Alfonzo works for a lean service company. It takes him 3/4 hour to mow a lawn. If he works more than 8 hours, he gets 1/2 lunch break. Write and solve an inequality to find the number of lawns he can mow if he works at least 14 hours.

As per the given rectangle, the length of EG is 5x - 7

We are given that DEFG is a rectangle, which means that its opposite sides are parallel and equal in length. Let's label the sides of the rectangle as follows:

DE = FG = a (since opposite sides of a rectangle are equal in length)

EF = DG = b (since opposite sides of a rectangle are parallel)

Now, we can use the given information to set up an equation for the length of EG:

EG = EF + FG = b + a

But we don't know the values of a and b. However, we are given that FD = 3x - 7 and EG = x + 5. We can use this information to solve for a and b.

We know that FD = DE - EF, so we can substitute the values we have:

3x - 7 = a - b

We also know that EG = FG - DG, so we can substitute the values we have:

x + 5 = a - b

Now we have two equations with two variables (a and b). We can solve for a and b by adding the two equations together:

3x - 7 + x + 5 = 2a

4x - 2 = 2a

a = 2x - 1

Now we can substitute this value for a in one of the earlier equations to solve for b:

3x - 7 = (2x - 1) - b

b = 3x - 6

Finally, we can substitute the values we found for a and b into the equation we set up earlier to find the length of EG:

EG = EF + FG = b + a = (3x - 6) + (2x - 1) = 5x - 7

Therefore, the length of EG is 5x - 7.

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No, Jack does not have enough rope. First, we need to convert all units to the same measurement.

Since there are 36 inches in a yard, Jack has 7 x 36 = 252 inches of rope. Additionally, 4 feet is equal to 4 x 12 = 48 inches of rope.

To determine if Jack has enough rope, we need to add the 84 inches needed for the packages and the 48 inches needed for the other project, which gives a total of 132 inches.

Since 132 inches is greater than Jack's total of 252 inches, he does not have enough rope.

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Answer:

0.119

Step-by-step explanation:

No. of sides a die has= 6 sides

No. of times it is rolled= 7 times

Total pairs= 6 x 7

                = 42 pairs

No. of 5 threes= 5 x 1

                        = 5

Probability of getting 5 threes= Favorable outcomes/Total outcome

                                                 = [tex]\frac{5}{42}[/tex]

                                                 = 0.119 chance

∴ probability of getting 5 threes is 0.119

Answer: - 3 1/4

Step-by-step explanation:

- 3 3/4 + 1/2

Get a common denominator

-3 3/4 + 2/4

-3 1/4

Answer:

142.5 ft^2

Step-by-step explanation:

You need to calculate each figure separately

area of the first rectangle = 5 x 4 = 20

area of the second rectangle = (5+6)x(4) = 44

area of 1/4 circle =  1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5

area of figure: 78.5 + 20 + 44 = 142.5

Answer:

To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.

Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:

Area = (b1 + b2) / 2 * h

where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.

Plugging in the values, we get:

Area = (6ft + 10ft) / 2 * 5ft

Area = 8ft * 5ft

Area = 40 sq ft

Area ≈ 3.73 sq m (rounded to two decimal places)

Therefore, the area of this figure is approximately 3.73 square meters.

(If it wasn't in decimals, it would be 40 square feet.)

Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]

9240

Step-by-step explanation:

In short, the maximum number of distinct ways the medals could be awarded in this race is 22 x 21 x 20 = 9240. This is calculated using a formula for permutations. Is there anything else you would like to know?

The sink's volume in cubic inches is 8182.8 cubic inches according to the radius of hemisphere.

The volume of hemisphere is calculated by the formula -

Volume = 2/3πr³, where r represents radius of the hemisphere.

Before beginning the calculation, convert radius from mixed fraction to fraction.

Radius = (15×4)+3/4

Performing multiplication and addition

Radius = 63/4 inches

Volume =

[tex] \frac{2}{3} \times \pi \times {( \frac{63}{4}) }^{3} [/tex]

Performing multiplication and taking cube

Volume = 8182.77 inches³

Rounding to nearest tenth

Volume = 8182.8 cubic inches

Hence, the volume of hemisphere is 8182.8 cubic inches.

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The complete question is -

Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be

15 3/4 inches. Find the sink's volume in cubic inches. Round your answer to the nearest tenth if necessary

I got ya.

I wrote the answers in the boxes.

The equation Pt=P₀[tex]e^-0[/tex]. 4t is used to predict the ticket sales of a movie after its release. For the latest blockbuster movie, the predicted ticket sales for the sixth week of the movie’s release is $7. 9 million to the nearest $0. 1 million.

The formula used to predict the number of ticket sales t weeks after a movie’s release is Pt=P₀[tex]e^-0[/tex]. 4t, where P₀ is the first week’s ticket sales. In the case of the latest blockbuster movie, the first week’s ticket sales was $16. 3 million. To calculate the predicted ticket sales for the sixth week, the time t must be set to 6. The equation then becomes , which simplifies to Pt=7. 9 million. The predicted ticket sales for the sixth week of the movie’s release is therefore $7. 9 million to the nearest $0. 1 million. The equation  is a useful tool for predicting the ticket sales of a movie over time. It reflects the fact that, generally, ticket sales for a movie will steadily decline over time, with the rate of decline being determined by the value of the exponent, -0. 4 in this case. By plugging in different values for t, one can easily calculate the predicted ticket sales for a movie at any given time.

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The number of signatures they got on the first day is 2.

The problem can be solved mathematically by using the formula for geometric sequences, which is:

an = a1 × r^(n-1)

where:

an = the nth term in the sequence

a1 = the first term in the sequence

r = the common ratio between consecutive terms

n = the number of terms in the sequence

In this case, we know that the number of signatures they get each day is twice as many as the day before, which means that the common ratio is 2. We also know that the number of signatures they got on the sixth day is 2^6 = 64.

Using the formula for geometric sequences, we can solve for a1 by substituting the known values

64 = a1 × 2^(6-1)

64 = a1 × 2^5

a1 = 64 / 2^5

a1 = 2

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Step-by-step explanation:

To simplify the expression 16+(-3)-3/7j-6/7j+4, we first need to combine like terms. The real numbers (16, -3, and 4) can be added together, and the imaginary numbers (-3/7j and -6/7j) can also be added together. So we have:

16 + (-3) + 4 + (-3/7j) + (-6/7j)

Simplifying the real numbers:

= 16 - 3 + 4

= 17

Simplifying the imaginary numbers:

= (-3/7j) + (-6/7j)

= (-9/7j)

Putting it all together, we get:

16 + (-3) - 3/7j - 6/7j + 4 = 17 - 9/7j

So the simplified expression is 17 - 9/7j.

The smallest number of peanuts that could be in the bag is 4320.

Let's use the Chinese Remainder Theorem to solve this problem.

Let:

x be the number of peanuts in the bag.

Then we know that x ≡ 2 (mod 8), x ≡ 2 (mod 9), and x ≡ 2 (mod 10).

Using the Chinese Remainder Theorem, we can find a solution for x as follows:

Let

M = 8 * 9 * 10 = 720, and let M1, M2, and M3 be the remainders when M is divided by 8, 9, and 10 respectively.

That is, M1 = 720 mod 8 = 0, M2 = 720 mod 9 = 0, and M3 = 720 mod 10 = 0.

Let b1 = 1, b2 = 1, and b3 = 1.

Then we need to find integers a1, a2, and a3 such that a1 * M1 * b1 + a2 * M2 * b2 + a3 * M3 * b3 = 1.

One solution is a1 = 5, a2 = -4, and a3 = 1,

so we have 5 * 720 * 1 + (-4) * 720 * 1 + 1 * 720 * 1 = 7201

= M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2.

This means that x = M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2 is a solution to the system of congruences.

Since M1 = 0, we have x ≡ 0 (mod 8).

Since M2 = 0, we have x ≡ 0 (mod 9).

Since M3 = 0, we have x ≡ 0 (mod 10).

Therefore, the smallest positive integer solution for x is x = 720 * 1 * 2 + 720 * 1 * 2 + 720 * 1 * 2 = 4320.

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Answer: o find an equation that is parallel to the given line, we need to use the fact that parallel lines have the same slope.

The given line has a slope of 1/2, so any parallel line must also have a slope of 1/2.

Now we can use the point-slope form of a line to find the equation of the parallel line that passes through (-6, 5):

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Plugging in m = 1/2 and (x1, y1) = (-6, 5), we get:

y - 5 = 1/2(x - (-6))

Simplifying:

y - 5 = 1/2(x + 6)

y - 5 = 1/2x + 3

y = 1/2x + 8

So the equation of the parallel line that passes through (-6, 5) is y = 1/2x + 8.

Brainliest is Appreciated.

The change in tempo and rhyme scheme in the final stanza both hint at the speaker's unclear identity. It gives satirical overtones to the creations.

Poets choose particular rhyme schemes to elicit different responses from their audiences. It fosters a particular atmosphere and mood that may affect how we respond to the poem's themes. Rhyme can be rigid or have satirical overtones, or it can have a playful or playful atmosphere.

When a poem has rhyme and meter, it is more musical. In traditional poetry, the anticipated enjoyment of a predictable rhyme aids in memorization for recitation. The use of a rhyme scheme also establishes the form. The shift in the poem's rhythm In the last stanza signifies the poets uncertain identity.

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Answer:

The area of a triangle is given by the formula A = 1/2 * base * height, where "base" is the length of the triangle's base and "height" is the length of the perpendicular line segment from the base to the opposite vertex.

If the base of a triangle is doubled, the height remains constant, and the area of the triangle will also double. This is because the area of a triangle is directly proportional to its base length.

In the case of the given triangle, if the base is doubled from 3 centimeters to 6 centimeters, the area of the triangle will become:

A = 1/2 * 6 cm * 6 cm = 18 cm²

Therefore, the area of the triangle will increase from 9 cm² to 18 cm² if the base is doubled while the height remains constant at 6 cm.

Step-by-step explanation:

Answer:

[-4, +∞)

Step-by-step explanation:

[-4, +∞)

The probability that exactly one of these 7 people have a hepatoma is 0.35 or 35%

The risk of hepatoma among alcoholics without cirrhosis of the liver is 24%.We need to find the probability that exactly one of these 7 people have a hepatoma. Let the probability of having hepatoma be P(A) = 24% = 0.24 (given). Therefore, the probability of not having a hepatoma is P(A') = 1 - P(A) = 1 - 0.24 = 0.76. We have n = 7 people.

The probability of exactly 1 person having a hepatoma is P(1 person having hepatoma) = C(7,1) × P(A) × [tex]P(A')^{6}[/tex].

C(n, x) is the combination of n things taken x at a time. C(7,1) = 7!/1!6! = 7P(1 person having hepatoma) = 7 × 0.24 × (0.76)⁶= 0.35

Therefore, the probability that exactly one of these 7 people have a hepatoma is 0.35 or 35%.

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303

Step-by-step explanation:

Answer:

110x

Step-by-step explanation:

its 110x

The domain of a function refers to the set of all possible input values. We can easily find the domain of the given function h(t) using the following rules:

Since the denominator cannot be zero, we must exclude the value t = -3 from the domain. This means that the domain is {t | t ≠ -3}.

Furthermore, the expression inside the square root cannot be negative since the square root of a negative number is undefined. Thus, we have t^2 - 16 ≥ 0, which implies t ≤ -4 or t ≥ 4.

Therefore, the domain of the function h(t) is given by {t | t ≠ -3, t ≤ -4 or t ≥ 4}. This can also be written in set-builder notation as {t : t ≤ -4 or t ≥ 4, t ≠ -3}.

Hence, the correct option is {\color{Red}\boxed{(-\infty,-4] \cup[4, \infty) \text { or }{x \mid x \leq-4 \text { or } x \geq 4}}}

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Answer:[tex]847\pi[/tex]

Step-by-step explanation:

[tex]v=\pi r^{2} h\\v=\pi 11^{2} 7\\v=847\pi[/tex]

The lower limit with 3 decimal places at 90% confidence is 29.266.

To determine the lower limit with 3 decimal places at 90% confidence given a sample of 10 widgets with a mean of 32.500 and standard deviation of 6.050, one would use the following steps:Step 1: Calculate the standard errorThe formula for standard error is: `standard deviation / square root of sample size`.So, `standard error = 6.050 / sqrt(10) = 1.916` (rounded to 3 decimal places).Step 2: Find the t-value for 90% confidence with degrees of freedom (df) = n - 1From a t-table or calculator, with df = 10 - 1 = 9 and 90% confidence, we find that the t-value is 1.833.Step 3: Calculate the lower limitThe formula for the lower limit of a confidence interval is: `sample mean - (t-value * standard error)`.So, `lower limit = 32.500 - (1.833 * 1.916) = 29.266` (rounded to 3 decimal places).Therefore, the lower limit with 3 decimal places at 90% confidence is 29.266.

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If the square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3, the value of x that satisfies the equation is x = 13.75.

Let's start by using the formula for the square of a binomial:

(a + b)^2 = a^2 + 2ab + b^2

In this case, we have:

(x + 1)^2 = x^2 + 2x + 1 (square of the binomial x+1)

(x - 3)^2 = x^2 - 6x + 9 (square of the binomial x-3)

We're told that the square of the binomial x+1 is 120 greater than the square of the binomial x-3. In other words:

(x + 1)^2 = (x - 3)^2 + 120

Substituting the expressions we found above, we get:

x^2 + 2x + 1 = x^2 - 6x + 9 + 120

Simplifying, we get:

8x = 110

Therefore, the solution is:

x = 13.75

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Complete question is:

The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3. what is value of x?

