Answer:
Your question indicates the ladder is at an angle of 60° to the wall, meaning the angle between the wall and the ladder is 60° and the angle between the ladder and the ground must be 30°. Not a very efficient way to set up a ladder.
5.7735 meters. The top of the ladder is 2.8868 meters off the ground.
Now, if you meant the ladder is 60° from the ground, that’s a different story.
Then, the ladder is 10 meters long and reaches 8.6603 meters from the ground.
A 30–60–90 right triangle is half of an equalateral triangle. Therefore the hypotenuse is double the length of the short leg, and by the Pythagorean theorum, we can determine that the other leg is the length of the short leg times the square root of 3.
All lengths in this answer are rounded to the nearest tenth of a millimeter.
Step-by-step explanation:
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
If the errors produced by a forecasting method for 3 observations are +3, +3, and −3, then what is the mean squared error?
Answer:
9
Step-by-step explanation:
The mean squared error (MSE)of a set of observations can be calculated using the formula :
(1/n)Σ(Actual values - predicted values)^2
Where n = number of observations
Steps :
Error values of each observation (difference between actual and predicted values) is squared.
Step 2:
The squared values are summed
Step 3:
The summation is the divided by the number of observations
The difference between the actual and predicted values is known as the ERROR.
(1/n)Σ(ERROR)^2
n = 3
Error = +3, +3, - 3
MSE = (1/3)Σ[(3)^2 + (3)^2 + (-3)^2]
MSE = (1/3) × [9 + 9 + 9]
MSE = (1/3) × 27
MSE = 9
plz someone help me with this question
Answer:
(x+3)^2=-4(y-3)
Step-by-step explanation:
(x-h)^2 = 4p(y-k)
P is the distance between the focus and vertex
P = 1 --> used distance formula for the points of -3,2 -3,3
Vertex is -3,3 --> according to picture
(x+3)^2=-4(y-3)
P is negative since it goes downwards in the picture.
In the diagram, XY bisects ZWXZ.
1
z
2
w
(5x + 3)
(7x - Y
х
mWYZ
type your answer.
In provided diagram angle WXY = angle YXZ
Angle WXY =( 7x-7)°
Angle YXZ = ( 5x +3)°
We have to find out the value of Angle WXZ
→ 7x-7 = 5x +3
→ 7x - 5x = 7+3
→ 2x = 10
→ x = 10/2
→ x = 5 .
Putting the value of x .
→ Angle WXY = 7(2)-7
→ 14-7 = 7°
→ Angle YXZ = 5(2)+3
→ 10+3 = 13°
Angle WXZ = 13° + 7 ° → 20°
So 20° is the required answer .
Answer:
SI
Step-by-step explanation:
find the derivative of f(x)=3x^2✓x
Answer:
[tex]f'(x)=\dfrac{15x\sqrt{x}}{2}[/tex]
Step-by-step explanation:
The power rule applies.
d(x^n)/dx = nx^(n-1)
__
[tex]f(x)=3x^2\sqrt{x}=3x^{\frac{5}{2}}\\\\f'(x)=3(\frac{5}{2})x^{\frac{3}{2}}\\\\\boxed{f'(x)=\dfrac{15x\sqrt{x}}{2}}[/tex]
What is the x-intercept?
12) A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state
Answer:
0.8343
Step-by-step explanation:
From the question, we have the following values:
Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75
Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25
P = 0.25
n = number of random variables = 9
The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:
P < 4 = P ≤ 3
n = 9
P(x) = n!/(n - x)! x! × p^x × q^(n - x)
x = 3
p = 0.25
q = 0.75
P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)
P(x) =0.8343
The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.
Given information:
75% of the vehicles passing through a checkpoint are from within the state.
So, the probability that the vehicle is from within the state is 0.75.
The probability that the vehicle is from outside the state will be 1-0.75=0.25.
Now, let x be the random variable. So, the value of n=9. and x<4
It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.
So, [tex]x< 4[/tex], p=0.25 and q=0.75.
So, the required probability can be calculated as,
[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]
Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.
For more details, refer to the link:
https://brainly.com/question/14282621
∠3 and ∠6 can be classified as:
Answer:
Alternate Interior Angles
Step-by-step explanation:
Since they are inside the parallel lines, Alternate Exterior Angles and any other similar theorems can be ruled out.
Since they are on opposite sides of each other, Corresponding Angles and any other similar theorems can be ruled out.
Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.
Therefore, we are left with Alternate Interior Angles.
Answer:
angle 3 and angle 6 are
1) Alternate Angles
2) Interior Angles
Step-by-step explanation:
(see attached for reference)
How much work is done in lifting a 1.4-kg book off the floor to put it on a desk that is 0.7 m high?
Use the fact that the acceleration due to gravity is g = 9.8 m/s^2. How much work is done in lifting a 21-lb weight 6 ft off the ground?
Answer:
Step-by-step explanation:
Work is said to be done when a force applied to an object cause the body to move in a specified direction.
Work-done = Force * Distance
Since Force = mass * acceleration due to gravity
Work-done = mass * acceleration due to gravity * distance
Given mass = 1.4kg, distance = 0.7m and g = 9.8m/s²
Workdone in lifting the book off the floor = 1.4*0.7*9.8
Workdone = 9.604Joules
- Similarly, work done in lifting a 21-lb weight book 6 ft off the ground is expressed using the same formula as above;
Given mass = 21-lb, g = 32ft/s² and distance = 6ft
Workdone = 21 * 32 * 6
Workdone = 4,032 lb-ft²/s²
Hence, work-done in lifting a 21-lb weight book 6 ft off the ground is 4,032 lb-ft²/s²
Select the best estimate of the capacity of a bath tub. A. 5 ml B. 500 ml C. 50 cl D. 500 L.
Answer:
D. 500 L
because ml cl is smaller than L
Answer:
D. 500 L
Step-by-step explanation:
Choice A (5 ml) is basically a teaspoon. A bathtub can most definitely hold much more then one teaspoon of water.
Choice B (500 ml) is about 17 ounces. Which is basically the amount of water in a normal water bottle. A bathtub can hold more then the amount of water in one water bottle.
Choice C (50 cl) is a little bit more then 2 cups of water. I believe a normal bathtub can hold about 1280 cups of water.
That rules out choices A, B, and C. By process of elimination, we can tell choice D is the answer. But let's just take a look at D.
Choice D (500 L) is about 132 gallons. This is the most plausible one, although some bathtubs don't hold as much water as that, it still is the best estimate of the capacity of a bath tub. \
Hope that helped!
If the mean difference gets larger and sample standard deviation stays the same, what happens to effect size?
Answer:
The effect size of the sample gets larger
Step-by-step explanation:
The effect size of the sample gets larger when the mean difference gets larger and the sample standard deviation stays the same. because the Cohen's effect size is proportional to mean difference and this can be proven below using the Cohen's formula
Cohen's effect size = Mean difference / standard deviation
form the question standard deviation is constant while the mean difference gets larger, hence the effect size will get larger as well
Simplify 10 - [14 = (3 + 4) · 2]+3
Answer:
There is a typo near the equal sign.
There can be two different answers if we think that = sign as + or -.
First way: Making = as +
=> 10 - [14 + (3+4) x 2] +3
=> 10 - [14 + 7 x 2] + 3
=> 10 - [14 + 14] + 3
=> 10 - 28 + 3
=> 10 + 3 - 28
=> 13 - 28
=> -15
=> So, -15 is the answer if we consider "=" sign as "+" sign.
Second way: Making = as -
=> 10 - [14 - (3+4) x 2] + 3
=> 10 - [14 - 7 x 2] + 3
=> 10 - [14 - 14] + 3
=> 10 - 0 + 3
=> 10 + 3
=> 13
=> So, 13 is the answer if we consider "=" sign as "-" sign.
Four members from a "55"person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer. How many different leadership structures are possible?
Answer:
8,185,320 different leadership structures
Step-by-step explanation:
Since the order at which the members of the committee are chosen matters, this is a permutation of 4 out 55 people and it is given by:
[tex]n=\frac{55!}{(55-4)!}=55*54*53*52 \\\\n=8,185,320[/tex]
8,185,320 different leadership structures are possible.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 7.2 to 4.5
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Given
7.2 : 4.5 ← multiply both parts by 10
= 72 : 45 ← divide both parts by 9
= 8 : 5
= [tex]\frac{8}{5}[/tex]
The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.
43 41 39 39 38 37 37 36 34 33 33 32
The lower limit for determining outliers for a box-and-whisker plot is______.
a. 23.75.
b. 20.0.
c. 22.5.
d. 25.25.
Answer:
d. 25.25.
Step-by-step explanation:
A whisker plot is a type of box plot which is graphical representation of five number summary. It is used for explanatory data analysis. The baseball league has data set whose median is 45. When the outliner are present in data set the median measures central tendency.
NEED HELP ASAP trig question!! Need to find y!!
Answer:
Hey there!
Tangent 70=12/y
Tangent 70y=12
y=12/Tangent 70
y=4.37 cm
Let me know if this helps :)
Please help me on question 4 and 5 I am really stuck thank you I would really appreciate it
Answer:
1. 5/4
2. 7
Step-by-step explanation:
1) Lets call the width as w
Therefore length would be:
w+4
To find the perimeter you use the formula:
2 (l+w)
Now substitute our values into this formula:
2 (w+4+w)
2( 2w+4)
4w+8
Now make this equal to 13:
4w +8 = 13
4w = 5
w = 5/4
2. In this question we will call length l
Therefore width would be:
l-5
Now we will do the steps we did above:
2 (l+l-5)
2 (2l-5)
4l -10
4l - 10 = 18
4l = 28
l = 7
A flagpole is 50 feet high. You are standing a distance from the flag pole. The angle of elevation from where you are standing to the top of the flagpole is 23°. How far away from the flagpole are you standing? Note that the angle of elevation is the angle formed by the ground and the line of sight to the top of the flagpole.
Answer:
x = 21.2 ft
Step-by-step explanation:
x = tanФ h
h = 50
Ф = 23°
x = tan(23°) * 50
x = 21.2 ft
In a zoo there are 6 orang-utans for every 3 baboons. There are 27 orang-utans and baboons altogether. How many are orang-utans?
Answer:
18
Step-by-step explanation:
Okay first we know that for every one baboon there is 2 orang-utans (6 / 3 = 2)
So, I like to play the guess and check:
Lets just use the numbers 12 orang-utans and 6 baboons. We know that those two don't equal 27, so thats not it.
Now we can have 18 orang-utans and 9 baboons. 18 + 9 = 27, which means there are 18 orang-utans.
Hope this helps, and have a good day.
I NEED HELP ASAP
191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students. Calculate the Margin of Error, rounded to the nearest tenth of a percent. Is it reasonable that the state education department claims the percentage for the entire state is 73%? Justify your answer.
Answer:
It is not reasonable that the state education department claims the percentage for the entire state is 73%.
Step-by-step explanation:
We are given that 191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of high school students who went outside more during school hours as elementary school students than they do now as high school students = [tex]\frac{191}{288}[/tex] = 0.66
n = sample of high school students = 288
p = population percentage for the entire state
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
The margin of error is given by;
M.E. = [tex]2 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
= [tex]2 \times \sqrt{\frac{0.66(1-0.66)}{288} }[/tex]
M.E. = 0.056 or 5.6%
So, the confidence interval so formed = [tex]\hat p \pm \text{Margin of error}[/tex]
= [[tex]0.66 - 0.056 , 0.66 + 0.056[/tex]]
= [0.604, 0.716]
Since the above interval does not include 0.73 or the population proportion of 73% falls outside the above interval. So, it is not reasonable that the state education department claims the percentage for the entire state is 73%.
The perimeter of a rectangular garden is 43.8 feet. It's length is 12.4t . What is it's width ?
Answer:5
Step-by-step explanation:
Find the value of NT
A. 4
B. 14
C. 12
D. 16
Answer:
14
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
12*x = 8 * (x+2)
Distribute
12x = 8x+16
Subtract 8x
12x-8x = 8x+16-8x
4x = 16
Divide by 4
4x/4 = 16/4
x = 4
We want NT
NT = 8+x+2
= 10 +x
= 10 +4
= 14
Figure ABCD is a square find the value of x
Answer:
x=3
Step-by-step explanation:
since its a square all sides equal each other
5x-2=x+10
4x -2 =10
4x=12
x = 3
PLZ HELP THANKS! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
The answer is
15x - y = - 126Step-by-step explanation:
To find the equation of the line we must first find the slope (m)
[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]
So the slope of the line using points
(-8,6) (-9,-9) is
[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]
So the equation of the line using point (-8,6) and slope 15 is
y - 6 = 15( x + 8)
y - 6 = 15x + 120
Writing the equation in the form
Ax+By=C
We have
15x - y = -120-6
The final answer is
15x - y = - 126Hope this helps you
The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in
Answer:
396 in^2
Step-by-step explanation:
The perimeter of a triangle is given by the formula:
● P = 2w+2L
L is the length and w is the width
■■■■■■■■■■■■■■■■■■■■■■■■■■
The width hereis 18 inches and the perimeter is 80 inches.
Replace w by 18 and P by 80 to find L.
● P= 2L+2w
● 80 = 2L + 2×18
● 80 = 2L + 36
Substrat 36 from both sides
● 80-36 = 2L+36-36
●44 = 2L
Divide both sides by 2
● 44/2 = 2L/2
● 22 = L
So the length is 22 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area of a rectangle is given by the formula:
● A= L×w
● A = 22×18
● A = 396 in^2
6. A car dealership would like to estimate the mean mpg of its new model car with 90% confidence. The population is normally distributed; however we are taking a sample of 25 cars with a sample mean of 96.52 and a sample standard deviation of 10.70. Calculate a 90% confidence interval for the population mean using this sample data.
Answer:
92.9997<[tex]\mu[/tex]<99.5203
Step-by-step explanation:
Using the formula for calculating the confidence interval expressed as:
CI = xbar ± Z * S/√n where;
xbar is the sample mean
Z is the z-score at 90% confidence interval
S is the sample standard deviation
n is the sample size
Given parameters
xbar = 96.52
Z at 90% CI = 1.645
S = 10.70.
n = 25
Required
90% confidence interval for the population mean using the sample data.
Substituting the given parameters into the formula, we will have;
CI = 96.52 ± (1.645 * 10.70/√25)
CI = 96.52 ± (1.645 * 10.70/5)
CI = 96.52 ± (1.645 * 2.14)
CI = 96.52 ± (3.5203)
CI = (96.52-3.5203, 96.52+3.5203)
CI = (92.9997, 99.5203)
Hence a 90% confidence interval for the population mean using this sample data is 92.9997<[tex]\mu[/tex]<99.5203
I need help with this question
Answer:
a. 2
b. x^2 + 10x + 26
c. x^2 + 2x + 2
Step-by-step explanation:
For each part, replace x with the value you are given and simplify.
f(x) = x^2 - 2x + 2
a.
f(2) = 2^2 - 2(2) + 2 = 2
b.
f(x + 6) = (x + 6)^2 - 2(x + 6) + 2
= x^2 + 12x + 36 - 2x - 12 + 2
= x^2 + 10x + 26
c.
f(-x) = (-x)^2 - 2(-x) + 2
= x^2 + 2x + 2
Complete the point-slope equation of the line through (2,3)(7,4). Use exact numbers. y-4=
Please help me, I would really appreciate it!
Answer:
The answer is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Step-by-step explanation:
To find the equation of a line given two points first find the slope and use the formula
[tex] y - y_{1} = m(x - x_{1})[/tex]Where m is the slope
To find the slope we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]The slope of the line using points
(2,3)(7,4) is
[tex]m = \frac{4 - 3}{7 - 2} = \frac{1}{5} [/tex]Equation of the line using point (7,4) and slope 1/5 is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Hope this helps you
Answer:
y-4=1/5(x-3)
Step-by-step explanation:
We plug in the x's and the y's and find the slope with:
[tex](y-y_{1} )/ x-x_{1})=m[/tex]
PLEASE HELP ! (2/4) - 50 POINTS -
Answer:
The correct answer would be 15.5 or C.
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
