what is the area of triangle ABC?

Answer: 24

Step-by-step explanation:

50% is just 0.5, or half. If half of the shapes are 12, then the total will be double of 12, or 24 shapes.

Complete question is;

Identify the type of sampling​ used: random,​ systematic, convenience,​ stratified, or cluster.

To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans

Answer:

Systematic Sample

Step-by-step explanation:

We are told that the quality control manager selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans.

Thus, the selection is from a large sample of produce.

This is synonymous with systematic sample because systematic sample can be defined as a type of probability sampling in which sample members from a larger population are selected according to a random starting point but with a set periodic interval.

This resonates with the statement in the question about selecting every 18th soup from the production assembly line.

Answer:

24

Step-by-step explanation:

√64 ×∛27

√64=√8²=8

∛27 = √3³=3

8*3=24

Answer:

41 degrees

Step-by-step explanation:

In a parallelogram, opposite angles are equal, so:

\(3x+11=5x-9\\-2x = -20\\x=10\\\\E = 3x + 11\\E = 3 * 10 + 11\\E = 30 + 11\\E = 41\)

Answer:

Hope that helps!!

18.84x

Answer:

More students prefer PE.

Step-by-step explanation:

20 × 70% = 14

14 > 4

14 students prefer PE

4 prefer social studies

OR

4 ÷ 20 = 0.2

0.2 = 20%

70% > 20%

70% of the students prefer PE

20% of the students prefer social studies

Answer:

1/27

Step-by-step explanation:

(1/27)^2016*27^2015 =

27^-2016 * 27^2015 =

27^(-2016+2015) =

27^-1 =

1/27

9514 1404 393

Answer:

  20.3

Step-by-step explanation:

The distance formula can be used to find the side lengths.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

For the first two points, ...

  d = √((3 -(-2))^2 +(6 -3)^2) = √(5^2 +3^2) = √34 ≈ 5.83

For the next two points, ...

  d = √((2 -3)^2 +(-2-6)^2) = √(1 +64) = √65 ≈ 8.06

For the last and first points, ...

  d = √((-2-2)^2 +(3-(-2)^2) = √(16 +25) = √41 ≈ 6.40

Then the sum of the side lengths is ...

  5.83 +8.06 +6.40 = 20.29 ≈ 20.3

The perimeter of the triangle is about 20.3 units.

At a significance level of 0.01, we can confidently state that the student's claim is true.

The hypothesis in this question can be stated as follows:

Null Hypothesis: H0: μ1 = μ2 (There is no difference between the mean of four-year college enrollment and two-year college enrollment.)

Alternative Hypothesis: H1: μ1 > μ2 (Mean enrollment of four-year colleges is greater than the mean enrollment of two-year colleges in the United States.)

The significance level (α) is given as 0.01, which represents the probability of rejecting the null hypothesis when it is actually true.

To calculate the test statistic, we can use the formula:

z = ((X1 - X2) - (μ1 - μ2)) / √((σ1² / n1) + (σ2²  / n2))

Substituting the given values:

z = ((6193 - 4305) - (0)) / √((598²  / 35) + (572²  / 35))

z = 10.33

Since this is a right-tailed test, we need to compare the test statistic with the critical value. At a significance level of 0.01, the critical value is 2.33.

The calculated test statistic (10.33) is greater than the critical value (2.33). Therefore, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

In conclusion, at a significance level of 0.01, we can confidently state that the student's claim is true. The mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

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No, it is not true that ∫_0^1 l(θ | x0) dθ = 1. The integral of the likelihood function l(θ | x0) over the parameter space [0, 1] does not necessarily equal 1.

The likelihood function l(θ | x0) measures the probability of observing the data x0 given the parameter value θ. It is a function of the parameter θ, and not a probability distribution over θ.

Therefore, the integral of the likelihood function over the parameter space does not have to equal 1, unlike the integral of a probability density function over its support.

