The system of four forces acts on the roof truss. Determine the equivalent resultant force and specify its location along AB, measured from A.

Answers

Answer 1

The equivalent resultant force is 1228.3 N and its location along AB, measured from A is 4.7 m.

The system of four forces acts on the roof truss. Determine the equivalent resultant force and specify its location along AB, measured from A.For the given system of forces, the components of each force should be determined first.The angle between the horizontal and the 500 N force is 60 degrees.Cos 60 = adjacent/hypotenuse Adjacent = cos 60 x 500 = 250 N This force is resolved into two components; one horizontal and the other vertical.250 N is the horizontal component.

The vertical component of this force is resolved as follows:Sin 60 = opposite/hypotenuse Opposite = sin 60 x 500 = 433 NThe system is now resolved and we get:Resolve force 700 N into components. The angle between the horizontal and the 700 N force is 30 degrees.Cos 30 = adjacent/hypotenuse Adjacent = cos 30 x 700 = 606 N

The vertical component of this force is resolved as follows:Sin 30 = opposite/hypotenuse Opposite = sin 30 x 700 = 350 N
Resolve force 600 N into components. This force acts horizontally and thus, it has no vertical component.Resolve force 800 N into components. This force acts vertically and thus, it has no horizontal component.

The components of the forces are summarized in the table below:Force components X component (N)Y component (N)5002504337006063506006000800 This information can now be used to determine the equivalent resultant force and its location.∑Fy = 250 N + 433 N + 350 N - 800 N = 233 N∑Fx = 606 N + 600 N = 1206 N Therefore;∑F = √[(∑Fx)² + (∑Fy)²]= √[(1206)² + (233)²]= 1228.3 N From the force diagram, the distance of the equivalent resultant force from A, measured along AB is given by the ratio of the moment of the force about A and the force itself:Moment of force about A = 250 x 6 + 606 x 2.5 + 600 x 1 = 5750 N.m Therefore, Distance of the force from A = Moment of force about A / ∑F= 5750 N.m / 1228.3 N= 4.7 m (to 1 decimal place)

Therefore, the equivalent resultant force is 1228.3 N and its location along AB, measured from A is 4.7 m.

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Related Questions

is the bottled water you are drinking really purified water? a study of various brands of bottled water conducted by the natural resources defense council found that 25% of bottled water is just tap water packaged in a bottle (scientific american, july 2003).

Answers

Yes, there is a chance that the bottled water you are drinking is just tap water packaged in a bottle. According to a study by the Natural Resources Defense Council, 25% of bottled water is just tap water that has been packaged in a bottle. [Scientific American, July 2003]

What is bottled water?

Bottled water is drinking water that has been packaged in bottles or containers for sale. Bottled water can come from a variety of sources, such as municipal supplies, springs, wells, and other sources. In some cases, bottled water is treated or purified to remove impurities and contaminants. However, not all bottled water is purified or treated, and some may be just tap water that has been packaged in a bottle.

What is purified water?

Purified water is water that has been treated to remove impurities and contaminants. Purified water can come from any source, including municipal supplies, wells, and other sources. Purification methods may include filtration, reverse osmosis, distillation, or other methods. Purified water is commonly used in medical and industrial applications, as well as in homes for drinking and cooking.

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Choose the correct answer.
When you get the sum of a data set and divide by the number of values collected, you get the
A)quantitative data
B)qualitative data
C)median
D)mean

Answers

A) it has sum big dog big bear
D)mean When you get the sum of a data set and divide by the number of values collected, you get the mean

Write each function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. cos(α+20∘)

Answers

The given function is cos(α+20°) and its cofunction can be expressed as cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).

Therefore cos(α+20°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.

The complementary angle of 20° is 70° because 20° + 70° = 90°.

So, we can rewrite cos(20°) as sin(70°) and sin(20°) as cos(70°).

Using the formula for the cosine of the sum of two angles, we can then substitute these values to get:

cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°)

Therefore, expression of cos(α+20°) in terms of its cofunctions is cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).

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What is the sum of the following equation? (2 points)

three tenths plus thirty-nine hundredths equal blank

A. thirty-six hundredths
B. forty-two hundredths
C. sixty-nine hundredths
D. ninety-six hundredths

Answers

Answer:

sixty nine hundredths

Step-by-step explanation:

three tenths can be expressed in decimal as 3/10

thirty nine hundredths can be expressed in decimal as 39/100

Therefore the sum of three tenths plus thirty nine hundredths equals

3/10 +39/100

We first find the l.c.m of the two fractions equals 100 so we have 100 as the denominator

then 100 divided by 10  multiplied by 3 +100 divided by 100 multiplied by 39 as illustrated below gives the answer

3/10 +39/100

=30+39/100

=69/100= sixty nine hundredths

45/43 as a percentage rounded to the nearest tenth of a percent​

Answers

Answer:

104.7% to the nearest tenth.

Step-by-step explanation:

Multiply the fraction by 100:

= (45 x 100) / 43

= 104.651.

Estimating the within-group variance. Refer to the previous exercise. Here are the cell standard deviations and sample sizes for cooking enjoyment: Find the pooled estimate of the standard deviation for these data. Use the rule for examining standard deviations in ANOVA from Chapter 12 (page 560) to determine if it is reasonable to use a pooled standard deviation for the analysis of these data.

Answers

In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

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Amir and Brandon are sharing a cake they bought for 10 dollars. Half of
the cake is chocolate and half of the cake is vanilla. Amir likes chocolate
twice as much as vanilla. Brandon likes chocolate four times as much as
vanilla. They decide to use the divider-chooser method to share the cake. (a) Give a way Amir might split the cake if he’s the splitter. State which
piece Brandon would choose and how much it’s worth to him. (b) Give a way Brandon might split the cake if he’s the splitter. State
which piece Amir would choose and how much it’s worth to him

Answers

(a) If Amir is the splitter, he can divide the cake into two equal halves, offer Brandon the first choice, who will likely choose the chocolate half worth 6.67 dollars to him, and Amir will take the vanilla half worth 3.33 dollars to him.

(b) If Brandon is the splitter, he can divide the cake into two equal halves, offer Amir the first choice, who will likely choose the chocolate half worth 5 dollars to him, and Brandon will take the vanilla half worth 5 dollars to him.

(a) If Amir is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Brandon the first choice of which half he wants. Since Brandon likes chocolate four times as much as vanilla, he will likely choose the chocolate half, which is worth 6.67 dollars to him (4/5 of the total value of the cake). Amir will then take the vanilla half, which is worth 3.33 dollars to him (1/5 of the total value of the cake).

(b) If Brandon is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Amir the first choice of which half he wants. Since Amir likes chocolate twice as much as vanilla, he will likely choose the chocolate half, which is worth 5 dollars to him (1/2 of the total value of the cake). Brandon will then take the vanilla half, which is worth 5 dollars to him (1/2 of the total value of the cake)

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On a piece of paper, use a protractor to construct △ABC with m∠A=30° , m∠B=60° , and m∠C=90° .


Which statements about the triangles are true?


Select each correct answer.

AC BC
a c is greater than b c

AC>AB
a c is greater than a b

AC

Answers

Answer:

AC<BC = 30+60=90 < 60+90= 150

Step-by-step explanation:

AC>AB 30+90= 120 > 30+60=90
AC<BC 30+60=90 < 60+90= 150

The exponential probability distribution is used with: A. A discrete random variable B. A continuous random variable C. Any probability distribution with an exponential term D. An approximation of the binomial probability distribution

Answers

The exponential probability distribution is employed with a random variable that is continuous in nature.


What do you mean by exponential probability distribution ?

In the field of probability, a probability distribution refers to a mathematical function that gives the probabilities of various possible outcomes of an experiment. The exponential probability distribution is a probability distribution that models the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. It is a continuous probability distribution, meaning that the random variable takes on values within a continuous range, as opposed to a discrete probability distribution, where the random variable takes on only a finite or countable set of values.

Explanation of the correct answer :
The exponential probability distribution is defined by a single parameter, [tex]\lambda[/tex] which represents the average rate of occurrence of events in the Poisson process.

