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2 years ago

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The diagram below represents the measurements of Jennie’s yard. The yard’s width is x feet shorter than its length. If the area

of the yard is 540 square feet, how many feet shorter than the length is the width?
A yard with a length of 30 feet and a width of (30 minus x) feet.

Which equation represents the scenario?
30 + (30 – x) = 540
540 – 30 = 30 – x
30(30 – x) = 540
540 – (30 – x) = 30

2 answers:

larisa [96]2 years ago

5 0

Answer:

30(30-x)=540

Step-by-step explanation:

AleksandrR [38]2 years ago

3 0

Answer:

30(30 – x) = 540

c

Step-by-step explanation:

hi , which grade r u in ?

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HURRY PLS!!!!!!!!

Feliz [49]

Answer:

The answer is D on edgen.

Step-by-step explanation:

D. 80

(all you do is add 40, 14 and 26 from the graph)

7 0

2 years ago

Read 2 more answers

Statistics In the manual “How to Have a Number One the Easy Way,” it is stated that a song “must be no longer than three minutes

dimaraw [331]

Answer:

We conclude that the sample is from a population of songs with a mean greater than 210 seconds.

Step-by-step explanation:

We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.

Assume that the standard deviation of song lengths is 54.5 sec.

Let $\mu$ = <u><em>population mean length of the songs</em></u>

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 210 seconds {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}

Alternate Hypothesis, $H_A$ : $\mu$ > 210 seconds {means that the sample is from a population of songs with a mean greater than 210 seconds}

The test statistics that will be used here is <u>One-sample z-test statistics </u>because we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean length of songs = 252.5 seconds

$\sigma$ = population standard deviation = 54.5 seconds

n = sample of current hit songs = 40

So, <u><em>the test statistics</em></u> = $\frac{252.5-210}{\frac{54.5}{\sqrt{40} } }$

= 4.932

The value of z-test statistics is 4.932.

Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so <u><em>we have sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.

4 0

2 years ago

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the wate

Masja [62]

Answer: a. 112 feet, b= 3 seconds, c= 256 feet, d = 6 seconds

Step-by-step explanation:

Here is the complete question:

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the water is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Find the actual value(s) now to each question. Use the solution from the previous question to assist you with what you are actual solving for.

(a) From what height was the quarter tossed?

The quarter was tossed at 112 feet.

(b) How long does it take the quarter to reach its maximum height?

It will take ________ seconds for the quarter to reach its maximum height.

(c) What is the maximum height of the quarter?

The maximum height of the quarter is ________ feet.

(d) How much time does it take for the quarter to hit the water?

It will take ______ seconds for the quarter to hit the water.

a. Since the function is

d(t) = −16t² + 96t + 112,

The coin is tossed at 112 feet. This is because it is the the initial value of the function. It is the constant term and does not depend on any other variable.

b. To calculate the maximum height, we have to find vertex of the function, that has coordinates of h,k and,

h = -b/2a and k = f(h).

From the question, we are aware that,

a = -16, b = 96, c = 112

Using the values, the vertex will be:

h = -b/2a

= -96/(2 × -16)

= -96/-32

= 3

k = f(3)

= 16t² + 96t + 112

= -16(3)² + 96(3) + 112

= -144 + 288 + 112

= 256

The maximum height is therefore 256 feet, and time needed to reach the height will be 3 seconds.

c. The maximum height has been calculated and it is 256 feet.

d. The time it take for the quarter to hit the water will be:

= 3 seconds × 2 = 6 seconds

Since the maximum height took 3 seconds, it would take another 3 seconds to hit the water. This makes it 6 seconds

4 0

2 years ago

rusak2 [61]

ANSWER TO QUESTION 1

The set of natural numbers that are factors of 20 are natural numbers that divides 20 exactly without a remainder.

These natural numbers are;

{ $1,2,4,5,10,20$ }

Therefore the correct answer is D

ANSWER TO QUESTION 2

Given that the universal set U has elements

{ $1,2,3,4,5,6,7,8,9,10$ }

and the set P also has elements

{ $2,4,6,8,10$ }

The elements of P' are the elements that are in the universal set but are not in set P.

These elements are;

{ $1,3,5,7,9$ }

The correct answer is C

ANSWER TO QUESTION 3

The distance is given by the absolute value equation

$d=|130-25t|$

If the is 15 feet away then $d=15$

This implies that;

$15=|130-25t|$

We now split the absolute value sign to obtain,

$15=130-25t$

or

$-15=130-25t$

We now solve for t to obtain;

$15-130=-25t$

or

$-15-130=-25t$

$\frac{115}{25}=t$

or

$\frac{145}{25}=t$

This gives us

$4.6=t$

or

$5.8=t$

The correct answer is C

ANSWER TO QUESTION 4

Given

P={ $0,1,2,3,4,56,7,8,9$ }

and

V={ $2,4,6,810,1216,18,20$ }

P $\cap$ V={2,4,6,8}

P\V are elements in P only .

This means that we have to take out the elements of the intersection of the two sets from P.

P\V ={0,1,3,5,5,7,9}

The correct answer is B

ANSWER TO QUESTION 5

The correct answer is B.

In listing the elements of a set, we do not repeat the element. In order words we list only distinct elements.

Blueberry is repeating in both sets but we have to list it once.

ANSWER TO QUESTION 6.

The correct answer is 220

We were told that 250 play basket ball

If 120 play both sports, then

250-120=130

play only basketball

Now the number of people who play only baseball

$350-250=100$

But the number of people who play baseball

$120+100=220$

see diagram

7 0

2 years ago

Conservation of Species A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sol

JulijaS [17]

Answer:

The turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

Ten years after the conservation measures are implemented the population will be 3260 turtles.

Step-by-step explanation:

To find the rate of growth of the turtle population at any time <em>t</em> you need to find $N'(t)$

$\frac{d}{dt}N(t)=\frac{d}{dt}(2t^3+3t^2-4t+1000)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dt}(2t^3)+\frac{d}{dt}(3t^2)-\frac{d}{dt}(4t)+\frac{d}{dt}(1000)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\N'(t)=6t^2+6t-4$

In particular, when t = 2 and t = 6, we have

$N'(2)=6(2)^2+6(2)-4=32\\\\N'(6)=6(6)^2+6(6)-4=248$

so the turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

The turtle population at the end of the tenth year will be

$N(10)=2(10)^3+3(10)^2-4(10)+1000\\N(10)=3260 \:turtles$

3 0

2 years ago