In fact, the integral of the likelihood function over the parameter space is often referred to as the marginal likelihood or the evidence, and is used in Bayesian inference to compute the posterior distribution of the parameter θ given the data x0. The marginal likelihood is given by: ∫_0^1 l(θ | x0) p(θ) dθ

where p(θ) is the prior distribution of the parameter θ. The marginal likelihood is used to normalize the posterior distribution so that it integrates to 1:
p(θ | x0) = l(θ | x0) p(θ) / ∫_0^1 l(θ | x0) p(θ) dθ

In conclusion, the integral of the likelihood function over the parameter space does not necessarily equal 1, and is used in Bayesian inference to compute the posterior distribution of the parameter θ given the data x0.

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The angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

To find the angle between two vectors, we can use the dot product formula and the magnitude of the vectors. The dot product of two vectors u and v is given by:

u · v = |u| |v| cos(theta)

where |u| and |v| are the magnitudes of vectors u and v, respectively, and theta is the angle between the vectors.

Given vectors u = <6, 4> and v = <7, 5>, we can calculate their magnitudes as follows:

|u| = sqrt(6^2 + 4^2) = sqrt(36 + 16) = sqrt(52) ≈ 7.21

|v| = sqrt(7^2 + 5^2) = sqrt(49 + 25) = sqrt(74) ≈ 8.60

Next, we calculate the dot product of u and v:

u · v = (6)(7) + (4)(5) = 42 + 20 = 62

Now, we can substitute the values into the dot product formula:

62 = (7.21)(8.60) cos(theta)

Solving for cos(theta), we have:

cos(theta) = 62 / (7.21)(8.60) ≈ 1.061

To find theta, we take the inverse cosine (arccos) of 1.061:

theta ≈ arccos(1.061) ≈ 43.7 degrees

Therefore, the angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

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Regular hexagon ABCDEF is inscribed in a circle with center H, the image of segment BC after 120 degree clockwise rotation about point H is the segment joining the points B' and C', which has endpoints (-0.5r\(\sqrt{3\), -0.5r) and (-0.5r, -0.5r).

Since the hexagon is inscribed in a circle with center H, we can conclude that H is also the center of the circle passing through vertices B, C, and D. Therefore, the circle passing through B, C, and D is also a 120 degree clockwise rotation of the circle passing through A, B, and C.

To find the image of segment BC after a 120 degree clockwise rotation about point H, we need to find the coordinates of B and C relative to H, and then apply a 120 degree rotation matrix to these coordinates.

Let the radius of the circle be r, and let the coordinates of H be (0,0). Then the coordinates of B and C are:

B: (r cos(60), r sin(60))

C: (r cos(0), r sin(0)) = (r, 0)

To apply a 120 degree clockwise rotation matrix, we can use the following matrix:

[ cos(-120) -sin(-120) ]

[ sin(-120) cos(-120) ]

Simplifying, we get:

[ cos(120) sin(120) ]

[ -sin(120) cos(120) ]

Applying this matrix to the coordinates of B and C, we get:

B': [ cos(120) sin(120) ][ r cos(60) ] = [ -0.5r \(\sqrt{3}\)]

[ -sin(120) cos(120) ][ r sin(60) ] [ -0.5r ]

C': [ cos(120) sin(120) ][ r ] = [ -0.5r ]

[ -sin(120) cos(120) ][ 0 ] [ -0.5r ]

Therefore, the image of segment BC after a 120 degree clockwise rotation about point H is the segment joining points B' and C', which has endpoints (-0.5r\(\sqrt{3}\), -0.5r) and (-0.5r, -0.5r), respectively.

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Answer:

1 vase arrangement when 10 roses are left

Step-by-step explanation:

1. so 50 divided by 5 is 10.

That means every arrangement is 10 roses.

2. it asks us to find how many vase arrangement will be needed to have only 10 roses left. We already know that we only need 1 arrangement, because we already found that out in step 1.

Answer:

Let the radius of the circumscribed circle be r.

The formula for calculating the radius r is

r

=

Δ

s

Where  

Δ

is the area of the triangle

s

is the semi-perimeter.

s

for any triangle is calculated as

s

=

a

+

b

+

c

3

Where,  

a

,

b

,

c

is the sides of the triangle

Δ

=

√

s

(

s

−

a

)

(

s

−

b

)

(

s

−

c

)

(Heron's Formula)

Plug in the values and get the answer.

Once you have the radius, you can easily find out the area of the circle.

Step-by-step explanation:

The solution to the differential equation x(dy/dx) - 4y = 7x^4 * e^x

is  \(y(x) = 7 * e^x + C * x^4.\)

To solve the differential equation x(dy/dx) - 4y = 7x^4 * e^x, follow these steps:

Step 1: Identify the type of differential equation. This equation is a first-order linear differential equation, as it has the form

x(dy/dx) + p(x)y = q(x).

Step 2: Find the integrating factor. The integrating factor is given by e^(∫p(x)dx).

In this case, p(x) = -4/x, so the integrating factor is

\(e^(\int ^(^-^4^/^x^)^d^x^) = e^(-4^l^n^|^x^|^) = x^(^-^4^).\)

Step 3: Multiply the entire differential equation by the integrating factor.

This gives \(x^(-4)(x(dy/dx) - 4y) = x^(-4) * 7x^4 * e^x\).

Step 4: Simplify the equation. The left side of the equation becomes (dy/dx) - 4/x * y, and the right side becomes 7 * e^x.

Step 5: Integrate both sides of the equation.

\(\int (dy/dx) - 4/x * y dx = \int7 * e^x dx.\)

Step 6: The left side becomes y(x), and the right side becomes 7 * e^x + C, where C is the constant of integration.

Step 7: Solve for y(x). The final solution is\(y(x) = 7 * e^x + C * x^4.\)
So, the solution to the differential equation \(x(dy/dx) - 4y = 7x^4 * e^x\)

is\(y(x) = 7 * e^x + C * x^4.\)

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The number of fliers that she has still not broadcasted will be 48 fliers.

Algebra is the study of ideational characters, while logic is the manipulation of all those opinions.

Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. Then the number of fliers staying is given as,

⇒ (1 - 1/5) x 90

⇒ (4/5) x 90

⇒ 72 fliers

This week, she posted 1/3 of the remaining fliers. Then the number of fliers that she has still not broadcasted is given as,

⇒ (1 - 1/3) x 72

⇒ (2/3) x 72

⇒ 48 fliers

The number of fliers that she has still not broadcasted will be 48 fliers.

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Answer: 68.75

Step-by-step explanation: I did the math myself so it may not be correct, but it's at least very close.

Answer:

the correct answer is D:68.75

Answer:

85

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

Bill would have to get the same grade as his average of his prior grades. Because those average to 85.

The coordinates after dilation are A (-0.5 , 1) , B(1,0.5) , C(0.5,-0.5) and D(0,0).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here , we need to find coordinates before using dilation. Then the coordinates are,

A=(-1,2) , B=(2,1) , C=(1,-1) and D=(0,0).

The scale factor = 0.5

For dilation coordinates we need to multiply coordinates by using scale factor. Then,

A = (-1,2) => (-1×0.5, 2×0.5) => (-0.5 , 1)

B = (2,1) => (2×0.5 , 1×0.5) => (1,0.5)

C = (1 , -1) => (1×0.5 , -1×0.5) => (0.5, -0.5)

D = (0 , 0) => (0×0.5 , 0×0.5) => (0,0)

Hence the coordinates after dilation are A (-0.5 , 1) , B(1,0.5) , C(0.5,-0.5) and D(0,0).

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To find the probability that a randomly selected adult has an IQ less than 136, we can use the standard normal distribution.

Given that adults' IQ scores are normally distributed with a mean (μ) of 100 and a standard deviation (σ) of 20, we need to convert the IQ score of 136 into a z-score using the formula z = (x - μ) / σ. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the corresponding probability.

