Answer:
sale prices = $252
Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252
Answer:
$189
Step-by-step explanation:
10% of 210 = 21
210 - 21 = 189
A rocket moves through outer space at 10,500 m/s. At this rate how much time would be required to travel the distance from Earth to the moon, which is 380,000 km?
Answer:
The answer is around 27.63 seconds.
Step-by-step explanation:
1 km equals 1000 meters so we have to multiply 10,500 and 1,000 which would equal 10,500,000 km. 10,500,000 divided by 380,000 which is around 27.63 seconds.
The lengths of nails produced in a factory are normally distributed with a mean of 5.02 centimeters and a standard deviation of 0.05 centimeters. Find the two lengths that separate the top 6% and the bottom 6%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
The length that separates the top 6% is 5.1 centimeters.
The length that separates the bottom 6% is 4.94 centimeters.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 5.02, \sigma = 0.05[/tex]
Find the two lengths that separate the top 6% and the bottom 6%.
Top 6%:
The 100-6 = 94th percentile, which is X when Z has a pvalue of 0.94. So X when Z = 1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.555 = \frac{X - 5.02}{0.05}[/tex]
[tex]X - 5.02 = 1.555*0.05[/tex]
[tex]X = 5.1[/tex]
So the length that separates the top 6% is 5.1 centimeters.
Bottom 6%:
The 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 5.02}{0.05}[/tex]
[tex]X - 5.02 = -1.555*0.05[/tex]
[tex]X = 4.94[/tex]
The length that separates the bottom 6% is 4.94 centimeters.
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
x²- 5²
(x+5)(x-5)
Step-by-step explanation:
Area of shaded region: area of square with side x - area of square with side 5
A= x²- 5²
A= (x+5)(x-5)
What is 27 ÷ 4 rounded to the nearest tenth?
Answer:
6.8
Step-by-step explanation:
27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.
what is the midpoint of the segment shown below?
(1, 2) (1,-5)
A. (1, -3/2)
B. (2, -3/2)
C. (2, -3)
D. (1, -3)
Answer:
The answer is A (1,-3/2)
Step-by-step explanation:
Add both x coordinates, divide by 2
Add both y coordinates, divide by 2
85 points!! | All of the following expressions have the same value, when x= -2 and y= 4, except
-2xy
0-4x2
0x²y
0 (-2) ²y
Answer:
They have two sets of equal answers...
Step-by-step explanation:
-2 * 2 * 4 = -16
0 - 4 * -2 * -2 = -16
0 * -2 * -2 * 4 = 0
0 * 4 * 4 = 0
At the beginning of the season,jamie pays full price for a ticket to see the panthers,her favorite baseball team.
Corrected Question
At the beginning of the season, Jamie pays full price($49.64) for a ticket to see the panthers, her favorite baseball team. Ticket prices decrease $0.41 for every game the panthers lose this season. the panthers currently have 33 wins and 31 losses.
(a)Represent the total change in the cost of a ticket given their losses.
(b) What is the cost of a ticket for the next game they play?
Answer:
(a)$(49.64-0.41x)
(b)$36.93
Step-by-step explanation:
(a)Cost of a Full Ticket =$49.64
Let x be the number of losses
The ticket price reduces by $0.41 for every loss
Therefore:
Ticket Price after x losses =$(49.64-0.41x)
Therefore, total change in the cost of a ticket given their losses=$(49.64-0.41x)
(b)For this season the Panthers has suffered 31 losses.
Number of Losses, x=31
Therefore, cost of a ticket for the next game they play
= $(49.64-0.41*31)
=49.64-12.71
=$36.93
A sports shop sells tennis rackets in 4 different weights, 2 types of string, and 3 grip sizes. How many different rackets
could they sell?
O 32
O 18
0 24
0 9
Answer: C) 24
Step-by-step explanation:
first we take down the information given to us
sports shop sells rackets in
4 different weights
2 types of strings
3 grip sizes
Now to get the number of different rackets they could sell, you simply take the multiplication of the number of racket gripe sizes, the types of strings and different weights they sell
so
4 * 2 * 3 = 24
therefore the sport shop could sell up to 24 different rackets .
Answer:
24
Step-by-step explanation: got it right on my test
Identify a reason why we should be skeptical of any claim or statistical evidence involving the following: A study shows that during the early 20th century, a strong correlation existed between the number of people who owned radios and the number of people put into insane asylums. Therefore, people who owned a radio were more likely to be declared insane and put into an insane asylum.a. correlation does not imply causality b. misleading graph c. self-interest survey d. voluntary response survey
Answer:
Option A
Step-by-step explanation:
Correlation does not imply causality. Correlation shows whether and how strongly pairs of variables are related.
Causality shows a situation between two events where one event is affected by the other
We would be skeptical of this survey because it is very difficult to assume that people who owned a radio were more likely to be declared insane and put into an insane asylum as listening to the radio cannot cause insanity unless proven.
Which expression is equivalent to (2g^3+4)^2
[tex]answer \\ 4g ^{6} + 16 \\ solution \\ ( {2g}^{3} + 4)^{2} \\ = 2 \times 2 \: g ^{3 \times 2} + 4 \times 4 \\ = 4 {g}^{6} + 16 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
4g^6+16 IS equivalent to (2g^3+4)^2
Which expression is equivalent to the given expression? (3m-4)^3(3m^5)
Answer: D.
Step-by-step explanation:
You want to cube each term in the parentheses. When you take an exponent to an exponent, you just multiply them. You get (27m^-12). In order to get rid of that negative exponent, you should put a one over the m term and make -12, +12:
[tex](\frac{27}{m^12} )(3m^5)[/tex]
Multiply the numerators to get:
[tex]81m^5[/tex]
You now have:
[tex]\frac{81m^5}{m^12}[/tex]
When you divide exponents, you subtract them. 5 - 12 = -7
You have m^-7 which is the same as 1/m^7. Finally, mulitply that by the 81 we left out to get the answer of D.
The expression equivalent to the given expression (3m⁻⁴)³(3m⁵) is 81/m⁷. So, option D is correct.
What is exponentiation?Exponentiation is a mathematical operation that involves two numbers, the base b, and the exponent or power n, and is pronounced as "b raised to the power of n." It is written as bⁿ and is pronounced as "b raised to the power of n."
When n is a positive integer, bⁿ = b × b × b ×...× b
and b⁻ⁿ = 1/bⁿ
If n = 0, then b⁰ = 1.
How to solve this problem?Here, (3m⁻⁴)³(3m⁵) = (3³)(m⁻⁴)³(3m⁵) = (27m⁻¹²)(3m⁵) = 81m⁵⁻¹² = 81/m⁷
Therefore, the expression equivalent to the given expression (3m⁻⁴)³(3m⁵) is 81/m⁷. So, option D is correct.
Learn more about exponentiation here -
https://brainly.com/question/14513824
#SPJ2
Given F1 = ∑ m(0,2,5,7,9) and F1 = ∑ m(2, 3,4,7,8) find the minterm expression for F1+F2. State a general rule for finding the expression for F1+F2 given the minterm expansions for F1 and F2. Prove your answer by using the general form of the minterm expansion.
Answer:
Step-by-step explanation:
The question tells us that;
Given F1 = ∑ m(0,2,5,7,9) and F1 = ∑ m(2, 3,4,7,8) find the minterm expression for F1+F2. State a general rule for finding the expression for F1+F2 given the minterm expansions for F1 and F2. Prove your answer by using the general form of the minterm expansion.
Note: The answer is provided in the image uploaded below
cheers i hope this helped !!!
Solve: x - 1 < 3 help me plssss
Answer:
x =2
Step-by-step explanation:
becaue 2-1 is smaller than 3
Answer:
Hello!
I believe your answer is:
x=2
If this is not correct, please let me know and I will try again!
Step-by-step explanation:
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use? Step 1 We need to find a so that P(X ≥ a) =
Answer:
The number of minutes advertisement should use is found.
x ≅ 12 mins
Step-by-step explanation:
(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)
Step 1For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.
Probability Density Function is given by:
[tex]f(t)=\left \{ {{0 ,\-t<0 }\atop {\frac{e^{-t/\mu}}{\mu}},t\geq0} \right. \\[/tex]
Consider the second function:
[tex]f(t)=\frac{e^{-t/\mu}}{\mu}\\[/tex]
Where Average waiting time = μ = 2.5
The function f(t) becomes
[tex]f(t)=0.4e^{-0.4t}[/tex]
Step 2The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01
The probability that a costumer has to wait for more than x minutes is:
[tex]\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt[/tex]
which is equal to 0.01
Step 3Solve the equation for x
[tex]\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01[/tex]
Take natural log on both sides
[tex]ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53[/tex]
ResultsThe costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger
In the first year if ownership, a new car lose 20% of its value. If a car lost $4,200 value in the first year, how much did the car originally cost?
Answer:
21,000$
Step-by-step explanation:
part to whole method
20/100 and 4,200/
How many 20s to get to 4,200?
Simplify 4^3•4^5.
help asap !
Answer:
D
Step-by-step explanation:
when there are exponents with same bases multiplied by each other, keep the base and add the exponents
4^(3)+4^(5)=4^8
4^8 is D in this question
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 1100 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?
Answer:
Length = 550 m
Width = 275 m
Area = 151,250 m2
Step-by-step explanation:
One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:
[tex]Perimeter = Length + 2*Width = 1100\ m[/tex]
And the area of the farmland is given by:
[tex]Area = Length * Width[/tex]
From the Perimeter equation, we have that:
[tex]Length = 1100 - 2*Width[/tex]
Using this in the area equation, we have:
[tex]Area = (1100 - 2*Width) * Width[/tex]
[tex]Area = 1100*Width - 2*Width^2[/tex]
Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:
[tex]Width = -b/2a[/tex]
[tex]Width = -1100/(-4)[/tex]
[tex]Width = 275\ m[/tex]
This width will give the maximum area of the farmland. Now, finding the length and the maximum area:
[tex]Length = 1100 - 2*Width = 1100 - 550 = 550\ m[/tex]
[tex]Area = Length * Width = 550 * 275 = 151250\ m2[/tex]
What is the quotient if 3/8 of 30 is divided by 15/16 of 5/10?
Answer:
24
Step-by-step explanation:
That would be:
(3/8)(30)
---------------
(15/16)(1/2)
This can be reduced in various ways. First, divide that 30 by 15, obtaining:
6/8
-----------
1/32
Now invert the divisor (1/32) and multiply:
(6/8)(32/1)
This reduces to 6*4, or 24.
A fuel oil tank is an upright cylinder, buried so that its circular top is 8 feet beneath ground level. The tank has a radius of 6 feet and is 18 feet high, although the current oil level is only 12 feet deep. Calculate the work required to pump all of the oil to the surface. Oil weighs 50\, \hbox{lb/ft}^3.
Answer:
1.504×10⁶ ft·lb
Step-by-step explanation:
We understand the top of the oil in the tank is 12 ft below ground level, and the bottom of the tank is 8+18=26 ft below ground level. Then the average depth of the oil is (12+26)/2 = 19 ft below ground level.
The height of the oil in the tank is 26-12=14 ft, so the volume of it is ...
V = πr²h = π(6 ft)²(14 ft) = 504π ft³ ≈ 1583.36 ft³
__
So, the work required to raise that volume of oil to the surface is ...
(1538.36 ft³)(50 lb/ft³)(19 ft) = 1.504×10⁶ ft·lb
Convert 5613, base 10 to
base 8
Answer:
12755 base-8
Step-by-step explanation:
You’re welcome :) please brainliest me btw.
Triangle XYZ is translated so that X’ is that (4,-2) which rule defines this translation?
Answer: y
Step-by-step explanation:
a is directly proportional to b. When a is 6, b is 72. Find b when a is 8. 3
Answer:
a) "K" is proportional Constant K= 0.0833
b) The value of b = 99.639
Step-by-step explanation:
Explanation :-
Given 'a' is directly proportional to 'b'
a ∝ b
a = k b ....(i)
where "K" is proportional Constant
Case(i):-
when a =6 and b=72
a = k b
⇒ 6 = k (72)
⇒ [tex]K = \frac{6}{72} = \frac{1}{12} = 0.0833[/tex]
Case(ii):-
Given a = 8.3
a = k b
⇒ 8.3 = 0.0833 ×b
⇒ [tex]b = \frac{8.3}{0.0833} = 99.639[/tex]
Final answer:-
a)"K" is proportional Constant K= 0.0833
b) The value of b = 99.639
An item is regularly priced at 40$. It is. On sale for 30% off the regular price. How much (in dollars) is discounted from the regular price?
Answer:
Step-by-step explanation:
12$
1. Is (6,7) a solution to the inequality y> 2x - 5?
2. Mathematically prove that it is or isn't below.
Answer:
[tex]\fbox{\begin{minipage}{8em}Not a solution\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Consider the assumption:
Generally, [tex](6, 7)[/tex]) is supposed to be the pair of 2 components, in which, the first component is x-component (domain), the second component is y-component (range).
Hence, [tex]x = 6, y = 7[/tex]
Step 2: Substitute [tex]x[/tex] and [tex]y[/tex] into the inequality
[tex]y > 2x - 5[/tex]
<=> [tex]7 > 2*6 - 5[/tex]
Step 3: Simplify
<=> [tex]7> 12 - 5[/tex]
<=> [tex]7 > 7[/tex]
Step 4: Evaluate
Invalid
Reason: [tex]7 = 7[/tex]
Step 5: Conclude
[tex](6, 7)[/tex] is not a solution to the inequality [tex]y > 2x - 5[/tex]
Hope this helps!
:)
Which expression is equivalent to 3(x-6)+5(x-4)
Answer:
[tex]8x-38[/tex]
Step-by-step explanation:
[tex]3(x-6)+5(x-4)\\3x-18+5x-20\\3x+5x-18-20\\8x-38[/tex]
In a group, 10 freshmen have mean GPA of 3.5; 20 sophomores have a mean GPA of 2.9; 25 juniors have a mean GPA of 3.2; and 15 seniors have a mean GPA of 3.4. What is the mean of the entire group
Answer:
[tex] T_1 = 10*3.5 = 35[/tex]
[tex] T_2 = 20*2.9 = 58[/tex]
[tex] T_3 = 25*3.2 = 80[/tex]
[tex] T_4 = 15*3.4 = 51[/tex]
[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n_1= 10 , \bar X_1 = 3.5[/tex] for freshmen
[tex] n_2= 20 , \bar X_2 = 2.9[/tex] for sophomores
[tex] n_3= 25 , \bar X_3 = 3.2[/tex] for juniors
[tex] n_4= 15 , \bar X_4 = 3.4[/tex] for seniors
For this case we can use the formula for the sample mean in order to find the total of each group:
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]T= \sum_{i=1}^n X_i = n *\bar X[/tex]
And replacing we got:
[tex] T_1 = 10*3.5 = 35[/tex]
[tex] T_2 = 20*2.9 = 58[/tex]
[tex] T_3 = 25*3.2 = 80[/tex]
[tex] T_4 = 15*3.4 = 51[/tex]
And the grand mean would be given by:
[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]
A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively. A sample of four pages is selected without replacement, and X and Y denote the number of pages with moderate and high graphics output in the sample. Determine: a. fxy(x, y) b. fx(x) c. E(X) d. fyß(y) e. E(Y | X = 3) g. Are X and Y independent?
Answer:
Step-by-step explanation:
Given that:
A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively.
