for the function graphed, determine the interval(s) where the derivative is (a) positive; (b) negative; and the x-value(s) at which the derivative is (c) equals zero; (d) does not exist.'

We can conclude after answering the provided question that Therefore, interest after 19 years, the amount in the account will be $1,418.50.

In mathematics, interest is the sum of money earned but rather owed on an initial investment or loan. You can use either simple or compound interest. Rate of return is computed upon that main fee plus any previously earned interest, whilst simple interest is given as a percent of the initial amt. If you invest $100 at a 5% each year simple interest rate, you will earn $5 through interest every year for four years, for a total of $15.

calculating the future value of an investment is:

[tex]FV = PV x (1 + r)^n\\FV = $500 x (1 + 0.08)^19\\FV = $500 x 2.837\\FV = $1,418.50[/tex]

Therefore, after 19 years, the amount in the account will be $1,418.50.

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The required  average number of people completing voting at any given time as per given 55 people per hour is equals to 27.5.

Average throughput voting facility process = 55 people per hour,

Calculate the average processing time per person ,

⇒ Processing time per person = 1 hour / 55 people

⇒ Processing time per person = 0.01818 hours/person

Average time taken by each person to complete the voting process = 30 minutes  

Convert this to hours by dividing by 60,

⇒ Flow time per person = 30 minutes / 60

⇒ Flow time per person = 0.5 hours/person

Now,

Average number of people in the voting facility using Little's Law,

which states that the average number of items in a system is equal to the average throughput multiplied by the average flow time.

⇒ Average number of people in facility = Average throughput x Average flow time

⇒ Average number of people in facility = 55 people/hour x 0.5 hours/person

⇒ Average number of people in facility = 27.5 people

Therefore, on average there are 27.5 people in the voting facility at any given time.

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The above question is incomplete, the complete question is:

Suppose that a voting facility processes an average of 55 people per hour (throughput) and that, on average, it takes 30 minutes for each person to complete the voting process (flow time).Calculate the average number of people  in the voting facility at any given time.

The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.

What is Inductive logic ?

Inductive logic, also known as induction, is a type of reasoning that involves drawing general conclusions based on specific observations or examples.

In inductive logic, a sample is considered representative of the population from which it is taken if it possesses the following two characteristics:

Randomness: The sample should be selected randomly from the population. This means that every individual in the population should have an equal chance of being selected for the sample. A random sample helps to reduce the potential for bias in the selection process.

Size: The sample size should be large enough to accurately represent the population. A larger sample size helps to reduce the impact of chance variation and provides a more accurate estimate of the characteristics of the population.

Therefore, The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.

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Answer:

25%

Step-by-step explanation:

The factorised form of the given expression as required to be determined in the task content is; p ( p + 1 ) - q (q - 1).

It follows from the task content that the factored form of the given expression is to be determined.

As evident from the task content; the given expression is; p² - q² + p - q.

On this note, by first collecting like terms; we have;

p² + p - q² - q

By factorisation; we have that;

p ( p + 1 ) - q (q - 1)

Ultimately, the factored form of the given expression is; p ( p + 1 ) - q (q - 1).

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Given a solution containing 30 mg of medication per 3 mL, you need to determine how many mL makeup 15 mg of medication. By setting up a proportion, it can be calculated that 1.5 mL should be administered per dose.

To solve this problem, we need to determine how many milliliters correspond to the required dose of medication (15 mg). Given that the pharmacy dispensed a solution containing 30 mg of medication per 3 mL, we can construct a proportion to find the needed milliliter amount.

30 mg/3 ml = 15 mg/x ml

To solve this equation for 'x', multiply both sides by 'x' and then divide by 30 mg to isolate 'x':

x = (15 mg * 3 ml) / 30 mg

Upon completing this calculation, you find that x equals 1.5 ml. Therefore, you would administer 1.5 mL of the medication per dose.

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To administer 15 mg of a liquid oral medication given a concentration of 30 mg/3 mL, you will need to administer 1.5 mL per dose.

To calculate the mL of the liquid oral medication to administer, we need to determine the amount of medication in each mL. In this case, the pharmacy has dispensed a concentration of 30 mg/3 mL, which means there is 10 mg of medication in each mL. Given that the doctor's order is for 15 mg, we can calculate the mL to administer by setting up a proportion:

10 mg/1 mL = 15 mg/x mL

Cross-multiplying, we get:

10x = 15

x = 1.5

Therefore, you will need to administer 1.5 mL per dose.

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Harris should expect to spin a sum that is 10 or greater than 100 times.

Part A:

To predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of spins, which is 500.

The possible outcomes of the first spinner are 1, 2, and 3, and the possible outcomes of the second spinner are 4, 5, 6, 7, and 8.

The minimum sum we can get is 1+4=5, and the maximum sum we can get is 3+8=11.

