Answer:
[tex]Z = 2[/tex]
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 of 21 and a standard deviation of 5.
This means that [tex]\mu = 21, \sigma = 5[/tex]
Find the Z score for a student that gets a 31
This is Z when X = 31. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 21}{5}[/tex]
[tex]Z = 2[/tex]
The braking ability of two types of automobiles was compared. Random samples of 64 auto mobiles were tested for each type. The recorded measurement was the distance required to stop when the brakes were applied at 40 miles per hour. The computed sample means and variances were as follows:
y¯¯¯1=118,y¯¯¯2=109 s21=102,s22=87
. Do the data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles? Give the attained significance level.
Answer:
The data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles
Step-by-step explanation:
Formulate the null and alternate hypothesis as
H0: u1= u2 against the claim Ha: u1≠ u2
The data given is
y`1=118, y`2=109 s21=102, s22=87
The test statistic used is t= y1`- y2`/ Sp√1/n1+ 1/n2
n1= n2= 64
And
Sp² = (n1-1) s12 + (n2-1) s22 / n1+n2-2
Sp² = 63*102+6*87/64+64-2
Sp² = 94.5
Sp= 9.7211
Putting the values in the test statistic
t= 118-108/9.7211√1/64+1/64
t= 5.237
Now finding the value of t at ∝=0.01 for two tailed test
t( 126,0.005)= ±2.6154
At alpha= 0.01 the null hypothesis is rejected.
Now finding the value of t at ∝=0.05 for two tailed test
t( 126,0.025)= ±1.979
Even at alpha= 0.05 the null hypothesis is rejected.
Also at alpha= 0.05 the null hypothesis is rejected because the critical value is ±1.657
Hence it is concluded that the data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find the
time that the rocket will hit the ground, to the nearest 100th of second.
y = -16x^2+ 181x + 59
Answer:
The rocket will hit the ground after about 11.63 seconds.
Step-by-step explanation:
A rocket is launched from a tower. Its height y in feet after x seconds is modeled by the equation:
[tex]y=-16x^2+181x+59[/tex]
We want to determine the time at which the rocket will hit the ground.
If it hits the ground, its height y above the ground will be 0. So, we can set y = 0 and solve for x:
[tex]0=-16x^2+181x+59[/tex]
Solve the quadratic. Factoring is too tedious or impossible, and completing the square is also very tedious. So, we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = -16, b = 181, and c = 59. Substitute:
[tex]\displaystyle x=\frac{-(181)\pm\sqrt{(181)^2-4(-16)(59)}}{2(-16)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{-181\pm\sqrt{36537}}{-32}[/tex]
Simplify:
[tex]\displaystyle x=\frac{181\pm\sqrt{36537}}{32}[/tex]
Hence, our solutions are:
[tex]\displaystyle x=\frac{181+\sqrt{36537}}{32}\approx 11.63\text{ or } x=\frac{181-\sqrt{36537}}{32}\approx-0.32[/tex]
Since time cannot be negative, we can ignore the second solution.
So, the rocket will hit the ground after about 11.63 seconds.
Write an equation of the circle with center (3,-2) and radius 11.
let h= 3, k=-2
radius (r) = 11 ,then
(x-h)^2 + ( y-k)^2 = r^2
(x-3)^2 + ( y+2)^2 = 11^2
x^2 -6x +9 + y^2 +4y +4 = 121
x^2 + y^2 - 6x +4y -108 = 0 is the required eq
Find the total surface area of the solid below. Round your answer to the nearest tenth.
x= 11.6, y = 6.3, and z = 15.5
Answer:
494.16 units²
Step-by-step explanation:
Total surface area of the solid = 4(area of a triangular face) + area of the square base
Area of a triangular face = ½*b*h
b = x = 11.6
h = z = 15.5
Area = ½*11.6*15.5 = 89.9 units²
Area of the four triangular faces = 4(89.9) = 359.6 units²
Area of the square base = s²
s = x = 11.6
Area = 11.6²
Area = 134.56 units²
✔️Total surface area of the solid = 359.6 + 134.56 = 494.16 units²
The ratio of parrots to cats in the pet store is 5 to 20. If there are 4 parrots
how many cats are there?
A. 16
B. 1
C. 20
D. 25
Answer:
A. 16
Step-by-step explanation:
HELP ASAP will give you brainlist
Answer:
24
Step-by-step explanation:
sorry if incorrect
Show the number of 76 at least 2 ways?
What is the probability of choosing a gray button replacing it and choosing a gray button ?
the answer is that you get the same outcome
A stores revenue is the function y = 150x where x is the number of items they sell. Its cost function is
y = 7x + 2200 where x is the number of items they sell. How many items do they have to sell to break-
even? Show how to solve this using inverses and not the table on your calculator.
NO LINKS TO FILES OR ANYTHING LIKE THAT.
9514 1404 393
Answer:
about 15 or 16 items
Step-by-step explanation:
The break-even point is where revenue is equal to cost.
150x = 7x +2200
143x = 2200 . . . . . . . subtract 7x
x ≈ 15.38 . . . . . . . . . . divide by 143 (multiply by the inverse of 143)
__
When 15 items are sold, revenue doesn't quite cover costs. Costs still exceed revenue by 55. When 16 items are sold, revenue exceeds costs by 95. (I would call this the break-even point, because I prefer a slight profit over a slight loss.)
What is the result of performing these steps?
1. Draw a line segment with endpoints A and B. 2. Draw point Canywhere
above AB
3. Fold the paper through C so AB lies on top of itself.
4. Fold the paper through C so that the fold line from Step 3 lies on top of
itself.
5. Draw a line segment from C to any point along the second fold.
answer choices:
A. The perpendicular bisector of AB
B. A line segment perpendicular to AB
C. A line segment parallel to AB
D. A bisected angle
The spray from a spinning lawn sprinkler makes
a circle with a 40 foot radius. If Ben and his
friends what to play and get wet, how much
space do they have?
Answer: [tex]5027.2\ ft^2[/tex]
Step-by-step explanation:
Given
The radius of the circle is [tex]r=40\ ft[/tex]
The area of the circle is given by [tex]\pi r^2[/tex]
Insert the value of radius and get the area to play
[tex]\Rightarrow \text{Area A=}\pi \times 40^2\\\\\Rightarrow A=3.142\times 1600\Rightarrow A=5027.2\ ft^2[/tex]
Thus, the area to play is [tex]5027.2\ ft^2[/tex]
Q8 Find the missing angle x and measurement of JLK
Answer:
Step-by-step explanation:
we know ∠K is 90° by Thales theorem
then
180 = 90 + 4x-1 + 4x -5
96 = 8x
12 = x
x = 12
∠JLk = 4(12)-1
∠JLk = 47°
NEED HELP ON MATH TEST ASAP!! Will give BRAINLY
Must show work on all problems!!
Find the surface area of the box with dimensions 125mm×64mm×84mm to the nearest mm?
Answer:
hi
Step-by-step explanation:
you should eat more sushi because it will help you digest food better! just letting you know to help you and make you feel healthy!
xoxo
It took lan three years to collect 25,413 aluminum cans to recycle. In the first year he collected 8,917 cans, and in the second year he collected 7.639 cans Which equation can be used to find x, the number of cans tan collected in the third year? A X = 25,413-8,917 - 7,639 B X = 25,413 +8,917 + 7,639 CX-8,917 +7,639 D 8,917-7,639
Answers:
1. 24 cans/lb x 15,000 lb/trailer = 360,000 cans/trailer
2. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 15,000 lb = $9,000
3. 15,000 lbs/trailer / 30 lbs/collector = 500 can collectors/trailer
4. 15,000 lbs/trailer / 800 lbs/bale = 18 complete bales (and 3/4 of another bale)/trailer
5. 24 cans/lb x 800 lb/bale = 19,200 cans / bale
6. 100 bales/boxcar x 800 lbs/bale = 80,000 lb. cans / boxcar
7. 100 bales/boxcar x 19,200 cans/bale = 1,920,000 cans / boxcar
8. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 80,000 lb/boxcar = $48,000/boxcar
Pick the right one.
what is 2/5 times 30 equal in simplets form
Answer:
2/5 times 30 equals 12.
Answer:Step-by-step explanation:
Hey guys can you please help me?? Thank you!
Answer:
17x+44+51 = 180
x=5
Step-by-step explanation:
The angles in a triangle add to 180, so set up the equation by adding the measures of each angle on one side and putting 180 on the other side, then solve:
17x+44+51 = 180
17x+95=180
17x=85
x=85/17=5
Hope this helps :)
Help me with Perpendicular angles
Answer:
x = 50°
x = 70°
Step-by-step explanation:
A right angle is indicated by a small box.
The angles shown are right angles = 90° each. Therefore:
✔️x + 40° = 90°
Subtract 40° from each side
x = 90° - 40°
x = 50°
✔️x + 20° = 90°
Subtract 20° from each side
x = 90° - 20°
x = 70°
Help me out with this please!
No links to websites other than Brainly.
Problem 1
Answers:
It costs 1.72 dollars to send a letter that is 1.5 ounces
It costs 1.72 dollars to send a letter that is 2 ounces
In short, both answers are 1.72 dollars
--------------------------------
Explanation:
The piecewise function may seem really ugly and complicated, and I can understand why many don't like them, but they aren't too bad once you get used to it.
A piecewise function is simply a collection of many functions glued together. Instead of listing four different functions, your teacher has combined them all into one super function of sorts.
Here are the rules for this function
If [tex]0 < w \le 1[/tex], then F(w) = 1.15If [tex]1 < w \le 2[/tex], then F(w) = 1.72If [tex]2 < w \le 3[/tex], then F(w) = 2.29If [tex]3 < w \le 3.5[/tex], then F(w) = 2.86As you can see, the definition of F(w) will change depending on what w is.
If the weight is w = 1.5 ounces, then we're on the interval [tex]1 < w \le 2[/tex] since 1.5 is between 1 and 2. So we go for the second definition shown above and we conclude that it will cost $1.72 to send this 1.5 ounce letter.
If you wanted, you could rewrite those four bulleted points into this equivalent form
If [tex]0 < w \le 1[/tex], then the cost is $1.15 to send the letterIf [tex]1 < w \le 2[/tex], then the cost is $1.72 to send the letterIf [tex]2 < w \le 3[/tex], then the cost is $2.29 to send the letterIf [tex]2 < w \le 3.5[/tex], then the cost is $2.86 to send the letterwhich is a less mathematical way of stating it. It might also help to make it into a chart, which would help customers better who may not want to deal with math.
A letter that's 2 ounces will cost $1.72 as well since w = 2 makes [tex]1 < w \le 2[/tex] true.
In short, both the 1.5 ounce and 2 ounce letters cost $1.72 each.
===========================================================
Problem 2
Answer: The graph is shown below (attached image)
--------------------------------
Explanation:
We have what is called a step function, or a staircase function. Either name will work. The graph consists of the horizontal portion of the stairs, but the vertical parts of the stairs are not drawn (or else we wouldn't have a function due to the vertical line test).
Note the placement of the open and closed endpoints. An open endpoint excludes the value in question, while a closed endpoint includes the value.
For instance, we have an open endpoint at (1, 1.72) while there's a closed endpoint at (1, 1.15). Each closed endpoint is directly connected to the "or equal to" portion of the inequality sign, and each open endpoint does not have the "or equal to" portion.
As the graph shows, we basically have the a certain flat cost for the four different regions. This corresponds to the costs given in the piecewise function. Each height is drawn from the list {1.15, 1.72, 2.29, 2.86}
The point labels of A,B,C,D,E,F,G,H are optional. I only put them in there to help identify which endpoints are open or closed. Points on the left side of each segment, or horizontal stair component, are open endpoints. Points on the right side are closed endpoints.
ANSWER THIS ASAP NO FILE AT ATT!! THIS MY LAST QUESTION JUST GET IT RIGHT PLEASE
Answer:
I believe the answer is A
Answer:
A is your answer I think
Step-by-step explanation:
maybe wait for someone else to answer as well haha
predict the next number in the table. cycle: 1,2,3,4,5. people told: 1,3,9,27,?
What is b<4 on a number line
Answer:
stay safe healthy and happy.Answer:
(SEE ATTACHED PICTURE)
Step-by-step explanation:
You put a circle above the number used in the inequality.
The circle is closed if the inequality is greater than or equal to, or less than or equal to. This indicates that the number is included.
The circle is open if the inequality is greater than, or less than. This indicates that the number is not included.
The arrow goes to the left if it is less than, and to the right if it is greater than.
So, for your problem, an open circle goes about the number 4 and points left.
Two of the statements are true; one is a lie.
Select the one that is a lie.
Then explain your reasoning.
The measure of ∠CAF is 25 degrees.
∠DAE ≌ ∠FAB.
∠BAF and ∠EAB are complementary.
Answer:
The statement "[tex]\angle BAF[/tex] and [tex]\angle EAB[/tex] are complimentary" is false.
Step-by-step explanation:
Complimentary angles are defined by angles that add up to [tex]90^{\circ}[/tex]. Angles BAF and EAB represent one side of a line, which is [tex]180^{\circ}[/tex]. Therefore, they are actually supplementary and not complimentary. Thus, the statement "[tex]\angle BAF[/tex] and [tex]\angle EAB[/tex] are complimentary" is false.
Angle Relationships
When solving for x, the sine of 44° is used. What other angle and trigonometric function could be used to solve for x?
a. tan 46°
b. cos 46°
c. tan 44°
d. cos 44°
Please select the best answer from choices provided
Answer:
B. cos 46°
Step-by-step explanation:
I calculated it logically
Answer:
b. cos 46
Step-by-step explanation:
There are three angles to choose from since there are three angles in a triangle. Of these, the 90° angle can't be used (90° angles don't work with trigonometric ratios), and neither can the 44° (we're told to use a different one from this), so we're left with the unmarked angle on the bottom right. Since the angles in a triangle add to 180, and the other two angles total 134 (90+44=134), we can say this angle is 46°.
Since cos46 is our only option that involves this angle (and since cos46=x/9), this is the option which could be used to find x.
CAN SOMEONE PLEASE HELP ME :(
Answer:
Step-by-step explanation:
d
Fitness can be measured by the rate of oxygen consumption during exercises with more fit people having higher rates. Unfortunately, this measurement is quite costly to obtain, and so an experiment was done to see if this measurement could be predicted from the time it takes (in minutes) to run 1500 m. The following computer output was obtained. Which of the following is NOT CORRECT?
a. For every additional minute it takes to run the 1500 m the estimated oxygen consumption rate decreases by 3.31.
b. The fitted regression line is approximately Y = 82.42(runtime)
c. A person who runs 1500 m in 10 minutes would have an estimated oxygen consumption rate of about 50.
d. There is good evidence that there is a relationship between oxygen consumption and the run time.
e. The slope is 82.42.
Answer:
b. The fitted regression line is approximately Y = 82.42(runtime)
Step-by-step explanation:
The regression line is Y= aX + b
here b= 82.42 a = -3.31
Hence the regression equation is
Y= 82.42- 3.31 X
where x is the runtime and the slope is given by b.
Option a is correct because from the above equation we see that for every additional minute it takes to run the 1500 m the estimated oxygen consumption rate decreases by 3.31.
Option b is incorrect because the runtime is not given by Y it is given by X.
Option C is correct as
Y= 82.42-3.31*10
Y= 82.42-33.1
Y= 49.32 almost 50
Option d is also correct that the equation line shows a relationship between oxygen consumption and the run time.
Option e is also correct because the slope is given by b and b= 82.42
The plumber charged Mrs. Evans $225.00 for materials and $35.00 an hour for labor to fix her leaky sink. The total bill came to $347.50. How many hours did it take the plumber to fix the sink?
Answer:
3.5 or 3[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
First, subtract. 347.50 - 225.00 = 122.50
Then, divide. 122.50 ÷ 35 = 3.5
Next, you can turn the decimal into a fraction 3[tex]\frac{1}{2}[/tex]
Lastly, have a wonderful day! :)
Name the diagonal segment in the figure.
Answer: 1 is a quadrilateral. I’m very sorry I don’t know the second shape.
Step-by-step explanation: a quadrilateral has 4 sides and two triangles.
Find the slope between the pair of points (1,-3) and (2,3)
If 4 television weigh 160 pounds , How much do 5 of those television weigh.
Must show your work
Answer:
Step-by-step explanation:
640
Answer:
200 pounds
Step-by-step explanation:
We can write a proportion to represent the problem. Let's take x as the weight of 5 televisions. If we know that 4 televisions weigh 160 pounds we can write: 4/160. Then, 5 televisions will weigh x pounds which is 5/x. Now, we can set up a proportion: 4/160 = 5/x
Cross multiply to get: 4x = 800
Isolate x: x = 800/4
Solve: x = 200
200 pounds