Answer:
[tex]F=\frac{32\sqrt{3}}{3}\text{\:or\:} \approx 18.48\:\text{N}[/tex]
Step-by-step explanation:
We can find the horizontal component of force he applied by using the formula for work:
[tex]W=F\Delta x[/tex]
Solving for force, we have:
[tex]160=F\cdot 10,\\F=16\:\text{N}[/tex]
However he applied the original force at an angle of [tex]30^{\circ}[/tex] to the horizontal. This force of 16 newtons is only the horizontal component of that force. To find the magnitude of the original force, we can use basic trigonometry:
[tex]\cos 30^{\circ}=\frac{16}{x},\\x=\frac{16}{\cos 30^{\circ}},\\\\x=\frac{16}{\frac{\sqrt{3}}{2}},\\\\x=16\cdot\frac{2}{\sqrt{3}}=\frac{32}{\sqrt{3}}=\boxed{\frac{32\sqrt{3}}{3}}[/tex]
What is the area of the regular trapezoid below?
- 6 cm
T
8 cm
10 cm
Answer:
Area = 64 cm²
Step-by-step explanation:
To find the area, we have to follow some steps:
=> Step 1: Make the bases similar:
Since we have 2 bases given 6 and 10 we have to come up with a third base by finding their average:
(6 + 10) / 2
(16) / 2
8
So now that we know our base,
=> Our second step is to multiply the base we found by the height of the trapezoid:
Area = common base * height
Area = 8 * 8
Area = 64 cm²
Hope this helps!
A pitcher contains 2 liters of liquid. Jin pours 368 milliliters of this liquid into a test tube.
How much liquid is left in the pitcher?
Enter your answer in the box.
Answer:
1,632 liters of liquid remain in the pitcher.
Step-by-step explanation:
Given that a pitcher contains 2 liters of liquid, and Jin pours 368 milliliters of this liquid into a test tube, to determine how much liquid is left in the pitcher the following calculation must be performed:
368 milliliters = 0.368 liters
2 - 0.368 = X
1.632 = X
Therefore, 1,632 liters of liquid remain in the pitcher.
m and p are complementary angles m/M = 56, and m/P = 2x + 4. Write and solve an equation to find the value of x.
two congruent squares are shown in figures 1 and 2 below
Answer:
Equal to, c^2, a^2+b^2, a^2 + b^2 = c^2
Answer:
The combined area of the shaded triangles in Figure one is equal to the combined area of the shadead triangles in figure 2. The area of the unshaded square in Figure 1 can be represented by c^2. The combined area of the two unshaded squares in Figure 2 can be represented by a^2+b^2. The areas of the squares in Figure 1 and Figure 2 who that a^2+b^2=c^2.
Step-by-step explanation:
I'm right and if you think I'm wrong then you're wrong
Assume that 24.5% of people have sleepwalked. Assume that in a random sample of 1478 adults, 369 have sleepwalked. a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.
b. Is that result of 369 or more significantly high? c. What does the result suggest about the rate of 24.5%?
Answer:
a) 0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b) 369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c) Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
A result is considered significantly high if it is more than 2.5 standard deviations above the mean.
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume that 24.5% of people have sleepwalked.
This means that [tex]p = 0.245[/tex]
Sample of 1478 adults:
This means that [tex]n = 1478[/tex]
Mean and standard deviation:
[tex]\mu = 1478*0.245 = 362.11[/tex]
[tex]\sigma = \sqrt{1478*0.245*0.755} = 16.5346[/tex]
a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.
Using continuity correction, this is [tex]P(X \geq 369 - 0.5) = P(X \geq 368.5)[/tex], which is 1 subtracted by the p-value of Z when X = 368.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{368.5 - 362.11}{16.5346}[/tex]
[tex]Z = 0.39[/tex]
[tex]Z = 0.39[/tex] has a p-value of 0.6517
1 - 0.6517 = 0.3483
0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b. Is that result of 369 or more significantly high?
362.11 + 2.5*16.5346 = 403.4
369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c. What does the result suggest about the rate of 24.5%?
Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.
Question 6
What is the missing value of the following synthetic division?
Answer:
Hello!
16
Step-by-step explanation:
Because
-5+16=11
julio sells hand-painted skateboards.
The graph shows how the price of a
skateboard is related to the amount of
time Julio spends painting it. Julio says
the equation of the line is y = 10x + 15
Answer:
you need to post a pic with it.
