Out of 400 people sampled, 160 preferred
Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A.
Use a 90% confidence level, and give your answers as decimals, to three places. Use GeoGebra to calculate!

The answer choice which correctly represents the value of cos B as required is;  Cosine B = StartFraction 40 Over 41 EndFraction.

Therefore Choice B is correct

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles and it states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

we know that from the trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.

Hence, we can say that:

cos B = 80 / 82

cos B = 40 / 41.

Inn conclusion, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.

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#complete question:

Evaluate the function requested. Write your answer as a fraction in lowest terms.

Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 82, adjacent B C is 18, opposite A C is 80.

Find cos B.

a.

Cosine B = StartFraction 9 Over 41 EndFraction

c.

Cosine B = StartFraction 9 Over 40 EndFraction

b.

Cosine B = StartFraction 40 Over 41 EndFraction

d.

Cosine B = StartFraction 41 Over 40 EndFraction

a.  There are 4 sample points in the sample space.

a) There are 4 sample points in the sample space.

b) The tree diagram and sample space are:

HH (two heads)

HT (one head, one tail)

TH (one head, one tail)

TT (two tails)

c) The probability that no tails are tossed (two heads) is 1/4 or 0.25.

d) The probability that exactly one tail is tossed (HT or TH) is 1/2 or 0.5.

e) The probability that two tails are tossed is 1/4 or 0.25.

f) The probability that at least one tail is tossed (HT, TH, or TT) is 3/4 or 0.75.

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The domain of g(x) = log (7x - 10) is all real numbers greater than 10/7.

Set-builder notation: x > 10/7. Interval notation: (10/7,∞)

Given the function in the question:

g(x) = log( 7x - 10 )

For the function g(x) = log (7x - 10), the domain consists of all the possible values of x that can be plugged into the function without resulting in an undefined expression.

Here, the logarithm (in this case, (7x - 10) must be greater than zero, since the logarithm of zero or a negative number is undefined in the real numbers.

So we set the argument of the logarithm to be greater than zero, and solve for x:

7x - 10 > 0

Solve for x

7x - 10 + 10 > 0 + 10

7x > 10

Dividing both sides by 7:

7x/7 > 10/7

x > 10/7

Therefore, the domain of g(x) = log (7x - 10) is x > 10/7

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The perimeter of the given triangle is 12.4x-8.0y+5.8z. Therefore, option C is the correct answer.

Given that, triangle has sides of lengths of (6.2x-9.4y) centimeters, (6.2x-2.5z) centimeters and (8.3z+1.4y) centimeters.

We know that, perimeter of triangle is sum of all the sides.

Now, perimeter = 6.2x-9.4y+6.2x-2.5z+8.3z+1.4y

= (6.2x+6.2x)+(-9.4y+1.4y)+(-2.5z+8.3z)

= 12.4x-8.0y+5.8z

Therefore, option C is the correct answer.

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Answer: 7 centimeters equals 70 millimeters :)

Answer:The graph of y = 4f(x-5) is not the same as the graph of y=f(x) because it is a transformation of the function f(x) that involves a horizontal shift to the right and a vertical stretch by a factor of 4.

It is true that the product of the index [tex](b^9)^3 = b^2^7[/tex]

Indices track asset performance in finance and specify array elements in math and programming; their use varies by subject. Different methods refer to list, vector, or matrix elements. Power law of indices: larger number or letter must match.

This can be expressed mathematically as am+n.

Additionally, there are several Laws of Indices that provide rules for simplifying calculations or expressions involving powers of the same base.

The given question is true or false is [tex](b^9)^3[/tex]= [tex]b^27(b^9)^3[/tex] = [tex](b^9)^3 = b^2^7[/tex]

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The solutions for the system of equations " 3x²-2y²+5=0 and 2x²-y²+2=0" are :

First Solution : x = 1, y = 2

Second Solution : x = 1, y = -2

Third Solution : x = -1, y = 2

Fourth Solution : x = -1 , y = 2.

In order to solve the system of equations 3x²-2y²+5=0 and 2x²-y²+2=0, we use substitution method;

From the second equation, we solve for y² in terms of x²:

The second equation is : 2x² - y² + 2 = 0;

We get, y² = 2x² + 2

Substitute this expression for y² into the first equation:

We get,

3x² - 2(2x² + 2) + 5 = 0

3x² - 4x² - 4 + 5 = 0

-x² + 1 = 0

x² = 1

We get, x = ±1

Substitute these values of x into the equation for y²:

y² = 2x² + 2

For x = 1, y² = 4,

Which means the solution set is (1,2) and (1,-2),

For x = -1, y² = 4

the solution set is (-1,2) and (-1,-2).

Therefore, the solutions to the system of equations are (1, 2), (1,-2), (-1,2) and (-1, 2).

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By permutation and combination we can say there are 25200 ways to allocate the bed

Mathematical concepts like permutation and combination count the number of possible arrangements or choices for an object.

The quantity of possible arrangements of objects in a given order is referred to as a permutation.

Combination refers to the variety of possible selections of objects that are made without respect to their sequence.

The number of ways to distribute the seven students' beds in a way that ensures student A doesn't share a bed with student B is equal to the number of ways to distribute the six students' beds in a way that ensures student A doesn't share a bed with student B multiplied by two. (since there are two possible positions for student B).

The following formula can be used to determine how many options there are to distribute the six available beds among the students so that Student A does not have a bed next to Student B:

In this instance, seven students with the identifiers A, B, C, D, E, F, and G will each receive seven bed places in a dormitory at the university. Because he is aware that student B snores, student A does not want to share a bed with him. As a result, we can group students A and B together and arrange them in six different ways.

Then we can arrange the remaining students C, D, E, F and G in 5! ways. Therefore, the total number of ways to allocate bed spaces to them if the concern of student A is to be honored is 6! * 5! = 17,280 .

the bed spaces to seven students such that student A does not get a bed next to student B

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Answer: x=3

Step-by-step explanation:

shaded part is 5/6 of the full circle, so just make an equation.

5/6 pi r^2(formula to find area)=15/2 pi(area given)

cancel out pi and simplify

r^2=9

r=+-3 but cant be negative so r=3

It will take about 711.12 minutes or approximately 11.85 hours to test all 400 units.

To find out how long it will take to test 400 units, we need to use the information given in the problem. We know that the quality expert can test 18 units in 32 minutes. We can use this information to find out how long it will take to test one unit.

First, we need to find out how many units can be tested in one minute:

18 units / 32 minutes = 0.5625 units per minute

This means that the quality expert can test 0.5625 units per minute. To find out how long it will take to test one unit, we can divide 1 by 0.5625:

1 / 0.5625 = 1.7778 minutes per unit

So it takes about 1.7778 minutes to test one unit. To find out how long it will take to test 400 units, we can multiply this value by 400:

1.7778 minutes per unit * 400 units = 711.12 minutes

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Note that the scatter plot (attached) for the given data is described below.

The scatter plot for the given data set shows a moderately strong negative linear relationship between x and y. The data points appear to form a somewhat linear pattern, indicating that there is a linear association between the variables.

The scatter plot suggests that as the x values increase, the corresponding y values decrease.

An appropriate sale for this data set would be a linear regression, which can provide a mathematical model for predicting y values based on x values.

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The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis

The ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.

If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).

If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).

The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.

Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.

Solving the given problem:

f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]

At x= 0 on the y- axis

f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]

Thus, only option C satisfies this condition.

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Answer:

B

Step-by-step explanation:

Vertex form is: y=a(x-h)²+k

Vertex would be (h,k)

Based on this, the only equation in vertex form is B

Answer:

Step-by-step explanation:

B is the easiest way to see vertex because that is the vertex form:

y=a(x-h)²+k     where (h,k) is the vertex

Vertex (2, 27)

We have 20 marbles in the bag. The probability of a marble that is not green is 20/20.

So the probability of the randomly that the marble is not green is 20/20 or just 20.

Answer:

The item when it is costs $50 and there is a 55% item, as the cost would be $22.50

Step-by-step explanation:

Whenever a discount is offered on a certain item, we can find the new price of the item using the formula.

[tex]N(P)=O-(P*O)[/tex], where N(P) is the new price (price when discount is applied), P is the percentage (converted to a decimal to simplify the problem), and O is the old price (price before discount is applied)

First store:  Since the item costs $60 (O) at this store and there is a 60% discount (60% becomes 0.60 and is our P value), we can find the new price aka N(P):

[tex]N(0.60)=60-(0.60*60)\\N(0.60)=60-36\\N(0.60)=24[/tex]

Second store:  For this store, our O value is $50, and our P value is 0.55 (55% becomes 0.55):

[tex]N(0.55)=50-(0.55*50)\\N(0.55)=50-27.50\\N(0.55)=22.50[/tex]

Thus, the second store has the better price

The actual rocket height is 1080 inches and the height of the actual rocket is 90 feet.

If the 1/20 scale model of the rocket stands 54 inches high, we can find the height of the actual rocket by multiplying the height of the model by 20:

Actual rocket height = 54 inches x 20 = 1080 inches

In order to convert inches to feet, we divide by 12:

Actual rocket height = 1080 inches / 12 = 90 feet

Therefore, the height of the actual rocket is 90 feet.

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The 1/20 scale model of the rocket stood 54 inches high What was the height of the actual rocket?

(b) Find the height of the actual rocket in feet.

Answer:

A

Step-by-step explanation:

The degree of a polynomial is the highest exponent of the variable in the polynomial.

In this case, the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2 is 5, because the highest exponent of x is 5 (in the term -3x^5). Therefore, the answer is 5.

a. The slopes of the lines are:

Slope of line 1 = 1/4

Slope of line 2 = -4

Slope of line 3 = -1/3

b.

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (-3 - 0) / (-4 - 8)

m = (-3) / (-12)

m = 1/4

m = (2 - 6) / (0 - (-1))

m = (-4) / (1)

m = -4

m = (-7 - (-4)) / (6 - (-3))

m = (-3) / (9)

m = -1/3

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

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The vector u+v can be represented as < √85, -41.19° >, which is obtained by adding vector u marked on the y-axis from 0 to 6 and vector v marked on the x-axis from 0 to -7 on a coordinate plane.

To add vectors on the coordinate plane. The vector u is marked on the y-axis from 0 to 6, and the vector v is marked on the x-axis from 0 to -7.

To add them, we start at the tail of u and move horizontally to the left by 7 units (since v has a negative x-component) and then vertically up by 6 units (since u has a positive y-component) to reach the head of the resulting vector. This gives us the vector u+v.

So, the vector u+v can be represented as

Magnitude √(6^2 + 7^2) = √85

Direction atan(6/(-7)) = -41.19 degrees (measured counterclockwise from the positive x-axis)

Notation < √85, -41.19° >

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Answer:

24

Step-by-step explanation:

14 + 17 + 21 + 28 +40 / 5

120 / 5

24

If Yogi Charges 4.30$ per square foot for the carpet plus $75 installation fee, the total cost of installing carpet in the hotel lobby with Yogi is $2,225.

To determine the total cost of installing carpet in the hotel lobby with Yogi, we need to know the area of the lobby in square feet. Once we have the area, we can use Yogi's pricing scheme to calculate the total cost.

Assuming that we have measured the area of the lobby to be 500 square feet, we can calculate the total cost as follows:

Cost of carpet = area × price per square foot

= 500 × $4.30

= $2,150

Cost of installation = $75

Total cost = cost of carpet + cost of installation

= $2,150 + $75

= $2,225

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We have proven that m∠C = m∠A.

We have,

We are given that m∠A + m∠B = m∠B + m∠C.

We want to prove that m∠C = m∠A.

Using algebra,

We can subtract m∠B from both sides of the equation, which gives us m∠A = m∠C.

This shows that the measure of angle A is equal to the measure of angle C, and therefore, m∠C = m∠A.

We can also use the transitive property of equality to show that

m∠A = m∠B, since m∠A + m∠B = m∠B + m∠C, which implies that

m∠A = m∠C.

Therefore,

We have proven that m∠C = m∠A.

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If house is purchased for $313,000 with a 15% down payment, the monthly payment for the mortgage is $1,906.33.

To find the monthly payment for a mortgage secured at 7% for 25 years on a house purchased for $313,000 with a 15% down payment, we can use the formula for calculating mortgage payments:

P = L[c(1 + c)ⁿ]/[(1 + c)ⁿ - 1]

Where P is the monthly payment,

L is the loan amount (which is the purchase price minus the down payment),

c is the monthly interest rate (which is the annual interest rate divided by 12),  

n is the total number of monthly payments (which is the number of years multiplied by 12).

Substituting the given values, we get:

L = $313,000 - 0.15($313,000) = $266,050

c = 0.07/12 = 0.00583

n = 25 x 12 = 300

Plugging these values into the formula, we get:

P = $266,050[0.00583(1 + 0.00583)³⁰⁰]/[(1 + 0.00583)³⁰⁰ - 1]

Simplifying the expression, we get:

P = $1,906.33

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The result of the operation that we have done here is -5√3.

We know that one of the most important things that we have to do in mathematics is that we have to convert word equations into mathematical equations and this is quite critical in how we can be able to work it so as to get the equation that we are looking for.

We now have that;

5/-3 * 3 * √3

5/-1 * √3

-5* √3

-5√3

We can see that after the computation of the word problem that we have here, the result is -5√3

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For the given function 'g':

domain = (-4, -2) ∪ (1, 3]

range = (-5, 4]

If the function is defined as f(x) = y, then the values of x for which the value of function exists, the set of that values is said to be the domain of the function f.

If the function is defined as f(x) = y, then the set of all possible values of the function that is the set of all possible values of y is said to be the range of the function f.

Here given the graph of 'g'.

From the graph we can see that for -4 < x < -2 and 1 < x [tex]\le[/tex] 3 the function has graph.

So the domain = (-4, -2) ∪ (1, 3]

And it is clear that the value of y lies between -5 < y [tex]\le[/tex] 4.

So the range = (-5, 4].

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