Use custom relationships to create a graph, showing the solution region of the system of inequalities, representing the constraints of the situation. Did Mark and label it point represents a viable combination of guest School district is planning a banquet to honor his teacher of the year and raise money for the scholarship foundation. The budget to hold the banquet in a hotel room and miles is $3375 the venue can hold no more than 125 guest the cost is $45 per adult but only $15 per student because caterer offers a student discount discount

The area of the net of the solid figure is 96 square inches

The image that completes the question is added as an attachment

From the image, we have:

Squares = 6

Length = 4

The area of the net is then calculated as:

Area = Squares * Length^2

This gives

Area = 6 * 4^2

Evaluate

Area = 96

Hence, the area of the net of the solid figure is 96 square inches

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Answer:

The value of h is B 5 3/7 hours

Step-by-step explanation:

7/8h + 1 1/4 =6 7/8h =4 3/4 h = 4 3/4 / 7/8 = 5 3/7 hours

Answer:

5 3/7 hours

Step-by-step explanation:

\(\frac{7}{8}h + 1\frac{1}{4}=6\\\\\frac{7}{8}h+\frac{5}{4}=6\\\\\frac{7}{8}h=6-\frac{5}{4}\\\\\frac{7}{8}h=\frac{6*4}{1*4}-\frac{5}{4}\\\\\frac{7}{8}h=\frac{24}{4}-\frac{5}{4}\\\\\frac{7}{8}h=\frac{19}{4}\\\\h=\frac{19}{4}*\frac{8}{7}\\\\h=\frac{19*2}{7}\\\\h=\frac{38}{7}\\\\h=5\frac{3}{7}\)

Answer: x≥5.5    y≤-3

Step-by-step explanation:

\(\displaystyle\\\left \{ {{4x+6y\leq 4\ \ \ \ (1)} \atop {2x+y=8\ \ \ \ \ (2)}} \right\\\\\\\)

Divide both parts of the equation (1) by 2:

\(\displaystyle\\\left \{ {{2x+3y\leq 2} \atop {2x+y=8}} \right\\\\\\\)

1)

\(\displaystyle\\\left \{ {{2x+3y\leq 2\ \ \ \ (3)} \atop {2x=8-y\ \ \ \ \ (4)}} \right\\\\\\\)

Let us substitute the value of 2x into equation (3):

\(8-y+3y\leq 2\\\\8+2y\leq 2\\\\8+2y-8\leq 2-8\\\\2y\leq -6\)

Divide both parts of the equation by 2:

\(y\leq -3\)

2)

\(\displaystyle\\\left \{ {{2x+3y\leq 2\ \ \ \ (3)} \atop {y=8-2x\ \ \ \ \ (5)}} \right\\\\\\\)

Let us substitute the value of y into equation (3):

\(2x+3(8-2x)\leq 2\\\\2x+24-6x\leq 2\\\\24-4x\leq 2\\\\24-4x+4x\leq 2+4x\\\\24\leq 2+4x\\\\24-2\leq 2+4x-2\\\\22\leq 4x\)

Divide both parts of the equation by 4:

\(5.5\leq x\\\\Thus,\ x\geq 5.5\)

Answer:

C.-85

Step-by-step explanation:

An arithmetic sequence is a sequence where the difference between each consecutive term is the same.

The nth term of an arithmetic sequence.

= a + (n - 1)d

The 61st term of the sequence is 85.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

-5, -7/2, -2, -1/2, 1

a = -5

d = -7/2 + 5

d = 3/2

Now,

The nth term of an arithmetic sequence.

= a + (n - 1)d

Now,

n = 61

61st term:

=  -5 + (61 - 1)(3/2)

= -5 + 60 x 3/2

= -5 + 30 x 3

= -5 + 90

= 85

Thus,

The 61st term of the sequence is 85.

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The number of months to reach 51 can be illustrated as 3060 - 100x = 51.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both.

