Answer:
$6.60
Step-by-step explanation:
12% = 0.12
12% of $55 = 0.12 x 55
=6.6
So, $6.60
In a car lot, the ratio of the number of new cars to the number of preowned cars is 6 to 5. The total number of new and preowned cars on the lot is 66. If 4 new cars and 2 preowned cars are sold and are removed from the lot, what fraction of the remaining cars on the lot are preowned?
The fraction of the remaining cars in the lot that are preowned is 7/15
In order to determine the fraction of the remaining cars in the lot that are preowned, we have to first determine the total number of new cars and preowned cars before the sale occurred.
Total number of preowned cars before the sales = (ratio of preowned cars / total ratio) x total number of cars
ratio of preowned cars = 5
total ratio = 6 + 5 = 11
total number of cars = 66
(5/11) x 66 = 30 cars
Total number of new cars before the sale = (ratio of new cars / total ratio) x total number of cars
ratio of new cars = 6
total ratio = 6 + 5 = 11
total number of cars = 66
(6/11) x 66 = 36 cars
Total number of new cars after the sale = total number of new cars before the sale - number of new cars sold
36 - 4 = 32
Total number of preowned cars after the sale = total number of preowned cars before the sale - number of preowned cars sold
30 - 2 = 28
The fraction of the remaining cars on the lot that are preowned = number of preowned cars after the sale / total number of cars on the lot after the sale
total number of cars on the lot after the sale = 28 + 32 = 60
28/60
to convert to the simplest term, divide the numerator and the denominator by 4
7/15
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Which expression is equivalent to 6x3 + 3y2 – 5x3 + 2y2?
Answer:
The answer is c because6X^3 minus 5X^3 is just X^3 and 3Y^2 plus 2Y^2 is 5Y^2.
I need you guy’s help answer thanks so much
Answer:
B. 7i
Step-by-step explanation:
first we need to find the root of the expression
[tex]\sqrt{-49} = \sqrt{49} *\sqrt{-1} \\ \\ \sqrt{49} = 7\\\\and\\\\ \sqrt{-1} = i[/tex]
so the answer is B. 7i
which function is positive for the entire interval (-3,-2)
Answer:
There can be several such functions; however, the basic condition that needs to be met for a function to be positive for the interval [–3, –2] is that it should be multiplied by (-1) Hence, one such function that is positive for the entire interval is f(x) = -x
Step-by-step explanation:
You randomly select one card from a 52-card deck. Find the probability of selecting the 9 of spades or the 3 of clubs.
The probabilitiy is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
2/52=1/26
Step-by-step explanation:
Y<3/2•x-4
Match the equation to a graph.
Answer:
Last option
Step-by-step explanation:
The slope 3/2 determines the line (although you can plot points to find (0,-4) and (4,2), connecting them, you'll get the equation of the line, and the area it covers will be to the right side, putting x = 0, y<-4, which is below the line, that's how you determine it.
Answered by GAUTHMATH
Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)
Answer:
A)
[tex]k=0[/tex]
B)
[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]
C)
[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]
A)
Given that h(1) = 20, we want to find k.
h(1) = 20 means that h(x) = 20 when x = 1. Substitute:
[tex]\displaystyle (20) = 20e^{k(1)}[/tex]
Simplify:
[tex]1= e^k[/tex]
Anything raised to zero (except for zero) is one. Therefore:
[tex]k=0[/tex]
B)
Given that h(1) = 40, we want to find 2k + 1.
Likewise, this means that h(x) = 40 when x = 1. Substitute:
[tex]\displaystyle (40) = 20e^{k(1)}[/tex]
Simplify:
[tex]\displaystyle 2 = e^{k}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]
By definition, ln(e) = 1. Hence:
[tex]\displaystyle k = \ln 2[/tex]
Therefore:
[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]
C)
Given that h(1) = 10, we want to find k - 3.
Again, this meas that h(x) = 10 when x = 1. Substitute:
[tex]\displaystyle (10) = 20e^{k(1)}[/tex]
Simplfy:
[tex]\displaystyle \frac{1}{2} = e^k[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]
Therefore:
[tex]\displaystyle k = \ln \frac{1}{2}[/tex]
Therefore:
[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]
Jill records the temperature outside every hour for 4 hours. She finds that the temperature dropped by the same amount each hour. After 4 hours, she finds that the temperature dropped a total of 20∘F. She writes this number sentence.