To get a sum less than 10, we can get:

1+4=5

1+5=6

1+6=7

1+7=8

1+8=9

2+4=6

2+5=7

2+6=8

2+7=9

3+4=7

3+5=8

3+6=9

There are 12 possible outcomes that result in a sum less than 10. So the probability of getting a sum less than 10 is 12/15, or 4/5.

To find the number of times Harris will spin a sum less than 10, we can use the equation:

probability of getting a sum less than 10 × total number of spins = x

So the equation that can be solved to predict the number of times Harris will spin a sum less than 10 is:

C) 12/15 = x/500

Part B:

To find the number of times Harris should expect to spin a sum that is 10 or greater, we can subtract the number of times he will spin a sum less than 10 from the total number of spins:

total number of spins - number of times he will spin a sum less than 10 = number of times he should expect to spin a sum that is 10 or greater

Substituting the values, we get:

500 - (12/15 × 500) = 500 - 400 = 100

So Harris should expect to spin a sum that is 10 or greater than 100 times.

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The price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

What is the selling price?

The price you will pay to purchase a share or any other commodity is known as the "buy" or "bid" price. The price you will receive when you sell that share or commodity is the "sell" or "ask" price.

Here, we have

Given: Tom and John are engaged in buying and selling certain products A and B. Tom buys 5 of product A but sells twice as much of product B. John on the other hand sells three times what Tom bought of product A and buys 13 of product B. At the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh 230,000.

Let's assume that the cost price for both products A and B is "x", and the selling price for both products A and B is "y". We can use this information to set up two equations, one for Tom and one for John, that relate the costs and profits for the two products:

Tom: 5x - 2(5y) = P₁

John: 3(5x) - 13x = P₂

where  P₁ and P₂ are the profits made by Tom and John, respectively.

We know that at the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh

230,000. So we can write:

P₁ = 230,000 - 5x

 P₂ = 110,000 - 18x

Substituting these values into the equations for Tom and John, we get:

5x - 2(5y) = 230.000 - 5x

Simplifying these equations, we get:

10x - 10y = 230,000

2x = 110,000

x = 55,000

Substituting this value back into the first equation, we can solve for y:

10(55,000) - 10y = 230,000

Simplifying this equation, we get:

y = 32,000

Hence, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

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5 days/8 days = 0.625 half lives

fraction left after 0.625 half lives = (1/2)^0.625

= 0.6484197773

Amount left = 27 x 0.6484197773 gms

= 17.51 gms to dp <<<

Answer:

45∘

Step-by-step explanation:

∠2 = 180∘ - 135∘ = 45∘

∠2 = ∠1 = 45∘

∠1 = ∠4 = 45∘

Minimum and maximum recommended width of the space between 6-inch by 6-inch tiles = 13/6 inches.

An inch is a unit of length in the Imperial system of units, which is primarily used in the United States, Canada, and the United Kingdom. One inch is equal to 1/12 of a foot or 2.54 centimeters. It is commonly used to measure the length or width of objects, such as a piece of paper, a television screen, or a piece of fabric. In the Imperial system, larger units of length, such as feet, yards, and miles, are based on inches.

by the question.

To simplify the expressions for the minimum and maximum recommended widths of the space between 6-inch by 6-inch floor tiles, we can convert the mixed numbers to improper fractions and then find the least common multiple (LCM) of the denominators.

First, let's simplify the minimum recommended width of the space:

[tex]2-2 inch = 2 + 2/12 = 2 + 1/6 = (2*6 + 1)/6 = 13/6 inches[/tex]

Next, let's simplify the maximum recommended width of the space:

[tex]2-1 inch = 2 + 1/12 = 2 + 2/24 = (2*12 + 2)/24 = 26/12 = 13/6 inches[/tex]

We can see that the minimum and maximum recommended widths of the space between the 6-inch by 6-inch tiles are the same, which is 13/6 inches. Therefore, we can simplify the expressions for both.

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The value of x = 2.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

According to our question-

y= -5x

6x+y=2

6x-5x=2

x=2

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Answer: Let x be the number of gallons of the first brand (30% pure antifreeze) that needs to be mixed, and let y be the number of gallons of the second brand (80% pure antifreeze) that needs to be mixed. We want to find the values of x and y that satisfy the following conditions:

The total amount of antifreeze mixed is 150 gallons: x + y = 150

The resulting mixture is 40% pure antifreeze: 0.3x + 0.8y = 0.4(150)

We have two equations with two unknowns, so we can solve for x and y. We'll use the first equation to solve for y in terms of x:

y = 150 - x

Substituting this expression into the second equation gives:

0.3x + 0.8(150 - x) = 60

Simplifying and solving for x:

0.3x + 120 - 0.8x = 60

-0.5x = -60

x = 120

Substituting this value back into y = 150 - x gives:

y = 150 - 120 = 30

Therefore, we need to mix 120 gallons of the first brand and 30 gallons of the second brand to obtain 150 gallons of a mixture that contains 40% pure antifreeze.

