Simplify the expression by using a double-angle formula.
sinπ/7·cosπ/7

[tex]VT=SR \implies 3y+7=25 \implies \boxed{y=6} \\ \\ \\ ○\ m\angle UTV=180^{\circ}-90^{\circ}-29^{\circ}=61^{\circ} \\ \\ \angle WRS \cong \angle UTV \implies 8x-27=61 \implies \boxed{x=11}[/tex]

The reading time calculated to be

The problem involves multiplication of fractions

The fraction required are:

let the reading time be x

1/2 time for 1 hour = 1/2 * x = x/2

three times a week

= x/2 * 3

= 3x/2

The reading time is 3/2 improper fraction and 1 1/2 mixed fraction

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Answer:

slope of line q = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

calculate the slope of line p using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )

m = [tex]\frac{4-7}{4-8}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes

then slope of line q = [tex]\frac{3}{4}[/tex]

Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.

What is composite function?

Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x

Main body:

according to question;

f(x) = 2x³

g(x) = 3x³ -2

we need to find composite function:

f o g (x) = 2(3x³-2)

{to find composite function , we replace one function as value of x in another}

f o g(x) = 6x³ -4

           = 6x³ -4

f o g(1) = 6*1 -

          = 2

g o f(x) = 3(2x³)-2

g o f(x) = 6x³ -2

           = 6x -2

g o f(1) = 6*1 -2

           = 5

Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.

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1.6 seconds. The ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.

To find the time it takes for the ball to hit the canopy, we need to solve the equation h(t) = 12 for t.

The given equation for h(t) is h(t) = -16t^2 + 52, so we can substitute this into the equation h(t) = 12 to get:

12 = -16t^2 + 52

To solve this equation, we can move all the terms to one side of the equation to get:

-16t^2 + 40 = 0

We can then divide both sides of the equation by -16 to get:

t^2 - 2.5 = 0

We can then use the quadratic formula to solve for t:

t = +/- sqrt(2.5)

t = +/- 1.58

Thus, the ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.

Rounding this answer to the nearest tenth gives us 1.6 seconds, so the correct answer is 1.6 seconds.

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When the costs of the two plans are equal, plan A will cost $37.81, whereas plan B will cost $25.65.

To find the number of calls at which the two plans cost the same, we need to set the costs equal to each other and solve for the number of minutes. The cost of plan A is $19 + $0.11 per minute, and the cost of plan B is $0.15 per minute. Setting these equal to each other, we get:

$19 + $0.11 per minute = $0.15 per minute

We can then solve for the number of minutes by dividing both sides by the per-minute cost:

$19 / $0.11 per minute = $0.15 per minute / $0.11 per minute

This simplifies to:

171 minutes = 135 minutes

Therefore, the two plans cost the same at 171 minutes of calling.

To find the cost at this point, we can substitute 171 minutes back into either of the original cost equations:

Plan A: $19 + $0.11 per minute × 171 minutes = $19 + $18.81 = $37.81

Plan B: $0.15 per minute × 171 minutes = $25.65

Thus, the cost when the two plans cost the same is $37.81 for plan A and $25.65 for plan B.

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Answer:

it will take rahim 16 months

Step-by-step explanation:

6:4:2

3000÷12=250

1500:1000:500

20% 100

100×16=1600

The distance is 244.56 feet, in feet, between point K and point L.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Recall the Pythagorean theorem formula:

a² + b² = c²

Given that Kim is standing on the deck, point k, which is 140.75 feet above ground level.

Louise point L, is standing 200ft from the base of the lighthouse directly below Kim’s position.

Thus the distance, in feet, between point K and point L

Replacing by the values we have;

200 ² + 140.75² = KL²

KL² = 59810.56

KL = 244.56

The distance is 244.56 feet, in feet, between point K and point L.

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Answer:

9.22 minutes

Step-by-step explanation:

You could use the form y=mx + b to find this equation

y will represent the total liters

x will represent the total number of minutes

b will represent the initial number of liters in the beginning

1. Plug 194 in for y, plug 9 in for m, put 111 in place of b

The equation should look be:  [tex]194 = 9x + 111[/tex]

2. Solve the equation

3. Subtract 111 on both sides. The equation would now be:  [tex]83 = 9x[/tex]

4. Divide both sides by 9 (to get x by itself). [tex]\frac{83}{9} = 9.22222222[/tex]

5. Round to the nearest hundredth place to get 9. 22 minutes

The ratio shows how many times one value is contained in another value.

The number of top dogs is 192.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of top dogs to fat cats was 24 to 19.

if they were 152 fat cats.

This means,

Number of top dogs = 24x

Number of fat cats = 19x

Now,

Number of fat cats = 152

This means,

152 = 19x

x = 8

Now,

Number of top dogs = 24x

= 24x

= 24 x 8

= 192

Thus,

The number of top dogs is 192.

