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Problem 1.

The force system shown is to be replaced with an equivalent system consisting of a horizontal force applied at b and a vertical force applied to the horizontal leg.

1.1. What is the magnitude of the vertical force, in Newton, applied to the horizontal leg? (rounded-off to the nearest whole number; do not write the unit)

Answer: its 22

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The number of desired outcomes is the total number of blue pens in the bag. There are seven outcomes that can be blue.

A total of 233 children and 867 adults rode the bus during the morning shift.

Let x represent the number of children and y represent the number of adults riding the bus during the morning shift.

We know that the total number of passengers is 1,100, so we can write the equation:

x + y = 1,100

The child's fare is $0.50, and the adult fare is $1.25. The total revenue from the fares is $1,200, so we can write another equation:

0.50x + 1.25y = 1,200

To solve this system of equations, we can use substitution or elimination.

Let's use substitution to solve for x:

From the first equation, we have: x = 1,100 - y

Substituting this into the second equation:

0.50(1,100 - y) + 1.25y = 1,200

Simplifying the equation:

550 - 0.50y + 1.25y = 1,200

0.75y = 650

y = 650 / 0.75

y ≈ 866.67

Since we can't have a fraction of a person, we can approximate y to the nearest whole number:

y = 867

Substituting this value of y back into the first equation:

x + 867 = 1,100

x ≈ 233

Therefore, approximately 233 children and 867 adults rode the bus during the morning shift.

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Given data: Outcome 0 1 2 Probability 0.26 0.35 0.39a)

The mean of the distribution is given by: Mean = $\sum x P(x)$The distribution can be represented as follows:

Outcome(x) Probability(P(x)) x P(x) 0 0.26 0 1 0.35 0.35 2 0.39 0.78 $\sum x P(x)=0+0.35+0.78=1.13$

Therefore, Mean = $\frac {\sum xP(x)}{n}=\frac {1.13}{3} =0.3767 ≈ 0.377$ (rounded to three decimal places)

b) The formula for standard deviation is given as: $$\sigma =\sqrt{\sum(x-\mu) ^2P(x)} $$where $\mu$ is the mean of the distribution

Substituting the given values in the above formula, we get:

\begin{align*}\sigma &=\sqrt{\sum(x-\mu) ^2P(x)} \\\sigma &=\sqrt{\sum(x-0.377) ^2P(x)} \end{align*} Outcome(x) Probability(P(x)) $x-μ$ $P(x)(x-μ)^2$ 0 0.26 -0.37746 0.03665 1 0.35 -0.02746 0.00076 2 0.39 1.01254 0.15709 Total 1 0.19450$$\sigma =\sqrt {0.1945}=0.441 ≈ 0.441$$

Therefore, the standard deviation of the distribution is approximately equal to 0.441 (rounded to three decimal places).

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The most reasonable estimate of 132% of 48 is 60. The correct answer is (C) 52.

To find the most reasonable estimate of 132% of 48,

A reasonable estimate does not exceed the original numbers in a problem. Let us look at a reasonable estimate.
we need to use the following formula:

Most reasonable estimate = Closest multiple of 10To use this formula, we first need to find 132% of 48.132% of 48 can be calculated as follows:132/100 x 48 = 63.36

Now, we need to find the closest multiple of 10 to 63.36.The closest multiple of 10 to 63.36 is 60.

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To find out the most reasonable estimate of 132% of 48, we can multiply the given percentage with 48.

Therefore, the most reasonable estimate of 132% of 48 is 64.

132% of 48 = (132/100) × 48

= 63.36

Since we are looking for an estimate, we can round off the above answer to the nearest whole number. Here, we have two possible options:

63 and 64.132% of 48 is slightly greater than half of 48 (which is 24) + 24. So, the answer should be slightly greater than 48 + 24 = 72. Therefore, the most reasonable estimate of 132% of 48 is 64. Thus, the correct answer is b.6.5.

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Answer:

IT's d!!!!!

Step-by-step explanation:

Answer:

The range is also all real numbers except zero. You can see that there is some point on the curve for every y -value except y=0 . Domains can also be explicitly specified, if there are values for which the function could be defined, but which we don't want to consider for some reason.

Step-by-step explanation:

hope this helps

Answer: c is the correct opcion

Answer:

B

Step-by-step explanation:

Hi,

Your slope is in front of the x and your y-intercept is what's being added or subtracted. In this case, 4x is your slope, and +1 is your y-intercept which means that B is correct.

