A bookshelf is 72 inches wide. If I plan to place books on the shelf that average ¾ inches in width, about how many books will fit on the shelf?

You want to setup an equation that will match the word problem. Let's call the amount of the first brand, F and the amount of the second brand, S.

We want the total mixture to be 310mL so: F + S = 310

Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)

Now, we can solve the system of equations using substitution.

F + S = 310

.06F + .11S = .08(310)

F = 310 - S      [solve 1st equation for F]

.06(310 - S) + .11S = .08(310)     [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

F + 124 = 310     [substitute answer for S back into original equation]

F = 186

Answer: to make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.

To make 240 milliliter of mixture that contain 8% vinegar, use 168 milliliter of first brand and 72 milliliter of second brand  

An equation between two variables that gives a straight line when plotted on a graph.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Given,

Quantity of vinegar in first brand = 5%

Quantity of vinegar in second brand = 15%

The chef wants to make 240 milliliter of a dressing that 8% vinegar

Consider,

Quantity of first brand =  x

Quantity of second brand = y

Then,

x + y = 240

x=240-y

We want total of 8% of mixture by adding first brand and second brand

0.05x + 0.15y = 0.08×240

Substitute the value of x in this equation

0.05(240-y) + 0.15y =19.2

12 - 0.05y + 0.15y = 19.2

0.1y = 7.2

y = 72

Substitute the value of y in first equation

x + y = 240

x + 72 =240

x = 168

Hence, to make 240 milliliter of mixture that contain 8% vinegar, use 168 milliliter of first brand and 72 milliliter of second brand  

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Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

You know:

m = 3

b = -4         So substitute/plug it into the equation

y = mx + b

y = 3x + (-4)

y = 3x - 4    Your answer is a

The equation representing a line with a slope of 3 and a y-intercept of -4 is y = 3x - 4. Hence, the correct option is (a).

The student's question pertains to finding the equation of a line with a given slope and y-intercept. In the slope-intercept form of a linear equation, which is y = mx + b, the m represents the slope, and the b represents the y-intercept. Therefore, for a line with a slope of 3 and a y-intercept of -4, the corresponding equation would be y = 3x - 4.

So, the correct answer is:

y = 3x - 4

This is because it directly shows a slope (m) of 3 and a y-intercept (b) of -4, which matches the line properties the question is asking for.

Answer:

Spread, Gap, Peak, Cluster

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

By remote exterior angle theorem:

[tex](12x + 14)\degree = (1 + 5x) \degree+ 76 \degree \\ 12x + 14 = 1 + 5x + 76 \\ 12x - 5x = 77 - 14 \\ 7x = 63 \\x = \frac{63}{7} \\ \huge \red{ \boxed{ x = 9}}[/tex]

Answer:

B

Step-by-step explanation:

Slope:

[tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2}} =\frac{6-1}{6-3} =\frac{5}{3}[/tex]

This eliminates answer options C and D

If you plug either set of coordinates into equation B then you will know that it works because both sides will end up equal to each other

The line that passes through the given points in the table is represented by the equation y = 3x + 9. You can verify this by plugging the x-values into the equation and arriving at the corresponding y-values or by checking if the points lie on the line in the graph.

To answer your question about which equation represents a line that passes through the two points given in the mentioned table, we can use the concept of linear equations and their graph. The equation of a line in slope-intercept form is given by y=mx+b where 'm' is the slope and 'b' is the y-intercept. From the information given, we can see the value of 'm' as 3 and 'b' as 9.

Therefore, the line that passes through the points provided is represented by the equation y = 3x + 9. To verify this, you can plug in the x-values from the table into this equation and you should be able to arrive at the corresponding y-values given in the table.

In the given figure, these points should lie on the line represented by the equation y = 3x + 9, verifying our solution.

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Answer:

A candle! They burn slower when they're bigger and fatter, but when they're thin they burn quicker! A slight breeze of wind can burn it out quickly.

P.S

Have a Amazing Day!

Faker/Tosrel

Answer:

3.7*10⁷ people.

Step-by-step explanation:

Estimated population of California = 3.9*10⁷ people

Estimated population of Maine = 1.3*10⁶ people.

Let x represent the estimated number of people that live in California more than Maine.

The number of people that live in California more than Maine can be found by finding the difference between the population of California to Maine.