. A sample of four pages is selected without replacement,
Let X and Y denote the number of pages with moderate and high graphics output in the sample
We are meant to determine
a) [tex]f_{XY}(x, y)[/tex] from the given data in the question;
However; the probability mass function can be expressed via the relation:
[tex]f_{XY}(x,y) = \dfrac{(^{30} _x ) ( ^{10} _y ) (^{60} _ {4-x-y} ) }{ ( ^{100}_4)}[/tex]
We can now have a table shown as :
[tex]X|Y[/tex] 0 1 2 3 4 Total [tex]f_X(x)[/tex]
0 0.1244 0.0873 0.02031 0.0018 0.0001 0.234
1 0.2618 0.13542 0.02066 0.00092 0 0.419
2 0.1964 0.0666 0.00499 0 0 0.268
3 0.0621 0.01035 0 0 0 0.073
4 0.0069 0 0 0 0 0.007
Total [tex]F_Y(y)[/tex] 0.6516 0.2996 0.0460 0.0028 0.0001 1
b) [tex]f_X(x)[/tex]
The marginal distribution definition of [tex]f_X(x)[/tex][tex]= P(X=x)[/tex]
[tex]f_X(x)[/tex] [tex]= \sum P(X=x, Y=y)[/tex]
From the table above ; the corresponding values of [tex]f_X(x)[/tex] are :
X 0 1 2 3 4
[tex]f_X(x)[/tex] 0.234 0.419 0.268 0.073 0.007
( since [tex]f_X(x)[/tex] represent the vertical column)
c) E(X)
By using the expression [tex]E(x) = \sum ^4 _{x= 0} x f_X(x)[/tex]
we have:
E(X) = [tex]0*0.234+1*0.419+ 2*0.268+3*0.073+4*0.007[/tex]
E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028
E(X) = 1.202
d) fyß(y)
Using the thesis of conditional Probability; we have :
[tex]P(A|B) = \dfrac{ P(A,B) }{ P(B) }[/tex]
The conditional probability for the mass function is then:
[tex]f_{Y|X=3}(y) = \dfrac{f_{XY}(3,y)}{f_{X}(x)}[/tex]
where;
[tex]f_X(3) = 0.0725[/tex]
values of [tex]f_{XY} (3,y)[/tex] for every y ∈ (0,1,2,3,4)
Therefore; the mass function is:
[tex]Y|{_X_3}:\left[\begin{array}{ccccc}0&1&2&3&4\\0.857&0.143&0&0&0\\ \end{array}\right][/tex]
e) E(Y | X = 3)
By using the expression [tex]E(Y|X=3) = \sum ^4 _{y= 0} y f_{y \beta} \ (y|x)[/tex]
we have:
⇒ [tex]0 * 0.857 + 1*0.143 +0 +0+0[/tex]
= 0.143
The value of E(Y | X = 3) = 0.143
g) Are X and Y independent?
To Check if X and Y independent; Let assume if [tex]f_{XY}(x,y) = f_X(x)f_{Y}(y)[/tex] ; then we can say that X and Y are independent.
From the above previous table :
[tex]f_{(XY)} (0.4) = 0.0001[/tex]
[tex]f_X (0)[/tex] = 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001
[tex]f_X (0)[/tex] = 0.234
[tex]f_X (4)=0.0001 +0+0 \\ \\ = 0.001[/tex]
[tex]f_{X}(0) f_Y(4) = 0.234*0.0001[/tex]
[tex]f_{X}(0) f_Y(4) = 0.00002[/tex]
We conclude that [tex]f_{(XY)} (0.4) \neq f_X(0) f_Y(y)[/tex]; As such X and Y are said to be non - independent.
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
Volume of balloon = 4/3πr³
= 4/3(3.14)(0.5)³
= 0.52 cubic feet
Now
A helium tank contains 50 cubic feet of helium So,
Spherical balloons = 50/0.52
= 95.4
≈ 100
describe the slope of the graph from 1 sec to 5.3 sec ( is the slope positive, negative, zero or non existent)
Answer:
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
Where x for this case represent the time and y the height waist off ground.
We have one point that can be extracted from the graph on this case:
[tex] x_1 = 1, y_1= 3[/tex]
Bout for the other point we have:
[tex] x_2 = 5.3 , y_2 = 9.6[/tex]
Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:
[tex] m =\frac{9.6-3}{5.3-1}= 1.535[/tex]
And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft
Step-by-step explanation:
In order to calculate the slope we need to use the following formula:
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
Where x for this case represent the time and y the height waist off ground.
We have one point that can be extracted from the graph on this case:
[tex] x_1 = 1, y_1= 3[/tex]
Bout for the other point we have:
[tex] x_2 = 5.3 , y_2 = 9.6[/tex]
Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:
[tex] m =\frac{9.6-3}{5.3-1}= 1.535[/tex]
And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft
If P(A)=0.4, P(A and B)=0.2,and P(A or B)=0.5, What is P(B)
Answer:
[tex]\boxed{\ P(B)=0.3 \ }[/tex]
Step-by-step explanation:
Hi,
We know that
P(A or B)=P(A)+P(B)-P(A and B)
so P(B)= P(A or B) - P(A) + P(A and B)
so
P(B) = 0.5 - 0.4 + 0.2 = 0.3
thanks