Mr. Johnston supports a young tree by using a stake and a string forming a right angle with the ground.
60 in.
33 in.
What is the length of the string? Round to the nearest tenth.

Answer: 8/15

Step-by-step explanation:

Vertical:     there are 4 shaded squares out of 5 total squares  →    4/5

Horizontal: there are 2 shaded squares out of 3 total squares  →    2/3

                                       \(\dfrac{4}{5}\times \dfrac{2}{3}\quad =\large\boxed{\dfrac{8}{15}}\)

Answer:

\(5(x - 2) = \frac{15x + 6}{3} - 12 \\ 5(x - 2) = \frac{15x + 6 - 36}{3} \\ 5(x - 2) = \frac{15x - 30}{3} \\ 5(x - 2) = \frac{15(x - 2)}{3} \\ 15(x - 2) = 15(x - 2)\)

Answer:

All real numbers

Step-by-step explanation:

Given

5(x - 2) = \(\frac{15x+6}{3}\) - 12

Multiply through by 3 to clear the fraction

15(x - 2) = 15x + 6 - 36 ← distribute left side and simplify

15x - 30 = 15x - 30

Since both sides are equal then any real value of x will be a solution.

Thus the solution is All real numbers

Answer:

The correct answer option is 'then'.

Step-by-step explanation:

Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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Answer:

$25.20

Step-by-step explanation:

This is the answer because:

1) 10 + 10 + 5 = 25

2) Next, dimes are equal to 0.10

25 + 0.10 + 0.10 = 25.20

Hope this helps! :D

The perimeter of the figure is 48 meters

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

length = 10 meters

width = 14 meters

The perimeter of the figure is then calculated as

Perimeter = 2 * (length + width)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (10 + 14)

Evaluate

Perimeter = 48

Hence, the perimeter is 48 meters

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Answer:

s=5

v=2

Step-by-step explanation:

Answer:

y = -8/15

Step-by-step explanation:

log (4y + 1) = log (y - 7) - 2log2

log (4y + 1) = log (y - 7) - log2² (power law)

log (4y + 1) = log [(y - 7)/4]

4y + 1 = (y - 7)/4 (remove log)

4(4y + 1) = y - 7

16y - y = -8

15y = -8

y = -8/15

The exponential function that models the situation in this problem is defined as follows:

y = 3(4)^x.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which:

Three friends start the project, hence the initial value represented by the parameter a is given as follows:

a = 3.

Each day, the number of people in the project is multiplied by four, hence the parameter b is given as follows:

b = 4.

Hence the function is:

y = 3(4)^x.

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On [0, 2], A(x) can be represented by the linear equation A(x) = (1/2)x.

This means that for every x in the interval [0, 2], the value of A(x) is equal to one-half times x. For example, when x = 1, A(x) = (1/2)x = (1/2) * 1 = 1/2.

On [0, 2], A(x) can be represented by the linear equation A(x) = (1/2)x.

On (2,4], A(x) can be represented by the linear equation A(x) = ((-1/2)x + 2). This means that for every x in the interval (2,4], the value of A(x) is equal to one-half times x minus 2. For example, when x = 3, A(x) = ((-1/2)x + 2) = (-1/2) * 3 + 2 = 2 - 1.5 = 0.5.

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Integers g(x) = \((x - 0)^2\) + 5 the desired form with a = 1, h = 0, and k = 5.

The function f(x) = \(x^2\), a translation 5 units up gives us the function:

g(x) = f(x) + 5

g(x) = \(x^2 + 5\)

The form \(a(x - h)^2\) + k, we need to complete the square.

We can do this by adding and subtracting \((h^2)\) inside the parentheses:

g(x) = \(x^2 + 5 + h^2 - h^2\)

The terms that involve x and those that do not:

g(x) = \((x^2 - h^2) + 5 - h^2\)

The expression \((x^2 - h^2)\) using the difference of squares formula:

g(x) = \((x - h)(x + h) + 5 - h^2\)

The coefficient of \((x - h)^2\) to be 1, so we can divide both sides by (x + h) and then multiply by a constant factor a:

g(x) = \(a(x - h)^2 + 5 - h^2\)

g(x) = \(a(x^2 - 2hx + h^2) + 5 - h^2\)

g(x) = \(ax^2 - 2ahx + ah^2 + 5 - h^2\)

To get the correct coefficients, we need to choose a and h such that:

2ah = 0 (so that the x term disappears)

\(ah^2 + 5 - h^2\) = 5 (so that the constant term is 5)

The first condition is satisfied if we choose h = 0.

The second condition is satisfied if we choose a = 1.

Then we have:

g(x) = \(1(x - 0)^2 + 5 - 0^2\)

g(x) = \((x - 0)^2\) + 5

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Answer:

299.03

Step-by-step explanation:

Answer:

a) the average of change for the number of bacteria from 0 to 6.8 hours is

\(the \: average \: of \: change \: = \frac{2292 - 1000}{6.8 - 0} = 190 \: bacteria \: per \: hour\)

b)

\(the \: average \: rate\: of \: change \: from \: 10.2 \: to \: 13.6 \: hours \: = \frac{5080 - 3856}{13.6 - 10.2} = 360\)

Answer:

you need to pour out 1/12 of the water.

