Answer:
z-score=2.17
Step-by-step explanation:
We are given that
Mean, [tex]\mu=0[/tex]
Standard deviation, [tex]\sigma=1[/tex]
Probability, p-value=0.9850
We have to find z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850.
To find the z score for the standard normal distribution we will use z-table.
From z- table we get
p-value =0.9850 when z -score=2.17
[tex]\implies[/tex]z-score corresponding to p-value=2.17
Therefore, the z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850=2.17
Supposed we saved 55$ and we saved 6$ each week what’s the total amount of t we will have after w weeks
Answer:
t=55+6w
Hope This Helps!!!
Find two numbers that have 2, 5, and 7 as factors.
Step-by-step explanation:
One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.
To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140
Seth and Ted can paint a room in 5 hours if they work together. If Ted were to work by himself, it would take him 1 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick
Answer:
Seth would need 10 hours to paint the room.
Step-by-step explanation:
Let's define:
S = rate at which Seth works
T = rate at which Ted works
When they work together, the rate is S + T
And we know that when they work together they can pint one room in 5 hours, then we can write:
(S + T)*5 h = 1 room.
We also know that Ted alone would need one hour more than Seth alone.
Then if Seth can paint the room in a time t, we have:
S*t = 1room
and
T¨*(t + 1h) = 1room
Then we have 3 equations:
(S + T)*5 h = 1
S*t = 1
T¨*(t + 1h) = 1
(I removed the "room" part so it is easier to read)
We want to find the value of S.
First, let's isolate one variable (not S) in one of the equations.
We can isolate t in the second one, to get:
t = 1/S
Now we can replace it on the third equation:
T¨*(t + 1h) = 1
T¨*( 1/S + 1h) = 1
Now we need to isolate T in this equation, we will get:
T = 1/( 1/S + 1h)
Now we can replace this in the first equation:
(S + T)*5h = 1
(S + 1/( 1/S + 1h) )*5h = 1
Now we can solve this for S
(S + 1/( 1/S + 1h) )= 1/5h
S + 1/(1/S + 1h) = 1/5h
Now we can multiply both sides by (1/S + 1h)
(1/S + 1h)*S + 1 = (1/5h)*(1/S + 1h)
1 + S*1h + 1 = 1/(S*5h) + 1/5
S*1h + 2 = (1/5h*S) + (1/5)
Now we can multiply both sides by S, to get:
(1h)*S^2 + 2*S = (1/5h) + (1/5)*S
Now we have a quadratic equation:
(1h)*S^2 + 2*S - (1/5)*S - (1/5h) = 0
(1h)*S^2 + (9/5)*S - (1/5h) = 0
The solutions are given by the Bhaskara's formula:
[tex]S = \frac{-(9/5) \pm \sqrt{(9/5)^2 - 4*(1h)*(-1/5h)} }{2*1h} = \frac{-9/5 \pm 2}{2h}[/tex]
Then the solution (we only take te positive one) is:
S = (-9/5 + 2)/2h
S = (-9/5 + 10/5)/2h = (1/5)/2h = 1/10h
Then Seth needs a time t to paint one room:
(1/10h)*t = 1
t = 1/(1/10h) = 10h
So Seth would need 10 hours to paint the room.
Consider the triangle.
Which statement is true about the lengths of the sides?
O Each side has a different length.
O Two sides have the same length, which iS less than
the length of the third side.
O The three sides have the same length.
O The sum of the lengths of two sides is equal to the
length of the third side.
Answer:
the last one
Step-by-step explanation:
this is because it is an equalactral triangle meaning that the line at the side is the only one which its degrees is 90 so if u add 45 and 45 its 90(hope this helps)
Answer:
Two sides have the same length, which iS less than
the length of the third side.
Step-by-step explanation:
Hypotenuce is a sode opposite to right angle, which is always bigger then any side of right triangle. since both angles are the same, Adjacent and Opposite are similar size as well.
ASAP ! PLSSSQ!!!!!!!
Answer:
16
Step-by-step explanation:
Solve: 1/3a^2-1/a=1/6a^2
Step-by-step explanation:
there are two answers for a
Answer:
The ANSWER IS 1/6
Step-by-step explanation:
What is the measure of ABC?
Answer:
60
Step-by-step explanation:
Information needed: a whole circle is 360 degrees.
Explanation: you need a protractor to see how many degree's it is
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 2 million barrels of oil in the well; six years later 1,000,000 barrels remain.
Required:
a. At what rate was the amount of oil in the well decreasing when there were 1,200,000 barrels remaining?
b. When will there be 100,000 barrels remaining?
Answer:
A. It was decreasing by -138,629.44 barrels
B. 26 years of time
Step-by-step explanation:
Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.
A. At 1200000
Bt = 1200000
-1/6ln2 x 1200000
Solve this using a calculator
= -138,629.4361
So the amount of oil is decreasing by -138,629.44 barrels
Help please, thanks
Answer: B. X It passes the vertical line test :)
Step-by-step explanation:
use complete sentences to describe the transformation of triangle ABC into its image.
Answer:
Move triangle ABC over 2 and up 1
Step-by-step explanation:
A transformation in geometry is to essentially move a shape. To move ABC onto A1B1C1 you would move triangle ABC over 2 and up 1.
What is the range of the function
Answer: [tex]-\infty < y < \infty[/tex] which is choice A
This is the set of all real numbers.
===========================================================
Explanation:
If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.
Another approach we could take is to swap x and y to get [tex]x = \sqrt[3]{y+8}[/tex] which solves to [tex]y = x^3-8[/tex] . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of
Domain of inverse = set of all reals
Range of original = set of all reals
SOMEBODY PLEASE HELP ME!!!! I NEED THIS!!!!
Answer:
47.1
Step-by-step explanation:
We know side LM corresponds with side OP with a factor of some number. The value of side LM is 8, and the value of side OP is 29. If we divide the two numbers, we will find the scale factor of which triangle NOP is larger than KLM. 29/8 simplifies to 3.625. Now, to find the value of side PN, we must find the side it corresponds to on triangle KLM. Because K corresponds with N, and M corresponds with P, we know the side that PN corresponds with on triangle KLM is side KM. Side KM has a value of 13, so side PN must be 3.625 times larger than 13.
13 times 3.625 = 47.125. The question says to round to the nearest tenth, so the answer would be 47.1
The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.0 minutes and standard deviation 1.6 minutes. Suppose that a random sample of customers is observed. Find the probability that the average time waiting in line for these customers is (a) Less than 10 minutes (b) Between 5 and 10 minutes (c) Less than 6 minutes Round your answers to four decimal places (e.g. 0.9876). (a) The probability is Enter your answer in accordance to the item a) of the question statement . (b) The probability is Enter your answer in accordance to the item b) of the question statement . (c) The probability is Enter your answer in accordance to the item c) of the question statement .
Answer:
Step-by-step explanation:
a)
*Prob-less 89.44%
b)
*Prob-Between 86.40%
Z1=-1.88 Z2=1.25
c)
*Prob-less 10.56%
Given f(x) = 6x + 2, find f(x – 3).
A. f(x – 3) = 6x – 1
B. f(x – 3) = 6x – 16
C. f(x - 3) = x - 1
D. f(x – 3) = 6x2 – 16x - 6
Answer: B. f(x - 3) = 6x - 16
Concept:
When encountering a question that gives you a function and the evaluation value, then basically plug the given value into the function.
Solve:
Given function and value
f(x) = 6x + 2
f(x - 3)
Substitute the value into the given expression
f(x - 3) = 6 (x - 3) + 2
f(x - 3) = 6x - 18 + 2
f(x - 3) = 6x - 16
Hope this helps!! :)
Please let me know if you have any questions
A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92.
Round your answers to two decimal places.
(a) State the point estimate for the population mean cost of fast food bills at this restaurant $
(b) Calculate the 95% margin of error. $
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
$
≤ µ ≤ $
(d) What sample size is needed if the error must not exceed $1.00?
n =
First, we find the point estimate, given by the sample mean. Then, with this, and the standard deviation of the population given, we can find the margin of error, and then, we can find the confidence interval and the minimum sample size necessary.
Doing this, we get that:
a) The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
b) The 95% margin of error is $1.64.
c) The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
d) The sample size needed is 135.
Question a:
The point estimate for the population mean is the sample mean, which is of $18.21.
The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
Question b:
We have to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a p-value of , so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{5.92}{\sqrt{50}} = 1.64[/tex]
The 95% margin of error is $1.64.
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
The lower end of the interval is the sample mean subtracted by M. So it is 18.21 - 1.64 = 16.57
The upper end of the interval is the sample mean added to M. So it is 18.21 + 1.64 = 19.85
The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
(d) What sample size is needed if the error must not exceed $1.00?
This is n for which M = 1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.96\frac{5.92}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.96*5.92[/tex]
[tex](\sqrt{n})^2 = (1.96*5.92)^2[/tex]
[tex]n = 134.6[/tex]
Rounding up:
The sample size needed is 135.
For a question in which you find a confidence interval using the z-distribution, you can check https://brainly.com/question/24175328
To find the minimum sample size for a confidence interval, you can check https://brainly.com/question/22667000
The area of a rectangle is 3,878 square centimeters. If the rectangle has a width of 14 centimeters, what is its length?
Answer:
277 cm
Step-by-step explanation:
[tex]A=l*w\\3,878=l*14\\l=\frac{3,878}{14} \\l=277[/tex]
A camera with a price of d dollars is discounted 25%. write two expressions to represent the price of the camera with the discount.
Answer:
17d/20
Step-by-step explanation:
100-25=85
85/100×d
=17/20×d
=17d/20
A class of kindergarteners is making get well cards for children in the houses how many different cards can be made from 2 shapes 4 card colors 3 colors of glitter and 8 colors of markers
Answer:
192
Step-by-step explanation:
Multiply all numbers together.
2 * 4 * 3 * 8 = 192
Answer:
it's 192 because you have to multiply all of the numbers to get 192
Which word MOST affects the tone of this sentence?
A slender woman walked into the room wearing a pink dress and a gaudy hat.