(−20)÷4=−5
What does the number sentence mean?
The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.
The total number of drops, 20, divided by 4 hours equals 5 times per hour. The temperature dropped 5 times per hour.
The total number of hours, 20, divided by 4∘F equals 5 hours. The temperature dropped once every 5 hours.
The total drop in temperature, −20∘F, divided by 4∘F in the first hour, equals −5 drops. The temperature dropped 5 times.
Answer:
It is the first one, The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.
Step-by-step explanation:
♥️♥️♥️♥️♥️♥️♥️♥️♥️ help me
9514 1404 393
Answer:
AC = 2.0 mm = 41.3 kgStep-by-step explanation:
The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.
__
a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).
The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)
These are equal, so we have ...
16(AC -1.5) = 7(3 -AC)
16AC -24 = 21 -7AC . . . . . eliminate parentheses
23AC = 45 . . . . . . . . . . . add 7AC+24
AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC
AC ≈ 2.0 meters . . . . rounded to 1 dp
__
b) The torques in this scenario are ...
M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m
M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M
M = 41.3 kg . . . . rounded to 1 dp
_____
Additional comment
Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.
A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups. Using the data provided below, conduct an F-test to determine whether you believe there is an association between race and average age at marriage.
Race N Mean
Black 113 25.39
White 904 22.99
Other 144 23.87
All Groups 1,161 23.33
Answer:
The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )
Step-by-step explanation:
Conducting an F-test to determine association between race and average age at marriage
step 1 : State the hypothesis
H0 : ц1 = ц2 = ц3
Ha : ц1 ≠ ц2 ≠ ц3
step 2 : determine the mean square between
Given mean value of all groups = 23.33
SS btw = 113*(25.39 - 23.33)² + 904*(22.99 - 23.33)² + 144*(23.89 - 23.33)^2 = 113(4.2436) + 904(0.1156) + 144(0.3136)
= 629.1876
hence: df btw = 3 - 1 = 2
df total = 1161 - 1 = 1160
df within = 1160 - 2 = 1158
SS within = 36.87*1158 = 42695.46
Therefore the MS between = 629.19 / 2 = 314.60
The F-ratio = 314.59 / 36.87 = 8.53
using the values for Btw the P-value = 0.00021
The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )
Points T, R, and P, define _____Points B, A, and E are:
Point A is located at (2, 4). Point B is located at (-2, 4). Point C is located at (-2, -4). Point D is located at (2, -4). Point E is located at (4, 4).
Answer:
Point T,R,P not seen how I don't understand your question.
A bucket contains 4 red balls that are numbered 1, 2, 3, 4. It also contains 6 black balls that are numbered 5, 6, 7, 8, 9, 10. Two balls are drawn from the bucket, one at a time, without replacement. Use this information to answer the following probability questions. Express answers as fractions, or round decimal answers to 4 decimal places. a. What is the probability that the first ball is even and the second ball is odd
The probability is 1/9
We want to find the probability that the first drawn ball is even, and the second is odd.
The probability of randomly drawing an even ball will be equal to the quotient between the number of balls with even numbers and the total number of balls in the bucket.
We have a total of 10 balls (4 red ones and 6 black ones)
and 5 of these have even numbers (2, 4, 6, 8, 10)
Then the probability of drawing a ball with an even number first is:
p = 5/10 = 1/5
now we want to get a ball with an odd number.
notice that we already got a ball with an even number and we did not replace it, so now there are 9 balls left in the bucket, 5 odd ones, and 4 even ones.
