The masses of four vehicles and the net forces acting on them as they enter a highway are recorded in the table below. Vehicle Mass (kg) Force (N) Sedan 1400 5250 SUV 1900 5250 Truck 2100 5250 RV 2500 5250 Which vehicle has the greatest acceleration as it enters the highway?

Answer:

x=-11

Step-by-step explanation:

-2(x+3)+5x=-39

Remove parenthesis

-2x-6+5x=-39

Collect like terms

3x-6=-39

Move the constant to the right

3x=-39+6

Calculate

3x=-33

Divide both sides by 3

x=-11

Standard deviations are used to measure the variability of the set

The reason they choose the standard deviation as the measure of variability is (a) when plotted, the data set had a normal distribution

When a data is distributed, the data can be measured using the median, the mean or the standard deviation.

If the data is a normal distribution, then the best measure of variability to use is the standard deviation

Hence, the true statement is (a) when plotted, the data set had a normal distribution

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To simplify the given rational expression, proceed as follows:

According to this:

The numerator is 6z-4y

The denominator is (y^2)z

The required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].

To determine the simplified value of  x² +7x +12 divided by x + 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
As per the given data,
Division of function,
=  x² +7x +12/ x + 2
= x² + 7x + 10 + 2 / x +2
= (x + 5)(x + 2) + 2 / x + 2
= (x + 5) (x + 2) / x + 2 + 2 / x + 2
= x + 5  + 2 / (x + 2)

Thus, the required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].

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A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Step-by-step explanation:

The three numbers are 4, 6, and 9.

Three numbers form a geometric progression.

Three numbers in a geometric progression can be written in terms of the first term (a) and the common ratio (r) as a, ar, ar². The second term is increased by 2, so the new terms are a, ar+2, ar².

Then the progression will become arithmetic: ar^2 - (ar+2) = (ar+2) - a

ar² - ar - 2 = ar + 2 - a

ar² - 2ar - a - 2 = 0 ...(1)

On solving equation (1), we get (r-1)(ar+2) = 0

If r = 1, then a, a+2, a+4 are in an arithmetic progression.

ar² + (ar+2+9) = (ar+2+9)²

ar² + ar + 11 = 0

On solving the above equation, we get:

r = (-1 ± √(1-4(11)a))/2a

As r ≠ 1, we have:

r = (-1+√(1-4(11)a))/2a

Substituting the value of r in equation (1), we get:

a = 4

Therefore, the three numbers are 4, 6, 9.

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Answer:

Step-by-step explanation:

\(8+9\div3\times6-5\\= 8+9\div \:3\times \left(6-5\right)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(6-5\right)\::\quad 1\\=8+9\div \:3\times \:1\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\div \:3\times \:1\::\quad 3\\=8+3\\\\= 11\)

\(5+3-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=5+3-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:5+3-2-2\::\quad 4\\=4\)

\(\left(5+3\right)-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(5+3\right)\::\quad 8\\=8-8\div \:4-2\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=8-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:8-2-2\::\quad 4\\=4\)

Answer:

isosceles

Step-by-step explanation:

Answer:

An isosceles

This expression gives us a present value of approximately $1,376,500.

To calculate the present value of John Doe's winnings, we need to find the present value of each individual payment and then sum them up.

The formula to calculate the present value of an annuity is:

PV = C * (1 - (1 + r)^(-n)) / r

Where PV is the present value, C is the annual payment, r is the discount rate, and n is the number of periods.

In this case, John Doe will receive $100,000 each year for 30 years, and the discount rate is 6%. Plugging these values into the formula, we get:

PV = $100,000 * (1 - (1 + 0.06)^(-30)) / 0.06

Calculating this expression gives us a present value of approximately $1,376,500.

Therefore, the correct answer is:

c. $1,376,500.

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The class limits for the class with the highest Frequency are 35 up to 45.

The given distribution table is related to cost of textbooks, frequency, and class limits. To find out the class limits for the class with the highest frequency, we need to determine the class interval with the highest frequency. From the given distribution table, it can be observed that the class interval with the highest frequency is 35 up to 45. The frequency of this interval is 20.

The class limit for this interval will be 35 up to 45, which is Option D. The class limit is the lowest and the highest possible value that can be included in a class interval. For example, if we take the class interval 35 up to 45, the lower class limit is 35 and the upper class limit is 45.

The steps to find the class limits for the class with the highest frequency are given below:

Step 1: Determine the class interval with the highest frequency from the given distribution table, we can determine the class interval with the highest frequency, which is 35 up to 45. This class interval has a frequency of 20.

Step 2: Find the class limits for this intervalThe class limits for the class interval 35 up to 45 will be 35 up to 45, which is Option D. The class limits refer to the smallest and largest values that can be included in a class interval.

Thus, the class limits for the class with the highest frequency are 35 up to 45.

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Answer:

5/8

Step-by-step explanation:

1/5 x 5

1

1/8 x 5

5/8

When comparing the two sets of data to determine the location with the most consistent temperature, the measure of variability that should be used is the interquartile range (IQR). Hence, the answer is: IQR, because Sunny Town is skewed.

The IQR is a measure of the spread or dispersion of data that is less influenced by extreme values or outliers, making it suitable for skewed distributions like Sunny Town. Skewness indicates that the data is not symmetrically distributed, and the IQR is more robust to such deviations.

In the given description, Sunny Town is mentioned as skewed, and therefore, using the IQR would be appropriate to measure the consistency of temperature in that location. The shaded bars in the histogram show different frequencies in each temperature interval, suggesting some variability in the temperature distribution.

On the other hand, the description does not mention any skewness in Desert Landing, which indicates a relatively symmetric distribution. In such cases, the range, which is the difference between the maximum and minimum values, could be a suitable measure of variability.

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Answer:

yes

Step-by-step explanation:

Hey There!

We can find the answer by using proportions of the other sides

What i mean by this is if ADs proportion to AE is the same as BDs proportion to EC then DE is proportional to BC

6/4=1.5

9/6=1.5

Therefore DE is proportional (or similar) to BC

Answer:

option 1

Answer:

Step-by-step explanation:

Let the distance between docks be d.

This is the opposite side to 45° angle of triangle with other sides 400 ft and 500 ft.

Use the law of cosines to find the value of d:

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

the first one ithink

Step-by-step explanation:

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Answer:

Step-by-step explanation:

The exact area between f(x) = 2x and g(x) = 9 – x from the vertical axis to their point of intersection is 13.5 square units. This was obtained by finding the intersection point, setting up and solving the integral, and evaluating the result.

First, we find the point of intersection of the two curves

2x = 9 - x

=> 3x = 9

=> x = 3

So the curves intersect at x = 3.

To find the area between the two curves from the vertical axis to x = 3, we need to integrate the difference between the two functions

QG = ∫(9 - x - 2x) dx, integrated from 0 to 3

= ∫(9 - 3x) dx, integrated from 0 to 3

= [9x - (3/2)x²] from 0 to 3

= (9(3) - (3/2)(3²)) - (9(0) - (3/2)(0²))

= (27 - 13.5) - (0 - 0)

= 13.5

Therefore, the exact area between f(x) = 2x and g(x) = 9 – x is 13.5 square units.

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Answer:

B

Step-by-step explanation:

I graphed the inequality on a graphing calc.

Answer:By solving a system of equations, we will see that the function is continuous for all values of x

Step-by-step explanation:

9 block rhombuses would create 3 hexagons.

In order to increase the total number by three, a hexagon can be divided into a minimum of three rhombuses, each of which can be further divided into four rhombuses. With n being a positive integer, the result is 3n. The top two hexagons in this image are each divided into 8 and 10 rhombuses. The total number of rhombuses that can fit in a hexagon is not limited to multiples of three, given that the total number of rhombuses dividing a hexagon can be raised by three by quartering a single component rhombus. The amount might actually be any integer larger than 7.

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Step-by-step explanation:

This equation does not describe the situation.

Let x be the number of donuts I made.

x-25= 40

(because there is 25 lesser cookies than donuts.

Answer: No; x-25=40

Step-by-step explanation:

40=x-25

cookies equals 25 less than donuts

because donuts is 25 less than cookies

donuts = 65

total = 40 + 40+65=145

Answer:

0.046

answer is correct i took k12 quiz

Answer:

cuz your questions are hard

a) The fourth root of 16 is 2, and cubing 2 gives us 8. b) \(27^{-2/3}\)= 1/9. c) \(5^1/2 * 5^1/2\) = 5 d) \(x^1/2 * x^2/3\) = x^7/6. e) (\(y^-2/5 * y^4\)) / (\(y^1/4\)) = \(y\frac{23}{20}\).

a)  16^(3/4) = 8

To evaluate this expression, we raise 16 to the power of 3/4. The numerator of the exponent, 3, is the power to which we raise the base 16, and the denominator, 4, is the root we take of the result.

In this case, raising 16 to the power of 3/4 is equivalent to taking the fourth root of 16 and then cubing the result. The fourth root of 16 is 2, and cubing 2 gives us 8.

b) 27^(-2/3) = 1/9

Here, we raise 27 to the power of -2/3. The negative exponent indicates that we need to find the reciprocal of the result. To evaluate the expression, we take the cube root of 27 and then square the reciprocal of the result.

The cube root of 27 is 3, and squaring the reciprocal of 3 gives us 1/9.

c) 5^(1/2) * 5^(1/2) = 5

In this case, we have the product of two terms with the same base, 5, and fractional exponents of 1/2. When we multiply terms with the same base, we add the exponents. So, 5^(1/2) * 5^(1/2) is equal to 5^(1/2 + 1/2), which simplifies to 5^1, resulting in 5.

d) x^(1/2) * x^(2/3) = x^(7/6)

Here, we have the product of two terms with the same variable, x, but different fractional exponents. To multiply these terms, we add the exponents. So, x^(1/2) * x^(2/3) is equal to x^(1/2 + 2/3), which simplifies to x^(7/6).

e) (y^(-2/5) * y^4) / (y^(1/4)) = y^(23/20)

In this case, we have a division of two terms with the same variable, y, and different fractional exponents. When dividing terms with the same base, we subtract the exponents.

So, (y^(-2/5) * y^4) / (y^(1/4)) is equal to y^(-2/5 + 4 - 1/4), which simplifies to y^(23/20).

Summary:

a) 16^(3/4) = 8

b) 27^(-2/3) = 1/9

c) 5^(1/2) * 5^(1/2) = 5

d) x^(1/2) * x^(2/3) = x^(7/6)

e) (y^(-2/5) * y^4) / (y^(1/4)) = y^(23/20)

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The probable question may be:
Evaluate the following:

a) 16 ^ (3/4)

b) 27 ^ (- 2/3)

c)  5 ^ (1/2) * 5 ^ (1/2)

d) x ^ (1/2) * x ^ (2/3)

e) (y ^ (- 2/5) * y ^ 4)/(y ^ (1/4))

Answer:

In part A first do addition of all 3 then add the no 6,2,3 then minus both the ans then you will find the final ans

The solution is

a) The equation is A = 6x + 2y + 3z , where x , y and z are the cost of one bubbles , beach ball and sand buckets respectively

b) The total cost is A = $ 23.44

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of all the purchase be represented as A

Now , the equation will be

The cost of one bubbles = x

The value of x = $ 1.49

The cost of one beach ball = y

The value of y = $ 2.00

The cost of one sand buckets = z

The value of z = $ 3.50

Now ,

The cost of 6 bubbles = 6x

The cost of 2 beach balls = 2y

The cost of 3 sand buckets = 3z

So , the total cost of all the purchase A = 6x + 2y + 3z   be equation (1)

On simplifying the equation , we get

A = 6 ( 1.49 ) + 2 ( 2.00 ) + 3 ( 3.50 )

A = 8.94 + 4 + 10.5

A = $ 23.44

Therefore ,the value of A is $ 23.44

Hence , the total cost is $ 23.44

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