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2 years ago

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A park has a grinkgo tree a dogwood tree and 2 blue spruce trees the blue spruce trees are 8 years old the grinkgo tree is 2 yea

rs less than three times the age of the dogwood tree the grinkgo tree is also half the sum of the ages of the dogwood tree and both if the blue spruce trees write and solve an equation to find the ages of the grinkgo and the dogwood trees.

1 answer:

enot [183]2 years ago

7 0

Answer:

The age of the grinkgo tree is 10 years old and the age of the dogwood tree is 4 years old

Step-by-step explanation:

Let

x -----> the age of the grinkgo tree

y -----> the age of the dogwood tree

z -----> the age of the blue spruce tree

we know that

$x=3y-2$ ------> equation A

$z=8$ ----> equation B

$x=\frac{1}{2}(y+2z)$

substitute the value of z

$x=\frac{1}{2}(y+2(8))$

$x=\frac{1}{2}(y+16)$ -----> equation C

equate equation A and equation C and solve for y

$3y-2=\frac{1}{2}(y+16)$

$6y-4=(y+16)$

$6y-y=16+4$

$5y=20$

$y=4$

Find the value of x (equation A or equation C)

$x=3(4)-2=10$

therefore

The age of the grinkgo tree is 10 years old and the age of the dogwood tree is 4 years old

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A patrolman spends three times as many hours patrolling as she does completing paper work. If she works 36 hours per week, how m

fomenos

Answer:

27 hours

Step-by-step explanation:

Let her work "x" hours for paperwork

Since, patrolling amount of hours is THREE TIMES that,

Patrolling = 3x hours

Total Hours = 36

That is including paperhour work (x) and patrolling (3x). So we can setup an equation in x and solve for x first:

x + 3x = 36

4x = 36

x = 36/4

x = 9 hours

Amount of Hours for Patarolling = 3x hours = 3(9) = 27 hours

So, she spends 27 hours patrolling

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2 years ago

the radius of the center circle of a basketball court is 6 feet. What is the circumference of the center circle.

Elena-2011 [213]

Remember the equation to find the circumference?

Equation of circumference: Pi x 2(radius)

Therefore, 3.141592654 x 2(6ft) = 37.7 feet

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2 years ago

Read 2 more answers

Solve the polynomial equation x3 + 7x2 − 16x −112 = 0 and select the correct answer below.

prohojiy [21]

X^3 + 7*x^2 + -16*x-112
=(x + 4)*(x + 7)*(x - 4)

7 0

2 years ago

Please help and show working (please)

Alexxandr [17]

In mathematical notation, ∑ means summation. So wherever you see the symbol, you have to sum over all elements in the set. Let's solve the question.

a. ∑m means, to sum all elements in the set m: ∑m = 12 + 15 + 20 + 30 = 77

b. ∑ $f^{2}$ means to sum all elements in the set f as the square of the elements f = $5^{2} + 9^{2} + 10^{2} + 16^{2} = 25 + 81 + 100 + 256 = 462$

c. ∑mf means to sum all elements as the product of the elements of m and f = (12×5) + (15×9) + (20 $(12^{2}(5)) + (15^{2}(9)) + (20^{2}(10)) + (30^{2}(16)) = 21145$ 10) + (30×16) = 875

d. ∑ $m^{2}f$ means to sum all elements as the product of the square of m and f = $((12*12)(5)) + ((15*15)(9)) + ((20*20)(10)) + ((30*30)(16)) = 21145$

4 0

2 years ago

Researchers studying starfish collected two independent random samples of 40 starfish. One sample came from an ocean area in the

krek1111 [17]

Answer:

The test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

Step-by-step explanation:

The experiment conducted here is to determine whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. north and south.

The hypothesis to test this can be defined as follows:

<em>H₀</em>: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ = <em>p</em>₂.

<em>Hₐ</em>: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ ≠ <em>p</em>₂.

The two-proportion <em>z</em>-test would be used to perform the test.

A sample of <em>n</em> = 40 starfishes are selected from both the ocean areas.

It provided that of the 40 starfish from the north, 6 were found to be over 8 inches in length and of the 40 starfish from the south, 11 were found to be over 8 inches in length.

Compute the sample proportion of starfish from north that were over 8 inches in length as follows:

$\hat p_{n}=\frac{6}{40}=0.15$

Compute the sample proportion of starfish from south that were over 8 inches in length as follows:

$\hat p_{s}=\frac{11}{40}=0.275$

The test statistic is:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

Compute the combined proportion <em>P</em> as follows:

$P=\frac{X_{n}+X_{s}}{n_{n}+n_{s}}=\frac{6+11}{40+40}=0.2125$

Compute the test statistic value as follows:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

$=\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$

Thus, the test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

8 0

2 years ago