The last step mentioned in building equations to solve real-world problems is to check your answer by substituting it into the original equation. Another way to check your answer is to use estimation and to make sure the answer is reasonable for the situation. In the problem above, are all of the solutions reasonable for the given situation? Why or why not?

Answer:

<

Step-by-step explanation:

Is this your question?

-7(4-1r) = 14

-28+7r=14

7r=32

r=32/7

Answer:

x > -22/7

Step-by-step explanation:

To find out which inequality is is equivalent, you solve for x.

-4(x+7) < 3(x-2): distribute variables

-4x-28 < 3x-6: Add 6 to both sided

-4x-22 < 3x: add 4x to both sides

-22 < 7x: divide by 7

-22/7 < x: you can switch sides if prefered but you have to switch sign too

x > -22/7

1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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Answer:

(+,-)

Step-by-step explanation:

quadrant 1 is (+,+)

quadrant 2 is (-,+)

quadrant 3 is (-,-)

quadrant 4 is (+.-)

Answer:

2% of 1kg

Step-by-step explanation:

20g/1kg x 100

= 20g/1000g x 100

1/50 x 100

=2

Therefore, 20g is 2% of 1kg

Hope it helps you

Answer:

2%

Step-by-step explanation:

1kg=1000g

=20/1000×100%

=2%

A standard deviation of 18 the scores were normally distributed 550 represents 100% of the total 24,000 students.

To find the percentage that 550 represents out of the total 24,000 students, to calculate the cumulative probability up to that score based on the given normal distribution parameters.

First to convert the raw score of 550 into a z-score, which represents the number of standard deviations away from the mean:

z = (x - μ) / σ

Where:

x = Raw score (550)

μ = Mean (56)

σ = Standard deviation (18)

z = (550 - 56) / 18

z = 494 / 18

z ≈ 27.44

Using a standard normal distribution table or a statistical calculator find the cumulative probability associated with a z-score of 27.44. However, since the z-score is significantly high, the cumulative probability extremely close to 1 (since the distribution is asymptotic).

consider the cumulative probability as 1.

To find the percentage multiply the cumulative probability by 100:

Percentage = 1 × 100 = 100%

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Answer:

Costs are $490

49 shirts are sold

Step-by-step explanation:

98 + 8x = 10x

98 = 2x

49 = x

98 + 8(49) = $490 in costs

49 shirts sold

Answer: A conclusion drawn from a study is considered to be an observation or an inference based on the data collected. In this case, the dentist conducted a survey to determine whether a certain brand of mouthwash improves gum health more than others. The conclusion drawn from the survey results is that the brand of mouthwash in question does improve gum health more than other brands.

It is important to note that this conclusion is based on the sample of patients that were surveyed. A sample is a subset of a population that is used to represent the characteristics of the entire population. In this instance, the sample of patients surveyed may not be representative of the entire population of people who use mouthwash. Therefore, the conclusion drawn from the study is based on the sample and may not be generalizable to the entire population.

The study conducted by the dentist is a survey study. A survey study is a research method in which data is collected through questionnaires or interviews from a sample of individuals.

Step-by-step explanation:

Using the volume x³ + 10x² + 19x  - 30, the missing side of the rectangular prism is (x + 6)

Two sides of a rectangular prism are x + 5 and x - 1. The volume of the rectangular prism is given as x³ + 10x² + 19x  - 30.

Let's find the missing side of the rectangular prism.

Therefore,

volume of a rectangular prism = lwh

where

Therefore,

volume of the prism = x³ + 10x² + 19x  - 30

Let's factorise it to find the missing side length

x³ + 10x² + 19x  - 30  = 0

(x - 1)(x² + 11x + 30)

let's factorise x² + 11x + 30

x² + 11x + 30

x² + 5x + 6x + 30

x(x + 5) + 6(x + 5)

(x + 6)(x + 5) = 0

Therefore, the side length of the rectangular prism are (x - 1), (x + 5) and (x + 6)

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Answer:

It depends on how many teacher has

Step-by-step explanation:

52 children divided by number of teacher

we have that

the radius is

r=12.1 in

the volume of a sphere is

substitute the given values

Part 2

In this problem we have the diameter of the sphere

D=13.6 mm

so

r=D/2=13.6/2=6.8 in

substitute in the formula

Answer:

k = 31

Step-by-step explanation:

The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).

Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.

We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:

P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4

Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:

P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563

P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015

P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159

P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747

P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340

P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824

Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

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The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

What is Standard Deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; Hence, the higher the standard deviation, the more dispersed the data.

We know that:

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

where \(x_{i}\)  is the mean and n is the number of observations.

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

98% Confidence interval:  

\(\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}\)

Putting the values, we get,  

\(t_{\text {critical }} \alpha_{0.02}\\=\pm 2.14535.07 \pm 2.145\left(\frac{6.02}{\sqrt{15}}\right)\\=35.07 \pm 3.33\\=(31.74,38.4)\)

Hence, The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

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Answer:

The answer is b= 7/2

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

4b-4+4=10+4

4b=14

4b/4 =14/4

B=7/2

Answer:

d

Step-by-step explanation:

Any piece of luggage must have a length, width, and height combined that is less than or equal to 150 cm. A traveler requests to take a package with the maximum permitted volume. if the length and width are to be equal, then the dimensions would be 48*96*72

Any piece of luggage must have a length, breadth, and height combined that is 216 cm or less.

L+W+H=216 (because we want the max volume, we may ignore the "less than part" and set them equal) (since we want the max volume, we can ignore the "less than part" and set them equal)

L = W if the length and width are equal.

Let's construct this new equation by swapping L for W.

Arrange H to the left so that H=216-2W when 2W+H = 216

Consequently, what is volume V=L*W*H=W=W2*(216-2W) =216W2-2W3 div./dW=432W-6W?

2\s432W-6W^2=0

72w-w2=0 divided by 6 on both sides.

W = 72 L H = 72 cm

L=2W is the only item that has altered.

Given that L+W+H=216 and that V=L*W*H=2W*W*(216-3W) =432W2-6W, 3W+H=216

864W-18W2 x 3 V prime

Set V prime to 0, solve it by dividing both sides by 18, and you'll get W = 48. dimensions will be

48, 96, and 72 cm in width ,lenght and height

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Answer:

He can buy 12 books

Step-by-step explanation:

150 divided by 12 = 12.5 but you can’t have half of a book so round it down and you get 12

Hope this helps!

Answer: Where P is.

Step-by-step explanation

The interest that Mark will earn at the end will be $3854.62.

Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time.

The given problem can be solved using the expression for the simple interest as (p × r × t)/100.

As per the question,

The interest obtained after 10 days is given as,

(5000 × 3.2 × 10)/100 = $1600

Then, the amount is 5000 + 1600 = $6600.

After withdrawal of $2000, the new principal becomes 6600 - 2000 = $4600.

Now, the interest is given for 8 days as,

(6600 × 3.2 × 8)/100 = $1689.6

The total amount after depositing $3500 is 6600 + 1689.6 + 3500 = $11789.6.

Again, the interest for another 5 days is,

(11789.6 × 3.2 × 8)/100 = $3018.13

The new principal for another seven days after depositing $250 is,

11789.6 + 3018.13 + 250 = 15057.13

The interest is calculated as,

(15057.13 × 3.2 × 8)/100 = $3854.62

Which is equivalent to the total interest earned.

Hence, the total interest earned by Mark is given as $3854.62.

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The solution of the given initial value problem can be expressed as y(x) = A*e^(r1*x) + B*e^(r2*x) + C*cos(w*x) + D*sin(w*x), where A, B, C, and D are constants, r1 and r2 are the roots of the characteristic equation, and w is the angular frequency.

The given initial value problem is a linear homogeneous differential equation with constant coefficients. To solve it, we first find the roots of the characteristic equation, which is obtained by substituting y = e^(rx) into the differential equation. The characteristic equation becomes r^4 + 18r^3 + 123r^2 + 378r + 442 = 0.

By solving the characteristic equation, we find the roots r1, r2, r3, and r4. Let's assume that the roots are real and distinct for simplicity. The general solution of the differential equation is then given by y(x) = A*e^(r1*x) + B*e^(r2*x) + C*e^(r3*x) + D*e^(r4*x), where A, B, C, and D are constants determined by the initial conditions.

In this particular problem, the roots of the characteristic equation may be complex conjugate pairs or repeated roots. In such cases, the general solution contains trigonometric functions in addition to exponential functions.

However, since the question only provides real and distinct roots, we can express the solution as y(x) = A*e^(r1*x) + B*e^(r2*x) + C*cos(w*x) + D*sin(w*x), where w is the angular frequency corresponding to the complex roots.

Finally, we can use the given initial conditions, y(0) = 5, y'(0) = -8, y"(0) = -34, and y"'(0) = 487, to determine the values of the constants A, B, C, and D, and obtain the specific solution for the given initial value problem.

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Answer:

$36

Step-by-step explanation:

$540÷15 = $36

Answer:

GCF is the largest factor that all terms have in common.

Answer:

By the given information about the sets A and B, we have :

A={1,2,3,4,6,9,12,18,36}

B={3,6,9,12,15,18,21,24,27,30,36,…}

since A is the set of factors of 36 and B is the set of multiples of 3.

SOLUTION - 1:-

Now, recall the definition of intersection of two sets. Intersection of two sets say set A and B, denoted by A∩B is the set of all those elements which belong to both the sets A as well as B.

Therefore, A∩B={3,6,9,12,18,36}.

SOLUTION - 2 :-

Now, we have to find A \ B.

A \ B is the set of all those elements which belongs to A but don't belong to the set B.

So, clearly A \ B = {1,2,4}

Step-by-step explanation:

Up there

Answer:

5.0

Step-by-step explanation:

Using Pythagorean Theorem:

a² + b² = c²

where a =? b= 12 in and c = 13 in

a² + (12)² = (13)²

a² + 144 = 169

a² = 169 - 144

a² = 25

a = √25 = 5

∴ a = 5.0

Pythagoras Theorem is usually applied when finding one missing side of a right-angle triangle.

The number of weeks needed to get $850 is 21 weeks.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.

Let the number of weeks be represented by w

Amount saved = $24

Amount needed = $850

Number of weeks = w.

This will be illustrated as:

24 + 40w = 850

Collect like terms

40w = 850 - 24

40w = 826

Divide

w = 826 / 40

w = 20.65 = 21 approximately

There'll be 21 weeks.

The complete question is written below.

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You have saved $24 towards the purchase of your own laptop. you get a job at the corner store cleaning after hours on sundays that pays $40 per week. the laptop you want costs $850 and includes everything you'll need to start college. How may weeks are needed?