The probability of getting an odd ball is computed in the same way thana above, as the quotient between the number of balls with odd numbers (5) and the total number of balls in the bucket (9)
q = 5/9
The joint probability (the probability that these two events happen together) is equal to the product of the individual probabilities, so we will get:
P = p*q = (5/9)*(1/5) = 1/9
The probability is 1/9
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Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
Volume 1=27m³
Volume 2=13m³
Volume 3= 23m³
|x|+|x+1|+|x+2|+|x+3|+...+|x+2021=2021x
Answer:
jo pahle wale X hai na na X + x plus 1 unhen Yad Karke answer 1 aaega FIR X + 2 =_= + 3 X + 3 yah answer Aaya 1 or 2 X + ka ok
Step-by-step explanation:
FIR hai x+ x and ++ 2021 x
2021x
FIR + Kannan donon ko x
ans
x - 3 X
x - 4042
yah answer aayega ine donon ka the solve this question ok friend
Question
(X-5y/y3)-1=
Answer:
[tex]x = y^3+5y[/tex]
Step-by-step explanation:
Complete question
[tex]\frac{x - 5y}{y^3} - 1=0\\[/tex]
Required
Solve for x
We have:
[tex]\frac{x - 5y}{y^3} - 1=0[/tex]
Collect like terms
[tex]\frac{x - 5y}{y^3} = 1[/tex]
Multiply through by [tex]y^3[/tex]
[tex]x - 5y = y^3[/tex]
Make x the subject
[tex]x = y^3+5y[/tex]
A 500-kg concrete block 95 cm longcm wide and cm high. It can exert three different pressures on a horizontal surface depending on which faceit rests on the highest pressure is
Pressure is force per unit area. If the block is sitting at rest on the surface, it applies a pressure of mg/A, where mg is the block's weight and A is the area of the face that makes contact with the surface.
The smaller the value of A, the larger the pressure. So the highest pressure the block can exert is achieved when it's resting on the face with the smallest dimensions.
If the block is a cube with side length 95 cm, then the pressure exerted by each face is the same.
A number plus 16 times its reciprocal equals 8. Find all possible values for the number.
Answer:
4
Step-by-step explanation:
[tex]n+16\frac{1}{n} = 8\\\\n^2+16=8n\\n^2 -8n+16=0\\[/tex]Factorizing we get the answer 4
Heather, a sociology major is interested in studying mass media topics. She is particularly interested in the percentage of mass media topics that relate to entertainment. Based on previous research, 72% of mass media topics relate to entertainment. She suspects this percent is different. During the process of hypothesis testing, she calculates a probability using the test statistic. What is the probability associated with the test statistic called
Answer:
Pvalue
Step-by-step explanation:
The Pvalue measure which takes up a value in the range 0 - 1 is a statistical measure used on hypothesis testing to measure the likelihood of obtaining result atleast as extreme as the outcome of the statistical hypothesis test, The Pvalue is used in hypothesis testing to make a case for the alternative hypothesis, which involves being compared with the α - value.
Lower p values favors the adoption of alternative depending on how extreme th α-value is. The Pvalue is dependent on the value if the test statistic.
A 90% confidence interval is (35 45). What is the margin of error?
A. 5
B.4.5
C.9
D.10
Answer:
option A 5
I hope it's correct
.....
2 1 /2 + 3 1 /3 + 1 5/6 =
Answer:
10 2/3 is ther answer simplified
Step-by-step explanation:
7 2/3
(Decimal: 7.666667)
If Ahmad’s balance is $85, what will the minimum payment be?
his balance will be 20 dollars
What is the remainder when x2+ 3 is divided by x - 1?
Answer:
Step-by-step explan
Multiply:
2 × (–21) × 7
A)
294
B)
–273
C)
–7
D)
–294
Answer:
[tex]2\times \left(-21\right)\times \:7[/tex]
PEMDAS order of operations:
[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]
[tex]=-42\times \:7[/tex]
[tex]=-294[/tex]
D) -294 is your answer
OAmalOHopeO
Stuck on this one!!
Shelly believes the honor roll students at her school have an unfair advantage in being assigned to the math class they request. She asked 500 students at her school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received math class requested 125 215 340
Did not get math class requested 80 80 160
Total 205 295 500
Help Shelly determine if all students at her school have an equal opportunity to get into the math class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Answer: No, there isn't equal opportunity
======================================================
Explanation:
Let's define the two events
A = person is on the honor rollB = person got the math class they requestedFrom the table, we see that
P(B) = 340/500 = 0.68
meaning that there's a 68% chance of picking someone who got the class they wanted (i.e. 68% of the people got the class they wanted)
------------
Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.
So,
P(B given A) = 125/205 = 0.609756
which rounds to 0.61
This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.
The chances have gone down from 68% to 61% roughly.
------------
It appears that being on the honor roll does affect your chances of getting into the class you want.
Therefore, all students do not have the same equal opportunity.
We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.
All students do not have equal opportunity.
From the table, we have the following parameters:
205 people are on honor roll call340 people got the math class requested500 people were surveyedThe above means that:
The probability that a person is on honor roll call is:
p1 = 205/500
p1 = 0.41
The probability that a person got the math class requested
p2 = 340/500
p2 = 0.68
Both probabilities are not equal.
