An ice skater is penalized 1.2 points for a fall. Write an expression for the ice skater’s final score.

Answer:

7

Step-by-step explanation: -13(-1) + 36 + 42(-1)

Step 1: -13(-1)= 13

Step 2: 13 + 36= 49

Step 3: 49 + 42(-1)= 49 + (-42)= 7

Solution: 7

By rounding each number to 1 significant figure estimate to 6235.1 x 21.5 is 120000.

The concept of significant fiqure is based on the looking for the first non zero number that is resnt in the numbers , and that will be one significant figure, and it goes like that.

Then let us round each of the given fiqures into 1 significant fiqure as instructed:

6235.1 to 1 significant figure will be 6000 , because 6 is the first significant fiqure and the value that follow 6 is less than 5, it can not been approximated

21.5 to 1 significant figure will be  20

Then (6000*20) =120000

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Option b. 96,909,120 is the correct answer. The number of ways in which the new site can be chosen to locate 6 stores in 96,909,120 ways

We can find the number of ways by multiplying the number of possibilities each store can have.

Store 1, can be placed on 24 sites. Store 2 can be placed on 23 sites (since store 1 is already on site 1). Store 3 can be placed on 22 sites. Store 4 can be placed on 21 sites. Store 5 can be placed on 20 sites. Store 6 can be placed on 19 sites

Therefore the number of ways is:

C = 24 * 23 * 22 * 21 * 20 * 19

C = 9,69,09,120 possibilities

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By basic arithmetic, the state board of education will have $1 left .

The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.

Addition, subtraction, multiplication, and division are the four operations employed in arithmetic.

The total amount the state board has = $5647

The cost of calculator = $ 2

The total number of calculators bought = 5647/2

= 2323.5

≈ 2823

So, the cost of 2323 calculators

= 2823 × 2

= 5646

So, the money the state board of education left = $5647 - $5646

= $1

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The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.

The branch of mathematics which deals with the analysis of random phenomena is called probability. The probability of an event is defined as the ratio of favorable events to the total number of events.

P(E) = F(E)/T(E)

Where P(E) = probability of an event which occur\

F(E) = Number of favorable events

T(E)= Total number of events

Here given that the total number of cars T(E) =12

And the number of cars that have acceptable emissions level F(E) = 4

Hence Probability that at least nine cars have an acceptable emission level

=4/12

= 1/3

= 0.333

The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.

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Answer: I think its B: x=-4

Step-by-step explanation:

The complete proof using the AAS congruence postulate and CPCTC is explained below to show that QT ≅  SR.

When two angles of a triangle, and one of its side that is nonincluded are congruent to corresponding two angles and a nonincluded side in the another triangle, then both triangles are congruent by the AAS congruence postulate.

If two triangles are congruent, then all its corresponding parts are also congruent to each other based on the CPCTC theorem.

Below is the two-column proof that proves that side QT is congruent to side SR.

Statement                                     Reasons                                    

1. ∠R ≅ ∠T, QT ≅ SR                    1. Given

2. ∠TQS ≅ ∠RSQ                         2. Alternate interior angles

3. QS ≅ QS                                   3. Reflexive property

4. ΔTQS ≅ ΔRSQ                          4. AAS

5. QT ≅  SR                                   5. CPCTC

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The converse of the statement that says that If an item is not worth five dimes, then it is not worth two quarters is:  If an item is worth five dimes it is worth two quarters.

By swapping the hypothesis and the conclusion, a statement can be made to mean the opposite. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel." If q, then p is the opposite of "if p, then q."

The converse of a statement may not always have the same truth value as the original. For instance, "All mammals are tigers" is the polar opposite of "All tigers are mammals." This is undoubtedly untrue.

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For x to be a solution, there must be the quantity x in the equation.

All the equations that contain x are :
+) 24 - 2x = 13
+) 4  + 5x = 18
+) 2x - 3 = 15
+) 3x + 2 = 25

We will solve for the value of x for each of the equation :

+) 24 - 2x = 13
-> 2x = 24 - 13 = 11
-> x = 11/2 = 5.5

+) 4 + 5x = 18
-> 5x = 18 - 4 = 14
-> x = 14/5 = 2.8

+) 2x - 3 = 15
-> 2x = 15 + 3 = 18
-> x = 18/2 = 9

+) 3x + 2 = 25
-> 3x = 25 - 2 = 23
-> x = 23/3.

We can see, only the equation 2x-3 = 15 has x=9 as a solution.

Answer: 11.1%

Step-by-step explanation:

The formula for percent error is:

|Actual-predicted/predicted| * 100%

In the context of the problem:

Actual = 16 ft

Predicted = 18 ft

Plug these values into the equation:

|16-18/18| * 100% = percent error

11.11% = percent error
If you have any other problems about percent error, you should be able to just plug these values into the formula

Answer:

Step-by-step explanation:

A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.

The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).

The identification process of direct proportion, inverse proportion and partitive proportion is show below.

Proportion is comparison of things or magnitudes in terms of size, amount.

In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.

In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.

Partitive proportion is when the division of a quantity into two or more equal or unequal parts.

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Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.

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Answer: 5+3*3(3)-2= 30

Step-by-step explanation: Replacing x with 2 and using PEMDAS

Answer:

y = x - 3

Step-by-step explanation:

y - y1 = m( x - x1 )

y - (-2) = 1 (x - 1)

y + 2 = x - 1

y = x - 3

The product of the fractions 1/7*5/3 is 5/21.

The product of the fractions= product of the numerator/product of the denominator.

The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively.

We multiply the 1 and 5, the numerators and 7 and 3 the denominators.

Therefore the product of the fractions is 5/21.

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Answer:

5/21

Step-by-step explanation:

Given problem,

→ (1/7) × (5/3)

Let's solve the problem,

→ (1/7) × (5/3)

→ (1 × 5)/(7 × 3)

→ 5/21

Thus, the answer is 5/21.

Answer:

9/16

Step-by-step explanation:

The GCF of the number given as 45 and 27 is 9 and the factored expression is 9(5 - 3)

From the question, we have the following statement

The greatest common factor of 45 and 27

Rewrite the given expression as follows

This is represented using

45 and 27

Factor out 3 from the expression

So, we have the following representation

15 and 9 => Factored 3

Factor out 3 from the expression

So, we have the following representation

5 and 3 => Factored 3 * 3

So, we have

Factored = 3 * 3 = 9

This represents the GCF

So, the GCF is 9

In (a), we have

5 and 3 => Factored 3 * 3

This means that

45 - 27 = 3 * 3(5 - 3)

Evaluate the product

45 - 27 = 9(5 - 3)

Hence, the factored expression is 9(5 - 3)

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The region common  to both the graphs as shown is the solution set.

A system of equations is a collection of two or more equations with a same set of unknowns

Given are the following  quadratic inequalities -

x² - 6x - 7 < 0

3x² - 28x + 32 ≤ 0

We have the following quadratic inequalities -

x² - 6x - 7 < 0

3x² - 28x + 32 ≤ 0

We will plot both of them. The common region be the possible set of solutions to the given inequalities. Refer to the graph attached. The region common to both the graphs is the solution set.

Therefore, the region common  to both the graphs as shown is the solution set.

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Answer:

A. 5/3

Step-by-step explanation:

The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point  3 units to the left.

We can model this using  rise/run

Rise = 5

Run = 3

5/3

The p-value of the distribution of population standard deviation of 33.17 texts per day is 0.9435

The test statistic's "p-value" measures how likely it is that future results will be at least as extreme as the one your sample yielded. You must understand that the null hypothesis is the underlying presumption to compute this probability.

The parameters are as follows:

The sample mean ([tex]\bar x[/tex]) = 118.4

The population standard deviation ([tex]\sigma[/tex]) = 33.17

The sample size (n) = 30

Calculate the z-score first.

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }[/tex]

according to the entire question, x = 128

So, we have:

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{\sqrt{30} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{5.477 } } }\\\\z = \bold{ \frac{9.6}{ 6.056} }\\\\z = 1.5852[/tex]

As determined by the z table of probability, p = 0.9435395

or p = 0.9435 (approx.)

Consequently, the distribution's p-value is 0.9435.

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Answer:

The result is 2 hours

Hope this helped!

The probability that a worker selected at random makes between $350 and $400 = 0.34134

What is a z score formula?

The standard score represents how far a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Positive standard scores are assigned to raw scores that are greater than the mean, while negative standard scores are assigned to raw scores that are less than the mean.

By using the z score formula:

z = (x - μ) / σ

Where,

x = raw score

μ = mean

σ = Standard deviation

We are told in the question to find the probability that a worker selected at random makes between $350 and $400

Consider, x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.

z1 = (x1 - μ) / σ = (350-400) / 50 = -1

z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0

From tables, P(z <= -1) = 0.15866

P(z <= 0) = 0.5

Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134

Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134

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A system of inequality to represent the maximum amount of flooring needed is c + h ≥ 2000.

A system of inequality to represent the maximum amount of money wants to spend is 4.50c + 8.25h ≥ 10,000.

In order to solve this word problem, we would assign variables to the number of square feet of carpet and the number of square feet of hardwood for the given flooring area, and then translate the word problem into an algebraic inequality as follows:

For the maximum amount of flooring needed, we have:

c + h ≥ 2000

For the maximum amount of money, we have:

4.50c + 8.25h ≥ 10,000.

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The reduced fraction is 6/7 using GCF method.

What is GCF method?

The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

Given,

the fraction = 24/28.

the factors of 24  = 2×2×2×3

The factors of 28 = 2×2×7

The gcf is 2 × 2 = 4

divide the denominator and numerator by 4

24 ÷ 4 = 6

28÷ 4 = 7

We get,

the fraction = 6/7.

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The solutions are,

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

Given that;

Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.

Radius (r) = 0.8km

Distance (s) = 2.3km

Here, we need to find three cases, they are;

Case(I): how many radians does wade sweep out;

The relation between radians and radius is given by,

s = rθ

2.3 = 0.8*θ

θ = 2.3/0.8

θ = 2.875

The radians wade sweep out is 2.875 radians.

Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;

Let, Ф = π - 2.875

      Ф = 0.266 radians

Then, x = r*cosФ

          x = 0.8*cos(0.266)

          x = 0.799

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;

Let, y = r*sinФ

      y = 0.8*sin(0.266)

      y = 0.003

When wade stops skiing, he is 0.003km above the center of the ski trail.

Therefore, the required solutions are;

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

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Answer:

The second option.

Step-by-step explanation:

We can figure this out by going down each option and checking if it works and is arranged from least to greatest.

The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.

This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.

The second option provides the numbers -3.5, -1/4, 1/3, 2.

This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.

If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.

Answer:

-------------------------

Answer: D.

Step-by-step explanation: