the department of transportation (DOT)sends a crew of workers to fix a pothole in front of North Mecklenburg High School. It takes 12 workers a total of 8 hours to finish the job. How long will the job take if 2 workers call in sick?

The surface area of the triangular prism be 108 ft²

The volume of the triangular prism be 48 ft³.

Given, a triangular prism (base is a right triangle).

Triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft.

Now, the surface area of the triangular prism is,

Surface Area = 2×Area of the base triangle + Side rectangle 1 +Side rectangle 2 + Side rectangle 3

Surface Area = 2×(1/2×3×4) + 5×8 + 3×8 + 4×8

Surface Area = 12 + 40 + 24 + 32

Surface Area = 108 ft²

Now, Volume of the triangular prism be,

Volume = Area of the base triangle × height

Volume = 1/2×3×4×8

Volume = 48 ft³

Hence, the surface area of the triangular prism be 108 ft²

and the volume of the triangular prism be 48 ft³.

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Answer:

1. 3<u<7

2. -2>d or d ≥ 2

3. -2.4 >s <5.2

4.  c >- 4 or c ⩽ -6 \(\frac{1}{2}\)

Step-by-step explanation:

Hope I am helpful!

Answer:

The inverse function h(x) = 4x + 48

Step-by-step explanation:

Here, we want to find the inverse of a function

The function is;

f(x) = x/4 -12

now, let this value equals m

so;

m = x/4 -12

we now try and make x the subject formula and this gives us the inverse.

m = (x-48)/4

4m = x -48

x = 4m + 48

substitute m for x

which implies 4x + 48

This is the inverse of the function

Answer:

D. h(x) = 4x + 48

Answer:

8 1/3 meters

Step-by-step explanation:

set up a proportion of corresponding sides:

TE/AY = JT/DY

25/AY = 18/6

cross-multiply:

18AY = 150

AY = 150/18 which is 8 1/3

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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The coordinate of point S from the giving coordinate point is (4,-19)

The formula for calculating the midpoint of coordinate point is expressed as:

M(x,y) = {(x₁+x₂)/2, (y₁+y₂)/2}

Determine the measure of the coordinate S
2 = 0+x₂/2

2(2) = 0+x₂

x₂ = 4-0

x₂ = 4

Similarly

-8 = 3+y₂/2

-8(2) = 3+y₂

y₂ = -19

Hence the coordinate of point S from the giving coordinate point is (4,-19)

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Answer: 0.0625

Step-by-step explanation: I plugged it into my calculator and this is what I got.

Answer:

Photo?

Step-by-step explanation:

If there is a photo linked I dont see it

Also: Dont click the stpid link below its malware

Answer: 2/3

Step-by-step explanation:

    We will turn all of these fractions into decimals by dividing to compare them easier.

3/5 ➜ 0.6

20/100 ➜ 0.2

6/10 ➜ 0.6

1/2 ➜ 0.5

2/12 ➜ 0.16666

2/3 ➜ 0.6666

    0.6666 > 0.6, so 2/3 > 3/5

    This means our answer is 2/3

Answer:

9

Step-by-step explanation:

The factors of 99 are 99, 33, 11, 9, 3, 1. The common factors of 54 and 99 are 9, 3, 1, intersecting the two sets above. In the intersection factors of 54 ∩ factors of 99 the greatest element is 9. Therefore, the greatest common factor of 54 and 99 is 9.

Hope this helps :)

Can I have brainliest?

Answer:

9

Step-by-step explanation:

9 x 11 = 99

9 x 6 = 54

The future value of the account at time t = 10 is approximately $2,223.13.

We can solve this differential equation using separation of variables:

dP/dt - 0.05P = 15

dP/ (P - 300) = 0.05 dt

Integrating both sides, we get:

ln \(|P - 300| = 0.05t + C\)

where C is the constant of integration.

To solve for C, we can use the initial condition P(0) = 1300:

In \(|1300 - 300| = CC = ln 1000\)

So the solution to the differential equation is:

ln |P - 300| = 0.05t + ln 1000

Taking exponentials of both sides, we get:

\(|P - 300| = e^{(0.05t + ln 1000)} = 1000e^{(0.05t)}\)

Since P(0) = 1300, we know that P - 300 is positive. Therefore, we can simplify the expression above to:

\(P - 300 = 1000e^{(0.05t)}\)

\(P = 1000e^{(0.05t)} + 300\)

To find the future value of the account at time t = 10, we can substitute t = 10 into the equation above:

\(P(10) = 1000e^{(0.05(10))} + 300\)

P(10) = $2,223.13 (rounded to the nearest cent)

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The statement that is true about the dot plots is:  Range for Week 1 equals range for Week 2.