Hence, it is true that all students do not have equal opportunity.
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Which expression is equivalent to
128xy
5 ? Assume x > 0 and y> 0.
2xy5
Moto
8
yax
8
BV
y
8.VY
X
Answer:
[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{128x^8y^3}[/tex] --- the complete expression
Required
The equivalent expression
We have:
[tex]\sqrt{128x^8y^3}[/tex]
Expand
[tex]\sqrt{128x^8y^3} = \sqrt{128* x^8 * y^3}[/tex]
Further expand
[tex]\sqrt{128x^8y^3} = \sqrt{64 * 2* x^8 * y^2 * y}[/tex]
Rewrite as:
[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2* 2 * y}[/tex]
Split
[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2} * \sqrt{2 * y}[/tex]
Express as:
[tex]\sqrt{128x^8y^3} = (64 * x^8 * y^2)^\frac{1}{2} * \sqrt{2y}[/tex]
Remove bracket
[tex]\sqrt{128x^8y^3} = (64)^\frac{1}{2} * (x^8)^\frac{1}{2} * (y^2)^\frac{1}{2} * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 * x^\frac{8}{2} * y^\frac{2}{2} * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 * x^4 * y * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]
Which expression is equivalent to (4x^(3)y^(5))(3x^(5)y)^(2)
Answer:
[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]
Step-by-step explanation:
Given
[tex](4x^3y^5)(3x^5y)^2[/tex]
Required
The equivalent expression
We have:
[tex](4x^3y^5)(3x^5y)^2[/tex]
Expand
[tex](4x^3y^5)(3x^5y)^2 = 4x^3y^5*9x^{10}y^2[/tex]
Further expand
[tex](4x^3y^5)(3x^5y)^2 = 4*9*x^3*x^{10}y^5*y^2[/tex]
Apply laws of indices
[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]
If lan does a job in 132 hours and with the help of Danielle they can do it together in 44 hours, how long
would it take Danielle to do it alone
Answer:
88 hours
Step-by-step explanation:
Ian = 132
Daniel + Ian = 44
Daniel = Ian - 44
= 132-44 = 88 hours
plz help with this:)
9514 1404 393
Answer:
-4
Step-by-step explanation:
The point (x, y) = (0, 0) is on the line, so it represents a proportional relation. Any ratio of y to x will be the slope. The choice that makes this computation easiest is ...
x = 1, y = -4
y/x = -4/1 = -4
The slope of the line is -4.
Quadrilateral JKLM is rotated - 270° about the origin.
Draw the image of this rotation
Need a visual answer please! Thanks!
Answer:
Step-by-step explanation:
When the quadrilateral JKLM is rotated - 270° about the origin then the image of rotated quadrilateral is shown below.
What is rotation?"It is a transformation in which the object is rotated about a fixed point. "
For given question,
Quadrilateral JKLM is rotated - 270° about the origin.
This means, quadrilateral JKLM is rotated 270° clockwise about the origin.
We know, if point P(x, y) is rotated 270° clockwise or 90° anticlockwise then the coordinated of rotated point would be (-y, x).
From figure, the coordinates of the quadrilateral JKLM are:
J = (3, 3)
K = (5, -5)
L = (-3, -7)
M = (3, -3)
After rotating -270° about the origin the coordinates of the quadrilateral would be,
J' = (-3, 3)
K' = (5, 5)
L' = (7, -3)
M' = (3, 3)
And the image of the rotated quadrilateral J'K'L'M' is shown below.
Therefore, when the quadrilateral JKLM is rotated - 270° about the origin then the image of rotated quadrilateral is shown below.
Learn more about rotation here:
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Which matrix equation represents the system of equations?
{-x+ 2y = 0
y= -2
We are given a system of equations,
[tex]\begin{cases}-x+2y=0\\y=-2\\ \end{cases}[/tex]
This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),
[tex]\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}[/tex]
The matrix will then be applied to the vector (lower dimensions on top),
[tex]\begin{bmatrix}x\\y\\ \end{bmatrix}[/tex]
And the result vector will be whats on the other side of equals sign,
[tex]\begin{bmatrix}0\\-2\\ \end{bmatrix}[/tex]
So to put everything together,
[tex]\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\begin{bmatrix}x\\y\\ \end{bmatrix}=\begin{bmatrix}0\\-2\\ \end{bmatrix}[/tex]
Hope this helps :)
