A farmer has 324 feet of fencing to make three identical adjacent rectangular pens, as shown in the picture. What dimensions of each pen will maximize the total enclosed area?

Answer:

[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]

assuming is simple interest

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]

Based on the alternative hypothesis, the value of μ that will have the greatest test power is μ = 7.

The alternative hypothesis is that Hₐ : μ < 14.

For the alternative hypothesis to be right, μ will have to be less than 1.4.

μ will also give a greater test power the lower it is below 14. From the options therefore, μ with the greatest test power would be 7.

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Answer:

μ = 7

Step-by-step explanation:

Got this right on the segment exam. Good luck, my FLVS fellows!

The mean number is 8.7 and the outliers 1 and 2 reduce the mean value

The dataset is given as:

10, 12, 8, 11, 13, 9, 2, 1, 9, and 12​.

The mean number is calculated using:

Mean = Sum/Count

So, we have:

Mean = (10+ 12+ 8+ 11+ 13+ 9+ 2+ 1+ 9+12​)/10

Evaluate

Mean = 8.7

Hence, the mean number is 8.7

Outliers are relatively far from other data elements of the dataset

In the given dataset, 1 and 2 are far from other data element.

So, the outliers are 1 and 2

Because 1 and 2 smaller than other data elements, they affect the mean by reducing the mean value

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Answer:87/10 is the answer because there are no tens

Step-by-step explanation:

We need to explain the steps to use coordinates in calculating the perimeter and area of the polygon.

We need to explain the procedure when working with diagonal sides and irregular shapes on the coordinate plane.

The location of a point in the XY-plane is determined by coordinates. The vertex, which is the point where two lines of a shape meet to form a corner, is a unique place. We can determine the perimeter and area of a figure after we have the coordinates for all of its vertices.

Steps to calculate the perimeter and area of a polygon:

Step 1: Plot the given points on the graph.

Step 2: Connect the points and identify the figure.

Step 3: Determine lengths by counting the grid lines.

Step 4: Use a formula to calculate the perimeter and area if one exists.

Step 5: If there are no formulas for a figure, the perimeter can be calculated by summing the lengths of the sides. We might estimate the area without an area formula by counting the number of small squares enclosed.

Note: If you are using diagonal to calculate the area, then use the distance formula to calculate the length of the diagonal.

We need to explain how the distance formula and slope formula

are used to classify various quadrilaterals and triangles.

Distance formula: [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Now, we use slope to find the angles i.e. If:

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The value of x of the cubic equation e³ˣ + eˣ - 6 = 0 will be 0.49

The cubic equation is given as ax³ + bx² + cx + d = 0. Then degree of the equation will be 3. Then we have

The cubic equation will be

e³ˣ + eˣ - 6 = 0

Let eˣ = u, then the equation will be

u³ + u - 6 = 0

Then the root of the equation is calculated by the calculator, then we have

u = 1.634, -0.817, -0.817

eˣ = 1.634, -0.817, -0.817

Take log on both sides, then we have

x = ln 1.634, ln(-0.817), ln(-0.817)

x = 0.49, not defined, not defined

Then the value of x will be 0.49.

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An equation that can be used to determine how much each cookie cost originally is ($13.32 + $7) / 16.

A coupon reduces the price of an item. Thus, the amount paid by Louis would be lower than the original price.

Original price = coupon + price paid

($13.32 + $7)

The cost per cookie, can be determined by dividing the original price by the total number of cookies bought.

($13.32 + $7) / 16

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Answer:

Step-by-step explanation:

Givens

Number of cookies = 16

Deduction =  7

Final Cost = 13.31

Equation

16c - 7 = 13.31

Solution

You are not asked for a solution but I'll put it here anyway.

16c - 7 = 13.32                      Add 7 to both sides

16c -7+7 = 13.32+ 7              Combine

16c = 20.32                          Divide by 16

16c/16 =  20.32/16                

c = 1.27

Answer:

x = - 1

Step-by-step explanation:

3(x + 1) = - 2(x - 1) - 4 ←  distribute parenthesis on both sides

3x + 3 = - 2x + 2 - 4

3x + 3 = - 2x - 2 ( add 2x to both sides )

5x + 3 = - 2 ( subtract 3 from both sides )

5x = - 5 ( divide both sides by 5 )

x = - 1

Answer:

5 times bigger

Step-by-step explanation:

(6-4) = 2

(6-4) x 5 = 10

Answer: I think the answer is A (4,6)

Step-by-step explanation:

Because point B is translated up you have to move the whole shape and pint D would end up at (4,6)

Answer:B

Step-by-step explanation:

The amoeba splits 24 times, meaning that the number of amoebas will be

2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 or 2^24

Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.

Answer:

Step-by-step explanation:

P(A∪B) = 1/6 + 1/2 = 2/3

The linear function that has a graph perpendicular to y = 2x – 4 is given by:

D. 2x + 4y = 1

A linear function is modeled by:

y = mx + b

In which:

If two lines are perpendicular, the multiplication of their slopes is of -1. The line y = 2x + 4 as a slope of 2, hence the slope of the perpendicular line will be given by m as such:

[tex]2m = -1[/tex]

[tex]m = -\frac{1}{2} = -0.5[/tex]

Hence option D is correct, as:

2x + 4y = 1

4y = -2x + 1

y = -0.5x + 0.25

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The solution of the inequality  3-x/2≥12 is x≤-18

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 3-x/2≥12

Three minus x by two greater than or equal to twelve

Subtract 3 from both sides

-x/2≥9

-x≥18

x≤-18

Hence, the solution of the inequality  3-x/2≥12 is x≤-18

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Answer:

x=11

y=0

Step-by-step explanation:

Don't know if this is what you're looking for but this is correct if you plug it in.

X + 4y = 11    Get x by itself.  x=-4y+11  and plug it into the bottom.

X - 6y = 11

simplify -4y+11-6y=11

11-10y=11

-10y=0

y=0 plug it into the original and you will get

x=11

x=11

Answer:

Range

Step-by-step explanation:

Range is found by subtracting the highest and lowest point in the dataset

Mode is the number that occurs most frequently in the set

Median is the central number in the dataset when arranged from lowest to highest

Mean is the sum of all the numbers in the dataset divided by how many numbers there are.

For example, take this list of numbers: 10, 10, 20, 40, 70.

The mean (also known as average) is found by: 10 + 10 + 20 + 40 + 70 / 5 = 30.

The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.

The inverse of the graph is (b)

To determine the inverse of the graph, we have to swap the x and the y axes.

This means that we plot the y coordinates on the x coordinates and vice versa.

The interpretation of this on the given curve is that:

The vertical curve becomes an horizontal curve (as seen in graph b)

Hence, the inverse of the graph is (b)

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Answer:

171

Step-by-step explanation:

180×95/100

180×95=17100

17100/100=171.

That is how I got my answer.

Answer:

1449.755 kilograms

Step-by-step explanation:

245 grams is .245 kilograms meaning that in order to get the answer you would need to subtract 1450 by .245 which is 1449.755 which means that the mass of jelly beans would be 1449.755 kilograms

3) [tex]\angle B \cong \angle Y[/tex]

4) [tex]\triangle ABC \sim \triangle ZYX[/tex] by the SAS similarity theorem

ΔABC is similar ΔZYX by the SAS similarity theorem. Therefore, option B is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

1. AB/ZY = BC/YX = 2

2. ∠B and ∠Y are right angles

3. ∠B=∠Y

4. ΔABC is similar ΔZYX by the SAS similarity theorem.

Therefore, option B is the correct answer.

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The results of factoring are presented below for each algebraic expression.

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: y²-y= y(y-1), where y is a common term.

You should apply the factor out a common term for solving the question.

       x(x+2) + y (x + 2) - 5(x + 2)

       x²+2x+xy+2y-5x-10

      x²-3x+xy+2y-10

      x(x-3)+y(x+2)-10

        [tex]5y^2 - 10y^3[/tex]

        5y²(1-2y)

        ax+ay+az

        a(x+y+z)

        yx(y+1) + 4x(y + 1) - 5(y + 1)

       xy²+xy+4xy+4-5y-5

       xy²+5xy-1-5y

       y(xy +5x-5)-1

        [tex]6p^2 - 3p^3[/tex]

       3p²(2-p)

        [tex]4x^4 + 2x[/tex]

        [tex]2x(2x^3+1)[/tex]

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The attached graph shows that the system of equation has no solution since there is no point of intersection

Inequalities are expressions not separated by an equal sign

Given the following inequalities

2y < -12x + 4

y <- 6x +4

_________________

2y < -6x + 4

y <- 6x +4.

Find the y-intercept. When x = 0

y < -6(0) + 4

y < 4

Plot the graphs and determine the point of intersection

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Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

[tex]7x - 9 = 28 + 4(x - 1) \\ 7x - 9 = 28 + 4x - 4 \\ 7x - 4x = 28 - 4 + 9 \\ 3x = 33 \\ \\ x = \frac{33}{3} \\ \\ x = 11[/tex]

Answer:

c) x = 11

Step-by-step explanation:

Given equation: 7x - 9 = 28 + 4(x - 1)

Steps:

1. Distribute 4 through the parentheses:

7x - 9 = 28 + 4(x) + 4(-1)

7x - 9 = 28 + 4x - 4 [simplify]

7x - 9 = 24 + 4x

2. Subtract 4x from both sides:

7x - 4x - 9 = 24 + 4x - 4x

3x - 9 = 24

3. Add 9 to both sides:

3x - 9 + 9 = 24 + 9

3x = 33

4. Divide both sides by 3:

3x ÷ 3 = 33 ÷ 3

x = 11

5. Check your work:

7x - 9 = 28 + 4(x - 1) [substitute 11 for x]

7(11) - 9 = 28 + 4(11 - 1) [simplify]

77 - 9 = 28 + 4(10) [simplify]

68 = 28 + 40 [add]

68 = 68 ✔

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Answer:

the visible number of cubes is 7

Step-by-step explanation:

Assuming that there are no hidden cubes, the # of visible cubes is 7

Answer:

See below ~

Step-by-step explanation:

P (first red) :

⇒ Original number of red balls / Total

⇒ 4 / 10

⇒ 0.4

⇒ 40%

===============================================================

Remember the first ball drawn is NOT replaced.

P (second red) :

⇒ Original number of red - 1 / Total - 1

⇒ 4 - 1 / 10 - 1

⇒ 3/9

⇒ 33%

Answer:

Answer = most college students do not use students loans.

Step-by-step explanation:

To find the percentage of students taking out student loans we take 1,000/6000 to get roughly 17%. This is a very small number of students taking out student loans.