Find the total of the areas under the standard normal curve to the left of t, and to the right of z. Round your answer to four decimal places in necessary 21 = - 1.88 2 = 1.88

Answer:

57

Step-by-step explanation:

Get the absolute value of subtracting -27 from 30 (absolute value essentially meaning you make the answer positive no matter what). -27-30 = -57, and its absolute value is 57, which is the distance.

The absolute value is there because the distance can't be negative, as in you can't travel negative 2 miles to the grocery store. Hope this helps.

Based on the fractional winning of ³/₈, the team's win-loss ratio is 3:5.

The ratio shows the relative size that one quantity or value has when compared to another quantity or value.

We depict ratios in decimals, fractions, or percentages.  We can also use the standard ratio form (:) to show ratios.

The fraction of games won by the team = ³/₈

The fraction of games lost by the ream = ⁵/₈ (1 - ³/₈)

The implication is that for every 8 games, the team won 3 but lost 5 games.

The ratio of win-loss = 3:5

The sum of ratios = 8 (3 + 5)

Learn more about ratios at https://brainly.com/question/2328454.

#SPJ1

Answer: 197.55

Step-by-step explanation:

multiply the two numbers 65.85 times 3

The probability that Sam gets exactly 10 A's out of 12 tests is 0.234 or about 23.4%.

To solve this problem, we can use the binomial probability formula. The formula is:
[tex]P(X=k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

Where:
- P(X=k) is the probability of getting exactly k successes
- n is the number of trials (tests)
- k is the number of successes (getting an A)
- p is the probability of success on each trial (getting an A)
- (n choose k) is the binomial coefficient, which can be calculated as [tex]n! /[/tex][tex](k! * (n-k)!)[/tex]

Using this formula, we can plug in the values given in the problem:

n = 12 (number of tests)
k = 10 (number of A's)
p = 0.75 (probability of getting an A)

P(X=10) = (12 choose 10) * 0.75^10 * (1-0.75)^(12-10)
P(X=10) = (12! / (10! * 2!)) * 0.75^10 * 0.25^2
P(X=10) = 66 * 0.0563 * 0.0625
P(X=10) = 0.234

Therefore, the probability that Sam gets exactly 10 A's out of 12 tests is 0.234 or about 23.4%.

Learn more about probability here:

https://brainly.com/question/11234923

#SPJ11

To model a data set f(x) by an exponential function for equally spaced values of x, the necessary relationship between successive values of f(x) is:
c) The ratios are approximately equal.

For a data set f x( ) to be modeled by an exponential function, the necessary relationship between successive values of f x( ) for equally spaced values of x is that the ratios are approximately equal. This means that the ratio of any two consecutive values of f x( ) is approximately the same, regardless of the specific values of x chosen. This property is known as exponential growth or decay, and it is a fundamental characteristic of many natural and social phenomena. Therefore, if we observe that the ratios of successive values of f x( ) are approximately equal, we can conclude that the data set is likely to be modeled by an exponential function.

To model a data set f(x) by an exponential function for equally spaced values of x, the necessary relationship between successive values of f(x) is:

c) The ratios are approximately equal.

In other words, when the values of x are equally spaced, the ratio of f(x+1)/f(x) should be approximately the same for each successive pair of points in the data set. This constant ratio is a characteristic of exponential functions.

visit here to learn more about exponential function :

brainly.com/question/15352175

#SPJ11

The mean of this probability distribution is 2.3 when rounded to one decimal place.

To find the mean of this probability distribution, you'll need to multiply each value by its corresponding probability and then sum the products.

1. Multiply each value by its probability:
  - 0 * 0.1 = 0
  - 1 * 0.2 = 0.2
  - 2 * 0.05 = 0.1
  - 3 * 0.65 = 1.95

2. Sum the products:
  - 0 + 0.2 + 0.1 + 1.95 = 2.25

So, the mean of this probability distribution is 2.3 when rounded to one decimal place.

To know more about Probability distribution:

https://brainly.com/question/14210034

#SPJ11

The price paid for buying makeup of $4.30 after a discount of 40% and the tax rate of 6% is $2.84

Marked price = $4.30

Discount percent = 40%

Discount price = Marked price - Discount amount

Discount amount = 40% of 4.30

= 0.4 * 4.30 = $ 1.72

Discount price = 4.30 - 1.72

= $ 2.58

Tax = 6%

Tax = 0.06 * 4.30

= $ 0.258

Final price = Discount price + tax

= 2.58 + 0.258

Final price = $2.84

The money paid for buying the makeup after a 40% discount and 6% tax is $2.84.

Learn more about Discount:

https://brainly.com/question/23865811

#SPJ4

The complete question can be "You are buying makeup for $4. 30. There is a 40% off sale on all makeup. The tax rate is 6%. What is the final price that you pay?"

The probability is 0.296 Therefore, the probability that a soccer player who tests positive takes steroids is about 0.296 or 29.6%

To find the probability that a soccer player who tests positive takes steroids, we can use Bayes' theorem.
1. Define the events:
A: A player takes steroids.
B: A player tests positive for steroids.

2. We are given the following probabilities:
P(B|A) = 0.96 (probability of testing positive given that a player takes steroids)
P(B|A') = 0.12 (probability of testing positive given that a player doesn't take steroids)
P(A) = 0.05 (probability that a player takes steroids)

3. We need to find P(A|B), the probability that a player takes steroids given that they tested positive.
The probability that a soccer player who tests positive takes steroids can be calculated using Bayes' theorem:
P(Steroids | Positive) = P(Positive | Steroids) * P(Steroids) / P(Positive)
where P(Positive | Steroids) = 0.96 (96% of players taking steroids test positive), P(Positive | No Steroids) = 0.12 (12% of players not taking steroids test positive), and P(Steroids) = 0.05 (5% of soccer players take steroids).

4. Bayes' theorem states:
P(A|B) = (P(B|A) * P(A)) / P(B)

5. We first need to find P(B). We can do this using the law of total probability:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')

6. We know P(A) and can calculate P(A') as the complement:
P(A') = 1 - P(A) = 1 - 0.05 = 0.95

7. Now, we can calculate P(B):
P(B) = 0.96 * 0.05 + 0.12 * 0.95 = 0.048 + 0.114 = 0.162

8. Finally, we can calculate P(A|B) using Bayes' theorem:
P(A|B) = (0.96 * 0.05) / 0.162 ≈ 0.2963

The probability that a soccer player who tests positive takes steroids is approximately 0.296, or 29.6%.

Learn more about Probability:

brainly.com/question/30034780

#SPJ11

The PDF of Y is1/(2*sqrt(y)), for 0 < y < 1 and  fX(e^(-Y)) * |-e^(-Y)|.

(a) To find the pdf of Y when Y = X² and fX(x) = 1, 0 < x < 1, we first find the inverse function of Y = X², which is X = sqrt(Y). Next, we compute the derivative of X with respect to Y: dX/dY = 1/(2*sqrt(Y)). Now, we apply the change of variables formula to find the pdf of Y:

fY(y) = fX(x) * |dX/dY| = 1 * |1/(2*sqrt(y))| = 1/(2*sqrt(y)), for 0 < y < 1.

(b) To find the pdf of Y when Y = -log(X) and X has pdf, we first find the inverse function of Y = -log(X), which is X = e^(-Y). Next, we compute the derivative of X with respect to Y: dX/dY = -e^(-Y). We need the pdf of X to proceed, which is not provided in the question. Assuming we have the pdf of X as fX(x), we apply the change of variables formula to find the pdf of Y:

fY(y) = fX(x) * |dX/dY| = fX(e^(-Y)) * |-e^(-Y)|.

Know more about derivative here:

https://brainly.com/question/30365299

#SPJ11

the product of the minimum and maximum possible degrees of $f(x)g(x)$ is $2 \times 14 = \boxed{28}$.

The product of the minimum and maximum possible degrees of $f(x)g(x)$ is equal to the degree of the product polynomial.

If $f(x)$ is a polynomial of degree 7, then it can be written as:

$f(x) = a_7x^7 + a_6x^6 + \cdots + a_1x + a_0$

Similarly, if $g(x)$ is a polynomial of degree 7, it can be written as:

$g(x) = b_7x^7 + b_6x^6 + \cdots + b_1x + b_0$

The product of $f(x)$ and $g(x)$ is given by:

$f(x)g(x) = (a_7x^7 + a_6x^6 + \cdots + a_1x + a_0)(b_7x^7 + b_6x^6 + \cdots + b_1x + b_0)$

When we expand this product using the distributive property, we get a polynomial of degree 14, which is the sum of all possible products of the terms of $f(x)$ and $g(x)$.

The degree of a term in the product polynomial is the sum of the degrees of the terms being multiplied. Therefore, the degree of the product polynomial will be at most $7+7=14$.

In order to obtain the minimum possible degree of the product polynomial, we need to construct a scenario where the highest degree terms in $f(x)$ and $g(x)$ multiply to give the highest degree term in the product polynomial, and similarly for the lowest degree terms.

Thus, we want to choose $f(x)$ and $g(x)$ such that $a_7b_7 \neq 0$ and $a_0b_0 \neq 0$. In this case, the highest degree term in the product polynomial will be $a_7b_7x^{14}$, and the lowest degree term will be $a_0b_0$.

Therefore, the minimum possible degree of the product polynomial is 2.

On the other hand, the degree of the product polynomial will be exactly 14 if $a_7b_7 \neq 0$ and $a_0b_0 \neq 0$. This can be seen from the fact that the sum of the degrees of all terms in the product polynomial is 14.

Therefore, the maximum possible degree of the product polynomial is 14.

Hence, the product of the minimum and maximum possible degrees of $f(x)g(x)$ is $2 \times 14 = \boxed{28}$.

learn about polynomial,

https://brainly.com/question/15702527

#SPJ11

Based on the information provided, we can assert with 99% confidence that the possible size of error in estimating the average number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year is within a range of +/- 774.14 kilometers. This is calculated using the formula:

Margin of error = z-score x (standard deviation / square root of sample size)

Where the z-score for a 99% confidence level is 2.576. Plugging in the values, we get:

Margin of error = 2.576 x (3900 / square root of 100)
Margin of error = 2.576 x 390
Margin of error = 1004.64 / 2
Margin of error = +/- 774.14

Therefore, we can assert that the estimated average number of kilometers driven by car owners in Virginia is within a range of 22,725.86 kilometers to 23,274.14 kilometers with 99% confidence.

Learn more about error  here:

https://brainly.com/question/19575648

#SPJ11

The measure of the other two angles of the triangle in the ratio 3:11 are 15° and 55° respectively.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.

We recall that the sum of interior angles of a triangle is 180° and given one angle 110° and the ratio of the other two as 3: 11, then by comparison using the variable x;

110° + 3x + 11x = 180°

110° + 14x = 180°

14x = 180° - 110° {collect like terms}

14x = 70°

x = 70/14 {divide through by 14}

x = 5

so the two angles will be:

3(5) = 15°

11(5) = 55°

Therefore, the measure of the other two angles of the triangle in the ratio 3:11 are 15° and 55° respectively.

Read more about ratio here: https://brainly.com/question/2328454

#SPJ1

To find the point on the curve r(t)=(2cost, 2sint, e^t) we need to evaluate the x, y, and z coordinates at a specific value of t. Let's choose t=0 for simplicity.

So, plugging in t=0 we have:

r(0) = (2cos(0), 2sin(0), e^0)
r(0) = (2, 0, 1)

Therefore, the point on the curve at t=0 is (2, 0, 1).

To find the point on the curve r(t) = (2cos(t), 2sin(t), e^t) for a specific value of t, you can plug in the value of t into the parameterized equation:

1. Replace t with the specific value you're interested in (e.g., t = a).
2. Compute 2cos(a) for the x-coordinate.
3. Compute 2sin(a) for the y-coordinate.
4. Compute e^a for the z-coordinate.

The point on the curve will be (2cos(a), 2sin(a), e^a).

Learn more about point on the curve here: brainly.in/question/4174294

#SPJ11

The sum of unit vectors for M(- 3/4, 5, 2/3) and N(6, - 9, ⅗) is (27/4√(8329/900))i - (14/√(8329/900))j - (1/15√(8329/900))k.

To write MN as the sum of unit vectors, we first need to find the vector MN, which is the difference between the position vectors of M and N. Then, we divide this vector by its magnitude to obtain a unit vector in the same direction. Finally, we express MN as the sum of these unit vectors.

MN = N - M = (6 - (-3/4), -9 - 5, 3/5 - 2/3) = (27/4, -14, -1/15)

|MN| = √((27/4)² + (-14)² + (-1/15)²) = √(8329/900)

Unit vector in the direction of MN = MN/|MN| = (27/4√(8329/900), -14/√(8329/900), -1/15√(8329/900))

Therefore, MN can be written as the sum of unit vectors:

MN = (27/4√(8329/900))i - (14/√(8329/900))j - (1/15√(8329/900))k

Learn more about the unit vectors at

https://brainly.com/question/30279109

#SPJ4

Answer:

Step-by-step explanation:

21x9

181

It should be noted that to accurately calculate the area of the larger house, one must initialise by ascertaining the scale factor of the original.

The customer and constructor hold antithetical perspectives, hence influencing their appraisals. The former presumes that the linear expansion of the area is direct proportionate to the scale factor; thus implying that an augmentation in upscaling would lead to an equal rise in size.

Relying on this, the more enlarged property possesses an area four times greater than the original since, when augmenting the earlier measurements by two, the resultant increase in acreage is marked as (2 x 2 = 4). Accordingly, the total region of the extended residence becomes quadruple the acreage of the initial home.

Learn more about area on

https://brainly.com/question/25292087

#SPJ1

The required, Option D "Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56." is correct.

Jace is correct. The sentence "56 is 14 more than a number" implies that you can start with a certain number (which is unknown) and add 14 to it to get 56. Jace correctly used addition to represent this relationship in equation 14 + p = 56, where p represents the unknown number. The phrase "more than" does not necessarily suggest the use of the symbol >, as it can also be interpreted as an additional relationship.

Therefore, Jace's work is accurate and correctly represents the relationship between 56 and a certain number that is 14 less than 56.

Learn more about the equation model here:

https://brainly.com/question/16107051

#SPJ1

When there is a treatment or behavior for which researchers want to study risk, they often compare it to the baseline risk, which is the risk without the treatment or behavior.

The baseline risk provides a reference point for evaluating the effect of the treatment or behavior on the outcome of interest.

For example, if researchers want to study the risk of a certain disease among smokers compared to non-smokers, the baseline risk would be the risk of the disease among non-smokers. By comparing the risk of the disease among smokers to the baseline risk among non-smokers, researchers can determine the extent to which smoking increases the risk of the disease.

Similarly, if researchers want to study the risk of a certain side effect associated with a medication, the baseline risk would be the risk of the side effect in the absence of the medication. By comparing the risk of the side effect among people taking the medication to the baseline risk among people not taking the medication, researchers can determine the extent to which the medication increases the risk of the side effect.

learn about baseline risk,

https://brainly.com/question/30545181

#SPJ11

The number of miles that one can walk in 110 minutes with such a pace that they cover 3 miles in 70 minutes is 4.72.

The unitary method refers to the process in which by dividing we find the value of one by dividing. And then finding the value of a specific quantity by multiplying the one by the given number.

Therefore, we are given the number of miles traveled in 70 minutes and we can find the number of miles covered in 1 minute by division.

Number of miles in 70 minutes = 3 miles

Number of miles in 1 minute = 3 ÷ 70

= 0.042 miles

According to the question, we have to find miles covered in 110 minutes. To find it we multiply the miles in one minute by 110.

Number of miles in 110 minutes = 0.042 * 110

= 4.72 miles

Learn more about the Unitary method:

https://brainly.com/question/24587372

#SPJ4

The absolute value equation that has a solution set of -1/2 and 3/2 is [tex]|x - \frac{1}{2} | = -1[/tex].

We are given the solution sets of the absolute value equation and we have to find the absolute value equation. The solution sets given are

x = { -1/2, 3/2}. The absolute value of the equation can be represented as [tex]| x -x_{1} | - x_{2} = 0[/tex]  in which [tex]x_{1}[/tex] is the mean of the given two numbers in the set and [tex]x_{2}[/tex] is the difference between the two numbers divided by 2.

Firstly, we will find the mean of the two numbers

[tex]x_{1}[/tex] = (-1/2 + 3/2)/ 2

[tex]x_{1}[/tex] = 1/2

Now, we will find the value of [tex]x_{2}[/tex]

[tex]x_{2}[/tex] = (-1/2 -3/2)/2

[tex]x_{2}[/tex] = -2/2

[tex]x_{2}[/tex] = -1

We will substitute the values of [tex]x_{1}[/tex] and [tex]x_{2}[/tex] in the absolute value equation.

[tex]| x -x_{1} | - x_{2} = 0[/tex]

[tex]| x - 1/2| - (-1) = 0[/tex]

[tex]| x - \frac{1}{2}| + 1 = 0[/tex]

[tex]| x - \frac{1}{2}| = -1[/tex]

Therefore, the absolute value equation that has a solution set of -1/2 and 3/2 is [tex]|x - \frac{1}{2} | = -1[/tex].

To learn more about the absolute value equation;

https://brainly.com/question/26954538

#SPJ1

The required function that has a similar rate of change as the function y = 7/4x + 3 is shown in C. Option C is correct.

Here,
Given function y = 7/4x + 3

Comparing the above equation with the standard equation of the linear function is y = mx + c

So, m = 7/4, which implies the slope is positive,
Similarly, the slope of the relationship given in the options is,
A, m = -1
B, m = 8/3
C = 7/4
D = -2

Thus, the required function that has a similar rate of change as the function y = 7/4x + 3 is shown in C. Option C is correct.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ1

The area of the given composite figure is: 156 sq. units

The formula for the area of a rectangle is expressed as:

Area = L * W

Where:

W is width

L is Length

The formula for the area of a circle is:

Area = πr²

Thus:

Area of composite figure = 13 * 12 = 156 sq. units

This is because the semi circle added is exactly the same area with the one removed.

Read more about Area of Composite Figure at: https://brainly.com/question/10254615

#SPJ1

Answer: Simplified answer is 8x+y+30

The decimal equivalent of a fraction with 7 as the numerator and 9 as the denominator is 0.77

To convert a fraction into decimals we have to divide the numerator and the denominator and the quotient we get is the answer.

First, we have to write the numerator as the Dividend and the denominator as the divisor. Thus, we get 7 ÷ 9.

Since the divisor is greater than the dividend, we add a zero after it and in the quotient, we add a decimal. Thus we get 70 ÷ 9

We write the largest multiple of 9 which is smaller than 70 which is 63

and add 7 in the quotient as 7 * 9 is 63 and we get the quotient as 0.7 and the remainder of 70 - 63 = 7.

We continue the above steps until two places of decimals or as much as required. And we get 0.77 as the answer.

Learn more about Decimals:

https://brainly.com/question/29782941

#SPJ4

(a) A department store reports that 83% of all customers who use the store's credit plan pay their bills on time.
Your answer: Population characteristic (b) A sample of 100 students at a large university had a mean age of 24.3 years.
Your answer: Statistic

(a) Population characteristic: There is no number in boldface type in statement (a) that represents a population characteristic.
Statistic: The number in boldface type is 83%, which represents the percentage of customers who use the store's credit plan and pay their bills on time. This is a statistic because it is calculated from a sample of customers who use the credit plan and does not represent the entire population of customers who shop at the department store.

(b) Population characteristic: The number in boldface type in statement (b) does not represent a population characteristic because the statement only refers to a sample of students, not the entire population of students at the university.
Statistic: The number in boldface type is 24.3 years, which represents the mean age of the sample of 100 students. This is a statistic because it is calculated from a sample of students and does not represent the entire population of students at the university.

Learn more about Population here:

https://brainly.com/question/27991860

#SPJ11

the probability of all three cubes landing on odd numbers given that the white cube landed on three is 1/24

Since the white cube landed on 3, we only need to consider the red and green cubes.

The probability of each cube landing on an odd number is 1/2, since there are 3 odd numbers out of 6 total on each cube.

The probability of both the red and green cubes landing on odd numbers is the product of their individual probabilities:

P(red and green both odd) = P(red odd) x P(green odd) = 1/2 x 1/2 = 1/4

Therefore, the probability of all three cubes landing on odd numbers given that the white cube landed on three is:

P(white=3 and red and green both odd) = P(red and green both odd | white=3) x P(white=3)

= (1/4) x (1/6) = 1/24

So the probability of all three cubes landing on odd numbers given that the white cube landed on three is 1/24

learn about probability,

https://brainly.com/question/13604758

#SPJ11

The assignment of probabilities cannot be legitimate because of option (C): P(A and B) cannot be greater than either P(A) or P(B). In this case, P(AB) = 0.5, which is greater than both P(A) = 0.4 and P(B) = 0.3. For probabilities to be valid, the intersection of two events (A and B) must not exceed the individual probabilities of each event.

The reason why this assignment of probabilities cannot be legitimate is because of option B - A and B are given as independent events, but option A - A and B are not given as disjoint events. If A and B are independent events, then the probability of their intersection (AB) should be equal to the product of their individual probabilities, which is not the case here (0.5 ≠ 0.4 x 0.3). Therefore, option D - The assignment is legitimate is incorrect. Additionally, option C - GP(A and B) cannot be greater than either P(A) or P(B) is also violated, but it is not the main reason why the assignment is illegitimate.
The assignment of probabilities cannot be legitimate because of option (C): P(A and B) cannot be greater than either P(A) or P(B). In this case, P(AB) = 0.5, which is greater than both P(A) = 0.4 and P(B) = 0.3. For probabilities to be valid, the intersection of two events (A and B) must not exceed the individual probabilities of each event.

To learn more about probabilities, click here:

brainly.com/question/30034780

#SPJ11

Based on the simulations from parts (A) thru (E), the shape of the distribution of "heads" is bell-shaped. Therefore, the correct answer is B. Bell-shaped.

What is the most probable distribution's shape?

Bell-shaped distributions, sometimes referred to as normal or Gaussian distributions in math and science, are the most significant probability distribution shapes since they are typically the result of sufficiently big data sets from naturally occurring random variables.

The mathematical idea known as the normal distribution, and also referred to as the Gaussian distribution, is commonly defined by the mound form.

When data points are utilized to plot a line for a particular item that satisfies the requirements of the normal distribution, a form called a mound is produced.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

The requried measure of the tangent IP is evaluated as x = 11.

For the given circle, following the property of tangent and secant to the circle,
Tangent² = secant × IN

Substitute the value in the above expression,
x² = 20×IN
x² = 20 * 6
x = √120
x ≈ 11

Thus, the requried measure of the IP is evaluated as x = 11.

Learn more about tangent and secant here:

https://brainly.com/question/15178974

#SPJ1

The actual length of the back patio is 30 meters.

Given information:

Ayana measured a house and its lot and made a scale drawing. She used the scale 14 millimeters: 5 meters.

In the drawing, the back patio is 84 millimeters long.

If 14 millimeters in the drawing represent 5 meters in reality, then we can set up a proportion to find the length of the actual patio:

14 mm : 5 m = 84 mm : x

Cross-multiplying, we get:

14 mm (x) = 5 m (84 mm)

To simplify, we have:

x = (5 m  84 mm) / 14 mm

x = 30 m

Therefore, x = 30 m.

To learn more about multiplication;

https://brainly.com/question/19634536

#SPJ1