A prism is 38 mm long. Its cross-section is a triangle with a base length of 19 mm and a perpendicular height of 26 mm. What is the volume of the prism? Give your answer in mm³​

Answer:

$42?

Step-by-step explanation:

Answer:

ray ts

Step-by-step explanation:

The length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.

16. Length of segment DF

DF=-1-(-4)
DF=3

19. Length of segment FR

FR=-1 1/3-(-4)

FR= 2 2/3

17. Length of segment DE

DE=2 -(-1)

DE=3

20. Length of segment GH

GH= 3 1/2 -(-1)

GH=4 1/2

18. Length of segment FG

FG=3 1/2 -2

FG=1 1/2

21. Length of segment EH

EH=3 1/2-(-1 1/3)

EH= 4 5/6

Therefore the length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.

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The percentage of people with blood pressure between 115 and 165 mm is 68.27% (closest to option e). The percentage of people with blood pressure between 140 and 165 mm is 89.4% (closest to option b). The percentage of people with blood pressure over 165 mm is 10.6% (closest to option a).

To solve this problem, we can use the properties of the normal distribution, which is a continuous probability distribution that is often used to model real-world data. In particular, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages of people with blood pressure within certain ranges. The empirical rule states that, for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean. Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard  deviations of the mean. Using this rule, we can estimate the following  percentages: The percentage of people with blood pressure between 115 and 165 mm: First, we need to find the z-scores for the lower and upper limits of the range: z_lower = (115 - 140) / 20 = -1.25.

z_upper = (165 - 140) / 20 = 1.25

We can then use a standard normal distribution table or a calculator to find the areas under the curve corresponding to these z-scores:

P(-1.25 < Z < 1.25) = 0.7887 - 0.1056 = 0.6831

So, approximately 68.31% of people have blood pressure between 115 and 165 mm.

The percentage of people with blood pressure between 140 and 165 mm: In this case, the lower limit is equal to the mean, so we only need to find the z-score for the upper limit: z_upper = (165 - 140) / 20 = 1.25

Using the same approach as before, we get:

P(Z < 1.25) = 0.8944

So, approximately 89.44% of people have blood pressure between 140 and 165 mm. The percentage of people with blood pressure over 165 mm:

In this case, we only need to find the area to the right of the upper limit:

P(Z > 1.25) = 0.1056

So, approximately 10.56% of people have blood pressure over 165 mm.

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Complete Question

The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.

a. 10.6%

b. 89.4%

c. 39.4%

d. 78.8%

e. 68.27%

___ The percentage of people with blood pressure between 115 and 165 mm.

___ The percentage of people with blood pressure between 140 and 165 mm.

___ The percentage of people with blood pressure over 165 mm.

The average angular velocity during the dive is 10.78 rad/sec.

Given,

displacement of the diver = 10.4m

as the diver falls freely then the acceleration will be g=9.8 \(m/s^2\)

To find average angular velocity during dive use formula,

\(\omega=\frac{\theta}{t}\)

where, θ=angular displacement and t= time taken to reach water

the diver makes 2.5 revolutions, here 1 revolution is 2π radians then total angular displacement is

θ=2.5* 2π=15.7 radian

To find time taken, use formula \(s=ut+\frac{1}{2}gt^2\)

here u=initial velocity=0

s=displacement of diver=10.4m

\(10.4=0+\frac{1}{2}9.8t^2\\\\10.4=4.9t^2\\\\2.122=t^2\\\\t=1.456 s\)

angular velocity, \(\omega=\frac{15.7}{1.456}=10.78\ rad/sec\)

Thus, the average angular velocity during the dive is 10.78 rad/sec.

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Answer:

The increase is 88.1% B

Step-by-step explanation:

2.22 = (x/100)(1.18)

x = 2.22(100)(1.18)

x = 188.1%

2.22=(188.1/100)(1.18)

2.22=2.22

The area under the standard normal curve to the left of z = 2.06 is approximately 0.9803.

The normal distribution function, also known as the Gaussian distribution or bell curve, is a probability distribution that is symmetric, bell-shaped, and continuous. It is defined by two parameters: the mean (μ) and the standard deviation (σ).

The normal distribution is widely used in statistics and probability theory due to its many desirable properties and its applicability to various natural phenomena. It serves as a fundamental distribution for many statistical methods, hypothesis testing, confidence intervals, and modeling real-world phenomena.

To find the area under the standard normal curve to the left of z = 2.06, you can use a standard normal distribution table or a calculator with a normal distribution function. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Using a standard normal distribution table, the area to the left of z = 2.06 can be found by looking up the corresponding value in the table. However, since the standard normal distribution table typically provides values for z-scores up to 3.49, we can approximate the area using the available values.

The closest value in the standard normal distribution table to 2.06 is 2.05. The corresponding area to the left of z = 2.05 is 0.9798. This means that approximately 97.98% of the area under the standard normal curve lies to the left of z = 2.05.

