Find the Z-score for the value 55, when the mean is 98 and the standard deviation is 5.Pick a choice A. Z= -8.60 B. z= -8.80 C. z= -0.51 D. z=0.51

Based on the illustration given above, the feet that she now need to ascend to get back to sea level is 40.5.

Note that the first descend was 20.6 - 12.5 =

8.1 feet

Then she drop 32.4 feet again

So to get back up she need to add:

= 32.4 feet + 8.1 feet

= 40.5

Therefore, based on the calculation given above, the feet that she now need to ascend to get back to sea level is 40.5.

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The probability of a even number less than 8 will be 3/10.

What is the definition of probability?

The possibility of an event is expressed by probability. This field of mathematics is concerned with the occurrence of a random event. The value varies from 0 to 1. In mathematics, probability is used to forecast the likelihood of occurrences occurring.

The potential of something happening is referred to as probability. The probability distribution makes use of this fundamental principle in probability theory. Before we can evaluate the likelihood of an event occurring, we must first know the total number of alternatives.

P(E) is the chance that an event will occur divided by the total number of outcomes.

Now,

Given sample space  S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

and Event E="Even number less than 8"

{2,4,6}

Then, Probability of event E=3/10

Hence,

          The probability of a even number less than 8 will be 3/10.

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Answer:

She has 12 quarters.

Step-by-step explanation:

You have two unknowns, the number of quarters and the number of dimes. You need one equation per unknown, so you need two equations. One equation deals with the number of coins. The other equation deals with the values of the coins.

The first step is to choose variables. We can go with x and y, but I prefer to choose q and d, so I remember more easily what they represent.

Let q = number of quarters.

Let d = number of dimes.

Let's deal with the numbers of coins first.

"Georgina has 14 more dimes than quarters"

She has q number of quarters, but the number of dimes is 14 more than the number of quarters. d is 14 more than q. Our first equation is

d = q + 14

Now we deal with the values of the coins.

We don't know yet the actual numbers of dimes and quarters, so we use d and q to represent those numbers.

One dime is worth $0.10; d number of dimes is worth 0.1d.

A quarter is worth $0.25; q number of quarters is worth 0.25q.

The total value of the dimes and quarters is the sum of the values of the two sets of coins:

0.1d + 0.25q

We are told "Georgina has $5.60 in quarters and dimes."

This gives us our second equation.

0.1d + 0.25q = 5.6

Now we have a set of two equations in two variables:

d = q + 14

0.1d + 0.25q = 5.6

There are several methods for solving a system of equations. Since the first equation is already solved for a variable, d, we can use the substitution method.

We rewrite the second equation, but we substitute q + 14 for d in the second equation.

Second equation:

0.1d + 0.25q = 5.6

Substitute q + 14 for d:

0.1(q + 14) + 0.25q = 5.6

Distribute on the left side:

0.1q + 1.4 + 0.25q = 5.6

Combine like terms on the left side:

0.35q + 1.4 = 5.6

Subtract 1.4 from both sides:

0.35q = 4.2

Divide both sides by 0.35:

q = 12

There are 12 quarters.

(You are asked only the number of quarters, so you can stop here. I will continue to find also the number of dimes for 2 reasons. 1) You see how it's done, so it will help with other problems. 2) By finding the numbers of dimes and quarters, then we can check if our solution is correct, which I will do below at the end.)

Now we use the first equation, d = q + 14. We substitute 12 for q and solve for d.

d = q + 14

d = 12 + 14

d = 26

There are 26 dimes.

Check:

We check the numbers of coins:

26 - 12 = 14 The number of dimes is indeed 14 more than the number of quarters.

We check the values of the coins:

0.1(26) + 0.25(12) = 2.6 + 3 = 5.6 The value of the coins is indeed $5.60.

Our answer is correct.

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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Answer:

a^2 + 2ab + b^2

(a+b)(a-b)

a^2 - 2ab + b^2

Step-by-step explanation:

Answer:

The correct options for the solution values are:

Step-by-step explanation:

Given the expression

\(x^2+10x+25=8\)

Subtract 25 from both sides

\(x^2+10x+25-25=8-25\)

Simplify

\(x^2+10x=-17\)

Add 25 or 5² to both sides

\(x^2+10x+5^2=8\)

as

\(x^2+10x+5^2=\left(x+5\right)^2\)

so the expression becomes

\(\left(x+5\right)^2=8\)

\(\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}\)

solve

\(x+5=\sqrt{8}\)

Subtract 5 from both sides

\(x+5-5=2\sqrt{2}-5\)

\(x=2\sqrt{2}-5\)

solve

\(x+5=-\sqrt{8}\)

Subtract 5 from both sides

\(x+5-5=-2\sqrt{2}-5\)

\(x=-2\sqrt{2}-5\)

Therefore, the solution to the equation

\(x=2\sqrt{2}-5,\:x=-2\sqrt{2}-5\)

Hence, the correct options for the solution values are:

Step-by-step explanation:

13) 4x-22+x+11+10x-4 =180

15x=195

x=13

<P=(10(13)-4)=126

<Q=(4(13)-22)=30

<R=13+11=24

Answer:

B  (1, 5), (2, 6), (3, 6), (4, 5), (5, 4)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The graient is 2 as gradient = diffrence of y/diffrence in x

x,y

take two points 1,0 and 2,2 and put them into the equation

2-0/2-1 = 2

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (6, 10) ← 2 points on the line

m = \(\frac{10-0}{6-1}\) = \(\frac{10}{5}\) = 2

Therefore, the saddle point is approximately (-0.2852, 0.9953), and the local minimum is approximately (0.9649, 2.0047).

To find the saddle point and local minimum of the function\(f(x) = x^3 + 7xy - 3y + y^2\), we need to calculate the partial derivatives with respect to x and y, and then find the critical points by setting these derivatives equal to zero.

The partial derivative with respect to x (f_x) is:

\(f_x = 3x^2 + 7y\)

The partial derivative with respect to y (f_y) is:

f_y = 7x - 3 + 2y

Setting f_x = 0 and f_y = 0, we can solve for the critical points:

From \(f_x = 3x^2 + 7y = 0:\)

\(3x^2 = -7y\\x^2 = -7/3 * y\)

From f_y = 7x - 3 + 2y = 0:

7x = 3 - 2y

x = (3 - 2y)/7

Substituting this value of x into\(x^2 = -7/3 * y\), we have:

\((3 - 2y)^2 / 49 = -7/3 * y\)

Expanding and simplifying the equation, we get:

\(9 - 12y + 4y^2 = -49y/3\)

Multiplying both sides by 3, we have:

\(27 - 36y + 12y^2 = -49y\)

Rearranging terms, we obtain:

\(12y^2 - 13y + 27 = 0\)

Solving this quadratic equation, we find two possible values for y: y ≈ 0.9953 and y ≈ 2.0047.

Substituting these values back into x = (3 - 2y)/7, we can determine the corresponding x-values.

For y ≈ 0.9953, x ≈ -0.2852.

For y ≈ 2.0047, x ≈ 0.9649.

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The name of the variable that is used to predict another variable is the explanatory variable.

The correct answer option is: b

What are response and explanatory variables?

The variable that researchers are attempting to explain or predict is known as the response variable. Because it is dependent on another variable, it is also known as the dependent variable.

The variable that is used to explain or predict the response variable is referred to as the explanatory variable.

What is the coefficient of determination and standard error of the estimate?

The coefficient of determination is a measurement used to explain how much variability in one factor can be explained by its relationship to another related factor.

The standard error of the estimate is an estimate of the accuracy of any predictions. It is denoted as SEE. The regression line decreases the sum of prediction deviations squared It is also referred to as the sum of squares error.

Dependent and independent variables are variables in mathematical modeling, statistical modeling, and experimental sciences, according to the question. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they depend, by some law or rule, on the values of other variables.

The name of the variable that is used to predict another variable is the explanatory variable.

The correct answer option is: b

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The player with the greater final score is of:

Barry.

Barry's final score is given as follows:

45.

Then we have to obtain Lee's score, from the description given in the missing information section.

Lee's scored is obtained as follows:

Thus Lee's final score is given as follows:

-55.

The classifications of the final scores according to the signals are given as follows:

A positive score will always be greater than a negative score, hence Barry had the greater final score.

Lee and Barry play a trivia game in which questions are worth different numbers of points. If a question is answered correctly, a player earns points. If a question is answered incorrectly, the player loses points. Lee currently has -350 points.

a. Before the game ends, Lee answers a 275 -point question correctly, a 70 -point question correctly, and a 50 -polnt question incorrectly. Write and find the value of an expression to find Lee's final score.

b. Barry's final score is 45. Which player had the greater final score?

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The original conditional statement is true: "If two angles are congruent, then they have the same degree measure." The converse is true: "If two angles have the same degree measure, then they are congruent." The inverse is true: "If two angles are not congruent, then they do not have the same degree measure." The contrapositive is true: "If two angles do not have the same degree measure, then they are not congruent."

The given conditional statement is: "If two angles are congruent, then they have the same degree measure."

The truth value of this conditional statement is true.

Reasoning:

The statement is a well-known mathematical fact. Congruent angles are defined as angles that have the same measure. Therefore, if two angles are congruent, it implies that they have the same degree measure. This statement holds true for all pairs of congruent angles.

Converse: "If two angles have the same degree measure, then they are congruent."

The converse of the given conditional statement is also true. If two angles have the same degree measure, it implies that they are congruent. This is a logical consequence of the definition of congruent angles.

Inverse: "If two angles are not congruent, then they do not have the same degree measure."

The inverse of the given conditional statement is also true. If two angles are not congruent, it implies that they do not have the same degree measure. This is the negation of the original statement.

Contrapositive: "If two angles do not have the same degree measure, then they are not congruent."

The contrapositive of the given conditional statement is true. If two angles do not have the same degree measure, it implies that they are not congruent. This is the negation of the converse statement.

In summary:

- The original conditional statement is true: "If two angles are congruent, then they have the same degree measure."

- The converse is true: "If two angles have the same degree measure, then they are congruent."

- The inverse is true: "If two angles are not congruent, then they do not have the same degree measure."

- The contrapositive is true: "If two angles do not have the same degree measure, then they are not congruent."

All related conditionals are true, and no counterexamples can be found for any of the statements.

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Answer: A 2 liter bottle equals . 528344 US gallons or . 439938 imperial gallons.

Step-by-step explanation:

Answer:

m=14°, n=28°

Step-by-step explanation:

Angles in a Circle

The central angle is formed between two radii and its vertex at the center of the circle.

An inscribed angle is formed between two chords whose vertex lies on the circumference of a circle.

The measure of the central angle a formed by the same lines that form an inscribed angle b is:

a = 2b

This means the angle of a = 98° is double of the inscribed angle of 35°+m:

98 = 2(35 + m)

Dividing by 2:

49 = 35 + m

Solving for m:

m = 49 - 35 = 14

m = 14°

Angles m and n are also formed by the same lines, and:

n = 2m

Thus:

n = 28°

Answer: m=14°, n=28°

Answer

They should deposit $7710.99

Explanation

Using compound interest formula,

Where:

A = Amount = $20,000

P = Principal = ?

r = Interesr rate = 10% = 0.1

n = 1

t = 10

The time required to fill 288 liters of water would be 288/6.4 = 45 minutes.Therefore, the time taken by the key to fill 288 liters of water is 45 minutes.

The given data in the problem is that a key delivers 32 liters of water in 5 minutes. We are required to calculate how much time it will take to fill 288 liters of water.So, let's proceed with the solution,Step 1: We need to find out how many liters of water is filled in one minute. We can use the unitary method to solve the problem. We know that 32 liters of water is filled in 5 minutes. Hence, in one minute, the amount of water filled would be32/5 = 6.4 litersStep 2: Now, we need to find the time required to fill 288 liters of water. Again, we can use the unitary method. We have found out that the amount of water filled in one minute is 6.4 liters. Therefore, the time required to fill 288 liters of water would be 288/6.4 = 45 minutes.Therefore, the time taken by the key to fill 288 liters of water is 45 minutes.

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The measure of ∠QPS must be 59° in order for the quadrilateral to be parallelogram.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Given is a quadrilateral PQRS.

Two opposite angles of the quadrilateral are given.

The measure of angle PQR is (6x+13) degrees and the measure of angle PSR is (7x-5) degrees.

If the quadrilateral is parallelogram, opposite angles must be equal.

6x + 13 = 7x - 5

6x - 7x = -5 - 13

-x = -18

x = 18

∠PQR = ∠PSR = 6x + 13 = 121°

Sum of the interior angles of a quadrilateral is 360°.

∠PQR + ∠PSR + ∠QPS + ∠QRS = 360°

121° + 121° + ∠QPS + ∠QRS = 360°

The other pair of opposite angles must be equal.

So, ∠QPS = ∠QRS

121° + 121° + 2∠QPS = 360°

242° + 2∠QPS = 360°

2∠QPS = 118

∠QPS = 59°

Hence the measure of ∠QPS = 59°

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Answer:

The mean of the given numbers is 97.

Step-by-step explanation:

To find the mean, we add up all the numbers and divide the sum by the total count of numbers.

96 + 100 + 100 + 95 + 93 + 98 + 97 + 97 + 98 + 96 = 970

There are 10 numbers

Dividing the sum by the count (10)

970 / 10 = 97

The mean is the average of a set of numbers. To find the mean of these numbers, we add them up and divide by the total number of numbers:

\(\begin{aligned}\text{Mean}& = \dfrac{96+100+100+95+93+98+97+97+98+96}{10}\\& = \dfrac{970}{10}\\& = 97\end{aligned}\)

\(\therefore\) The mean is 97.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list.

When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list. This list is managed by the Federal Trade Commission (FTC), which enforces the Telephone Consumer Protection Act (TCPA) in the United States. If someone's phone number is on the DNC registry, the registry rules apply indefinitely. This means that even if the individual's phone number is still listed after a period of time, telemarketers are prohibited from calling that number. If the individual wishes to receive telemarketing calls again, they must remove their phone number from the list by dialing the DNC registry's phone number, which is 1-888-382-1222. The process of removing a phone number from the list is a simple one. Dial the number on your phone, and then follow the instructions that the voice prompt gives you. Furthermore, it is important to know that calls from organizations that you have given permission to call you are still allowed even if your number is on the DNC registry.

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Answer:

f(g(4)) = -10

(g o f)(-4) = -16

Step-by-step explanation:

Function composition is an operation where one or more functions are substituted into another function.

Given functions:

\(\begin{cases}f(x)=x^2+6x-2\\g(x)=x-6\end{cases}\)

The given composite function f(g(4)) means to substitute the function g(4) in place of the x in function f(x). The function g(4) is the value of function g(x) when x = 4.

\(\begin{aligned}f\left(g(4)\right)&=\left(g(4)\right)^2+6\left(g(4)\right)-2\\&=\left(4-6\right)^2+6\left(4-6\right)-2\\&=\left(-2\right)^2+6\left(-2\right)-2\\&=4-12-2\\&=-8-2\\&=-10\end{aligned}\)

The given composite function (g o f)(-4) means to substitute the function f(x) in place of the x in function g(x), then substitute x = -4 into the resulting function.

\(\begin{aligned}\left(g \circ f \right)(-4)&=g\left(f(-4)\right)\\&=\left(f(-4)\right)-6\\&=((-4)^2+6(-4)-2)-6\\&=(16-24-2)-6\\&=-10-6\\&=-16\end{aligned}\)

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The answer is 400, which is 20% of 2,000.

Answer:

$100 we use on food each month.

Step-by-step explanation:

20% of $2000=$100

Answer:

x=0.9

Step-by-step explanation:

What I đid was

3(.9+2) mulitply two times bc of 2 equal sides

you should get 17.4

then, 6(2(0.9) +3) would get you 57.6, when adding it all together, you should get 75.

Answer:

√ (p(1-p) / n)

Step-by-step explanation:

Standard Error(SE) of the Sample Proportion: √ (p(1-p) / n). Note: as the sample size increases, the standard error decreases.

Hope this helps you! Feel free to give feedback

Answer:a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The coefficient is the constant in front of the variable.

Answer:

11

Step-by-step explanation:

7 1/3 ÷ 2/3 = 11

(please give brainliest)

Answer: 1/11

Explanation:

KCF

(keep, change, flip)

There are 70 ways to split 8 people into two teams of 4. There are 1680 ways to split 9 people into 3 teams of 3. There are 945 ways to choose 2 teams of 4 from 10 prospects.

To find the number of ways to split 8 people into two teams of 4, we can first choose the first team in $\binom{8}{4} = 70$ ways, and the second team will be the remaining 4 people.

To split 9 people into 3 teams of 3, we can first choose the first team in $\binom{9}{3} = 84$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{3} = 20$ ways. The final team will be the remaining 3 people.

To choose 2 teams of 4 from 10 prospects, we can first choose the first team in $\binom{10}{4} = 210$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{4} = 15$ ways. However, since the order in which we choose the two teams does not matter, we must divide by 2 to get the final answer of $\frac{210 \cdot 15}{2} = 945$.

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