Evaluate the expression: -(8 - 12) + 6° + (-4)2.
Answer:
-4 + 6°
Step-by-step explanation:
- (8 - 12) + 6° + (- 4)2 = - ( - 4) + 6° - 8 = 4 + 6° - 8 = - 4 + 6°
Question 3 (Fill-In-The-Blank Worth 3 points) (04.04) Point R is at (2, 1.2) and Point T is at (2, 2.5) on a coordinate grid. The distance between the two points is such as 8.2.) (Input numbers and decimal point only, Answer for Blank 1:
9514 1404 393
Answer:
1.3
Step-by-step explanation:
The two points are on the same vertical line, so the distance between them is the distance between their y-coordinates:
2.5 -1.2 = 1.3
The distance between the two points is 1.3 units.
A sample of 1300 computer chips revealed that 50% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 47% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Make the decision to reject or fail to reject the null hypothesis at the 0.01 level.
Answer:
The pvalue of the test is 0.03 > 0.01, which means that we fail to reject the null hypothesis at the 0.01 level.
Step-by-step explanation:
The company's promotional literature states that 47% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.
This means that at the null hypothesis we test that the proportion is 47% = 0.47, that is:
[tex]H_0: p = 0.47[/tex]
And at the alternate hypothesis, we test that the proportion is different from 47%, that is:
[tex]H_a: p \neq 0.47[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
47% is tested at the null hypothesis:
This means that [tex]\mu = 0.47, \sigma = \sqrt{0.47*0.53}[/tex]
A sample of 1300 computer chips revealed that 50% of the chips do not fail in the first 1000 hours of their use.
This means that [tex]n = 1300, X = 0.5[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.5 - 0.47}{\frac{\sqrt{0.47*0.53}}{\sqrt{1300}}}[/tex]
[tex]z = 2.17[/tex]
Pvalue of the test and decision:
The pvalue of the test is the probability that the proportion differs from 0.47 by at least 0.5 - 0.47 = 0.03, which is P(|Z| > 2.17), which is 2 multiplied by the pvalue of Z = -2.17
Z = -2.17 has a pvalue of 0.015
2*0.015 = 0.03
The pvalue of the test is 0.03 > 0.01, which means that we fail to reject the null hypothesis at the 0.01 level.
what is the value of x?
The average of an electrician's hourly wage and a plumber's hourly wage is $33. One day a contractor hires an electrician for 7hr of work and the plumber for 4hr of work and pays a total of $396 in wages. Find the hourly wage for the electrician and for the plumber.
Answer:
Electrician = 44
Plumber = 22
Step-by-step explanation:
Let :
Electrician Hourly wage = x
Plumber's hourly wage = y
Average = 33
(x + y ) /2 = 33
x + y = 66 - - - - (1)
7x + 4y = 396 - - - (2)
From (1)
x = 66 - y
Put x = 66 - y in (2)
7(66-y) + 4y = 396
462 - 7y + 4y = 396
-3y = - 66
y = 22
x = 66 - 22
x = 44
Electrician = 44
Plumber = 22
Enter the measure of YVZ in degrees
Answer:
(3x+5)+(2x) = 90
5x + 5 = 90
5x = 85
x = 17
YVZ = 3×17 +5
=56°
What is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x^3, the x-axis, and the vertical line x=2 is revolved about the x-axis?
Show work.
A
[tex]4[/tex]
B
[tex] \frac{128}{7} [/tex]
C
[tex]4\pi[/tex]
D
[tex] \frac{128\pi}{7} [/tex]
Answer:
The first thing we need to do is to find the area bounded by:
y = x^3
y = 0
between:
x = 0 and x = 2
This is the integral of the given function between x = 0 and x = 2, written as:
[tex]\int\limits^2_0 {x^3} \, dx = \frac{2^4}{4} - \frac{0^4}{4} = 2^2 = 4[/tex]
This means that the area of the bounded region is 4 square units.
Now, if we do a full rotation around the x-axis, the volume generated will be equal to the area that we obtained times 2*pi units.
The volume is:
V = (4 square units)*(2*pi units) = 8*pi cubic units.
(Notice that no option coincides with this, there may be a mistake in the options)
mong 500 marriage license applications chosen at random in a givenyear, there were 48 in which the woman was at least one year older than the man, and among400 marriage license applications chosen at random six years later, there were 68 in which thewoman was at least one year older than the man. Construct a 99% confidence interval for thedifference between the corresponding true proportions of marriage license applications in whichthe woman was at least one year older than the man. Interpret the CI in the context of theproblem.
Answer:
CI 99% = ( 0,022 ; 0,126 )
Step-by-step explanation:
First sample
n₁ = 500
x₁ = 48
p₁ = x₁ / n₁ = 48 / 500 p₁ = 0,096 p₁ = 9,6 %
Second sample
n₂ = 400
x₂ = 68
p₂ = x₂ / n₂ = 68 / 400 p₂ = 0,17 p₂ = 17 %
CI = 99 % significance level α = 1 % α = 0,01
z(c) for α = 0,01 is from z- table z(c) = 2,325
CI = ( p₂ - p₁ ) ± z(c) *√ p*q* ( 1/n₁ + 1 / n₂ )
Where
p₂ - p₁ = 0,17 - 0,096 = 0,074
p = ( x₁ + x₂ ) / n₁ + n₂
p = ( 48 + 68 ) /( 500 + 400)
p = 116/ 900 p = 0,1288 and q = 1 - p q = 0,8712
z(c) *√ p*q* ( 1/n₁ + 1 / n₂ ) = 2,325 * √ 0,1288*0,8712 ( 1 / 500 + 1/ 400)
2,235 * 0,02247
z(c) *√ p*q* ( 1/n₁ + 1 / n₂ ) = 0,052
Then
CI 99 % = 0,074 ± 0,052
CI 99% = ( 0,022 ; 0,126 )
The difference between the groups shows that the proportion in the second group was bigger than in the first group.
The CI in the context of the problem is CI 99% = ( 0,022 ; 0,126 )
What will be the Solution of This problem?
Given first sample is
n₁ = 500
x₁ = 48
[tex]P_{1} =\dfrac{X_{1} }{n_{1} }[/tex] [tex]P_{1} =\dfrac{48}{500}[/tex]
p₁ = 0,096 p₁ = 9,6 %
Given second sample
n₂ = 400
x₂ = 68
[tex]P_{2} =\dfrac{X_{2} }{n_{2} }[/tex] [tex]P_{2} =\dfrac{68}{400}[/tex]
p₂ = 0,17 p₂ = 17 %
Since given CI = 99 % so significance level α = 1 % α = 0,01
From Z-Table z(c) for α= 0,01 is = 2,325
CI = [tex](P_{2} -P_{1}[/tex] ± [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]
Where
p₂ - p₁ = 0,17 - 0,096 = 0,074
[tex]P= \dfrac{X_{1} +X_{2} }{n_{1}+n_{2} }[/tex]
[tex]P=\dfrac{48+68}{500+400}[/tex]
[tex]P=\dfrac{116}{900}[/tex]
p = 0,1288 and q = 1 - p q = 0,8712
[tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex] [tex]2325\times\sqrt[2]{0.1288\times 0.8712} (\dfrac{1}{500_{} } +\dfrac{1}{400_{} } )[/tex]
[tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )=0.052[/tex]
Then
CI 99 % = 0,074 ± 0,052
CI 99% = ( 0,022 ; 0,126 )
Hence the difference between the groups shows that the proportion in the second group was bigger than in the first group.
To know more about Chi square follow
https://brainly.com/question/4543358
Find the slope of the line.
Please Help
Leslie is installing blue carpet that will cover the entire floor of a room.
What is the area, in square feet, of the room Leslie will cover with blue
carpet?
I need it step by step please
Answer:
392 ft²
Step-by-step explanation:
The composite figure can be divided into a rectangle, 2 triangles and a square
Area of rectangle = Length * width
Area of rectangle = 21 feets * 14 feets = 294 feet²
Area of triangle = 0.5 * base * height
Area of triangle = 0.5 * 7 * 7 = 24.5
AREA of square = a² = 7² = 49 feets²
Total area :
294 feets + (2 * 24.5) feets² + 49 feets²
294 + 49 + 49 = 392 ft²
will someone help me with this?
height of movable brigde 37cm
width of movable brigde 85 cm
What's another name for qualitative variables?
Answer:
A qualitative variable, also called a categorical variable, is a variable that isn't numerical.
PLSS HELPPPPPPPPPPPP
Answer:
c Melindas account will have about 5.40 more than olivia's account
Step-by-step explanation:
Giving brainliest!!!!!
Answer:
434 [tex]cm^3[/tex]
Step-by-step explanation:
volume of bottom: 6 x 10 x 5 = 300 [tex]cm^3[/tex]
volume of top:
[tex]V = (\frac{4}{3}\pi r^3)/2\\\\= (\frac{4}{3}\pi(4)^3)/2\\[/tex]
≈ 134.041 [tex]cm^3[/tex]
300 + 134.041 = 434.041
they want to the nearest tenth, so it would just be 434.0
Need help!! algebra!!!
Part A: The area of a square is (4a2 − 20a + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (9a2 − 16b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Part A
we have to solve the associated equation
4a^2 - 20a + 25 = 0
first of all we have to find the delta/4
Δ/4 = (b/2)^2 - ac where a is the term that multiply a^2, b is the term that multiply a and c is the therm without the variable
Δ/4 = (-10)^2 -100 = 100-100 = 0
the delta is equal to 0 that is mean that the equation has two coincident solutions, that can be find thanks to this formula
a1,a2 = -b/2/a = 10/4 = 5/2
now we can factorize the trinomial in this way:
4(a-5/2)(a-5/2)
4[(2a-5)/2][(2a-5)/2]
(2a-5)(2a-5)
the side of the square is 2a-5
Part B
the area of the rectangle is expressed as difference by two squares, so it can be rewritten as
(3a+4b)(3a-4b)
so the dimension of the rectangle are
3a+4b and 3a-4b
4 * (3.4+2)-(56 divided by 7)= 13.6, please give an explanation to this problem!!
Answer:
[tex]=13.6[/tex]
Step-by-step explanation:
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]=4\left(3.4+2\right)-\frac{56}{7}[/tex]
[tex]=21.6-8[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:21.6-8=13.6[/tex]
[tex]=13.6[/tex]
PLS ANSWER QUICK! Thanks!
Answer:
The correct answer would be [tex]a=\sqrt{c^2-b^2}[/tex]
Step-by-step explanation:
given [tex]a^2+b^2=c^2[/tex] we want to solve for a
How?
We can do this by using basic algebra ( isolating the variable (a ))
Step 1 subtract [tex]b^2[/tex] from each side
[tex]a^2+b^2-b^2=a^2\\c^2-b^2=c^2-b^2[/tex]
now we have [tex]a^2=c^2-b^2[/tex]
step 2 take the square root of each side
[tex]\sqrt{a^2} =a\\\sqrt{c^2-b^2} =\sqrt{c^2-b^2}[/tex]
we're left with [tex]a=\sqrt{c^2-b^2}[/tex]
Hence your answer is A
A student records the repair cost for 22 randomly selected dryers. A sample mean of $98.78 and standard deviation of $15.49 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value that should be used is T = 2.0796.
The 95% confidence interval for the mean repair cost for the dryers is between $91.912 and $105.648.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 22 - 1 = 21
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0796, which is the critical value that should be used.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0796\frac{15.49}{\sqrt{22}} = 6.868[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 98.78 - 6.868 = $91.912
The upper end of the interval is the sample mean added to M. So it is 98.78 + 6.868 = $105.648
The 95% confidence interval for the mean repair cost for the dryers is between $91.912 and $105.648.
the peremeter of a square is 16 inches what is the lenth of each side
Answer:If the figure is a square with a perimeter of 16 inches, then each side of the square is 4 inchest in length.
Step-by-step explanation:
Answer:
The length of each side is 4 inches.
Step-by-step explanation:
Since the shape is a square, all sides are equal so you do 16÷4 since there are 4 sides to get your answer of 4 inches.
please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
√11 = 3.31....
option 1. Irrational: √11 = 3.3
Answer:
Irrational [tex]\sqrt{11}[/tex] = 3.3
Step-by-step explanation:
Have a nice day!! :)
Question 7 (5 points)
Find the distance between a point (-3, 4) and a vertical line at x = 4.
A) -7
B) 8
O
C) 1
OD 7
Answer:
D.7
Step-by-step explanation:
[tex] 4 - ( - 3) = 4 + 3(because \: - \times - ) \: it \: is \: positive \\ = 7[/tex]
Plsssss help it is khan academy!!!
Which set of numbers is in DESCENDING order?
* 1 point
WILL GIVE BRANLIEST
55, -8, -2, -282
55, -2, -8, -282
-282, -8, -2, 55
-282, 55, -8, -2
The quadrilateral shown is a rectangle. What is m∠ZVY?
A) 39°
B) 59°
C) 61°
D) 119°
Answer: hey bro i can solve this for you but you need to show the quadrilateral. without it i can't solve it.
Step-by-step explanation:
3 cm
.
.
5 cm
If the base is halved and the height is quadrupled, then which of the following statements
about its area will be true?
Answer:
I think 7
Step-by-step explanation:
if the moon is purple then what toothpaste do u use on your but
A trader buys 30 shirts for #x each. He sells
them all for #y each. What is his profit
Help me out pls, i’m new to this whole hypotenuse thing
Answer:
x = 6.5
Step-by-step explanation:
Reference angle = 54°
Length of Side opposite to 54° = x
Hypotenuse = 8 cm
Recall: SOHCAHTOA.
Apply SOH:
Sin 54 = Opp/Hyp
Sin 54 = x/8
x = 8*sin 54
x = 6.47213595 ≈ 6.5 cm (nearest tenth)
Find the sum of the following arithmetic series:
(a) 6-5-16 - .... -115 (b) 21
(c) 13 + 6 -1 - .... -106
Find the sum of the first 500 odd numbers.
Answer:
12345678910
Step-by-step explanation:
CHARRRRRRRRR joke lang bestie
18 out of 20 to percentage
Answer:
90%
Step-by-step explanation:
Which type of sequence is shown? 5, 10, 15, 20, 25, . . .
geometric
both arithmetic and geometric
arithmetic
neither arithmetic nor geometric
Answer:
Arithmetic Sequence
Step-by-step explanation:
In Arithmetic sequence each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k.