A student answers ​90% of the questions on a math exam correctly. If she answers 27 questions​ correctly, how many questions are on the​ exam?

If both the upstairs and downstairs switches are in the up position, the light will be off

The given parameters are

Switches = 2 i.e. top and bottom

Also, we have:

When the upstairs switch is up and the downstairs switch is down, the light is turned on.

This means that the light is only on when the upstairs switch is up and the downstairs switch is down

Any other position of the switches, the light is off

From the question, we have

Both the upstairs and downstairs switches are in the up position

This is different from the required position to on the light

Hence, the light will be off

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1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

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

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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Answer:

V = 192 m3

Step-by-step explanation:

The central angle of the sector with a radius of 5 cm and an area of 5π cm² is 72 degrees.

To find the central angle of a sector, we need to use the formula that relates the sector area to the central angle and the radius of the circle. The formula for the area of a sector is:

Area = (θ/360) * π * r^2

Where:

Area is the sector area

θ is the central angle in degrees

π is a mathematical constant (pi)

r is the radius of the circle

In this case, we are given the radius of the circle as 5 cm and the sector area as 5π cm². Let's substitute these values into the formula and solve for θ.

5π = (θ/360) * π * 5^2

Simplifying the equation:

5π = (θ/360) * 25π

To eliminate π, we can divide both sides of the equation by π:

5 = (θ/360) * 25

Now, let's isolate θ by multiplying both sides of the equation by (360/25):

5 * (360/25) = θ

Simplifying the equation:

θ = 72

Therefore, the central angle of the sector is 72 degrees.

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The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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Answer: The answer is 3

Step-by-step explanation:

12 out of 20 are full.

Divide full by total cans and then multiply by 100:

12/20 = 0.6 x 100 = 60 %

Answer: 60% are full

The value of the x would be 25.723 cm.

What is the area of the circle?

For any circle, if 'r' is the radius of the circle then the area of the circle would be

      Area = π×r²

Where π = 3.14 (or) π = 22/7.

And the diagonal of the square with side 'a' is √2*a.

Given:

The square is inscribed into a circle.

The length of the side of the square is 'x' cm.

and the area of the circle is 56 cm².

            Area of circle = π.r²

                56 = 22/7×r²

                r² = 57 * 7/22

                r² = 18.1363

Taking square root on both sides, we get

                  r = 4.25

Now as the square is inscribed into a circle, then the radius will be half the diagonal of the square.

                Diagonal = 2 × r

                 √2x =  36.27

                    x = 36.27/√2

                    x = 25.723 cm

Hence, the value of the x would be  25.723 cm.

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Karen should order 41 square meters of carpet, and the cost will be $1,024.59 (taxes included).

An algebraic expression is a mathematical phrase that consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It is a combination of constants, variables, and operators that represent a value or a relationship between values.

For example, "3x + 5" is an algebraic expression where "3" and "5" are constants, "x" is a variable, and "+" is an operator. The expression can be evaluated by substituting a value for "x" and performing the necessary operations.

Algebraic expressions can also be simplified by combining like terms and using the rules of arithmetic to simplify the expression. For instance, the expression "2x + 3x" can be simplified to "5x" by adding the coefficients of the like terms "x".

Algebraic expressions are used extensively in algebra to represent equations and relationships between variables. They are also used in a wide range of mathematical and scientific applications, including physics, engineering, and finance.

To calculate the amount of carpet Karen needs to order, we first need to convert the measurements of her living room from feet to meters:

Length: 18 feet = 5.4864 meters (rounded to four decimal places)

Width: 24 feet = 7.3152 meters (rounded to four decimal places)

To find the area of the living room in square meters, we multiply these two values:

Area: 5.4864 meters x 7.3152 meters = 40.0637 square meters (rounded to four decimal places)

Since Karen can only order full square meters of carpet, she should order 41 square meters (to be safe).

To calculate the cost of the carpet, we simply multiply the area by the cost per square meter:

Cost: 41 square meters x $24.99/square meter = $1,024.59

So Karen should order 41 square meters of carpet, and the cost will be $1,024.59 (taxes included).

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Answer:

63

Step-by-step explanation:

Answer:

the area is 43cm²

Step-by-step explanation:

First, you find the area of the left side. 7cm - 3cm= 4cm

Secondly, you multiply 4cm x 4cm = 16cm

Then, you find the area of the bottom bit. 9cm x 3 cm = 27cm

Lastly, you add 27cm + 16cm, which brings your answer to...

43cm² :-)

(It's squared because you are finding the area)

Answer:

True

Step-by-step explanation:

True. A z-score, also known as a standard score, is a statistical measure that helps to determine how far a particular value is from the mean relative to the data set's standard deviation.

A z-score is a dimensionless quantity that expresses the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean. A positive z-score indicates that the value is above the mean, while a negative z-score indicates that the value is below the mean.

To calculate the z-score for a given value, the formula is: z = (x - μ) / σ where z is the z-score, x is the value being considered, μ is the mean of the data set, and σ is the standard deviation of the data set.

For example, if the mean of a data set is 50 and the standard deviation is 10, and we are interested in finding the z-score for a value of 65, the calculation would be: z = (65 - 50) / 10 = 1.5. This indicates that the value of 65 is 1.5 standard deviations above the mean of the data set.

Z-scores are useful for comparing values across different data sets or for identifying extreme values in a data set. Values with high positive or negative z-scores are typically considered to be outliers, indicating that they are further from the mean than most other values in the data set.

In summary, the statement "z-score helps to determine how far a particular value is from the mean relative to the data set's standard deviation" is true. Z-scores are a statistical measure that help to express the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean.

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The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who have part-time jobs, P(A) = 73%

Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%

Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:

P(B|A) = P(A∩B)/P(A)

          = 42/73

          = 0.58

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Answer:

0.575

Step-by-step explanation:

nice job

Answer:

Center (-13 , -2); Radius = 9

Step-by-step explanation:

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Km = miles x 1.609

240 x 1.609 = 386.24 km

The answer is D. 386 kilometers

Answer:

D. 386

Step-by-step explanation:

If we know that we have 240 miles then we need to find the Km/m which is 1.60934 Km to 1 M, and we have the equation y= 1.60934(x), y bing the total amount of Km, or in other words, your answers, and x is the miles. Now change that x into 240 so now you have y= 1.60934(240) which comes out to 386.2416 Km or 386Km as seeing you have to round tho the nearest whole number.

Yes and No, if you divide 6 by 3, 2, or 1, it will have a quotient less than 6. Dividing 6 by 3 = 2, 6 by 2 = 3, 6 by 1 = 6.

Answer:

Step-by-step explanation:

There are several things we need to do/know to figure this out. First we have to know that the perpendicular slope to a line is the opposite reciprocal of the slope of which it is perpendicular (did that make sense?!). In other words, we have to find the slope of the line 5x - 8y + 24 = 0 and then take the opposite reciprocal of it. Solving for y:

\(y=\frac{5}{8}x+3\) with a slope of 5/8. The perpendicular slope, then, is -8/5. So we have m now in y = mx + b. Now onto the second equation...

The equation for which we need the same x-intercept is 7x - 12y - 70 = 0. The x-intercept exists when y = 0, so filling in a 0 for y:

7x - 12(0) = 70 and

x = 10. Now we know x. We also know, however, that when x = 10, y = 0, so we have everything we need to sub into the linear equation and solve for b:

0 = -8/5(10) + b and

0 = -16 + b so

b = 16 and the equation we are looking for is

y = -8/5x + 16

Step-by-step explanation:

Let Jack's present age be x

Hence, his fathers present age=4x

Jacks age after 5 years= (x+5)

Jacks Fathers age after 5 years= (4x+5)

We know.. that the difference between their ages fives years later is 10.. hence

4x+5-(x+5)=10

4x+5-x-5=10

3x = 10

x= 3.3 years old...

Hence,

Jacks present age = 3.3 years

Fathers present age= 13.2 years...

Hope it helps .. I know that the answer comes in decimals... but the questions' like that..

The solution is that the rancher should buy 26 steers and 13 cows

Let's start by setting up a system of equations based on the given information.

The total amount of money the rancher has is $1000, and they plan to buy steers at $25 each and cows at $26 each. Let's say they buy s steers and c cows, then we have:

$25s + $26c = $1000 (Total amount spent)

We also know that s and c are both positive integers (whole numbers greater than zero).

We can solve for s and c by using some algebraic techniques. First, let's simplify the equation by dividing both sides by $1 to get rid of the dollar sign

25s + 26c = 1000

Now we can use a technique called "integer division" to solve for s and c. We'll start by assuming that the rancher buys all steers and no cows, which gives us

25s + 26(0) = 1000

25s = 1000

s = 40

So the rancher could buy 40 steers with their $1000. However, we need to account for the fact that they can also buy cows. Let's say they buy c cows, then we can set up another equation based on the total number of animals they buy

s + c = Total number of animals

Since we don't know the total number of animals, we'll leave that as a variable for now. We can use this equation to solve for c in terms of s:

c = Total number of animals - s

Now we can substitute this expression for c into the first equation:

25s + 26c = 1000

25s + 26(Total number of animals - s) = 1000

25s + 26Total number of animals - 26s = 1000

-Taking 25s to the right side

26Total number of animals = 1000 + s

dividing both sides by 26

Total number of animals = 38 + s/26

So the total number of animals must be a whole number, which means that s/26 must be a positive integer. We can try different values of s to see which ones work

If s = 26, then s/26 = 1 and Total number of animals = 39. This gives us c = 39 - 26 = 13, so the rancher would buy 26 steers and 13 cows.

If s = 52, then s/26 = 2 and Total number of animals = 40. This gives us c = 40 - 52 = -12, which doesn't make sense since c must be a positive integer.

If s = 78, then s/26 = 3 and Total number of animals = 41. This gives us c = 41 - 78 = -37, which again doesn't make sense.

So the only solution that works is when the rancher buys 26 steers and 13 cows. This would cost

25(26) + 26(13) = $650 + $338 = $988

So the rancher would have $12 left over from their $1000 budget.

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The given question is incomplete, the complete question is:

With $1000 a rancher is to buy steers at  $25 each and cows at $26 each. If the number of steers s and the number of cows c are both positive integers, what is the solution?

The system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries.

Suppose the number of pounds of apples and strawberries is x and y respectively.

If the total of 35 pounds of apples and strawberries as a result,

x + y = 35-------(1)

If each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 then,

2x + 3y = 80---------(2)

Multiply equation 1 by 2 and subtract from equation 2 as

2x + 3y -2(x+y) = 80 - 2(35)

y = 10

Substitute the value of y we get x = 25

As a result, there are 25 pounds of apples and 10 pounds of strawberries in all.

Thus, the system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

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The maximum possible value for the objective function is b) 1200, which occurs at the corner point (0, 120).So the answer is (b) 1200.

To find the maximum possible value of the objective function, we need to evaluate it at each of the feasible corner points and choose the highest value.

Evaluating the objective function at each corner point:

(48, 84): 4(48) + 10(84) = 912

(0, 120): 4(0) + 10(120) = 1200

(0, 0): 4(0) + 10(0) = 0

(90, 0): 4(90) + 10(0) = 360

Therefore, the maximum possible value for the objective function is 1200, which occurs at the corner point (0, 120).

So the answer is (b) 1200.

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To find the maximum possible value for the objective function, we need to evaluate the objective function at each of the feasible corner points and choose the highest value.

- At (48, 84): 4(48) + 10(84) = 888
- At (0, 120): 4(0) + 10(120) = 1200
- At (0, 0): 4(0) + 10(0) = 0
- At (90, 0): 4(90) + 10(0) = 360

The highest value is 1200, which corresponds to the feasible corner point (0,120). Therefore, the answer is (b) 1200.
To find the maximum possible value for the objective function, we will evaluate the objective function at each of the feasible corner points and choose the highest value among them. The objective function is given as:

Objective Function (Z) = 4X + 10Y

Now, let's evaluate the objective function at each corner point:

1. Point (48, 84):
Z = 4(48) + 10(84) = 192 + 840 = 1032

2. Point (0, 120):
Z = 4(0) + 10(120) = 0 + 1200 = 1200

3. Point (0, 0):
Z = 4(0) + 10(0) = 0 + 0 = 0


Comparing the values of the objective function at these corner points, we can see that the maximum value is 1200, which occurs at the point (0, 120). Therefore, the maximum possible value for the objective function is:

Answer: (b) 1200

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The test that can be used to assess whether variances are equal between multiple groups is the Levene test.

The Levene test is a hypothesis test for the equality of variances in a statistical population. It is named after the American statistician Howard Levene. It is commonly used to check the null hypothesis of homoscedasticity or equal variances across k groups. The test is used to determine if two or more groups have different variances or if the variance is unequal. The null hypothesis of the Levene test is that the variance of the populations from which the groups are drawn is equal. The Levene test is an alternative to the F-test for equal variances. Therefore, it can be concluded that the Levene test can be used to assess whether variances are equal between multiple groups.

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3x + 2y = 5; 2x - 3y = 7. Hence, the given lines are intersecting. So, the given pair of linear equations has exactly one solution and therefore it is consistent.

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

If a system has no solution, it is said to be inconsistent . Represent parallel lines.

if Both line slope are same and parallel to each other.

So,  no solution

System is  inconsistent.

if Both equation represent the same line. So, infinite many solution.

System is consistent.

if Both lines are parallel. So, no solution.

System is inconsistent.

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Total for 1500 tickets= $48,250.

Cost adults= $45 x

Cost children= $10. or (x-35)

Number of adult tickets sold= 950

Number of children tickets sold= 550.

To find the correct form of the partial fraction decomposition for the expression:   \(\(\frac{9x^2 - 8}{(3x^2 - 4)^2}\)\)

We need to factor the denominator and decompose it into partial fractions. Let's factor the denominator first:

\(\(3x^2 - 4 = (3x - 2)(x + 2)\)\)

Now, we can decompose the expression into partial fractions using the following general form:

\(\(\frac{A}{3x - 2} + \frac{B}{x + 2} + \frac{C}{(3x - 2)^2} + \frac{D}{(x + 2)^2}\)\)

To determine the values of A, B, C, and D, we need to find the common denominator and equate the numerators:

\(\(9x^2 - 8 = A(x + 2)(3x - 2) + B(3x - 2)(x + 2) + C(x + 2) + D(3x - 2)\)\)

Now, we can solve for A, B, C, and D by comparing the coefficients of like terms on both sides of the equation.

However, by following the steps outlined above, you can determine the specific values and complete the partial fraction decomposition.

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