The farmer planted 3,060 tomato plants in his garden.

Let's assume there's a decrease of 100 monthly.

The number of months, x, it will take for the number of tomato plants in his crop to reach 51 = c

This will be:

3060 - 100x = 51.

This illustrates the equation for the number of months.

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The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

\(10 \div 1.25 = 8\)

thats the answer

Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

Answer: 0.25

Step-by-step explanation:

the mean is 7.25. the median is 7. so, the difference is 0.25.

Answer:

Step-by-step explanation:

Test the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.02 significance level.

GPA-Night GPA-Day 3.15 3.47 3.68 3.49 3.34 3.07 3.07 3.31 3.31 3.28 3.2 3.05 3.07 3.12 2.8 3.5 3.04 3.04 3.13 3.19 3.54 3.26 3.24 3.31 3.02 3.45 3.44 2.9 2.79 2.76 3.18 2.69 2.99 3.46 3.28 3.09 3.16 2.72 3.08 3.14 2.47 3.08 3.03 2.99 3.02 3.11 2.58 2.84 3.36 2.99 3.04 2.99

(1) The null and alternative hypothesis would be:

a.H0:μN≥μD

H1:μN>μD.

b.H0:μN=μD

H1:μN≠μD.

c.H0:pN≥pD

H1:pN d.H0:pN=pD

H1:pN≠pD.

e.H0:μN≤μD

H1:μN<μD

f.H0:pN≤pD

H1:pN>pD.

(2) The test is:_______.

a. right-tailed.

b. two-tailed.

c. left-tailed.

(3) The sample consisted of 70 night students, with a sample mean GPA of 2.12 and a standard deviation of 0.08, and 70 day students, with a sample mean GPA of 2.08 and a standard deviation of 0.02

The value of x in the chord of the circle using the chord-chord power theorem is 0.

The chord-chord power theorem simply state that "If two chords of a circle intersect, then the product of the measures of the parts of one chord is equal or the same as the product of the measures of the parts of the other chord".

From the figure:

The first chord has consist of 2 segments:

Line segment 1 = 27

Line segment 2 = ( x + 16 )

The second chord also consist of 2 sgements:

Line segment 1 = 24

Line segment 2 = ( x + 18 )

Now, usig the Chord-chord power theorem:

27( x + 16 ) = 24( x + 18 )

Solve for x:

27x + 432 = 24x + 432

27x - 24x = 432 - 432

3x = 0

x = 0

Therefore, the value of x is 0.

Option D) 0 is the correct answer.

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Answer:

The hypotenuse. Since it is the opposite of the right angle

The largest number is the hypotenuse

therefore, 15 is the answer.

Answer:

c

Step-by-step explanation:

The hypotenuse. Since it is the opposite of the right angle

The largest number is the hypotenuse

therefore, 15 is the answer.

Answer:

\(2\frac{3}{50}\)

Step-by-step explanation:

So 2 would be your whole number

and since 6 is in the hundredths place the fraction would be 6/100 which is reduced to 3/50

Carlos's score in his first game was 14.

Addition in maths, a process of combining two or more numbers.

Given that, Carlos scored a total of 60 points in his last three basketball games. be improved in each game by scoring 6 more points than in the previous game.

Let the first score be x,

x+x+6x+6+6=60

3x+18 = 60

3x = 42

x = 14

Hence, Carlos's score in his first game was 14.

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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we  two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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Answer:

210

Step-by-step explanation:

simple, arrange the numbers in descending order zero being the last !!!

Answer:

210

Step-by-step explanation:

Arrange the numbers in descending order :)

The result of the expression 20 - 6 is 14.

To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.

Step 1: Start with the given expression, 20 - 6.

Step 2: Evaluate the subtraction operation: 20 - 6 = 14.

Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.

This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.

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The measure of the variable 'b' from the line is 11

Collinear points are points that lies on the same straight line. From the given diagram:

XY = YZ  (since Y is the midpoint of XZ)

where:

XY = 2b + 7

YZ = 3b - 4

Substitute the given parameters to have:

2b + 7 = 3b - 4

2b - 3b = -4 - 7

-b = -11

b = 11

Hence the measure of the value of b from the line is 11

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The chance of rolling a die and landing on a three is 1/6. The reason for this is because there are 6 sides on a die, and only one 3 on the die.

Given:

The theoretical probability of rolling a sum of 8 is 1/11, the experimental probability is 5/36 and the odds is 5 : 31

When two dice are rolled, the possible sum are

Sum = 2 to 12

In the above sum, we have

n(8) = 1

Total = 11

This means that

P(sum of 8) = 1/11

For the experimental probability, we have

n(Sum of 8) = 5

Total = 36

So, we have

P(sum of 8) = 5/36

In (b), we have

P(sum of 8) = 5/36

This means that

Odds = 5 : 36 - 5

Odds = 5 : 31

Hence, the odds of rolling a sum of 8 is 5 : 31

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Answer:

7/48,0.5,9/16,0.75

Step-by-step explanation:

Hope this helps

The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

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Answer:

It is true!!!'djjfdjidjdneidid

Answer:

If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Step-by-step explanation:

We are given that the means of two populations using paired observations. Suppose that \(\bar D\) = ​3.125, \(s_D\) =​ 2.911, and n =​ 8, and that you wish to test the hypothesis below at the​ 10% level of significance.

Let D = difference between the two paired observations.

So, Null Hypothesis, \(H_0\) : \(\mu_D\) = 0    

Alternate Hypothesis, \(H_A\) : \(\mu_D\) > 0

The test statistics that would be used here is Paired t-test for dependent samples;

                     T.S. =  \(\frac{\bar D-\mu_D}{\frac{s_d}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar D\) = ​3.125, \(s_D\) =​ 2.911, and n =​ 8

The decision rule for rejecting the null hypothesis in the given hypothesis​ test would be;

Answer:

24 minutes

Step-by-step explanation:

We use 1/a + 1/b = 1/c

where a and b are the individual times and c is the time together

1/40 + 1/60 = 1/c

Multiply each side by 120c

120c( 1/40 + 1/60 = 1/c)

3c + 2c = 120

5c = 120

Divide each side by 5

5c/5 = 120/5

c = 24

Answer: 24 minutes

Step-by-step explanation: To solve this kind of a problem which is called a work problem, it's important to understand the following idea.

Since Elam can wire a light in 40 minutes, we know that in 1 minute,

Elam can wire 1/40 of the light and in 2 minutes, Elam can wire 2/40 of it.

Therefore, in t hours, Elam can wire t/40 of the light.

The same applies for Michael, in t hours, he can wire t/60 of the light.

So to solve the problem, we use the following formula:

Part of job done by Elam + part of job done Michael = 1 job done

The part of the job done by Elam is t/40 and t/60 for Michael.

So we have t/40 + t/60 = 1.

Now multiply both sides by 120 to get 3t + 2t = 120

or 5t = 120 so t = 24.

So it takes 24 minutes if they work together.

A line passes throught the origin (-1, 1) and (4, n). Find the value of n. enter the correct answer in the box. I'd say (4, -2)

If I'm wrong sorry. If I'm correct May I Have Brainliest? <3

Answer:

Step-by-step explanation:

Median: C) 13

First Quartile: A) 8.5

Third Quartile: B) 17.5

Explanation:

To find the median, we need to arrange the numbers in ascending order:

{3, 5, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(10 + 11)/2 = 10.5.

To find the first quartile, we need to find the median of the lower half of the data set.

The lower half is {3, 5, 5, 8, 9, 10, 11, 12}.

Since there are an even number of values, we take the average of the middle two numbers:

(8 + 9)/2 = 8.5.

To find the third quartile, we need to find the median of the upper half of the data set.

The upper half is {14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(17 + 18)/2 = 17.5.

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

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