Since z = 2.06 is slightly larger than 2.05, the area to the left of z = 2.06 will be slightly larger than 0.9798.

Therefore, rounding the answer to four decimal places, the area under the standard normal curve to the left of z = 2.06 is approximately 0.9803.

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So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

We can use the formula for the area of a triangle, which is A = (1/2)bh, where b is the length of the base and h is the height. In this case, we know that the base has length 2a, so we need to find the height.

Let's call the third side of the triangle, which is not given, b. We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, so we have:

a + 2a > b

3a > b

We can rearrange this to solve for b:

b < 3a

Now, let's use the formula for the area of a triangle:

A = (1/2)bh

We want to maximize A, so we want to maximize h. We know that h is the height of the triangle, which is perpendicular to the base, so it forms a right angle. We can use the Pythagorean theorem to find h in terms of a and b:

\(h^2 = b^2 - a^2\)

We can substitute our inequality for b:

\(h^2 < (3a)^2 - a^2\)

\(h^2 < 8a^2\)

h < √(8\(a^2\))

h < 2 √(2)a

Now we can use the formula for the area of the triangle again:

A = (1/2)bh

A < (1/2)(2 √(2)a)(a)

A < \(a^2\) √(2)

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

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The numbers ordered from least to greatest are 3.6, 3.621, 3.63, 3.702, 3.73, 3.785

The numbers are written in decimals. A decimal is a standard method used to write non-integers. A decimal is made up of integers and non-integers that are separated by a decimal point. An example of a decimal is 3.63.

In order to write decimals, from the least to the greatest, if the unit digit and tenth digit are the same, look at the hundredth digit, if the hundredth digit. Order the numbers on the basis of its hundredth digit. Based on this explanation, in the digits 3.6,  3.621, 3.63, 3.6 is the smallest and 3.63 is the largest.

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Answer:

its 15

Step-by-step explanation:

Answer:

see photo below

Step-by-step explanation:

This actual has a photo attached not a link

Answer:

8

Step-by-step explanation:

20/250% is 20/2.5 which is 8.

Hope this helps hit the crown :D

\( \: \: \: \: \: \: \)

\(6! = 720 \\ \\ 7! = 5040\)

Step-by-step explanation:

\(6!\)

\(6 \times 5 \times 4×3× 2×1\)

\( = 720\)

\(7! = \)

\(7 \times 6 \times 5 \times 4×3×2×1\)

\( = 5040\)

\( \: \: \: \: \: \: \: \)

Answer:

720 and 5040

Step-by-step explanation:

Using the definition of n! ( n factorial )

n! = n(n - 1)(n - 2) ...... × 3 × 2 × 1

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Answer:

The formula for calculating the probability of two independent events is the product of the probabilities of each event occurring. In other words, if event A and event B are independent, then the probability of both events occurring is calculated as P(A and B) = P(A) * P(B).

Answer:

d. 20°

Step-by-step explanation:

First, we need to solve for m<Q

m<Q+m<R+m<S=180°

where m<R=90° and m<S=70°

m<Q+90°+70°=180°

m<Q=20°

Since m<Q=m<M

Then, m<M=20°

Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

\(f(x)=x^3\)

If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.

\(f(x)=(x-8)^3\)

graph shifted toward right by \(8\) units right

\(f(x)=(x-8)^3+3\)

graph shifted toward right by \(3\) units up

Thus the new function is:

\(g(x)=(x-8)^3+3\)

Answer:

x = 24

x = 20

Steps :

\(1) \ \frac{x}{3} - 2 = 6\\\\\\)

 \(\frac{x - 6 }{3} = 6\\\\\ \ x-6 = 6 \times 3\\\\\ \ x - 6 = 18\\\\\ \ x = 24\)

\(2) \frac{x}{5} + 1 = 5\)

  \(\frac{x+5}{5} = 5\\\\x + 5 = 5 \times 5\\\\x + 5 = 25\\\\x = 20\)

Answer:

3.5 inches

Step-by-step explanation:

From the information given, it can be deduced that the length of the candle at 11:00PM will be 3.5 inches tall. Since the family lights candles

A point, a line, and a plane are undefined words in geometry.

A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.

2D shapes, which include flat shapes such squares, circles, and triangles, are a subset of flat geometry. The length and width are the only 2 dimensions of these forms.

A solid figure, object, or shape with three dimensions—length, breadth, and height—is referred to as a three-dimensional shape in geometry. Three-dimensional shapes contain thickness or depth, in contrast to two-dimensional shapes.

In terms of geometry, an angle is the shape created when two rays intersect at a single terminal. The sign is used to denote an angle. A protractor is used to measure angles in degrees (°).

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Answer:

Step-by-step explanation:

Given the following explicit formula, we are to calculate the first four (4) terms of the sequence.

