Answer:
8 is 4% of 200, 1% of 200 is 2
If u + t = 5 and u-t=2, what is the value of
(u – t)(u² - 12) ?
Answer:
(u – t)(u² - 12) is equal to 0.5.
Step-by-step explanation:
First let's find u and t:
Given u + t = 5, and u - t = 2
We'll substitute one of those into the other equation.
Let's solve the second one for u:
u - t = 2
u = 2 + t
Now we can substitute that definition into the first equation:
u + t = 5
(2 + t) + t = 5
2 + 2t = 5
2t = 3
t = 1.5
Now we can substitute that into either of the original equations to find u:
u = 2 + t
u = 2 + 1.5
u = 3.5
So t = 1.5 and u = 3.5. Now we can substitute them into the given expression to solve it:
(u – t)(u² - 12)
= (3.5 – 1.5)(3.5² - 12)
= (3.5 – 1.5)(12.25 - 12)
= 2 × 0.25
= 0.5
Answer:
0.5
Step-by-step explanation:
You know that u-t is 2, so it'll be 2([tex]u^{2}[/tex] -12)
Now, system of equations to solve for u. if u+t=5, this means t=5-u, you can plug it in into u-t=2, so u-(5-u)=2. Now you know that u is 3.5, so do the calculations.
Lengths of full-term babies in the US are Normally distributed with a mean length of 20.5 inches and a standard deviation of 0.90 inches. (Each question is worth 3 points) What percentage of full-term babies are between 19 and 21 inches long at birth
Answer:
66.48% of full-term babies are between 19 and 21 inches long at birth
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean length of 20.5 inches and a standard deviation of 0.90 inches.
This means that [tex]\mu = 20.5, \sigma = 0.9[/tex]
What percentage of full-term babies are between 19 and 21 inches long at birth?
The proportion is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19. Then
X = 21
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21 - 20.5}{0.9}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a p-value of 0.7123
X = 19
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 20.5}{0.9}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a p-value of 0.0475
0.7123 - 0.0475 = 0.6648
0.6648*100% = 66.48%
66.48% of full-term babies are between 19 and 21 inches long at birth
An artist wants to scale down the surface area of an image by 20%. The image initially has a length of 22 ft. and a width of 22 ft. What is the width of the scaled down image? Round to the nearest hundredth.
17.08 ft.
17.89 ft.
18.78 ft.
19.68 ft.
Answer:
17.89 ft if I'm correct.....
Answer:
D. 19.68 ftStep-by-step explanation:
Area is the product of two dimensions.
If the scale factor is k, the ratio of areas is k².
20% down means 0.8 times:
k² = 0.8k = √0.8 = 0.8944Now the width of the image is:
22*0.8944 = 19.68 ft (rounded)Correct choice is D
What is the perimeter of the triangle
Answer:
56 units
Step-by-step explanation:
add each side, you can get the hypotenuse using the formula a^2+b^2=c^2
2/7, 3/4, 2/3. Arrange it in ascending order
Answer:
2,7 2,3 3/4
Step-by-step explanation:
2,7 = 0.29 2,3 = 0.67 3/4 = 0.75
I need help with this asap thank you
Answer:a
Step-by-step explanation:a
Type the correct answer in the box. If cos x=sin(20 + x) and 0° <x<90°, the value of x is:
Answer:
the value of x is 90 Your answer
Step-by-step explanation:
4(q-5) = 16
help pleaseee
Answer:
q = 9
Step-by-step explanation:
the key thing to understand in this problem is the distributive property. which basically means we can muliply what's on the interior of the parenthestes ( in this case q-5) by what's on the outside (4).
so 4 will distrubute to both the q and the -5
4q - 20 = 16
add 20 to both sides
4q = 36
divide both sides by 4
q = 9
A newly electric vehicle is designed to have a battery range of 400 miles and a standard deviation of 20 miles. assume the battery range distribution is normally distributed. the company tests 39 vehicles to determine if the battery is operating at specifications. the average range of the 39 vehicles is 398 vehicles with a standard deviation of 20 miles. find the 95% confidence interval for average battery range of the newly produced vehicle.
a) (393.72 , 406.28)
b) (391.52, 404.48
c) (393.52, 406.48)
d) (391.72, 404.28)
Answer:
b) (391.52, 404.48)
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 = 39 - 1 = 38
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 38 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0244
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0244\frac{20}{\sqrt{39}} = 6.48[/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 398 - 6.48 = 391.52.