Step-by-step explanation:

\(\frac{3}{4} -\frac{2}{3}\)

you need to find like denominators

\(\frac{9}{12} -\frac{8}{12 }\)

Now subtract

\(\frac{1}{12}\)

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Using proportions, the amount of money that Sam would need each month to pay his bills is of:

b. at least $425.32.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, his annual social security benefit is of 42% of $37,991, hence:

A = 0.42 x 37991 = $15,956.22.

Hence the monthly amount is given by:

M = 15956.22/12 = $1,329.68

He needs $1,755 monthly, hence the amount he needs is of at least:

An = 1755 - 1329.68 = $425.32.

Which means that option b is correct.

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Answer:

C

Step-by-step explanation:

the hypotenuse and the leg of the first right angle are congruent to the other triangle's.

The correct answer is b) unchanged. Cutting a chocolate bar in half does not affect its density.

When a chocolate bar is cut in half, its density remains unchanged. Density is a physical property of a substance that is determined by its mass per unit volume. When the chocolate bar is cut in half, the mass is also divided into two equal parts, resulting in a reduction of the volume by half as well. Since both the numerator and denominator in the density formula change proportionally, the density remains the same.

For example, if the density of a chocolate bar is 1 gram per cubic centimeter, cutting it in half would result in two smaller bars, each with half the volume and half the mass. The density of each of the new bars would still be 1 gram per cubic centimeter, even though they are smaller in size.

Therefore, the correct answer is b) unchanged. Cutting a chocolate bar in half does not affect its density.

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Answer:

120.8 feet

Step-by-step explanation:

Answer:

inside

120

Step-by-step explanation:

E D G E N U I T Y

Stay safe and have a wonderful day/afternoon/night!!!!!

Brainliest?!?!

Answer:

1.) Inside

2.) 120

Step-by-step explanation:

Give Him/Her Brainliest!    ↑   ( ˙ ˘ ˙)

ʕ •ᴥ•ʔ  εїз

Answer:

9.1 is the nearest tenth

9.11 to the nearest hundredth

just slightly to the right of 9.1

Step-by-step explanation:

sqrt(83)

sqrt(81) = 9

So we know that it is slightly greater than 9

9.1*9.1 =81.81

9.2*9.2=84.64

9.1 is closer

9.11 * 9.11 =82.9921

9.12 * 9.12 =83.1744

9.11 is closer

Answer:

9.1 is the nearest tenth

9.11 to the nearest hundred

to the right of 9.1

Step-by-step explanation:yi did it on i ready6

Answer:we need to know the size of the wall

Step-by-step explanation:

Step-by-step explanation:

3x^2-2x+1

3(2)^2-2(2)+1

3(4)-4+1

12-4+1

8+1=9 Answer

Step-by-step explanation:

3(2)^2 - 2x + 1

=3x4 - 2x + 1

=12 - 2x + 1

= 13 - 2x

Answer: 13 - 2x

Answer:

5.7 gal / hour

5.7 gal / 60 min

5.7(16) c / 60 min

Answer:

71°

Step-by-step explanation:

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, forming the sides of the angle.

If we know that all 3 of a triangle's angles must add up to 180°, we can use this expression to solve for the missing angle:

Inserting our 2 angles into the expression gives:

To solve for angle 3, we can rearrange the equation above:

Solving this equation gives us:

Therefore, the measure of the missing angle is 71°

Answer:

71°

Step-by-step explanation:

What is an angle?

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, forming the sides of the angle.

If we know that all 3 of a triangle's angles must add up to 180°, we can use this expression to solve for the missing angle:

angle 1 + angle 2 + angle 3 = 180°

Inserting our 2 angles into the expression gives:

68° + 41° + angle 3 = 180°

To solve for angle 3, we can rearrange the equation above:

180 - (68 + 41) = angle 3

Solving this equation gives us:

71° = angle 3

Therefore, the measure of the missing angle is 71°

The lower limit is 0.481 and upper limit is 0.579 .

Given

a=0.05,

Z(0.025)=1.96 (from standard normal table)

So

lower limit is

p= -Z* √(p*(1-p)/n)

=0.53-1.96* √(0.53*(1-0.53)/400)

=0.481

So upper limit is

p = +Z*√(p*(1-p)/n)

=0.53+1.96*√(0.53*(1-0.53)/400)

=0.579

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Based on the figure provided, it is clear that each man has a preference for a certain woman. Specifically, man 1 prefers woman 3, man 2 prefers woman 5, man 3 prefers woman 2, man 4 prefers woman 4, and man 5 prefers woman 1.

Using this information, we can determine the number of matchings by considering each man and his preferred woman.

Starting with man 1, he must be matched with woman 3. There is only one possible match for him.

Moving on to man 2, he must be matched with woman 5. Again, there is only one possible match for him.

For man 3, his preferred woman is already matched with man 1. Therefore, he must be matched with woman 4.

For man 4, his preferred woman is already matched with man 2. Therefore, he must be matched with woman 2.

Finally, for man 5, his preferred woman is already matched with man 3. Therefore, he must be matched with woman 1.

Putting all of these matches together, we have:

Man 1 -> Woman 3
Man 2 -> Woman 5
Man 3 -> Woman 4
Man 4 -> Woman 2
Man 5 -> Woman 1

Therefore, there is only one possible matching of the five men with the five women given the constraints in the figure above.

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