state how the 2 triangles are congruent?? SSS and SAS HELP ASAPPP??

The perimeter of the equilateral triangle whose area is 16root3/4 is 15.9\(\sqrt{3/4} cm\)

You should understand that a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted

An equilateral triangle is a special case of an isosceles triangle in which all three sides have the same length

Let the sides of the triangle be a

a + a + a = 16root3/4

3a = 16\(\sqrt{3/4}\)

a = 5.3\(\sqrt{3/4}\)

Therefore the perimeter of the equilateral triangle is

5.3\(\sqrt{3/4} + 5.3\sqrt{3/4} +5.3\sqrt{3/4}\)

Therefore, the  perimeter is 15.9\(\sqrt{3/4} cm\)

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The volume of the given triangular prism is 315 cm³.

The volume of a triangular prism, we need to multiply the base area of the triangular base by the height of the prism.

The triangular base has a base length of 5 cm and a height of 7 cm, and the height of the prism is 9 cm.

Calculate the area of the triangular base.

The area of a triangle can be calculated using the formula:

Area = (base length × height) / 2

Plugging in the values, we have:

Area = (5 cm × 7 cm) / 2

Area = 35 cm²

Calculate the volume of the prism.

The volume of a prism can be calculated by multiplying the base area by the height of the prism.

Volume = Base area × Height

Volume = 35 cm² × 9 cm

Volume = 315 cm³

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The quality control manager at Sony uses systematic sampling to estimate the percentage of defects in a manufacturing batch of music CDs. Therefore, the quality control manager can estimate that approximately 20% of the entire manufacturing batch of music CDs may have defects based on the systematic sample she obtained.

Systematic sampling involves selecting items from a population at regular intervals. In this case, the quality control manager selects every 16th music CD starting from the ninth. This method ensures that every CD has an equal chance of being selected, providing a representative sample of the batch.

By using systematic sampling, the quality control manager obtains a sample of 140 music CDs. She can then examine these CDs to determine the number of defective ones. Let's assume she finds 28 defective CDs in the sample.

To estimate the percentage of defects in the manufacturing batch, the quality control manager can use the formula:

Defect percentage = (Number of defective CDs / Sample size) *100

Substituting the values, we have \((\frac{28}{140}) * 100 = 20%\).

Therefore, the quality control manager can estimate that approximately 20% of the entire manufacturing batch of music CDs may have defects based on the systematic sample she obtained. This estimation provides valuable information for assessing the quality of the batch and taking necessary actions for improvement.

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ANSWER and EXPLANATION

B. We are to describe the relationship between bridge length and breaking weight.

To do this, we need to check the graph.

In doing that, we will see that the breaking weight appears to decrease as the Bridge length increases.

We can conclude then that the breaking weight and bridge length have an inverse relationship.

That is shown in the graph.

The highest value of the breaking weight is 14 and that is when the value of bridge length is at its lowest (4).

The lowest value of the breaking weight is 3 and that is when the value of the bridge length is at its highest (11)

Hence, there is an inverse relationship between them.4)

The values of C, α, and the normalization constant need to be determined to calculate the exact probabilities.

To find the probabilities associated with the measurements of the square of the angular momentum for the given wave packet, we need to determine the quantum numbers and their corresponding probabilities.

The square of the angular momentum operator is given by:

L^2 = Lx^2 + Ly^2 + Lz^2

For a spherically symmetric potential, the wave function can be written as:

ψ(x, y, z) = C(xy + yz + zx) e^(-αr)

Let's analyse each part separately.

1. Probability of obtaining L^2 = 0:

For L^2 = 0, the only possibility is when all three components of the angular momentum, Lx, Ly, and Lz, are zero. In other words, l = 0.

The probability of this occurring is given by the square of the coefficient of the corresponding term in the wave function:

P(L^2 = 0) = |C(xy + yz + zx)|^2

2.Probability of obtaining L^2 = 6ℏ^2:

or L^2 = 6ℏ^2, we need to consider the possible values of l. Since l = 2 is given, the possible values of m are -2, -1, 0, 1, and 2. The probability for each value of m is given by the square of the coefficient of the corresponding term in the wave function.

Here, m represents the projection of the angular momentum along the z-axis.