Range is simply the difference between the highest data point and the lowest data point in a data set.

Range for Week 1:

Range = 89 - 62

= 27

Range for Week 2:

Range = 89 - 62

= 27

The sentence of median and mean doesn't satisfy the situation.

Hence, Range for Week 1 equals range for Week 2.

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The data shows that the prevalence of hai (healthcare-associated infections) is higher in individuals over the age of 85 compared to those under the age of 65.

The prevalence rate for hai in individuals over 85 is 11.5%, while it is 7.4% in patients under 65. This indicates that age is a factor that influences the occurrence of hai. The data reflects that the prevalence of healthcare-associated infections (hai) is significantly higher in individuals over the age of 85 compared to patients under the age of 65. Specifically, the prevalence rate for hai in individuals over 85 is 11.5%, while it is 7.4% in patients under 65. This difference suggests that age plays a significant role in the occurrence of hai. Older individuals may have weakened immune systems and are more susceptible to infections. Additionally, factors such as longer hospital stays, multiple comorbidities, and exposure to invasive procedures can contribute to the higher prevalence of hai in this age group. The higher prevalence rate in patients over 85 implies a need for targeted infection prevention and control measures in healthcare settings to minimize the risk of hai among this vulnerable population.

In conclusion, the data indicates that the prevalence of healthcare-associated infections (hai) is higher in individuals over the age of 85 compared to those under the age of 65. Age is a significant factor that influences the occurrence of hai, with a prevalence rate of 11.5% in individuals over 85 and 7.4% in patients under 65. This difference can be attributed to factors such as weakened immune systems, longer hospital stays, multiple comorbidities, and exposure to invasive procedures in older individuals. To mitigate the risk of hai in this vulnerable population, targeted infection prevention and control measures should be implemented in healthcare settings.

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The number of students should be invited to a party to make sure that ap least two of them have the same initials are equals to the 677 (students).

The solution of this problem is obtained by using the pigeonhole principle, which states if there are N boxes and N+1 pigeons, at least two pigeons must be in the same box. We have to determine the number of students invited in party to make make sure that at least two of them have the same initials. Now, first we figure out what N is to solve the problem. Here, box for this problem is labelled by first and last initials. If we are using the A-Z alphabet, then there are 26×26 = 676 possible sets of initials.

As soon as there are N+ 1 or 677 people, at least two must have the same first and last initials. Hence, required value is 677.

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Answer:

see explanation

Step-by-step explanation:

(1)

5(x - 3y) + 4(4y - x) - 2(x - y) ← distribute all 3 parenthesis

= 5x - 15y + 16y - 4x - 2x + 2y ← collect like terms

= 3y - x

(2)

3 - 2(x + 2) = 6 ( subtract 3 from both sides )

- 2(x + 2) = 3 ( divide both sides by - 2 )

x + 2 = - 1.5 ( subtract 2 from both sides )

x = - 3.5

solution set = { - 3.5 }

(3)

The median is the middle value of the data in ascending order

1  4  4  7  8 ← in ascending order

       ↑ median = 4

The mean is the sum of the values divided by the count

mean = \(\frac{1+4+4+7+8}{5}\) = \(\frac{24}{5}\) = 4.8

The mode is the value which occurs most often

mode = 4

Thus the mode is equal to the median → C

(4)

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (A(1 - a, b + 1 ) and (x₂, y₂ ) = B(1 + a, 1 - b )

m = \(\frac{1-b-(b+1)}{1+a-(1-a)}\)

= \(\frac{1-b-b-1}{1+a-1+a}\)

= \(\frac{-2b}{2a}\) ( cancel 2 on numerator/ denominator )

= \(\frac{-b}{a}\) → d

Answer:

d

Step-by-step explanation:

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Answer:the answer is A

Step-by-step explanation:

Answer:

4 cm

Step-by-step explanation:

V = πr²h

or, 36π = π(3)²×h

or, 36 = 9h

or, 4 = h

So the height is 4 cm

Answered by GAUTHMATH

Tina sold 206 veggies in the month of September.

Given, Tina’ taco truck sold 3 times as many veggies taco in August than in September. She sold twice a many in September than in October. She sold 927 veggies taco during the three month.

Let the number of veggies sold in October, x

veggies sold in September = 2x

veggies sold in August = 6x

also, x + 2x + 6x = 927

9x = 927

x = 103

So, the number veggies sold in September be 206.

Hence, Tina sold 206 veggies in the month of September.

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Craig can make 5 of these biscuits with the 30 gram of sugar he has.

To find out how many biscuits Craig can make with 30 g of sugar, we can set up a proportion based on the given information.

The recipe uses 120 g of sugar for 20 biscuits. We can express this as:

120 g sugar / 20 biscuits = 30 g sugar / x biscuits

Cross-multiplying the proportion, we get:

120 g sugar * x biscuits = 30 g sugar * 20 biscuits

Simplifying, we have:

120x = 600

To solve for x, we divide both sides of the equation by 120:

x = 600 / 120

x = 5

Therefore, Craig can make 5 of these biscuits with the 30 g of sugar he has.

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A project to investigate the American West has been the Clark as well as Lewis Expedition, which was supported by the federal government.

The main goal of the mission was to study the Missouri and Columbia river in search of tributaries that would traverse from the heart of the nation to the Western Pacific.

This fleet's main goals are to investigate the Missouri River, investigate the newly acquired Lands, and discover a land way to the Pacific Ocean.

The Lewis and Clark Expedition represented the first time that Americans traveled this far out towards the West by sea and rivers.

Pike, who lost his life in the conflict, rose to fame among American soldiers. Lewis and Clark subsequently eclipsed him with his legacy. Presently, he is famed for his unsuccessful attempt to scale Pike's Peak.

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Answer:

A

Step-by-step explanation:

Simple interest gains interest only on the principal sum and so each year has the same interest. So, this example is not simple interest. Compound interest is calculated on the principal and the accumulated interest of the previous years. So, this is compound interest.

      Interest is 4%.

      \(A = P*(1 + R \%)^n\)

Here A is the amount we receive after n years, P is the principal and R is the rate of interest.

        A = $1300 , R = 4%

            \(1300 = P * (1+0.04})\\\\1300 = P * 1.04\\\\\dfrac{1300}{1.04}=P\\\\\\\dfrac{130000}{104}=P\)

            P = $ 1250

Answer:

BC ≈ 8.6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle , that is

BC² = AB² + AC² = 7.3² + 4.6² = 53.29 + 21.16 = 74.45 ( square root both sides )

BC = \(\sqrt{74.45}\) ≈ 8.6 ( to 1 dec. place )

Answer:

$297

Step-by-step explanation:

Tuesday:

7AM to 11:30AM (4.5 hours)

12PM to 3:45PM (3.75 hours)

Wednesday:

7AM to 11:45AM (4.75 hours)

12:30PM to 4PM (3.5 hours)

Then add:

4.5+3.75+4.75+3.5= 16.5

Then multiply:

16.5*18= 297

Hope this helps!

The total time of Tuesday and Wednesday will be 16.5 hours. Then the total amount that she made on Tuesday and Wednesday is $297.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Lydia worked the following hours last Tuesday and Wednesday.

Tuesday: 7AM to 11:30AM and 12PM to 3:45PM

Wednesday: 7AM to 11:45AM and 12:30PM to 4PM

If Lydia is paid $18 an hour. Then the equation will be

y = 18x

where x is the number of hours.

Then the number of hours on Tuesday will be

→ 11:30 AM - 7:00 AM = 4:30

→ 3:45 PM - 12:00 PM = 3:45

The total hours will be

→ 5:30 + 3:45 = 8:15

Then the number of hours on Wednesday will be

→ 11:45 AM - 7:00 AM = 4:45

→ 4:00 PM - 12:30 PM = 3:30

The total hours will be

→ 4:45 + 3:30 = 8:15

Then the total time of Tuesday and Wednesday will be

→ 8:15 + 8:15 = 16:30

The time can be written as

→ 16:30 = 16.5 hours

Then the total amount she made will be given as

y = 18 × 16.5

y = $297

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Answer:

The width is 24 inches and the length is 120 inches.

Step-by-step explanation:

Let x represent the width of the carpet

The length can be represented by x + 96

Create an equation:

x + x + x + 96 + x + 96 = 288

Add like terms and solve for x:

4x + 192 = 288

4x = 96

x = 24

So, the width is 24 inches. Plug this into x + 96 to find the length:

x + 96

24 + 96

= 120

So, the width is 24 inches and the length is 120 inches.

Answer:

In 3 hours Henry can write 5 pages. So, In 1 hour Henry can write pages. Now, In 8 hours Henry can write pages. In 8 hours Henry can write 13.3 pages.

Step-by-step explanation:

Answer:

C. AOE

Step-by-step explanation:

Supplementary means 180 degrees which is a straight line

Only angle AOE combined with DOE is a straight line