Mr. Lee left his fortune to his 3 sons, 4 daughters and his wife. Each son received twice as much as each daughter and his wife received $6000, which was a quarter of the money. How much did each son receive?

Answer:

13 times

Step-by-step explanation:

You divide 91 and 7 to get your answer as the answer is asking for times.

Answer:

the answer is 13

Step-by-step explanation:

91/7=13

70/7=10 and 21/7=3

Answer:

7/16.  

Step-by-step explanation:

The first triangle has no shading.

The second triangle has 1/4 shaded.

The third has 3/9.

The fourth has 6/16.

Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.

The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.

So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.

Hope this helps!

Answer:

b= 10.39

c = 20.79

Step-by-step explanation:

a = 60 °

b = 30°

c= 180-(60+30)

c = 180-(90)

c = 90°

Length facing angle a = 18

Let's look for length facing angle b

b/sinb = a/sin a

b/sin 30 = 18/sin 60

b =( 18 * sin30)/sin 60

b = (18*0.5)/0.8660

b = 9/0.8660

b= 10.39

Let's look for c

c/sin c = a/sin a

c/sin 90 = 18/sin 60

c = (18 * sin 90)/sin 60

c =18/0.8660

c = 20.79

Answer:

The expected number of sales of this store from this sample of 30 is 6.

Step-by-step explanation:

For each prospect, there are only two possible outcomes. Either there is a trade, or there is not. Prospects are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability.

This means that [tex]p = 0.2[/tex]

Suppose 30 prospects are randomly selected from a city-wide mailing.

This means that [tex]n = 30[/tex]

What is the expected number (mean) of sales of this store from this sample of 30?

[tex]E(X) = np = 30*0.2 = 6[/tex]

The expected number of sales of this store from this sample of 30 is 6.

The expected number (mean) of sales of this store from this sample of 30 is 6.

Since A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.

So here the expected mean should be

= 20% of 20

= 6

Hence, The expected number (mean) of sales of this store from this sample of 30 is 6.

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Answer:

Check Explanation

Step-by-step explanation:

- Write a statement that interprets that prediction interval.

The prediction interval (58.2 kg, 124.6 kg) represents the range of values that the true predicted weight for a height of 185 cm using the regression obtained from the data can actually, possibly take on to a certain level of confidence.

- What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.4 kg​?

The prediction interval is better to use instead of just using a predicted weight because in computing the prediction interval, we consider all the factors, biases and significant factors that can introduce uncertainties into the regression used to just find the predicted weight.

So, the prediction interval is more encompassing and has a better chance of containing the true weight that corresponds to the height 185 cm because it incorporates so many things thay can go wrong with the regression into its computation unlike the predicted weight.

- Why is the terminology of prediction interval used instead of confidence​ interval?

This is because the interval is obtained from the regression results, used in predicting weights, given height.

Confidence interval is used for numerical distributions to estimate the interval of range of values where the true population mean can be found with a certain level of confidence.

Hope this Helps!!!

Interval values describes a range of values in which the the true or actual value will likely reside based on a certain level of Confidence.

1.)

Tbe prediction interval describes a range of values which will contain the actual value based on a certain level of confidence.

2.)

The prediction interval gives an interval estimate rather than a point estimate, which increases the probability of obtaining a true value.

3.)

The prediction interval is used instead of confidence interval, because it is concerned with prediction using a linear model while confidence interval is associated with estimating the population mean from a sample.

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Answer:

Sqrt 3

Step-by-step explanation:

The value of tan(G) is √3

Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.

In ΔGYK

∠GYK = 90°

∠KGY = 60°

∠GYK = 30°

side GK = 27

Let side KY = x

tan(Y) = tan30° = GK/KY

1/√3 = 27/x

x = 27√3

So side KY = 27√3

tan(G) = KY/KG

tan(G) = 27√3/27

tan(G) = √3

Hence, the value of tan(G) is √3

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Answer:

[tex] \boxed{\sf x \degree = 62 \degree} [/tex]

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

[tex] \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree[/tex]

In the given figure, the value of x is 62°.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

The given angles are,

x°, 38° and 100°.

To find the value of angle x, use exterior angle property.

According to exterior angle property,

The  sum of two interior angles is equal to exterior angle.

Since, 100° is the exterior angle of x and 38.

x + 38 = 100

x = 100 - 38

x = 62.

The required value of angle x is 62°.

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Answer:

24.95 kg

Step-by-step explanation:

one pound =0.45356 kg

55 lbs=55*45356 =24.95 kg

Answer:

The number of women teachers attending the lecture is 1

Step-by-step explanation:

Let M denotes men , W denotes women and T denotes teachers.