A- room
B- gaudy
C- woman
D- slender
Answer:
B
Step-by-step explanation:
Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. FH is ___________.
Answer:
FnH = {Meagan}
Step-by-step explanation:
Given the following sets and events:
S = {Albert, Betty, Abel, Jack, Patty, Meagan}
F = {Betty, Patty, Meagan},
H = {Abel, Meagan}
P = {Betty, Abel}.
In order to get FnH
The intersection of F and H is the element that is common to both sets. Hence for the set given, we can see that Meagan is common to both sets, therefore:
FnH = {Meagan}
At a concession stand; three hot dogs and two hamburgers cost $9.75; two hot dogs and three hamburgers cost $10.25. Find the cost of one hot dog and the cost of one hamburger.
9514 1404 393
Answer:
hot dog: $1.75hamburger: $2.25Step-by-step explanation:
Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...
3x +2y -9.75 = 0
2x +3y -10.25 = 0
We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:
3, 2, -9.75, 3
2, 3, -10.25, 2
Now, we can form differences of cross-products in adjacent pairs of columns:
d1 = (3)(3) -(2)(2) = 9 -4 = 5
d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75
d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25
Then the solutions are found from ...
1/d1 = x/d2 = y/d3
x = d2/d1 = 8.75/5 = 1.75
y = d3/d1 = 11.25/5 = 2.25
The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.
_____
Additional comment
This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.
For a given pair of columns with coefficients ...
a b
c d
The cross-product we form is ad -cb.
When the function f(x) = 4(2)x is changed to f(x) = 4(2)x − 13, what is the effect? (5 points)
Select one:
a. There is no change to the graph because the exponential portion of the function remains the same.
b. The x-intercept is 13 spaces higher.
c. The y-intercept is 13 spaces lower.
d. All input values are moved 13 spaces to the left.
Answer:
C
If x = o then f(0) = 4(2) * 0 = 0
If f(x) = 4(2) 0 - 13
then f(x) = -13 at x = 0
Answer:
it will indeed be c
Step-by-step explanation:
deesnuts
If you were going to install a new window in your bathroom, what needs to be measured? What
else might you need to consider?
measure horizontally
measure vertically
measure depth..
31
?
40
Find the measure of the indicated angle to the nearest whole degree.
Answer:
51°
Step-by-step explanation:
Reference angle (θ) = ?
Opposite side length = 31
Hypotenuse length = 40
Apply SOH, which is;
Sin θ = Opp/Hyp
Plug in the values
Sin θ = 31/40
θ = sin^{-1}(31/40)
θ = 51° (neatest whole degree)
Given the equation y/x = -6/7 the constant of variation is:
Answer:
[tex]{ \tt{ \frac{y}{x} = - \frac{6}{7} }} \\ { \tt{y = - \frac{6}{7}x }} \\ { \boxed{ \bf{constant = - \frac{6}{7} }}}[/tex]
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total surface area of the prism. Please explain.
a) 315 cm2 squared
b) 480 cm2 squared
c) 510 cm2 squared
d) 570 cm2
Answer:
Option (C)
Step-by-step explanation:
Surface area of a right prism = 2(Area of the triangular base) + Ph
Here, P = Perimeter of the base
h = Height of the prism
Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]
= [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Height of the prism = 15 cm
Perimeter of the base = (5 + 12 + 13)
= 30 cm
Surface area of the right prism = 2(30) + 30(15)
= 60 + 450
= 510 cm²
Therefore, Option (C) will be the correct option.
Solve for x Round to the nearest tenth one place after the decimal !
Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4
Please help, I really need this
9514 1404 393
Answer:
(a) -- the correct choice is highlighted
Step-by-step explanation:
The units of specific heat tell you what quantities make up the ratio.
[tex]\dfrac{390\text{ J}}{1\text{ kg$\cdot^\circ$C}}=\dfrac{-12.0\text{ J}}{0.012\text{ kg}\cdot\Delta T}\\\\\Delta T=\dfrac{-12.0}{0.012\cdot390}\ ^\circ\text{C}\approx-2.56\text{ $^\circ$C}[/tex]
The temperature will decrease by 2.56 C.
30 POINTS PLEASE HELP
Answer:
Answer:
Solution given:
f(x)=5x-3
let
y=f(x)
y=5x-3
interchanging role of x and y
x=5y-3
x+3=5y
y=[tex]\frac{x+3}{5}[/tex]
$o,
f-¹(x)=[tex]\frac{x+3}{5}[/tex]
we conclude that
f-¹(x)≠g(x)
Each pair of function are not inverses.
g(x)=x/5+3
let g(x)=y
y=x/5+3
interchanging role of x and y
x=y/5+3
x-3=y/5
doing crisscrossed multiplication
5(x-3)=y
y=5x-15
g-¹(x)=5x-15
So
g-¹(x)≠f-¹(x)
Each pair of function are not inverses.
The weight of bags of fertilizer is normally distributed with a mean of 50 pounds and standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh:
a. Between 45 and 55 pounds?
b. At least 56 pounds?
c. At most 49 pound?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
Normal Distribution:
[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]
For point a:
[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]
[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]
For point b:
[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]
For point c:
To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]
[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]