P(m = 2) = |C(xy)|^2

P(m = 1) = |C(yz)|^2

P(m = 0) = |C(zx)|^2

P(m = -1) = |C(yz)|^2

P(m = -2) = |C(xy)|^2

Please note that the probabilities for m = 1 and m = -1 are the same because the coefficients for the corresponding terms are the same.

The values of C, α, and the normalization constant need to be determined to calculate the exact probabilities.

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The height of the tower if the distance AB is 50m is 22.36m.

What is distance?
While distance and displacement appear to have the same meaning, they actually have very different definitions and meanings. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object had also covered during its motion." Let's examine the distinction between distance as well as displacement in this article. Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.

Sol-Here in right ∆AOB

AB= 50m (as per given question)

Let height of the tower is =OD = A meters

in ∆AOD , tan theta= DO/AO

Tan 38= A/∆O

∆O= A /tan 38= a/0.78

Also in ∆ BOD

tan 29 = DO/BO

BO = a/tan 29°

=9/0.55

So a^2 = 500

=>a=10√5=22.36 approx.

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The probability that you deal the 7 of Spades followed by a King is 0.1.

Given is that you randomly shuffle a deck of cards and deal two cards from the top.

We can write the probability as -

P{E} = 1/52 + 4/51

P{E} = 0.02 + 0.08

P{E} = 0.1

Therefore, the probability that you deal the 7 of Spades followed by a King is 0.1.

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The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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Answer:

Step-by-step explanation:

Use the Law of Cosines for this. If we want the measure of angle B, then the equation is set up like this:

\(b^2=a^2+c^2-2accosB\)

Filling in:

\(9^2=14^2+6^2-2(14)(6)cosB\) and simplifying a bit:

81 = 196 + 36 - 168cosB and a bit more:

81 = 232 - 168cosB and even more:

-151 = -168cosB and divide both sides by -168 to get

.9378881988 = cosB

Now use the 2nd button on your calculator along with the cos button to find the missing angle. Make sure your calculator is in degree mode first. Your angle should be 20.30012152

Answer:

98

Step-by-step explanation:

As it is a little bit of a few questions about the other one I have to the store go back tomorrow and will get back tomorrow and I have been working

Peter doesn't get wet on solving the simultaneous

equations.

A system of simultaneous linear equations is any set of two or more linear equations that share the same unknown variables. To solve such a system, finding values for the unknown variables that simultaneously satisfy all of the equations is required.

We can utilize the following parameters in our calculation based on the question:

y = 2x - 1/4x²

y = 1/4x - 1

Through substitution, we now.

2x - 1/4x² = 1/4x - 1

By multiplying by 4,

This results,

8x - x² = x - 4

Analyze similar terms,

x² - 7x - 4 = 0

We have developed a graphical tool to

x = -0.531 and x = 7.531

In y = 2x - 1/4x2, replace x = -0.531 and x = 7.531.

y = 2(-0.531) - 1/4(-0.531) (-0.531) ²

y = -1.13

y = 2(7.531) - 1/4(7.531) ²

y = 0.88

Thus, we have

(-0.531, -1.13) and (7.531, 0.88) (7.531, 0.88)

(-0.531, -1.13) and (7.531, 0.88) do not meet the standards (8, 1)

So, Peter avoids getting wet.

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Part A: The area of the large pizza (AL) is given by AL = 2As.

Part B: The radius of the small pizza (rs) is given by rs = sqrt(As/π).

Part C: The radius of the large pizza (rL) is given by rL = sqrt(2A/π).

Part D: The radius of the large pizza is not twice as large as the radius of the small pizza. The answer is no.

The area of the large pizza (AL) can be written in terms of the area of the small pizza (As) as follows:

AL = 2As.

The area of the small pizza (As) is given by

As = πrs^2. To find the radius of the small pizza (rs), we can rearrange the formula as

rs = sqrt(As/π).

The area of the large pizza (AL) is given by AL = πrL^2.

Using the information from Part A, we know that AL = 2As.

Substituting this into the equation, we get 2As = πrL^2.

Rearranging the formula, we can write rL in terms of A as rL = sqrt(2A/π).

Comparing the radii of the two pizzas, we find that the radius of the large pizza (rL) is not twice as large as the radius of the small pizza (rs).

Instead, the radius of the large pizza (rL) can be found using the formula

rL = sqrt(2A/π), while the radius of the small pizza (rs) can be found using the formula

rs = sqrt(As/π).

