A rectangular room is 11 feet by 14 feet. The ceilings are 9 feet high. If a gallon of paint covers 250 square feet. How many gallons of paint are needed to paint the room?

We can solve this by substitution method.

Look at the second equation. If we rearrange to find 7x, we can substitute in the value into the first equation.

[tex]5y-7x=12[/tex]

[tex]5y-7x-12=0[/tex]

[tex]5y-12=7x[/tex]

Therefore, [tex]7x=5y-12[/tex]

Now replace the 7x in the first equation with 5y - 12:

[tex]2y+7x=-5[/tex] (substitute in 7x = 5y - 12)

[tex]2y+(5y-12)=-5[/tex]

[tex]7y-12=-5[/tex]

[tex]7y=7[/tex]

[tex]y=1[/tex]

Now that we know y, we can find x by substituting in y = 1 into any equation we want. I will use the equation: 7x = 5y - 12

[tex]7x=5y-12[/tex] (substitute in y = 1)

[tex]7x=5(1) -12[/tex]

[tex]5x=5-12[/tex]

[tex]7x=-7[/tex]

[tex]x=-1[/tex]

__________________________________________________________

Answer:

[tex]y=1\\x=-1[/tex]

Answer:

You have to simplify the fraction and turn it into a decimal.

Step-by-step explanation:

Meaning: Make the fraction smaller and turn it into the correct decimal.

EXAMPLE:

2/4 simplified is 1/2

1/2 is equal to 0.50

GE = 26

Step-by-step explanation:

OP = 16 + 9 = 25

PE - OG = 7

Using Pythagorean theorem,

(GE)^2 = (OP)^2 + (PE - OG)^2

=(25)^2 + (7)^2

= 625 + 49

= 674

or

GE = √674 = 25.96 or 26

Answer: 4 X's on 2 1/2, 3 X's on 3, 2 X's on 3 1/2, 1 X on 4

Step-by-step explanation:

Answer:

Slope=-3/4

Step-by-step explanation:

The slope is the rise/run or y/x

Points given for A are (-4, 3), for B (4, -3)

The formula for slope is m=y^2-y^1/x^2-x^1

https://calcworkshop.com/graphing-linear-equations/slope-formula/

So we'll plug in the information given into the formula.

-4-4/3--3

-8/3+3

-8/6

so our slope is m=-3/4

Answer:  [tex]\frac{\pi}{18}[/tex]

Step-by-step explanation:

To convert from degree to radians, multiply by [tex]\frac{\pi}{180}[/tex], the conversion ratio.

Thus, 10 x [tex]\frac{\pi}{180}[/tex] = [tex]\frac{\pi}{18}[/tex]

Answer:

Part a:  Since the calculated value of t = 2.412 does not fall in the critical region t > ± 2.539 we conclude that population mean expense ratio does not exceed 1% at 0.01 significance level.

Part b:  Yes we accepted the null hypothesis when it is false so we made a type II error.

Part c: Power = 0.6591=0.66

Step-by-step explanation:

Part a:

Let the null and alternate hypotheses be

H0: u ≤ 1 against the claim Ha: u > 1

The significance level is ∝=0.01

As the standard deviation of the population is not given we use t- test which has n-1= 20-1= 19 degrees of freedom

This is one tailed test the critical region is t > ± 2.539

The mean is calculated to be 1.24 and standard deviation of the sample = s= 0.4486

We take population mean = u= 1

The test statistic is

t = x`-u/ s/ √n

t= 1.24-1 / 0.445/√20

t= 0.24/0.0995

t= 2.412

Since the calculated value of t = 2.412 does not fall in the critical region t > ± 2.539 we conclude that population mean expense ratio does not exceed 1% at 0.01 significance level.

Part b:

Type I errors are those errors when the null hypothesis is true and is rejected.

Type II errors are those in which the null hypothesis is false and is accepted.

If we had rejected the null hypothesis as it was true then we would have made a type I error.

Population mean = u = 1.33

And our null hypothesis is u= 1

Yes we accepted the null hypothesis when it is false so we made a type II error.

Part c:

When σ= 0.5

For Part a: μ= 1.33

Power = P (reject H0/ H0 is false)

= 1-β

P (reject H0/ H0 is false) = P (z > 2.539+ (u`-u0) / σ*√n)

= P (z > 2.539+ (1-1.33) /0.5 *√20)

=P (z > 2.539-2.9516)

= P (z > 0.4126)

= 0.5 - P (z= 0.2938)                                         from the area of table.

= 0.5- 0.1591

=0.3409

Power = 1-β = 1- 0.3409= 0.6591=0.66

Answer:

76 books

Step-by-step explanation:

2/3 × 114 = 76

__________

Solution :

From the table,

Number of countries = [tex]$N_i$[/tex]

Mean = [tex]$\overline Y_i$[/tex]

Standard deviation = [tex]$\sigma_i$[/tex]

Margin of error of B = 50,000 acres

So we determine the [tex]$\text{sample size n}$[/tex] and then allocate the four regions of [tex]$n_1, n_2, n_3$[/tex] and [tex]$n_4$[/tex].

Under the [tex]$\text{proportional allocation}$[/tex], the [tex]$\text{equation}$[/tex] for the value of [tex]$n_1$[/tex] which yields [tex]$V(\overline Y_{st}) = D = \frac{B^2}{H}$[/tex]  is given by :

[tex]$n=\frac{\sum_{K=1}^L N_K \sigma^2_K}{ND+\frac{1}{N}\sum_{K=1}^L N_K \sigma^2_K}$[/tex]

Let us complete the numerator

[tex]$\sum_{K=1}^L N_K \sigma^2_K = N_1\sigma_1^2 + N_2\sigma_2^2 + N_3\sigma_3^2 + N_4\sigma_4^2$[/tex]

                [tex]$= 1052 \times (271)^2 + 210 \times (79)^2 + 1376 \times (244)^2 + 418 \times (837)^2 $[/tex]

                = 453329920

The bound on the error of estimation is B = 50,000 acres

Hence we get

[tex]$D=\frac{B^2}{H}$[/tex]

  [tex]$=\frac{50000^2}{4}$[/tex]

  = 625,000,000

[tex]$n=\frac{\sum_{K=1}^L N_K \sigma^2_K}{ND+\frac{1}{N}\sum_{K=1}^L N_K \sigma^2_K}$[/tex]

  [tex]$=\frac{453329920}{3056 \times 625 + \frac{1}{3056} \times 453329920}$[/tex]

 = 220.24044

≈ 221 (approximately)

Therefore, the sample size under the proportional allocation from each stratum are given by :

[tex]$n_1=n\left[\frac{N_1}{\sum_{K=1}^\mu N_K}\right]$[/tex]

   [tex]$=221\left[\frac{1052}{3056}\right]$[/tex]

   ≈ 76

[tex]$n_2=n\left[\frac{N_2}{\sum_{K=1}^\mu N_K}\right]$[/tex]

   [tex]$=221\left[\frac{210}{3056}\right]$[/tex]

   ≈ 15

[tex]$n_3=n\left[\frac{N_3}{\sum_{K=1}^\mu N_K}\right]$[/tex]

   [tex]$=221\left[\frac{1376}{3056}\right]$[/tex]

   ≈ 100

[tex]$n_4=n\left[\frac{N_4}{\sum_{K=1}^\mu N_K}\right]$[/tex]

   [tex]$=221\left[\frac{418}{3056}\right]$[/tex]

   ≈ 30

Thus, we should select 76 counties from North central region, 15 counties from the north east region, 100 from south region and 30 from west region.

We can also estimate mean acreage of each county across all the county with a margin of error of 50,000 acres.

Answer:

Ed's answer of [tex]\frac{3}{8}[/tex] is correct because he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer.

Step-by-step explanation:

To solve for m in [tex]\frac{2}{3}m=\frac{1}{4}[/tex] you want to isolate m by dividing by [tex]\frac{2}{3}[/tex] on both sides, therefore he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer of [tex]\frac{3}{8}[/tex], and his answer is correct.

Answer: The answer is 5/4 :)

Answer:

5/4 or 1 1/4

Step-by-step explanation:

khan academy

9514 1404 393

Answer:

  B.  y = x + 0.5

Step-by-step explanation:

The y-intercept of 0.5 eliminates choices A and C.

When x increases by 1, y increases by 1, eliminating choice D.

The equation of choice B is graphed.

  y = x + 0.5

Answer:

x^20 please mark me brainliest

Step-by-step explanation:

Answer:

i

Step-by-step explanation:

Answer:

did you forget a picture?

Step-by-step explanation:

if you did, either add it in the comments, or make a new question

Hence, the approximate length of the ladder​ is [tex]12ft[/tex].

What is the approximation value?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.

A calculation can be approximated by rounding the values within it before performing the operations.

Here given that,

[tex](x)^2=(11.5)^2+(3.5)^2\\X^2=132.25+12.25\\X^2=144.5 \\X=\sqrt{144.5}\\X=12 feet[/tex]

Hence, the approximate length of the ladder​ is [tex]12ft[/tex].

To know more about the approximation value

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Answer:

the probability that they are assigned adjacent cubicles is  1 ÷ 4

Step-by-step explanation:

Given that

There is 8 new graduates are hired

2 of the graduates are bill and cathy

And, each one is assigned on random basis

We need to find out the probability

So,

= (2) (7!) ÷ (8!)

= (2) ÷ (8)

= 1 ÷ 4

Hence, the probability that they are assigned adjacent cubicles is  1 ÷ 4

The same would be relevant

Answer: $1,540.00 is the total amount needed for the class trip

Step-by-step explanation:

Data: $110.00 earned for class trip

14th of the money needed

Money needed: x

Step one, Make the equation

110x14=x

Reason: Since we know 110.00 is a 14th of the money needed, we know multipling it by 14 will get us the money needed for the class trip. Having it in an equation will make it easier to solve.

Step two, Evaluate the equation

110x14=x=1540=x

Reason: The only thing that was left to do was to multiply 110 by 14 to get 1540 since the x was already isolated to begin with. That leaves us with the  answer of x=1540.

However, since this is a real world problem, we have to make the answer more realistic so the final answer is '$1,540.00 is the total amount needed for the class trip'

I hope this helps!

Answer:

52 miles

Step-by-step explanation:

total miles needed to average 56

56 * 6 = 336

miles after 5 days

51 + 62 + 61 + 47 + 63 = 284

miles needed on last day

336 - 284 = 52 miles

Answer:

The average rate of change of the function over the interval is of 6.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function h(x) over an interval [a,b] is given by:

[tex]A = \frac{h(b)-h(a)}{b-a}[/tex]

In this question:

Over the interval [-9,-2], so [tex]a = -9, b = -2, b - a = -2 -(-9) = 7[/tex]

The function is:

[tex]h(x) = -x^2 - 5x + 14[/tex]

[tex]h(-9) = -9^2 -5(-9) + 14 = -81 + 45 + 14 = -22[/tex]

[tex]h(-2) = -2^2 -5(-2) + 14 = -4 + 10 + 14 = 20[/tex]

Then

[tex]A = \frac{h(-2)-h(-9)}{7} = \frac{20-(-22)}{7} = \frac{42}{7} = 6[/tex]

The average rate of change of the function over the interval is of 6.

Answer:

See image

Step-by-step explanation:

I clicked submit and it was right

Also dude I remember doing this and struggling before

Answer:

.01 + .3 = 0.31

Step-by-step explanation:

Answer:

[tex]\frac{a^2 + b^2 +c ^2}{a*b + a*c + b*c} = -2[/tex]

Step-by-step explanation:

if:

a + b + c = 0

then we can rewrite:

c = -a - b

Now we can replace this in our expression:

[tex]\frac{a^2 + b^2 + c^2}{a*b + a*c + b*c} = \frac{a^2 + b^2 + (-a - b)^2}{a*b + a*(-a - b) + b*(-a - c)}[/tex]

Now we can rewrite:

(-a - b)^2 = a^2 + 2*a*b + b^2

Then we can rewrite our expression as:

[tex]\frac{a^2 + b^2 + a^2 + b^2 + 2*a*b}{a*b - a^2 - a*b - b^2 - b*a}[/tex]

Let's keep simplifying this:

[tex]\frac{2*(a^2 + b^2 + a*b)}{-a*b - b^2 - a^2}[/tex]

Here is easy to see the simplification we need to do, as we have the same factor in the denominator as in the numerator (just a different of sign).

[tex]\frac{2*(a^2 + b^2 + a*b)}{-a*b - b^2 - a^2} = \frac{2*(a^2 + b^2 + a*b)}{-(a^2 + b^2 + a*b)} = -2[/tex]

Then the expression is equal to -2

[tex]\frac{a^2 + b^2 +c ^2}{a*b + a*c + b*c} = -2[/tex]

Answer:

Parallel = AB and CD

Perpendicular = EF and CD

Neither: GH and EF

Step-by-step explanation:

Parallel lines will go on forever without touching, they are aligned with each other.

Perpendicular lines intersect with 4 right angles

The Parallel lines are AB and CD and Perpendicular lines are  EF and CD.

It is required to find the solution.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The given figure shown as four lines are given AB , CD ,EF , CD  ,GH and EF.

According to given question we have

Parallel = AB and CD

Perpendicular = EF and CD

Neither parallel nor perpendicular lines: GH and EF

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions

Perpendicular lines are lines that intersect at a 90-degree angle.

Therefore , the Parallel lines are AB and CD and Perpendicular lines are  EF and CD.

Learn more details about Lines here:

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Answer:

Area= 90

Step-by-step explanation:

triangle area: (b x h) / 2

(12 x 15) / 2

(180) / 2

a= 90

Answer:

Look at the image.

Step-by-step explanation:

Answer:

Step-by-step explanation:

-4<n≤5

Answer:

y= 3/5x+5

Step-by-step explanation:

The y intercept is 5 and the graph is going upwards so it is a postive slope. If you look at at the graph from the y intercept point to point B you can see it goes up by 3 and right by 5 so the slope is 3/5. This makes the equation y=3/5x+5

Answer:

3000 in3 ? I haven't actually done this i-ready before- but I believe it's

Width x Length x Height = Final result?

Step-by-step explanation: