#1) a normal distribution has a mean of 101 and a standard deviation of 4.2. what is the z-score of 105?

Answer:

y = 17(2)^x

Step-by-step explanation:

If the graph of y = ab^x goes through (0, 17), then

                        17 = ab*0, or a = 17

Then the function is y = ab^x with a = 17, or

                                  y = 17*b^x and we must find b.

If the graph of y = 17*b^x also goes through (6, 1088), then the following must be true:   1088 = 17*b^6

which reduces to 64 = b^6

Taking the sixth root of both sides, we get 64^(1/6) = b, and so b = 2

Then the desired exponential function is

y = 17(2)^x

The required, rate of change of function B is greater than the rate of change of Function A.

Rate of change is defined as the change in value with rest to another entity is called rate of change.

Here,
For function 1 rate of change is given by the slope of the function,

m = (y₂ - y₁) / (x₂ - x₁)
m = 2 - 1 / 4 - 0
m = 1/4

m = 0.25

For function B, y = 0.75x - 2 rate of change has defined the slope of the function from the equation slope is m = 0.75.

So Slope of function B > Slope of function A

Thus, the rate of change of function B is greater than the rate of change of Function A.

Learn more about the rate of change here: https://brainly.com/question/13103052

#SPJ1

The required two numbers are 6 and 8.

Let us denote the required numbers by c and d.

Given that the difference between two natural numbers is 2.

If we assume d > c, then d – c = 2

⇒ d = 2 + c → equation 1.

Also given that the sum of their squares is 100.

⇒ c² + d² = 100

⇒ c² + (2 + c)² = 100 (using the value of d from equation 1)

⇒ 2c² + 4c + 4 = 100

⇒ 2c² + 4c = 96

⇒ 2c(c+2) = 96

⇒ c(c+2) = 48

Using the factorization for 48, we get 6 × 8 = 48

⇒ c = 6

⇒ c+2 = 8

⇒ d = 8

Therefore, the required two numbers are 6 and 8.

Learn more at:

https://brainly.com/question/10005040

#SPJ9

Answer:

6.9282

Step-by-step explanation:

I can't give a step by step sorry

Answer: 5 units

Step-by-step explanation:

The margin of error if we want a 90% confidence interval for the true population mean age is calculated to be 1.62 years, therefore option (a) is correct.

We can use the formula for the margin of error:

Margin of error = z × (σ / √(n))

where z is the z-score for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the z-score is 1.645. Substituting the given values, we get:

Margin of error = 1.645 × (9.84 / √(100)) = 1.62

Therefore, the margin of error is 1.62 years, which is option (a).

Learn more about Standard Deviation :

https://brainly.com/question/23907081

#SPJ4

Answer:

picture #1 - 50.27 square units

picture #2 - 113.10 square units

picture #3 - 380.13 square units

Step-by-step explanation:

picture #1 - area = πr^2 -> π*4^2 = 50.27 square units

picture #2 - area = πr^2 -> π*6^2 = 113.10

picture #3 - area = πr^2 -> π*11^2 = 380.13

Answer:

The solution to the system of equations g(x) = x - 1 and f(x) = x^2 - 5 is the point where the two functions intersect, which is the point (1,0).

To confirm this, we can substitute x = 1 into each equation and see that they both equal 0:

g(1) = 1 - 1 = 0

f(1) = 1^2 - 5 = -4 + 1 = -3 = 0

So (1,0) is the solution to the system of equations.

The value of the model expression when simplified is (d)

From the question, we have the following representation that can be used in our computation:

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

Read more about expression at

brainly.com/question/723406

#SPJ1

Answer:60m^2

Step-by-step explanation:you have to find the height of the triangle first which is easy bc it’s been split in half so the are now two right triangles. use the pythagorean theorem to determine the height, the height is 12, the formula for the area of a triangle is 1/2bxa and half of the base is already given to you, 5 so 5 x 12 equals 60

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

To know more about matrix,

https://brainly.com/question/31494894

#SPJ11

The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.

The ratio of boy to girl who play kickball at race is 6 to 2

6 boys: 2 girls

Multiply the number of girls by the ratio:

18 girls x (6 boys / 2 girls) = 18 x 3 = 54

Subtract the number of girls from the total to get the number of boys:

54 - 18 = 36

Therefore, there are 12 boys who play kickball at race.

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

Answer:

4FT TO 1FT

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

If you divide 8 by 2, then you get 4.

Hope that this helps!

Answer:

Hello! Yes, when completing the square, you are essentially transforming a quadratic equation from standard form to vertex form. The vertex form of a quadratic equation is given by:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola and 'a' is a constant that determines the shape and direction of the parabola.

To convert a quadratic equation from standard form (ax^2 + bx + c) to vertex form, we follow these steps:

1. Divide both sides of the equation by 'a' to make the coefficient of x^2 equal to 1.

2. Move the constant term (c/a) to the right-hand side of the equation.

3. Complete the square by adding and subtracting (b/2a)^2 on the left-hand side of the equation.

4. Factor the left-hand side of the equation as a perfect square trinomial.

5. Write the equation in vertex form by identifying the values of 'a', 'h', and 'k'.

The new function after applying the sequence of transformation include: B. 1/2f(x + 5) - 11

In Mathematics and Geometry, the translation of a graph to the left means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x + N)

Conversely, the translation of a graph downward means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

Since the parent function f(x) was translated 11 units downward, 5 units to the left, and vertically compressed (making it wider) by a factor of 1/2, the equation of the image g(x), we have:

g(x) = 1/2f(x + 5) - 11

Read more on function and translation here: brainly.com/question/31559256

#SPJ1

Complete Question:

If f(x) is transformed by compressing the function vertically (making it wider) by a factor of 1/2, shifting 5 units to the left, and shifting 11 units downward, what will be the new function?

Answer:

-19.68

-1/10x+8/5

25 1/3

-50

22.75

Step-by-step explanation:

Answer:

6) 22.75gallons

7) -50feets

8) 25⅓ inches

9)2/5

10) -19.68

The number of elements in the set (((A∪B)∪C)′) is 5. Thus, the correct answer is C.

Let's construct a Venn Diagram using the given information:

1. Start by drawing three overlapping circles to represent sets A, B, and C.

2. Label the intersection regions: A∩B, A∩C, and B∩C.

3. Fill in the values we have: n(A) = 22, n(B) = 29, n(C) = 37, n(A∩B) = 3, n(A∩C) = 4, n(B∩C) = 6, and n(A∩(B∩C)) = 2.

The Venn Diagram should look something like this:

         _________

        /         \

       /    C     \

      /___________\

     |      /      |

     |   A  |   B  |

     |______|______|

4. Now, let's find n((A∪B)∪C) by adding the elements from A, B, and C, while removing any overlap:

n((A∪B)∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(A∩C) - n(B∩C) + n(A∩(B∩C))

          = 22 + 29 + 37 - 3 - 4 - 6 + 2

          = 77

5. Finally, we need to find n(((A∪B)∪C)′), which is the complement of ((A∪B)∪C) with respect to the universal set U:

n(((A∪B)∪C)′) = n(U) - n((A∪B)∪C)

              = 82 - 77

              = 5

Therefore, the number of elements in the set (((A∪B)∪C)′) is 5. Thus, the correct answer is C.

Learn more about Venn Diagram here:

https://brainly.com/question/20795347

#SPJ11

\(f(x)=-\cfrac{1}{2}x^2 + 5x\hspace{13em}g(x)=x^2+2 \\\\[-0.35em] ~\dotfill\\\\ g(-2)=(-2)^2+2\implies g(-2)=4+2\implies g(-2)=6 \\\\[-0.35em] ~\dotfill\\\\ f(~~g(-2)~~)\implies f(6)\implies f(6)=-\cfrac{1}{2}(6)^2+5(6) \\\\\\ f(6)=-\cfrac{36}{2}+30\implies f(6)=-18+30\implies \stackrel{f(~~g(-2)~~)}{f(6)}=12\)

The two studies indicate that 150 minutes of intense exercise per week is effective in reducing mortality risks.

Study 1 was carried out by the National Cancer Institute and Harvard University, and they collected information about the exercise habits of around 661,000 middle-aged adults from six large ongoing health surveys. They then divided the data into various segments based on the weekly exercise time as a parameter.

The group with no exercise had the highest risk of premature death. Minimal exercise that is less than the recommended levels could still reduce the risk of premature death by 20%.

The group that followed the standard exercise guidelines of 150 min/week of moderate exercise had a 31% lower probability of premature death. Individuals who exercised three times the recommended levels had the best benefits, with a 39% reduction in the risk of premature death.

However, increasing the exercise time did not have a significant effect on mortality risk rates. Study 2 was conducted by James Cook University in Cairns. They collected health survey data for over 200,000 Australian adults, which was then analyzed with corresponding death statistics. Their analysis was more detailed than the first study since they divided the data according to exercise stress levels ranging from normal to strenuous.

The results were similar to the first study, but there were some additional findings. The study showed that adhering to the general recommended exercise guidelines substantially decreased the risk of premature death, even with moderate exercise like walking. Intense exercise had little to no effect on mortality rates.

However, those who spent up to 30 percent of their weekly exercise time in vigorous activities were 9 percent less likely to die prematurely. With more than 30% of their time dedicated to strenuous activities, people gained an extra 13% reduction in early mortality, compared with people who stuck to moderate exercise levels. Very high levels of intense exercise did not improve mortality risk rates significantly.

In conclusion, the two studies indicate that 150 minutes of intense exercise per week is effective in reducing mortality risks.

learn more about mortality risks here:

https://brainly.com/question/4689314

#SPJ11

The major variable in this statistics class is considered a nominal variable.

The major variable is considered a nominal level of measurement because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.

In other words, the values assigned to different majors (e.g. Engineering, English, History) do not represent numerical quantities or differences.