Step-by-step explanation:

Thus, infants are deemed preterm if they arrive on or before 240 days (rounded to the next integer).

The study of chance and uncertainty is covered in the mathematical field of probability. It is a way to gauge how likely something is to happen. Probability can be expressed as a number between 0 and 1, with 0 indicating that an occurrence is impossible, and 1 indicating that an event is certain. Probability is frequently employed in real-world situations to forecast the results of random occurrences like tossing a coin, rolling a die, or drawing cards from a deck. The probability of an occurrence is estimated by dividing the number of possible outcomes by the number of possible ways the event could occur.

given

a. We need to locate the region to the right of 307 under the normal distribution curve in order to determine the likelihood that a pregnancy would last 307 days or longer.

By standardizing the value of 307, we may make use of the standard normal distribution:

(X - mu) / sigma = z

z = (307 - 268) / 15\sz = 2.6

A basic normal distribution table or calculator can be used to determine that a z-score larger than 2.6 has a probability of about 0.0047.

Thus, the likelihood of a pregnancy lasting at least 307 days is roughly 0.0047, or 0.47%.

b. We must determine the gestational period that sets the lowest 3% of pregnancies apart from the others. The value with a cumulative probability of 0.03 to its left is this one.

The z-score for a cumulative probability of 0.03 can be calculated using a conventional normal distribution table or calculator. It is roughly -1.88.

To determine the corresponding length of pregnancy, we can apply the z-score formula:

z = (x - mu)/sigma -1.88 = (x - 268)/15 -28.2 = x - 268 x = 239.8

Thus, infants are deemed preterm if they arrive on or before 240 days (rounded to the next integer).

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On diffrentiating  1.f'(x)=8xsinx + 4x²cosx

Putting the value variable x=4, 2. f'(4)=66.07

Differentiation in mathematics is a function's derivative with respect to an independent variable. Calculus's concept of differentiation may be used to calculate the function per unit change in the independent variable.

Y = f would be a function of x. (x)

Secondly, the following is the formula for the rate of change of "y" per unit change in "x":

dy / dx

Given function:

f(x)=4x²tanx/secx

f(x)=(4x²sinx/cosx)× cosx

f(x)=4x²sinx

On differentiating f(x), we get

f’(x)=8xsinx+4x²cosx

Putting the values at x=4, we get

f’(4)=8×4×sin4+4(4)²cos4

f’(4)=66.07

Hence, f’(x)=8xsinx + 4x²cosx

f’(4)=66.07

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The difference between the balances of Ashley and Fwam after 15 years is given as follows:

$5,650. (Ashley will have $5,650 more than Fwam).

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

Hence Ashley's amount after 15 years is given as follows:

A(15) = 59000 x (1 + 0.03125/365)^(365 x 15)

A(15) = $94,280.

Fwam's amount is given as follows:

F(15) = 59000 x (1 + 0.0275)^(15)

F(15) = $88,630.

Then the difference is of:

94280 - 88630 = $5,650.

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Answer:5650

Step-by-step explanation:

94279.8393-88629.7389=5650.1009

Therefore, the slant height of the pyramid is 7.5 cm.

I believe you meant to ask about "height". Height is a measurement of how tall something is, typically referring to the distance from the ground or base to the top of an object. It can be measured in various units, such as feet, inches, meters, or centimeters. People often use height to describe the physical stature of individuals or objects, such as the height of a person, building, or tree.

by the question.

let's start by recalling the formula for the lateral surface area of a pyramid:

[tex]Lateral Surface Area = (1/2) x Perimeter of Base x Slant Height[/tex]

We are given that the lateral surface area is 120 cm2 and the base area is 64 cm2. Since the base is a square, we can find the length of one side by taking the square root of the area:

Side of Base = sqrt(64 cm2) = 8 cm

The perimeter of the base is then 4 times the length of one side:

[tex]Perimeter of Base = 4 x 8 cm = 32 cm[/tex]

Now we can substitute the values we have into the formula and solve for the slant height:

[tex]120 cm2 = (1/2) x 32 cm x Slant Height[/tex]

[tex]Slant Height = (120 cm2) / (16 cm) = 7.5 cm[/tex]

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None explains the use of 0.5 for the most conservative sample size. Thus E is the correct one.

A confidence interval is a range of values that is likely to contain the true population parameter, and a wider confidence interval allows for a greater chance of accurately capturing the true population parameter.

The use of 0.5 as an estimate of the sample proportion is most conservative because it produces the widest confidence interval.

A larger sample size is generally used when the confidence interval is wider, as it improves the precision of the estimate.