Number of women = n(W)=29

Number of men = n(M)=23

Number of teachers=n(T)=4

We are given that 24 are either men or teachers.

So,n(M∪T)=24

We are supposed to find the number of women teachers attending the lecture. ​

n(M∪T)=n(M)+n(T)-n(M∩T)

24=23+4-n(M∩T)

n(M∩T)=3

So,No. of teachers those are men is 3

Total number of teachers = 4

So,  the number of women teachers attending the lecture= 4-3 = 1

Hence the number of women teachers attending the lecture is 1

Answer:

The answer is explained below

Step-by-step explanation:

stiffness        frequency

2480             23

2440             35

2400             40

2360             33

2320             21

a) The mean for the population is calculated using the formula:

[tex]mean (\mu)=\frac{\Sigma f_ix_i}{\Sigma f_i} \\=\frac{x_1f_1+x_2f_2+.\ .\ .+x_nf_n}{x_1+x_2+.\ .\ . +x_n} \\=\frac{(2480*23)+(2440*35)+(2400*40)+(2360*33)+(2320*21)}{23+35+40+33+21} =\frac{365040}{152}=2401.6[/tex]

b) The standard deviation is given by:

[tex]\sigma=\sqrt{ \frac{\Sigma f_i(x_i-\mu)^2}{\Sigma f_1} } \\=\sqrt{ \frac{f_1(x_1-\mu)^2+f_2(x_2-\mu)^2+.\ .\ .+f_n(x_n-\mu)^2}{f_1+f_2+.\ .\ .+f_n} } \\=\sqrt{ \frac{23(2480-2401.6)^2+35(2440-2401.6)^2+40(2400-2401.6)^2+33(2360-2401.6)^2+21(2320-2401.6)^2}{23+35+40+33+21 }}\\=\sqrt{\frac{390021.12}{152} }= 50.7[/tex]

c) We have to find the z score for x = 2350. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2350-2401.6}{50.7}=-1.02[/tex]

From the z table:

The probability that stiffness would be less than 2350 for any given channel section = P(x < 2350) = P(z < -1.02) = 0.1539 = 15.39%

Step-by-step explanation:

Let's say the coordinates of Q are (h, k).

The slope of PQ is perpendicular to the tangent line.

(k − 2) / (h − 2) = -⅓

3(k − 2) = -(h − 2)

3(k − 2) = 2 − h

Solving for h:

h = 2 − 3(k − 2)

h = 2 − 3k + 6

h = 8 − 3k

(2, 2) is a point on the circle, so:

(2 − h)² + (2 − k)² = r²

Substituting:

9 (k − 2)² + (2 − k)² = r²

10 (k − 2)² = r²

The equation of the circle is:

(x − 8 + 3k)² + (y − k)² = 10 (k − 2)²

Without more information, there are an infinite number of possible solutions.  For example, if k = 1, the equation of the circle is:

(x − 5)² + (y − 1)² = 10

Answer:

(a) 95% of people have an IQ score between 66 and 134.

(b) 32% of people have an IQ score of less than 83 or greater than 117​.

(c) 16% of people have an IQ score greater than 117.

Step-by-step explanation:

We are given that scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 17.

Let X = scores of an IQ test

SO, X ~ Normal([tex]\mu=100, \sigma^{2} = 17^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                      Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

Now, the empirical rule states that;

(a) The percentage of people having an IQ score between 66 and 134 is given by;

     z score for 66 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{66-100}{17}[/tex]  = -2

     z score for 134 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{134-100}{17}[/tex]  = 2

This means that the percentage of people having an IQ score between 66 and 134 is 95%.

(b) Firstly, we have to find the percentage of people having an IQ score between 83 and 117;

     z score for 83 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{83-100}{17}[/tex]  = -1

     z score for 117 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{117-100}{17}[/tex]  = 1

This means that the percentage of people having an IQ score between 83 and 117 is 68%.

This means that the percentage of people having an IQ score of less than 83 or greater than 117 = 100% - 68% = 32%.

(c) In the above part, we find that there are 32% of the values that have an IQ score of less than 83 or greater than 117.

This means that half of this will be less than 83 and half of this will be greater than 117.

So, the percentage of people having an IQ score greater than 117​ = [tex]\frac{32\%}{2}[/tex] = 16%.

Answer:

Combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation

Step-by-step explanation:

The first thing to keep in mind is the difference between combination and permutation.

The main difference is that in the combinations the order does not matter, whereas in the permutations the order does matter.

Combination example:

Choose 7 people for a project.

Example of permutation:

Choose 5 men for each specific role in a soccer team.

Therefore, "group of 5 senators is chosen to be part of a special committee" is a combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation.

Answer:

y = (x - 4)² + 2 , x ≥ 4.

Step-by-step explanation:

Finding the inverse of

f(x) = 4 + √(x - 2)

Begin by swapping the x and y variables in the equation:

x = 4 + √(y - 2)

Subtract 4 from both sides:

x - 4 = √(y - 2)

Square both sides:

(x - 4)² = y - 2

Add 2 to both sides to get your equation:

y = (x - 4)² + 2

However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.

Answer:

His final velocity is 48.03 m/s

Step-by-step explanation:

Using SI units  (m, kg, s)

a = 3.7

x0 = 25

x1 = 300

v0 = 16.5

Apply kinematics formula

v1^2 - v0^2 = 2a(x1-x0)

solve for v1

Final velocity

v1 = sqrt(2a(x1-x0)+v0^2)

= sqrt( 2(3.7)(300-25)+16.5^2) )

= 48.03 m/s

Answer:

Step-by-step explanation:

y-|x|+3

y=|x|+3

vertex=(0,3)

y=|x-4|-7

vertex(4,-7)

Answer:

5/8

Step-by-step explanation:

1 + 3/8 - 3/4 =

1 + (1 × 3)/(1 × 8) - (2 × 3)/(2 × 4) =

1 + 3/8 - 6/8 =

1 + (3 - 6)/8 =

1 - 3/8

- 3/8 already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

3 is a prime number;

8 = 23

1 - 3/8 =

(1 × 8)/8 - 3/8 =

(1 × 8 - 3)/8 =

5/8

Hope this helpes

be sure to give brainliest

Answer:

Group B is farther from the airport.

Step-by-step explanation:

To find the distance of each group to the airport we can use the law of cosines in the triangle created with the two movements done and the resulting total distance.

Law of cosines:

[tex]c^2 = a^2 + b^2 - 2ab*cos(angle)[/tex]

For group A, we have the sides of 200 miles and 75 miles, and the angle between the sides is (180-68) = 112°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(112)[/tex]

[tex]c^2 = 56863.198[/tex]

[tex]c = 238.46\ miles[/tex]

For group B, we also have the sides of 200 miles and 75 miles, and the angle between the sides is (180-51) = 129°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(129)[/tex]

[tex]c^2 = 64504.612[/tex]

[tex]c = 253.98\ miles[/tex]

The distance from group B to the airport is bigger, so group B is farther from the airport.

Answer:

The answer is 27

Step-by-step explanation:

9+9+9=27

9*3=27

9+9=18+9=27

Answer:

27

Step-by-step explanation:

9+9=18

18+9=27

This can also be expressed as 9*3=27

Answer:

Can 1 will contain more stew

Step-by-step explanation:

diameter= 8

radius=d/2=4

height=4

therefore volume= [tex]\pi[/tex] r2 h= 201.06

Diameter= 6

radius=d/2=3

height= 7

therefore volume= [tex]\pi[/tex] r2 h= 197.92

The cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

The more volume of a can is, the more stew it can store.

For first can:

Since radius = diameter/2, so radius of base = 8/2 = 4 inches.

Thus, volume of first can: [tex]V = \pi (4)^2 (4) = 64\pi \: \rm unit^3[/tex]

For second can:

Since radius = diameter/2, so radius of base = 6/2 = 3 inches.

Thus, volume of first can: [tex]V = \pi (3)^2 (7) = 63\pi \: \rm unit^3[/tex]

Thus, as π > 0, so first can can contain more stew.

Thus, the cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

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Answer and Step-by-step explanation:

The rate of change of an area of a circle in respect to tis radius is given by:

ΔA / Δr = [tex]\frac{\pi(r_{1}^{2} - r_{2}^{2}) }{r_{1} - r_{2}}[/tex]

(i) 2 to 3:

ΔA / Δr = [tex]\frac{\pi(3^{2} - 2^{2}) }{3-2}[/tex] = 5π

(ii) 2 to 2.5

ΔA / Δr = [tex]\frac{\pi(2.5^{2} - 2^{2}) }{2.5-2}[/tex] = 4.5π

(iii) 2 to 2.1

ΔA / Δr = [tex]\frac{\pi(2.1^{2}-2^{2})}{2.1-2}[/tex] = 4.1π

Instantaneous rate of change is the change of a rate at a specific value. In this case, it wants at r = 2, so take the derivative of area and determine the area with the specific radius:

[tex]\frac{dA}{dr}[/tex] = π.r²

A'(r) = 2.π.r (1)

A'(2) = 4π

Note that expression (1) is the circumference of a circle, so it is shown that to determine the instantaneous rate of change of the are of a circle, is the circumference of any given radius.

The circles in the attachment shows a circle with radius r (light green) and a circle with radius r + Δr (darker green).

The rate of change between the two circles is the area shown by the arrow:

ΔA = π,[r² - (r+Δr)²]

ΔA = π.[r² - r² + 2rΔr + Δr²]

ΔA = π.(2rΔr + Δr²)

If Δr is too small, Δr² will be approximately zero, so

Δr²≈0

ΔA = π.(2rΔr)

The rate of change with respect to its radius will be:

ΔA / Δr = π.(2rΔr) / Δr

ΔA / Δr = 2.π.r

which is the circumference of a circle, so, this is the geometrical proof.

Answer:

Step-by-step explanation:

Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...

  10d +5(d-9) = 180

  15d -45 = 180 . . . . . simplify

  d -3 = 12 . . . . . . . . . .divide by 15

  d = 15

  15 -9 = 6 = number of nickels

Sue has 15 dimes and 6 nickels.

Answer:

15 dimes, 6 nickels

Step-by-step explanation:

D = # of dimes, and N = # of nickels

10D + 5N = 180

D = N + 9

Substitute:

10 (N + 9) + 5N = 180

10N + 90 + 5N = 180

15N = 90

N = 6

D = 15

Answer:

Step-by-step explanation:

A "rate of change" is usually referring to ...

  "something" per "something else"

The "per" signifies division, as in a fraction, so this can also be written ...

  "something" / "something else"

When the "something else" is one of it (1 week, for example), the rate is called a "unit rate."

When you're dealing with a graph, the "rate of change" usually refers to the slope of the line or curve on the graph. That is why it is computed as ...

   rate of change = (vertical change)/(horizontal change)

So, you can find what the "something" is by looking at the chart label and the vertical axis label. You can find what the "something else" is by looking at the horizontal axis label.

__

1. The rates of change in this problem represent ...

  total savings $ per week

__

2. Alyssa's higher rate of change means Alyssa's savings per week are higher than Sarah's.

__

3. The "initial value" is the value of the curve or line where the number on the horizontal axis is zero (0). It is usually, but not always, at the left side of the graph. It is also often called the "y-intercept", because it it the value where the curve intercepts the vertical (y) axis. Here, you're asked for an ordered pair, so you want the (x, y) values at that point. We've already said the x-value is zero.

  Sarah's initial value: (0, 8)

  Alyssa's initial value: (0, 0)

Answer:

180 degrees

Step-by-step explanation:

The sum of all the interior angles in a triangle is always equal to 180 degrees.

Answer:

The correct answer is TRUE.

Step-by-step explanation:

Find the measure of x.

Begin by setting up an equation of the five angles equal to 180°.

x + 37° + 41° + 29° + 51°  = 180° • The sum of the angles is 180°.

x + 158° = 180°       • Add the known values on the left side.

x = 22° • Subtract 158° from both sides.

The measure of angle x is 22°.

Given that,

ABC and ADC are triangles.

The area of ΔADC is 52 m².

Suppose , AD is the median.

According to figure,

We need to find the area of ΔABC

Using theorem of triangle

[tex]\bigtriangleup ADB +\bigtriangleup ADC=\bigtriangleup ABC[/tex]

Here, Δ ADB = Δ ADC

So, [tex]2 \bigtriangleup ADC=\bigtriangleup ABC[/tex]

Put the value of Δ ADC

[tex]\bigtriangleup ABC =2\times52[/tex]

[tex]\bigtriangleup ABC = 104\ m^2[/tex]

Hence, The area of ΔABC is 104 m².

Answer:

hello your question is incomplete here is the complete question

Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81

Answer : [tex]\frac{4 \pi }{3} [729 - 65\sqrt{65} ][/tex]

Step-by-step explanation:

The given data

cylinder  = x^2 + y^2 = 16

sphere = x^2 + y^2 +z^2 = 81

from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then  multiply the sesult by 2

Note : we are restricting our attention to the cylinder  x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well

the r parameter goes from 0 to 4

ATTACHED IS THE REMAINING PART OF THE SOLUTION

showing the integration

Answer:

the square root is approximately 12.04

12.0415945788

Hope This Helps

Answer:

350 mL of water

Step-by-step explanation:

Well she starts with 200mL of water and there is 800 mL of acid of water.

She drains 100 mL of acid and adds 100 mL of water so there is 300 mL of water.

And she stirs meaning the compounds have mixed.

Then she drains 100 mL and she they are mixed she drains half of acid and half of water so she has 250 mL of water.

The she adds 100 mL of water so now there’s 350 mL of water left.