The level of measurement of a variable determines the type of statistical analyses that can be conducted with that variable. In this case, the major variable is considered a nominal variable because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.

Nominal variables are often used to categorize or group data based on non-numeric characteristics, such as gender, race, or occupation. By collecting data on both GPA and major, the statistics instructor can explore relationships between these variables, such as whether certain majors tend to have higher or lower GPAs.

In conclusion, the major variable in this statistics class is considered a nominal variable.

To know more about nominal variable visit:

brainly.com/question/30869438

#SPJ11

(A) The parametric equations for the line segment from (1,2,4) to (3,0,6) can be written as:

x = 1 + t(3 - 1) = 2t + 1

y = 2 + t(0 - 2) = -2t + 2

z = 4 + t(6 - 4) = 2t + 4, where t is a parameter that varies between 0 and 1 to trace out the segment. The orientation of the curve is from (1,2,4) to (3,0,6).

(B) The parametric equations for the portion of the parabola y = x² - 1 from (1,0) to (-1,0) can be written as:

x = t

y = t² - 1, where t varies between -1 and 1 to trace out the portion of the parabola. The orientation of the curve is from (1,0) to (-1,0).

(C) The parametric equations for the ellipse x²/4 + y²/9 = 1, traced counterclockwise starting from (-2,0), can be written as:

x = 2 cos(t) - 2

y = 3 sin(t), where t varies between 0 and 2π to trace out the ellipse counterclockwise. The curve is oriented counterclockwise.

The parametric equations for the ellipse x²/4 + y²/9 = 1, traced clockwise starting from (-2,0), can be written as:

x = -2 cos(t) + 2

y = 3 sin(t), where t varies between 0 and 2π to trace out the ellipse clockwise. The orientation of the curve is clockwise.

To know more about parametric equations click here

brainly.com/question/30748687

#SPJ11

To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

The number of socks chosen at random will be denoted by the letter "n." Given by: The anticipated number of blue socks in "n" pairs

Expected number of blue socks = n * 1/4

In order for there to be four blue socks as expected, we need to determine the value of "n." Thus, we can construct the equation:

n * 1/4 = 4

And solving for n:

n = 4 / (1/4) = 4 * 4 = 16

So, To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

To learn more about construct, visit the link below:

https://brainly.com/question/8606089

#SPJ4

The measure of the arc 13cm long with a radius = 1  is 13rad

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

Length of an arc = ∅/360 x 2πr

where ∅ = subtended angle in degree

r = 1 = radius of the complete circle

length = 13

13 =  ∅ /360 x  2 x π x 1

but 2π rad = 360  degrees

substitute  2π rad  for 360 into the equation

13 =  ∅/2π rad  x 2 x π x 1

By cross multiplying

∅ = 13 x 2π rad / 2 x π

∅ = 13 rad

In conclusion, the angle subtended by the arc in radians is 13 rad.

Learn more about arc of a circle: https://brainly.com/question/23394322

#SPJ1

Answer:

24°

Step-by-step explanation:

m∠DCE = 180° - 90° - 41° - 25° = 24° (angles on a straight line are supplementary)

This is a question on angles . If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

When U = 10, the value of n is 112.604.

We are given that the number n is the algebraic sum of two terms:

Term 1 varies directly as u.

Term 2 varies inversely as U².

Let's denote the first term as k1 u, where k1 is the constant of proportionality.

And let's denote the second term as k2/U², where k2 is another constant of proportionality.

We have,

When U = 2, n = 22.

When U = 8, n = 56.5.

So, Equation 1: n = k1u + k2/U²

Equation 2: 22 = k1(2) + k2/(2)²

Equation 3: 56.5 = k1(8) + k2/(8)²

Let's solve these equations to find the values of k1 and k2.

Equation 2 becomes: 22 = 2k1 + k2/4

Equation 3 becomes: 56.5 = 8k1 + k2/64

To eliminate k2, let's multiply Equation 2 by 64:

1408 = 128k1 + k2

Now we have two equations with two variables:

128k1 + k2 = 1408

8k1 + k2/64 = 56.5

Let's subtract Equation

120k1 = 1351.5

k1 = 1351.5 / 120

k1 = 11.2625

Substituting the value of k1 back into Equation 2:

22 = 2(11.2625) + k2/4

22 = 22.525 + k2/4

k2/4 = 22 - 22.525

k2/4 = -0.525

k2 = -2.1

Now we have the values of k1 and k2:

k1 = 11.2625

k2 = -2.1

Finally, we can find the value of n when U = 10 by substituting these values into Equation 1:

n = k1u + k2/U²

n = 11.2625(10) - 2.1/(10)²

n = 112.625 - 2.1/100

n = 112.625 - 0.021

n ≈ 112.604

Therefore, when U = 10, the value of n is 112.604.

Learn more about Proportional relation here:

https://brainly.com/question/9184010

#SPJ1

Answer:

1103.30

Step-by-step explanation: