For the acute angles in a right triangle, sin(5x)° = cos(3x + 2)°.


What is the number of degrees in the measure of the smaller


angle?

5.13 U. S. Dollars will it cost to buy a gallon of gas in Canada. The correct answer to the question is A

Given in the question,

Cost of 1 liter gasoline = 1.50 Canadian dollars

1 gallon = 3.8 liters

Thus, to calculate the price of 1 gallon we multiply the cost of 1 liter by 3.8

Cost of 3.8 liters of gasoline = 1.5 * 3.8

= 5.70 Canadian dollars

1 Canadian dollar = 0.9 U. S. dollars

5.70 Canadian dollars = 5.70 * 0.9

= 5.13 U. S. dollars

That is the cost of 1 gallon of gas in Canada is 5 U S dollars and 13 cents.

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The radius of circle A is 4.

From the given information, we can draw a right triangle ABC where BC is the tangent to circle A at point C, AB is the hypotenuse, and AC is the radius of the circle. By the Pythagorean theorem, we have:

AC² + BC² = AB²

Substituting the given values, we get:

AC² + 3² = 5²

AC² = 25 - 9

AC² = 16

Taking the square root of both sides, we get:

AC = 4

Therefore, the length of the radius of circle A is 4.

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The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.

The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.

The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0

The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)

where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.

Since each roll of the die is independent, the variance of the sample mean for each sample is given as:

σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584

σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292

Substituting these values in the above equation, we get:

σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468

Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:

σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)

Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.

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John would have the option of taking 10 different cones

The questions says that there is the option of having the flavors that are available ice cream flavors are: chocolate (C), mint chocolate chip (M), strawberry (S), rainbow sherbet (R), and vanilla (V).

The available flavors are then 5 in number

Then the number of scoops that he can have from each of the cone is said to be 2

Hence we would have 5 x 2

= 10

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The surface area of the first triangular prism is 174.58 square feet and second triangular prism is 1721.6 square feet.

To calculate the surface area of a triangular prism, we need the measurements of the base and the height of the triangular bases, as well as the length of the prism.

For the first triangular prism with measurements:

Base: 5 ft

Height: 8 ft

Length: 6 ft

To calculate the surface area, we need to find the areas of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is:

Surface Area = 2 * (Area of triangular base) + (Perimeter of triangular base * Length)

The area of a triangle can be calculated using the formula: Area = 1/2 * Base * Height.

Area of triangular base = 1/2 * 5 ft * 8 ft = 20 ft²

The perimeter of a triangle is the sum of its three sides.

Perimeter of triangular base = 5 ft + 8 ft + √(5 ft² + 8 ft²) = 5 ft + 8 ft + √89 ft ≈ 5 ft + 8 ft + 9.43 ft ≈ 22.43 ft

Surface Area = 2 * 20 ft² + (22.43 ft * 6 ft) = 40 ft² + 134.58 ft² = 174.58 ft²

Therefore, the surface area of the first triangular prism is approximately 174.58 square feet.

For the second triangular prism with measurements:

Base: 6 ft

Height: 2.5 ft

Length: 115 ft

Area of triangular base = 1/2 * 6 ft * 2.5 ft = 7.5 ft²

Perimeter of triangular base = 6 ft + 2.5 ft + √(6 ft² + 2.5 ft²) = 6 ft + 2.5 ft + √40.25 ft ≈ 8.5 ft + 6.34 ft ≈ 14.84 ft

Surface Area = 2 * 7.5 ft² + (14.84 ft * 115 ft) = 15 ft² + 1706.6 ft² = 1721.6 ft²

Therefore, the surface area of the second triangular prism is approximately 1721.6 square feet.

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The surface area of the triangular prism is x - 0 = -3

If the solution to an absolute value equation is x = -3, then we know that the distance between x and 0 is 3 units. Since the absolute value of a number is the distance between the number and 0 on the number line, we can write the absolute value equation that corresponds to x = -3 as:

| x - 0 | = 3

To write this equation in the form x - b = c, we can simplify the absolute value expression by removing the absolute value bars. This gives us two possible equations:

x - 0 = 3 or x - 0 = -3

Simplifying further, we get:

x = 3 or x = -3

Therefore, the absolute value equation in the form x - b = c that has the solution set {x = -3} is:x - 0 = -3

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The form in which is easier to identify the x-intercepts is the one in option B. Intercept form.

