3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors. (True or False)

The expression for the area of the triangle is given as follows:

A = 1.5x^4 + x³ - 0.5x².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5(3x² - x)(x² + x)

A = 0.5(3x^4 + 3x³ - x³ - x²)

A = 0.5(3x^4 + 2x³ - x²)

A = 1.5x^4 + x³ - 0.5x².

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The sets of transformations that result in the same image when performed in any order are:

Translation, dilation with center (0,0)

Two translations

In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.

Here,

For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.

For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.

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a) The linear equation is:

y = 25 + x

b) When the daughter's is one third of her mother's age​ we will have x = 12.5

We know that the mother is 25 years older than the daughter, so, if the daughter's age is x, the mother's age can be defined as the linear equation:

y = 25 + x

b) When the daughter's age is one third of her mother's, we have:

x = (1/3)*y

3x = y

Replacing that in the equation above we will get:

3x = 25 + x

3x - x = 25

2x = 25

x = 25/2 = 12.5

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The only prism with a volume between 10 and 20 cubic inches is Prism C, which has a volume of 16 cubic inches.

To find the volume of each prism, we need to use the formula of volyume for prisms which is: Volume = Base Area x Height. Now we will go ahead to find the volumes for all the prisms as follows:

Prism A:

Base Area = 4 x 5 = 20

Height = 2

Volume = 20 x 2 = 40 cubic inches

Prism B:

Base Area = 3 x 4 = 12

Height = 3

Volume = 12 x 3 = 36 cubic inches

Prism C:

Base Area = 4 x 4 = 16

Height = 1

Volume = 16 x 1 = 16 cubic inches

Prism D:

Base Area = 4 x 4 = 16

Height = 6

Volume = 16 x 6 = 96 cubic inches

So, the prism whose volume falls between 10 to 20 is the third prism.

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If you know that a girl plays soccer, then the probability that she also plays basketball = 0.23

The correct answer is an option (c)

Let's assume that event S: a girl plays soccer

event B: a girl plays basketball

Here, the probability that the girl plays soccer would be,

P(S) = P(SB) + P(SB')

where B' means a girl does not play basketball

here, P(SB) = 0.075 and P(SB') = 0.250

So, P(S) = 0.075 + 0.250

P(S) = 0.325

We need to find the probability that a girl plays basketball knowing that she plays a soccer.

i.e., the conditional probability P(B|S)

Using formula for the conditional probability,

P(B|S) = P(BS) / P(S)

           = 0.075 / 0.325

           = 0.23

Therefore, the correct answer is an option (c)

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Find the complete question below.

Trigonometric ratios allow us to determine the value of Cos²θ to be = 5/9. As a result, choice D is the best one.

Triangle side ratios are known as ratios of trigonometry. These ratios demonstrate how a right triangle's edges to angles ratio functions in mathematics. The sine, cosine, and tangent trigonometric ratios are the fundamental three. The sin, cos, and tan functions can be used for calculating the other significant trig ratios, cosec, sec, and cot.

Here in the question,

Sinθ = 2/3

Now,

Cos²θ = 1 - Sin²θ

= 1- (2/3) ²

= 1 - 4/9

= (9-4)/9

= 5/9

Therefore, the value of Cos²θ = 5/9.

Option D is the correct option.

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The complete question is:

Given: sinθ = 2/3 and is in the second quadrant; evaluate the following expression: cos²θ

a). -7/9

b). -1/9

c). 1/9

d). 5/9

Answer:

$14,766.00

Step-by-step explanation:

Interest = principle x rate x time

I = 13800 (.14)(.5)

I = 966

Total:

Principle plus interest

13800 + 966 = 14,766

Helping in the name of Jesus.

The function f(x) that has a local minimum at (0,0) and a local maximum at (1,3) is f(x) = 2x³ - 3x².

From the information, we can set up a system of equations as follows:

f'(x) = 3ax² + 2bx + c = 0 (at x=0)

f'(x) = 3ax² + 2bx + c = 0 (at x=1)

Plugging in x=0, we get:

f'(0) = c = 0

Plugging in x=1, we get:

f'(1) = 3a + 2b + c = 0

3a + 2b = -c = 0

3a + 2b = 0 (since c=0)

Solving the system of equations, we get:

a = 2

b = -3

c = 0

d = 0

The function is f(x) = 2x³ - 3x²

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(a) The point estimate is 92/160 = 0.575 or 57.5%.

(b) Using the salt program, the 90% confidence interval is [0.502, 0.648].

(c) Using the salt program, the 95% confidence interval is [0.476, 0.674].

(d) The 95% confidence interval is wider than the 90% confidence interval.

(a) The point estimate for the above problem is the proportion of people who support new gun regulations, which is 92/160 = 0.575 or 57.5%.

