sarah has 8 3/4 cups of flour each batch takes 1 2/3 cups of flour which is the best answer for how many batches of sarah can make.
a.3 b. 4 c.5 d.6

Answer:

Step-by-step explanation:

(9^2)^(1/3) = 9^(2 * 1/3) = 9^(2/3)

The simplification of the given expression is \(9^\frac{2}{3}\).

Rational exponents are numbers which are written in the form of \(x^\frac{p}{q}\), where x is the base with positive integer and p/q is the rational exponent and q ≠ 0.

Given expression is (9^2)1/3.

We can write this in radical form as ∛(9²).

But we have to simplify it using rational exponents.

There is a rule of exponent that,

(xᵃ)ᵇ = xᵃᵇ

Applying the rule here,

(9^2)1/3 = \((9^2)^\frac{1}{3}\)

             = \(9^{(2*\frac{1}{3})\)

             = \(9^\frac{2}{3}\) ≈ 4.32

Hence the simplified form is \(9^\frac{2}{3}\).

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A. Ram spent $18 on six pens and six books. The grand total is $72.

B. The cost of each pen is $9.

C. The variable is called x.

What is an equation?

A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).

Here, we have

Given: the equation 6x + 18 = 72:

A. The issue is that Ram spent $18 on six pens and six books. The total amount he paid is $72.

B. The following equation will be used to demonstrate this:

6x + 18 = 72

Compile similar terms.

6x = 72 - 18

6x = 54

On dividing,

x = 54 / 6.

x = $9

Hence, each pen will set you back $9.

C. The variable's value is x = 9.

Hence, the pen's price is 9.

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Answer: 8/3 or 2 2/3

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The interest earned on the principal amount at the end of 10 years is 1662 (rounded to the nearest dollar).

Given that the principal amount invested is 2000 and the annual rate of interest is 6.5%, compounded quarterly.

We need to find the amount of interest earned on the principal amount at the end of 10 years.

Using the compound interest formula, the future value of the principal amount after 10 years is:

\(FV = P(1 + r/n)^(nt)\)

where

P = 2000,

r = 6.5% = 0.065,

n = 4 (quarterly compounding), and

t = 10 years

So, the future value of the principal amount after 10 years is:

\(FV = 2000(1 + 0.065/4)^(4×10)= 3662.14\)

The interest earned on the principal amount is the difference between the future value and the principal amount, which is:

3662.14 - 2000= 1662.14

Therefore, the interest earned on the principal amount at the end of 10 years is 1662.

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Answer:

Step-by-step explanation:

If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.

In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.

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Answer:

11/12

Step-by-step explanation:

\(3\frac{1}{4}=\frac{13}{4}=\frac{39}{12} \\ \\ 2\frac{1}{3}=\frac{7}{3}=\frac{28}{12} \\ \\ \frac{39}{12}-\frac{28}{12}=\frac{11}{12}\)

Answer:

(B ) joint is the answer.  

Solution

The centre of a circle is given as; (1, 4)

The radius is 2 units

Therefore, the equation of a circle is;

(x - 1)² + (y-4)² = 4

Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

The theorem that verifies that ASTU AXYZ is the HL (Hypotenuse-Leg) theorem. The correct answer is A.

The HL theorem states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent. In this case, the given information is ASTU and AXYZ, which are two right triangles. To prove that they are congruent, we need to show that their hypotenuses and one leg are congruent.

The options provided are AA (Angle-Angle), OO (Other-Other), HL (Hypotenuse-Leg), AA (Angle-Angle), HA (Hypotenuse-Angle), and LA (Leg-Angle). Out of these options, the HL theorem is the one that matches the given information and verifies the congruence of the two triangles. Therefore, the correct answer is option A.

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The reference angles of -320 is 40 degrees and the reference angle of 19π/12 is 5π/12

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

Angle = -320

The reference angle is caculated as

Reference = 360 + Angle

So, we have

Reference = 360 - 320

Evaluate

Reference = 40

For the other angle, we have

θ = 19π/12

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 2π - 19π/12

Evaluate the difference

Reference angle = 5π/12

Hence, the reference angle is 5π/12

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Using my learning about filing income taxes to complete the following sentences is:

1) Citizens file income taxes to ensure that they will receive a refund if they paid too much in taxes throughout the year.

2) Employers supply a W-2 form to help citizens file their tax returns.

3) Taxes returns can be filed either by mail or online.

Income taxes are compulsory levies that governments make on the incomes and profits of employees, businesspersons, and entities within their jurisdictions.

Individuals use W-2 forms to file their tax returns.  The W-2 form shows an individual's total earnings and tax withholdings.

