Find the area of a circle with radius 6 ft.

Answer:

a,d,e

Step-by-step explanation:

In this question, we apply limit concepts to get the desired limit, finding that the correct options are: A, D and E, leading to the result of the limit being \(\frac{1}{6}\).

Limit:

The limit given is:

\(\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7}\)

If we apply the usual thing, of just replacing x by 7, the denominator will be 0, so this is not possible.

When we have a term with roots, we rationalize it, multiplying both the denominator and the denominator by the conjugate.

Multiplication by the conjugate:

The term with the root is:

\(\sqrt{x+2} - 3\)

It's conjugate is:

\(\sqrt{x+2}+3\)

Multiplying numerator and denominator by the conjugate, meaning option A is correct:

\(\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3}\)

We do this because at the numerator we can apply:

\((a+b)(a-b) = a^2 - b^2\)

Thus

\(\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3} = \lim_{x \rightarrow 7} \frac{(\sqrt{x+2})^2 - 3^2}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x+2-9}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x-7}{(x-7)(\sqrt{x+2}+3)}\)

Thus, we can simplify the factors of x - 7, meaning that option D is correct, and we get:

\(\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3}\)

Now, we just calculate the limit:

\(\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3} = \frac{1}{\sqrt{7+2}+3} = \frac{1}{3+3} = \frac{1}{6}\)

Thus, option E is also correct.

Using a limit calculator, as given by the image below, we have that 1/6 is the correct answer.

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Answer:

Step-by-step explanation:

4/mx

1.) The probability that the sample mean will be greater than 48 minutes is 0.9332.

2.) The probability of the sample mean being between 44 and 49 minutes is 0.6687.

3.) The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean.

To solve this problem, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means tends to be approximately normally distributed, regardless of the shape of the original population, when the sample size is large enough.

1.) Probability of sample mean > 48 minutes:

To calculate this probability, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the population mean (μ) is 45 minutes, the population standard deviation (σ) is 12 minutes, and the sample size (n) is 36. We want to find the probability of the sample mean being greater than 48 minutes.

Calculating the z-score:

z = (48 - 45) / (12 / √36) = 3 / 2 = 1.5

Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.5 is approximately 0.9332. Therefore, the probability that the sample mean will be greater than 48 minutes is approximately 0.9332.

2.) Probability of sample mean between 44 and 49 minutes:

To calculate this probability, we need to find the z-scores for both 44 and 49 minutes and then calculate the area between those z-scores.

Calculating the z-scores:

For 44 minutes:

z1 = (44 - 45) / (12 / √36) = -1 / 2 = -0.5

For 49 minutes:

z2 = (49 - 45) / (12 / √36) = 4 / 2 = 2

Using the standard normal distribution table or calculator, we find the probabilities corresponding to z1 and z2:

P(z < -0.5) ≈ 0.3085

P(z < 2) ≈ 0.9772

The probability of the sample mean being between 44 and 49 minutes is approximately P(-0.5 < z < 2) = P(z < 2) - P(z < -0.5) ≈ 0.9772 - 0.3085 = 0.6687.

3.)Conclusion from 100 samples with a mean of 65 minutes:

If 100 samples were collected, and the sample mean was 65 minutes, we would need to assess whether this value is significantly different from the population mean of 45 minutes.

To make this assessment, we can calculate the z-score for the sample mean of 65 minutes:

z = (65 - 45) / (12 / √36) = 20 / 2 = 10

The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean. This is an extremely large deviation, suggesting that the sample mean of 65 minutes is highly unlikely to occur by chance.

Given this, we can conclude that the sample mean of 65 minutes is significantly different from the population mean. It may indicate that there is a systematic difference in the delivery times between the sample and the population, possibly due to factors such as increased demand, traffic, or other external variables

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Solution:

The equation is given below as

Collect similar terms, we will have

add 2 to both sides

Hence,

The final answer is

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

88

Step-by-step explanation:

60-(-15)+(13)

We open the braket which is

60+15+13

How we got + in d 60+15?

60-(-15)so we did minus ➖ × minus ➖ =+

What am trying to say is minus multipled by minus is plus.

So we add up 60+15+13

60+15=75

75+13=88

FINAL ANSWER =88.

Answer:

A) ∠BEC is one-half of ∠BAC

B) ∠BEC = 60°

C) ∠BDC = 120°

Step-by-step explanation:

C) arc BDC = 120°

arc BEC = 360° - 120° = 240°

∠BDC = 1/2(240°) = 120°

What is the maximum height of the ball 182.25 feet

How many seconds does it take until the ball hits the ground 6 seconds

The maximum height will occur at the vertex v(h', k)

h' = -b/2a

From the equation h = − 16 t^2 + 84 t + 72

a = -16

b = 84

h' = -84/(2 * -16)

h' = t = 2.625

k = h = − 16 t^2 + 84 t + 72 at t = 2.625

= − 16 * 2.625^2 + 84 * 2.625 + 72

= 182.25 feet

The ball hits the ground when h = 0

0 = − 16 t^2 + 84 t + 72

solving the quadratic equation gives

t = 6 OR -3/4

Use the positive value

t = 6 seconds

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Answer:

42 units

Step-by-step explanation:

Area of a trapezoid is always 1/2(b1+b2)*h

so here base 1 is 4 units, and base 2 is 10 units. When we add these we get 14, divided by 2 which is 7, and multiplied by height of 6, which is 42

Answer:

Ann has $30

Ryan has $63

Keith has $21

Step-by-step explanation:

First I assigned variables to the amounts each owns. It doesn't really matter what letters, but I said x represents Ann's money, y represents Ryan's money, and z represents Keith's money.

