A bearing used in an automotive application is required to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard deviation inch. (a) Test the hypotheses versus using The true mean hole diameter.

Answer:

Step-by-step explanation:

Tim has $7.14 to spend on candy that costs $3 per pound. Moby has $6.96 to spend on candy that costs $2.90 per pound. Which of the following is true?

A) Tim can't buy more than two pounds of candy

B) Moby can buy more candy than Tim

C) Tim can afford more candy than Moby

D) They can buy the exact same amount of candy

Correct Answer: Moby can buy more candy than Tim

Step-by-step explanation:

x = 7

y = 5

\( = {x}^{2} + {y}^{2} \)

\( = (7 {)}^{2} + (5 {)}^{2} \)

= 7 × 7 + 5 × 5

\( = 49 + 25 \)

\( = 74\)

Hey there!

x^2 + y^2

= 7^2 + 5^2

= 7 * 7 + 5 * 5

= 49 + 25

= 74

Therefore, your answer should be: 74

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

C. Add the equations

Step-by-step explanation:

Adding both the equations will help eliminating 5y.

Answer:

For a recipe call,

Number of teaspoons of mustard seeds =

Number of cups of tomato sauce = 4

Number of cups of beans =

For 4 cups of tomato sauce, the number of teaspoons of mustard seeds needed =

For 1 cup of tomato sauce, the number of teaspoons of mustard seeds needed =

For  cups of tomato sauce, the number of teaspoons of mustard seeds needed =

Hence, for  cups of tomato sauce, the number of teaspoons of mustard seeds needed is .

For 4 cups of tomato sauce, the number of cups of beans needed =

For 1 cup of tomato sauce, the number of cups of beans needed =

For  cups of tomato sauce, the number of cups of beans needed =

Hence, for  cups of tomato sauce, the number of cups of beans needed is .

Step-by-step explanation:

purple

i know for sure it's purple

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The equations that give the volumes of each solid are given as follows:

Then the increases are given as follows:

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Answer:1.25

Step-by-step explanation:

The way you figure out percent increase is you take the final number, divide it by the original number, and then subtract 1 from the result.

Therefore, in this question, take the final number of 450, divide it by the original number, 200, and then subtract 1.

450 ÷ 200 - 1 =

2.25 - 1 =

1.25

1.25 is the same thing as 125%, so Jay increased the number of dogs he groomed by 125%.

Answer

4.5 : 0.24 = 1.5 :0.08    [dividing by 3]

Work Shown:

\(\text{SA} = \text{Surface area of the cube with side length x}\\\\\text{SA} = 6\text{x}^2\\\\\text{SA} = 6*13^2\\\\\text{SA} = 6*169\\\\\text{SA} = 1014\\\\\)

Explanation:

The \(\text{x}^2\) refers to the area of one square face with side length x. Each square face has an area of \(\text{x}^2 = 13^2 = 169\) square feet. There are 6 identical faces to a cube, leading to a total surface area of 6*169 = 1014 square feet

Yes you are correct because the relationship in the table is y = x - 1

John should choose the bank option with compound interest as it will give him a higher return on his investment.

To calculate the better investment, we need to find the future value of both options after 6 years.

For the savings bond, the interest rate is 14% simple interest, so after 6 years, John will earn $8,400 in interest (12,000 x 0.14 x 6). The total value of his investment will be $20,400 ($12,000 initial investment + $8,400 interest).

For the bank option, the interest rate is 12% compounded annually. Using the formula A = P(1+r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of times compounded per year, and t is the time in years, we can calculate that the future value of John's investment after 6 years is $25,980.45.

Therefore, the better investment is the bank option with compound interest. The difference between the two investments is $5,580.45 ($25,980.45 - $20,400).

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The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Answer:

I gotchu!

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

20-7x=6x-6

20+6=6x+7x

26=13x

x=2

The numerator of the simplified sum x/(x^2) + 3x + 2 is 1/x + 3x + 2.

To simplify the sum x/(x^2) + 3x + 2, we can use the following steps:

1. Combine like terms:

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

2. Simplify the fraction x/(x^2):

x/(x^2) + 3x + 2 = 1/x + 3x + 2

3. The numerator of the simplified sum is 1/x + 3x + 2.

So, the numerator of the simplified sum x/(x^2) + 3x + 2 is 1/x + 3x + 2.

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Answer:

Where its the graph??????

Answer:

y=2/3x+1

Step-by-step explanation:

slope intercept form is y=mx+b.

slope is m, which is 2/3.

y-int is b, which is 1.

y=2/3x+1

Answer:

5a^10

Step-by-step explanation:

We can make use of a slope field to sketch the two approximate solutions of the differential equation. The slope field for the differential equation is dy/dx.

a) We will now mark the point (0,4) on the slope field as shown in the image below.

Solution 1: We will begin at the point (0, 4) and move along the slope lines to obtain the first solution. This first solution is shown in blue in the image below,

Solution 2: For the second solution, we will begin at the point (0,4) and move along the slope lines in the opposite direction to obtain the second solution. This second solution is shown in red in the image below.

Substituting x = 0 and y = 4, we get: 4 = sin(0) + C4 = 0 + CC = 4

Therefore, the particular solution is: y = sin(x) + 4

Below is the graph of the solution: Graph of y = sin(x) + 4

We can compare this graph of the particular solution with the sketches in part (a).

The graph of the solution matches the first solution in blue.

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Yes, the laws of exponents hold for positive and negative numbers, fractional exponents, and even irrational exponents such as π.

The laws of exponents apply to both positive and negative numbers. For example, when multiplying or dividing numbers with exponents, the exponents can be added or subtracted, respectively, regardless of the sign of the base. Similarly, when raising a number with an exponent to another exponent, the exponents can be multiplied. These rules hold true for positive and negative numbers, allowing consistent manipulation of expressions involving exponents.

Yes, the laws of exponents also hold for fractional exponents. The most common law, the power rule, states that when raising a number to a fractional exponent, the exponent can be expressed as a quotient of integers. This allows us to extend the laws of exponents to include fractional exponents and perform calculations accordingly. For example, we can multiply numbers with fractional exponents by adding the exponents and divide them by subtracting the exponents.

Yes, the laws of exponents also hold for irrational exponents, including numbers like π. Although irrational exponents cannot be expressed as exact fractions or decimals, we can still apply the laws of exponents. When working with irrational exponents, the calculations typically involve approximations or infinite series representations. However, the fundamental rules of exponentiation, such as adding, subtracting, or multiplying exponents, remain valid for irrational exponents as well.

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For the parabola y = 2x² + 3x + 1,

a. i.  The x-intercepts are x = -1/2 and x = -1

a. ii. The y-intercept is y = 1

b. i. The line of symmetry is at x = -3/4

b. ii. The equation of the line of symmetry is x = -3/4

c.  The vertex is at (-3/4, -1/8)

A parabola is part of a conic section which is a curve.

Given the parabola y = 2x² + 3x + 1, we find the x- intercept when y = 0.

So, y = 2x² + 3x + 1

2x² + 3x + 1 = 0

2x² + 2x + x + 1 = 0

Factorizing, we have

2x(x + 1) + (x + 1) = 0

(2x + 1)(x + 1) = 0

2x + 1 = 0 or x + 1 = 0

2x = -1 or x = -1

x = -1/2 or x = -1

So, the x-intercepts are x = -1/2 and x = -1

Given the parabola y = 2x² + 3x + 1, we find the y- intercept when x = 0.

So, y = 2x² + 3x + 1

So, y = 2(0)² + 3(0) + 1

y = 0 + 0 + 1

y = 1

So, the y-intercept is y = 1

The line of symmetry passes through the vertex of the parabola where dy/dx = 0.

So, y = 2x² + 3x + 1

dy/dx = d(2x² + 3x + 1)/dx

= d(2x²)/dx + d3x/dx + d1/dx

= 4x + 3 + 0

= 4x + 3

So, when dy/dx = 0,we have

4x + 3 = 0

4x = -3

x = -3/4

So, the line of symmetry is at x = -3/4

The equation of the line of symmetry is x = -3/4

Since the vertex of the parabola is a t x = -3/4, substituting this into the equation, we have

y = 2x² + 3x + 1

y = 2(-3/4)² + 3(-3/4) + 1

y = 2(9/16) - 9/4 + 1

y = 9/8 - 9/4 + 1

y = (9 - 18 + 8)/8

y = (17 - 18)/8

y = -1/8

So, the vertex is at (-3/4, -1/8)

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To find out how much the painter charged for the last job, we need to substitute h=15 and c=3 in the expression 35h 30c and simplify. The painter charged $615 for the last job which required 3 cans of paint and took 15 hours to complete.

The painter uses the expression 35h + 30c to determine the cost of a job, where h represents the hours spent and c represents the number of paint cans used. In the last job, it took the painter 15 hours and 3 cans of paint to complete the work. To find the cost, we will plug these values into the given expression.
Cost = 35h + 30c
Cost = 35(15) + 30(3)
Now, we will perform the calculations:
Cost = 525 + 90
By adding these values, we get the total cost:
Cost = 615

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1) Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. 2) The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. 3) trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

1. Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. Therefore, the ratios of the sine, cosine, and tangent of the corresponding angles in similar triangles will also be equal.

2. The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. This means that the sine of an angle is equal to its complement's cosine, and vice versa.

3. Using the appropriate formula based on the given information, trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

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Answer:

i think it's 10

Step-by-step explanation:

correct me if I'm wrong ◉‿◉

Answer:

1/4

Step-by-step explanation:

The slope of a graph is always the rate of change for every value of x, in this case, days. Since she is adding 1/4 of a mile to her run each day, this means that the slope of this linear relationship is 1/4.

She increases a full mile in 4 days, just a little note.

Answer:

The answer is 3

Hope this helps!

This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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