(b) To find the 90% confidence interval, we can use the following formula:

[tex]CI = p ± z*(sqrt(p*(1-p)/n))[/tex]

where p is the point estimate, z is the z-score corresponding to the confidence level (90% in this case), and n is the sample size. Using a standard normal distribution table, we find that the z-score for a 90% confidence level is 1.645. Substituting the values, we get:

[tex]CI = 0.575 ± 1.645*(sqrt(0.575*(1-0.575)/160)) = (0.500, 0.650)[/tex]

Therefore, the 90% confidence interval for the proportion of people who support new gun regulations is (0.500, 0.650).

(c) To find the 95% confidence interval, we can use the same formula but with a different z-score. The z-score for a 95% confidence level is 1.96. Substituting the values, we get:

[tex]CI = 0.575 ± 1.96*(sqrt(0.575*(1-0.575)/160)) = (0.480, 0.670)[/tex]

Therefore, the 95% confidence interval for the proportion of people who support new gun regulations is (0.480, 0.670).

(d) The 95% confidence interval is wider than the 90% confidence interval, which is expected because a higher confidence level requires a wider interval to capture the true population proportion with higher probability.

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If one zero of the polynomial 3x^2 + 8x + k is  the reciprocal of the

other, then k = 3 by applying product of roots formula.

The quadratic polynomial is 3x^2 + 8x + k.

Let the roots of  3x^2 + 8x + k be m and n where m and n are reciprocal of each other. Therefore, n = 1/m

Thus, the product of roots is = m*n = m*(1/m) = 1 ____(1)

The general equation of a quadratic equation can be written as,

ax^2 + bx + c = 0

where a and b are coefficients of x^2 and x respectively and c is a constant term.

From product of roots formula we know that,

Product of roots =constant term/ coefficient of x^2 = c/a

Therefore, for polynomial is 3x^2 + 8x + k we get,

Product of roots = k/3 ____(2)

From equating equation (1) and (2) we get,

k/3 = 1

⇒ k = 3

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The given question is incomplete, the complete question is

"If one zero of the polynomial 3x^2+8x+k is the reciprocal of the other, then find the value of k."

To discover the probability that the ceramics piece is painted, we basically separate the number of painted pieces by the whole number of pieces: P(painted) = 183/837 ≈ 0.2185

b. To discover the likelihood that the painted ceramics piece is painted in a curvilinear enhancement, we utilize Bayes' hypothesis:

P(curvilinear | painted) = P(painted | curvilinear) * P(curvilinear) / P(painted)

We are given that there are 183 painted pieces, of which 14 are painted in a curvilinear enrichment. In this manner,

P(painted | curvilinear) = 14/183 ≈ 0.0765

We are moreover given that there are 837 pieces in add up, of which 183 are painted.

P(painted) = 183/837 ≈ 0.2185, we ought to discover the likelihood that a painted piece is painted in a curvilinear enrichment, which is given as 14 out of 183 painted pieces. P(curvilinear) = 14/183 ≈ 0.0765

P(curvilinear | painted) = (0.0765) * (0.0765) / (0.2185) ≈ 0.0266

thus, given that the pottery piece is painted, the likelihood that it is painted in a curvilinear enhancement is roughly 0.0266, or 2.66%.

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The evaluated solution for the  given  question comprises of sample point of a that are  {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4  below under the condition of a fair coin is tossed three times, and the events a and b are defined.

a)  Points sample  for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points  sample  for event b: {HTT, THT, TTH, HHH}
Points  sample  for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
  Points  sample for event ac: {TTT}
  Points  sample for event a c: {TTT, HHHH}

b)  Event a probability= 7/8 = 0.875
  Event b probability= 1/2 = 0.5
  Event ab probability = 3/8 = 0.375
  Event ac probability   = 1/8 = 0.125
  Event a c probability  = 1/16 + 1/8 = 0.1875

c) Probability of a b implementing additive rule
    P(a b) = P(a) + P(b) - P(a ∩ b)
     P(a ∩ b) = P(a) + P(b) - P(a b)
     P(a ∩ b) = (7/8) + (1/2) - (3/8)
     P(a ∩ b) = 9/8 - 3/8
     P(a ∩ b) = 6/8
     P(a ∩ b) = 3/4

d)  Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.


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The correct statement is:

O It is the ratio of the area of the circle to the area of the square from a cross section.

In the deriving of formula for volume of a cone, it is determined that the volume of the cone equates to one third the volume of the cylinder in which it fits within.

The one third factor emanates from the ratio between the base areas of the cone and cylinder found in cross sectional analysis. The base of the cone being constructed as a circle while the foundation of the cylinder consisting of a square; since the former is encased within the latter, the side of the square is precisely equal to the diameter of the circle.

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Answer:

1300 milliliters

Step-by-step explanation:

There are 1000 milliliters in one liter. so 1.3 liters would be 1300. 1.3 x 1000 = 1300.

Answer:

[tex]y = {1.5}^{x} [/tex]

[tex] ln(y) = ln( {1.5}^{x} ) [/tex]

[tex] ln(y) = x ln(1.5) [/tex]

[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]

[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]

(a) The probability that both missiles will hit the target is 1/10.

(b) The probability that at least one missile will hit the target is 11/20.

To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting

P(both missiles hit) = P(first missile hits) × P(second missile hits)

P(both missiles hit) = (1/4) × (2/5)

P(both missiles hit) = 2/20

P(both missiles hit) = 1/10

So the probability that both missiles will hit the target is 1/10.

(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)

P(at least one missile hits) = 1 - P(both missiles miss)

P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)

P(at least one missile hits) = 1 - (3/4) × (3/5)

P(at least one missile hits) = 1 - 9/20

P(at least one missile hits) = 11/20

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The true statements are:

A. Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars.

C. Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.

Mean Absolute Deviation (MAD) is a measure of variability in a set of numerical data. It is calculated by finding the average absolute difference between each data point and the mean of the dataset.

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The tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass cutting process.

The tank has four vertical rectangular sides, a bottom, and no top. Since there is no top, we do not need to include the area of any glass for the top of the tank.

The area of each rectangular side is given by multiplying the height by the width. The area of the bottom is given by multiplying the length by the width. Therefore, the total area of glass used to make the tank is:

Area = 2(height x width) + 2(height x length) + (length x width)

Substituting the given values, we get:

Area = 2(23 x 18) + 2(23 x 12) + (18 x 12)

Area = 1,656 + 1,656 + 216

Area = 3,528

Therefore, the tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass-cutting process.

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Answer:

1E+30

Step-by-step explanation:

Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be (c) 11.

The dot-plot displays a unimodal distribution with a moderate to large spread of the data.

The spread of the data is roughly from 0 to 40, with most of the dots being between 10 to 30.

The spread of the dots, it is unlikely that the standard deviation of the data is as small as 5 or 8.

Similarly.

It is unlikely that the standard deviation is as large as 20 or 15 as there are a significant number of data points that lie within the 20-30 range.

Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be around 11.

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It will take approximately 268.08 cubic feet of air to fill the giant beach ball.

A sphere is a three-dimensional geometric shape that is perfectly round in shape, with every point on its surface equidistant from its center. It is a type of round solid figure that has no edges or vertices. The surface of a sphere is continuous, and it encloses a fixed volume of space.

The formula for the volume of a sphere is:

V = (4/3) × π × r³

where r is the radius of the sphere.

In this case, the radius of the beach ball is 4 feet, so we can substitute this value into the formula:

V = (4/3) ×π × (4)³

V = (4/3) × π × 64

V = 268.08 cubic feet (rounded to two decimal places)

Therefore, it will take approximately 268.08 cubic feet of air to fill the giant beach ball.

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Answer:

[tex] \frac{36}{12} = \frac{39}{x - 10} [/tex]

[tex] 3 = \frac{39}{x - 10} [/tex]

[tex]3(x - 10) = 39[/tex]

[tex]x - 10 = 13[/tex]

[tex]x = 23[/tex]

Answer:

0.06

6/100

Step-by-step explanation:

6% is equivalent to the decimal number 0.06 or the fraction 6/100.

Answer:

6/100 or 0.06

Step-by-step explanation:

hope this helps!

Answer:$2.7 would be saved

Step-by-step explanation:

Multiply 18 by .15 which gives you 2.7 which is the answer.

Answer:

Let's first calculate the number of students who passed the test and completed the assignment. We know that 15 students passed the test and 6 students who failed the test and did not complete the assignment. Therefore, there are 25 - 15 - 6 = 4 students who failed the test but completed the assignment.

Now we can calculate the probability that a student who completed the homework passed the test by dividing the number of students who passed the test and completed the assignment by the total number of students who completed the assignment.

The number of students who passed the test and completed the assignment is 15 - 6 = 9. The total number of students who completed the assignment is 16 - 6 = 10. Therefore, the probability that a student who completed the homework passed the test is 9/10 or 0.9.

Step-by-step explanation:

Answer:22x121=2662

Step-by-step explanation:

The multiplicand is 22, the multiplier is 121 and the product is 2662.

The volume of the cheese head is 192 cubic inches.

Explain the term volume

Volume refers to the amount of space that an object or substance occupies in three dimensions. It is typically measured in units such as cubic meters or cubic feet. The volume of an object can be calculated using various formulas, depending on its shape and dimensions.

According to the given information

The volume V of a triangular prism is given by the formula:

V = (1/2) * b * h * L

In this case, the base of the triangle is 12 inches, the height of the triangle is 8 inches, and the length of the prism (depth of the 3D shape) is 4 inches. Substituting these values into the formula, we get:

V = (1/2) * 12 * 8 * 4

V = 192 cubic inches

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Yes, the sample size of 4,706 is large enough to justify the use of the z formula.

To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.

One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.

In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.

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