Which of the following numbers is divisible by 3?
a) 539
b) 85
c) 9,285
d) 640

Answer:

150 m^2

Step-by-step explanation:

Area of a rectangle (which describes this wall) is A = L * W.

In this case, the area is A = (15 m)(10 m) = 150 m^2

On solving the provided question, we can say that -  here in graph we have on solving equation \(x^2+ 3y^2 \\\)  =  \(4+3 = 7\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here-

from graph, x= 2

y = 1

\(x^2+ 3y^2 \\\)

\(4+3 = 7\)

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True. Small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

Small p-values indicate that the observed sample data provides strong evidence against the null hypothesis. The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of observing the obtained sample data, or more extreme data, if the null hypothesis is true.

When the p-value is small (typically less than a predetermined significance level, such as 0.05), it suggests that the observed sample data is unlikely to have occurred by chance under the assumption of the null hypothesis. In other words, a small p-value indicates that the observed data is inconsistent with the null hypothesis.

Conversely, when the p-value is large (greater than the significance level), it suggests that the observed sample data is likely to occur by chance even if the null hypothesis is true. In such cases, there is not enough evidence to reject the null hypothesis. Therefore, small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

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Answer:

look below

Step-by-step explanation:

a)

x ÷ 60 = num of days

b)

if we substitute x for 280,

280 ÷ 60 = 4.3333...

It will take 4.333 days (4 days 8 hr) to complete the novel.

Answer:

These angles are called angle pairs. ... Supplementary angles are two angles whose sum is equal to \begin{align*}180^\circ\end{align*}. In other words when you add the measure of one angle in the pair with the other angle in the pair, they equal 180 degrees.

Step-by-step explanation:

Hope this helps you <3

The cost of 8 family passes to the amusement park is $432 when a family pass to the amusement park costs $54.

To find the cost of 8 family passes to the amusement park, we can use the Distributive Property of multiplication over addition. The Distributive Property states that a(b + c) = ab + ac, where a, b, and c are numbers. In this case, we can use the Distributive Property to write:

8 x $54 = (5 x $54) + (3 x $54)

We can see that we have broken 8 down into two smaller numbers that we can multiply by $54 individually, and then add together. The first term, 5 x $54, represents the cost of 5 family passes, while the second term, 3 x $54, represents the cost of 3 family passes. Adding these two values together, we get:

(5 x $54) + (3 x $54) = $270 + $162 = $432

Therefore, the cost of 8 family passes to the amusement park is $432.

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The average speed for the first part of the trip is 60 miles.

Given:

1st leg DATA:

distance = 120 miles ;

rate = x mph ;

time = d/r = 120/x hrs

2nd leg DATA:

distance = 220 miles ;

rate = x-5 mph ;

time = 220/(x-5) hrs

hence the equation we frame is:

Equation:

120/x + 220/(x-5) = 6

120(x-5) + 220x = 6x(x-5)

120x - 600 + 220x = 6x² - 30x

-6x² + 340x + 30x - 600 =0

-6x² + 370x - 600 = 0

-3x² - 185x + 300 = 0

(3x-5)(x-60)

3x = 5 or x-60=0

x = 5/3 or x = 60

hence x-5 = 60-5

= 55 miles per hour.

Hence we get the answer as 60 miles.

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Answer:

  ∠MAR = 28

Step-by-step explanation:

Given angle MAR bisected by ray AT to form angle MAT = (6x-4) and RAT = (2x+8), you want to know the measure of MAR.

An angle bisector divides an angle into two congruent parts:

  ∠MAT = ∠RAT

  6x -4 = 2x +8

  4x = 12 . . . . . . . . add 4-2x

  x = 3 . . . . . . . divide by 4

Then the measure of one of the halves is ...

  ∠RAT = 2x +8 = 2·3 +8 = 14

So, the measure of the whole is ...

  ∠MAR = 2·14

  ∠MAR = 28

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Answer:

I can be measured by a displacement can

Answer:

\(\frac{1}{2^5}\)

Step-by-step explanation:

a.)Gross pay = $400

b.) Total deductions = $89.25

c .) Net pay = $310.75

For question a.) The gross pay of Omark is calculated as thus:

The number of days per week = 7 days

The of working hours per week = 50 hours.

The amount paid per hour = $10

Therefore gross payment for a week = 40×10 = $400

For question b.)

The total deductions = 9.25+15.25+48.50+9.50+2.75+4.00 = $89.25

For question c )

Omark net payment = gross payment - total deductions = 400- 89.25 = $310.75

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Elections give rise to a deficit bias due to the strategic behavior of incumbent governments seeking re-election. In this scenario, we have an incumbent government facing an election at the end of period 1. The equations provided are:

V1 = E[Σ(au(Mi)3)] + (1 - a)u(N)

Lt=1

M2 + N1 = W + D

M2 + N2 = W - D

Where V1 represents the incumbent's expected utility from being re-elected, E denotes the expectation operator, a represents the weight given to military spending (Mi), u(.) represents the utility function, L represents the loyalty of voters, W represents income, D represents government debt, and N represents non-military spending.

The known probability of a right-wing electoral victory, represented by p, can also influence the incumbent's decision-making. If p is high, the right-wing incumbent may prioritize policies that are popular among voters, even if it leads to a higher deficit. Conversely, if p is low, the incumbent may adopt more fiscally conservative policies to appeal to voters who prioritize fiscal responsibility.

Overall, elections introduce a deficit bias as incumbent governments strategically adjust their policies to maximize their chances of re-election, potentially prioritizing short-term benefits over long-term fiscal sustainability.

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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

3

Step-by-step explanation:

For a graph not to be a function, it means that a particular value of x has more than one corresponding value of y. Looking at the graph, at the point where x = 3 on the horizontal axis, there are so many value of y. Plus, the graph below is not a function at x = 3

The correct option is 3

Answer:

\(\frac{-4+6}{2} , \frac{3+2}{2} =1,4\\\\\frac{6+6}{2} ,\frac{5+(-1)}{2} =6,2\\\\\frac{-4+6}{2} ,\frac{3+(-1)}{2} =1,1\)

Step-by-step explanation:

hope it helps have a nice day!!

Answer:

the square of the hypotenuse is 149 squared

Step-by-step explanation:

c= the square root of a^2+b^2=the square root of 7^2+10^2=12.20656

The civil engineer can build his house on a rectangular platform of 10 meters long by 8 meters wide with a corridor of uniform width of 2.05 meters.

Let's call the width of the corridor "w". Since the corridor runs around the perimeter of the rectangle, we can calculate its total area by subtracting the area of the house from the area of the rectangle:

Total area of corridor = Area of rectangle - Area of house

Total area of corridor = 80 - 48

Total area of corridor = 32 square meters

Now we can use the formula for the area of a rectangle to calculate the width of the corridor:

Area of rectangle = length x width

Total area of corridor = (10 + 2w) x (8 + 2w) - 80

32 = 2w² + 36w

2w² + 36w - 32 = 0

We can solve this quadratic equation using the quadratic formula:

w = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 36, and c = -32. Plugging these values into the formula, we get:

w = (-36 ± √(36² - 4(2)(-32))) / 4

w = (-36 ± √(1680)) / 4

w ≈ 2.05 or w ≈ -8.05

Since the width of the corridor cannot be negative, we can disregard the negative solution and conclude that the width of the corridor is approximately 2.05 meters.

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Complete Question:

A Civil Engineer wants to build his house downtown of a rectangular  platform of 10 meters long by 8 meters wide, the area of ​​the house is 48 square meters, the part not built is a corridor of uniform width. How many meters is the width of the hallway?

Answer: $9.18

Step-by-step explanation:

The payment of $823.76 will go towards both interest and principal repayments.

Find out the interest paid from the amount and deduct it from the monthly payment to find the principal repayment.

Monthly interest payment:

= (85,000 * 11.5%) / 12 months

= $814.58

Principal repayment = 823.76 - 814.58

= $9.18

The measure of the angle x will be 65°. Then the correct option is B.

Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.

Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.

Let y be the corresponding angle of x and linear pair of 115°.

∠y + 115° = 180°

         ∠y = 65°

Then the angle y and angle x are corresponding angles. Then we have

∠x = ∠y

∠x = 65°

Then the correct option is B.

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Answer: 65

Step-by-step explanation:

The value of the angles are;

1. x = 5

2.RT = x + 5

3.M = 2x - 5

4.Y = 3x - 30

5.A = 3x - 38

6.T = 4x -38

7.G = -x - 38

We need to know the following;

From the information given, we have'

1, 5x + 1 + 124 = 180

collect the like terms, we get;

5x = 180 - 125

5x = 55

Divide by the coefficient

x = 5

2. the diagonals of a rectangle are equal

RT = QS

QS = 2(5) - 5 = 10 - 5 = 5

RT = x + 5

3. 18x - 19 + x - 3 = 180

collect like terms

M = x + x - 5 = 2x - 5

4. 2x- 5 - x - 25

collect like terms

Y = 3x - 30

5. x - 8

(3x - 8) - 30

expand the bracket

A = 3x - 38

6. T = 7x - 3x - 38

collect like terms

T = 4x -38

7. G = 3x - 4x - 38

G = -x - 38

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We observed Function h(x) is greater than function g(x) for all values of x.

A mathematical expression represents the relationship between independent variables and dependent variables.

when we plot the domain and ranges of a function in the XY coordinate, we get a collection of points. In the next, we join the coordinate to obtain  

line, curves and so on based on the expression of function.

From the graph given in question, we observed that h(x) is greater than g(x) because the domain and ranges of h(x) is greater than g(x).

If we compare for each value of x, we observe that h(x) is always bigger than g(x)

hence, function h(x) is > function g(x) for any values of x

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Answer:  

(-16,-22)

Step-by-step explanation:

B (24,16)

Mid point (4,-3)

24 is -20 away from 4

16 is -19 away from -3

4-20=  -16

-3-19= -22

A confidence interval is constructed to estimate the value of a parameter.

In statistics, a parameter refers to a numerical characteristic of a population, such as the population mean or population proportion. When we want to estimate the value of a parameter, we construct a confidence interval.

A confidence interval provides a range of values within which we believe the true parameter value is likely to fall, based on our sample data. It is constructed using sample statistics and takes into account the variability and uncertainty in the estimation process.

A confidence interval is constructed to estimate the value of a parameter, not a statistic.

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The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).

Mean time that employees spend on personal issues each week(M) = 4.9 hours

Standard deviation = 0.35 hours

The following formula is used to get the confidence interval for the sample mean and standard deviation given:

μ = M ± t(sM)

where; M = sample mean

t = T-statistic based on confidence interval

Degree of freedom = n - 1

From the question, n = 55

Degree of freedom = 55 - 1

Degree of freedom = 54

(Standard errors)sM = √(s^2/n)

Now putting the value

sM = √(0.352/55)

sM = 0.05

t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)

Now the confidence interval

μ = M ± t(sM)

μ = 4.9 ± 2.005 × 0.05

μ = 4.9 ± 0.095

μ = (4.9 - 0.095, 4.9 + 0.095)

μ = (4.805, 4.95)

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The possible triangle orientations are given below -

The relation is that the sum of the two sides of the triangle is greater than the third side. Mathematically -

a + b > c

Given are the sides of a triangle as shown in the triangle.

{ 1 } -

2 yd , 7 yd , 8 yd

7 + 2 > 8

9 > 8    {true}

It forms a triangle.

{ 2 } -

1.5 cm, 2.3 cm, 3.8 cm

2.3 + 1.5 > 3.8

3.8 > 3.8    {false}

It does not form a triangle.

{ 3 } -

3 in. , 4 in. , 5in.

4 + 3 > 5

7 > 5  {true}

It forms a triangle.

{ 4 } -

5 m , 9 m , 14.5 m

9 + 5 > 14.5

14 > 14.5   {false}

It does not form a triangle.

{ 5 } -

14 ft , 15.8 ft , 33 ft

15.8 + 14 > 33

29.8 > 33    {false}

It does not form a triangle.

{ 6 } -

2.8 mm , 7.1 mm , 9.5 mm

7.1 + 2.8 > 9.5

9.9 > 9.5 {true}

It forms a triangle.

Therefore, the possible triangle orientations are given below -

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Answer:

Step-by-step explanation:

-2.5,-0.15,0.50,5/8

The domain and range of this square root function y = 5/2√(-5x + 1) - 87 are as follows;

Domain = {x|x ≤ 1/5}.

Range = {y|y ≥ -87}.

The domain and range of this square root function y = -315√(11x - 3) - 15/88 are as follows;

Domain = {x|x ≥ 3/11}.

Range = {y|y ≤ -15/88}.

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below for the given square root function y = 5/2√(-5x + 1) - 87 and y = -315√(11x - 3) - 15/88, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, 1/5} or {x|x ≤ 1/5}.

Range = {-87, ∞} or {y|y ≥ -87}.

Domain = {3/11, ∞} or {x|x ≥ 3/11}.

Range = {-∞, -15/88} or {y|y ≤ -15/88}.

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