Step-by-step explanation:
115
A jet skier departs from Pier 1, travels 796 meters directly to a buoy, makes a turn, and travels 1054 meters directly to Pier 2, which is 411 meters from Pier 1.
How many degrees was the jet skier's turn?
Round your answer to the nearest whole degree.
9514 1404 393
Answer:
160°
Step-by-step explanation:
The path is a triangle with side lengths 796, 1054, and 411 meters. The turn is opposite the short side. The interior angle of the triangle at that point can be computed using the law of cosines. If we label the sides a, b, c, respectively, then ...
c² = a² + b² - 2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab)) = arccos(1575611/1677968) ≈ 20.116°
The external angle at the buoy is 180° -20° = 160°.
The jet skier's turn was about 160°.
Point D has coordinates (8,3). Point G has coordinates (-4,3). What is the length of segment DG?
Answer:
0
Step-by-step explanation:
Coolin
Use OZ with VW – XY
What is XY ?
A 30
B. 35
C. 40
D 50
Answer:
40
Step-by-step explanation:
From the diagram;
VW = 2(20)
VW = 40
Simce VW is similar to XY, hence VW = XY = 40
Hence the length of XY is 40
What is the area of the triangle?
A.) 12 squares meters
B.) 20 square meters
C.) 24 square meters
D.) 40 square meter
Answer:
[tex]Area \ of \ traingle = \frac{1}{2}*base * height = \frac{1}{2}* 6*4= 12m^2\\\\option A[/tex]
"I think of a number, take away 1 and multiply the result by 3."
Answer:
I got 6.
Step-by-step explanation:
I picked my number to be 3. I took away 1 to make it 2. I then multiplied 2 by 3, to get 6.
A recipe for oatmeal raisin cookies requires 2 eggs for every dozen cookies . Which equation shows the relationship between eggs ( e ) and dozen cookies ( c ) ?
Answer:
2e = c
Step-by-step explanation:
Let :
Egg = e
Cookies = c
2 eggs for every 1 dozen of cookies
This gives the Mathematical expression :
2 eggs = 1 c
2e = c
An orange juice manufacturer advertises a new orange juice product that contains 50% less sugar. This new product is expected to increase profits substantially because they create the 50% less sugar product by replacing 50% of the juice with water while selling it for the same price. An inspector wants to investigate whether the actual percentage of water in the product is within 5% of the intended 50%.
He selects a random sample of 500 containers of orange juice and determined the percentage of each that is water. He plans to conduct a significance test at the a = 0.01 level to see if there is convincing evidence that the proportion of water added is different from 0.50. What is the probability that the inspector makes a Type I error?
Answer:
0.01
Step-by-step explanation:
The probability of making a Type I error is equal to \alphaα = 0.01, the significance level of the test
The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
An orange juice manufacturer advertises a new orange juice product that contains 50% less sugar.
An inspector wants to investigate whether the actual percentage of water in the product is within 5% of the intended 50%.
He plans to conduct a significance test at a = 0.01 level to see if there is convincing evidence that the proportion of water added is different from 0.50.
Type I error is referred to as false positives and it means that when a statistically significant difference is validated by the researcher even though the results aren't statistically significant.
Type I error is when one rejects the null hypothesis even though it's true. In this case, the inspector rejects the hypothesis that the proportion of water that is contained in the product is 0.5.
The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ2
What is sin 49° to the nearest tenth?
Answer:
sin49= 0.7
Step-by-step explanation:
What is the perimeter of rectangle JKLM
Answer:
16 units
Step-by-step explanation:
A wall of a building is made from blocks that are each 1 cubic foot.
The wall is 6 feet high and 6 feet wide.
A window is made by removing some blocks as shown below.
The window is 2 feet high by 2 feet wide.
The wall is 6 feet high and 6 feet wide. The window is 2 feet high by 2 feet wide is cut from the centre of the wall.
What is the volume of the wall after the window is made? Enter your answer in the box.
Answer:
6×6×1-(2×2×1)=36-4=32.