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The area under the graph using the first two and then four rectangles = 0.221 unit square

According to the graphs given in the below figure,

Given in the question,

f(x) = [tex]x^{3}[/tex] when x = 0 and x = 1

The first rectangle of the first graph goes from 0 to 0 .6,

Width = 0.6

Height measured from the middle point = 0.3

f( 0.3) = [tex]( 0.3)^{3}[/tex]

f(0.3) = 0.027 units.

Area of first rectangle = 0.6 x 0.027 = 0.0162 unit square

Now taking the second rectangle of the first part,

It is going from 0.6 to 1.0,

Width = 0.4 units

height = 0.8 units

Height measured from the middle-

f(0.8) = [tex](0.8)^{3}[/tex] = 0.512

Area of the second part of the rectangle = 0.512 x 0.4

= 0.2048 unit square

Final area = 0.2048 + 0.0162 = 0.221 square units

Therefore, the same could be done with the second part rectangle of 4

For the given first part of four rectangles = width = 0.6 units and height = 0.1 unit

so f(0.1) = [tex]0.1^{3}[/tex]

= 0.001 units

Therefore, the area under the graph using the first two and then four rectangles = 0.221 unit square

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By using the concept of unitary method, it can be calculated that

a) For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required

b) For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here, unitary method will be used

The double number line has been shown below-

a) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required

   For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 350[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]\frac{35}{4}[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required

b)  For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required

   For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 50[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]\frac{5}{4}[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required

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Answer:

C is the answer

Step-by-step explanation:

Stem and leaf plots were also confusing to me at first, but once you understand they are actually easy!

Look at the first column where it says 2,3,4,5 and 6. Those are the tens place. The columns next to it with 2,3,8,9,etc are the ones place. For example, the first column has two, so we know that the number has a two in the tens place.

2_

Look at the numbers next to it, there's 2,3, and 8.

Since there's 3 numbers, that means that there are three numbers that have a two in the ones place. 2,3 and 8 are the numbers that go in the ones place.

So in the graph there is 22,23 and 28.

If you look at your choices, you can find all of them except 38, since on the row with the 3, next to it is the number 9 and not the number 8.

Answer:

4:81

Step-by-step explanation:

κμΛζΖυ

The ratio of area of squares is 4:81. Therefore, option C is the correct answer.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of perimeters of a squares is 2:9.

We know that, perimeter of square is 4a, where a is side of a square

Now, 4x/4y =2/9

x/y =2/9

As we know area of square is a², where a is side of a square

So, x²/y² =2²/9²

x²/y² =4/81

The ratio of area of squares is 4:81. Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

If the ratio of perimeters of a squares is 2:9, then the ratio of their areas is

A) 2:9

B) 5:21

C) 4:81

D) 8:729

Answer:

11/9

Step-by-step explanation:

If this is an addition question then this is your answer.

Answer:

-5

Step-by-step explanation:

The rate of change, also known as slope, would be -5.

Slope can be found with two points and the formula y minus y divided by x minus x or the change of y divided by the change in x.

To identify the slope on the equation is easy since this is slope-intercept form.

y=mx+b

where m is the slope

m in this case is -5, so -5 is your answer

The probability that a resident own a cat or a dog is 48%

From the question, we have the following parameters that can be used in our computation:

P(Own a cat) = 70%

P(Own a dog) = 59%

P(Own a cat and a dog) = 42%

The probability a resident own a cat or a dog is then calculated as

Probability a resident own a cat or a dog = P(Own a cat) + P(Own a dog) - P(Own a cat and a dog)  

Substitute the known values in the above equation, so, we have the following representation

Probability a resident own a cat or a dog = 70% + 59% - 42%

Evaluate the sum and the difference

Probability a resident own a cat or a dog = 48%

Hence, the probability is 48%

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Complete question

59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find:

the probability a resident own a cat or a dog

(round to 4 decimal places where possible)

The possible number of 3 -letter words that can be formed with given conditions.

(a) No condition is imposed: 343

(b) No letter can be repeated in a word: 210

(c) Each word must begin with the letter 'a' : 49  

(d) The letter 'c' must be at the end: 49

(e) The second letter must be a vowel: 98

In this question we have been given that 3 -letter words' are formed using the letters a, b, c, d, e, f, g.

We need to find the possible number of 3 -letter words that can be formed with given conditions.

(a) No condition is imposed.

the possible number of 3 letters words would be,

7³ = 343

(b) No letter can be repeated in a word.

Using the formula of Permutation,

^{7}P_3 = 7!/(7 - 3)!

             = 210    

(c) Each word must begin with the letter a.  

If each word begins with letter 'a' there would be possible combinations of remaining 6 letters at 2nd and 3rd position of 3-letter word.

So, the possible number of 3 letters words would be,

7² = 49  

(d) The letter c must be at the end.

If each word ends with letter c there would be possible combinations of remaining 6 letters at 1st and 2nd position of 3-letter word.

So, the possible number of 3 letters words would be,

7² = 49  

(e) The second letter must be a vowel.

In the 3 letter word, the second letter must be vowel which is either a or e.

So, the possible number of 3 letters words would be,

49 + 49 = 98

Therefore, the possible number of words would be (a) No condition is imposed: 343

(b) No letter can be repeated in a word: 210

(c) Each word must begin with the letter 'a' : 49  

(d) The letter 'c' must be at the end: 49

(e) The second letter must be a vowel: 98

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The complete question is:

3 -letter words'' are formed using the letters a, b, c, d, e, f, g. How many such words are possible for each of the following conditions?

(a) No condition is imposed.

(b) No letter can be repeated in a word.

(c) Each word must begin with the letter a.

(d) The letter c must be at the end.

(e) The second letter must be a vowel.

The possible ways the corner convenience store can sell candy packages to spend at least $3.00 is

An equation is a mathematical model showing the equality of two opposite sides or an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given parameters are

20c, 30c and 50c

Least cost =$3

Let the possible ways be x

20x+30x+50x=3.00

Solving the equation we have:

100x=3.00

make x the subject

100x=3

x=3/100

This can be expressed in decimal as 0.03

In conclusion, he can sell it in 3/100 or 0.03 ways to spend at least $3.00 on a candy.

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7) ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) ∠ACD = 102 degree

What do you mean by co interior angle?

Co-interior angles, or consecutive interior angles, are two angles on the same side of a transverse line. Co interior angles are interior angles that add up to 180 degrees. This means that the sum of the two interior angles on the same side of the horizontal side are complementary.

7) Given :

∠EFG = 32 degree

∠GFH = 56 degree

∠EFG = ∠EFG + ∠GFH = 32 + 56 = 88 degree

Therefore, ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) As AB and CD are parallel to each other therefore , ∠BAC and ∠ACD are cointerior angle and sum of co interior angles is 180 degree.

6x + 6 + 9x - 6 = 180

15x = 180

x = 180/15 = 12

∠ACD = (9x - 6) degree = 9(12) - 6 = 108 - 6 = 102

Therefore, ∠ACD = 102 degree

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Answer:

-2

Step-by-step explanation:

If both sides are identical, there will be infinitely many solutions.

The mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1. It can be solved by rate of work.

The rate lawns per employee gives the lawns mowed by one employee.

The rate hours per lawn gives the number of hours required to mow one lawn.

The rate employee per lawn gives how many employees are required to mow one lawn.

The rate lawns per day gives the number of lawn mow in one day.

Since the mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1.

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We know that we need to sell out 53 candles to break even using mathematical operations.

The process of calculating a value using operands and a math operator is known as a mathematical "operation."

The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, the total expense of the shop:

$100 + $32.50 = $132.50

No, the candle costs $2.50.

The selling price of a candle is $5.

Profit in each candle is: 5 - 2.50 = $2.50

A number of candles that we need to sell to break even are:

132.50/2.50

53

Therefore, we know that we need to sell out 53 candles to break even using mathematical operations.

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Answer:sales tax rate would be 0.1

using the formula

Sales tax rate = Sales tax percent / 100

The probability that the sample's Republican percentage will be higher than 44% is 0.089.

Probability is a metric used to express the possibility or chance that a particular event will occur.

Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.

To determine the probability of a sample proportion, the normal probability is used as the z-test statistic of one sample proportion.

When the sample size is big, the z-test statistic, a normal test statistic, is employed.

So, the probability will be:

We know that the sample size is n = 488 and the proportion is p = 0.41.

Now, obtain P(p > 0.44) as follows:

[tex]\begin{aligned}& P(\hat{p} > 0.44)=1-P\left(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} \leq \frac{0.44-p}{\sqrt{\frac{p(1-p)}{n}}}\right) \\& P(\hat{p} > 0.44)=1-P\left(Z \leq \frac{0.44-0.41}{\sqrt{\frac{0.41(1-0.41)}{488}}}\right) \\& P(\hat{p} > 0.44)=1-P(Z \leq 1.347)\end{aligned}[/tex]

Excel function for the p-value:

P(p > 0.44) = 1 - 0.911

P(p > 0.44) = 0.089

Therefore, the probability that the sample's Republican percentage will be higher than 44% is 0.089.

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Answer: The expression a²+4b² can be factored in the following way:

a²+4b² = (a² + 2ab + 2ab + 4b²)

= (a+b)²

In general, the square of a binomial (a+b) can be written as (a+b)² = a² + 2ab + b². This is known as the "square of a sum" formula. In this case, we can apply this formula to the binomial a+b to obtain a² + 2ab + b² = (a+b)². We can then use the fact that the square of a binomial can be written as the square of each term plus twice the product of the two terms. This allows us to write the expression as (a+b)² = a² + 2ab + b² = a² + 2ab + 2ab + 4b² = (a² + 2ab + 2ab + 4b²) = (a²+4b²). Therefore, the fully factored form of a²+4b² is (a+b)².