PLS HELP
Chris was standing at the cash register when he realized he was $1.20 short. He was buying a mouse and a mousepad. He realized the mouse cost 95% of his money, and the mousepad cost 15% of his money. How much does the mouse cost, and how much does the mousepad cost?

The number of batteries expected to last between three years and one month and three years and seven months, is 12,500 batteries.

Given that the mean shelf life of the flashlight batteries is three years and four months and the standard deviation is three months.

To find the number of batteries that can be expected to last between three years and one month (3.08 years) and three years and seven months (3.58 years), we need to calculate the probability within this range.

First, we convert the given time intervals to years:

Three years and one month = 3.08 years

Three years and seven months = 3.58 years

Next, we calculate the z-scores for these values using the formula:

z = (x - μ) / σ

For 3.08 years:

z1 = (3.08 - 3.33) / 0.25 = -1

For 3.58 years:

z2 = (3.58 - 3.33) / 0.25 = 1

Now, we can use the standard normal distribution table or a calculator to find the probabilities corresponding to these z-scores.

The probability of a value falling between -1 and 1 is the difference between the two probabilities.

Let's assume that the distribution is symmetric, so half of the batteries would fall within this range.

Therefore, the number of batteries that can be expected to last between three years and one month and three years and seven months is approximately:

Number of batteries = 0.5 × Total number of batteries = 0.5 × 25,000 = 12,500 batteries.

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Answer:

Step-by-step explanation:

Given right angle XOV and 30° angle XOW, you want to know the measure of angle WOV. You also want to find the measure of angle YOZ, which is opposite angle VOW, where XOY is a right angle, and WOZ is a straight angle.

The angle addition theorem tells you that ...

  ∠XOW +∠WOV = ∠XOV

Angle XOV is given as a right angle, and angle XOW is shown as 30°, so we have ...

  30° +∠WOV = 90°

  ∠WOV = 60° . . . . . . . . . subtract 30° from both sides

Angle WOV is 60° using the angle addition theorem.

Rays OY and OV are opposite rays, as are rays OZ and OW. This means angles YOZ and VOW are vertical angles, hence congruent.

  ∠YOZ = ∠WOV = 60°

Angle YOZ is 60° using the congruence of vertical angles.

As in part 2, angle WOZ is a straight angle, so measures 180°. The angle addition theorem tells you this is the sum of its parts:

  ∠ZOY +∠YOX +∠XOW = ∠ZOW

  ∠ZOY +90° +30° = 180°

  ∠ZOY = 60° . . . . . . . . . . . . . subtract 120° from both sides

Angle YOZ is 60° using the measure of a straight angle.

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Answer:

27

thanks for the points

A ratio shows us the number of times a number contains another number. The minimum ordered boxes of 4candies and 10 candies are 5 and 2.

A ratio shows us the number of times a number contains another number.

Given that Two orders are placed, one has only boxes of 4 candies and one only has boxes of 10 candies.

Now, let the number of boxes of 4 candies ordered be represented by x, while the number of boxes of 10 candies ordered be represented by y. Further, it is mentioned that the number of candies in the two orders is equal. Therefore, we can write,

4x = 10y

x/y = 10/4

x/y = 5/2

Therefore, the number of boxes of 4candies and the number of boxes of 10 candies ordered will be in a ratio of 5:2. Thus, the ordered boxes of 4candies and 10 candies can be 5 and 2, 10 and 4, 15 and 6, etc.

Hence, the minimum ordered boxes of 4candies and 10 candies are 5 and 2.

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Answer:

For x = height:

x(x + 20) = 576.

Step-by-step explanation:

The area is 576 cm^

Area = width * height

Let the height be x,  then the width is (x + 20) cm

So the expression for the area can be written

x(x + 20) = 576.

Answer:

x²   +  20x  -  576  =  0

Step-by-step explanation:

If x is height:

 width = (20 + x)

         area = width  x  height

         576  =  (20 + x)     x      x

         576  =  20x   + x²

      ∴ x²   +  20x  -  576  =  0

Step-by-step explanation:

I guess the question is how many ounces are needed per paint. right ?

the colors are mixed in a ratio 3:5.

what that tells us is that there are 8 units of the whole paint (3+5), and yellow gets 3 out of these 8, and blue 5 out of these 8.

the total is 32 ounces.

so, each of the 8 units represents

32/8 = 4 ounces.

and now we know :

yellow has 3 units

3×4 = 12 ounces

blue has 5 units

5×4 = 20 ounces

The total number of ways the jobs can be ordered in the queue so that job a is completed before job b is 2. 9!

What is probability?

The probability of an event occurring is defined by probability. There are numerous instances in real life where predicting an outcome is necessary.

What is experimental probability?

The quantity of trials is frequently included in probabilities. Because it is based on actual trials and highly good recordings of event occurrences, it is also sometimes referred to as empirical probability.

The total number of jobs in the queue is 10.

Let Job a be fixed as first job, then the number of ways in which other jobs can be arranged is 9!

Let Job b be last job, then the number of ways in which other jobs can be arranged is 9!

The probability of job a completes some time before job b is 9! + 9! = 2. 9!

Hence the probability of jobs to be ordered such that job a completes before job b is 2. 9!

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Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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The calculated area of the minor sector is 90π square cm

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

The circle (see attachment)

Where, we have

The area of the minor sector is then calculated as

Area = θ/360 * πr²

Substitute the known values in the above equation, so, we have the following representation

Area = 36/360 * π * 30²

Evaluate

Area = 90π

Hence, the area is 90π

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If there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

each slice of the 12-inch thin-crust cheese pizza would have an equal distribution of sauce and toppings. This means that each slice would have the same amount of sauce and toppings spread evenly across its surface.

Since the pizza is cut equally into eight slices, each slice would represent 1/8th of the total pizza. Therefore, each slice would have an equal portion of the sauce and toppings.

It's important to note that the exact amount of sauce and toppings on each slice would depend on the original distribution applied to the pizza before it was sliced. If the pizza was prepared with a uniform distribution of sauce and toppings across the entire pizza, then each slice would indeed have an equal amount. However, if there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

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Answer:

I filled out the PDF to make it easy hope this helps

Step-by-step explanation:

let me know if you need help understanding how I did things.

Answer: C

Step-by-step explanation:

just took the quiz

The conclusion based on the statement would be option C. Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We need to Compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon.

The conclusion based on the statement would be;

C. P(pass morning) = 0.48

P(pass | afternoon) = 0.82

Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.

Therefore, the correct option is C.

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The given number "-68.555" is a: B. rational number.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics, there are six (6) common types of numbers and these include the following:

In this context, we can infer and logically deduce that -68.555 is a rational number.

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The solutions to the system of equations involving quadratic function f(x) and linear function g(x) are (-1,5) and (4/3,29/3), respectively.

To find the solution to the given system of equations:

Given quadratic equation: f(x) = 3x^2 + x + 3

The two point formula is: y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(2) = 11, g(1) = 9

g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)

or, g(x) - 9 = ((11-9)/(2-1))*(x-1)

or, g(x) - 9 = 2(x-1)

or, g(x) = 2x - 2 + 9 = 2x + 7

g(x) = 2x +7, is the linear function g(x)

We are asked to solve the system of equations f(x) and g(x).

To get the solution, we must first determine what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).

3x² + x + 3 = 2x + 7

or, 3x² - x - 4 = 0

or, 3x² + 3x - 4x - 4 = 0

or, 3x(x+1) -4(x+1) = 0

or, (3x-4)(x+1) = 0

∴ Either 3x-4=0 ⇒ x = 4/3

or, x+1=0 ⇒ x = -1.

g(-1) = 5 (from the table)

f(-1) = 3(-1)² + (-1) + 3 = 3 - 1 + 3 = 5

g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3

f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3

∴ f(-1) = g(-1) and f(4/3) = g(4/3).

Therefore, the solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).

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The correct question is given below:

What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?

f(x) = 3x^2 + x + 3

Answer:

20) a) 6.8 b) 7

21) a) 26.2 b) 26

22) a) -7.8 b) -8

23) a) -10.2 b) -10

24) a) 2.6 b) 3

25) a) -12.9 b) -13

9) Real number

10) Real number

11) Real number

12) Real number

13) Real number

14) Real number

15) Not a real number

16) Real number

Explanation

In order to find the estimated integer of a square root, you simply find the perfect squares closest to the specified square root. For example, the closest perfect squares to \(\sqrt{46}\) are \(\sqrt{36}\) and \(\sqrt{49}\). Now, we need to find which perfect square is the closest between those two. 46 and 36 have a difference of 10, while 46 and 49 have a difference of 3. So, we know that 49 is the closest perfect square. Now, we simplify

Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

The margin of error for the proportion of all U.S. adults who think things are on the wrong track for 90% confidence is approximately 2.2%.

To calculate the margin of error, we first need to find the standard error, which can be calculated using the formula:
Standard Error = Square Root [ (p * q) / n ]
where p is the proportion of the sample who said things are on the wrong track (0.747), q is the complement of p (1 - p, which is 0.253), and n is the sample size (1997).
Plugging in the values, we get:
Standard Error = Square Root [ (0.747 * 0.253) / 1997 ] = 0.014
To find the margin of error at 90% confidence, we need to multiply the standard error by the z-score corresponding to 90% confidence, which is 1.645.
Margin of Error = 1.645 * 0.014 = 0.022 or approximately 2.2%

Hence, we can say with 90% confidence that the true proportion of all U.S. adults who think things are on the wrong track is between 72.5% and 77.0% (74.7% ± 2.2%).

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The amount of discount on the jacket is Birr 144.

We can use the following formula :

Discount amount = Original price - Discounted price

We must determine the original pricing of the jacket given that it has a discounted price of Birr 576 and the discount is 20%.

Assume "x" stands in for the original price.

The information provided indicates that the discounted price is 80% (100% - 20%) of the original cost:

Discounted price = 80% of the original price

576 = 0.8x

To find the original price, we can divide both sides of the equation by 0.8:

x = 576 / 0.8

x = 720

Now that we have the original price, we can calculate the amount of discount:

Discount amount = Original price - Discounted price

Discount amount = 720 - 576

Discount amount = Birr 144

Therefore, the amount of discount on the jacket is Birr 144.

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Answer:

4in^3

Step-by-step explanation:

The four smallest positive solutions to the equation \(8 \sin \left(\frac{\pi}{6} x\right) = 6\) are approximately \(x = 0.94, 3.18, 5.46, 6.78\).

To solve this equation, we can start by isolating the sine term by dividing both sides of the equation by 8:

\[\sin \left(\frac{\pi}{6} x\right) = \frac{6}{8} = \frac{3}{4}\]

Next, we can take the inverse sine (arcsine) of both sides to cancel out the sine function:

\[\frac{\pi}{6} x = \arcsin \left(\frac{3}{4}\right)\]

Finally, we can solve for \(x\) by multiplying both sides of the equation by \(\frac{6}{\pi}\):

\[x = \frac{6}{\pi} \arcsin \left(\frac{3}{4}\right)\]

Using a calculator or a mathematical software, we can evaluate this expression to find the approximate values for \(x\). The four smallest positive solutions are approximately \(x = 0.94, 3.18, 5.46, 6.78\).

In the given equation, we have \(8 \sin \left(\frac{\pi}{6} x\right) = 6\). To find the solutions, we first divide both sides by 8, yielding \(\sin \left(\frac{\pi}{6} x\right) = \frac{6}{8} = \frac{3}{4}\). This means we are looking for angles whose sine value is \(\frac{3}{4}\). Taking the inverse sine (arcsine) of both sides gives \(\frac{\pi}{6} x = \arcsin \left(\frac{3}{4}\right)\).

To solve for \(x\), we multiply both sides by \(\frac{6}{\pi}\), resulting in \(x = \frac{6}{\pi} \arcsin \left(\frac{3}{4}\right)\). This formula gives us the general solution, but to find the specific solutions, we need to evaluate the arcsine expression.

Using a calculator or mathematical software, we find that \(\arcsin \left(\frac{3}{4}\right) \approx 0.8481\). Substituting this value into the formula, we get \(x \approx \frac{6}{\pi} \cdot 0.8481 \approx 0.94\). This is the first solution.

To find the other three solutions, we add integer multiples of the period of the sine function to the angle \(\frac{\pi}{6} x\). The period of the sine function is \(2\pi\), so we add \(2\pi\) to \(\frac{\pi}{6} x\) to obtain the second solution: \(x \approx \frac{6}{\pi} \cdot 0.8481 + \frac{2\pi}{\pi} \approx 3.18\).

Repeating this process, we obtain the third and fourth solutions by adding \(2\pi\) to the angle each time: \(x \approx 5.46\) and \(x \approx 6.78\).

Therefore, the four smallest positive solutions to the equation are approximately \(x = 0.94, 3.18, 5.46, 6.78\).

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According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.

In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.

Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.

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Amount of discount allowed = 640 Rs.

VAT meaning value added tax that is attached to an item of product while bought by the buyer and also in each stage of production, distribution level. It is almost similar to a sales tax that is paid within the item price.

given, discount allowed = 20% on the market price.

VAT = 10% on the market price.

Buyer paid as VAT = 320 Rs

Assume, market price of radio = X Rs

now amount of discount = 20/100× X = 0.2X

amount of VAT = 10/100×X = 0.1X

it is said that VAT paid by buyer = 320 Rs

now 320 = 0.1X

X = 320 / 0.1 = 3200 Rs

market price of radio = 3200 Rs

amount of discount = 20/100× 3200 = 640 Rs

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Answer:

x = 108

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

x/-18 = -6

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that -6 does indeed equal -6.

∴ x = 108 is the solution to the equation.

The value r², called the coefficient of determination, measures the proportion of variability in one variable that can be determined from its relationship with the other variable.

The higher the value of r2, the more of the variation in the dependent variable can be attributed to the independent variable(s), and therefore the better the relationship between the two variables is. Overall, the coefficient of determination is an important statistical measure that is used to evaluate the strength and fit of regression models. It allows researchers to determine how much of the variation seen in the dependent variable can be explained by the independent variable(s), which can help in making predictions and drawing conclusions from the data.

It represents the strength and direction of the correlation between two variables, helping to quantify their linear association. A higher r² value indicates a stronger relationship between the variables, while a value close to zero signifies a weak or no relationship.

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9

using Bodmas rule

\(\sf B - brackets, \ O - order, \ D - division, \ M - multiplication, \ A - addtion, \ S - subtraction\)

⟼                   ⟼                 ⟼               ⟼                ⟼              ⟼

Solve:

6 ÷ 2(1+2)           [simplify the following inside brackets]

6 ÷ 2(3)              [divide]

(3)(3)                 [multiply]

  9                     [final answer]

Hey there!

6 ÷ 2(1 + 2)

= 6 ÷ 2(3)

= 3(3)

= 9

Therefore, your answer should be:

9

Good luck on your assignment & enjoy your day!

~Amphitrute1040:)

The histogram provides a visual representation of the distribution of the data.

   Frequency

      |

10 | x x x x

11  | x x

12 | x x x x x x x

13 | x

14 | x x x x

15 | x x

      -  -  -  -  -

     0 1 2 3 4

First, let's determine the frequency for each leaf value:

Stem 10 has leaves 1, 5, 6, and 8, so the frequency for each leaf value is 1, 1, 1, and 1, respectively.

Stem 11 has leaves 1, 5, and 7, so the frequency for each leaf value is 1, 1, and 1.

Stem 12 has leaves 3, 6, 8 (three times), and 9 (two times), so the frequency for each leaf value is 1, 1, 3, 3, and 3.

Stem 13 has leaf 2, so the frequency is 1.

Stem 14 has leaves 4, 5, 7 (two times), and 8, so the frequency for each leaf value is 1, 1, 2, and 2.

Stem 15 has leaves 2, 6, and 9, so the frequency for each leaf value is 1, 1, and 1.

Now, we can plot the histogram. The x-axis represents the stems (10, 11, 12, 13, 14, and 15), and the y-axis represents the frequency of the leaves:

In this histogram, the height of the bars represents the frequency of each stem-leaf combination. For example, the stem-leaf combination "12-8" has a frequency of 3, so the bar above the stem 12 is three units high.

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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