Anne's Road Paving Company mixed 16 1/4 tons of cement. They used 6 3/4 tons of the cement to pave a street downtown. How much cement did they have left?

The required answers ar(a)P = $2,000,r = 4.5%,n = 2 (b)$ 2985.17, (c) 4.45%

(A) Using the given information, we can identify the following values:

P = $2,000 (the present value or initial deposit)

r = 4.5% (the annual percentage rate)

n = 2 (the number of times per year that interest is compounded, since it is compounded semi-annually)

(B) To find the future value of the account balance after 9 years, we can use the formula:

\(S(t) = P(1 + r/n)^{nt}\)

where t is the time in years. Substituting the given values:

\(S(9) = $2,000(1 + 0.045/2)^{2*9}= $2,000(1.0225)^{18}\)

= $2,000(1.505016)

= $2985.17

Therefore, Monique will have $$2985.17 in the account in 9 years.

(C) The annual percentage yield (APY) takes into account the effect of compounding on the effective interest rate. It is calculated as:

\(APY = (1 + \frac{r}{n})^n - 1\)

Substituting the given values:

\(APY = (1 + 0.045/2)^2 - 1\)

= 0.0445 or 4.45%

Therefore, the annual percentage yield for the savings account is 4.45% rounded to 3 decimal places.

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's solve ~

Assume width of rectangle be " x ", length = 3×width + 8 = 3x + 8 ~

Now, Perimeter of rectangle is :

\(\qquad \sf  \dashrightarrow \:2(l + w) = 56\)

\(\qquad \sf  \dashrightarrow \:2(3x + 8 + x) = 56\)

\(\qquad \sf  \dashrightarrow \:2(4x + 8) = 56\)

\(\qquad \sf  \dashrightarrow \:4x + 8 = 56 \div 2\)

\(\qquad \sf  \dashrightarrow \:4x + 8 = 28\)

\(\qquad \sf  \dashrightarrow \:4x = 28 - 8\)

\(\qquad \sf  \dashrightarrow \:x = 20\div 4\)

\(\qquad \sf  \dashrightarrow \:x =5 \: cm\)

Hence, width = x = 5 cm

\(\qquad \sf  \dashrightarrow \:l = 3w + 8\)

\(\qquad \sf  \dashrightarrow \:l = 3(5)+ 8\)

\(\qquad \sf  \dashrightarrow \:l = 15+ 8\)

\(\qquad \sf  \dashrightarrow \:l =23 \:cm\)

And, length = 26 cm

Answer:

CE = 3.2 cm

DH = 4.5 cm

Explanation:

Given:

MNPR ≅ CEDH

≅ - means approximately equal

Lengths of the shape:

MN = CE = 3.2 cm

NP = ED = 6.5 cm

PR = DH = 4.5 cm

RM = HC = 9 cm

A random sampling method could be used to find the percentage of students in your grade who eat five servings of fruit and vegetables each day.

This method involves selecting a random sample of students from the entire population of your grade and surveying them about their eating habits.

In other word, its involves randomly selecting a subset of students from the entire grade population and collecting data on their eating habits. By selecting students at random, the sample is more likely to be representative of the entire grade. This cam provide accurate insights into the percentage of students meeting the desired dietary recommendation.

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Answer:

1. 2.997

2. 29.93

Step-by-step explanation:

1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.

2. Same thing, gotta multiply all given values

Answer:

a) 15.52mm

b) 25.8275mm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, or the area to the left side of the curve. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, that is, the area to the right side of the curve.

A) What wing-span has an area of 0.1005 on it left side under the standard normal curve?

This is X when Z has a pvalue of 0.1005. So it is X when Z = -1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.28 = \frac{X - 20}{3.5}\)

\(X - 20 = -1.28*3.5\)

\(X = 15.52\)

This wing-span is 15.52mm.

B) What wing-span has an area of 0.0480 on it right side under the standard normal curve?

This is X when Z has a pvalue of 1 - 0.0480 = 0.9520. So this is X when Z = 1.665.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.665 = \frac{X - 20}{3.5}\)

\(X - 20 = 1.665*3.5\)

\(X = 25.8275\)

This wing-span is 25.8275mm.

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Make's absolutely no sense. Please rephrase this as a question.

A function assigns the values. The profit-maximizing quantity of labour to hire is 15 workers.

A function assigns the value of each element of one set to the other specific element of another set.

Given the marginal revenue product, MRP = 40-(Q/10)

The cost of labour, WL = 10

The production function, Q = 20 L

For profit maximizing quantity of labour to hire where,

MRP = WL

40-(Q/10) = 10

40-(20L/10)=10

40-2L=10

-2L = 10-40

-2L=-30

L=15

Hence, the profit-maximizing quantity of labour to hire is 15 workers.

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Answer:

42

Step-by-step explanation:

(7)x6

42

Answer:

42

Step-by-step explanation:

Remember:

P arenthesess

E xponent

M ultiplictaion

D ivision

A ddition

S ubtraction

First,

3 + 4 = 7

Then,

7 x 6 = 42

Have a good day. :)

Hope this helps!

(brainliest would be appreciated)

We need to first identify the center of the circle.

We see that the coordinate point of the center of the circle is (-1, -2).

The equation of a circle is given with the equation

where h is x, k is y, and r is the radius of the circle.

Therefore, we can plug in the coordinates first to find the h and k of the equation.

Then, we need to determine r.

The circle intersects points (-6, -2) and (4, -2). We can simply subtract the x-coordinates from each other to find the diameter of the circle.

Finally, we know the radius is half of the diameter:

We can plug in the radius into the equation.

Therefore, our final equation is Choice D:

The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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This is an example of exponential growth.

Since the population doubles in size every 29 hours,

and the initial population is 30000,

then in 29 hours,

the population = 30000 x 2 = 60000

and in

another 29 hours (total of 58 hours from the start),

the population = 60000 x 2 = 120000

Hence the population after 58 hours is 120000 bacteria.

The probability that the sample mean would be less than 23,013 dollars if a sample of 134 persons is randomly selected is approximately 0.0000397.

We can use the central limit theorem to approximate the distribution of the sample mean as a normal distribution, with a mean of μ = 23,037 dollars and a standard deviation of σ/√n = √(149,769/134) = 33.23 dollars.

Then we can standardize the sample mean using the z-score formula:

z = (\(\bar{X}\) - μ) / (σ/√n)

where \(\bar{X}\) is the sample mean.

Plugging in the given values, we get:

z = (23,013 - 23,037) / 33.23 ≈ -0.722

Using a calculator, we can find that the probability of getting a z-score less than -0.722 is approximately 0.0000397.

Therefore, the probability that the sample mean would be less than 23,013 dollars if a sample of 134 persons is randomly selected is approximately 0.0000397.

This is a very small probability, indicating that it is unlikely to obtain a sample mean this low if the true population mean is 23,037 dollars.

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To find the work needed to pump all the water from a cylindrical tank to a level 1 ft above the rim, we need to calculate the weight of the water and then multiply it by the distance it is pumped. The weight of the water is determined by its volume and specific weight, while the distance is the height of the tank plus the additional 1 ft. By plugging in the given values and using the formulas for the volume of a cylinder and the weight of water, we can calculate the final answer in terms of π.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. In this case, the tank has a radius of 3 ft and a height of 10 ft. The volume of water in the tank is then V = π(3^2)(2) = 18π ft^3.

The weight of the water is determined by its volume and specific weight. The specific weight of water is given as 64 lb/ft^3. Therefore, the weight of the water in the tank is W = (18π)(64) = 1152π lb.

To pump all the water to a level 1 ft above the rim, we need to pump it a total distance of 10 + 1 = 11 ft. The work required is given by the formula W = force × distance. In this case, the force is the weight of the water and the distance is 11 ft. Therefore, the work needed is W = (1152π)(11) = 12672π ft-lb.

Hence, the exact answer for the work needed to pump all the water is 12672π ft-lb.

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Answer:

Step-by-step explanation:

The equation for the direct variation is, for us (using f and m instead of y and x):

f = km, where k is the constant of proportionality. We need to solve for this first using the first set of given values:

-19 = k(14) so

\(k=-\frac{19}{14}\) Now plug that in with second set of givens, namely to find f when m is 2:

\(f=(-\frac{19}{14})(2)\) and

\(f=-\frac{19}{7}\)

There will be a total of 1620 four digit numbers having an even second digit and a fourth digit that is atleast twice of the second digit.

Possible second digits allowed = 0,2,4

digits 6 and 8 are also even but cant be included as their twice yeild double digits.

For each of the allowed digits, the possible fourth digit ranges from 0-9(if second digit is zero), 4-9(if second digit is considered as 2) and 8-9(if second digit is 4). Hence the total number of fourth digits allowed            = 10+6+2=18.

The first digit can be any non zero number whereas the third digit can be from 0-9.

Hence the total number of four digits allowed: 9×10×18 = 1620.

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The length of the steering device will be 4.5 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The steering device extends to point T, and the diameter of the steering wheel is 15 inches long. Then the length of the steering device is given as,

7.5² = h² + 6²

56.25 = h² + 36

h² = 56.25 - 36

h² = 20.25

h = 4.5 inches

The length of the steering device will be 4.5 inches.

The diagram is given below.

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The minimum score required for the scholarship is 646.765.

Standard deviation is a measure of the distribution of statistical data, whereas variance is a measure of how data points differ from the mean. The main distinction between the two is that whereas variance is expressed in squared units, standard deviation is expressed in the same units as the data's mean.

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = \(\frac{X - mean}{s.d.}\)

In this problem, we have that:

mean  = 488 , s.d. = 113

What is the minimum score required for the scholarship?

Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.

Z =  (X - mean) / s.d.

1.405 = (X - 488) / 113

X = (1.405 x 113) + 488

X =   646.765

the minimum score required for the scholarship is 646.765.

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The right proportion: (500 miles)/(2 days) = (x miles)/(5 days) . Therefore, the given proportion is False.

Given that if you drive 500 miles in 2 days.

To calculate how many miles you would drive in 5 days, the right proportion:

you drive 500 miles in 2 days.

Therefore, 250 miles in one day.

Further, calculate in 5 days as,

5 days × (500 miles)/(2 days) = (x miles)

(500 miles)/(2 days) = (x miles)/(5 days)

Here, x is the number of miles you drive in 5 days.

Therefore, the correct proportion would be:

(500 miles)/(2 days) = (x miles)/(5 days).

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1. Independent random samples arise when one random sample is split into groups differing by an observed feature is incorrect.

2. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

1. Independent random samples arise when individuals in a sample are randomly assigned to experimental groups, data is recorded repeatedly on a random sample of individuals, or random samples are selected separately. The statement that one random sample is split into groups differing by an observed feature does not accurately describe independent random samples.

2. The margin of error in a confidence interval represents the range of values within which the true population parameter is likely to fall. It is calculated by taking half of the width of the confidence interval. Therefore, the correct answer is that the margin of error is equal to half the width of the confidence interval.

In summary, the incorrect statement is that independent random samples arise when one random sample is split into groups differing by an observed feature. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

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Answer:

see below

Step-by-step explanation:

do long division

for example 42/8 = 5 2/8 =5 1/4 =5.25

Answer:

\(\frac{91+129+16}{44}\)

Step-by-step explanation:

Answer:

8 pints 3 people

Step-by-step explanation:

13 x's therefore 13 people participate

8 is the median

Therefore the answer is D

The actual calculation depends on the specific vector field you are working with. You need to substitute the appropriate expressions for P and Q into the integrals and evaluate them accordingly.

To evaluate the line integral around the clockwise-oriented triangle with corners at the origin (0,0), (1,0), and (0,1), we need to sketch the vector field and the triangle and then calculate the integral.

Next, let's assume there is a vector field defined over the plane. Since you haven't provided the vector field explicitly, let's use a general notation and consider a vector field F = (P, Q), where P and Q are functions of x and y.

To calculate the line integral, we need to parameterize the triangle. We can divide the triangle into three line segments and parametrize each segment separately.

Line segment from (0,0) to (1,0):

Let's parameterize this segment as r(t) = (t, 0), where 0 ≤ t ≤ 1.

Line segment from (1,0) to (0,1):

Let's parameterize this segment as r(t) = (1 - t, t), where 0 ≤ t ≤ 1.

Line segment from (0,1) to (0,0):

Let's parameterize this segment as r(t) = (0, 1 - t), where 0 ≤ t ≤ 1.

Now, we can calculate the line integral for each segment and sum them up:

Line integral along the first segment:

\(\int(0 to 1) P(t, 0) dt + \int(0 to 1) Q(t, 0) dt\)

Line integral along the second segment:

\(\int(0\: to \:1) P(1 - t, t) dt + \int(0 \:to\: 1) Q(1 - t, t) dt\)

Line integral along the third segment:

\(\int(0 \:to \:1) P(0, 1 - t) dt + \int(0\: to \:1) Q(0, 1 - t) dt\)

Finally, the total line integral around the triangle is the sum of these three line integrals:

Total Line Integral = Line integral of segment 1 + Line integral of segment 2 + Line integral of segment 3

Please note that the actual calculation depends on the specific vector field you are working with. You need to substitute the appropriate expressions for P and Q into the integrals and evaluate them accordingly.

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The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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