Therefore, the large radius is not twice the size of the small radius. The answer is no.

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a. The probability that 20 paperback books will fit on a 36 cm shelf is 0.2010.

b. The probability that 8 paperback books and 8 hardback books will fit on a 36 cm shelf is 0.0008.

c. The smallest length of shelving so that 16 hardback books have at least a 99% chance to fit on is 32.1 cm.

a) The probability that 20 paperback books will fit on a 36 cm shelf is:

P(20 paperback books fit on a 36 cm shelf) = P(total thickness < 36 cm)

The total thickness of 20 paperback books is normally distributed with mean 20 * 1.9 = 38 cm and variance 20 * 0.90 = 18 cm.

The probability that the total thickness is less than 36 cm is:

P(total thickness < 36 cm) = P(Z < (36 - 38) / √(18))

= P(Z < -0.833)

= 0.2010

b) The probability that 8 paperback books and 8 hardback books will fit on a 36 cm shelf is:

P(8 paperback books and 8 hardback books fit on a 36 cm shelf) = P(total thickness < 36 cm)

The total thickness of 8 paperback books and 8 hardback books is normally distributed with mean 8 * 1.9 + 8 * 3.2 = 46.4 cm and variance 8 * 0.90 + 8 * 1.80 = 34.4 cm.

The probability that the total thickness is less than 36 cm is:

P(total thickness < 36 cm) = P(Z < (36 - 46.4) / √(34.4))

= P(Z < -3.228)

= 0.0008

c) The smallest length of shelving so that 16 hardback books have at least a 99% chance to fit on is:

Z = -2.326

Total thickness = Z * √(16 * 1.80) + 16 * 3.2

Total thickness = 32.1 cm

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The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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The required points on difference between a stratified sample and a cluster sample are explained.

In a stratified sample the populace is partitioned into various portions and afterward we take irregular components from each section.

In a group test, the example is separated into sections (or bunches) and afterward the example is taken by choosing different clusters.

Consequently, in the group test we take ALL components from various bunches while in a separated example we take A few components from the various segments.

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The statement supported the graph is

The axis of symmetry is x = 3

The coordinates of the y-intercept are (0,7)

A line that divides an object into two equal halves and produces a mirror-like reflection of each side of the object is known as an axis of symmetry.

1. The axis of symmetry is x = 3

The axis of symmetry is the central axis of the graph, which signifies the middle point of the graph. It is evident that this graph is centered on x = 3.

2. The coordinates of the y-intercept are (0,7)

The y intercept is the point where the graph meets the y-axis, that is, the value of y on the graph when x=0.

From the graph, the coordinates of the y-intercept is (0, 7)

3. The X-intercept is located at (-3,0)

The x intercept is the point where the graph meets the x-axis, that is, the value of x on the graph when y=0.

From the graph the curve x axis at x= 1.5 and x= 4.5

So, the x-intercept is truly located at (1.5, 0) and (4.5,0)

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a) The ratio of oj concentrate to water is 1:3.

b) The ratio of concentrate to total juice is 1:4.

c) 300 ml of frozen concentrate is needed to make 1200 ml of juice.

b) There are 150 red jellybeans, 60 white jellybeans, and 90 pink jellybeans.

We have,

a) To compare the amount of orange juice (oj) concentrate to water, we can write the ratio in simplest form.

The amount of oj concentrate is 350 ml, and the amount of water is 1050 ml.

Ratio of oj concentrate to water:

350 ml : 1050 ml

We can simplify this ratio by dividing both values by their greatest common divisor, which is 350:

350 ml : 1050 ml

1 : 3

b) To compare the amount of concentrate to the total juice, we need to consider both the amount of oj concentrate and the amount of water.

Amount of oj concentrate: 350 ml

Amount of water: 1050 ml

Total amount of juice: 350 ml + 1050 ml = 1400 ml

The ratio of concentrate to total juice:

350 ml : 1400 ml

We can simplify this ratio by dividing both values by their greatest common divisor, which is 350:

350 ml : 1400 ml

1 : 4

c) To determine how much frozen conmuch-frozencentrate is needed to make 1200 ml (or 1.2 liters) of juice, we need to find the ratio of concentrate to total juice.

