Complete the factored form of the linear expression 21x + 14y = ( ) ( + )​

Answer:

x<4

Step-by-step explanation:

\(x + 1 > -5( 7-2x) \\\\\mathrm{Expand\:}-5\left(7-2x\right):\quad -35+10x\\x+1>-35+10x\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\x+1-1>-35+10x-1\\\\Simplify\\x>10x-36\\\\\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}\\x-10x>10x-36-10x\\Simplify\\-9x>-36\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-9x\right)\left(-1\right)<\left(-36\right)\left(-1\right)\\\\Simplify\\9x<36\)

\(\mathrm{Divide\:both\:sides\:by\:}9\\\frac{9x}{9}<\frac{36}{9}\\\\x<4\)

Answer:

Sodas: 72

Hotdogs: 42

Step-by-step explanation: First you take 114 and subtract 30 from it since there are 30 more sodas. You then would take the remaining 84, and divide it between the two giving you 42 hotdogs and 42 sodas. Now remember the 30 we had? Youre gonna add that to the 42, giving you 72 sodas and 42 hotdogs.

Hey this is only 5 points

Answer:

18

Step-by-step explanation:

The coordinates of point P, which is 2/5 of the way from A to B on the directed line segment AB, are approximately (-12/5, 32/5).

To find the point P that is 2/5 of the way from A to B on the directed line segment AB, we can use the following formula:

P = A + (2/5) * (B - A)

Given:

A = (-8, -2)

B = (6, 19)

Let's calculate the coordinates of point P:

P = (-8, -2) + (2/5) * ((6, 19) - (-8, -2))

P = (-8, -2) + (2/5) * (14, 21)

P = (-8, -2) + (28/5, 42/5)

P = (-8 + 28/5, -2 + 42/5)

P = (-40/5 + 28/5, -10/5 + 42/5)

P = (-12/5, 32/5)

Therefore, the coordinates of point P, which is 2/5 of the way from A to B on the directed line segment AB, are approximately (-12/5, 32/5).

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Answer: 0.512

Step-by-step explanation:

256/32=8

8*(0.4)^3=

8*0.064=0.512

y=0.512

The value of y is 0.8 when x is 256.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

x is directly proportional to the cube of y.

Implies that,

x ∝ y³

Or x = k . y³        (1)

Here, k is a constant.

Substitute x = 32 and y = 0.4 in equation (1),

32 = k (0.4)³
32 = k (64/1000)

k = 1000/2

k = 500

To find the value of y when x = 256 and k = 500,

From equation (1)

256 = 500 y³

y³ = 256 / 500

y³ = 64/ 125

y = 4/5

y = 0.8

The required value of y is 0.8 when x = 256.

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The monthly rate for the given loan is 1.0118%.The annual rate for this loan is 12.1423%.

Given loan: $150,000

Payment per month: $1,770

Duration of loan: 10 years

Interest = ?

The formula for monthly payment is given by:

\(PV = pmt x (1 - (1 + r)^-n) / r\)

Where, PV is the present value, pmt is the payment per period, r is the interest rate per period and n is the total number of periods.Solving the above formula for r will give us the monthly rate for the loan.

r = 1.0118%The monthly rate for the given loan is 1.0118%.The annual rate can be calculated using the following formula:

Annual rate = \((1 + Monthly rate)^12 - 1\)

Annual rate = 12.1423%

The annual rate for this loan is 12.1423%.The effective annual rate can be calculated using the following formula:

Effective annual rate =\((1 + r/n)^n - 1\)

Where, r is the annual interest rate and n is the number of times interest is compounded per year.If interest is compounded monthly, then n = 12

Effective annual rate = (1 + 1.0118%/12)^12 - 1

Effective annual rate = 12.6801%

The effective annual rate for this loan is 12.6801%.

Total amount paid after 10 years = Monthly payment x Number of payments

Total amount paid after 10 years = $1,770 x 120

Total amount paid after 10 years = $212,400

The total amount paid after 10 years is $212,400.

The future value for this loan can be calculated using the following formula:

FV = PV x (1 + r)^n

Where, PV is the present value, r is the interest rate per period and n is the total number of periods.If the loan is paid off in 10 years, then n = 120 (12 payments per year x 10 years)

FV = $150,000 x (1 + 1.0118%)^120

FV = $259,554.50

The future value for this loan is $259,554.50.

Thus, the monthly rate for the loan is 1.0118%, the annual rate for this loan is 12.1423%, the effective annual rate for this loan is 12.6801%, the total amount paid after 10 years is $212,400 and the future value for this loan is $259,554.50.

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The smallest value of x in the Poisson distribution is 0, which means that no cars can pass through the intersection in a given minute.

For explain further, a Poisson distribution is a statistical model that describes the probability of a given number of events occurring in a fixed period of time, such as cars passing through an intersection in a minute.

In a Poisson distribution, the probability of x events occurring in a given minute is given by the equation P(x) = e-λλx/x!, where λ is the average number of events in a given minute. In this case, λ would be the average number of cars that pass through the intersection per minute.

The probability of 0 cars passing through the intersection in a given minute is e-λλ0/0! = 1, which is the highest probability in the distribution. Therefore, the smallest value of x in a Poisson distribution is 0.

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if you do 24 x 4 you get 96  so that mean multiply 3 x 4 too and you get 12 so the answer is he can run 12 miles in 96 minutes

Answer:

Hello!!

Alan can run 3 miles in 24 minutes. If he maintains the same pace, what the greatest number of miles he can run in 96 minutes is 12 miles.

Step-by-step explanation:

\(96\) ÷ \(24=4\)

\(4\) × \(3=12\)

Hope this helps!!

Answer:B

Step-by-step explanation: had the question before

The smallest value within the class is the lower class limit, and the largest value within the class is the upper class limit.

A class limit is a set of boundary values in the form of a range that describes the lowest and highest data values that a class can contain. The lower class limit refers to the smallest data value in a class, whereas the upper class limit refers to the largest data value in a class. The width of a class is determined by the difference between the upper and lower class limits. Here are a few examples to give you a better understanding of how this works:

Class:              5-9 5 9

Lower Limit:    10-14 10 14

Upper Limit:    15-19 15 19

This shows class limits for three different classes.

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After d days, the number of lily pads in the pond can be calculated using the formula 2^d. So, if d is the number of days, then the number of lily pads after d days would be 2^d.

Each day, the number of lily pads doubles. So, on the first day, there is 1 lily pad. On the second day, the number doubles to 2. On the third day, it doubles again to 4, and so on. This doubling pattern continues for d days.

To calculate the number of lily pads after d days, we raise 2 to the power of d (2^d). This is because each day, the number of lily pads doubles, which can be represented as 2^1, 2^2, 2^3, and so on. By substituting the value of d into the equation, we can find the number of lily pads after d days.

For example, if d = 5, then the number of lily pads after 5 days would be 2^5 = 32. This means that there would be 32 lily pads in the pond after 5 days.

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Answer:

7q-35

Step-by-step explanation:

Answer: The answer is B!

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

x=27/28

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−14+x3=2

Step 1: Simplify both sides of the equation.

2x−14+x3=2

2x+−14+13x=2

(2x+13x)+(−14)=2(Combine Like Terms)

73x+−14=2

73x+−14=2

Step 2: Add 1/4 to both sides.

73x+−14+14=2+14

73x=94

Step 3: Multiply both sides by 3/7.

(37)*(73x)=(37)*(94)

x=27/28

Answer:

x=27/28

Answer:

999

Step-by-step explanation:

i got this by adding 288 and 711

hope this helps

The answer is a.) The probability of landing on orange is greater than the probability of landing on purple.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

A spinner with repeated colors numbered from 1 to 8 is shown.

Sections 1 and 8 are purple.

Sections 2 and 3 are yellow.

Sections 4, 5, and 6 are blue.

Section 7 is orange.

A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.

so, we get,

true statement about probability is,

The probability of landing on orange is greater than the probability of landing on purple.

because, there are more spaces for blue than any other section.

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The first car has a higher miles per gallon rating with 27.03

The miles per gallon (mpg) rating for a car, we can use the formula

mpg = 100 / (gallons per 100 miles)

For the first car with a rating of 3.7 gallons per 100 miles

mpg = 100 / 3.7 ≈ 27.03 mpg

For the second car with a rating of 4.3 gallons per 100 miles

mpg = 100 / 4.3 ≈ 23.26 mpg

Comparing the two mpg ratings, we find that the first car has a greater mpg rating of 27.03 mpg compared to the second car with a rating of 23.26 mpg. Therefore, the first car has a higher mpg rating.

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1) The gravimetric moisture content of the soil at field capacity is approx 27.62%.

2) The dry bulk density of the sample is approximately 1.193 g/cm^3.

3) The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.

1) The gravimetric moisture content of the soil at field capacity can be calculated using the following formula:

Gravimetric Moisture Content = ((Wet Weight - Dry Weight) / Dry Weight) * 100

Given:

Wet Weight = 274.1 g

Dry Weight = 214.7 g

Using the formula, we can substitute the values:

Gravimetric Moisture Content = ((274.1 - 214.7) / 214.7) * 100

Gravimetric Moisture Content = (59.4 / 214.7) * 100

Gravimetric Moisture Content ≈ 27.62%

The gravimetric moisture content of the soil at field capacity is approximately 27.62%.

The gravimetric moisture content represents the amount of water present in a given mass of soil. By subtracting the dry weight of the soil from the wet weight and dividing by the dry weight, we can determine the proportion of water in the sample. Multiplying by 100 gives the moisture content as a percentage.

1a. The dry bulk density of the sample can be calculated using the following formula:

Dry Bulk Density = Dry Weight / Sample Volume

Given:

Dry Weight = 214.7 g

Sample Volume = 180 cm^3

Substituting the values into the formula:

Dry Bulk Density = 214.7 g / 180 cm^3

Dry Bulk Density ≈ 1.193 g/cm^3

The dry bulk density of the sample is approximately 1.193 g/cm^3.

Dry bulk density refers to the mass of dry soil per unit volume. To calculate it, we divide the dry weight of the soil by the sample volume.

1b. The porosity of the sample can be calculated using the following formula:

Porosity = (1 - (Dry Bulk Density / Particle Density)) * 100

The particle density for soil is usually around 2.65 g/cm^3.

Given:

Dry Bulk Density = 1.193 g/cm^3

Particle Density = 2.65 g/cm^3

Substituting the values into the formula:

Porosity = (1 - (1.193 / 2.65)) * 100

Porosity ≈ 54.96%

The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.

Porosity represents the void space within a soil sample. It is calculated by subtracting the ratio of the dry bulk density to the particle density from 1 and multiplying by 100 to get the percentage. In this case, the particle density of 2.65 g/cm^3 is a typical value for soil.

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The relative frequency distribution of the values of the mean of these 15,504 different samples would specify the sampling distribution of the mean.

The sampling distribution of the mean refers to the distribution of sample means obtained from repeated sampling from the same population.

In this case, we have 15,504 different samples of size 5 drawn from a population of 20 hospitals.

Each sample has its own sample mean. The relative frequency distribution of these sample means would specify the sampling distribution of the mean.

The sampling distribution of the mean is important in statistics because it allows us to make inferences about the population mean based on the distribution of sample means.

It helps us understand the variability of sample means and provides a basis for constructing confidence intervals and conducting hypothesis tests.

Therefore, the relative frequency distribution of the mean values from the different samples would describe the characteristics of the sampling distribution of the mean..

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Answer:

70

Step-by-step explanation:

Answer:

(70 / 185) x 100 = 37.84%

Step-by-step explanation:

Answer:

Step-by-step explanation:

To Find :

\( \sf \dashrightarrow \: \frac{4 {}^{8} }{(4 {}^{2} {)}^{ - 3} } \div {4}^{4} = 4 {}^{n} \\ \\ \sf \dashrightarrow \: \frac{4 {}^{8} }{ {4}^{ - 6} } \div {4}^{4} = 4 {}^{n} \\ \\ \sf \dashrightarrow \: {4}^{8 - ( - 6)} \div {4}^{4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{8 + 6} \div {4}^{4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{14} \div {4}^{4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{14 - 4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{10} = 4 {}^{n} \\ \\ \red{\boxed{ \bf \: n = 10}}\)

Solution:

A few changes were made:

New equation:

Solving the equation:

Correct option is B.

Answer:

B)

Step-by-step explanation:

4 + 0.3 + 0.09 = 4.39

standard form is written in the form of \(a \times 10^n\), where \(a\) is a number bigger than or equal to 1 and less than 10.

Therefore, 4.39 written in standard form is \(\mathsf{4.39 \times 10^0}\)

   To solve this problem use the property of similar triangles,

 "Corresponding sides of the similar triangles are proportional"

By using this property, height of the parasailer is 160 feet.

From the figure attached,

Let the height (PQ) of the parasailer = x ft

Height of the parasailer AB = 25 ft.

And the length of the rope AC = 2.5 ft.

Since, both the triangles ΔABC and ΔPQR are the similar triangles, their corresponding sides will be proportional.

\(\frac{AB}{PQ}=\frac{AC}{PR}\)

\(\frac{2}{x} =\frac{2.5}{200}\)

\(x=\frac{200\times 2}{2.5}\)

\(x=160\) ft

        Therefore, height of the parasailer is 160 feet.

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Answer:

4(x+2)=3(x-2)

Step-by-step explanation:

4x+8=3x-6

4x-3x=-8-6

x=-14