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Answer:

3√3 ft or 5.20 ft

Step-by-step explanation:

The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3. Where “x” is the cube side.

x = L × √3

x = 3 × √3

x = 3 × 1.7

x = 5.20 ft

The sum of the arithmetic sequence is 987

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

For example, the sequence, 2,4,6,8,10... is an arithmetic sequence.

The sum of an arithmetic sequence is given as;

Sn=n/2[2a+(n−1)d]. Where d is the common difference and a is the first term.

the last term is 87

therefore;

87= 7+(n-1) 4

87= 7+4n-4

91-7 = 4n

84 = 4n

n = 84/4

n = 21

therefore 87 is the 21st term

Sn=n/2[2a+(n−1)d]

= 21/2(2×7+(21-1)4

= 21/2 ( 14+80)

= 21×94/2

= 987

therefore the sum of the arithmetic sequence is 987

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Answer:

Step-by-step explanation:

3 hours of babysitting = $27

if he needs $180 per week he needs to work at least 12 hours in landscaping.

12 hours of Landscaping = $156

156 + 27 = 183

It cuts down about an hour of work.

If I misunderstood something, please let me know. Have a good day :)

Answer: 16-4√x/16-x is the answer.

Step-by-step explanation:

=> 4/4+√x*4-√x/4-√x

=> 4(4-√x)/(4)²-(√x)²  {using identity - (a+b) (a-b)=a² - b²}

=> 16-4√x/16-x

Answer: D

Step-by-step explanation: 60x9=540 and 540x80=43,200

The force applied to the input piston is  136.25 N.

This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.

Thus, we can equate  the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:

P₁ = P₂

F₁/A₁ = F₂/A₂    (Pressure = Force/Area)

F₂ = 2000 * 9.81 = 19620 N   (F = mg)

A₁ = π * r₁² = π * 5² = 25π cm²

A₂  = π * r₂ ² = π * 60² = 3600π cm²

F₁ = F₂/A₂ * A₁

F₁ = (19620/3600π) * 25π

F₁ = 136.25 N

Therefore, the force applied to the input piston is  136.25 N.

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Question in English

A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?

The probability that the marble choose is not green is 9/10

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.

Probability is expressed as;

probability = sample space/total outcome

total number of marble = 8+6+2+4 = 20marbles

Probability that it is green = 2/20 = 1/10

therefore probability that Is not green = 1-1/10

= 10-1)/10

= 9/10

therefore the probability that a marble chosen is not green is 9/10.

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The sequence 1, 6, 30, 60, . . . is not a geometric sequence

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

1, 6, 30, 60, . . .

To check if the sequence is geometric, we calculae the common ratio of the sequence using

r = next term/previous term

Using the above as a guide, we have the following:

r = 6/1 = 6

r = 30/6 = 5

r = 60/30 = 2

The common ratios of the sequence calculated above are different

This means that the sequence is not geometric

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Wwe can reject the null hypothesis and deduce that there is sufficient empirical evidence to validate the presumption that seatbelts are competent for mitigating fatalities.

Null Hypothesis: There is no discernible distinction between the proportion of fatalities among occupants wearing seat belts and those without.

Alternative Hypothesis: The portion of fatalities experienced by those in vehicles donning seatbelts will be demonstrably lower in comparison to individuals not utilizing them.

The z-value was computed, finding that (0.0113 - 0.0024) / √(0.0047 * (1 - 0.0047) * (1/2915 + 1/7848)) = 12.43.

For a two-tailed test at a 0.05 significance level with 2915 plus 7848 less 2 = 10761 degrees of freedom, the critical value range would be ±1.96. With the calculated z-value of 12.43 surpassing the critical threshold, we can reject the null hypothesis.

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Answer:

"B".  Domain is all real numbers, and the Range is all positive real numbers

Step-by-step explanation:

It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form [tex]y=a*b^x[/tex] where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.

Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).

The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.

The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.

Since "a" is positive, the Range is positive numbers only.

Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.

Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero".  There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0".  So, the Range is written as { y | y>0 }.

Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.

Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"

It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.

To solve this problem, we can use the formula:

1/T = 1/T₁ + 1/T₂

where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.

Substituting the given values into the formula, we get:

1/T = 1/9 + 1/11

Simplifying the right-hand side of the equation, we get:

1/T = (11 + 9)/(9 x 11)

1/T = 20/99

Multiplying both sides by 99, we get:

T = 99/20

Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.

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Answer: To factorize x² + 18x, we can first find the greatest common factor (GCF) of the two terms, which is x:

x(x + 18)

This is the fully factorized form of x² + 18x.

The probability is given as follows:

P(34 < X < 46) = 0.5468 = 54.68%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 40, \sigma = 8[/tex]

The probability is the p-value of Z when X = 46 subtracted by the p-value of Z when X = 34, hence:

Z = (46 - 40)/8

Z = 0.75

Z = 0.75 has a p-value of 0.7734.

Z = (34 - 40)/8

Z = -0.75

Z = -0.75 has a p-value of 0.2266.

Hence:

0.7734 - 0.2266 = 0.5468 = 54.68%.

The probability is:

P(34 < X < 46).

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The total surface area of the pyramid is:260 ft²

The area of a triangle is expressed as:

A = ¹/₂bh

where:

b denotes the base of the triangle

h denotes the height of the triangle

Area of rectangle is:

A = l * w

where:

l denotes the length of the rectangle

w denotes the width of the rectangle

Thus, the total surface area of the given pyramid is:

Total Surface Area =  4(¹/₂(10 * 12)) + (10 * 10)

Total Surface Area  = 240 + 20

Total Surface Area  = 260 ft²

Therefore, we can conclude that is the calculation of the total surface area of the composite figure.

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Answer:

Step-by-step explanation:

In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.

Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

So, the correct answer is:

For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.

For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

It will take about 711.12 minutes or approximately 11.85 hours to test all 400 units.

To find out how long it will take to test 400 units, we need to use the information given in the problem. We know that the quality expert can test 18 units in 32 minutes. We can use this information to find out how long it will take to test one unit.

First, we need to find out how many units can be tested in one minute:

18 units / 32 minutes = 0.5625 units per minute

This means that the quality expert can test 0.5625 units per minute. To find out how long it will take to test one unit, we can divide 1 by 0.5625:

1 / 0.5625 = 1.7778 minutes per unit

So it takes about 1.7778 minutes to test one unit. To find out how long it will take to test 400 units, we can multiply this value by 400:

1.7778 minutes per unit * 400 units = 711.12 minutes

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14.4 is the value of x in triangle .

What is known as a triangle?

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. 180 degrees is the sum of the triangle's three angles.  

                                Triangular shapes have three vertices, three angles, and three sides. 180 degrees is the sum of a triangle's three interior angles. The length of a triangle's two longest sides added together exceeds the length of its third side.

17² = 9² + X²

289 = 81 + x²

289 - 81 = x²

208 = x²

 x = √208

     = 14.4

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well, let's find out how much she made on each week

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]

Note that in order to map A onto B, Kyle would have to dilate the given figure by a scale factor or 3.

A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.

The original point of figure A which has 4 points are


(0,02)
(-1, 2)
(0, 1)
(1, 2)

Multiply all th e points by 3, and you get,

(0,02) x 3 = (0, -6) =
(-1, 2) x 3 = (-3, 6)
(0, 1) x 3 = (0, 3)
(1, 2) x3 = (3, 6)

Plotting the new values will give us the transformation (dilation) required. See the attached image.

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Assuming that the policyholder is healthy and has an average life expectancy, we can estimate the expected value of the policy by multiplying the probability of dying during the policy period by the amount that will be paid out in the event of death.

The probability of dying during the policy period can be estimated using actuarial tables, which provide information on life expectancies based on age, gender, and other factors. For a healthy 28-year-old female, the probability of dying during a one-year policy period is very low, likely less than 0.1%.

If we assume a probability of dying of 0.1%, the expected value of the policy would be:

Expected value = 0.001 x $200,000 = $200

This means that, on average, the policyholder can expect to receive $200 in benefits from the policy. However, it's important to note that this is just an estimate and actual benefits may be higher or lower depending on the policyholder's individual circumstances.

Therefore, there are 3,628,800 different routes possible for the delivery truck to visit all 10 locations only once.

Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by an exclamation mark (!) placed after the number. Factorial notation is often used in combinatorics to calculate the number of possible permutations and combinations of a set of objects.

Here,

The number of different routes possible for the delivery truck can be calculated using factorial notation.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

This simplifies to:

10! = 3,628,800

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Answer:

-----------------------

Given equation to solve:

The result of the first step:

The second step:

And its result is:

The matching choice is C.

The calculated measure of the angle Y is 38°

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

The angle S and angle Y are corresponding angles

This means that the angles are congruent

So, we have

Y = S

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

Y = 38°

Hence, the measure of the angle Y is 38°

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Complete question

Lines MN and GH are parallel. If mS is 38°, then what is mY?

See attachment for figure

Answer:n=-7

Step-by-step explanation: (-2y+5)+(-5y-3)=-7y+2 so our answer is -7.

Answer:

logb28 ≈ 1.634.

Step-by-step explanation:

logb28 = (log428)/(log47)

We can then substitute the given values for logb4 and logb7:

logb28 = (log428)/(log47) = (log28)/(log24 + log27) = (log28)/(1.386 + 1.946)
1.386+1.946=3.332

logb28/3.332
logb28 ≈ 1.634.

Answer:

--------------------

Given:

Use the following identity to find [tex]log_b28[/tex]:

Apply the identity to the given:

The inequality can be solved to get x < 2, the graph is on the image at the end.

Here we have the inequality.

x + 5 < 7

To solve this, we need to isolate the variable, subtracting 5 in both sides we will get.

x < 7 - 5

x < 2

The graph of this inequality will be a number line with an open circle at x = 2, and an arrow that extends to the left side (because x is smaller than 2)

Then we will get the graph that you can see in the image at the end.

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Step-by-step explanation:

Here is a graph from Desmos....you should be able to see where the function is > 0

The measure of angle B is given as follows:

m < B = 49.2º.

Two angles are said to be complementary angles when the sum of their measures is of 90º.

The measures are given as follows:

As the angles are complementary, the value of x is obtained as follows:

x + 21 + 4x - 30 = 90

5x - 9 = 90

5x = 99

x = 19.8.

Hence the measure of angle B is obtained as follows:

m < B = 4 x 19.8 - 30

m < B = 49.2º.

The measures are given as follows:

The angles are complementary, and it asks for the measure of angle B.

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Answer:

x = 3, -5/2

Step-by-step explanation:

First, you move the 15 onto the left of the equation by subtracting it from both sides.

Second, you plug your info into the quadratic equation.  (1 +- sqrt(1+4*15*2))/4