Given that the ratio of concentrate to total juice is 1:4 (as found in part b), we can set up a proportion to solve for the unknown amount of concentrate (x):

1 / 4 = x / 1200

To solve for x, we can cross-multiply and then divide:

4x = 1 * 1200

4x = 1200

x = 1200 / 4

x = 300

b) If we have 300 Valentine's jellybeans with a ratio of red to white to pink as 5:2:3, we can determine the number of each color by dividing the total into parts according to the given ratio.

Total jellybeans: 300

Red: 5/10 * 300 = 150 jellybeans

White: 2/10 * 300 = 60 jellybeans

Pink: 3/10 * 300 = 90 jellybeans

Thus,

a) The ratio of oj concentrate to water is 1:3.

b) The ratio of concentrate to total juice is 1:4.

c) 300 ml of frozen concentrate is needed to make 1200 ml of juice.

b) There are 150 red jellybeans, 60 white jellybeans, and 90 pink jellybeans.

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Answer:

k = -7

Step-by-step explanation:

Find the difference of the y-values of both vertexes:

f(x): y = 1

g(x): y = -6

g(x) - f(x)

-6 - 1 = -7

When we express the equation 2x - y = 12 in slope intercept form, the result obtained is y = 2x - 12 (2nd option)

The slope intercept form for an equation is written as illustrated below:

y = mx + c

Where

With the above information, we can obtain the slope intercept form of the equation. Details below:

2x - y = 12

Rearrange to make y the subject of the expression, we have

2x = 12 + y

y = 2x - 12

Thus, we can conclude that the equation in the slope intercept form is

y = 2x - 12 (2nd option)

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Complete question:

Given the equation 2x - y = 12, which equation is written in slope intercept form?

y = -2x + 12

y = 2x - 12

y = 2x + 12

y = -2x - 12

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer:

A: first choice

x^4

Step-by-step explanation:

When you divide two powers with the same base, you subtract the exponents, not divide.

The step x^8/x^4 is correct.

The next step should be x^(8 - 4), not x^8/4.

The correct simplification is x^4.

Answer:

A: first choice

x^4

The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:

\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)

Therefore, t(0) = (3, 3, 0).

To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:

\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)

Substituting 0 for t in r''(t), we have:

\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)

Therefore, r''(0) = (12, 12, 12).

Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:

\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)

\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)

Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

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Answer:

5 is good plz mark me plxzzzzzzzzzzzzzzz-zzzzzzzzzzzzzzz

Answer:

16.26°

Step-by-step explanation:

1. tanΘ= 7/24

2.\(tan^-1(\frac{7}{24} ) =\)Θ

3. Θ = 16.26°

Answer:

32=x+2x+4x

32=7x

x=4.571428571428571428

and,2x=9.142857142857142857

and,4x=18.28571428571428571

Step-by-step explanation:

hope it helps

mark me as brainliest

Answer:

Lengths are 32/7, 64/7, and 128/7

I recommend seeing the explanation. I included the answers in decimal, how I got each answer, and which sides is for which expression

Step-by-step explanation:

A perimeter is the length of all sides and we know the perimeter of this triangle is 32 meters. It's given that the three sides of the triangle are x, 2x, and 4x, so if we add these sides together, we get 32

x + 2x + 4x = 32

We have to solve for x before we proceed to anything else

x + 2x + 4x = 32

Add like terms

7x = 32

Divide both sides by 7

x = 32/7 or 4.5714

Now that we have solved for x, we can now move on to find the sides. One of the sides is x meters and we already know x is equal to 32/7, so that is our answer.

To find 2x meters, we will have to multiply 2 by 32/7

2 * 32/7

We have to find a denominator for 2 that will both terms like fractions. 14/7 is the same as 2 so we will replace 2 with that (or you could find the LCM)

14/7 * 32/7 = 448/49

448 and 49 has a common factor of 7, so we will divide the numerator and denominator by 7

448 ÷ 7/49 ÷ 7 = 64/7

2x = 64/7 or 9.1428

To find 4x meters, we wil lhave to multiply 4 by 32/7

4 * 32/7

We will use the same method of making 4 into a fraction that is like terms with 32/7 (or find the LCM again)

28/7 * 32/7 = 896/49

896 and 49 has a common factor of 7, so we will divide the numerator and denominator by 7

896 ÷ 7/49 ÷ 7 = 128/7

4x = 128/7 or 18.2857