If a quadratic equation has a leading coefficient a and x-intercepts x₁ and x₂, then the quadratic equation can be written as:

y = a*(x - x₁)*(x - x₂)

That is called the factored form or the intercept form.

Notice that if the quadratic equation is written in that form, is really easy to identify the x-intercepts of the equation, then that would be the most beneficial form in order for Kristen to quickly identify the coordinates, the correct option is B.

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Answer:

5,005

Step-by-step explanation:

This is a combination problem. The formula for combination is:

nCr = n! / (r!(n-r)!)

Where n is the total number of items, and r is the number of items to be selected.

Using this formula, we can calculate the number of ways to choose 9 varieties from 15:

15C9 = 15! / (9!(15-9)!) = 5005

Therefore, there are 5,005 ways to choose 9 varieties from 15 varieties of pansies.

It would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.

The formula for calculating the future value (FV) of an investment that is continuously compounded is FV = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years. In this case, P = $5400, r = 7% = 0.07, and FV = $8000. Substituting these values into the formula, we get:

$8000 = $5400e^(0.07t)

Dividing both sides by $5400 and taking the natural logarithm of both sides, we get:

ln(8000/5400) = 0.07t

Simplifying the left side of the equation, we get:

ln(4/3) = 0.07t

Solving for t, we get:

t = ln(4/3)/0.07 ≈ 7.62 years

Therefore, it would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.

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If sales increase by 66,000, income will increase by 220,000.00

Net operating income 37,200.00

The margin of safety is 14.01%

Statement showing Computations  

particulars Amount Per unit

Sales 628,000.00 40.00

Variable Expenses 439,600.00 28.00

Contribution Margin 188,400.00 $ 12.00

Fixed Expenses 151,200.00

Net operating income 37,200.00

'

1)  BEP in unit sales = 151,200/12 12,600.00

.BEP in sales $ = 12,600 * 40 504,000.00

2)  Total Contribution margin at BEP = Fixed costs 151,200.00

3)a Target Profit $ 64,800.00

Fixed Expenses 151,200.00

Desired Contribution 216,000.00

3b. No of units to be sold = 216,000/12 18,000.00

Sales 720,000.00

Variable Expenses 504,000.00

Contribution Margin 216,000.00

Fixed Expenses 151,200.00

Net operating income 64,800.00

4)  Margin of safety = 628,000.00-540,000.00 88,000.00

MOS in % = 88,000/6280001 14.01%

5)CM Ratio = 188,400/628,000 0.3

If sales increase by 66,000, income will increase by 220,000.00

66,000/0.3

=220,000.

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The inequality to solve is 56 - x > 0. The solution is x < 56. Therefore, the domain of the function g(x) is x < 56. So, the answer is option B.

The function is defined as g(x) = log(56 - x).

The domain of a logarithmic function is all the values that make the argument of the logarithm positive. In other words, the argument of the logarithm (56 - x) must be greater than 0.

So, we solve the inequality 56 - x > 0 for x

56 - x > 0

Subtract 56 from both sides

-x > -56

Divide both sides by -1, and remember to reverse the inequality

x < 56

Therefore, the domain of the function g(x) is all real numbers x such that x < 56. So, the correct answer is B).

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--The given question is incomplete, the complete question is given

" The domain of g(x) = log 56 - x) can be found by solving the inequality

A. 56-x<0 ,B. 56-x>0,C. 56-x>=0, D. 56-x<=0 "--

The area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.

To find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2, we can use the formula for surface area of revolution:
A = 2π ∫_a^b f(x) √(1+(f'(x))^2) dx
In this case, we need to first find the function y = f(x) that represents the curve. Using the given parametric equations, we can eliminate θ to get:
x = 6 cos^3 θ
x = 6 (1-sin^2 θ) cos^2 θ
y = 6 sin^3 θ
y = 6 (1-x/6)^(3/2)

So the function that represents the curve is y = 6 (1-x/6)^(3/2). Now we can use the formula for surface area of revolution:
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+(-3/4 (1-x/6)^(-1/2))^2) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+9/16 (1-x/6)^(-1)) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √((25-9x)/(16(1-x/6))) dx
This integral can be evaluated using substitution and partial fractions. The final answer is:
A = 96π/5

Therefore, the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.

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The solution for the given linear expression is 11.25 (45/4).

A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=11x+9. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=11 and b=9.

The question gives the expression:7z+9z+7-7 =180. Then, you should find the variable z.

7z+9z+7-7 =180

16z+0=180

16z=180

z=180/16=90/8=45/4=11.25

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Answer:

40.7, my answer needs to be 20+ characters sooo....

The mistake, Aleks made, while measuring the angle is, he measure the angle from the wrong side of the line.

Angle is a dimensionless vector quantity, that is, it is very important, to take care of the directions, while measuring the angle.

That is, to measure the angle, say ∠ABC, the 0°(reference) line of the protractor, must be on one either AB or BC, to measure the angle rightly.

And since the angles between two lines are supplementary in nature, that is, the two angles will add up to make 180°, that is why, the angle measure by Alek and Melanie, add up to make 180°.

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The number of nickels and pennies in the pocket is 5 and 16 respectively.

To find the number of coins, Let's assume the number of nickels is x and the number of pennies is y.

According to the problem, we have two equations:

The total value of the coins is $0.41:

0.05x + 0.01y = 0.41

The total number of coins is 21:

x + y = 21

Now we can solve this system of equations to find x and y. One way to do this is to use substitution.

Solving the second equation for y, we get:

y = 21 - x

Substituting this into the first equation, we get:

0.05x + 0.01(21 - x) = 0.41

Simplifying:

0.05x + 0.21 - 0.01x = 0.41

0.04x = 0.2

x = 5

So we have 5 nickels.

Substituting this into the equation y = 21 - x, we get:

y = 21 - 5 = 16

So we have 16 pennies.

Therefore, the number of nickels and pennies in the pocket is 5 and 16 respectively.

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Answer:

Step-by-step explanation:

Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.

I think sorry if I’m wrong

Answer:

252 mi

Step-by-step explanation:

volume= L x W x H

9x 7 x 4 = 252 mi

The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.

dA ≈ (dA/dx)dx

At the lower end of the possible range for x, we have:

x = 9 31/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches

At the upper end of the possible range for x, we have:

x = 10 1/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches

Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(b) The percent error in computing the area of the square is given by:

(percent error) = (error / actual value) x 100

(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.

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The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.

The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.

The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.

The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.

The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.

Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.

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Answer:

Step-by-step explanation:

(2-5)3=-9. (-9)5 =-45

The value of the variables are a = 1 and b = -1

Given that the equations are;

a - 3 = 2b

4a + 5b- 8 = 0

Using the substitution method, we have;

Make 'a' the subject of formula from equation (1)

a = 2b + 3

Now, substitute the value of the variable in the second equation

4(2b + 3) + 5b - 8 = 0

expand the bracket, we have;

8b + 12 + 5b - 8 = 0

collect the like terms, we get;

8b + 5b = 0 - 5

add or subtract the values

5b = -5

b = -1

Substitute the value of b as =-1

a = 2(-1) +3

expand the bracket

a = -2 + 3

a = 1

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The score that marks the 11% of all scores is approximately 56.875 .

To find the score that marks the 11% of all scores, we need to use the standard normal distribution table, also known as the Z-table, since the given distribution is a normal distribution.

The first step is to find the Z-score that corresponds to the 11th percentile, which is given by: Z = invNorm(0.11) ≈ -1.225

Here, "invNorm" represents the inverse of the standard normal cumulative distribution function, which can be computed using statistical software or a calculator.

The second step is to use the Z-score formula to find the raw score that corresponds to this Z-score:Z = (X - μ) / σ

where X is the raw score we want to find, μ is the mean of the distribution, and σ is the standard deviation. Plugging in the values we have:

-1.225 = (X - 63) / 5

Solving for X, we get:

X = -1.225 * 5 + 63 = 56.875

Therefore, the score that marks the 11% of all scores is approximately 56.875

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Option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

Given integers are m, n, p and q

And q ≠ 0 and p ≠ 0

A = m / p

B = n/ q

Adding A and B

A + B = m / p + n / q

A + B = (mq + np) / pq

as p ≠ 0 and q ≠ 0 so, pq ≠ 0

So, A + B = (mq + np) / pq is a rational number

Therefore, option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

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Given question is incomplete, the complete question is below:

Keisha's teacher gives her the following information:

• m, n, p, and q are all integers, and p≠ 0 and q≠0

•A= m/q and B= n/p

What conclusion can Keisha make?

A: A +B = (mp + nq)/pq, so the sum of a rational number and an irrational number is an irrational number.

B: A•B= (mp + nq)/pq, so the product of two irrational numbers is an irrational number.

C: A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

D: A•B= (mp + nq)/pq, so the product of two rational numbers is a rational number.​

The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.

An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:

(x, y)                               →              (-x, y)

Coordinate = (-1, 1/10)   →  Coordinate A' = (-(-1), 1/10) = (1, 1/10).

Furthermore, the transformation rule for the translation of a point by k units up is given by;

(x, y + k)         →  (x', y')

(1, 1/10 + k)       →  E(1, 4 1/10)

1/10 + k = 4 1/10

k = 4 1/10 - 1/10

k = 4.

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This prompt is about probability. The answers are given as follows;

Identifying the   probability of an event is crucial to making predictions based on its likelihood. T his involves calculating the probability either through historical data or experimentation.

Once determined, utilizing this value enables one to make future predictions regarding the occurrence of such events; for instance, 80% probability of precipitation tomorrow implies an 80% chance of rain.

Calculating probabilities has proven essential to sports betting because it helps bookmakers given some degree of foresight on which teams are going to win specific games or tournaments. Operating under the premise that there will always be two probable outcomes (either one side wins while another loses), these bookmakers could assign numerical values on what percentage they deem worthy enough for each team's chances.

Subsequently, using precise mathematical formulas and equations, bettors assess wagering-related uncertainties based on these predetermined likelihoods before deciding whether or not they should place money bets.

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Answer:

push-up = 1 second

sit-up = 3 seconds

Step-by-step explanation:

let p represent the # of push-ups

let s represent the # of sit-ups

System of equations:

19p+8s=43

12p+12s=48

i'll eliminate s by multiplying the top equation by 3 and the bottom equation by -2

57p+24s=129

-24p-24s=-96

33p=33

p=1 second

now solve for s (i'll plug p into the 2nd equation)

12(1) + 12s=48

12s=36

s=3 seconds

Answer:

  g(x) = h(x -7) +5

Step-by-step explanation:

Given h(x) defines a parabola that opens upward with a vertex at (-2, -7) and g(x) defines the same parabola with its vertex at (5, -2), you want to express g(x) in terms of h(x).

The graph of f(x) is translated right h units and up k units by ...

  f(x -h) +k

We see that g(x) is a translation of h(x) right by 7 units and up by 5 units. This means (h, k) is (7, 5), and the translated function is ...

  g(x) = h(x -7) +5

__

Additional comment

This is confirmed by the plots in the second attachment.

Answer:  g(x)=h(x-7) +5

Step-by-step explanation:

The graph g(x) has been shifted up 5   (+5)   and right 7

When shift a function, the y change, up/down, goes at end of function

When shift in x direction happens, you take opposite sign so we will do -7

g(x)=h(x-7) +5

About 125 students play a sport and about 65 students are in the play.

To find the number of students who play a sport and those who are in the play, we need to use the given percentages and round the answers to the nearest whole.
Find the number of students who play a sport:
Multiply the total number of students (145) by the percentage of students who play a sport (86%).
145 × 0.86 = 124.7
Round the answer to the nearest whole number:
Approximately 125 students play a sport.
Find the number of students who are in the play:
Multiply the total number of students (145) by the percentage of students who are in the play (45%).
145 × 0.45 = 65.25
Round the answer to the nearest whole number:
Approximately 65 students are in the play.

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