A landscape plan includes a rectangular flower bed that is surrounded the wood planks. In the drawing, the
rectangular flower bed is 4 in. by 5 in. The length and width of the actual flower bed will be 30 times larger
than the length and width in the drawing.
(a) What is the perimeter of the drawing? Show your work.

(b) What is the perimeter of the actual flower bed? Show your work.

(c) What is the effect on the perimeter of the flower bed with the dimensions are multiplied by 24? Show

Answer:

kionda sold 15 and jeremy 10

Step-by-step explanation:

A circle is 360 degrees so 360 = b + 96 + 209

360 = b + 305

b = 55 degrees.

The calculated values of x and y in the figure are x = 2 and y = 4

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

The figure

Where, we have

equal side lengths

This means that

2y - 1 = 3y - 5

Evaluate

y = 4

Next, we have

x + 3 = 3/2x + 2

So, we have

1/2x = 1

This gives

x = 2

Hence, the values of x and y in the figure are x = 2 and y = 4

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9514 1404 393

Answer:

Step-by-step explanation:

Let g represent the age of the garden. Then the age of the tree is 15g. The sum of their ages is ...

  g +15g = 128

  16g = 128 . . . . . collect terms

  g = 128/16 = 8 . . . . divide by the coefficient of g

The garden is 8 years old; the tree is 120 years old.

The amount that each theater make if they received the same number of moviegoers will be $2550.

From the information, 5,780 people saw a new movie at 17 different theaters and each theater sold tickets at $7.50 a piece.

Therefore, the amount that each theater make if they received the same number of moviegoers will be:

= (5780 × $7.50) / 17

= $43350 / 17

= $2550

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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Answer:

Down below

Step-by-step explanation:

   a. Net income= $100,000 (as given in the question)

   b. Return on equity= (net income)/(shareholder’s equity)

Shareholder’s equity= $400,000

Thus return on equity= 100000/400000 = 0.25  or 25%

   a. Net income= $100000 + 50000 –  12800 (debt interest 8% of     $160000)

= $137,200

b. Return on equity= (net income)/(shareholder’s equity)

= 137200/400000

=0.343  or 34.3%

a. Net Income= $100000 + 50000

= $150000

b. Return on equity= (net income)/(shareholder’s equity)

= 150000/(400000 + 160000)

Where ($560,000) 400000 + 160000 is shareholder’s equity

= 0.27 or 27%

Answer:

The t-statistic for a hypothesis test that is designed to answer the question is 2.4.

Step-by-step explanation:

Our test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation of the saple and n is the size of the sample.

A store manager designs a new accounting system that will be cost effective if the mean monthly charge account balance is more than $50.

This means that \(\mu = 50\)

A sample of 100 accounts is randomly selected. The sample mean balance is $56 and the sample standard deviation is $25.

This means that \(X = 56, s = 25, n = 100\). So

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}\)

\(t = \frac{56 - 50}{\frac{25}{\sqrt{10}}\)

\(t = \frac{6}{2.5}\)

\(t = 2.4\)

The t-statistic for a hypothesis test that is designed to answer the question is 2.4.

Answer:

4-d=8

Step-by-step explanation:

First, you must know what a mathematical sentence and a variable is. A mathematical sentence is  equivalent (same) as an equation.

To be an equation/mathematical sentence,

You need the following:

~ Numbers/variables

~ Equal sign

A variable is just an unknown number  (It's still a number, you just don't know what it is yet- think- VARI is the same meaning as vary, the number can vary.)

Let's look back at the problem.

4-d=8

Has an equal sign

Has both numbers (remember a variable is still counted as a number)

So there's one you missed!

4-v, no, as there is no equal sign.

6, no, it's just a lone number.

5g, means 5xg, but there is no equal sign-no.

So there you have it. I hope this helped you!!! ^^

Answer:

Step-by-step explanation:

\(\frac{x}{11}=\frac{7}{17}\\\\\mathrm{Multiply\:both\:sides\:by\:}11\\\\\frac{11x}{11}=\frac{7\cdot \:11}{17}\\\\\mathrm{Simplify\:}\frac{11x}{11}:\quad x\\\\\mathrm{Simplify\:}\frac{7\cdot \:11}{17}:\quad \frac{77}{17}\\\\x=\frac{77}{17}\)

The properties of the graph of the function y = f(x) indicates;

a) The domain is [-4, 6]

b) The range is; [-8, 5.5]

c) The function is neither even nor odd

d) f(x) = -3 for x = -4, x ≈ -1, x ≈ 5.26

e) The local maximum is; (-2, 4.5)

The local minimum is; (3, -8)

f) The function increases in the intervals; [-4, -2] and [5, 6]

The function decreases in the interval; [-2, 3]

A function is a relationship between two sets. It is mathematical rule that maps each of the elements of a set, known as the domain, to exactly one element from another set, known as the range.

a) The domain of the function y = f(x) is the set of the x-values for which the function is defined. The information obtained from the graph indicates that the function is defined from x = -4 and x = 6, therefore, the domain of f(x) is; [-4, 6]

b) The range of f(x) is the set of y-values of the function, based on the domain of the function. The details on the graph indicates that the maximum value of the function is 5.5 and the minimum y-value is -8, therefore, the range is; [-8, 5.5]

c) The function is even, odd or neither if f(-x) = f(x, f(-x) = -f(x), or neither, or if the function is symmetric to the y-axis, the origin or neither. The graph of the function indicates that the function is not symmetric to the y-axis or the origin, so the function is neither even nor odd.

d) To solve f(x) = -3, the x-values where f(x) = -3 are required. The point (-4, -3) on the graph indicates that when f(x) = -3, x = -4.

Similarly, an horizontal line, f(x) = -3, indicates that when f(x) = -3, x = 1

The equation of the straight line portion is; y + 6 = ((-6 - 5.5)/(5 - 6))·(x - 5)

y + 6 = 11.5·(x - 5) = 11.5·x - 57.5

y = 11.5·x - 63.5

When f(x) = y = -3, we get; -3 = 11.5·x - 63.5

x ≈ 5.26

Therefore; f(x) = -3 when x = -4, x ≈ 1, and x ≈ 5.26

e) The local maximum are the points where the y-values are higher compared to the surrounding points.

The local maximum is the point (-2, 4.5)

The local minimum are points where the function is point that is lower compared to the surrounding points on the graph, therefore;

The local minimum is the point (3, -8)

f) The details on the graph indicates that the function increases between x = -4 and x = -2, and between x = 5 and x = 6.

The function decreases between x = -2 and x = 3

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The solution to the equation 8^(2x) = 4096 is x = 2.

To solve the equation 8^(2x) = 4096, we can follow the steps outlined below:

Step 1: Recognize the base

The equation involves the base 8. Since 8 can be written as 2^3, we can rewrite the equation as (2^3)^(2x) = 4096.

Step 2: Apply the power rule

Using the power rule of exponents, we can simplify the equation further. By multiplying the exponents, we have 2^(3 * 2x) = 4096.

Step 3: Simplify the equation

Continuing from Step 2, we simplify the equation to 2^(6x) = 4096.

Step 4: Write 4096 as a power of 2

Since 4096 can be expressed as 2^12, we rewrite the equation as 2^(6x) = 2^12.

Step 5: Apply the exponent rule

Equating the exponents, we get 6x = 12.

Step 6: Solve for x

Dividing both sides of the equation by 6, we find x = 2.

Therefore, the solution to the equation 8^(2x) = 4096 is x = 2.

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Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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Answer: x^2+2x-90

Step-by-step explanation:

The cost of making 35 items is 1100 and the domain is (-∞,∞)

The cost of making 35 items :

plug the value into the cost equation

C(35) = 10(35) + 800

C(35) = 350 + 800

C(35) = 1100

Hence, cost of making 35 items is 1100

Since the value of X can be any real number, we can plug in any real number for x and get a real number output.

Hence, the domain = (-∞,∞)

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Answer:

"Compactness" is the right answer.

Step-by-step explanation:

So that the above would be the correct answer.

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

The true statements are the study does not involve a voluntary response, the first stage creates a stratified random sample and the whole study creates a multistage random sample.

In the given question, the study done ideally creates a multistage random sample. There are two parts to the sampling process for the study in the given question. Initially, a combined sample of thousand of individuals was assembled by combining a randomly selected sample of fifty individuals, that were from each of the 20 regions of each nation. The next step was to choose a random sample of fifty individuals from every one of the five income groups represented among those 1,000 individuals.

Additionally, because the study doesn't entirely rely on a discretionary answer, individuals were picked by a random sample approach rather than explicitly or through self-selection. A stratified random sample is also created during the initial step. This shows that a random sample was drawn from each subgroup after the dataset was separated into groups. 

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Answer:

-3

Step-by-step explanation:

Substitute -1 for x in the expression 2x-1

2*-1-1

-2-1

-3

Answer:

-3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

a) 0.5 = 50% probability that an NPN transistor will be selected.

b) 0.3333 = 33.33% probability that it came from the cabinet that contains both types

c) 66.67% probability that it comes from the cabinet that contains only NPN transistors

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that an NPN transistor will be selected?

1/3 probability that the first cabinet is chosen. This cabinet has two transistors, both of which are NPN, so 100% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, both of which are PNP, so 0% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, one of which is NPN, so 50% probability of selecting a NPN transistor.

So

\(p = \frac{1}{3}*1 + \frac{1}{3}*0 + \frac{1}{3}*0.5 = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = 0.5\)

0.5 = 50% probability that an NPN transistor will be selected.

b) Given that the hobbyist selects an NPN transistor, what is the probability that it came from the cabinet that contains both types?

Here we use the conditional probability formula.

Event A: NPN transistor

Event B: From the third cabinet.

50% probability that an NPN transistor will be selected, so \(P(A) = 0.5\).

1/6 probability that it is from the third cabinet and NPN, so \(P(A \cap B) = \frac{1}{6}\)

The desired probability is:

\(P(B|A) = \frac{\frac{1}{6}}{0.5} = 0.3333\)

0.3333 = 33.33% probability that it came from the cabinet that contains both types.

c) Given that an NPN transistor is selected what is the probability that it comes from the cabinet that contains only NPN transistors?

Either it comes from the cabinet with only NPN transistors, or it comes from the cabinet with both types of transistors. The sum of the probabilities of these outcomes is 100%. So

x + 33.33 = 100

x = 66.67

66.67% probability that it comes from the cabinet that contains only NPN transistors

The solution to the first number line is x ≤ 5.

The solution to the second number line is x > 5.

The solution to the third number line is x ≤ 5.

The solution to the fourth number line is x ≥ 5.

In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a number line graph and these include the following:

In this context, we can logically deduce that x ≤ 5 is a solution to the first number line graph because the dotted point is located at five (5) with the arrow pointing to the left.

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The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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Answer:  8x+10

-1

Step-by-step explanation:

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(x-y=8\implies -y=-x+8\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-8\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 1 \implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1} \implies \text{\LARGE -1}}}\)

We have the next function

First we need to obtain the first derivate

Then we find the value of x when the derivate is 0

The critical point of the function is x=-8

Answer:

The number can be expressed in multiple forms

Fraction form \(x=\frac{2962}{67}\)  or decimal form  \(x=44.21\)

Step-by-step explanation:

Lets break the problem down

"times" is multiplication *

The difference between 2 numbers is subtraction  \((x-y)\)

A number plus a number is addition \(x+y\)

\(68(x-45)=x+-98\)

Lets solve for \(x\).

Lets start on the left side.

Distribute 68 to the terms inside the parenthesis.

\(68x-3060=x+-98\)

A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign.

\(68x-3060=x-98\)

Subtract \(x\) from both sides of the equation.

\(68x-3060-x=-98\)

Subtract \(x\) from \(68x\).

\(67x-3060=-98\)

Add 3060 to both sides of the equation.

\(67x=2962\)

Divide both sides of the equation by 67.

\(x=\frac{2962}{67}\) or as a decimal \(x=44.21\)