The magnitude of the vertical force applied to the horizontal leg in the equivalent force system.
To determine the magnitude of the vertical force applied to the horizontal leg, we need to find the vertical component of the given force system. Looking at the diagram, we observe that the force system consists of a vertical force at point A and a horizontal force at point B. We can use trigonometry to find the vertical component of the force at point A.
Let's denote the magnitude of the force at point A as F_A and the angle it makes with the horizontal leg as θ. The vertical component of the force can be calculated using the formula: Vertical component = F_A * sin(θ).
Since the vertical component of the force should be equal to the force we are trying to find, we can set up the equation: Vertical component = F_vertical.
Now, we can substitute the given values into the equation and solve for F_vertical. Once we have the value, we can round it off to the nearest whole number, as instructed.
Please note that without specific values or angles provided in the problem statement or accompanying diagram, it is not possible to provide a precise numerical answer.
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someone please help
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 :)
explain why zero is excluded from the domain and range
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
The total number of passengers riding a certain city bus during the morning shift is 1,100. If the child's fare is $0.5o, the adult fare is $1.25, and the total revenue from the fares in the morning shift is $1,200, how many children and how many adults rode the bus during the morming shift? (Letx and y denote the number of children and adults, respectively.)
=1,000
=1,200
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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Six times the quantity x -2 is 24. Find the number x
Which type of display is for One-Variable data set
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:
A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.
How many desired outcomes should Denato use in his probability calculation?
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.
PLEASE HELPPPPP
WILL GIVE BRAINLIEST
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.
Which expression is equivalent to x+2+[4x-x^2+6x+8 over x+4?
Answer:
-x^3-7x^2-46x-16/x+4
Step-by-step explanation:
The slash is a fraction! Also the fraction is negative :)
Find the radius of the button.
3 and 1/2 in
radius:
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
What is a circle?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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Need to know if this is write. if not, please correct.
Classify each pair of angles listed below as adjacent or vertical.
Mr. Cresta spends $6.00 for every $3.00 he saves. Write a ratio equivalent to Mr. Cresta's spending
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:
Solving systems of equations using Substitution
Y= -4x +3
Y= 4x +3
Justin lives 5 4/5 miles from his grandfathers house. Write the mixed number as a fraction greater than 1
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".
A backpack is on sale for 30% off. If the sales price is $15.75, what is the original price? Show your work.
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.
question a circle has a radius of 21 inches. what is the length of the arc intercepted by a central angle that measures 4π7 radians? express the answer in terms of π . enter your answer in the box.
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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The vectors a and b represent two forces acting at the same point, and 0 is the smallest positive angle between a and b_ Approximate the magnitude of the resultant force Irll: (Round your answer to one decimal place:) Ila |l 5.3b, Ilb |I 6,9 Ib; 60" Irll'
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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Which is the most reasonable estimate of 132% of 48?
a.5.2
b.6.5
c.52
d.65
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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Write an equation in point-slope form and slope-intercept form for each line
1. passes through (1, 9), slope = 2
2. passes through (4, -1), slope = -3
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
The temperature increases from 18°F to 27° F.
What is the percent increase of the temperature
A) 3%
B) 9%
C) 33%
D) 50%
D) 50%
Explanation: 18 + (18x.50) = 27
The graph of g(x) is a parabola that opens upward with a vertex at (-3, 4). Which statement is true?
Consider the discrete probability distribution below. Complete parts and to the right Outcome Probability 0.26 035 2 0.00 0.00 0 1 a. Calcutate the mean of this distibution - Type an integer or a decimal) b. Calculate the standard deviation of this distribution 0.18 3 4 5 6 0.04 0.02 (Round to three decimal places as needed.)
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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A sequence can be generated by using an=an−1+4, where a1=5 and n is a whole number greater than 1.
What are the first 5 terms in the sequence?
5, 20, 80, 320, 1280
4, 9, 14, 19, 24
4, 20, 100, 500, 2500
5, 9, 13, 17, 21
The first 5 terms of the arithmetic sequence are: 5, 9, 13, 17, 21.
How to find the first 5 terms?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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What is the volume 9inches 3inches 5inches
Answer:
135 can i have brain list
Step-by-step explanation:
9X3X5
Which equation is equivalent to 29p + 32?
A 32 - 29p
B 32 + 29p
C 32p + 29
D 32(29-p)
PLEASE HELP!!!
I’ll give 40 points!!!
Answer: c is the correct opcion
PLEASE HELP, ONLY HAVE A FEW MIN LFT!!!!
A bookstore tracked the data of the weight of their deliveries and the number of books in each box. They created a scatterplot and trend line based on the data.
Which statement would be a reasonable prediction based on the scatterplot and trend line?
A box with 10 books should weigh about 2 pounds.
A box with 10 books should weigh about 4 pounds.
A box with 10 books should weigh about 6 pounds.
A box with 10 books should weigh about 12 pounds.
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
Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 4.8329
5.8304 is the standard deviation of the second sample.
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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Luigi will roll two cubes with faces numbered 1 through 6. Eace face of each cube has one number on it. No number repeats on a cube Luigi records the product of the numbers that land face up. What is the probability that the product of the two numbers will be an odd number less than 20? ОА. ОВ. 8 ΟΟΟ m Ga A-N-ONS
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
when loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is there times that of the empty lorry . find the mass or iron.
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
Can someone plz help me
Answer:
IT's d!!!!!
Step-by-step explanation: