each with a base of 10 ft (half of 20 ft). We can use the Pythagorean theorem to find the length of the altitude:

h*h = 225 - 100

h*h = 125

h = 11.2

h = 11.2 ft (rounded to the nearest tenth)

Now we can calculate the area of the triangle:

Area = (20 * 11.2) / 2

Area = 112 square feet (rounded to the nearest tenth)

Therefore, we would need approximately 112 square feet of carpet to cover the floor of the triangular room.

The answer that is closest to this value is (b) 13.2 square ft, but this is clearly incorrect. Therefore, none of the given answer choices are correct.

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Answer:

slope = 3/7

Step-by-step explanation:

Locations of points: (-4 , 1) and (3 , 4)

slope = rise / run

between two plotted points this means that:

slope = change in y / change in x

slope = (4 - 1) / (3 - (-4))

slope = (4 - 1) / (3 + 4)

slope = 3/7

Answer:

$1.85 = £1

Step-by-step explanation:

55680/72.50 = 786

55680/128 = 435

435x = (786 + 19.80)

x = 805.8/435

x = 1.85

Answer:

£1 = $1.72

Step-by-step explanation:

55680/72.50=768

55680/128=435

768.00 - 19.80 = 748.20

x = 748.20 / 435

x = $1.72

Answer:

621 i guess

Step-by-step explanation:

18x² + 2x² - 7

Tap on a clip to paste it in the text box.

Answer:

a) 9×2=18

b)16×2=32

c)14×9=126

d)20×10=200

e)10×3=30

Answer:

B

Step-by-step explanation:

We have the equation \(-x-2y=-4\) and we want to find which ordered pair is in the solution \(-x-2y\leq -4\)

First, let's convert the inequality to slope-intercept form. So, we have:

\(-x-2y\leq-4\)

Add x to both sides:

\(-2y\leq x-4\)

Divide both sides by -2. Since we're dividing by a negative, we will flip the sign:

\(y\geq- \frac{1}{2}x+2\)

Therefore, our original inequality will be the same as above.

Notice that our y is greater than our equation.

Therefore, the shaded area will lie above our line.

So, any point that falls within the region above our line (in the graph) and on the line is a solution to our inequality.

(-4, 1) is below our line, so it's not a solution.

(-1, 4) is above our line. So, (-1, 4) is our answer.

(-4, -1) is again below our line. So, it's not a solution.

Finally, (4, -1) is also below our line, so it's not a solution.

Therefore, our final solution is B: (-1, 4).

Let's check this. Substitute -1 for x and 4 for y. This yields:

\(-(-1)-2(4)\stackrel{?}{\leq}4\)

Multiply:

\(1-8\stackrel{?}{\leq}{4}\)

Subtract:

\(-7\stackrel{\checkmark}{\leq}4\)

So, (-1, 4) is indeed our solution.

And we're done!

The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given trinomial,

a² + 2a - 3 = 0

a² + 2a = 3

Add 1 on both sides,

a² + 2a + 1 = 3 + 1

(a + 1)² = 4

(a + 1)² - 4 = 0

As per the given trinomial,

a² - 2a - 8 = 0

a² - 2a = 8

Add 1 on both sides,

a² - 2a + 1 = 8 + 1

(a - 1)² = 9

(a - 1)² - 9 = 0

As per the given trinomial,

p² + 16p - 22 = 0

p² + 16p = 22

Add 64 on both sides,

p² + 16p + 64 = 22 + 64

(p + 8)² = 86

(p + 8)² - 86 = 0

Hence "The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively".

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After simplification of the given expression, the resultant answer is (B) −3.03u + (−8).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

Keep in mind that terms can be coefficients, constants, or variables. So, 1+1 is a straightforward example of an expression.

This equation has one operation, two constant terms, and (addition). x3 is another illustration.

So, the given expression is:

(4.57u − 14) − (−6 + 7.6u)

Then, solve as follows:

4.57u - 14 - ( -6 + 7.6u)

4.57u - 14 + 6 - 7.6u

4.57u - 7.6u = -3.03u AND -14 + 6 = -8

-3.03u - 8 (or -3.03u + (-8) )

Therefore, after simplification of the given expression, the resultant answer is (B) −3.03u + (−8).

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Correct question:

Simplify the expression.

(4.57u − 14) − (−6 + 7.6u)

A. −3.03u + (−20)

B. −3.03u + (−8)

C. 12.17u + (−20)

D. 12.17u + (−8)

Answer:

slope = 1

y intercept = (0,8)

Step-by-step explanation:

the equation y = x + 8 is put in y = mx + b form

where m = slope and b = y intercept

in the equation y = x + 8 , the value of "m" is 1 meaning the slope is 1 and the value of "b" is 8 so the y intercept is (0,8)

Answer:

m = 1 and b = 8

Step-by-step explanation:

y = x + 8

Here the slope is 1, since y = mx+ b. m is the slope so m = 1. b is the

y-intercept so b=8

Answer:

First step: Combine like terms, Answer: \(x=15\)

Step-by-step explanation:

First, we need the variable on the left side and constants on the right.

So, we combine like terms to get \(3x=36+9=45\).

Then, we can divide both sides by \(3\) to isolate the variable and get \(\boxed{x=15}\).

It can be inferred that the amount of nuts that Allen requires depends on the amount of the recipe that he wants to make.

According to the information provided, one serving of the recipe calls for one cup of nuts. According to this, it can be inferred that to make a smaller or larger portion of the recipe, this amount must be divided or multiplied.

For example, if Allen calls for making two servings of the recipe, he would use two cups of nuts, while if he calls for making a half serving, he would use half a cup of nuts.

Note: The question is missing because there is some missing information. However I can answer it based on my general prior knowledge.

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Answer:

1/6

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

-4 x 13 = -52

Hope that helps :)

The number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

Proportion can be defined as the mathematical comparison of two numbers.

It is also said to be an equation defining two given ratios as equivalent to each other.

From the information, we have that;

By recycling 1 ton of paper, 6, 953 gallons of water was saved

To determine the gallons of water that would be saved after recycling 4 tons of paper, we have to;

If 1 ton of paper = 6, 953 gallons of water

Then 4 tons of paper = x

cross multiply

x × 1 = 6953 × 4

multiply through

x = 27, 812 gallons

The number of gallons that would be saved after the recycling would be

27, 812 gallons

Thus, the number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

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Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Firstly, convert this percentage into a decimal. All you have to do is move the decimal point two digits to the left.

Your percentage is currently 140.00. The decimal would be 1.40.

Next, take the given number (15 in this case) and multiply it by the decimal number:

15 * 1.40 = 21.

Hope this helped!

Answer:

(1)19°

Step-by-step explanation:

The diagram is drawn and attached below.

Let x=mAC = 72°; and

y=mBD = 34°

By the Angle-Arc relationship, the external angle is half the difference.

\(\angle P=\frac{1}{2}(x^\circ-y ^\circ)\\$Therefore:\\m\angle P=\frac{1}{2}(72^\circ-34 ^\circ)\\m\angle P=19^\circ\)

Answer:

False

Explanation:

A relation is a function each term of the first set is related to only one term of the second set. In this case, 1 is related to 5 and to 10, so it is not a function.

Therefore, the answer is

False

The graph shows a maximum wolf population size of 500 individuals, which occurred in 2017.

The graph depicts the magnitude of the wolf population in a certain location during the previous 25 years. The population size is shown to have changed over time, with the peak population count of 500 people happening in the year 2017. A population size of 450 people, which is a little less than the highest population level, was then reached in 2018. The year 2000 saw the lowest population size, with only 200 people living there. In 2017, there were 500 people in the population, which had grown considerably over the years. This suggests that over the past 25 years, the wolf population has been growing which occurred in 2017.

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The complete question is

based upon the data presented in the graph, which of the following best identifies the highest wolf population size which occurred in 2017?

Answer: 21 new children have come.

Data :

We simply have to subtract the number of children playing from the number of children who arrived after a while:

\(\bf \: 43 - 22 = 21\)

We check:

\(\bf \: 22 + 21 = 43\)

Rpt: 21 new children have come.

The ordered pairs that represent points on the graph of y = 2x - 3 are (0,-3), (5,7), (-2,-7), (2,1), and (4,5).

An ordered pair is a pair of numbers written in a specific order (x,y) that represents a point in the coordinate plane.

A graph is a visual representation of data or a mathematical function that is plotted on a coordinate plane, usually with an x and y-axis. It is used to analyze trends and relationships between variables.

According to the given information:

To determine whether a given ordered pair represents a point on the graph of the equation y = 2x - 3, we need to substitute the values of x and y into the equation and see if the equation is true.

a) (3,-3):

y = 2x - 3

-3 = 2(3) - 3

-3 = 3

This is not true, so (3,-3) is not on the graph.

b) (0,-3):

y = 2x - 3

-3 = 2(0) - 3

-3 = -3

This is true, so (0,-3) is on the graph.

c) (5,7):

y = 2x - 3

7 = 2(5) - 3

7 = 7

This is true, so (5,7) is on the graph.

d) (-2,-7):

y = 2x - 3

-7 = 2(-2) - 3

-7 = -7

This is true, so (-2,-7) is on the graph.

e) (2,1):

y = 2x - 3

1 = 2(2) - 3

1 = 1

This is true, so (2,1) is on the graph.

f) (4,5):

y = 2x - 3

5 = 2(4) - 3

5 = 5

This is true, so (4,5) is on the graph.

Therefore, the ordered pairs that represent points on the graph of the equation y = 2x - 3 are: (0,-3), (5,7), (-2,-7), (2,1), and (4,5). Answer: b), c), d), e) and f).

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Answer:

A.) Population : All employees at a firm

B.) μ = 5.4

C.) Sample : 80 employees at a firm

D.) Sample mean, x bar = 4.5

Step-by-step explanation:

From the question :

E.)

H0: μ ≥ 5.4

H1 : μ < 5.4

F.)

If Pvalue < α ; Reject H0

G.)

Test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(4.5 - 5.4) ÷ (2.7/sqrt(80))

-0.9 ÷ 0.3018691

= - 2.98

H.)

Pvalue fro Zscore calculator, α = 0.10 = 0.002882

I.)

Decision :

0.002882 < 0.10

Since, Pvalue < α ; We reject the Null

J.)

We Can conclude that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced

Answer:

Yes, it is!

Step-by-step explanation:

How to know if the ordered pairs is a function? Just look at the x values! If any of the x values repeat more than 1 time, then it is not a function. In this relation, none of the x values repeat more than 1 time, so this is a function!

Here are the ordered pairs on a graph (it passes the vertical line test):

Answer:

Associative property

Step-by-step explanation:

This property states that when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends (or the multiplicands).

eg. a+(b+c) is same as (a+b)+c

To sketch the graph of the function f(x) = 2cos^2(x) - 3x + 4 for the values of x between 0 and 2, we can follow these steps:

1. Determine key points: Find the critical points and important features of the function within the given range. This includes the x-intercepts, local maxima, and minima.

2. Plot the x-intercepts: To find the x-intercepts, set f(x) = 0 and solve for x. In this case, cos^2(x) = (0 + 3x - 4)/2. Find the values of x where this equation holds true.

3. Identify local maxima and minima: Use calculus or other methods to find the local maximum and minimum points of the function within the given range.

4. Sketch the graph: Once you have the key points, plot them on a graph and connect them smoothly. Pay attention to the shape and behavior of the function.

Since the process of sketching a graph is best done visually, I'm unable to provide an image here. However, by following the steps outlined above, you can plot the graph of f(x) within the range of x between 0 and 2. Remember to label the axes and indicate any important points you have found.

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Answer:

The probability that the mean monitor life would be greater than 96.3 months in a sample of 84 monitors

P(X⁻ ≥ 96.3) = 0.0087

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 95

Given that the standard deviation of the Population = 5

Let 'X' be the random variable in a normal distribution

Let X⁻ = 96.3

Given that the size 'n' = 84 monitors

Step(ii):-

The Empirical rule

         \(Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }\)

        \(Z = \frac{96.3 - 95}{\frac{5}{\sqrt{84} } }\)

       Z = 2.383

The probability that the mean monitor life would be greater than 96.3 months in a sample of 84 monitors

    P(X⁻ ≥ 96.3) = P(Z≥2.383)

                      =  1- P( Z<2.383)

                      =  1-( 0.5 -+A(2.38))

                      = 0.5 - A(2.38)

                     = 0.5 -0.4913

                    = 0.0087

Final answer:-

The probability that the mean monitor life would be greater than 96.3 months in a sample of 84 monitors

P(X⁻ ≥ 96.3) = 0.0087

The surface area of Cone is 452.16 unit².

The surface area of a cone is equal to the curved surface area plus the area of the base: π r² + πlr

where r is the radius and l is the slant height.

Given:

Radius= 8 unit

height= 6 unit

slant height, l = √8²+6²= √64+36 =√100= 10units

So, the Surface area of Cone

= πr (l +r)

= 3.14 x 8 ( 10 + 8)

= 25.12 x 18

= 452.16 unit²

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The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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Answer:

b = 54; A = 34.7°; C = 19.3°

Step-by-step explanation:

To solve the triangle means that we have to calculate the values of the missing angles and the missing sides.

We are given;

B = 126°, a = 38, and c = 22

Using law of cosines, we can find side b.

So;

b² = a² + c² - 2ac*cosB

Thus;

b² = 38² + 22² - 2(38 × 22)cos 126

b² = 1444 + 484 - 1672(-0.5878)

b² = 2910.8016

b = √2910.8016

b = 53.9518 ≈ 54

Using Law of sines, we can find the other 2 angles a and c.

Thus;

a/sin A = b/sinB = c/sinC

Thus, for A;

a/sin A = b/sin B

38/sin A = 53.9518/sin 126

sinA = (38 × sin 126)/53.9518

sinA = 0.5698

A = sin^(-1) 0.5698

A = 34.7363° ≈ 34.7°

Likewise;

b/sinB = c/sinC

53.9518/sin 126 = 22/sinC

sinC = (22 × sin 126)/53.9518

sinC = 0.3299

C = sin^(-1) 0.3299

C = 19.2627 ≈ 19.3°

Answer:

B

Step-by-step explanation:

200+50m >1250

This means that for every month her grandmother gives 50 for an unknown amount of months along with the first 200 dollars.

The greater than 1250 shows that until she is greater than 1250 she'll keep getting money