No. Of people living in California - no. Of people living in Maine = estimated no of people that live in California more than Maine.

X = 3.9*10⁷ - 1.3*10⁶

X = 3.7*10⁷ people

About 3.7*10⁷ people live more in California than Maine

how many more people live in California than live in Maine is 37.7 × 10⁶ people.

Since 3.9 × 10⁷ people live in California and about 1.3 × 10⁶ people live in Maine. To find how many more people live in California than live in Maine, we take the difference of the two values.

Difference,D = N - n where

So, substituting the values of the variables into the equation, we have

D = N - n

D = 3.9 × 10⁷ - 1.3 × 10⁶

D = 39 × 10⁶ - 1.3 × 10⁶

D = 37.7 × 10⁶ people

So, how many more people live in California than live in Maine is 37.7 × 10⁶ people.

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Yes, the playgrounds shape is the right angle triangle.

Step-by-step explanation:

The sides of the triangular ground are 480 ft. 140 ft. And 500ft.

We can find if the sides given are the sides of a right triangle by using pythogoras theorem.

Here, the largest side is 500ft.

So,

√[(480x480) +(140x140) ]

= √[(230400) +(19600) ]

= √(250000)

= 500

The pythogoras theorem is proved.

So, the playground is in the shape of triangle.

Answer:

11

Step-by-step explanation:

22/2=11

Answer:

Can you put a better pic of it I can’t really see what it’s asking

Step-by-step explanation:

I’ll be glady to help

Answer: A. He would not have to pay

Step-by-step explanation:

Answer:

He would not have to pay any deductible because he was not at fault.

Step-by-step explanation:

AP3X

Answer:

D

Step-by-step explanation:

I just did it on usatestprep so. its D

Answer:

d

Step-by-step explanation:

The value of the exponential function will eventually exceed the value of the linear function. A quantity increasing exponentially eventually exceeds a quantity increasing linearly.

Answer:

it is (7,-6)

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=25000(0.84)^t

y=25000(0.84)^3

y=$14817.6

Final answer:

To calculate Mr. Rich's take-home pay, add together the regular and overtime pay, then subtract the deductions. The result is a take-home pay of $10,737 that is option A is correct.

Explanation:

The student is asking how to calculate the take-home pay for Mr. Rich after deductions from his income. To find the take-home pay, we first add together Mr. Rich's regular pay and overtime pay to get his total earnings. Then, we subtract the deductions to find the amount he takes home.

Regular pay: $9,278

Overtime pay: $2,132

Total earnings before deductions: $9,278 + $2,132 = $11,410

Deductions (taxes and loan): $673

Take-home pay: $11,410 - $673 = $10,737

Answer:

See explanation below.

Step-by-step explanation:

We are looking for the mean and the standard deviation of the sampling distribution of the sample of mean x, given that the mean and standard deviation of sampled population are as follows:

Mean=μ= 77.4

Standard deviation = σ = 4.0

Sample size n = 255

so, the mean of sample mean x will be same as mean of the sampled population:

μₓ = μ = 77.4

and the standard deviation of sample mean x will be standard deviation of the sampled population divided by square root of sample size:

σₓ = σ / √ n

  = 4.0 / √225

= 4.0 / 15

  = 0.3

Answer:

Tyey spent 3/25 on clothes and 1/4 on food

Step-by-step explanation:

12% is 12/100 which simplifies to 3/25

25% with 25/100 which simplifies to 1/4

Answer:

Clothes: 3/25

Food: 1/4

Step-by-step explanation:

Clothes: 12/100 = 3/25

Food: 25/100 = 1/4

Answer:

x=5/2

Step-by-step explanation:

The value of x in the equation is 4.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Here,

The equation given is,

g⁽ˣ⁻¹⁾- 2 = 25

g⁽ˣ⁻¹⁾ = 27

g⁽ˣ⁻¹⁾ = 3³

Therefore,

x - 1 = 3

x = 4

Hence,

The value of x in the equation is 4.

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Answer:

>50

Step-by-step explanation:

It says there is at most 50 people so it'd be less than 50

The inequality for "There are at most 50 people on the bus." is b≤ 50.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

As, we know that the sign for atmost ≤.

Now, There are at most 50 people on the bus.

let the number of bus represented by 'b'.

Then, the inequality is

b≤ 50.

Hence, the inequality is b≤ 50.

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Answer:

The answer is 75%

Step-by-step explanation:

Answer:

75 people

Step-by-step explanation:

Answer: .123

Step-by-step explanation: use random variable e-s which will follow a normal distribution with a mean of 70-60=10 and SD= sq root of 25+49. P(e-s<0)=.123

The probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

We have the number of thousands of miles that the standard model tires last has a mean:

[tex]\rm \mu_S = 60[/tex]  

And standard deviation:

[tex]\rm \sigma_s = 5[/tex]

The number of miles that the extended life tires last has a mean:

[tex]\rm \mu_E = 70[/tex]

And standard deviation:

[tex]\rm \sigma_E = 7[/tex]

As the mileages for both tires follow a normal distribution curve.

If we use the E-S random variables and these random variables follow the normal distribution.

Now:

[tex]\rm E =\mu_E- \mu_S[/tex]

E = 70 - 60 ⇒ 10   and

[tex]\rm S= \sqrt{\sigma_S ^2+\sigma_E^2}[/tex]

[tex]\rm S= \sqrt{5^2+7^2}[/tex]

S = √74 ⇒ 8.6023

Now from the normal distribution table the value of the probability:

=P(E - S<0)

= 0.123

Thus, the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123

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Answer:

2 1/5, 1/10, - 2 3/4, -4

Step-by-step explanation:

If you're ever confused about whether a number is greater than another number, think about them on a number line. If the number is further to the left than another number, it is less (for example, 0 is further to the left than 2).

The difference between the mean weight of Chicken B's eggs and the mean weight of Chicken A's eggs to the nearest tenth is 1.8 grams.

A normal distribution is a probability distribution that is symmetric around the mean, with most of the data points falling close to the mean and fewer data points falling farther away from it.

The shape of a normal distribution is often referred to as a bell curve because when the distribution is graphed, the resulting curve resembles a bell

We have,

Since both data sets follow a normal distribution, we can use the empirical rule (also known as the 68-95-99.7 rule) to find the mean weight of each chicken's eggs.

For Chicken A, we know that 68% of the eggs fall between 50.9 grams and 60.1 grams. This means that the mean weight of Chicken A's eggs is the average of these two values:

Mean of A = (50.9 + 60.1) / 2 = 55.0 grams

For Chicken B, we know that 68% of the eggs fall between 51.9 grams and 61.7 grams. This means that the mean weight of Chicken B's eggs is the average of these two values:

Mean of B = (51.9 + 61.7) / 2 = 56.8 grams

The difference between the mean weight of Chicken B's eggs and the mean weight of Chicken A's eggs is:

Difference = Mean of B - Mean of A

= 56.8 - 55.0

= 1.8 grams

Therefore,

The difference between the mean weight of Chicken B's eggs and the mean weight of Chicken A's eggs to the nearest tenth is 1.8 grams.

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Answer:

x = 10

Step-by-step explanation:

x² = 4×25

x² = 100

x = √100

x = 10

AB² = BD×BC

Answer:

those fractions are perpendicular

Step-by-step explanation:

-27/62

62/27

Answer:

2

Step-by-step explanation:

The slope given two points is found by

m= (y2-y1)/(x2-x1)

   = (2 - -6)/(2 - -2)

   =(2+6)/(2+2)

   =8/4

    2

Answer:

[tex]10p+3[/tex]

Step-by-step explanation:

To work this out you would add up all of the like terms

1) Add the like terms.

[tex]6p+4p=10p[/tex]

2)Add the 3

[tex]10p+3[/tex]

Answer:

84*(1/4)^x

Step-by-step explanation:

84 is the constant as it is the starting amount. However each round (x because the amount of rounds is constantly changing) divides the team by 4 or multiplies by 1/4 (Reciprocal).

So, if you wanted to see if the amount of teams after three rounds you would do:

84 * 1/4 * 1/4 * 1/4. However, any number times itself is an exponent, so we would simplify to 84³. But due to the fact we do not know how many rounds we are going to calculate we change the exponent to x.

Answer:

3min 12sec

Step-by-step explanation:

Turn 2min 6sec into seconds

2m 6sec = 126 secs

divide 525 by 126

525/126 = 4.16666667

divide 800 by 4.16666667

800/4.16666667 = 192

192 to min secs = 3min 12sec