The area of the triangle below is 1/8 square feet . What is the length of the base ? Express your answer as a fraction in simplest form.

The requried larger number x is 80 and the smaller number y is 27.

Let's use the given variables:

x be the larger number

y be the smaller number

According to question

The sum of two numbers is 107 is represented by x + y = 107

The difference between the two numbers is 53 is represented by x - y = 53.

Solving the system of equations:

(x + y) + (z - y) = 107 + 53

2x = 160

x = 80

Now, z = 80, substitute this value into one of the original equations to solve for y.

x + y = 107

80 + y = 107

y = 27

Therefore, the requried larger number x is 80 and the smaller number y is 27.

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The minimum value of the objective function is 47, which occurs at the point (3,2), and the maximum value is 117, which occurs at the point (0,9).

To solve this linear programming problem, we need to first graph the feasible region defined by the given constraints:

The first constraint, x ≥ 0, represents the non-negative values of x along the x-axis.

The second constraint, 4x + 8y ≥ 32, can be rewritten as y ≥ -(1/2)x + 4, which is a line with a y-intercept of 4 and a slope of -(1/2). The feasible region is above this line.

The third constraint, 10x - y ≤ 30, can be rewritten as y ≥ 10x - 30, which is a line with a y-intercept of -30 and a slope of 10. The feasible region is above this line as well.

The fourth constraint, x + 6y ≤ 54, can be rewritten as y ≤ -(1/6)x + 9, which is a line with a y-intercept of 9 and a slope of -(1/6). The feasible region is below this line.

The feasible region is therefore the polygon bounded by the lines y = -(1/2)x + 4, y = 10x - 30, y = -(1/6)x + 9, and x = 0. To find the minimum and maximum values of the objective function f(x,y) = 11x + 13y, we need to evaluate this function at each corner of the feasible region and compare the results.

The corners of the feasible region are (0,4), (3,2), (5,4), and (0,9). Evaluating the objective function at these corners, we get:

f(0,4) = 52

f(3,2) = 47

f(5,4) = 89

f(0,9) = 117

Therefore, the minimum value of the objective function is 47, which occurs at the point (3,2), and the maximum value is 117, which occurs at the point (0,9).

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This statement is false because , the value of the 7 in the hundredth place is greater than the value of the 7 in the thousandth place.

Each digit in a number has a particular place value dependent on its position in the decimal number system. The digits in the number 824.377 have the following place values:

The 7 in the hundredth position has a value of 7/100, or 0.07. This is because the digit 7 is in the hundredth position, which is in the second position to the right of the decimal point.

The value of the 7 in the thousandth place is 7/1000, or 0.007. This is due to the fact that the digit 7 is in the third place to the right of the decimal point

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The angle subtended by the arc AB in the circle is 68.75 degrees.

We have,

We know that the circumference of a circle is given by 2πr,

where r is the radius of the circle.

The circumference of the circle with a radius of 6 cm is.

C = 2πr = 2π(6) = 12π cm

Since the arc AB of the circle is 9 cm, we can find the angle subtended by this arc using the formula:

angle = (arc length / circumference) x 360°

Plugging in the values we have:

angle = (9 / 12π) x 360°

angle = 68.75°

Therefore,

The angle subtended by the arc AB is 68.75 degrees.

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The concentration of copper(II) sulfate in one brand of soluble plant fertilizer is 0.0700% by weight. A 24.0 g sample of this fertilizer is dissolved in 2.00 L of solution. Number of moles of copper ions available in the solution is 8.77×10⁻⁵mole.

In chemistry, a mole, usually spelt mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, and other predetermined particles. The mole designates 6.02214076 1023 units, which is a very large number. In this the Worldwide System of Units (SI), the mole is defined as this number as of May 20, 2019, per the decisions of the General Conference upon Measurements and Weights. Amount of copper sulfate available in  24.0  grams of the sample =

0.07/100× 24.0 =0.014g

number of moles of copper sulfate=0.014/159.6=8.77×10⁻⁵

Number of moles of copper ions available in the solution=8.77×10⁻⁵mole

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To complete the job in 12 days, they need 100 workers.