We know that with all their money added up, they have 114. This gives us our first equation;

114=x+y+z

Ryan has 3 times what Keith has, which, in terms of variables, is

y=3z

Keith has nine dollars less than Ann. Less, in word problems, always means subtraction. This gives us our third equation:

z=x-9

Okay so the impulse is to put z=x-9 and y=3z into the first equation, but the goal is to create an equation with only one variable so this will not work.

What we do instead is sub z=x-9 into y=3z. This gives

y=3(x-9)=3x-27

Now that both y and z are in terms of x, we plug those equations into the first and then solve for x;

114=x+3x-27+x-9

114=5x-36

150=5x

30=x

Now that we know x, we can find z and y using the equations from earlier:

z=30-9=21

y=3(21)=63

x=30, y=63, and z=21, thus Ann has $30, Ryan has $63, and Keith has $21.

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer: 59

Step-by-step explanation:

On 15th day Kyle will do 59 crunches.

An equation is a statement that consists of algebraic expressions equated with other algebraic expressions by an equal sign.

The crunches Kyle did on Day 1 are 3

The rate by which he is increasing per day is 4 crunches/per day

let t represent the number of days

Let the number of crunches on t day be y

Then the equation formed will be

y = 3 + 4(t-1)

On 15th day, he will do

y = 3+ (15-1) *4

y = 3+56

y = 59

Therefore, on 15th day Kyle will do 59 crunches.

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Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

\( \frac{1}{ log(y) } = x\)

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

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Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

1)

You tutor for 9 hours.

2)

You tutor for 4 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the tap diagram,

1)

You have three parts.

A friend has one part.

This means,

4 parts = 12 hours

1 part = 3 hours

Now,

You = 3 parts = 3 x 3 = 9 hours.

2)

You have two parts.

A friend has four parts.

This means,

6 parts = 12 hours

1 part = 2 hours

Now,

You = 2 parts = 2 x 2 = 4 hours.

Thus,

You tutor for 9 hours.

You tutor for 4 hours.

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Answer:

f(9) = 61

Step-by-step explanation:

You know f(x) = 8x - 11. So, to find f(9), you have to replace x with 9 on the other side.

f(9) = 8(9) - 11

You can solve this.

f(9) = 72 - 11

f(9) = 61

Answer:

I'm very sure this is Simple Random Sampling.

Answer:

6

Step-by-step explanation:

Adding the two polynomials gives

(x^3 + 3x^2 + 4x - 7) + (-7x^4 +5x^3 + x^2 - 7) =

-7x^4 + (x^3 + 5x^3) + (3x^2 + x^2) + 4x + (-7-7) =

- 7x^4 + 6x^3 + 4x^2 + 4x -14

The x^3 term is 6x^3, so the desired coefficient is 6.

Answer:

Step-by-step explanation:

Volume of the entire figure = L (Area 1  + Area 2)

where L = 10 m

Area 1 (blue prism) = 4 x 3 = 12 m²

Area 2 (brown prism = 1 x 7 = 7 m²

plugin  values into the formula:

Volume of the entire figure = L (Area 1  + Area 2)

                                             = 10 (12 + 7)

                                             = 120 m³ + 70 m³

                                             = 190 m³

Answer:

Step-by-step explanation:

\(\text{$\therefore$ the system of linear equation has only one solution}\)

The confidence interval is 0.559 < p < 0.641 and expected value is 0.600

To construct a confidence interval for the true population proportion, we can use the formula:

p ± Z * √((p × (1 - p)) / n)

Where:

p = sample proportion (336/560)

Z = critical value for the desired confidence level

95% confidence = Z-value of approximately 1.96

n = 560

Let's calculate the confidence interval:

p = 336/560 ≈ 0.600

Z ≈ 1.96 (for a 95% confidence level)

n = 560

Plugging these values into the formula:

p ± Z × √((p × (1 - p)) / n)

0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)

0.600 ± 1.96 × √((0.240) / 560)

0.600 ± 1.96 × √(0.0004285714)

0.600 ± 1.96 × 0.020709611

0.600 ± 0.040564459

The confidence interval is:

0.559 < p < 0.641

Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.

For proportions, the expected value is simply the sample proportion, which is approximately 0.600.

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Answer:

The answer is A

Step-by-step explanation:

0.2% of 500 is 1 so in two year she would have 502$

The solution of the equation is to the nearest ten-thousandth is x = 2.7712.

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459. Typically, the natural logarithm of x is expressed as ln x, loge x, or, if the base e is implicit, just log x.

The given equation is \(3^{x-1} = 7\).

Take natural log on both sides of the equation:

\(\ln (3^{x-1} )=\ln( 7)\)

(x - 1) ln(3) = ln(7)

x - 1 = ln(7) / ln(3)

x = 1 +  ln(7) / ln(3)

x = 2.7712

Hence, the solution of the equation is to the nearest ten-thousandth is x = 2.7712.

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The numeric values for this problem are given as follows:

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

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Answer:

$6.88

Step-by-step explanation:

16Tbs. =1 cup,

4 pies =2 cups of lemon juice, so you need 32 Tbs. of lemon juice

32/2=16

16*0.43=$6.88

Answer: $ 6.88

Step-by-step explanation:

In one cup there is 16 tablespoons.

each lemon costs .43 and gives 2 tablespoons

Half a cup would give us 8 tablespoons = 4 lemons at the cost of 1.72

1.72 times 4 pies

Making the whole thing of 4 pies cost 6.88

Giving us the answer of 6.88.

(correct me if i'm wrong)