The 95% confidence interval for the population proportion who favor an amendment for organized prayer in public schools does not provide convincing evidence that more than two-thirds.

Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S.The 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). This means that if the same poll was conducted over and over again, 95% of the time the results would fall within this interval. Since the interval includes values less than 2/3, it is possible that 2/3 or less of the population favor such an amendment. Therefore, there is not convincing evidence that more than two-thirds of  important to note that the confidence interval does not provide conclusive evidence either way, only an indication of the likely proportions in the population.

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On solving the provided question we cans ay that As a result, X is 2477, function rounded to the closest tenth.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

To find X, we must isolate it on one side of the equation by executing the identical procedure on both sides.

X + 23 = 2500

Taking 23 off both sides:

X = 2500 - 23

To simplify: X = 2477

As a result, X is 2477, rounded to the closest tenth.

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Answer:

x = 3

y = -2

Step-by-step explanation:

-x + 12y = -27

-5x + 3y = -21

Time the first equation by -5

5x - 60y = 135

-5x + 3y = -21

-57y = 114

y = -2

Now put in -2 for y and solve for x

-5x + 3(-2) = -21

-5x -6 = -21

-5x = -15

 x = 3

Let's check

-5(3) + 3(-2) = -21

-15 - 6 = -21

-21 = -21

So, x = 3 and y = -2 is the correct answer.

The table are shown below

From the question, we have:

f(x) = x^2 - 1  x <= 0

        2x - 2  0 < x <= 5

        3  x > 5

So, we make the table using the x values in the domain

x   f(x) = x^2 - 1

0                -1

-1               0

-2              3

-3             8

x   f(x) = 2x - 1

1                1

2               3

3               5

4               7

5              9

x   f(x) = 3

6         3

7         3

8         3

The domain are given in the question

So, we have the domains of the three functions to be

x <= 0, 0 < x <= 5 and x > 5

Using the table of values, we have the range of the three functions to be

f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3

Here, we use a graphing calculator

The graph of the function is added as an attachment

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The increase in price for both appliances is the same, which is ₹400

Let's first find the increase in price for the toaster:

Increase in price = New price - Old price

Increase in price = ₹800 - ₹400

Increase in price = ₹400

Now, let's find the increase in price for the microwave:

Increase in price = New price - Old price

Increase in price = ₹10400 - ₹10000

Increase in price = ₹400

As we can see, the increase in price for both appliances is the same, which is ₹400.

The increase in price for both appliances is ₹400. This is found by subtracting the old price from the new price for each appliance. For the toaster, the increase is ₹800 - ₹400 = ₹400. For the microwave, the increase is ₹10400 - ₹10000 = ₹400. Since both appliances had the same increase in price, we can conclude that the percentage increase is different for each appliance. In this case, the percentage increase for the toaster is 100% [(₹800 - ₹400)/₹400 x 100%], while the percentage increase for the microwave is only 4% [(₹10400 - ₹10000)/₹10000 x 100%].

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The level of private saving in the given closed economy is $4 trillion.

Given, Y = $14 trillion C = $8 trillion G = $3 trillion S pub = $1 trillion T = $5 trillion We have to find the level of private saving, spriv, in this economy.

In a closed economy: Y = C + I + G Here, I = investment in the economy Thus, Y = C + S + T When we add G to both sides of the equation we get, Y + G = C + S + T + G Now, from the given data we have, Y + G = $14 + $3 = $17 trillion C = $8 trillion T = $5 trillion

So, we have, Y + G = C + S + T + G Solving for S, we get; S = Y + G - C - TS = $17 trillion - $8 trillion - $5 trillion S = $4 trillion Therefore, the level of private saving in the given closed economy is $4 trillion.

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The given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees.

The given statement implies that the international company has a total number of employees working in various countries. Out of these, 22.9% of the employees are working in a particular country, which amounts to 19700 employees in that country.

To find out the total number of employees working in all countries, we can use the following formula:

Total number of employees = Number of employees in the given country / Percentage of employees in the given country

Substituting the values given in the problem, we get:

Total number of employees = 19700 / 0.229

Total number of employees = 85939.3

Therefore, the international company has approximately 85939 employees working in various countries.

It's important to note that this calculation assumes that the proportion of employees working in the given country is representative of the proportion of employees working in other countries. However, if the proportion of employees working in other countries is significantly different, then the actual number of employees in the company could be different from the calculated value.

In conclusion, the given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees. We can use this information to approximate the total number of employees working in all countries.

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complete question :

An international company had 19700 employes in one country that is 22. 9 percent of there employies. Find the total number of employes in the company ?