To find the probability that a randomly selected adult has an IQ less than 136, we first calculate the z-score corresponding to an IQ of 136. The z-score formula is z = (x - μ) / σ, where x is the value of interest (136 in this case), μ is the mean (100), and σ is the standard deviation (20). Substituting the values, we get z = (136 - 100) / 20 = 1.8.

Next, we look up the probability associated with a z-score of 1.8 in the standard normal distribution table or use a calculator. The table or calculator will provide the cumulative probability from the left tail up to the z-score. The cumulative probability is the probability that a randomly selected adult has an IQ less than 136.

Using the standard normal distribution table or calculator, we find that the cumulative probability for a z-score of 1.8 is approximately 0.9641. Therefore, the probability that a randomly selected adult has an IQ less than 136 is 0.9641, rounded to four decimal places.

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Answer: 4

Step-by-step explanation: if u want the slope it’s 4 since formula 2y-1y /2x-1x

The area of the shaded region in this problem is given as follows:

995.44 cm².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it's measure is given as follows:

r = 21 cm.

Then the area of the entire circle is given as follows:

A = π x 21²

A = 1385.44 cm².

The right triangle has two sides of length 39 cm and 20 cm, hence it's area is given as follows:

A = 0.5 x 39 x 10

A = 390 cm².

Then the area of the shaded region is given as follows:

1385.44 - 390 = 995.44 cm².

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

D. 7

Step-by-step explanation:

\( \frac{ \sqrt{196} }{\sqrt{4} } \\ \)

\( \frac{14}{2} \)

=7

Answer:

\( \frac{ {x}^{ - 2} {y}^{ \frac{1}{2} } }{ \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{ {x}^{2} \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{6 {x}^{2}y \sqrt{x} } = \frac{1}{6 {x}^{ \frac{5}{2} } {y}^{ \frac{1}{2} } } = \frac{1}{6} {x}^{ - \frac{5}{2} } {y}^{ - \frac{1}{2} } \)

\( \frac{1}{6} \times - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{24} \)

Based on this trendline, if a student scores 75 on the midterm, the predicted grade on the final exam would be around 83.

The scatter chart for the "Student Grades" data shows a linear trendline indicating a relationship between midterm and final exam grades.

By analyzing the "Student Grades" data in the Excel file, a scatter chart can be constructed to visualize the relationship between midterm and final exam grades. The scatter chart plots the midterm grades on the x-axis and the corresponding final exam grades on the y-axis for each student in the dataset. Additionally, a linear trendline can be added to the scatter chart, which represents the best-fit straight line through the data points.

The trendline in the scatter chart allows us to make predictions about the final exam grades based on the midterm grades. In this case, if a student has a midterm grade of 75, we can use the trendline to estimate their expected final exam grade. By following the line from the x-axis value of 75 up to the trendline, we can find the corresponding y-axis value, which represents the predicted final exam grade. Based on the trendline, the predicted grade for a student with a midterm score of 75 would be around 83.

It's important to note that the accuracy of the prediction may depend on the quality and representativeness of the dataset. The trendline assumes a linear relationship between the two variables, but there could be other factors or variables that affect the final exam grades. Therefore, while the trendline provides a reasonable estimate, individual variations and other factors may impact the actual final exam grade for a specific student.

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Answer:

231.78 lbs

Step-by-step explanation:

total amount of cementis needed= volume of form

volume of form in ft³= length × depth × height

                        = 35.5/12 × 20/12 × 6/12

                           = 2.465ft³

density of cement= 94.01651 lb/ft³

mass of cement= density × volume

                          = 2.465 × 94.01651

                         = 231.78lb

Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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Answer: 171

Step-by-step explanation:

An obtuse angle means more than 90 degrees. (90 degrees would be the inside corner of your notebook paper) a straight line would be 180 degrees. 171 is the closest to 180