Every week, Petra saves 1/4 of the money she earns at work. Last week, she earned $60 working. This week, she saved $10 more than she saved last week. How much did Petra earn working this week?

Answer:

20% of $50 is $10. This means that the pair of jeans now cost $60 since it got marked up.

Answer = $60

The given statement is True for the scoring rule in bowling.

Scoring Rule in Bowling

The number of frames in a game of bowling is ten. According to the scoring rule in bowling, the bowler will have two opportunities to use their bowling ball to remove as many pins as they can throughout each frame.

Every bowler will complete their frame in a predefined order before the next frame starts in games with more than one bowler, which is typical.

Rule for Spare

A bowler is given a strike if they can remove all 10 pins with their first ball. A spare is achieved when the bowler uses both of the two balls in a frame to remove all 10 pins.

Depending on whether the next two balls (for a strike) or the next ball (for a goal) are scored, bonus points are given for both of these (for a spare), as per the scoring rule.

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Answer:

m∠ABD= 22°

Step-by-step explanation:

Answer:

the other line is over more the line that is on the left so its 6 units to the left

First we have to factorise the denominator \(\rm{x^3+1.}\)

It can be factorised as,

\(\rm{x^3+1=(x+1)(x^2-x+1)}\)

Then the fraction can be written as,

\(\longrightarrow\rm{\dfrac{x^2+1}{x^3+1}=\dfrac{x^2+1}{(x+1)(x^2-x+1)}\quad\dots(1)}\)

This fraction can be resolved into partial fractions by writing it as the sum of a fraction having denominator \(\rm{x+1}\) and a fraction having denominator \(\rm{x^2-x+1.}\)

Since \(\rm{x+1}\) is a first degree polynomial, the numerator of the fraction having this term as denominator should be a zero degree polynomial, or a constant term, assumed as \(\rm{A.}\)

Since \(\rm{x^2-x+1}\) is a second degree polynomial, the numerator of the fraction having this term as denominator should be a first degree polynomial, assumed as \(\rm{Bx+C.}\)

So let,

\(\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{A}{x+1}+\dfrac{Bx+C}{x^2-x+1}}\)

\(\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{A(x^2-x+1)+(Bx+C)(x+1)}{(x+1)(x^2-x+1)}}$}\)

Equating numerators,

\(\longrightarrow\rm{x^2+1=A(x^2-x+1)+(Bx+C)(x+1)}\)

\(\small\text{$\longrightarrow\rm{x^2+1}=\cal{(A+B)}\rm{x^2}+\cal{(-A+B+C)}\rm{x}+\cal{(A+C)}$}\)

Equating corresponding coefficients,

\(\rm{A+B=1}\)

\(\rm{-A+B+C=0}\)

\(\rm{A+C=1}\)

Solving these three equations we get,

\(\rm{A=\dfrac{2}{3}}\)

\(\rm{B=\dfrac{1}{3}}\)

\(\rm{C=\dfrac{1}{3}}\)

Thus,

\(\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{2}{3(x+1)}+\dfrac{x+1}{3(x^2-x+1)}}$}\)

\(\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{1}{3}\left[\dfrac{2}{x+1}+\dfrac{x+1}{x^2-x+1}\right]}$}\)

So (1) becomes,

\(\longrightarrow\underline{\underline{\bf{\dfrac{x^2+1}{x^3+1}=\dfrac{1}{3}\left[\dfrac{2}{x+1}+\dfrac{x+1}{x^2-x+1}\right]}}}\)

Hence the given fraction is resolved into partial fractions.

The p-value to the significance level (5%) to make a decision. If the p-value is less than 0.05, we reject the null hypothesis (rh0). Otherwise, if the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis (frh0).

To determine whether there is evidence at the 5% level to support the retailer's belief that average sales are greater for salespersons with a college degree, we can perform a hypothesis test using the given data.

The hypotheses for this test are as follows:

Null Hypothesis (H0): The average sales for salespersons with a college degree are not significantly greater than the average sales for salespersons without a college degree.

Alternative Hypothesis (H1): The average sales for salespersons with a college degree are significantly greater than the average sales for salespersons without a college degree.

We can conduct a two-sample t-test to compare the means of the two samples. Given the sample sizes (35 and 32), we can assume that the sampling distributions of the sample means are approximately normally distributed.

Calculating the test statistic:

t = (3455 - 3155) / √((468²/35) + (642²/32))

Now, we can calculate the degrees of freedom (df) using the formula:

df = (s1²/n1 + s2²/n2)² / [(s1²/n1)²/(n1 - 1) + (s2²/n2)²/(n2 - 1)]

Once we have the test statistic and degrees of freedom, we can find the p-value associated with the test statistic using a t-distribution table or statistical software.

Finally, we compare the p-value to the significance level (5%) to make a decision. If the p-value is less than 0.05, we reject the null hypothesis (rh0). Otherwise, if the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis (frh0).

Please note that the precise calculations and decision should be made using statistical software or a calculator.

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Based on a survey of 400 non-fatal accidents, where 173 involved faulty equipment, the point estimate for the population proportion (p) of accidents that involved faulty equipment is 173/400 = 0.4325.

To calculate the point estimate for the population proportion, we divide the number of accidents involving faulty equipment (173) by the total number of accidents surveyed (400).

This gives us a ratio of 0.4325, which represents the estimated proportion of accidents involving faulty equipment in the population.

A point estimate is a single value that serves as an approximation or best guess for an unknown population parameter.

In this case, the population proportion (p) represents the proportion of all accidents that involved faulty equipment. The point estimate of 0.4325 suggests that approximately 43.25% of non-fatal accidents may involve faulty equipment based on the sample data.

It's important to note that this point estimate is subject to sampling variability and may not perfectly reflect the true population proportion. To obtain a more precise estimate with a measure of uncertainty, one would need to consider confidence intervals or conduct hypothesis testing using statistical methods.

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The standard form of the given equation is; x + (-y) = -5

We are given the equations;

x + 6 = 0  -----(1)

y - 3 = 4   -----(2)

Add 4 to both sides of equation 2 to get;

y - 3 + 4 = 0

y + 1 = 0    -----(3)

Put y + 1 for 0 in eq 1 to get;

x + 6 = y + 1

The standard form of an equation is expressed in the form;

Ax + By = C

Thus;

x + 6 = y + 1 can be rewritten as;

x + (-y) = 1 - 6

x + (-y) = -5

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Answer:

Formula for volume of cylinder;

V = π\(r^{2}\)h

Where 'π' represents pi(22/7 or 3.14), and 'r' is the radius which is squared, and 'h' is the height.

Plug in your values:

V = π\(r^{2}\)h

V = 3.14(9^2) x 4

V = 3.14(81) x 4

V = 254.34 x 4

V = 1,017.36^3 feet or 1,017.36 cubic feet.

The probability that the daily production of the cow herd is between 20.1 and 44.8 liters is approximately 0.8541, rounded to four decimal places.

To calculate this probability, we can standardize the values using the z-score formula: z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation.

For 20.1 liters:

z1 = (20.1 - 30) / 8 = -1.1125

For 44.8 liters:

z2 = (44.8 - 30) / 8 = 1.8

Using a standard normal distribution table or a calculator, we can find the probability associated with these z-scores. The probability between the two values is equal to the cumulative probability at z2 minus the cumulative probability at z1.

P(20.1 < x < 44.8) = P(z1 < z < z2)

By looking up the z-scores in the standard normal distribution table or using a calculator, we find that P(-1.1125 < z < 1.8) is approximately 0.8541.

Therefore, the probability that the daily production of the cow herd is between 20.1 and 44.8 liters is approximately 0.8541, rounded to four decimal places.

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The solution of the equation will be the value of t, which should yield equal values on either side of the equation, which is 21.

To solve the equation, we need to begin with multiplication or opening of bracket on either side of the equation.

6t - 30 = 4t + 12

Rearranging the equation

6t - 4t = 30 + 12

Performing subtraction on Left Hand Side and addition on Right Hand Side of the equation

2t = 42

Rewriting the equation according to t

t = 42/2

Performing division

t = 21

Hence, the value of t is 21.

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9514 1404 393

Answer:

  b

Step-by-step explanation:

Use the distance formula with the two points Q and P, then simplify and match the pattern of the answer.

  \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(b-0)^2+(-c-(-a))^2}\\\\\boxed{d=\sqrt{b^2+(-c+a)^2}}\)

The value b goes in the green box.

The false statement is B. 50% of houses in Ames are smaller than 1,499.69 square feet.

Statistics uses both the mean and median as gauges of central tendency, although their definitions and methods of computation vary. A number's mean is determined by adding together all of the values and dividing by the total number of values. A group of numbers has a median, which is the midpoint value, with half of the values above and below.

The median size of a home in Ames is 1,499.69 square feet, thus this claim is untrue. Therefore, 50% of the homes are smaller and 50% are larger than 1,499.69 square feet. Thus, assertion B is untrue.

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The area of triangle is 7.4833 ft².

Heron's formula used to calculate the areas of various triangles, including quadrilaterals and the equilateral, isosceles, and scalene triangles.

The Heron's Formula states that the area of a triangle is equal to √s(s-a)(s-b)(s-c), where s is the triangle's semi-perimeter and a, b, and c are its three side lengths.

s= (a+ b+ c)/2

Given:

sides: 3 feet, 5 feet and 6 feet.

semi- perimeter, s= 3+5+6/2 = 7

Now, Using Heron's Formula

= √s(s-a)(s-b)(s-c)

=√7(7-3)(7-5)(7-6)

=√7 x 4 x 2 x 1

=√56

= 7.4833 ft²

Hence, the area of triangle is 7.4833 ft².

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Answer:

The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth. What you need in your answer: The graphs are reflections of each other over the y-axis. The g(x) function represents exponential decay.

Answer:

recyclble materials include Milk bottles, news papaers and soda cans

the rest is compost

20 items is the total

13 are recycble

13/20 as a decimal is 0.65

multiply by 100

and answer is

Step-by-step explanation:

Answer:

B 65%

Step-by-step explanation:

To determine the number of students who took the test, we need to count the stems in the stem-and-leaf diagram. From the given diagram, we can see that there are 4 stems: 6, 7, 0, and 9. Each stem represents a ten's place value, so there are 10 students for each stem. Therefore, the total number of students who took the test is:

4 stems × 10 students per stem = 40 students

To find the lowest score on the test, we look at the smallest leaf value in the diagram, which is 1. However, since the smallest leaf value corresponds to the stem 0, we need to combine them to determine the lowest score. Therefore, the lowest score on the test is 01.

To find the highest score on the test, we look at the largest leaf value in the diagram, which is 9. Since the largest leaf value corresponds to the stem 9, the highest score on the test is 99.

The mean score on the test is calculated by adding up all the scores and dividing by the total number of students. Let's calculate it:

Mean score = (6 + 7 + 7 + 0 + 0 + 0 + 0 + 0 + 9 + 9 + 9 + 3 + 4) / 40

Mean score = 63 / 40

Mean score ≈ 1.575

The midrange of test scores is calculated by adding the lowest and highest scores and dividing by 2. Let's calculate it:

Midrange = (01 + 99) / 2

Midrange = 100 / 2

Midrange = 50

Therefore, the mean score on the test is approximately 1.575, and the midrange of test scores is 50.

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Answer:

The fourth option is the answer.

Step-by-step explanation:

This parabola is in vertex form, the vertex is (5,4)

Since a is negative, the parabola will facing and opening downwards, so this means our vertex is the highest possible y value. So our range will be (- infinity, 4).

A domain of a Parabola accept in real number so the domain there is all reals or negative ♾ to positive ♾.

Answer:

43.4

Step-by-step explanation:

The geometric solid suggested by a typical American house is:

d. Prism

A typical American house often has a rectangular base and parallel, congruent faces.

This shape is best represented by a rectangular prism.

The geometric solid suggested by a typical American house is a prism, specifically a rectangular prism.

A prism is a three-dimensional solid that has two congruent and parallel bases that are connected by a set of parallelograms.

A rectangular prism has two rectangular bases and rectangular faces that are perpendicular to the bases.

Most American houses are rectangular in shape and have a flat roof, which suggests that they are in the form of a rectangular prism.

The walls of the house form the rectangular faces of the prism, and the roof forms the top face of the prism.

The rectangular shape of the house provides a practical and functional design that allows for efficient use of interior space.

It is also an aesthetically pleasing design that has become a standard for American homes.

d. Prism.

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Using the formula for the confidence interval and provided value for mean and the upper interval. The answer is 0.05.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

The alpha value is 0.025, and the associated critical value is 1.96 for a two-tailed 95% confidence interval. This indicates that we can subtract 1.96 standard deviations from the mean, or the mean, to determine the upper and lower boundaries of the confidence interval.

sample mean = 0.17

upper limit = 0.29

upper limit = sample mean + margin

margin = 0.29-0.17 = 0.12

lower limit = sample mean - margin

=0.17-0.12 = 0.05

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The fraction of defective that can be used in a p-chart for quality control purposes when there are 40 total defects from 8 samples, each sample consisting of 200 individual items in a production process is 0.025.

The p-chart is a control chart that is used in statistical process control to decide whether or not a process or manufacturing procedure is in control or requires modification. It's used to keep track of the proportion of nonconforming units in a batch or process.

The formula for the proportion defective in a p-chart is:

P = (number of defectives in a sample) / (sample size)

We have the following data:

Total number of samples = 8

Total number of individual items = 8 x 200 = 1600

Total number of defects = 40

So, the fraction defective (p) is:

P = (number of defectives in a sample) / (sample size)

P = 40 / 1600

P = 0.025

Thus, the fraction of defective that can be used in a p-chart for quality control purposes is 0.025. Therefore, the correct answer is 0.0025.

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The missing values of the proportion are;

a. 18

b. 19.5

c. 45%

d. 180

The percentage of a number can be defined as the fraction of a number and hundred.

It is represented with the symbol, %.

From the information given, we have that'

1. 6% of 30

This is represented as;

60 /100 × 30

Multiply the values

18

2. 65% of 30

This is represented as

65/100 × 30

Multiply the values

1950/100

19.5

3. 18/40 × 100

Multiply the values

1800/40

45%

4. 81 = 45/100x

cross multiply the values

x = 180

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Answer:

Distributive Property

Step-by-step explanation:

If we have an equation where we multiply something in parentheses by a certain term, then we can apply the distributive property to simplify it.

In this case: \(5(x-7)=55\)

We can multiply \(x-7\) by 5 to simplify this equation - this is the distributive property.

\(5x - 35 = 55\)

So the property used to write the equation in Step 2 was the distributive property.

Hope this helped!

Answer:

the answer is didrtbutive

Step-by-step explanation:

hope it helps.

have a good day:)

The power of the function is 4 and the leading term will be positive

The zeros of the function are

-2, -1, -1, 1

The zero that occurs at -2 and 1 has a multiplicity of 1. while the zero at -1 have a multiplicity of 2.

The y-intercept is where the graph cuts the y-axis and this is at

Equation of the polynomial function

f(x) = a(x + 2) (x +1)² (x - 1)

using point (0, -2) to solve for a

-2 = a(0 + 2) (0 +1)² (0 - 1)

-2 = a(2) (1)² (--1)

-2 = -2a

a = 1

hence the equation is f(x) = (x + 2) (x +1)² (x - 1)

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Answer:

To calculate the mean length of the insects found, we can use the following formula:

Mean length = (Sum of lengths) / (Number of lengths)

We can calculate the sum of lengths by adding up the lengths of all the insects and dividing by the number of insects:

Sum of lengths = Length (0) + Length (10) + Length (20)

Sum of lengths = 0 mm + 10 mm + 20 mm

Sum of lengths = 30 mm

Number of lengths = 3

Mean length = Sum of lengths / Number of lengths

Mean length = 30 mm / 3

Mean length = 10 mm

Therefore, the mean length of the insects found is 10 mm.

Mmm, x is equals to -7....

The value of the x is -7.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

We can use the rule for multiplying powers with the same base to simplify the left-hand side of the equation:

6⁹ × 6ˣ = 6⁽⁹⁺ˣ⁾

Now we can rewrite the equation as:

6⁽⁹⁺ˣ⁾ = 6²

Since the bases on both sides of the equation are the same, we can equate the exponents:

9 + x = 2

Subtracting 9 from both sides gives:

x = -7

Therefore, the value of x in the given equation is -7.

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Answer: Answer is 0.52

Step-by-step explanation:

So we have the fraction 13 Out of 25.

step 1: here we divide numerator(which is 13) by denominator(which is 25).

step 2: first we make denominator 100 by multiplying by 25 with 4 and also 13 with 4.

ie. \(\frac{13 * 4}{25 * 4}\)

step 3: we get \(\frac{52}{100}\)

step 4: now we can easily write the decimal fraction. ie. 0.52

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The probability that more than 5 engines are defective is approximately 0.1685 using the binomial approximation.

The binomial approximation is used to approximate the probability of a given event occurring a certain number of times in a specified number of trials, given a certain probability of the event occurring on each trial.

We can use this approximation to calculate the probability that more than 5 engines are defective.

Let X be the number of defective engines out of 40.

Then X follows a binomial distribution with n = 40 and p = 0.03, where p is the probability that any given engine is defective.

Using the binomial approximation, we can approximate the distribution of X with a normal distribution with mean

μ = np and standard deviation σ = √(np(1-p)).

We can then use the normal distribution to approximate the probability that more than 5 engines are defective.

P(X > 5) = P(X >= 6)

We can use the normal distribution to approximate this probability as follows:

Z = (X - μ) / σZ

= (6 - (40*0.03)) / √(40*0.03*(1-0.03))Z

= 0.9577

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 0.9577 is approximately 0.1685.

Therefore, P(X > 5) = P(X >= 6) ≈ 0.1685.

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The derivative of h(x) is zero, indicating that the function h(x) is a constant function

To find the derivative of the function h(x) = ∫[1 to 8] e× ln(t) dt using the first part of the Fundamental Theorem of Calculus, we can directly differentiate the integral with respect to x.

Let F(x) be the antiderivative of the integrand e× ln(t). By the first part of the Fundamental Theorem of Calculus, we have:

h(x) = F(8) - F(1)

To find the derivative of h(x), we differentiate both sides of the equation with respect to x:

d/dx [h(x)] = d/dx [F(8) - F(1)]

Since F(8) and F(1) are constants, their derivatives with respect to x are zero. Therefore, we have:

h'(x) = 0 - 0

Thus, the derivative of h(x) is zero, indicating that the function h(x) is a constant function.

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