A circle has a diameter of 35 cm. What does the circumference of the circle

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Answer:

You’ll need to purchase at least 12 pizzas to handle your group

Step-by-step explanation:

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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Answer:

The correct answer is 8 miles

Step-by-step explanation:

. If Yasmin runs at a pace of 7 miles per hour ... to run will always reduce down to the same fraction on a straight line

The initial deposit should be changed to $1,000.This is because if $1,000 is deposited in an account with an interest rate of 3.5% compounded annually, it will be worth $1,735.98 after 10 years.

Interest is a fee charged by a lender for the use of borrowed money. It is the cost of borrowing money and is typically expressed as a percentage of the principal (the amount borrowed). Interest is also earned on money that is saved or invested. The amount of interest earned or charged depends on a variety of factors, including the amount borrowed, the length of the loan, and the prevailing market conditions. Interest rates can be fixed, meaning they remain constant throughout the life of the loan, or they can fluctuate with changing market conditions.

Therefore, the initial deposit should be changed to $1,000 in order to achieve the desired balance of $1,735.98 by the year 2027.

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Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.

The value of x is x=p(m-n).

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Given expression: m=n+(x/p)

To find: Make x the subject.

To make x the subject we have to separate the x to one side.

Expression m=n+(x/p)

Take n to another side,

(x/p)=m-n

Cross multiply,

x=p(m-n)

Therefore, the value of x is x=p(m-n).

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Answer:

17x + 56 = 0

Step-by-step explanation:

add 2x and 15x

Step-by-step explanation:

I hope this answer is helpful ):

A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.

We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding

m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.

m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.

m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).

m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.

m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

Based on the above analysis, the statements that are always true regarding the diagram are

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°

m∠2 + m∠3 + m∠5 = 180°

Therefore, the correct options are B, C, and E.

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Answer:

The 16 ounce bottle is the cheapest costing only .15 cents per ounces wile the 12 ounce bottle costs .16 cents and ounce.

Step-by-step explanation:

Answer:

\( 180 - 16 - 126 = 38\\ 13x = 180 - 16 - 38\\ 3x = 126 \\ 3x = 126 \\ x = \frac{126}{3} = 42\)

Answer:

Step-by-step explanation:

Hello!

To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:

Group 1: Ate healthy breakfast

X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.

n₁= 26

Group 2: Did not eat healthy breakfast

X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.

n₂= 20

After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:

p'₁= 0.50

p'₂= 0.40

The parameters of study are the population proportions, if the claim is true then p₁ > p₂

And you can determine the hypotheses as

H₀: p₁ ≤ p₂

H₁: p₁ > p₂

α: 0.05

\(Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')[\frac{1}{n_1} +\frac{1}{n_2}] } } }\)≈N(0;1)

pooled sample proportion: \(p'= \frac{x_1+x_2}{n_1+n_2} =\frac{13+8}{46} = 0.46\)

\(Z_{H_0}= \frac{(0.5-0.4)-0}{\sqrt{0.46(1-0.46)[\frac{1}{26} +\frac{1}{20}] } } }= 0.67\)

p-value: 0.2514

The decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.

At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.

So having a healthy breakfast doesn't seem to improve the grades of students.

I hope this helps!

TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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Answer:

151+8x>_367

Step-by-step explanation:

x=sets of glasses.

151+8x>_367

          ^is greater than equal to i dont

have a sign for that.

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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The equation represents the value of the collection after 2 years is V = 140(1 + 0.15)^2.

When the value of an asset appreciates,it means that the price of the item increases with the passage of time.

The formula for calculating future value with appreciation is:

FV = P (1 + r)^n

V = 140(1 + 0.15)^2.

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Answer:

Step-by-step explanation:

V=140(1+0.15)

2

The probability of picking a white marble is 3/10

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

four green marbles, six white marbles, and ten red marbles

This means that

Total = 4 + 6 + 10

Evaluate the sum

Total = 20

The probability of picking a white marble is

P = White/Total

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

P = 6/20

Evaluate

P = 3/10

Hence, the probability of picking a white marble is 3/10

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Answer:

  sin(x) = ±(√357)/29 ≈ ±0.651533

Step-by-step explanation:

The relation between sine and cosine is ...

  sin(x) = ±√(1 -cos(x)^2)

  sin(x) = ±√(1 -(-22/29)^2) = √(1 -484/841) = √(357/841)

  sin(x) = ±(√357)/29

_____

Additional comment

The sign of the cosine is negative, which places the angle in quadrant II or III. In quadrant II, the sine is positive; in quadrant III, the sine is negative. That is, we cannot tell which sign to apply from the information given.

(20, 21, 29) is a Pythagorean triple. We suspect a typo in the question: 22 is used where 20 or 21 is likely intended.

Answer:

-1

Step-by-step explanation:

\(f(x)=k \implies f^{-1}(k)=x\)

The required 95% confidence interval for the mean breaking force of acrylic bone cement is approximately 267.29 to 344.85 newtons.

Find the critical value (t*) for a 95% confidence level and (n - 1) degrees of freedom.

The degrees of freedom (df) is equal to the sample size minus 1 (df = 7 - 1 = 6). From a t-table or statistical software, the critical value for a 95% confidence level and df = 6 is approximately 2.447.

Calculate the standard error of the mean (SE).

The standard error of the mean is given by SE = (sample standard deviation) / sqrt(sample size).

\(SE =\dfrac{41.96}{\sqrt{7}}\)

   ≈ 15.85

Calculate the margin of error (MoE).

The margin of error is MoE = (t*) * SE.

MoE ≈ 2.447 * 15.85
        ≈ 38.78

Calculate the confidence interval.

The confidence interval is given by: Mean ± MoE.

Mean ± MoE ≈ 306.07 ± 38.78

Calculate the lower and upper bounds of the confidence interval.

Lower bound ≈ 306.07 - 38.78
                       = 267.29

Upper bound ≈ 306.07 + 38.78
                       = 344.85

Therefore, the 95% confidence interval for the mean breaking force of acrylic bone cement is approximately 267.29 to 344.85 newtons.

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Answer:

$22.5%.....i think....not sure

Step-by-step explanation:

i've added $18 plus tax%.....not sure if its the answer

Answer: $5.63

Step-by-step explanation:

4.5% Divided By 100 To Get 0.045 Then I Multiplied That By $125 And Got 5.625 .. I Rounded It To $5.63