I hope this helps :)

The magnitude of the resultant force, given two forces represented by vectors a and b with magnitudes 5.3 N and 6.9 N, respectively, and an angle of 60 degrees between them, can be approximated to 8.5 N.

To find the magnitude of the resultant force, we can use the law of cosines. According to the law of cosines, the magnitude of the resultant force (Ir) can be calculated using the formula: [tex](Ir)^2 = |a|^2 + |b|^2[/tex] - [tex]2|a||b|cos(theta)[/tex], where |a| and |b| represent the magnitudes of vectors a and b, and theta is the angle between them.

Given that |a| = 5.3 N, |b| = 6.9 N, and theta = 60 degrees, we can substitute these values into the formula and solve for Ir. Plugging in the values, we have [tex]Ir^2 = (5.3)^2 + (6.9)^2[/tex]- 2(5.3)(6.9)cos(60).

Simplifying the equation, we get [tex]Ir^2[/tex] = 28.09 + 47.61 - 36.66. Combining the terms, we have [tex]Ir^2[/tex] = 39.04.

Taking the square root of both sides, we find Ir ≈ √39.04 ≈ 6.2 N. Rounded to one decimal place, the magnitude of the resultant force is approximately 8.5 N.

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Answer:

-x^3-7x^2-46x-16/x+4

Step-by-step explanation:

The slash is a fraction! Also the fraction is negative :)

Answer:

If you look at the bar graphs, histograms, and circle graphs, they all look at one variable at a time and display the number of times or percentage of times an individual point or interval is counted.

Step-by-step explanation:

The length of the arc is given by (4π/7) times the circumference of the circle. Hence, the length of the arc intercepted by a central angle of 4π/7 radians in a circle with a radius of 21 inches is 12π inches.

The circumference of circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is 21 inches. Therefore, the circumference of the circle is C = 2π(21) = 42π inches.

The central angle of 4π/7 radians is a fraction of the full angle (2π radians). The ratio between the central angle and the full angle is (4π/7)/(2π) = 2/7.

To find the length of the intercepted arc, we multiply the ratio 2/7 by the circumference of the circle:

Length of arc = (2/7) * (42π) = 12π inches.

Hence, the length of the arc intercepted by a central angle of 4π/7 radians in a circle with a radius of 21 inches is 12π inches.

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An equation of a line in point-slope form:  y - y₁ = m(x - x₁)

1.

passes through (1, 9)   ⇒   x₁ = 1,  y₁ = 9

slope: m = 2

The equation:

y - 9 = 2(x - 1)          ←  point-slope form      

y - 9 = 2x - 2           {add 9 to both sides}

y = 2x + 7                ←    slope-intercept form  

2.

passes through (4, -1)   ⇒   x₁ = 4,  y₁ = -1

slope: m = -3

The equation:

y + 1 = -3(x - 4)           ←  point-slope form      

y + 1 = -3x + 12           {subtract 1 from both sides}

y = -3x + 11                ←    slope-intercept form  

Answer:1.75

Step-by-step explanation:

formula= R= D/2

convert 3 1/2 into a decimal

3.5

do 3.5 divided by 2 (R= 3.5/2) = 1.75

so the Radius is 1.75 inches !! hope this helped :)

The radius of the button 3 and 1/2 in would be; 1.75

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

The formula= Radius= D/2

Now convert 3 and 1/2 into a decimal;

3.5

Now, 3.5 divided by 2 (R= 3.5/2)

= 1.75

Hence, the Radius is 1.75 inches .

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Answer:

Step-by-step explanation:

From the given table,

A. The unit rate for each car is,

Car A = [tex]\frac{416}{13}[/tex]

          = 32 miles per gallon

Car B = [tex]\frac{544}{16}[/tex]

          = 34 miles per gallon

Car C = [tex]\frac{665}{19}[/tex]

          = 35 miles per gallon

Car D = [tex]\frac{775}{25}[/tex]

          = 31 miles per gallon

B. From the derived values in A, the car that uses the least amount of gas is Car C.

C. Total distance covered = 496 miles x 4

                                           = 1984 miles

The gallons of gas the Car A would need for the journey can be determined by;

Car A requires 1 gallon for 32 miles

So that for 1984 miles = [tex]\frac{1984}{32}[/tex]

                                    = 62 gallons

Car A would need 62 gallons of gas to make the trip.