F(x) =X+4
g(x) = 3x² -7
Find (f-g) (x)
Algebra 2 sem 1
Answer:
[tex]B. ~(f+g)(x)=6x^3+4x-2[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2+4x-5[/tex]
[tex]g(x)=6x^3-2x^2+3[/tex]
[tex]Find~(f+g)(x)[/tex]
[tex]=2x^2+4x-5+6x^3[/tex]
[tex]-2x^2+3[/tex]
[tex](f+g)(x)=6x^3+4x-2[/tex]
--------------------------------
hope it helps....
have a great day!!
What is the distance between the point (4,7) and its reflection over the x-axis, as shown on the graph below?
Answer: 14
Step-by-step explanation:
Question 3 of 10
On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.
Answer:
Step-by-step explanation:
SEVEN
Plz hurry
The number of hours worked by each of the employees last week at two stores are listed below.
Vr
Hours Worked in a Week at Two Stores
Store 1
16, 28, 36, 40, 78
Store 2
22, 27, 33, 36, 40
Which statements are true and supported by the data in the table? Check all that apply.
A
2 The data for store 1 shows greater variability.
The median number of hours worked for the two stores is the same.
O The mean of the data for store 1 is greater than the mean of the data for store 2.
0 The interquartile range of both data sets is the same.
O The range
of the data for store 1 is less than the
range of the data for store 2.
Answer:
Data for store #1 shows greater variability and
The mean for store #1 is greater than the mean for store #2
Step-by-step explanation:
Answer:
a and b
Step-by-step explanation:
1 Mrs. Thiel has 178 papers to grade.
She graded 49 papers this morning
and 56 paper this afternoon. How many
papers does Mrs. Thiel have to grade
this evening?
Answer:
73 Papers
Step-by-step explanation:
Let's start by finding out how many papers Mrs. Thiel has already graded.
56 + 49 = 105
Now, let's subtract how many papers she has already graded from how many she has to grade in total.
178 - 105 = 73
So, Mrs. Thiel has to grade 73 papers this evening.
Simplify 3x^(1/2)*5x^(2/5)
Answer:
= 15x^9/10
Step-by-step explanation:
Multiply the numbers: 3 . 5 = 15
= 15x^1/2x2/5
Apply exponent rule: a^b . A^c = a^b + c
= 15x^1/2+2/5
1/2 + 2/5 = 9/10
= 15x^9/10
Identify the parts of a sphere,
a is the
bis the
c is the center
d is the radius
diameter
great circle
HELP 50points
Answer:
Hello, it appears you did not provide an image that was supposed to be included in order to help answer your question, so I'm afraid I cannot assist you without seeing it. If you supply the necessary photo, I would be more than happy to help you.
WILL
GIVE BRAINLIST FOR MATH
....
What is the answer?
Answer:
x^2(x-5)
Step-by-step explanation:
f(x)=x-5
g(x)=x^2
g(f(x)=?
x^2(f(x)=?
x^2(x-5)
If this helps please mark as brainliest
9514 1404 393
Answer:
D. (x -5)²
Step-by-step explanation:
Replace the variable with the function argument.
G(F(x)) = G(x -5) = (x -5)² . . . . . matches choice D
In the xy-plane, the graph of function f(x) has zeros at −5, −2, and 2. Write the polynomial function.
Answer:
[tex]f(x) = x^3 +5x^2-4x-20[/tex]
Step-by-step explanation:
Given
[tex]Zeros: -5,-2,2[/tex]
Required
The polynomial function
If a function has a, b and c as its zeros, the function is:
[tex]f(x) = (x - a)(x - b)(x - c)[/tex]
So, we have:
[tex]Zeros: -5,-2,2[/tex]
[tex]f(x) = (x - (-5))(x - (-2))(x - 2)[/tex]
Open the inner brackets
[tex]f(x) = (x +5)(x +2)(x - 2)[/tex]
Expand the difference of two squares
[tex]f(x) = (x +5)(x^2 - 4)[/tex]
Expand
[tex]f(x) = x^3 +5x^2-4x-20[/tex]
Try Solve
4/7 + -8/9 + -5/21 + 1/3 = ???
Answer:
hey:)
the answer is -8.11
there is no step-by-step explanation, because you have to either do it with a calculator or do it by yourself
solve for y: -4y + 5 > -15
Step-by-step explanation:
-4y+5>-15
-4y>-15-5
-4y>-20
divide both (-)
4y>20
divide through by 4
y>20/4
y>5
541,829 541,840 which one of those are greater
829541
Step-by-step explanation:
541,840,829541