Which list contains only composite numbers? 12, 37, 54, 80, 117,
31, 44, 57, 64, 92,
26, 53, 66, 84, 96,
6, 24, 51, 72, 105,​

Answer:

2√97

Step-by-step explanation:

BD² = BC² + DC²

⇒ BD = √BC² + DC²

= √(18)² + (8)²

= √324 + 64

= √388

Rewrite 388 as 2² · 97.

Factor 4 out of 388.

√4(97)

Rewrite 4 as 2².

√2² · 97

Pull terms out from under the radical.

2√97

The result can be shown in multiple forms.

Exact Form:

2√97

Decimal Form:

19.69771560...

do it in your own answer

To determine the values of a and b, we need to establish the similarity between triangles ABC and DEF and find the corresponding coordinates.

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.

First, let's find the lengths of the sides of triangle ABC:

AB = √((-2 - (-2))^2 + (3 - 1)^2) = √0 + 4 = 2

BC = √((0 - (-2))^2 + (3 - 3)^2) = √4 + 0 = 2

AC = √((-2 - 0)^2 + (1 - 3)^2) = √4 + 4 = √8 = 2√2

Now, let's find the lengths of the sides of triangle DEF:

DE = √((a - 4)^2 + (b - (-1))^2)

EF = √((0 - 4)^2 + (-1 - (-1))^2) = 4

DF = √((a - 0)^2 + (b - (-1))^2)

Since the triangles are similar, the ratios of the corresponding side lengths must be equal:

AB/DE = BC/EF = AC/DF

2/(DE) = 2/4 = 2√2/(DF)

Simplifying, we get:

DE = 4

2/(4) = 2√2/(DF)

Solving the equation, we find:

1/2 = 2√2/(DF)

DF = 4√2

Therefore, the length of DF is 4√2. From the coordinates of F(0, -1), we can determine that the y-coordinate of point D must also be -1. Hence, b = -1. To find the x-coordinate of point D, we equate the lengths of AB and DE: 2 = √((a - 4)^2 + (1 - (-1))^2)

4 = (a - 4)^2 + 4

(a - 4)^2 = 0

a - 4 = 0

a = 4

Therefore, the values of a and b are a = 4 and b = -1, respectively.

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Answer:

a = b(10)

Step-by-step explanation:

Amy made 10x the amount of muffins than the bakery. So if the bakery made 10 muffins, Amy made 100 muffins. Hopefully this helps!

Answer:

(A). X + 27

Step-by-step explanation:

4(x+3) + 3(5-x)

Answer:

4(x+3)+3(5-x)

=4x+12+(15-3x)

=4x+12+15-3x

=x+27

so its A (x+27)

The stress in a concrete cylinder with a diameter of 6 inches and subjected to a compressive force of 122,700 pounds is approximately 4,812.5 pounds per square inch (psi).

Stress is defined as the force applied per unit area of a material. To calculate stress, we divide the applied force by the cross-sectional area of the object.

For the steel rod, the applied tension force is 120,000 pounds, and the cross-sectional area is 2.4 square inches. Therefore, the stress can be calculated as:

Stress = Tension Force / Cross-sectional Area

= 120,000 pounds / 2.4 square inches

= 50,000 psi

Hence, the stress in the steel rod is 50,000 pounds per square inch.

For the concrete cylinder, the compressive force is 122,700 pounds, and the cross-sectional area can be calculated using the formula for the area of a circle:

Cross-sectional Area = π * (radius)^2

= π * (3 inches)^2

= π * 9 square inches

≈ 28.27 square inches

Therefore, the stress in the concrete cylinder can be calculated as:

Stress = Compressive Force / Cross-sectional Area

= 122,700 pounds / 28.27 square inches

≈ 4,812.5 psi

Thus, the stress in the concrete cylinder is approximately 4,812.5 pounds per square inch.

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The estimated cost of producing the 15th unit is $10.30.

Given the following information about a process that makes high-end boards that get mounted on skateboards:Process starts with a unit cost of $13 for the first unit. Learning rate of LR = 0.90.

Solution :Let's use the learning curve formula to calculate the estimated cost of producing the 15th unit.C = a * N^b .Where:

C = cost per unit ,N = cumulative production volume, a = the unit cost of the first unit, b = log(LR) / log(2) = log(0.90) / log(2) = -0.152N = 15a = 13 (given)

Now, b = -0.152

Therefore ,C = 13 * (15)^(-0.152)C = 13 * 0.789C = 10.3 dollars.

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An equation that represent the red graph include the following: B. y = f(x/-1).

In Geometry and Mathematics, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric figures such as bridges, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Generally speaking, a function or an equation y = f(x) can be horizontally enlarged (increased or stretched) by a factor of "k" based on the following transformation rule;

y = f(x/k)

Scale factor, k = -2/2

Scale factor, k = -1.

Therefore, the equation for the red graph is given by:

y = f(x/-1).

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Answer:

hope this helps

Step-by-step explanation:

Answer:

The number is already in standard form: 13450000000

Step-by-step explanation:

This number isn't in scientific notation. It is written like a regular number, which is also standard form.

Answer:

13450000000

Step-by-step explanation:

The number is already in standard form.

Answer:

the answer is y = 1/2 x + 4

Step-by-step explanation:

I really don't know if it was -4 but if it was negative four you put -4 so hopefully this help

Answer:

Explanation:

Given the expression:

First, rewrite the fraction by separating the constants, and variables a and b.

Next, apply the division rule of exponents:

So, we have:

The simplified form of the expression without any negative exponent is:

The ratio of Eesha's share to Dev's share is 4:5 in its simplest form.

Let's start by assigning variables to the shares of Dev, Carly, and Eesha.

Let D be the amount Dev receives.

Then Carly's share is D + £90, since Carly receives £90 more than Dev.

And let E be Eesha's share.

We know that the total amount shared is £720, so we can write the equation:

D + (D + £90) + E = £720

Simplifying the equation, we have:

2D + £90 + E = £720

Next, we are given that the ratio of Carly's share to Dev's share is 7:5. This means that:

(D + £90) / D = 7/5

Cross-multiplying, we get:

5(D + £90) = 7D

Expanding, we have:

5D + £450 = 7D

Subtracting 5D from both sides, we get:

£450 = 2D

Dividing both sides by 2, we find:

D = £225

Now we can substitute the value of D back into the equation to find E:

2(£225) + £90 + E = £720

Simplifying, we have:

£450 + £90 + E = £720

Combining like terms, we get:

£540 + E = £720

Subtracting £540 from both sides, we find:

E = £180

Therefore, the ratio of Eesha's share to Dev's share is:

E : D = £180 : £225

To simplify this ratio, we can divide both values by 45:

E : D = £4 : £5

Hence, the ratio of Eesha's share to Dev's share is 4:5 in its simplest form.

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The production phase could have a larger contribution to acidification potential than the use and end-of-life phases for both conventional vehicles and EVs. The distance traveled in one year of normal commuting could be more suitable in this case.

A. The functional unit, which is defined as the quantified performance of a product system or service that will be used as a reference for conducting the life cycle assessment, is important for evaluating the impacts of products or systems on the environment.

The following are the different functional units that are acceptable or not acceptable to assess the environmental impacts of the product or system.

The first functional unit, one vehicle, is not appropriate as it doesn't represent the amount of driving a person could expect to do if they bought a new car and drove it until the end of its life.

The second functional unit, distance traveled in one full gas tank or battery charge, would not be appropriate for our purpose as it is not clear what type of vehicle it will be used for.

The third functional unit, one year of normal commuting, would not be appropriate as it does not consider all the environmental impacts over the lifetime of the vehicle.

The fourth functional unit, 1 kg of vehicle, would not be appropriate as it is too small of a functional unit to evaluate the environmental impacts of the vehicle.

B. If we also wanted to consider riding the public bus as a personal transportation option, 200,000 miles driven would not be an appropriate choice of functional unit. This is because buses are used for transportation purposes, and they will have different environmental impacts than cars.

Therefore, the distance traveled in one year of normal commuting could be more suitable in this case.

C. One other impact category we could consider is the acidification potential. The production phase could have a larger contribution to acidification potential than the use and end-of-life phases for both conventional vehicles and EVs.

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Answer:

The ratio in simplest form is 8:1

Step-by-step explanation:

Ratio of chairs to tables

chairs: tables

160:20

Divide each side by 20.

160/20 : 20/20

8:1

The ratio in simplest form is 8:1

Answer:

D. 8 to 1

Step-by-step explanation:

To find the ratio of chairs to tables, we can divide the number of chairs by the number of tables:

Ratio of chairs to tables = Number of chairs / Number of tables

Ratio of chairs to tables = 160 / 20

Ratio of chairs to tables = 8

Therefore, the ratio of chairs to tables in the cafeteria is 8 to 1, which is option D.

Therefore, 150 is the largest integer that is a factor of both 1450 and 2400.

Prime factorization is the process of breaking down a positive integer into its prime factors, which are prime numbers that can divide the integer without a remainder. Every positive integer can be written as a product of prime numbers in a unique way, called its prime factorization.  Prime factorization is important in many mathematical applications, such as finding the greatest common divisor and least common multiple of two or more integers, simplifying fractions, and solving problems related to divisibility, prime numbers, and modular arithmetic.

Here,

To find the largest integer that is a factor of both 1450 and 2400, we need to first express both numbers in terms of their common prime factors and then find the product of the common prime factors raised to their lowest exponent.

The prime factorization of 1450 is 2 × 5² × 29.

The prime factorization of 2400 is 2⁴ × 3 × 5².

To find the common factors of these two numbers, we need to look for the prime factors that appear in both factorizations. These common prime factors are 2, 5², and 3.

To find the largest integer that is a factor of both 1450 and 2400, we need to multiply these common prime factors raised to their lowest exponent:

2 × 5² × 3 = 150

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It can be said that the best Model for the data is for Variable A,

What is Scatter Plot?

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.

In the given two Scatter Plots of Variable A and Variable B

By carefully observing the Scatter Plots it can be said that the best Model for the data is for Variable A,

This is because the deviation of points from the main line representing data is less than that for Variable B

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Answer:

\(5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5\)

The required percentage of regular grade gasoline are;

a) 34%

b) 95.5%

c)4.5%

(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.

$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.

Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.

Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.

(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.

$3.85$ is $1.5$ standard deviations above the mean.

Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.

Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.

(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.

Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.

Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.

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iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855%  of the population has an iq score between 70 and 115

What is z-score?

The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.

Using z tables, you may calculate the proportion of the population that is either below or above the score.

Now, according to the question;

IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.

A z score is determined as follows:

z = (x - μ)/σ

μ = mean of the distribution

σ = standard distribution of the sampling.

Calculation for the z score for x = 70 and  115

z= (70-100)/15

= -30/15

=-2

and x=115

z = (115 - 100)/15

= 15/15

z = 1.0

Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,

P( -2 < z < 1)= P(z<1) - P(z< -2)

                   =  0.8413 - 0.02275

                  = 0.81855

Therefore, the percent of the population has an iq between 70and 115 is 81.855%.

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1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline is dynamic stretching.

2. The stretching technique emphasized in the scenario of a runner performing various stretches for 30 seconds on each side after a run is static stretching.

1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline five times is dynamic stretching. Dynamic stretching involves performing controlled movements that mimic the motions of the activity or sport being performed. In this case, the tennis player is incorporating dynamic movements to warm up and prepare their muscles for the specific demands of playing tennis.

2. The stretching technique emphasized in the scenario of a runner performing a quadriceps stretch, gastrocnemius stretch, and a runner's stretch for 30 seconds on each side of the body after a run is static stretching. Static stretching involves holding a stretch in a stationary position for a certain period of time. In this case, the runner is holding each stretch for 30 seconds, which is a characteristic of static stretching. Static stretching is commonly used to improve flexibility and promote muscle relaxation after exercise.

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In the given scenario, the type of stretching technique being emphasized is Dynamic Stretching.

Dynamic stretching is a type of stretching technique that involves active movements to improve flexibility and range of motion. It is typically performed as part of a warm-up routine before engaging in physical activity. Unlike static stretching, which involves holding a stretch for an extended period, dynamic stretching incorporates dynamic movements that mimic the actions performed during the activity. This helps to warm up the muscles, increase blood flow, and prepare the body for the upcoming exercise or sports activity.

In the given scenario, the type of stretching technique being emphasized is Static Stretching.

Static stretching, on the other hand, is a stretching method where a stretch is held in a fixed position for a prolonged period of time, typically ranging from 15 to 60 seconds. This technique is often used to improve flexibility and increase the length of muscles and tendons. Static stretching is commonly performed during the cooldown phase after exercise or physical activity. It helps to relax the muscles, reduce muscle soreness, and improve overall flexibility and joint mobility.

Both dynamic stretching and static stretching have their benefits and serve different purposes in a fitness or sports routine. Dynamic stretching is effective for warming up the body and preparing it for physical activity, while static stretching is useful for improving flexibility and promoting relaxation in the muscles. It's important to choose the appropriate stretching technique based on your specific goals and the context of your exercise or sports regimen.

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The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

Explanation:

The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.

To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:

Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute

To find the time interval, we can subtract 2 from 8:

Δt = 8 - 2 = 6 minutes

Now we can use the formula for average acceleration:

a = Δv/Δt = (-220)/6 = -40 meters per minute squared

Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

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If the hockey team scores 9 goals in their next game, it means that; the mean would be the most affected.

We are given the data set as;

3, 6, 2, 1, 2, 3, 0, 4, 5, 1, 5, 4.

Let us rearrange in ascending order to get;

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6.

The mean = (0 + 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5 + 6)/12 = 3

Median = (3 + 3)/2 = 3

Mode = 1, 2, 3, 3, 5

Now, if they score 9 goals in their next game, it means that;

Mean = 45/13 = 3.46

Median = 3

Mode remains the same

Thus, mean will be the most affected.

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The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

Trigonometry is a discipline of mathematics that deals with the sides and angles of a right-angled triangle in geometry. As a result, trig ratios are evaluated in terms of sides and angles.

Thus, The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

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Answer: i) We can use the present value of an annuity formula to determine how much Mr. Kyeremeh needs to deposit today:

PV = A * [(1 - (1 + r)^-n)/r]

Where PV is the present value, A is the annual payment, r is the effective annual interest rate, and n is the number of periods.

In this case, A = $1000, r = 3.5%, and n = 10. We can substitute these values into the formula to get:

PV = $1000 * [(1 - (1 + 0.035)^-10)/0.035] ≈ $8,578.32

Therefore, Mr. Kyeremeh needs to deposit approximately $8,578.32 today to provide his daughter with $1000 a year for ten years, assuming a 3.5% effective annual interest rate.

ii) If the daughter saves the income from her father in an account also paying 3.5% effective annual interest, then the future value of the ten payments would be:

FV = A * [(1 + r)^n - 1]/r

Where FV is the future value, A is the annual payment, r is the effective annual interest rate, and n is the number of periods.

In this case, A = $1000, r = 3.5%, and n = 10. We can substitute these values into the formula to get:

FV = $1000 * [(1 + 0.035)^10 - 1]/0.035 ≈ $12,365.86

Therefore, if the daughter saves the income from her father in an account also paying 3.5% effective annual interest, she will have approximately $12,365.86 when she receives the final $1000 payment.

b) After three years, Kofi will have:

FV = P * (1 + r/n)^(n*t)

Where FV is the future value, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $1000, r = 4%, n = 4 (since interest is compounded quarterly), and t = 3. We can substitute these values into the formula to get:

FV = $1000 * (1 + 0.04/4)^(4*3) = $1,343.92

After six years, Kofi will have:

FV = $1,343.92 + $1000 = $2,343.92

Now, we need to find the amount that Ama needs to deposit into her account such that after five years, she will have the same amount as Kofi.

Let X be the amount that Ama deposits. Then after five years, Ama will have:

FV = X * e^(∫0^5 1/6+t dt)

Where FV is the future value and e is the exponential function.

Simplifying the integral, we have:

FV = X * e^(ln(2)) = 2X

Therefore, we need to solve the equation:

2X = $2,343.92

X = $1,171.96

Therefore, Ama needs to deposit approximately $1,171.96 into her account to have the same amount as Kofi after five years.

Answer and Step-by-step explanation:

Ok, it's basically just parts of a circle circumference and area equation. Let's start first by writing down both equations.

C = 2πr

C = πd

A = π\(r^{2}\)

Now, all we have to do is plug in the values into those equations!

4. C = 2π(12)                  A = π(\(12^{2}\))

r = 12

d = 24     <---- (12 times 2 equals 24)

C = 24π

A = 144π   <---- (12 times 12 (itself) equals 144)

5. C = π4.8                  A = π(\(4.8^{2}\))

r = 2.4            <------- (4.8 divided by 2 equals 2.4)

d = 4.8

C = 4.8π

A = 23.04π    <------- (4.8 times 4.8 equals 23.04)

6.  20π = 2πr                  A = π\(r^{2}\)

r = 10            <------- (20π divided by π and divided by 2)

d = 20          <------- (20π divided by π)

C = 20π

A = 100π    <------- (10 times 10 equals 100)

7.  C = 2πr                  81π = π\(r^{2}\)

r = 9            <------- (81π divided by π and square rooted equals 9)

d = 18          <------- (9 times 2 equals 18)

C = 18π      <------- (2 times 9 equals 18, times π)

A = 81π

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Answer:

1.8 $

Step-by-step explanation:

15/100 = 0.15

0.15 * 12 = 1.8

because you are finding dollars/cents which comes in 100 so divide 15/100. Then you have to multiply by 12 because 1% = 0.15 so you are trying to find 12% which is 1.8 dollars

She will be paid 16.8$ from now on.