D. Amount spent on gas for Car A = $2.12 x 62

                                          = $131.44

E. speed = [tex]\frac{distance}{time}[/tex]

⇒ time = [tex]\frac{distance}{speed}[/tex]

Given the for Car A, speed = 68 miles per hour.

time = [tex]\frac{1984}{68}[/tex]

       = 29.1765

time = 29 hours

It would take approximately 29 hours for Car A to cover the total distance of 1984 miles.

Answer:

29/5

Step-by-step explanation:

Answer:

29/5

Step-by-step explanation:

As an improper fraction, your answer is 29/5.

I'm not sure what it means by writing it as a fraction "greater than 1".

The first 5 terms of the arithmetic sequence are: 5, 9, 13, 17, 21.

Here we have an arithmetic sequence, such that the recursive formula is:

[tex]a_n = a_{n- 1} + 4[/tex]

Such that:

a₁ = 5.

Using that formula we can get the next 4 terms. For the second term we use n = 2, so we get:

[tex]a_2 = a_1 + 4 = 5 + 4 = 9[/tex]

For the third term we have:

[tex]a_3 = a_2 + 4 = 9 + 4 = 13[/tex]

For the fourth term we have:

[tex]a_4 = a_3 + 4 = 13 + 4 = 17[/tex]

For the fifth term we have:

[tex]a_5 = a_4 + 4 = 17 + 4 = 21[/tex]

Then the first 5 terms of the sequence are:

5, 9, 13, 17, 21.

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The F-test statistic is approximately 1.455.

To find the F-test statistic to test the claim of equal variances for two populations, you need the standard deviations of both samples. Given that the standard deviation of the first sample is 4.8329 and the standard deviation of the second sample is 5.8304, we can proceed with the calculation.

The F-test statistic is calculated as the ratio of the variances of the two samples. In this case, since we only have the standard deviations, we need to square them to obtain the variances.

First, square the standard deviations:

Variance of the first sample (s1^2) = (4.8329)^2 = 23.3747

Variance of the second sample (s2^2) = (5.8304)^2 = 34.0051

Next, calculate the F-test statistic by dividing the larger variance by the smaller variance:

F-test statistic = (larger variance) / (smaller variance)

F-test statistic = s2^2 / s1^2

F-test statistic = 34.0051 / 23.3747

Using the given values, the F-test statistic is approximately 1.455.

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Answer:

12:6 or $12 for every $6 he saves

Step-by-step explanation:

If he spends $6.00 for every $3.00, he would save $6 if he spends $12. In this case you could multiple or divide 6 by any number, and do the same to 3 to get an equivalent ratio. Ex. Multiple 6 times 2 to get $12 and 3 times 2 to get $6.

Answer:

300

Step-by-step explanation:

D) 50%

Explanation: 18 + (18x.50) = 27

Step-by-step explanation:

There are 36 possible rolls

to be an odd number product.....both dies must be odd numbers

1st      2nd

1        1  3  5

3        1 3 5

5        1 3                   that is it for less than 20 product

8 rolls that would be less than 20  product

8 out of 36     probability

Answer: According to the trendline it would be about 6 lbs

Step-by-step explanation:

Answer:

C.

Step-by-step explanation: I did the test </3

Complete Question

When loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is three times that of the empty lorry, find the mass of iron.

Answer:

3000kg

Step-by-step explanation:

Let us represent

Mass of lorry = x

Mass of iron rods = y

x + y = 12000kg..... Equation 1

x = 12000kg - y

We are told that:

If the mass of iron rods is three times that of the empty lorry, find the mass of iron.

x = 3y

We substitute 3y for x in Equation 1

x = 12000kg - y

3y = 12000kg - y

Collect like terms

3y + y = 12000kg

4y = 12000kg

Divide both sides by 4

y = 12000kg/4

y = 3000kg

Note that:

Mass of iron rods = y

Hence, Mass of iron rods = 3000kg

Answer:

135 can i have brain list

Step-by-step explanation:

9X3X5

Answer:

$22.50

Step-by-step explanation:

As it is 30% off, $15.75 is 70% of the full price. You can then divide 15.75 by 70 [= 0.225] to get 1% of the full price. Multiply 0.225 by 100 to get the full price. 0.225 x 100 = 22.5

We can check that this answer is correct by multiplying 22.50 by 0.7. If you get 15.75 you know the answer is correct as 15.75 is 70% of the full price.