The probability density function (pdf) of the exponential distribution is given by [tex]f(x) = \lambda e^{(-\lambda x)}[/tex], where x is the time between events. The cumulative distribution function (cdf) is given by [tex]F(x) = 1 - e^{-\lambda x}[/tex].

The exponential probability distribution is used in many applications, such as queuing theory, reliability theory, and finance. For example, it can be used to model the time between customer arrivals in a queue, the time between machine failures in a manufacturing process, or the time until default on a bond.

In summary, the exponential probability distribution is a continuous probability distribution that is used with a continuous random variable, specifically to model the time between events in a Poisson process.
Hence, option B is correct.

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f(x)=3x^2+12+11 in vertex form

Answers

Answer:

y = -3(x - 2)^2 + 1. Explanation: x-coordinate of vertex: x = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1

Step-by-step explanation:

Answer:x-coordinate of vertex:

x = -b/(2a) = -12/-6 = 2

y-coordinate of vertex:

y(2) = -12 + 24 - 11 = 1

Vertex form:

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

Check.

Develop y to get back to standard form:

y = -3(x^2 - 4x + 4) + 1 = -3x^2 + 12x - 11.

Step-by-step explanation:

I need to show my work please help

Answers

Answer:

x=15

Step-by-step explanation:

use the side splitter theorem

(x-6)/x = 3/5 (cross-multiply)

3x=5(x-6) distributive property

3x=5x-30

2x = 30

x = 15

What is the value of the expression?

1/2 ÷ 6

Answers

Answer:

0.25

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.

So we first simplify the expression by dividing 1/2 by 6:

1/2 ÷ 6 = 1/2 × 1/6

Next, we multiply the two fractions by multiplying their numerators and denominators:

1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12

Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.

solve the linear system using elimination. -5x+3y=19 and -5x+7y+11

Answers

Answer:

x = -5

y = -2

Step-by-step explanation:

-5x + 3y = 19

-5x + 7y = 11

Time the first equation by -1

5x - 3y = -19

-5x + 7y = 11

4y = -8

y = -2

Now put -2 in for y and solve for x

-5x + 3(-2) = 19

-5x - 6 = 19

-5x = 25

x = -5

Let's Check

-5(-5) + 3(-2) = 19

25 - 6 = 19

19 = 19

So, x = -5 and y = -2 is the correct answer.

three fair, standard six-faced dice of different colors are rolled. in how many ways can the dice be rolled such that the sum of the numbers rolled is 10? (mathematics teacher calendar problem)

Answers

There are a total of 27 combinations that give a sum of 10 when rolling three dice.

We have,

The possible outcomes in the sample space for rolling three dice:

S = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 1, 6),

(1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6),

(1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 3, 6),

(1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 4, 5), (1, 4, 6),

(1, 5, 1), (1, 5, 2), (1, 5, 3), (1, 5, 4), (1, 5, 5), (1, 5, 6),

(1, 6, 1), (1, 6, 2), (1, 6, 3), (1, 6, 4), (1, 6, 5), (1, 6, 6),

(2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 1, 6),

(2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 2, 5), (2, 2, 6),

(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5), (2, 3, 6),

(2, 4, 1), (2, 4, 2), (2, 4, 3), (2, 4, 4), (2, 4, 5), (2, 4, 6),

(2, 5, 1), (2, 5, 2), (2, 5, 3), (2, 5, 4), (2, 5, 5), (2, 5, 6),

(2, 6, 1), (2, 6, 2), (2, 6, 3), (2, 6, 4), (2, 6, 5), (2, 6, 6),

(3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 1, 4), (3, 1, 5), (3, 1, 6),

(3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 2, 4), (3, 2, 5), (3, 2, 6),

(3, 3, 1), (3, 3, 2), (3, 3, 3), (3, 3, 4), (3, 3, 5), (3, 3, 6),

(3, 4, 1), (3, 4, 2), (3, 4, 3), (3, 4, 4), (3, 4, 5), (3, 4, 6),

(3, 5, 1), (3, 5, 2), (3, 5, 3), (3, 5, 4), (3, 5, 5), (3, 5, 6),

(3, 6, 1), (3, 6, 2), (3, 6, 3), (3, 6, 4), (3, 6, 5), (3, 6, 6),

(4, 1, 1), (4, 1, 2), (4, 1, 3), (4, 1, 4), (4, 1, 5), (4, 1, 6),

(4, 2, 1), (4, 2, 2), (4, 2, 3), (4, 2, 4), (4, 2, 5), (4, 2, 6),

(4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 3, 4), (4, 3, 5), (4, 3, 6),

(4, 4, 1), (4, 4, 2), (4, 4, 3), (4, 4, 4), (4, 4, 5), (4, 4, 6),

(4, 5, 1), (4, 5, 2), (4, 5, 3), (4, 5, 4), (4, 5, 5), (4, 5, 6),

(4, 6, 1), (4, 6, 2), (4, 6, 3), (4, 6, 4), (4, 6, 5), (4, 6, 6),

(5, 1, 1), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 1, 5), (5, 1, 6),

(5, 2, 1), (5, 2, 2), (5, 2, 3), (5, 2, 4), (5, 2, 5), (5, 2, 6),

(5, 3, 1), (5, 3, 2), (5, 3, 3), (5, 3, 4), (5, 3, 5), (5, 3, 6),

(5, 4, 1), (5, 4, 2), (5, 4, 3), (5, 4, 4), (5, 4, 5), (5, 4, 6),

(5, 5, 1), (5, 5, 2), (5, 5, 3), (5, 5, 4), (5, 5, 5), (5, 5, 6),

(5, 6, 1), (5, 6, 2), (5, 6, 3), (5, 6, 4), (5, 6, 5), (5, 6, 6),

(6, 1, 1), (6, 1, 2), (6, 1, 3), (6, 1, 4), (6, 1, 5), (6, 1, 6),

(6, 2, 1), (6, 2, 2), (6, 2, 3), (6, 2, 4), (6, 2, 5), (6, 2, 6),

(6, 3, 1), (6, 3, 2), (6, 3, 3), (6, 3, 4), (6, 3, 5), (6, 3, 6),

(6, 4, 1), (6, 4, 2), (6, 4, 3), (6, 4, 4), (6, 4, 5), (6, 4, 6),

(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6),

(6, 6, 1), (6, 6, 2), (6, 6, 3), (6, 6, 4), (6, 6, 5), (6, 6, 6)}

Now,

The combination where the sum is 10 is 27.

ie.

{(1, 3, 6), (1, 4, 5), (1, 5, 4), (1, 6, 3), ........, (6, 1, 3), (6, 2, 2,), (6, 3, 1)}

Thus,

There are 27 ways of combination where the sum is 10.

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a rectangular prism has a height of 1/5 m and a square base with an area of 7 1/2 m^2. What is the volume of the rectangular prism?

Answers

The volume of the rectangular prism is approximately 0.2996 cubic meters.

What is rectangular prism and its volume?

Six rectangular faces that are congruent and parallel to one another make up the three-dimensional solid known as a rectangular prism. A rectangular cuboid is another name for it.

By multiplying the prism's length, width, and height, one may get the volume of a rectangular prism, which is the volume of the interior space of the prism.

Given that, area of the square base is 7 1/2 sq. m.

The side of the square base is thus,

√(7 1/2) ≈ 2.7386 m

The volume of the rectangular prism is given as:

Volume = length x width x height

Volume ≈ 2.7386 x 2.7386 x 1/5 m

Volume ≈ 0.2996 cubic meters.

Hence, the volume of the rectangular prism is approximately 0.2996 cubic meters.

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Does someone mind helping me with this problem? Thank you!

Answers

the answer to the problem that you need to is 1024

Select the interval where

h

(

x

)

>

0

h(x)>0h, left parenthesis, x, right parenthesis, is greater than, 0.

Choose 1 answer:

Choose 1 answer:


(Choice A)

A



1

<

x

<

0

−1

Answers

The correct statement regarding where the graph of h(x) = x³ has positive signal is given as follows:

x > 0.

How to classify a function as positive or negative?