We know that 30 workes can complete 1 job in 40 days, then if each worker works at a rate R, then we can write:

30*R*40 days = 1 job

R = (1/1200) job/day

Then if they need to complete the job in 12 days, the number N of workers needed is:

N*(1/1200)*12 = 1

N = (1200/12) = 100

100 workers are needed.

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The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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The amount invested at 15% is $2,840 and at 6% is $2,741. The interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 6% by $261.54.

Let's assume that the amount invested at 15% is x, and the amount invested at 6% is y. We know that

x + y = 5,581 (equation 1) (since the total amount invested is $5,581)

We also know that the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 6% by $261.54. This can be expressed as

0.15x - 0.06y = 261.54 (equation 2)

(since the interest earned is equal to the amount invested multiplied by the interest rate)

Now, we can use these two equations to solve for x and y.

First, we will isolate y in equation 1

y = 5,581 - x

Next, we will substitute this expression for y into equation 2

0.15x - 0.06(5581 - x) = 261.54

Simplifying this equation gives

0.15x - 334.86 + 0.06x = 261.54

0.21x = 596.40

x = 2,840

Now that we know x, we can use equation 1 to find y

2,840 + y = 5,581

y = 2,741

Therefore, $2,840 is invested at 15%, and $2,741 is invested at 6%.

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The expression What is 2.00x + 1.50y = cannot be added/evaluated because 2.00x and 1.50y are not like terms

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

What is 2.00x + 1.50y =

The above statement is an addition expression that adds the values of 2.00x and 1.50y

However, the terms of the expression are not like terms

i.e. 2.00x and 1.50y are not like terms

This means that the expression cannot be added/evaluated

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If AOC and BOD are diameters of a circle, centre O, we can prove that triangle ABD and triangle DCA are congruent by RHS.

First, we can observe that angle AOB and angle COD are both right angles since they are angles subtended by diameters of the circle.

Since AO and BO are equal radii of the circle, they have the same length. Similarly, CO and DO are equal radii of the circle and have the same length. Thus, we have:

AO = BO = CO = DO

Now, consider triangle ABD and triangle DCA. We have:

AB = DC (both are diameters of the circle, hence have the same length)

AD = AD (common side)

∠ADB = ∠CDA = 90° (both are right angles)

Therefore, by the RHS (Right Angle-Hypotenuse-Side) congruence criterion, we can conclude that triangle ABD and triangle DCA are congruent.

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Answer: below

Step-by-step explanation:

The first equation y = x + 5 is the equation of a straight line with slope 1 and y-intercept 5. We can plot this line by starting at the point (0, 5) and then moving up one unit for every one unit to the right.

The second equation y = -(x + 5) is also the equation of a straight line, but with slope -1 and y-intercept -5. We can plot this line by starting at the point (0, -5) and then moving down one unit for every one unit to the right.

The third equation y = |x + 5| is the equation of a V-shaped graph, or an absolute value function, centered at x = -5. We can plot this graph by first plotting the portion of the graph for x < -5, which is given by y = -(x + 5). Then, we can plot the portion of the graph for x > -5, which is given by y = x + 5. Finally, we can connect these two portions of the graph at x = -5 by drawing a vertical line segment from (-5, 0) to (-5, 10).

Answer:

First, let's start with y = x + 5.

To graph this equation, we can use a table of values. We'll choose a few values of x, and then plug them into the equation to find the corresponding values of y.

x | y

--|---

-5 | 0

-4 | 1

-3 | 2

-2 | 3

-1 | 4

0 | 5

1 | 6

2 | 7

3 | 8

4 | 9

5 | 10

Now, we can plot these points on a graph and connect them with a straight line.

```

| *

10|

| *

| *

| *

|*

| -------------

| -5 -4 -3 -2 -1 0 1 2 3 4 5

```

This is the graph of y = x + 5.

Next, let's look at y = -(x + 5).

This equation is similar to the first one, but with a negative sign in front of the parentheses. This means that the graph will be a mirror image of the first one, reflected across the y-axis.

So, we already know some of the points on this graph. If we take the points from the first graph and flip them horizontally (i.e. change the sign of the x-coordinate), we'll get the points for the second graph.

x | y

--|---

5 | 0

4 | -1

3 | -2

2 | -3

1 | -4

0 | -5

-1 | -6

-2 | -7

-3 | -8

-4 | -9

-5 | -10

Plotting these points on a graph and connecting them with a straight line, we get:

```

|*

10| *

| *

| *

| *

| *

| *

| *

|---------------

| -5 -4 -3 -2 -1 0 1 2 3 4 5

```

This is the graph of y = -(x + 5).

Finally, let's look at y = |x + 5|.

This equation involves absolute value, which means that the graph will be "V"-shaped. The vertex of the "V" will be at x = -5.

To find some points on this graph, we can again use a table of values. We'll choose some values of x, and then plug them into the equation, being careful to take the absolute value of the result.

x | y

--|---

-10 | 5

-5 | 0

0 | 5

5 | 10

10 | 15

Now, we can plot these points on a graph and connect them to form a "V" shape.

```

| *

15| *

| *

| *

| *

| *

|-------------

|-10 -5 0 5 10

```

This is the graph of y = |x + 5|.

The value for the missing length ST of the similar to triangle ∆STU is equal to 234

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Given that the triangle ∆STU is similar to the triangle ∆SGF, then SF correspond to SU, and SG correspond to ST. So;

SF/SU = SG/ST

75/270 = 65/ST

ST = (65 × 270)/75

ST = 13 × 18

ST = 234

Therefore, the value for the missing length ST of the similar to triangle ∆STU is equal to 234

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Answer:

When rolling two number cubes, the possible outcomes of the sum of the numbers on the top faces are from 2 (1+1) to 12 (6+6). Since we want to know how many times we can expect the sum to be 7, we need to count the number of ways to get a sum of 7.

The pairs of numbers that add up to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, there are 6 ways to get a sum of 7.

Each time we roll the two number cubes, the probability of getting a sum of 7 is 6/36 or 1/6, since there are 6 possible outcomes that result in a sum of 7 out of a total of 36 possible outcomes.

Therefore, if we repeat this process 300 times, we can expect to get a sum of 7 approximately (1/6) x 300 = 50 times.

So we can expect the two cubes to add to exactly 7 about 50 times when rolled 300 times.

Step-by-step explanation:

The length of the side of his garden can be16.6 ft

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

He has enough compost to cover an area of 276 square feet.

This means that

Area = 276 276 square feet.

The area of a square is calculated as

Area = Length^2

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

Length^2 = 276

Take the square root of both sides

Length = 16.6

Hence, the length is 16.6 ft

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Answer:

all triangle angle measures should add up to 180.  So given that,

40+60+80=180

Therefore it can be done

The probability that a randomly selected ticket will be a number that is not a multiple of 9 is 0.9.

To find the probability that a randomly selected ticket will not be a multiple of 9, we need to find the total number of tickets that are not multiples of 9 and divide it by the total number of tickets in the bowl.

There are 7 multiples of 9 between 1 and 70, namely 9, 18, 27, 36, 45, 54, and 63. Therefore, there are 70 - 7 = 63 tickets that are not multiples of 9.

So, the probability that a randomly selected ticket will not be a multiple of 9 is:

P(not multiple of 9) = 63/70

This can also be written as a decimal or percentage:

P(not multiple of 9) ≈ 0.9 or P(not multiple of 9) ≈ 90%

Therefore, there is a high probability that a randomly selected ticket will not be a multiple of 9.

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For a unique solution is: [tex]\frac{10}{a}\neq \frac{5}{b}[/tex]

For an infinitely many solution is: [tex]\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}[/tex]

An equation of the form ax+by+c=0 is called a linear equation where a, b, c∈R

We have the linear equation is:

10x + 5y = 20

Now, we have to find the unique solution and infinitely many solution:

Firstly, For a unique solution, we need an equation ax+by+c=0 such that

[tex]\frac{10}{a}\neq \frac{5}{b}[/tex]

Now, For an infinitely many solutions, we need an equation ax+by+c=0 such that:

[tex]\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}[/tex]

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For, complete question, to see the attachment.

The length of the third side is given as follows:

x = 3√3.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the third side is given as follows:

x² + 3² = 6²

x² + 9 = 36

x² = 27

x = √3³

x = 3√3.

The triangle is given by the image presented at the end of the answer.

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The triangle triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Triangle ∆BCD is not similar to the triangle ∆BTS, BT does not correspond to BC, and BS does not correspond to BD. Also, the angle m∠SBT does not correspond to m∠DBC.

Therefore, the triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

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The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

We have,

We want to maximize the production output

P = L^0.8 K^0.2

subject to the constraint 10L + 20K = 2700.

We can solve for K in terms of L from the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10L) / 20

K = 135 - 0.5L

Substitute this expression for K into the production function:

P = L^0.8 K^0.2

P = L^0.8 (135 - 0.5L)^0.2

We want to maximize P with respect to L.

Taking the derivative of P with respect to L:

dP/dL = 0.8L^-0.2 (135 - 0.5L)^0.2 + 0.2L^0.8 (135 - 0.5L)^-0.8 (-0.5)

dP/dL = 0.16(135 - 0.5L)^0.2 L^-0.2 - 0.1(135 - 0.5L)^-0.8 L^0.8

Setting dP/dL equal to zero and solving for L:

[tex]0.16 (135 - 0.5L)^{0.2} L^{-0.2} - 0.1 (135 - 0.5L)^{-0.8} L^{0.8} = 0[/tex]

0.16(135 - 0.5L)^0.2 = 0.1(135 - 0.5L)^-0.8 L^1

1.6(135 - 0.5L) = (135 - 0.5L)^-0.8 L

1.6 = (135 - 0.5L)^-1.8 L^-1

1.6L = (135 - 0.5L)^1.8

1.6L = (135^1.8 - 0.5L)^1.8

1.6L = 2.24474e+15 - 4.52222e+14 L + 1.22313e+13 L^1.8

1.22313e+13 L^1.8 - 4.52222e+14 L + 2.24474e+15 - 1.6L = 0

This equation can be solved numerically using a solver or a graphing calculator.

The solution is L = 69.06 units of labor.

To find the corresponding value of K, we can use the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10(69.06)) / 20

K = 67.47 units of capital

Therefore,

The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

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There is a statistically significant difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables by hypothesis

State the null hypothesis and the alternative hypothesis.

The null hypothesis (H₀) is that there is no difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables.

The alternative hypothesis (Ha) is that there is a difference in life expectancy between the two groups.

H₀: μ₁ = μ₂

Ha: μ₁ ≠ μ₂

Determine the appropriate test statistic and significance level.

Since we are comparing the means of two independent samples, we can use a two-sample t-test.

We will use a significance level of α = 0.05.

We can use a calculator or statistical software to calculate the test statistic.

t = -2.379

df = 8.98

p-value = 0.042

where t is the test statistic

The p-value is 0.042, which is less than the significance level of 0.05.

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Answer: b

Step-by-step explanation:Remember that the Cartesian coordinates are given by the formulas

xy=rcosθ=rsinθ

We are told that r=8 and θ=11π6, so we can plug in to find that

x=rcosθ=(8)(cos11π6)=(8)(3‾√2)=4√3

Similarly, we find that

y=rsinθ=(8)(sin11π6)=(8)(−12)=−4

So the final answer is (4√3,−4).

The formula for the volume of a rectangular prism is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of Caleigh's jewelry box is 14 cubic inches, and the area of the base is 7 square inches. Since the base of the box is a rectangle, we can use the formula for the area of a rectangle to find the length and width of the base:

A = l x w

7 = l x w

We don't know the exact values of l and w, but we do know that their product is 7.

Now we can use the formula for the volume of a rectangular prism to find the height:

14 = l x w x h

We know that l x w = 7, so we can substitute 7 for l x w:

14 = 7 x h

Dividing both sides by 7 gives:

h = 2

Therefore, the height of Caleigh's jewelry box is 2 inches.

In order to decrease the margin of error, the best option in this instance is by decreasing the confidence level would make the interval to be narrower.

The correct option is D.

The margin of error, also known as the confidence interval, provides information on how closely your survey results will likely reflect the opinions of the general community.

The margin of error is a measure of the potential uncertainty in your survey results. It is more likely that the results will deviate from the "true figures" for the entire population the wider the margin of error.

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The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1

Total numbers on wheel = total possible outcomes

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Grey colored portion = {3}

White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}

X = Event that wheel stops on a white slice

P(X) = number of white slices ÷ total number of slices

P(X) = 9 / 10 = 0.9

P(not X) = 1 - P(X)

P(not X) = 1 - 0.9 = 0.1

Hence the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1

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The equation that represents number of hours "h" which Ezekiel spend doing "math-homework" during the next 5 days is (d) h = 5t/4.

If Ezekiel spends 1/4 of his time on math homework, then he spends 3/4 of his time on other subjects. This means that out of every 4 hours he spends on homework, he spends 1 hour on math and 3 hours on other subjects.

So, in "t" hours, he will spend "t/4" hours on math homework.

To find the number of hours he will spend on math homework during the next 5 days, we multiply the time he spends on math homework in one day by the number of days.

⇒ Number of hours spent on math homework in 1 day = t/4,

⇒ Number of hours spent on math homework in 5 days = 5 × (t/4) = 5t/4,

The required equation is h = 5t/4,

Therefore, the correct option is (d).

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The blanks will be -

(a) Capital Gain = $4000

(b) Percent of Capital Gain = 14.8%

(c) Purchase price per share = $5

(d) Percent of capital gain = 140%

(e) The selling price per share = $35.65

(f) Capital Gain = $3022.5

(g) Purchase price per share = $29

(h) Percent of capital loss = 20.7%

(i) Purchase price per share $54 and selling price per share $62.

The number of shares is 500.

So, Capital Gain = (500*62 - 500*54) = $4000

Percent of Capital Gain = (4000/(500*54))*100% = 14.8% (rounding to nearest tenth)

(ii) Number of shares = 100 and selling price of per share = $12 and capital gross = $700.

Purchase price per share = (12*100 - 700)/100 = 500/100 = $5

So the percent of capital gain = (700/(5*100))*100% = 140%

(iii) Number of shares = 650 and purchasing price per share = $31 and percent of capital gain = 15%

The selling price per share = 31*(100+15)/100 = $35.65

Capital Gain = (31*650)*15% = $3022.5

(iv) Number of shares = 1300 and selling price of per share = $23 and capital loss = - $7800

Purchasing price per share = $ (23*1300+7800)/1300 = $29

Percent of capital loss = (7800/(29*1300))*100% = 20.7% (rounding to nearest tenth)

Hence, (a) $4000; (b) 14.8% (gain); (c) $5; (d) 140% (gain); (e) $35.65; (f) $3022.5; (g) $29; (h) 20.7% (loss).

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The contrapositive statement is option D

If the hypothesis and conclusion of an earlier conditional statement are reversed, a contrapositive statement is produced.

Technically speaking, the contrapositive of a conditional statement that starts with "If p, then q" is "If not q, then not p." The initial assertion and its contrapositive, then, are both true because they are logically equivalent.

Thus the contrapositive statement as shown is the statement ~q ~p

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The system of inequalities that represents the graph is

y ≥ x² - 2x + 4 and y < -x² + 4 is the

Option B is the correct answer.

We have,

The inequality y ≥ x² - 2x + 4 represents a parabola that opens upwards and has a vertex at (1,3) as shown below:

The inequality y < -x² + 4 represents an inverted parabola that opens downwards and has a vertex at (0,4) as shown below:

Therefore,

The system of inequalities that represents the graph is

y ≥ x² - 2x + 4 and y < -x² + 4 is the

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