An architecture firm creates blueprints for office buildings. Last week, they produced four rectangular blueprints for four different projects. Project A: A 20-inch by 15-inch blueprint with a scale of 1 inch to 4 feet and a projected cost of $22,000. Project B: A 10-inch by 8-inch blueprint with a scale of 1 inch to 8 feet and a projected cost of $25,000. Project C: A 15-inch by 12-inch blueprint with a scale of 1 inch to 6 feet and a projected cost of $27,000. Project D: An 8-inch by 6-inch blueprint with a scale of 1 inch to 12 feet and a projected cost of $30,000. Order the projects from greatest to least projected cost per square foot of the actual offices. Project C Project B Project D Project A

Answer:

  b.  Miguel ends up with $35 less than he started with

Step-by-step explanation:

He spends $35 × 4 = $140.

He earns $21 × 5 = $105.

His net increase is $105 -140 = -$35.

Miguel ends up with $35 less than he started with.

Answer:

74

Step-by-step explanation:

tan?=7/2

tan^-1(7/2)=?

?=74

Answer:

16°

Step-by-step explanation:

A ladder leans against a building . The foot of the ladder is 2 feet from the building and reaches to a point 7 feet high on the building . The measured angle formed by the ladder and building can be computed below.

The illustration forms a right angle triangle. Two sides are given and we are told to find an angle

Distance form the foot of the ladder to the building = 2 feet

The ladder reaches a point in the building which is the height of the building the ladder head started from = 7 feet

Using SOHCAHTOA principle

tan ∅ = opposite /adjacent

where

opposite = 2 ft

adjacent = 7 ft

∅ = angle formed by the ladder and the building

tan ∅ = 2/7

∅ = tan⁻¹ 2/7

∅ =  15.9453959

∅ ≈ 16°

Answer:

The temperature in the morning was [tex]-10.5^o[/tex]

Step-by-step explanation:

we know that

1) The high temperature in Fairbanks, Alaska was 15.7 degrees

That night it fell 38.4 degrees

so

The temperature at night was

[tex]15.7^o-38.4^o=-22.7^o[/tex]

2) The next morning, it rose 12.2 degrees.

so

The temperature in the morning was

[tex]-22.7^o+12.2=-10.5^o[/tex]

Answer:

[tex]24.68\ ft[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

Let

x ----> ladder height in ft

Applying the Pythagorean Theorem

[tex]25^2=4^2+x^2[/tex]

solve for x

[tex]625=16+x^2[/tex]

[tex]x^2=625-16[/tex]

[tex]x^2=609[/tex]

[tex]x=\sqrt{609}\ ft[/tex]

[tex]x=24.68\ ft[/tex]

The ladder reaches up 24.7 ft on the garage wall.

The ladder reaches up 24 ft on the garage wall.

To find the height the ladder reaches, we can use the Pythagorean theorem, where the ladder is the hypotenuse:

Height² + Base² = Hypotenuse²

Height² + 4² = 25²

Height² + 16 = 625

Height² = 609

Height = √609

Height =24.67 ≈ 24.7 ft

Answer:The percent of increase of the area of the deck is 12.5%

Step-by-step explanation:

The initial area of the deck is 160 square feet. You and your family have decided to increase the area of your deck to 180. The amount by which the area of the deck was increased is is 180 - 160 = 20 square feet.

The percent of increase of the area of the deck would be

Increase / initial area × 100.

20/160 × 100 = 12.5℅

Answer:

11 hours 15 mins

Step-by-step explanation:

Wilma & Betty both have a pool that holds 10500 gallons of water each.

Wilma's garden hose fills at the rate of 700 gallons per hour.

Betty's garden hose fills at a rate of 400 gallons per hour.

Volume = Rate * time

Time = Volume /rate

The time it will take for Wilma's pool to be filled = 10500/700

= 15 hours

The time it will take for Betty's pool to be filled = 10500/400

= 26.25hours

= 26 hours 15 minutes

it will take Betty (26.25 - 15) to fill her pool than Wilma.

= 11.25hours

= 11 hours 15 mins

Answer:

Smaller Number = 10

Larger Number = 33

Step-by-step explanation:

Let the smaller number be "x" and the larger number be "y"

5 TIMES smaller is SUBTRACTED from TWICE larger, the result is 16, we can write:

2y - 5x = 16

and

Larger increased by 3 TIMES SMALLER, result is 63, so we can write:

y + 3x = 63

We can write this in terms of x, as:

y = 63 - 3x

Now we put this in equation 1 and solve for x first:

2y - 5x = 16

[tex]2(63 - 3x) - 5x = 16\\126-6x-5x=16\\11x=110\\x=10[/tex]

Now,

y = 63 - 3x

y = 63 - 3(10)

y = 63 - 30

y = 33

Smaller Number = 10

Larger Number = 33

Answer:

[tex]\large\tt\boxed{D. \ \tt -5j^{2}-5j+5}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to simplify the Polynomial.}[/tex]

[tex]\large\underline{\textsf{What is a Polynomial?}}[/tex]

[tex]\textsf{A Polynomial is an \underline{expression} that is made up of 1 or more terms.}[/tex]

[tex]\textsf{Terms can be a single whole number, variables, or a combination.}[/tex]

[tex]\large\underline{\textsf{How to Simplify a Polynomial?}}[/tex]

[tex]\textsf{There are a few ways to simplify a Polynomial. Let's identify them.}[/tex]

[tex]\textsf{A way to simplify a polynomial is by using the Distributive Property.}[/tex]

[tex]\textsf{Another way is to combine like terms.}[/tex]

[tex]\textsf{For this problem, we will have to do both!}[/tex]

[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\textsf{Distributive Property is a property that allows us to distribute a number left to a set}[/tex]

[tex]\textsf{of parentheses inside the values of the parentheses.}[/tex]

[tex]\underline{\textsf{How the Distributive Property works;}}[/tex]

[tex]\textsf{Example;} \tt -2(x+y)[/tex]

[tex]\textsf{-2 would multiply with x and y.}[/tex]

[tex]\mathtt{ -2(x+y)=\boxed{-2x-2y}}[/tex]

[tex]\large\underline{\textsf{What is Combining Like Terms?}}[/tex]

[tex]\textsf{Combining Like Terms is a simple way to simplify an expression by adding/subtracting}[/tex]

[tex]\textsf{like terms. This helps to make the expression much simpler.}[/tex]

[tex]\textsf{Now, we should know how to simplify the given polynomial.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Begin by using the Distributive Property on the left side of the Polynomial.}[/tex]

[tex]\textsf{Afterwards, Combine Like Terms.}[/tex]

[tex]\large\underline{\textsf{Simplifying;}}[/tex]

[tex]\tt -(5j^{2}+2j-7)-(3j+2)[/tex]

[tex]\textsf{The negative sign on the left side of the parentheses is the same as -1. Turn terms}[/tex]

[tex]\textsf{into their opposite value.}[/tex]

[tex]\tt -(5j^{2}+2j-7) \rightarrow (-1 \times 5j^{2})+(-1\times2j)-(-1\times-7)[/tex]

[tex]\tt -(3j+2) \rightarrow (-1 \times3j) + (-1 \times 2)[/tex]

[tex]\underline{\textsf{After Simplifying;}}[/tex]

[tex]\tt -5j^{2}-2j+7-3j-2[/tex]

[tex]\underline{\textsf{Combine All Like Terms;}}[/tex]

[tex]\tt -5j^{2}\boxed{-2j}+7\boxed{-3j}-2[/tex]

[tex]\tt -5j^{2}-5j\boxed{+7}\boxed{-2}[/tex]

[tex]\large\tt\boxed{D. \ \tt -5j^{2}-5j+5}[/tex]

Answer:

Andre got better paid when he mowed for neighbor's and uncle's lawn which is $20/hr than Community center's lawn which is $15/hr.

Step-by-step explanation:

Given:

Andre mowed a neighbor's lawn for 1/2 hour and earned $10.

For 1/2 hour = $10

So for 1 hour = Money earned in 1 hour.

By using Unitary method we get;

Money earned in 1 hour = [tex]\frac{10}{\frac{1}{2}} = \frac{10\times2}{1} = \$20[/tex]

Hence Andre hourly rate to mowed neighbor's lawn is $20.

Also Given:

Andre mowed a Uncle's lawn for 3/2 hour and earned $30.

For 3/2 hour = $30

So for 1 hour = Money earned in 1 hour.

By using Unitary method we get;

Money earned in 1 hour = [tex]\frac{30}{\frac{3}{2}} = \frac{30\times2}{3} = \$20[/tex]

Hence Andre hourly rate to mowed Uncle's lawn is $20.

Also Given:

Andre mowed Community center's lawn for 2 hour and earned $30.

For 2 hour = $30

So for 1 hour = Money earned in 1 hour.

By using Unitary method we get;

Money earned in 1 hour = [tex]\frac{30}{2}=\$15[/tex]

Hence Andre hourly rate to mowed Community Center's lawn is $15.

Now Since we can see that when he mowed neighbor and uncle's lawn he was paid at rate of $20 and when he mowed Community Center's lawn he got paid at rate of $15.

Hence Andre got better paid when he mowed for neighbor's and uncle's lawn which is $20/hr than Community center's lawn which is $15/hr.

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

Step-by-step explanation:

Part 1) Graph the system of inequalities

we have

[tex]y> 5x+5[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dashed line [tex]y=5x+5[/tex]

The slope pf the dashed line A is positive m=5

The y-intercept of the dashed line A is (0,5)

The x-intercept of the dashed line A is (-1,0)

[tex]y>-\frac{1}{2}x+1[/tex] ----> inequality B

The solution of the inequality B is the shaded area above the dashed line [tex]y=-\frac{1}{2}x+1[/tex]

The slope pf the dashed line B is negative m=-1/2

The y-intercept of the dashed line B is (0,1)

The x-intercept of the dashed line B is (2,0)

The solution of the system of inequalities is the shaded area above the dashed line A and above the dashed line B

using a graphing tool

see the attached figure

Part B) Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

substitute the value of x and the value of y in each inequality

For x=-2, y=5

Verify inequality A

[tex]5>5(-2)+5[/tex]

[tex]5>-5[/tex] ---> is true

so

The ordered pair satisfy inequality A

Verify inequality B

[tex]5>-\frac{1}{2}(-2)+1[/tex]

[tex]5>2[/tex] ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

Answer:

[tex]P = \frac{2}{3}[/tex]

Step-by-step explanation:

All the points in the plane that are 20 inches from P constituing a circle with center in P and with radius 20 inch

We need find the angle in this circle by which the point R is closer to P than it is to Q. The limit situation occurs when the distances from P to R and from R to Q are equals and have the value 20 inches. In this situation the points P, R y Q form a equilater triangle with angles of value 60°.

Thus, the point R is closer to P than it is to Q in 240° of the circle, except 60° above of the line PQ and 60° below the line PQ.

Then the probability is

[tex]P= \frac{240}{360} = \frac{2}{3}[/tex]

Answer:

a) Mean = 0.30, SD = 0.017

Step-by-step explanation:

The mean and sampling distribution of the sample proportion can be found using the equations

Mean= p

[tex]SD=\sqrt{\frac{p*(1-p)}{n} }[/tex]

where

Using these information:

Mean = 0.30

[tex]SD=\sqrt{\frac{0.30*0.70}{750} }[/tex] ≈ 0.017

Final answer:

The mean of the sampling distribution of the sample proportion is 0.30, and the standard deviation is found to be approximately 0.017. Therefore, the correct answer is Mean = 0.30, SD = 0.017.

Explanation:

To determine the mean and standard deviation of the sampling distribution of the sample proportion p, we use the formulas related to binomial distributions, since the survey outcome (believe that performance-enhancing drugs are a problem or not) follows a binomial distribution. The mean of the sampling distribution of the proportion is simply the population proportion, which is given as 0.30.

The standard deviation (SD) of the sampling distribution of p can be calculated using the formula SD = √[p(1-p)/n], where p is the population proportion and n is the sample size. In this case:

SD = √[0.30(1-0.30)/750] = √[0.21/750] = √[0.00028] ≈ 0.0167

Thus, the correct answer is a) Mean = 0.30, SD = 0.017

Answer:

In general if speed limit is not posted it will be 25 mph in residential area  

Step-by-step explanation:

When speed limit is not posted then it is 25 mph in residential area or school zones

But its also depend on the density of population in that area is density is very low then speed limit can go up to 35 mph and if density of population is high then speed limit will be restricted up to 25 mph

So in general if speed limit is not posted it will be 25 mph in residential area  

Answer:

6 dresses

Step-by-step explanation:

Given: sales price is $d

           Regular price is 3 times of sales price

           Janine has money to buy 2 dresses at regular price.

Now, finding the number of dresses Janine can buy at the sales price, if sale price is d

Regular price= [tex]3\times d= 3d[/tex]

Janine has total money= [tex]3d\times 2= 6d[/tex] (∵ regular price is 3d)

∴ Number of dresses bought by Janine= [tex]\frac{Total\ money}{sale\ price\ of\ one\ dress}[/tex]

⇒ Number of dresses bought by Janine= [tex]\frac{6d}{d} = 6\ dresses[/tex]

∴ Number of dresses bought by Janine is 6.

Answer:

See proof below

Step-by-step explanation:

Let x,y be arbitrary real numbers. We want to prove that if x≠y then f(x)≠f(y) (this is the definition of 1-1).

If x≠y, we can assume, without loss of generality that x<y using the trichotomy law of real numbers (without loss of generality means that the argument in this proof is the same if we assume y<x).

Because f is strictly increasing, x<y implies that f(x)<f(y). Therefore f(x)≠f(y) because of the trichotomy law, and hence f is one-to-one.

Answer:

The answer to your question is

a) [tex]\frac{480 mi}{min}[/tex]

b) distance = 2400 mi

Step-by-step explanation:

a) 8 mi/s  convert to mi/min

[tex]\frac{8 mi}{s}  x  \frac{60 s}{1 min}  = \frac{8 x 60 mi }{min}  = \frac{480 mi}{min}[/tex]

b) [tex]speed = \frac{distance}{time}[/tex]

          distance = speed x time

          distance = [tex]\frac{480 mi}{min} x 5 min[/tex]

         distance = 2400 mi

The sub-questions for this question are:

a) construct a binomial distribution using n=6 and p=0.34

b) graph the binomial distribution using a histogram and describe it's shape

c) what values of the random variable would you consider unusual? Explain your reasoning.

Answer:

a)

P(X=0) =0.0827

P(X=1) = 0.255

P(X=2) = 0.329

P(X=3) = 0.226

P(X=4) = 0.087

P(X=5) = 0.018

P(X=6) = 0.0015

b) graph D

c) x=5 and x=6

Step-by-step explanation:

a)

Formula for binomial distribution:

nCx(p^x)(q^(n-x))

Number of sample, n = 6

probability of success, p = 0.34

probability of failure, q = 1-p = 0.66

P(X=0) = 6C0(0.34^0)(0.66^6)

= 1*1*0.0827 = 0.0827

P(X=1) = 6C1(0.34^1)(0.66^5)

= 6*0.34*0.1252 = 0.255

P(X=2) = 6C2(0.34^2)(0.66^4)

= 15*0.1156*0.1897 = 0.329

P(X=3) = 6C3(0.34^3)(0.66^3)

= 20*0.0113 = 0.226

P(X=4) = 6C4(0.34^4)(0.66^2)

= 15*0.0058 = 0.087

P(X=5) = 6C5(0.34^5)(0.66^1)

= 6*0.003 = 0.018

P(X=6) = 6C6(0.34^6)(0.66^0)

= 1*0.0015 = 0.0015

b) the shape of the graph is the graph shape. Referring to the attachment, the correct graph is D

c) the unusual values would be x=6 and x=5, because those values are too small and lower than 0.05

Answer:

As x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].

Therefore, x = -5, x = 2 and y = 3 is the right option.

Step-by-step explanation:

As the given function is

[tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex]

Determining Vertical Asymptote:

The line x = L is a vertical asymptote of the function if if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

Such as

[tex]x^{2} +3x -10 = 0[/tex]

[tex](x-2)(x-5)=0[/tex]

[tex]x=2[/tex]  [tex]or[/tex]  [tex]x=-5[/tex]

x=−5 , check:

[tex]\lim_{x \to -5^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]

Since, the limit is infinite, then x = -5 is a vertical asymptote.

x = 2, check:

[tex]\lim_{x \to 2^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]

Since the limit is infinite, then x = 2 is a vertical asymptote.

Determining Horizontal Asymptote:

Line y=L is a horizontal asymptote of the function y = f(x), if either

[tex]\lim_{x \to \infty^{}}{f(x)=L}[/tex] or [tex]\lim_{x \to -\infty^{}}{f(x)=L},[/tex] and L is finite.

Calculating the limits:

[tex]\lim_{x \to \infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]

[tex]\lim_{x \to -\infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]

Thus, the horizontal asymptote is y=3.

So, x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].

Therefore, x = -5, x = 2 and y = 3 is the right option.

Keywords: asymptote, vertical asymptote, horizontal asymptote, equation

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I believe the answer is a.

Answer:

x  =  15  hours  

y  =  25  hours

Step-by-step explanation:

Lets call  "x"  number of working hours of Clark family sprinklers

and   " y "  number of working hours of Thomas family sprinklers

Then they both worked in such way that

x  +  y  =  40   (1)

On the other hand the total water output  1100 lts were supplied according to:

35 lts/h *  y (hours)   +  15 lts/h *  x (hours)  =  1100 lts

Then  

35*y   +  15*x  =  1100   (2)

Equations 1 and 2 become a system of two equations with two uknown variables  x  and  y

We solve that system

y   =  40  -  x        and     35* ( 40 - x ) +  15* x    =  1100

1400  -  35x   +  15x   = 1100    ⇒    -  20x  = -300

x  =  15  hours

And

y  =  40  -  15   =  25  hours

Answer:

We fail to reject H₀ as there is insufficient evidence at 0.5% level of significance to conclude  that the mean hours of TV watched per day differs from the claim.

Step-by-step explanation:

This is a two-tailed test.

We first need to calculate the test statistic. The test statistic is calculated as follows:

Z_calc = X - μ₀ / (s /√n)

where

Therefore,

Z_calc = (3.02 - 3) / (2.64 /√(1326))

           = 0.2759

Now we have to calculate the z-value. The z-value is calculated as follows:

z_α/2 = z_(0.05/2) = z_0.025

Using the p-value method:

P = 1 - α/2

  = 1 - 0.025

  = 0.975

Thus, using the positive z-table, you will find that the z-value is

1.96.

Therefore, we reject H₀ if | Z_calc | > z_(α/2)

Thus, since

| Z_calc | < 1.96, we fail to reject H₀ as there is insufficient evidence at 0.5% level of significance to conclude  that the mean hours of TV watched per day differs from the claim.

Using a statistical hypothesis test, we do not find sufficient evidence to conclude that the mean number of hours per day people spend watching TV in 2012 differs from the sociologist's claim of 3 hours.

The question pertains to evaluating a claim about population mean using a sample mean. Given the data, we can perform hypothesis testing. The null hypothesis (H0) is that the mean number of hours spent watching TV is 3, and the alternative hypothesis (H1) is that the mean is not 3. The sample mean is 3.02, standard deviation is 2.64, and the sample size is 1326.

Firstly, we need to calculate the standard error: SE = standard deviation/sample size square root = 2.64/ sqrt(1326) = 0.072. Then, we calculate the test statistic (Z): Z = (sample mean - population mean)/SE = (3.02-3)/0.072 = 0.278. Given α=0.05, the Z value for a two-tailed test is +/- 1.96.

The computed Z value of 0.278 falls within the acceptance region (-1.96 < Z < 1.96), so we do not reject the null hypothesis. Therefore, the data do not provide sufficient evidence to conclude that the mean hours of TV watched per day differs from the sociologist's claim.

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Answer:$308.44

Step-by-step explanation:

$70.00/5= $14.02 an hour

14.02*22 = $308.44

Amount of money earned in 22 hour is 308

Amount of money earned in 5 hour = 70

Amount of money earned in 22 hour

Amount of money earned in 22 hour = 22[70/5]

Amount of money earned in 22 hour = 22[14]

Amount of money earned in 22 hour = 308

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The rate of change of the function is -35.7

Step-by-step explanation:

The rate of change of a function [tex]f(x)[/tex] between two points [tex]x_1[/tex] and [tex]x_2[/tex] is given by the ratio between the increment of the function itself and the increment of the x-variable:

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

The function of this problem is

[tex]f(x)=480 (0.3)^x[/tex]

For [tex]x_1=1[/tex], the value of the function is

[tex]f(1)=480(0.3)^1=144[/tex]

For [tex]x_2=5[/tex], the value of the function is

[tex]f(5)=480(0.3)^5=1.2[/tex]

Therefore, the rate of change of the function is

[tex]m=\frac{f(5)-f(1)}{5-1}=\frac{1.2-144}{5-1}=-35.7[/tex]

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Answer:

[tex]12+17+y+z[/tex] or [tex]29+y+z[/tex].

Step-by-step explanation:

We have been given that Nigel is planning his training schedule for a marathon over a 4-day period. He is uncertain how many miles he will run on two days. One expression for the total miles he will run is [tex]12+y+17+z[/tex].

The Commutative Property of Addition states that we can add numbers in any order. For example a and b be two numbers.

According to Commutative Property of Addition [tex]a+b=b+a[/tex].

Similarly, we can write an equivalent expression to our given expression as:

[tex]12+17+y+z[/tex]

We can simplify our expression as:

[tex]29+y+z[/tex].

Therefore, our required expression would be [tex]12+17+y+z[/tex] or [tex]29+y+z[/tex].

The dealer sold 120 pairs of gloves at $6 each.

To find out how many pairs of gloves were sold at $6 each, we can set up a system of equations based on the given information.

Let's assume x represents the number of pairs of gloves sold at $6 each.

Since the dealer sold a total of 200 pairs, the number of pairs sold at $11 each would be 200 - x.

We can now set up the equation: 6x + 11(200 - x) = 1600.

Simplifying the equation, we get 6x + 2200 - 11x = 1600.

Combining like terms, we have -5x + 2200 = 1600.

Now, we can solve for x: -5x = 1600 - 2200.

-5x = -600.

x = -600 / -5 = 120.

Therefore, the dealer sold

120 pairs

of gloves at $6 each.

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So, the dealer sold 120 pairs of gloves at $6 each.

Let's denote the number of pairs of gloves sold at $6 per pair as [tex]\(x\)[/tex], and the number of pairs sold at $11 per pair as [tex]\(200 - x\)[/tex] (since the total number of pairs is 200).

The total receipts from selling [tex]\(x\)[/tex] pairs at $6 each and [tex]\(200 - x\)[/tex] pairs at $11 each is given by the equation:

[tex]\[ 6x + 11(200 - x) = 1600 \][/tex]

Now, let's solve for [tex]\(x\)[/tex]:

[tex]\[ 6x + 2200 - 11x = 1600 \][/tex]

Combine like terms:

[tex]\[ -5x + 2200 = 1600 \][/tex]

Subtract 2200 from both sides:

[tex]\[ -5x = -600 \][/tex]

Divide by -5:

[tex]\[ x = 120 \][/tex]

Answer:

Step-by-step explanation:

50

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

So, the lines of this system are:

1) [tex]y= 2x + 1[/tex]

Where:

[tex]m=2\\b=1[/tex]

2) [tex]y=2x- 2[/tex]

Where:

[tex]m=2\\b=-2[/tex]

Notice that:  

- Since both lines have the same slope, they are parallel.

- The symbol of the first inequality is [tex]\geq[/tex] . This indicates that the line is solid and the shaded region must be above the line.

- The symbol of the second inequality is [tex]\leq[/tex] . This indicates that the line is solid and the shaded region must be below the line.

Therefore, the  second graph represents the system of linear inequalities.

Answer:

b

Step-by-step explanation:

Answer:

C) I and III only

Step-by-step explanation:

Let full pool is denoted by O

Days Hose x takes to fill pool O = a

Pool filled in one day x = O/a

Days Hose y takes to fill pool O = b

Pool filled in one day y = O/b

Days Hose z takes to fill pool O = c

Pool filled in one day z = O/c

It is given that

                         a>b>c

[tex]a>b>c>d\\\implies x<y<z<(x+y+z)\\[/tex]

Days if if x+y+z fill the pool together = d

1 day if x+y+z fill the pool together [tex]=O(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=\frac{O}{d}---(1)[/tex]

I) d < c

d are days when hose x, y, z are used together where as c are days when only z is used so number of days when three hoses are used together must be less than c when only z hose is used. So d < c

III) [tex]\frac{c}{3}<d<\frac{a}{3}[/tex]

Using (1)

[tex]\frac{bc+ac+ab}{abc}=\frac{1}{d}\\\\d=\frac{abc}{ab+bc+ca}\\\\As\quad(a>b>c)\\(ab+bc+ca)<3ab\\\\d=\frac{abc}{ab+bc+ca}>\frac{abc}{3ab}\\\\d>\frac{c}{3}[/tex]

Similarly

[tex]\frac{bc+ac+ab}{abc}=\frac{1}{d}\\\\d=\frac{abc}{ab+bc+ca}\\\\As\quad a>b>c\\(ab+bc+ca)>3bc\\\\d=\frac{abc}{ab+bc+ca}<\frac{abc}{3bc}\\\\d<\frac{a}{3}[/tex]

So,

[tex]\frac{c}{3}<d<\frac{a}{3}[/tex]

Answer:

(-1,3), (0,-1)

(-1-3)/(0+1)= -4/1= -4

the answer is d

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\text{look at the picture}\ \#1\\\\\text{The fomula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Form the graph wi hate points:}\\\\(-1, 3)\ \text{and}\ (0, -1).\\\\\text{Substitute:}\\\\m=\dfrac{-1-3}{0-(-1)}=\dfrac{-4}{1}=-4[/tex]

[tex]\bold{METHOD\ 2:}\\\\\text{look at the picture}\ \#2\\\\slope=\dfrac{rise}{run}\\\\rise=-4\\run=1\\\\slope=\dfrac{-4}{1}=-4[/tex]

The distance between the two kites is approximately 380 ft.

To find the distance between the two kites, we can use the law of cosines. Let's call the distance between the two kites as 'd'. We can use the equation:

d^2 = 380^2 + 420^2 - 2 * 380 * 420 * cos(30)

By plugging in the values, we get:

d^2 = 144400

Taking the square root of both sides, we find:

d = 380 ft

So, the distance between the two kites is approximately 380 ft.

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Answer:

11.2

Step-by-step explanation:

tan( angle ) = opposite / adjacent