write the ratio as a fraction in simplest form 2 1 3 feet 4 1 2 feet

Answer: 8.9

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A because 16(x + y) = (16x + 16y)

Answer:

16(x+y)

Step-by-step explanation:

16 times x + 16 times y= 16x+16y

2(2x+6y)=4x+12y

(2x+6y)+(2x+6y)=4x+12y

4(x+3y)=4x+12y

Hence, 16(x+y) is not equivalent to 4x+12y.

The equation for finding w is  4 + 2 * w = 35 and the weight of each bag is found to be w = 15.5 kg.

What is an equation?

The equals sign is a symbol that indicates the equality of two expressions in a mathematical equation. By utilising the equal sign ("="), two expressions are joined in an equation. The two expressions on either side of the equals sign are referred to as the equation's "left" and "right" sides, respectively. We typically think of the right side of an equation as zero. If there is no symbol indicating "equal to," a statement is not an equation. That will be taken into consideration as an expression. Equations can be of several sorts, including linear, quadratic, cubic, and others. Many terms, variables, and operators are not necessary for an equation to have one or both sides.

The complete question is given below.

In the question, it is mentioned that,

the weight of the bags w is the same.

The weight of the backpack = 4kg

Total weight of the baggage = 35 kg

We are asked to find the equation to determine w.

So according to the given information, we can write the equation as:

4 + 2 * w = 35

Now solving this equation, we can find the weight w.

2w = 35-4 = 31

w = 15.5kg

Therefore the equation for finding w is  4 + 2 * w = 35 and the weight of each bag is found to be w = 15.5 kg.

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Answer:

\((f o g)(x) = f(g(x))\\ = f(x-6)\\ = (x-6)^{2} +4(x-6)-60\\ = x^{2} -12x+36+4x-24-60\\ = x^{2} -8x-48\\ = (x-12)(x+8)\)

Step-by-step explanation:

After calculating the unit rate for coffee we can infer that she bought 5 pounds of coffee.

A rate in mathematics is the ratio of two related variables stated in different units. If one of these variables is written as a single unit in the denominator of the ratio and it is assumed that this quantity can be changed on a regular basis (i.e., is a variable and the independent), the ratio's numerator indicates the corresponding rate of change in another (dependent) variable.

A rate is commonly referred to as an output-input ratio or a benefit-cost ratio. Miles per hour, for example, is the output (or profit) in terms of miles travelled from a few hours of travelling somewhere (a cost in time) (at this velocity).

Money on the gift card = $80

Amount left after buying coffee = $ (80-43.70) = $ 36.30

Unit rate of coffee =$ 7.26

Now we have to divide the total amount of money by the unit rate to calculate the amount of coffee bought.

amount of coffee bought = $(36.30 ÷ 7.26) = 5 pounds

Hence she bought 5 pounds of coffee.

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Thus, the equation that connects C and X is C = 100X + 5.33X² and the depth of the well if the cost is 12000 naira is 38.85 meters.

1. Deriving an equation that connects C and X together The cost C of sinking a well X meters deep varies partly as X and partly X². That is,C = kX + pX²,Where k and p are constants to be determined. To determine the value of k and p, we can use the information given that the cost is 5000 naira if the depth is 30m and cost is 8000 naira if the depth is 50m.From the above information, we can get two equations:

5000 = 30k + 30²p8000 = 50k + 50²p

We can use the first equation to get the value of k and substitute it in the second equation.

5000 = 30k + 900p ⇒ k = 166.67 - 10p

Substituting k in the second equation gives:

8000 = 50(166.67 - 10p) + 2500p

Solving the above equation gives:

p = 5.33 And, k = 100.00

Substituting k and p in the cost equation gives:

C = 100X + 5.33X²2. Finding the depth of the well if the cost is 12000 naira

Given that C = 12000, we need to find the value of X.C = 100X + 5.33X² ⇒ 5.33X² + 100X - 12000 = 0

Solving the above quadratic equation using the quadratic formula gives:

X = (-b ± √(b²-4ac))/2a = (-100 ± √(100² - 4×5.33×(-12000)))/2×5.33= (-100 ± 540.71)/10.66= 38.85 or -23.45

'Since the depth can't be negative, the depth of the well is X = 38.85 meters when the cost is 12000 naira.

Thus, the equation that connects C and X is C = 100X + 5.33X² and the depth of the well if the cost is 12000 naira is 38.85 meters.

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If Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. Then after 14 weeks Megan and Connor have saved the same amount.

Two or more expressions with an equal sign is called as equation.

Let  x=the number of weeks

For Megan we have:

50+5.5x

For Connor we have:

18.50+7.75x

Let us equate Megan's and Connor to have same amount.

50+5.5x=18.50+7.75x

Let us take variables on one side and numbers on other side.

50-18.50=7.75x-5.5x

31.5=2.25x

Divide both sides by 2.25

x=14

Hence after 14 weeks Megan and Connor have saved the same amount.

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Answer:

\(g(x) = \frac{1}{4}x^2 - 3x + 8\)

Step-by-step explanation:

g(x) = 1/4(x - 4) (x - 8)

g(x) = 1/4(x^2 - 8x - 4x + 32)

g(x) = 1/4(x^2 - 12x + 32)

g(x) = 1/4x^2 - 3x + 8)

Answer:

145 ft below the surface of the ocean

Step-by-step explanation:

Simply subtract 165 feet from 310 feet because the depth is decreasing.  It can also help to sketch out the submarine to better visualize it :)

Answer:

1/6 = 0.1667

Step-by-step explanation:

sample space = 6

the probability of rolling a number equal to 1 = 1/6

Using a quadratic function, it is found that:

a) The coordinates of the second x-intercept are: (50,0).

b) The vertex shows the maximum flight of the projectile.

c) The coordinates of the vertex are (25, 62).

3) The graph of the equation y = -0.0992(x² - 50x) is given at the end of the answer.

A quadratic function has two x-intercepts, x' and x'', and is defined as follows:

y = a(x - x')(x - x'').

The intercepts are given as follows:

The vertex is found as follows:

Hence the coordinates are: (25, 62).

The equation can be defined as follows:

y = ax(x - 50)

y = a(x² - 50x).

When x = 25, y = 62, hence the leading coefficient is found as follows:

62 = a(25² - 50(25))

-625a = 62

a = -62/625

a = -0.0992.

Hence the equation is:

y = -0.0992(x² - 50x).

The domain of the function is between the roots, hence 0 ≤ x ≤ 50, and the graph is sketched at the end of the answer.

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Answer: 0.6763 cm∧2

Step-by-step explanation: Variance is one of the measures of dispersion which is the the second central moment in probability. It is defined as a measure of by how much the values in a data set differs from the mean of the values. Thus it is the average of the squares of the deviations from the mean as this ensures that both the negative and positive deviations do not cancel each other out.

The sample variance would be calculated as follows:

Population size is 7 (5.6 4.9 6.0 5.1 5.5 5.1 7.5)

Mean: Sum of samples / population size ;

(5.6 4.9 6.0 5.1 5.5 5.1 7.5) / 7 = 5.67

Applying the formula for variance: [ Summation (x - mean) ] / population size =( |5.6 - 5.67| + |4.9 - 5.67| + |6.0 - 5.67| + (|5.1 - 5.67|) * 2 + | 5.5 - 5.67| + |7.5 - 5.67|) / 7 = 0.6763 cm^2

Answer:

251 miles

Step-by-step explanation:

To answer this, we first must subtract the total Bill ended up paying by the base fee:

222.77 - 16.95 = 205.82

Now, we divide this total by 82 cents:

205.82 / 0.82 = 251

So, Bill drove the truck 251 miles

Hope this helps :)

Answer:

2×3×3×5

Step-by-step explanation:

2×

\({3}^{2} \)

×5

In hybridization experiments with peas, the probability of an offspring pea having green pods is 0.75. The offspring peas are randomly selected in groups of 28.

In this scenario, the probability of an offspring pea having green pods is given as 0.75. This means that out of every 100 offspring peas, we can expect approximately 75 of them to have green pods.

When the offspring peas are randomly selected in groups of 28, we can use the concept of probability to determine the expected number of peas with green pods in each group. Since the probability of an individual pea having green pods is 0.75, the expected number of peas with green pods in a group of 28 can be calculated by multiplying the probability by the group size:

Expected number of green pods = 0.75 * 28 = 21

Therefore, in each group of 28 randomly selected offspring peas, we can expect approximately 21 of them to have green pods. This probability and expected number provide insights into the distribution and characteristics of the offspring peas in the hybridization experiments.

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Comparing this estimated change with the actual change, we can see that the actual change in f is -0.978, while our estimate from the total differential is -0.09. Therefore, our estimate using the total differential is not very accurate, as it differs significantly from the actual change in f.

To approximate the change in the values of the function f(x, y, z) from point P to point Q, we can use the concept of total differential. The total differential allows us to estimate how small changes in the variables x, y, and z will affect the value of the function f. The total differential of f(x, y, z) can be written as:

df = (∂f/∂x)dx + (∂f/∂y)dy + (∂f/∂z)dz

Where (∂f/∂x), (∂f/∂y), and (∂f/∂z) are the partial derivatives of f with respect to x, y, and z, respectively.

The function f(x, y, z) = x + y + z / xyz, and the points P(-1, -2, 4) and Q(-1.04, -1.98, 3.97), we can calculate the total differential df from P to Q. To do this, we need to identify the partial derivatives (∂f/∂x), (∂f/∂y), and (∂f/∂z) and substitute the values of dx, dy, and dz for the corresponding changes in x, y, and z from P to Q.

Let's calculate the partial derivatives:

(∂f/∂x) = 1 + yz / xyz (∂f/∂y) = 1 + xz / xyz (∂f/∂z) = 1 + xy / xyz

Now, let's calculate the changes in x, y, and z from P to Q:

dx = Qx - Px = -1.04 - (-1) = -0.04

dy = Qy - Py = -1.98 - (-2) = -0.02

dz = Qz - Pz = 3.97 - 4 = -0.03

Substituting these values into the total differential equation, we get:

df = (1 + yz / xyz)(-0.04) + (1 + xz / xyz)(-0.02) + (1 + xy / xyz)(-0.03)

Simplifying this expression, we get the approximate change in f from P to Q. To compare this estimate with the actual change in f, we need to calculate the value of f at both points P and Q. Substituting the coordinates of P into the function f(x, y, z), we get:

f(P) = f(-1, -2, 4) = (-1) + (-2) + 4 / (-1)(-2)(4) = 1 / 8 = 0.125

Substituting the coordinates of Q into the function f(x, y, z), we get:

f(Q) = f(-1.04, -1.98, 3.97)

= (-1.04) + (-1.98) + 3.97 / (-1.04)(-1.98)(3.97)

= -6.99 / 8.193552

= -0.853

The actual change in f from P to Q is given by:

Δf = f(Q) - f(P) = -0.853 - 0.125 = -0.978

Now, we can compare this actual change in f with our estimated change in f from the total differential. By evaluating the expression for df that we obtained earlier, we identify:

df ≈ -0.04 + (-0.02) + (-0.03) = -0.09

As the given question is difficult to understand and incomplete, the complete question is "Given the function f(x, y, z) = (x + y + z) / (XYZ), use a total differential to approximate the change in the values of f from point P to point Q. Compare your estimation with the actual change in f. Point P has coordinates (-1, -2, 4), and point Q has coordinates (-1.04, -1.98, 3.97)."

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Answer:

25 times

Step-by-step explanation:

From the question:

Number of :

Yellow = 2

Red = 3

Blue = 5

P(blue) = required outcome / Total possible outcomes = 5/ 10 = 1/2

If marble is drawn with replacement :

Number of times a blue marble is drawn from 50 trials :

P(blue marble) * 50

1/2 * 50

= 25 times

The quotient is 1111. The process continues until the result is less than the divisor.

To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:

Step 1: Initialize the dividend and divisor

Divisor: 00011

Dividend: 1011

Step 2: Append zeros to the dividend

Divisor: 00011

Dividend: 101100

Step 3: Determine the initial guess for the quotient

Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.

Step 4: Subtract the divisor from the dividend

101100 - 00011 = 101001

Step 5: Determine the next quotient bit

Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

Step 6: Subtract the divisor from the result

101001 - 00011 = 100110

Step 7: Repeat steps 5 and 6 until the result is less than the divisor

Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100110 - 00011 = 100011

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100011 - 00011 = 100001

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100001 - 00011 = 011111

Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.

011111 - 00000 = 011111

Step 8: Remove the extra zeros from the result

Result: 1111

Therefore, the quotient is 1111.

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Answer:

tha points ssry

Step-by-step explanation:

ssry

Answer:

The answer would be the second one.

Step-by-step explanation:

The answer is this because 65% as a decimal is .65 and the second equation is the only one with a .65 in it. It is also the only equation with 24 in it as well.

The statement "If A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3"  is true as the determinant of a 3x3 matrix equals the volume of the parallelepiped determined by its columns.  The correct option is B).  The second statement "det A^T = (- 1)det A" is false as det A^T = (-1)^(number of row interchanges) det A for any n x n matrix A. So, the correct option is B).

The first statement is true, and the correct answer is: "The statement is true because if A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3. Because det A greater than or equal to 0 for all 3 times 3 matrices A, it follows that |det A| = det A." So, the correct answer is B).

The second statement is also false, and the correct answer is: "The statement is true because a row interchange is needed to turn a matrix into its transpose. A row interchange changes the sign of the determinant." So, the correct ansnwer is B).

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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The approach described by the hospital marketing manager, which involves handing out patient satisfaction surveys to every 20th patient who leaves the urgent care facility for the next week, uses the "systematic sampling" method.

The hospital marketing manager's approach to having the patient coordinator hand out the patient satisfaction survey on discharge to every 20th patient who leaves the urgent care facility for the next week is an example of systematic sampling. This means that the patients are selected at regular intervals, in this case, every 20th patient, based on their coordinates in the discharge process. The approach is only valid for the specified week and may not be representative of the overall patient satisfaction levels of the hospital.

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Answer:

346,733 rounded to the nearest thousand is 347,000

Step-by-step explanation:

the thing he did wrong was he rounded down instead of up, you should know to go up or down by looking at the hundreds and seeing if it's closer the last hundred or the next hundred.

Assuming a normal distribution, about 95% of the data lies within 2 standard deviations of the mean.

This means that if we have data on the number of cars per household and the distribution follows a normal distribution, about 95% of the households will have a number of cars within 2 standard deviations of the mean. For example, if the mean number of cars per household is 2.5 and the standard deviation is 0.75, then about 95% of the households will have a number of cars between 1 and 4 (i.e., within 2 standard deviations of the mean). This corresponds to a range of 1.75 to 3.25 cars, which includes 2.5 cars (the mean).

It's important to note that this is an approximate value, and the actual percentage may vary slightly depending on the specific characteristics of the distribution.

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Answer:

(5) 84° and 96° ; (6) 40° and 50°

Step-by-step explanation:

5) Supplementary angles are in the ratio 7 : 8

So 7x + 8x = 180°

15x = 180

x = 180/15

x = 12

The angles are 7x = 7 * 12 = 84° ; 8x = 8 * 12 = 96°

6) Complementary angles are in the ratio 4 : 5

So 4x + 5x = 90°

9x = 90

x = 90/9

x = 10

The angles are 4x = 4 * 10 = 40° ; 5x = 5 * 10 = 50°

There are two types of elastic forces- compression and tension.Something that is elastic can return to its original shape after being stretched or compressed. tension- The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process

y³√45x⁷y⁵ in its simplest form is 3√5y⁵x³√x√y

An expression is combination of variables, numbers and operators.

The given expression is y³√45x⁷y⁵

y³√9×5 x⁷y⁵

In the given expression x and y are the variables.

=y³3√5x³.√x. y²√y.

=y⁵.3√5x³√y√x

=3√5y⁵x³√x√y

Hence,y³√45x⁷y⁵ in its simplest form is 3√5y⁵x³√x√y

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The given inequality is

Let's solve for x.

Given that the inequality is "less than or equal to", the interval mos include 2.