1)  f(n) = 9+8n

When n = 1

f(1) = 9+8(1)

f(1) = 17

when n = 2

f(2) = 9+8(2)

= 9+16

= 25

When n = 3

f(3) = 9+8(3)

f(3) = 33

when n = 4

f(4) = 9+8(4)

= 41

= 25

The first four terms are 17, 25, 33 and 41

2) f(n) = 8(n+1)-13

When n = 1

f(1) = 8(2)-13

f(1) = 3

when n = 2

f(2) =  8(3)-13

= 24-13

= 11

When n = 3

f(3) =  8(4)-13

f(3) = 32-13

= 19

when n = 4

f(4) =  8(5)-13

= 40-13

= 27

The first four terms are 3, 11, 19 and 27

3) f(n) = 65-9n

When n = 1

f(1) = 65-9(1)

f(1) = 56

when n = 2

f(2) = 65-9(2)

= 65-18

= 47

When n = 3

f(3) = 65-9(3)

f(3) = 65-27

= 38

when n = 4

f(4) = 65-9(4)

= 65-36

= 29

The first four terms are 56, 47, 38 and 29

If the function n(t) is real, the geometric phase will vanish. However, if a phase factor is added to the eigenfunctions, the Berry connection becomes modified, resulting in a non-zero Berry phase. The total Berry phase for a closed loop in parameter space cannot be determined without specific information about the system and Hamiltonian.

(a) To show that the geometric phase vanishes when n(t) is real, we start with the definition of the geometric phase:

γ = ∮ A · dR

Where A is the Berry connection and dR is the infinitesimal displacement in parameter space. Since n(t) is real, the Berry connection A = i〈n|∇n〉 is purely imaginary. Therefore, the dot product A · dR will also be purely imaginary. As the integral of a purely imaginary quantity over a closed loop, the geometric phase γ will be zero.

(b) If we tack a phase factor onto the eigenfunctions, i.e., considering eigenfunctions of the form |n\((t)⟩ = e^iφ(t)|n(t)⟩\), where φ(t) is an arbitrary real function, the Berry connection becomes:

A = i〈n(t)|∇n(t)〉 = \(i(e^-iφ(t)〈n(t)|∇n(t)〉e^iφ(t))\) = i〈n(t)|∇n(t)〉 + (∇φ(t)) · n(t)

The first term is the original Berry connection, which is purely imaginary, and the second term involves the gradient of φ(t). Integrating this modified Berry connection over a closed loop will result in a non-zero Berry phase.

(c) Evaluating this in a closed loop in parameter space, with R = Rf, would require specific details about the system and the parameter dependence of the Hamiltonian. Without further information, it is not possible to determine the total Berry phase for R = Rf.

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Answer:

the answer is 6.72

Step-by-step explanation:

Instead of a diagram you can do 4.2 times 1.6 and after you finishes doing that You put the decimal 2 times and you should get 6.72

The answer is 6.72

The length and width of a rectangle are defined by the factors being multiplied in an area model, which is a rectangular diagram used in mathematics to solve multiplication problems. Therefore, the area of the rectangle is the product. Subsequently, it is known as the "Region model for augmentation".

Given (4.2) x (1.6)

by area drawing method make an rectangle of 4.2 and 1.6 units and make perpendicular lines at distance of 4 units and 1 units on length and breadth, the rest distance will be 0.6 and 0.2 units, now we have four different rectangles as shown in image now find area of each rectangle and add all the areas.

area of rectangle 1 = 4 x 1 = 4

area of rectangle 2 = 1 x 0.2 = 0.2

area of rectangle 3 = 4 x 0.6 = 2.4

area of rectangle 4 = 0.2 x 0.6 = 0.12

total area = 4 + 0.2 + 2.4 + 0.12

total area = 6.72

Hence  (4.2) x (1.6) = 6.72

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SOLUTION:

Step 1:

In this question, we are given the following:

Write the equation of the circle centered at ( − 2, 6 ) with a radius of 5.

Step 2:

The equation of a line is given as:

This implies that:

The graph showing the equation of the circle is given as:

CONCLUSION:

The equation of the circle is given as:

Answer:

Step-by-step explanation:

The slope for the given situation will be $2.96. 5.92/2 = $2.96 per meal

Answer:

B. There is no solution to the equation.

Step-by-step explanation:

Every step in the solution is correct.

Since the last line is a false statement, 5 = 1, that means there is no solution.

Answer: B. There is no solution to the equation.

Answer:

Mrs. Sigmon

Step-by-step explanation:

Mrs. Sigmon 480/3= 150 seconds/lap

Mrs. Huss  500/4= 125 seconds/lap

Mrs. Leatherman 230/2 =115 seconds/lap

Answer:

Negative

Step-by-step explanation:

Answer:

96 sq yards

Step-by-step explanation:

40-24 is 16, and 16/2 is 8. 8 is the second length, so 8 times 12 is 96 which is the area

Answer:

7

Step-by-step explanation: