One spinner is divided into four equal parts. A second spinner is divided into five equal parts. The grid shows the possible outcomes when each spinner is spun once.
a. How many possible outcomes are there?
b. What is the probability that an outcome contains numbers that are both greater than 3?
c. Find the probability of spinning the same two numbers.

Answer:

3.009 first then 3.09 than 3.56 than lastly 3.3

The normal distribution is solved and the retirement ages are normally distributed

P(x ≤ 62) ≈ 22.7%

P(x ≥ 70) ≈ 10.6%

P(55 ≤ x ≤ 60) ≈ 14.5%

P(60 ≤ x ≤ 70) ≈ 78.9%

Given data ,

To solve these probability questions, we can use the properties of the normal distribution. Let's calculate each probability:

a)

P(x ≤ 62):

To find this probability, we need to calculate the z-score corresponding to x = 62 and then find the area under the standard normal distribution curve to the left of that z-score. The formula to calculate the z-score is:

z = (x - mean) / standard deviation

In this case:

z = (62 - 65) / 4 = -0.75

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = -0.75 is approximately 0.2266 or 22.7%

b)

P(x ≥ 70):

To find this probability, we need to calculate the z-score corresponding to x = 70 and then find the area under the standard normal distribution curve to the right of that z-score. Again, we use the z-score formula:

z = (x - mean) / standard deviation

In this case:

z = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1.25 is approximately 0.1056 or 10.6%

c)

P(55 ≤ x ≤ 60):

To find this probability, we need to calculate the z-scores corresponding to x = 55 and x = 60, and then find the area between those two z-scores under the standard normal distribution curve. Again, we use the z-score formula:

z = (x - mean) / standard deviation

For x = 55:

z1 = (55 - 65) / 4 = -2.5

For x = 60:

z2 = (60 - 65) / 4 = -1.25

Using a standard normal distribution table or a calculator, we can find that the area between z = -2.5 and z = -1.25 is approximately 0.1446 or 14.5%

d)

P(60 ≤ x ≤ 70):

To find this probability, we need to calculate the z-scores corresponding to x = 60 and x = 70, and then find the area between those two z-scores under the standard normal distribution curve.

Using the same z-score formula as above:

For x = 60:

z1 = (60 - 65) / 4 = -1.25

For x = 70:

z2 = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find that the area between z = -1.25 and z = 1.25 is approximately 0.7887 or 78.9%

To learn more about normal distribution click :

https://brainly.com/question/17199694

#SPJ1

The values for each probability are:

P(x ≤ 62) is approximately 22.7%.

P(x ≥ 70) is approximately 10.6%.

P(55 ≤ x ≤ 60) is approximately 9.9%.

P(60 ≤ x ≤ 70) is approximately 89.4%.

We have,

To solve these probability problems, we can use the standard normal distribution and Z-scores.

First, we need to convert the given values to Z-scores using the formula: Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation.

a)

P(x ≤ 62):

Z = (62 - 65) / 4 = -0.75

Using a standard normal distribution table or a calculator, we can find the corresponding area under the curve for a Z-score of -0.75.

This gives us a probability of approximately 0.2266.

To convert this probability to a percentage, we multiply by 100: 0.2266 * 100 ≈ 22.7%

b)

P(x ≥ 70):

To find the probability of x being greater than or equal to 70, we can use the complement rule: P(x ≥ 70) = 1 - P(x < 70)

Z = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find the probability of a Z-score being less than 1.25, which is approximately 0.8944.

Now,

We can calculate P(x ≥ 70) = 1 - P(x < 70) = 1 - 0.8944 = 0.1056.

To convert this probability to a percentage, we multiply by 100: 0.1056 * 100 ≈ 10.6%

c)

P(55 ≤ x ≤ 60):

Z1 = (55 - 65) / 4 = -2.5

Z2 = (60 - 65) / 4 = -1.25

Using a standard normal distribution table or a calculator, we can find the probability of a Z-score being less than -1.25, which is approximately 0.1056.

Using the same method, we can find the probability of a Z-score being less than -2.5, which is approximately 0.0062.

Now, we can calculate the probability between -2.5 and -1.25 by subtracting the two probabilities:

P(-2.5 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -2.5) = 0.1056 - 0.0062 = 0.0994.

To convert this probability to a percentage, we multiply by 100: 0.0994 x 100 ≈ 9.9%

d)

P(60 ≤ x ≤ 70):

Using the same Z-scores as in part c), we can find the probability of a Z-score being less than -1.25, which is approximately 0.1056.

Using the complement rule, we can find P(60 ≤ x ≤ 70) = 1 - P(x < 60) = 1 - 0.1056 = 0.8944.

To convert this probability to a percentage, we multiply by 100: 0.8944 * 100 ≈ 89.4%

Therefore,

P(x ≤ 62) is approximately 22.7%.

P(x ≥ 70) is approximately 10.6%.

P(55 ≤ x ≤ 60) is approximately 9.9%.

P(60 ≤ x ≤ 70) is approximately 89.4%.

Learn more about normal distribution here:

https://brainly.com/question/15103234

#SPJ1

The value of the experimental probability of tossing heads is,

⇒ 1 / 3

We have to given that;

Coin Toss Results: T, H, T, H, T, H, T, T, T, T, H, T, H, T, T

Where, H stands for heads and T stands for Tails.

Hence, Total outcomes = 15

And, Head outcomes = 5

Thus, The value of the experimental probability of tossing heads is,

⇒ 5 / 15

⇒ 1 / 3

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

Answer:

b = 25 degrees

c = 81 degrees

d = 64 degrees

Answer: for the first graph all real numbers bc it keeps going up and d: {r}

for second graph also real numbers but i think it horizontally shifted by 2 units to the left. d: {r}

The expressions that are completely factored are:

The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.

For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.

Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).

learn more about factorization: https://brainly.com/question/10718512

#SPJ1

Answer:

16a^5−20a^3=4a^3(4a^2−5)

and

24a^4+18=6(4a^4+3)

Step-by-step explanation:

The correct option for the given sum is option B. The point (2,-9) paired with (2, 3), will make a side equal to this length.

Let the other point of the pentagon will be M(n, o).

The given point be A (a, b)

Also given one of the sides of a pentagon has length 12.

Now, we need to find the distance between the two points,

Distance between two points: |AM| = √\((a-n)^2+(b-o)^2\)

Now,

\(12 = \sqrt{(2-n)^2+(3-o)^2}\)

\((12)^2\) = \((2-n)^2+(3-o)^2\)

\((2-n)^2+(3-o)^2\) = 144 ----------------------------- eq (1)

Now, check every point for the values to match with equation (1)

Option A: \((2-14)^2+(3-15)^2\) = 288. So the option is false.

Option B:

\((2-2)^2+(3-(-9))^2\) =114

0+114 =114

Therefore option B is correct. The other point is (2,-9).

Learn more about Pentagon:

https://brainly.com/question/4343134

#SPJ1

Answer: To factorize the expression 6x + 8 fully, we can first look for the greatest common factor (GCF) of the two terms. In this case, the GCF is 2.

Step 1: Factor out the GCF:

2(3x + 4)

Now, we have the expression 3x + 4 inside parentheses. This expression cannot be further factorized since there are no common factors other than 1.

Therefore, the fully factorized form of 6x + 8 is:

2(3x + 4)

Step-by-step explanation:)

The factored expression is:

Step-by-step explanation:

To factor the expression, look at its GCF (greatest common factor).

Clearly the GCF of both terms is 2. So what we do next is we divide both terms by 2 :

The result is :

And now the 2 goes outside the parenthesis:

Hence, the answer is 2(3x + 4).

The relationship in the figure is a function because each input has only one output to which they are linked

A function is a definition or rule that maps each element in a set of input values to exactly one element in a set output values.

The data in the sets can be presented as follows;

x  \({}\)               f(x)

-1 \({}\)      →         2

0\({}\)        →        2

1\({}\)         →        -3

2\({}\)         →       -2

8\({}\)         →        3

The above table indicates that each x-value has only one f(x) value, which indicates that the relationship s a function. The relationship is still a function with the presence of an f(x) value, 2, having two x values, -1 and 0, as the condition satisfies the definition of a function.

Learn more on functions here: https://brainly.com/question/29869165

#SPJ1

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

Read more on rotation here: brainly.com/question/28854313

#SPJ1

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

Read more about Trigonometric ratios at: https://brainly.com/question/13276558

#SPJ1

Answer:

Step-by-step explanation:

new length=15+x

width=19+x

then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²

original area=15×19=285 ft²

then 285+98=x²+34x+285

or

x²+34x-98=0

x²+34x+17²=98+17²

(x+17)²=98+289=387

x+17=√387=3√43

x=3√43-17 ft

Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: \(g(x) = -\sqrt{9(x - 1)} + 2\)

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

\(g(x) = -\sqrt{9(x - 1)} + 2\)

Read more on translation here: brainly.com/question/4521517

#SPJ1

Answer:

B) −4<x<−1  or  x>1

Inequality Form: −4<x<−1  or  x>1

Interval Notation: (−4,−1)  ∪  (1,∞)

Step-by-step explanation:

Solve: x^3 + 4x^2 > x + 4

Subtract x from both sides of the inequality.

x^3 + 4x^2 − x > 4

Convert the inequality to an equation.

x^3 + 4x^2 − x = 4

Move 4 to the left side of the equation by subtracting it from both sides.

x^3 + 4x^

2 − x − 4 = 0

Factor the left side of the equation

(x + 4)(x + 1)(x − 1) = 0

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to 0

x + 4 = 0

x + 1 = 0

x − 1 = 0

Set x + 4 equal to 0 and solve for x

x = −4

Set x + 1 equal to 0 and solve for x

x = −1

Set x + -1 equal to 0 and solve for x

x = 1

The final solution is all the values that make (x + 4)(x + 1)(x − 1) = 0  true

x = −4, −1, 1

Use each root to create test intervals.

x < −4

−4 < x < −1

−1 < x < 1

x > 1

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the

inequality.

x < −4  ←False

−4 < x < −1  ←True

−1 < x < 1  ←False

x > 1  ←True

The solution consists of all of the true intervals.

−4 < x < −1 x > 1

The solution consists of all of the true intervals is −4 < x < −1   x > 1.

−4<x<−1  or  x>1

Inequality Form: −4<x<−1  or  x>1

Interval Notation: (−4,−1)  ∪  (1,∞)

x^3 + 4x^2 > x + 4

Subtract x from both sides of the inequality.

x^3 + 4x^2 − x > 4

Convert the inequality to an equation.

x^3 + 4x^2 − x = 4

Move 4 to the left side of the equation by subtracting it from both sides.

x^3 + 4x^2>x+4

2 − x − 4 = 0

Factor the left side of the equation

(x + 4)(x + 1)(x − 1) = 0

If any individual factor on the left side of the equation is equal to, the entire expression will be equal to 0

x + 4 = 0

x + 1 = 0

x − 1 = 0

Set x + 4 equal to 0 and solve for x

x = −4

Set x + 1 equal to 0 and solve for x

Inequality is the difference in social status, wealth, or opportunity between people or groups. People are concerned about social inequality.

x = −1

Set x + -1 equal to 0 and solve for x

x = 1

The final solution is all the values that make (x + 4)(x + 1)(x − 1) = 0  true

x = −4, −1, 1

Use each root to create test intervals.

x < −4

−4 < x < −1

−1 < x < 1

x > 1

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the

inequality.

x < −4  ←False

−4 < x < −1  ←True

−1 < x < 1  ←False

x > 1  ←True

The solution consists of all of the true intervals.

−4 < x < −1 x > 1

To learn more about the inequalities visit:

https://brainly.com/question/24372553

#SPJ5

Answer:

a is greater

Step-by-step explanation:

Place value is the system in which the position of a digit in a number determines its value.

Using place-value strategies without calculating we find that,

Renee says 4 x 800 is less than 8 x 4,000 is correct.

It is the system in which the position of a digit in a number determines its value.

Example:

135789

9 - ones

8 - tens

7 - hundreds

5 - thousands

3 - ten thousands

1 - hundred thousands

We have,

4 x 800:

Here we are multiplying a hundred-place value number.

= 3200

This can be said to be in place value of thousands.

8 x 4000:

Here we are multiplying a thousand-place value number.

= 32000

This can be said to be in place value of ten thousands.

We can say that,

8 x 4000 is greater than 4 x 800

Thus,

Renee says 4 x 800 is less than 8 X 4,000 is correct.

Learn more about place value here:

https://brainly.com/question/27734142

#SPJ5

Answer:

68.11% probability that the firm involved is firm B

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Cost overrun

Event B: Agency B used.

A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15.

This means that \(P(B) = 0.45\)

From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively.

This means that \(P(A|B) = 0.14\)

Probability of cost overrun.

Firm A is used 40% of the time, with 1% of these having cost overrun. B is used 45%, with 14% of these having cost overruns. C is used 15% of the time, with 17% of these having cost overruns.

So

\(P(A) = 0.4*0.01 + 0.45*0.14 + 0.15*0.17 = 0.0925\)

What is the probability that the firm involved is firm B

\(P(B|A) = \frac{0.45*0.14}{0.0925} = 0.6811\)

68.11% probability that the firm involved is firm B

On a number​ line, the coordinates of​ X, Y,​ Z, and W are −7​, −2​, 2​, and 7​, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and

Answer:

5

Step-by-step explanation:

your answer is 5 hope it help

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we need to use the Pythagorean Theorem to find the third side. We will then use the law of cosines to find the angle.

2√15² = 2√6² + b²

60 = 24 + b²

Subtract 24

36 = b²

b = 6

Now, that we have all three sides, we will use the law of cosines to figure out the angle.

c² = a² + b² - 2abCosC°

Substitute the values in.

6² = 2√15² + 2√6² - 2(2√15)(2√6)CosC°

36 = 60 + 24 - 2(37.947331922)CosC°

36 = 60 + 24 - 75.894663844CosC°

36 = 84 - 75.894663844CosC°

Subtract 84

-48 = -75.9CosC°

0.63241106719 = CosC°

Arccos (0.63241106719) = 50.77176844°

The largest acute angle is approximately 50.8°

The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}

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

Set = prime numbers

Cardinality = 5

The cardinality implies that the number of elements in the set is 5

5 prime numbers greater than 11 are 13, 17, 19, 23, 29

Hence, the set is {13, 17, 19, 23, 29}

Read more about set at

https://brainly.com/question/24713052

#SPJ1

Answer:

D) 1/2

Step-by-step explanation:

The pattern shown in the sequence is that every number is divided by 4 (left to right)  or multiplied by 4 (right to left). How did I get 4? I multiplied 64 by 16 (64/16) !

64 / 4 = 16

16 / 4 = 4

4 / 4 = 1

1 / 4 = 1/4  or 0.25 >> not 1/2 or 0.50!!

I hope this helps!!

The value that each term can be multiplied by to eliminate the decimals in the equation is 4

The equation is given as

0.5x + 1 = 0.75x

Represent the terms as a fraction

So, we have

1/2x + 1 = 3/4x

The denominators in th​e above fractions are

2 and 4

The LCM of 2 and 4 is 4

Hence, the value that each term can be multiplied by to eliminate the decimals in the equation is 4

Read more about equations at

https://brainly.com/question/13763238

#SPJ1

Answer:

$0.50 per pound

Step-by-step explanation:

divide the amount in pounds by the amount in dollars. Hope this helps <3

Answer:

60°

Step-by-step explanation:

they are equal.....

Answer:

5% Dextrose

Step-by-step explanation:

Dextrose is primarily used as a carbohydrate for nutrition and as a source of fluid. Whereas Sodium chloride is primarily used as a source of fluid and electrolytes.

A patient needs fluid and carbohydrates for nutrition. The fluid that the patient is likely to be administered is TNP. The patient needs fluid and carbohydrates for nutrition. The correct option is b.

Total parenteral nutrition (TPN) is a feeding technique that omits the digestive system. The majority of the body's nutritional requirements are met by a specific formula administered intravenously.

When a person cannot or shouldn't receive feedings or fluids orally, the technique is utilized. The term "parenteral nutrition," sometimes known as "total parenteral nutrition," refers to the practice of administering a unique type of food through a vein (intravenously).

The treatment's aim is to treat or stop malnutrition. TPN is made up of many components that are mixed together. These components include dextrose, lipid emulsions, amino acids, vitamins, electrolytes, minerals, and trace elements.

Therefore, the correct option is b, total parenteral nutrition.

To learn more about TNP, refer to the link:

https://brainly.com/question/28188329

#SPJ2

The question is incomplete. Your most probably complete question is given below:

a. protein

b. total parenteral nutrition.

c. iodine

d. fats

There are three primary sorts of operations done on sets in a set theory, such as:

Sets' union (∪)

Sets intersecting (∩)

Set difference (- )

Sets help in the identification of related groupings of objects. Set operations such as relations and functions are used to connect and manipulate sets.

Bowls, glasses, cups, and saucers are kept separate from plates, while pans and utensils have their own compartments. Cooking utensil sets and other collections are separated in storage. As seen above, there are countless examples of sets in our daily lives.

Learn more about set theory:
https://brainly.com/question/16823768
#SPJ1