the histogram to the right displays the height of 122 trees and Mr. Maciag's subdivision. He is very excited about autumn and the leaves changing colors. Height ranged between 108 cm and 345 cm. Let the function "f" map a tree height to the frequency of the column that tree belongs to. What is the value of f(250)? Explain the steps you followed to find the value.​

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

\(3x - (2x + 1) \\ = 3x - 2x - 1 \\ = x - 1\)

x - 1

Answer: x-1

Step-by-step explanation: in the picture

_________

\( \: \)

\( \frac{j}{3} = 4.5\)

\(j = 4.5 \times 3\)

\(j = \bold{13.5}\)

Answer:

A. y<-2x-1

Step-by-step explanation:

not C or D because it is a dashed line meaning the linear equation will either have the symbol ≥ or ≤.

when y is less than, you shade below

thus, the answer is A

Answer:

9 mi

Step-by-step explanation:

V = 1385.44 mi³, radius r = 14/2 = 7 mi, find h

Use V = πr²h

1385.44 = 3.14 * 7² * h = 153.86 h

so

h = 1385.44/153.86 = 9 mi

Answer:

The value of k that makes the relationship shown in the table below proportional is \(\mathbf{\frac{1}{2}}\)

Step-by-step explanation:

The relation is proportional if \(y=kx \:or\:k=\frac{y}{x}\)

Putting values of x and y to find k.

For x =2 and y =1 k is: \(k=\frac{y}{x}=\frac{1}{2}\)

For x =4 and y =2 k is: \(k=\frac{y}{x}=\frac{2}{4} =\frac{1}{2}\)

For x =6 and y = 3 k is: \(k=\frac{y}{x}=\frac{3}{6} =\frac{1}{2}\)

For x = 8 and y = 4 k is: \(k=\frac{y}{x}=\frac{4}{8} =\frac{1}{2}\)

For x =10 and y = 5 k is: \(k=\frac{y}{x}=\frac{5}{10} =\frac{1}{2}\)

So, The value of k that makes the relationship shown in the table below proportional is \(\mathbf{\frac{1}{2}}\)

Answer:

4.9 feet

Step-by-step explanation:

First, we need to determine the height of the building using the following:

\(L^2 = H^2 + B^2\)

Where

H = Height of the building

L = Length of the first ladder = 20ft

B = Distance from the base of the building = 10ft

So, we have:

\(20^2 = H^2 + 10^2\)

\(400 = H^2 + 100\)

\(H^2 = 400 - 100\)

\(H^2 = 300\)

\(H = \sqrt{300\)

Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:

\(L_2^2 = H^2 + B_2^2\)

Where

\(L_2 = 18\) --- Length of the second ladder

\(H = \sqrt{300\) ----- Height of the building

So, we have:

\(18^2 = \sqrt{300}^2 + B_2^2\)

\(324 = 300 + B_2^2\)

\(B^2_2 = 324 - 300\)

\(B^2_2 = 24\)

Solving for B2, we have:

\(B_2 = \sqrt{24\)

\(B_2 = 4.9\)

The given points are (-1,0) and (4,2).

We find the distance between these points using the following formula.

Using the given points, we have

The exponential function that represents this situation is f(x) = 0.0625(2)ˣ

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

(x, y) = (1, 0.125) and (2, 0.25)

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * rˣ

Where

r = 0.25/0.125

So, we have

r = 2

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

f(x) = a * (2)ˣ

Using the points, we have

a * (2)² = 0.25

So, we have

a = 0.0625

Hence, the function is f(x) = 0.0625(2)ˣ

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To round any decimal number the rule is as follows:

If the decimal value is greater or equal that 5, then round it up to the next value.

If the decimal value is less than 5, round it to the previous integer.

For the example 7.299, the third and second decimal values are grearter than 5 so you have to round the decimal in the tenth place to 3

7.299≅7.3

Now to round it to the nearest integer, the decimal value 3 is less than 5 so you have to round it to the previous integer:

7.3≅7

Correct choise is A)

The volume of the sculpture is 92.316 feet³.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

Cone-shaped sculpture:

Height = 5 feet

Base circumference = 26.376

This means,

2πr = 26.376

r = 26.376/(2 x 3.14)

r = 4.2 feet

Now,

The volume of the sculpture.

= 1/3 x 3.14 x 4.2 x 4.2 x 5

= 92.316 feet³.

Thus,

92.316 feet³ is the volume of the sculpture.

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Answer:

y = -\(\frac{1}{2}\)x - 4

Step-by-step explanation:

2y + x = -8

2y = -x - 8

\(\frac{2y}{2}\) = \(\frac{-x - 8}{2}\)

y = -\(\frac{1}{2}\)x - 4

y = \(\frac{-1}{2} x - 4\)

Answer:

25

Step-by-step explanation:

l x w = h

25 x 7.2 = 180

Answer:

605

Step-by-step explanation:

11x55=605

Answer:

Price decresed to 124.00

Step-by-step explanation:

Answer:

A, D and B must be in a straight line.

Step-by-step explanation:

If D is between A and B, than AD+DB=AB

This would mean A, D and B would be in a straight line.

Given

To find

we know that

Inserting the value of radius

Answer:

y-intercept

Step-by-step explanation:

Both lines intercepts the y-axis at y = 5.

Therefore the y-intercept of both lines is 5. At this point, x = 0 for both lines.

This implies that both lines shown on the graph have the same y-intercept value, which is 5.

Answer:

3.7ml/hr

Step-by-step explanation:

From the question

A nurse is preparing to administer dopamine 2 mcg/kg/min by continuous IV infusion

Step 1

The patient weighs 110lb(pounds

Convert the patients weight to kilogram

1 lb = 0.454kg

110lb =

Cross Multiply

110lb × 0.454kg

= 49.94kg

The patient weight = 49.94kg

Step 2

The dosage to to be administered by the nurse = 2 mcg/kg/min

If 1 kg = to be administered 2mcg/min

49.94 kg =

(49.94kg × 2mcg/min)/1

= 99.88mcg/min

Therefore, for the patient's body weight, the patient's dosage = 99.88mcg/min

Step 3

Available dopamine is 400mg in 250ml

We have to convert this to mcg

Hence,

1 mg = 1000mcg

400mg =

Cross Multiply

= 400mg × 1000mcg

= 400000mcg

Hence, the available dopamine is administer in 250ml/400000mcg

Part 3

Since 60 minutes is 1 hour

The nurse should set the IV pump to deliver how many ml/hr

(99.88mcg/min × 250ml × 60mins)/ 400000mcg

= 3.7455ml/hr

Approximately to the nearest tenth = 3.7ml/hr

Answer:

y = \(\frac{2}{3}\) x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = \(\frac{4-0}{0-(-6)}\) = \(\frac{4}{0+6}\) = \(\frac{4}{6}\) = \(\frac{2}{3}\)

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = \(\frac{2}{3}\) x + 4 ← equation of line

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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i think the answer is 35° because the triangles are congruent to each other

THE MIDPOINT FORMULAR IS GIVEN BY

\(( \frac{x1 + x2}{2} . \frac{y1 + y2}{2} ) \\ \\ = (\frac{ - 2 + ( - 4)}{2} . \frac{ - 3 + 10}{2} ) \\ = ( \frac{ - 6}{2} . \frac{7}{2} ) \\ = ( - 3. \frac{7}{2} )\)

ATTACHED IS THE SOLUTION

Answer:

5/6 ÷ 3/4 = 20/18 as simplified as 10/9 in fraction form. 5/6 ÷ 3/4 = 1.1111 in decimal form.

Step-by-step explanation:

The value of 5/6 divided by 3/4 is 10/9.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

5/6 divided by 3/4

as, fraction does not perform proper division

So,  5/6 ÷ 3/4

= 5/6 x 4/3

= 20 / 18

= 10 / 9

Hence, the resultant value is 10/9

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Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.

The sum of angles in a circle is always equal to 360 degrees or 2π radians.

This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.

With regard to the above problem,

We are given three angles in a circle named as follows:

a) 81°

b) 164°

c) x

The above rule state that

81 + 164 + x = 360°

thus, x = 360 - 81 - 164

x = 360 -245

x = 115°

Thus the value of ∠x is  115°

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Full Question:

See attached image.

Hi, there!

 ______

\(\begin{tabular}{c|1} \boldsymbol{Things \ to \ Consider} \\\cline{1-3} \end{tabular}\)

(1)

 - The slopes of parallel lines are identical.

{The line \(\sf{y=7x-1}\) has a slope of 7}

Thus,

{The slope of the line that is parallel to the aforementioned line (whatever its equation happens to be) is \(\sf{7}\).}

(2)

 - The slopes of perpendicular lines are negative inverses of each other.

The negative inverse of 7 is

\(-\dfrac{1}{7}\).

Therefore,

\(\textsc{Answers:\begin{cases} \bf{7} \\ \bf{-\dfrac{1}{7}} \end{cases}}\)

Hope the answer - and explanation - made sense,

happy studying!!                                                                 \(\tiny\boldsymbol{Frozen \ melody}\)

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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