The upper end of the interval is the sample mean added to M. So it is 398 + 6.48 = 404.48.
The CI is (391.52, 404.58), and the correct answer is given by option B.
PLEASEEEE HELP MEEEEEEE
Answer:
The answer is A.
Step-by-step explanation:
If you count how many blocks it takes on the y axis, you will get 7 but note that it is reflected so it is -7. If you count how many blocks it takes on the x axis you get -3. So the answer is (-3,-7).
Kate's dog was learning to balance a ball on his nose. The
first day he balanced the ball 6 out of 20 times; the second
day, 8 out of 25 times. Which day did he do better?
Answer:
The answer is the first day
An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
Answer:
225,000 revolutions
Step-by-step explanation:
An air conditioning fan makes 125 revolutions per second
The number of revolution in 30 minutes can be calculated as follows
60 secs= 1 min
x= 30 min
= 30×60
= 1800 secs
1800×125
= 225,000
Hence the airconditioning makes 225,000 revolutions in 30 minutes
Verify the identity:
sin(A + B)
sin( A B)
tan(-4) + tan(B)
tan(4) tan(B)
Answer:
i think is the answer is
sin(A+B)
Answer:
Numerator:
sin (A + B) = sin A cos B + cos A sin BDivide by cos A cos B:
sin A /cos A + sin B /cos B = tan A + tan BDenominator:
sin (A - B) = sin A cos B - cos A sin BDivide by cos A cos B:
sin A /cos A - sin B /cos B = tan A - tan BConnect all bits together to get:
sin(A + B) / sin(A - B) = (tan A + tan B) / (tan A - tan B)Goldilocks needs to find at least 12 lbs gold and 18 lbs silver to pay monthly rent. Each day in Mine 1 she finds 2 lbs gold and 2 lbs silver. Each day in Mine 2, she finds 1 lb gold and 3 lbs silver. Set up and solve using either LPsolve or on-line solver How many total days in the mines
Answer:
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
Step-by-step explanation:
Requirement : 12 Ibs gold and 18 Ibs silver to pay monthly rent
Mine 1 ; 2 Ibs of gold , 2Ibs of silver.
Mine 2; 1 Ib of gold , 3 Ibs of silver
using LP
Gold : aX1 + bX2 ≥ 12 ---------- ( 1 )
Silver: cX1 + dX2 ≥ 18 --------- ( 2 )
where; X1 = days spent in Mine 1
X2 = days spent in Mine 2
Total days spent in mines : X1 + X2 =
a = Gold found in mine 1 = 2
b = Gold found in mine 2 = 1
c = silver found in mine 1 = 2
d = silver found in mine 2 = 3
Back to equations 1 and 2
2X1 + X2 ≥ 12 ----------- ( 3 )
2X1 + 3X2 ≥ 18 ------------ ( 4 )
solving equations 3 and 4
= 0 + 2X2 ≥ 6 ∴ X2 ≥ 3 days ( days spent in mine 2 )
Input value into ( 3)
2X1 ≥ 12 - 3 = 9
∴ X1 ≥ 4.5 days ( days spent in mine 1 )
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
Can someone help me please.....
Answer:
the third one
Step-by-step explanation:
2 1/2
What is the area of this composite figure
48.56cm2
49.12cm2
74.24cm2
36.56cm2
Answer:
D. 36.56 cm²
Step-by-step explanation:
The composite figure is composed of a rectangle and two semicircles.
The two semicircles makes 1 full circle.
Thus:
Area of the composite figure = area of rectangle + area of circle
= L*W + πr²
L = 6 cm
W = 4 cm
r = ½(4) = 2 cm
Area = 6*4 + π*2²
Area = 24 + 12.56
Area = 36.56 cm²
The graph shows Micah’s pay for working different numbers of hours. Graph of a diagonal line on a coordinate plane with ALTDCTime worked in hoursALTDC on x-axis and ALTDCPay in dollarsALTDC on y-axis. The diagonal line is going up and to the right. Line passes through points (0, 0), (2, 30), (4, 60), A and (14, 210). A is at (8, 120) Part A What are the coordinates of Point A on the graph? Enter your answer in the boxes. ( , ) LIVE Part B What does the ordered pair for Point A represent? Use the drop-down menus to show your answer. When Micah works hours, he makes $ .
Answer:
Step-by-step explanation:
The coordinates for point A is (8,120)
How many different squads of 5 players can be picked from 10 basketball players?
Answer:
2 squads of five can be picked from 10 basketball players
Step-by-step explanation:
To solve this problem you have to divide 10 ÷ 2 which equals to 5.
Find an
angle in each quadrant with a common reference angle with 146°, from
o°=0<360°
Answer:
The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.
The equivalent angle on the third quadrant is 214º.
The equivalent angle on the fourth quadrant is 316º.
Step-by-step explanation:
On the first quadrant:
The equivalent in the second quadrant of a angle on the first quadrant a is 180 subtracted by the angle, that is, 180 - a.
In this question, the reference angle is 146º, which is on the second quadrant.
So, on the first quadrant:
146 = 180 - a -> a = 180 - 146 = 44.
The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.
Third quadrant:
The equivalent angle on the third quadrant is 2 multiplied by 180 and subtracted by the second quadrant angle. So
2*180 - 146 = 360 - 146 = 214º.
The equivalent angle on the third quadrant is 214º.
Fourth quadrant:
The equivalent angle on the fourth quadrant is 360 subtracted by the angle on the first quadrant. So
360 - 44 = 316º
The equivalent angle on the fourth quadrant is 316º.
2/3 divided by 7/12
PLSLSLSLSLSLLSLSL
Answer:
0.00793650794 or 8/7 in fraction form
Step-by-step explanation:
Find the reciprocal of the divisor
Answer help on this !
If the triangles are similar, then the angles are all congruent.
Therefore, we can start by setting the two middle angles equal to each other.
4x + 7 = 5x - 10
7 = x - 10
x = 17
Middle angle = 75
Now that we know our x-value, we can simply plug in x for our other two expressions.
3 * 17 = 51
4(17) - 14 = 54
We can check to make sure that our angle measures are correct by adding them all up and making sure they equal 180.
54 + 51 + 75 = 180
180 = 180
Hope this helps!! :)
Answer:
54, 51, 75
Step-by-step explanation:
4x+7=5x-10 because they are vertical angles and are therefore equal to eachother. x=17.
After plugging the 17 into the equations you get 4(17)+7=75. 3(17)=51. All angles in a triangle add up to 180. We already have 75 and 51 in the first triangle, to get the third length you need to subtract that from 180. 180-75+51=54.
The second triangle will give you the same lengths. 5x-10=75. 4(17)-14=54. Again, 180-75-54=51.
Your final lengths are 75,51,54.
Mary’s bedroom rug is shown below. Find the perimeter and area of the rug.
3. Find the volume of the following figure. 62 units 58 units 60 units) 64 units3
Answer:
60 units
Step-by-step explanation:
Its a 5 × 3 × 4 cube
To find volume multiply the dimensions and you will get 60
Answer:
60 units
Step-by-step explanation:
I did the test.
Find the volume of the trapezoidal prism.
7 in.
6 in.
12 in.
4 in.
Answer: 48
Step-by-step explanation: you will have to multiply
This is urgent please help me out.The side lengths of different triangles are given. Which triangle is a right triangle?
Answer:
C. √18, √7, 5
Step-by-step explanation:
_____________
What is the length of NP?
Answer:
[tex]c=\sqrt{174}[/tex]
Step-by-step explanation:
First, find the length of MP. This can be done with the Pythagorean Theorem.
We can use x as angle MP.
a² + b² = c²
10²+ 7² = x²
100 + 49 = x²
x² = 149
Take the square root to get
x = √(149)
Now do the Pythagorean Theorem for Triangle MNP. We can again use x for angle NP.
a² + b² = c²
5² + √(149)² = c²
25 + 149 = c²
c² = 174
c = √(174)
A birthday cake was cut into equal pieces, and five pieces were eaten. The fraction below shows how much cake was left over. According to the fraction, into how many pieces was the cake cut? 8 /13
A. 5
B. 13
C. 18
D. 8
Answer:
13
Step-by-step explanation:
Answer:
B. 13
Step-by-step explanation:
if 5 were eaten, that's 5/13, and there's 8/13 left. 5 out of thirteen total were eaten and 8 out of thirteen total were left.
the polynomial x^+3x - 1 is a factor of x^3+2x^2-5x-6
Answer:
If its x^2 + 3x - 1 it is not a factor.
Step-by-step explanation:
x^2+3x - 1 is a factor of x^3+2x^2-5x-6?
Try dividing:
x^2+3x - 1 ) x^3 + 2x^2 - 5x - 6( x - 1
x^3 + 3x^2 - x
- x^2 -4x - 6
-x^2 - 3x + 1
- x - 7 <------- remainder.
What is the measure, in degrees, of the highlighted angle?
Answer:
[tex]36^\circ[/tex]
Step-by-step explanation:
If you add the measures of the two marked angles, you get [tex]180^\circ[/tex]. The two angles form what some call a linear pair.
Set up and solve an equation.
4x + x = 180
5x = 180
x = 180 / 5
x = 36 degrees
A sample of 28 sales transactions at Costco shows a mean transaction time of 296 seconds with a standard deviation of 48 seconds. Costco is interested in finding out whether the mean transaction time is less than 310 seconds. Answer the following questions. a) Write down the null and alternative hypotheses. b) Find the test statistic and the critical value at 1% significance level. c) At 1% level of significance, what is your conclusion
Answer:
a) The null hypothesis is [tex]H_0: \mu = 310[/tex] and the alternative hypothesis is [tex]H_1: \mu < 310[/tex].
b) The test statistic is [tex]t = -1.54[/tex]. The critical value is [tex]t_c = -2.473[/tex].
c) The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.
Step-by-step explanation:
Question a:
Costco is interested in finding out whether the mean transaction time is less than 310 seconds.
At the null hypothesis, we test if the mean is of 310 seconds, that is:
[tex]H_0: \mu = 310[/tex]
At the alternative hypothesis, we test if the mean is of less than 310 seconds, that is:
[tex]H_1: \mu < 310[/tex]
b) Find the test statistic and the critical value at 1% significance level.
Test if the mean is less than a value, sample of 28, and standard deviation for the sample. Thus, we have a left-tailed t-test with 28 - 1 = 27 degrees of freedom and a 0.01 significance level, and the critical value is [tex]t_c = -2.473[/tex].
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation pf the sample and n is the size of the sample.
310 is tested at the null hypothesis:
This means that [tex]\mu = 310[/tex].
A sample of 28 sales transactions at Costco shows a mean transaction time of 296 seconds with a standard deviation of 48 seconds.
This means that [tex]n = 28, X = 296, s = 48[/tex].
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{296 - 310}{\frac{48}{\sqrt{28}}}[/tex]
[tex]t = -1.54[/tex]
The test statistic is [tex]t = -1.54[/tex].
c) At 1% level of significance, what is your conclusion
The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.