The graph of a function is positive in the regions where the function values are greater than zero, and negative in the regions where the function values are less than zero.

The comparisons to zero are given as follows:

Greater than zero -> above the x-axis.Less than zero -> Below the x-axis.

Hence, considering the function defined by the rule y = x³, the graph of the function is classified as positive or negative as follows:

Negative for x < 0.Positive for x > 0.

Missing Information

The function is h(x) = x³, and it's graph is given by the image presented at the end of the answer.

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A triangle has one side with length 9 and another side with length 6. The angle opposite the side of length 6 measures 40. what is the measure of the angle opposite the side of length 9?

Answers

Answer: the angle opposite the side length 9 is 74.62 degrees I think .

Step-by-step explanation:

In a certain class of 40students, 90% passed ssce mathematics examinations and 75% passed English. If 2 students failed both mathematics and English, what percentage of students passed both examinations

Answers

30% percent of the students passed both Mathematics and English.

What is Percentage?

A rate, number, or amount in each hundred is known as a percentage

Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.

We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.

We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.

where the number in each section represents the number of students who passed the respective exam.

To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:

percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%

= (28 + 2) / 40 × 100%

= 30%

Therefore, 30% of the students passed both Mathematics and English.

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linear equations in one variable

Answers

Answer:

x = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]\frac{x+1}{3}[/tex] - [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1+2x}{3}[/tex]

multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions

2(x + 1) - 3(x - 1) = 2(1 + 2x) ← distribute parenthesis on both sides

2x + 2 - 3x + 3 = 2 + 4x

- x + 5 = 2 + 4x ( subtract 4x from both sides )

- 5x + 5 = 2 ( subtract 5 from both sides )

- 5x = - 3 ( divide both sides by - 5 )

x = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]

A taxi service charges $2 for the first mile and then $1. 20 for every mile after that. The farthest the taxi will

travel is 25 miles.

If a represents the number of miles traveled, and y represents the total cost of the taxi ride, what is the most

appropriate domain for the situation?

Answers

The appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

Explain about the linear equation?

In a two-variable linear equation, x and y have a linear connection, meaning that the value of any one of the variables, y, relies upon that value of the other, x.

Cost for first mile of  taxi service  = $2.00

Additional cost = $1.20 per mile.

Peak distance = 25 miles.

a = number of miles traveled by taxi.

y = total cost of the taxi ride

The linear equation forms:

y = $1.20a + $2.00

When a = 0; y = $2.00

a = 25 ; y = $1.20*25 + $2.00 = 32

Thus, the appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

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Rina is climbing a mountain. She has not


yet reached base camp. Write an inequality


to show the remaining distance, d, in feet


she must climb to reach the peak.

Answers

The inequality that shows the remaining distance Rina must climb to reach the peak is 0 < d < P

Let's assume that the distance from Rina's current position to the peak of the mountain is "P" feet and the distance from her current position to the base camp is "B" feet.

Then, the remaining distance, "d", that she must climb to reach the peak can be calculated as follows

d = P - B

Since Rina has not yet reached the base camp, the distance she has traveled so far is less than the distance to the base camp, which means:

B > 0

Substituting this inequality in the equation for "d", we get

d = P - B < P

Therefore, the inequality that shows the remaining distance Rina must climb to reach the peak is:

0 < d < P

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Draw and label the height of each parallelogram.​

Answers

Based on the image given, the height of the parallelogram can be expressed as 2 units.

What is the height of a parallelogram?

Parallelograms are two-dimensional figures that include four sides as rectangles. However, in parallelograms, the opposite sides are parallel and the vertical or horizontal sides are diagonal. Due to this, the height in a parallelogram can be determined by measuring the distance between the top and bottom lines. Based on this principle, the height of the parallelogram would be 2.

Note: Below I attach the missing image in this question:

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The amount of daily daylight is unrelated to levels of depression in older adults. What type of hypothesis is this?
a) Null hypothesis
b) Alternative hypothesis
b) Research hypothesis
d) Nonsignificant hypothesis

Answers

The amount of daily daylight is unrelated to levels of depression in older adults. The hypothesis "The amount of daily daylight is unrelated to levels of depression in older adults" is an example of the null hypothesis.

A null hypothesis is a statement that there is no significant difference between two variables or a relationship between them.The null hypothesis assumes that the observed results or changes in the experiment or data are due to random fluctuations or errors in the measurement process. It is the default hypothesis that is typically tested against an alternative hypothesis.

A researcher tries to disprove or reject the null hypothesis by conducting experiments or collecting data to support the alternative hypothesis. If the null hypothesis is rejected, then the alternative hypothesis is accepted as true. However, if the null hypothesis cannot be rejected, then it remains as the plausible explanation for the observations or outcomes in the experiment.

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The volume of this prism is 4950cm3. The area of the cross-section is 110cm2. Work out x .

Answers

Answer:

answer will be my albert enistein calculation is 4500000⁹7765⁵44³=6425786

The measure of an angle is 40.6°. What is the measure of its supplementary angle?

Answers

Answer: 139.4

Step-by-step explanation:

a supplementary angle is equal to 180 so all we have to do is subtract 40.6 from 180

180 - 40.6 = 139.4

Elena is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Elena spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Elena get a higher ratio of correctly spelled words to total words?

Answers

Answer:

To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.

For last week's test, the ratio of correctly spelled words to total words is:

16/20 = 0.8

For this week's test, the ratio of correctly spelled words to total words is:

13/15 ≈ 0.867

Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.

You ride your bicycle 40 meters. How many complete revolutions does the front wheel make?

Answers

The distance that the front wheel travels in one revolution is equal to the circumference of the wheel. Let's assume that the diameter of the wheel is 0.7 meters, which is a typical diameter for a bicycle wheel.

The circumference of the wheel can be calculated as follows:

Circumference = π x Diameter
Circumference = 3.14 x 0.7 meters
Circumference = 2.198 meters

Therefore, the front wheel makes 18.2 complete revolutions (rounded to one decimal place) to travel a distance of 40 meters.

This can be calculated as follows:

Number of revolutions = Distance traveled / Circumference of wheel
Number of revolutions = 40 meters / 2.198 meters
Number of revolutions = 18.2 revolutions (rounded to one decimal place)

So, the front wheel makes 18.2 complete revolutions to travel a distance of 40 meters.

Suppose the water depth during low tide at a certain bay is about 3.0 m, and at high tide it is about 9.0 m. The natural period of oscillation is about 12 hours, and on a particular day, high tide occurred at 6:45 a.m. Find the amplitude (in meters) of the model. Xm

Answers

The amplitude of the model is 3.0 meters.

The amplitude of a harmonic oscillator represents the maximum displacement from the equilibrium position. In the case of tidal oscillations, the equilibrium position is the average water level.

The amplitude of the model can be determined by considering the difference between the high and low tide water depths, which represents the maximum displacement of the water from the average level. Dividing this difference by two gives us the amplitude of the model.

The amplitude of the model can be found using the formula:

Xm = (H - L)/2

where H is the high tide water depth, L is the low tide water depth, and Xm is the amplitude of the model.

Substituting the given values, we get:

Xm = (9.0 - 3.0)/2

Xm = 3.0 meters

Therefore, the amplitude of the model is 3.0 meters.

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Please help me please it would be very appreciated.

Answers

the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]

What is quadratic equation?

A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x²

The equation of a quadratic function is generally given by:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola and "a" determines the shape of the parabola.

To move the function to the left by three units, we need to replace "x" with "(x + 3)" inside the parentheses:

[tex]y = a(x + 3 - h)^2 + k[/tex]

To move the function up by four units, we need to add four to the value of "k":

[tex]y = a(x + 3 - h)^2 + (k + 4)[/tex]

To stretch the function by a scale factor of two, we need to multiply "a" by two:

[tex]y = 2a(x + 3 - h)^2 + 2(k + 4)[/tex]

Combining these transformations, we get the final equation:

[tex]y = 2(x + 3 - 0)^2 + (0 + 4)[/tex]

[tex]y = 2(x + 3)^2 + 4[/tex]

Therefore, the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]

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