Using 0.5 as the estimated proportion will produce the widest confidence interval and thus, a larger sample size.

This is why 0.5 is used to calculate the most conservative sample size.

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The value of the product  7 × 3 1/4 is 22 3/4

It is important to note that fractions are defined as the part of a whole variable, element or number.

There are different types of fractions, such as;

From the information given, we have;

7 = A whole number

3 1/4 = a mixed fraction

Let's convert it to an improper fraction by multiplying the denominator by the whole number, then adding the numerator

13/4

Multiply the values

7 × 13/4

91/4

Divide the values

22 3/4

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Answer:

4 centimetres is the length of each edges of the cube

Answer:

4 centimeters

Step-by-step explanation:

Answer: congruent

Step-by-step explanation:

they look like the same shape

Answer:

There are about 12 people with genetic mutation.

Step-by-step explanation:

If you write out the equation, it should look like this:

600*0.02 = 12

Therefore, the answer is that there are about 12 people with genetic mutation.

The derivative of the function is determined as 6πx^(π - 1) + 54.15x^(4.7).

To find the derivative of f(x), we need to apply the power rule and the constant multiple rule.

Using the power rule for f(x) = 6x^π+ 9.5x^5.7 + π^5.7, we have:

f'(x) = 6πx^(π - 1) + 9.5(5.7)x^(5.7 - 1)

Next, applying the constant multiple rule, we get:

f'(x) = 6πx^(π - 1) + 54.15x^(4.7)

So the derivative of f(x) is:

f'(x) = 6πx^(π - 1) + 54.15x^(4.7)

Thus, the derivative of the function is determined by applying the power rule as shown above.

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As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.

A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to Pythagoras' Theorem, is equal to the sum of the squares of the lengths of the other two sides (the legs). Formally, Pythagoras' theorem asserts that if a right triangle has legs of lengths a, b, and c, and a hypotenuse of length c, then:

[tex]a^2 + b^2 = c^2[/tex]

Pythagoras, an ancient Greek mathematician, is credited with discovering and proving this theorem, therefore it bears his name.

given

The Pythagorean theorem can be used to determine the length of the omitted side. Let x be the length of the side that is missing. The right triangle that results has a hypotenuse that is top-bottom in length and legs that are x and slant in length. This can be expressed as:

x2 + slant2 = (top - bottom)2

$$

To put it simply, we have:

\begin{align*} \s(top - bottom) (top - bottom)

2 &= x 2 + slant 2, top 2 - 2top "cdot bottom + bottom 2 - slant 2," x 2 &= "sqrt" top 2 - 2top "cdot bottom + bottom 2 - slant 2," and "end align"

begin-aligning* x = sqrt((5),2,5,8,and(8),2,-7,2). sqrt = 25 - 80 + 64 - 49; sqrt = 40; sqrt = boxed 2i sqrt 10; end align;

As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.

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Answer:

≈41,4∘

Step-by-step explanation:

I added a photo of my solution

Answer: 0.0294117647

The surface area οf each dοg tοy is apprοximately 28.26 square inches.

Surface area refers tο the tοtal area οf the οuter surface οf a three-dimensiοnal οbject. It is measured in square units, such as square inches οr square meters.

The fοrmula fοr the surface area οf a sphere is:

A = 4πr²

where r is the radius οf the sphere.

The diameter οf the dοg tοy is given as 3 inches. The radius, which is half οf the diameter, is therefοre:

r = 3/2 = 1.5 inches

Substituting this value intο the fοrmula fοr surface area, we get:

A = 4π(1.5)²

A = 4π(2.25)

A = 9π

Using a calculatοr tο apprοximate the value οf π tο 3.14, we get:

A ≈ 28.26

Therefοre, the surface area οf each dοg tοy is apprοximately 28.26 square inches.

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Answer:

C. 180° (since x and y are supplementary angles).

Using expressions, we can get the following:

a. If W (6.5) =75, H (6.5) = 85

b. If W (2) = 60, H (2) = 70

c. W (x) + 10

Expressions are statements in mathematics that include variables, numbers, or both, as well as at least two terms connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations.

The equation x + y, which combines the terms x and y with an addition operator, serves as an illustration. Expressions can be classified into two categories in mathematics: algebraic expressions, which also contain variables, and numerical expressions, which only contain numbers.

W(x) gives the temperature W in the apartment x hours after midnight.

H(x) gives the temperature H x hours after midnight when it is hot outside.

When it is hot outside, the owner changes the settings to be exactly 10 degrees warmer than W.

So,

H (x) = W(x) + 10

If W (6.5) =75, then

H (6.5) =W (6.5) + 10

= 75+10

= 85

If W (2) = 60, then

H (2) = W (2) + 10

= 60+ 10

= 70

The expression of H in terms of W:

W (x) +10

Hence the equation:

H(x) = w(x) + 10

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