Thus, taxes returns by individuals and entities are filed either by mail or online (electronically).

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If the random variable x is normally distributed with a mean equal to 0.45 and a standard deviation equal to 0.40, then P(x ≥ .75) is 0.9227.

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

Given the problem above, we need to find what the z-score is when P(x ≥ .75).

The formula for calculating a z-score is given by:

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

Where:

Now,

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

\(Z=P(\text{x} \geq 0.75) = \huge \text(\dfrac{P(Z \geq (0.75 - 0.45)}{0.40}\huge \text)\)

\(Z= P\huge \text (\dfrac{Z \geq0.30}{0.40}\huge \text)\)

\(Z=P(Z \geq 0.75) = 1 - P(Z < 0.75)\)

\(Z=1 - 0.077337\)

\(Z\thickapprox 0.9227\)

Therefore, the z-score of P(x ≥ .75) is 0.9227.

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Answer:

$886.47

Step-by-step explanation:

The correct statement:

The slope is positive because as the age increases, the value increases.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The table:

x → y

5 →  0.75

10 → 5.75

15 →  10.75

20 → 15.75

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = 15.75 - 10.75 / 20 - 15

m = 1

Therefore, the slope is positive because as the age increases, the value increases.

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The area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 is 11.8334.

The graph of the question is given below:

We have to evaluate the integral needed to determine the area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 i.e. x = y^2-y.

Now the area A of the given region is:

A = \(\int^1_{y=0}\left[g(y)-f(y)\right]dy+\int^4_{y=1}\left[g(y)-f(y)\right]dy\)

A = \(\int^1_{y=0}\left[(y^3-4y^2+3y)-(y^2-y)\right]dy+\int^4_{y=1}\left[(y^2-y)-(y^3-4y^2+3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-4y^2+3y-y^2+y)\right]dy+\int^4_{y=1}\left[y^2-y-y^3+4y^2-3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-5y^2+4y\right]dy+\int^4_{y=1}\left[5y^2-y^3-4y)\right]dy\)

Further simplification

A = \(\left[\frac{y^4}{4}-\frac{5y^3}{3}-\frac{4y^2}{2}\right]^1_{y=0}+\left[\frac{5y^3}{3}-\frac{y^4}{4}-\frac{4y^2}{2}\right]^4_{y=1}\)

A = \(\left[(\frac{1}{4}-\frac{5}{3}-2)\right-(0-0+0)]+\left[(\frac{320}{3}-64-32)\right-(\frac{5}{3}-\frac{1}{4}-2)]\)

A = (3-20+24)/12 + 320/3 - 96 - (20-3-24)/12

A = 7/12 + 32/3 + 7/12

A = (7+128+7)/12

A = 142/12

A = 11.8334

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Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Answer:First system: no solution

Second system: one solution

Third system: one solution

Fourth system: infinite solutions

Fifth system: no solution

Step-by-step explanation:

Answer:

0.25-1/4

0.14-7/50

1.4-7/5

0.4-2/5

0.375-3/8

Answer:

7:30 pm

Step-by-step explanation:

pretty much just add on all the times

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Answer:

1/4 x 3/4 = 3/16

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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Answer:

Step-by-step explanation:

2(f^4)^2f3 divided by 6f² is simplified to give 2/ 3 f^2

Given the expression;

2(f^4)^2f^3 divided by 6f^9

We have to expand the expression:

= \(\frac{2f^4 * 2f^3}{6f^9}\)

Find the common factor, we get:

= \(\frac{2 * 2 }{6f^2}\)

Multiply the numerator

= \(\frac{4}{6f^2}\)

Let's divide through to get simpler terms

= \(\frac{2}{3f^2}\)

= 2/ 3 f^2

Thus, 2(f^4)^2f^3 divided by 6f^9 is simplified to give 2/ 3 f^2

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Answer:

x = 24°

Step-by-step explanation:

If two parallel lines are being intersected by the same line, the opposite inside angles are congruent. This means that ∠EFH should be equal to ∠JHF. However, we cannot set these angles equal because we do not know the value of ∠JHG.

Line IG is intersected by line HJ. This means the value of ∠JHG is 24° (180° - 156° = 24°). Know that we know this value, we can set up an equation to find "x".

∠EFH = 2x

∠JHG = 24°

∠GHF = x

∠EFH = ∠JHF                                  <----- Opposite interior angles are equal

∠EFH = ∠JHG + ∠GHF                   <----- Break ∠JHF into 2 angles

2x = 24 + x                                      <----- Insert values

x = 24                                             <----- Subtract x from both sides