a) The probability is P = 1/9
b) The probability is P = 1/3.
How to get the probability?First, we need to count the total number of outcomes (different cars that can be made with the given options):
There are 2 versions (electric and hybrid).There are 3 exterior colors (red, blue, green).There are 3 interiors (fabric, leather, vinyl)Then there are 2*3*3 = 18 different cars.
a) Picking a blue hybrid car with an interior that is not leather.
There are 2 cars that meet that condition:
blue hybrid with fabric.blue hybrid with vinyl.2 out of the 18 cars meet the condition, then the probability is:
P = 2/18 = 1/9
b) picking an electric car in a color other than blue is
The cars that meet the condition are:
Green electric with any interior (3 options here)Red electric with any interior (3 options here)So 6 out of the 18 cars meet the condition, then the probability is:
P = 6/18 = 1/3
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PLEASE HELP ME WITH THIS QUESTION
6
Answer:
45
Step-by-step explanation:
Assuming this is a trapezoid,
[tex]\frac{29+WZ}{2}=37 \\ \\ 29+WZ=74 \\ \\ WZ=45[/tex]
. x is directly proportional to y. When x = 5, y = 3. Work out the value
of y when x =9
Answer: y = 5.4
Step-by-step explanation: This is a proportional statement. So we can set up a system of proportions.
So we know when x is 5, y is 3. Thus, we can set up a proportion [tex]\frac{x}{y}[/tex] such that substituting will give [tex]\frac{5}{3}[/tex].
Now, we know when x is 9, y is some unknown number. So we can set up the second proportion as [tex]\frac{9}{y}[/tex].
Since 5/3 and 9/y are directly proportional, these 2 expressions are therefore equal. So we have [tex]\frac{5}3}[/tex] [tex]= \frac{9}{y}[/tex].
Cross multiplying, we get [tex]5y = 27[/tex].
Dividing by 5, we get [tex]y = 5.4[/tex]
Hope this helped!
Working together a small pipe and large pipe can fill a big pool in 6 hour. It takes the smaller pipe 5 hours longer than the large pipe to fill the big pool working alone. How long does it take the smaller pipe to fill the pool by itself ?
The time taken for the smaller pipe to fill the pool by itself is 15.71 hours
Rate of workTime taken for both pipes = 6 hoursTime taken for long pipe = xTime taken for small pipe = x + 6Rate of work of both pipes = 1/6Rate of work of long pipe = 1/xRate of work of small pipe = 1/x + 61/6 = 1/x + 1/(x+6)
1/6 = (x+6)+(x) / (x)(x+6)
1/6 = (x+6+x) / x²+6x
1/6 = (2x+6)(x² + 6x)
cross product1(x² + 6x) = 6(2x+6)
x² + 6x = 12x + 36
x² + 6x - 12x - 36 = 0
x² - 6x - 36 = 0
Using quadratic formulax = 9.71 or -3.71
The value of x cannot be negative
Therefore, the
Time taken for long pipe = x
= 9.71 hours
Time taken for small pipe = x + 6
= 9.71 + 6
= 15.71 hours
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The coefficient of 2(3)(6)Q is
The coefficient of 2(3)(6)Q is 2(3)(6)
How to determine the coefficient?The expression is given as:
2(3)(6)Q
For an expression
AQ
Where A is a number or product of numbers and Q is a variable
The number A represents the coefficient
By comparing:
AQ and 2(3)(6)Q
We have
A = 2(3)(6)
Hence, the coefficient of 2(3)(6)Q is 2(3)(6)
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Divide the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x. (27x 4 - 18x 3 + 9x 2) ÷ 3x
Answer:
9x3 - 6x2 + 3x
Step-by-step explanation:
(27x 4 - 18x 3 + 9x 2) ÷ 3x
Dividing each term between 3x we have:
9x3 - 6x2 + 3x
We can check the result:
(9x3 - 6x2 + 3x) * (3x)
= (27x4 - 18x3 + 9x2)
Find the Riemann sum for
f(x) = 2x − 1, −6 ≤ x ≤ 4,
with five equal subintervals, taking the sample points to be right endpoints.
Explain, with the aid of a diagram, what the Riemann sum represents.
Mathematically speaking, the Riemann sum of the linear function is represented by A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}, whose representation is represent by the graph in the lower left corner of the picture.
What figure represents a Riemann sum with right endpoints?
Graphically speaking, Riemann sums with right endpoints represent a sum of rectangular areas with equal width with excess area for positive y-values and truncated area for negative y-values generated with respect to the x-axis. Mathematically speaking, this case of Riemann sums is described by the following expression:
A ≈ [(b - a) / n] · ∑ f[a + i · [(b - a) / n]], for i ∈ {1, 2, ..., n}
Where:
a - Lower limit
b - Upper limit
n - Number of rectangles
i - Index of a rectangle
If we know that f(x) = 2 · x - 1, a = - 6, b = 4 and n = 5, then the Riemann sum with right endpoints of the area below the curve is:
A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}
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Find the square.
(7m-3) 2
49m²-21m-9
Step-by-step explanation:
(7m - 3)² = 49m² - 42m + 9
play it through and do the actual multiplication behind the square :
(7m - 3)² = (7m - 3)(7m - 3) =
= 7m×7m + 7m×(-3) + (-3)×7m + (-3)(-3) =
= 49m² - 2×21m + 9 = 49m² - 42m + 9
Which relation is also a function?
A.
A dot plot graph shows on a coordinate plane passes through (4, minus 8), (2, minus 4), (2, minus 3), (1, minus 1), (0, 1), (minus 1, 2), (minus 1, 4), (minus 3, 5), and (minus 4, 7)
B. (,)
C. circle graph
A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).
D.
x y
The relation that is also a function is described as follows:
A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).
When a relation is a function?A relation is a function if each value of the input is mapped to only one value of the output.
In this problem, we have that:
For the dot plot graph, input 2 is mapped to -3 and -4, hence it is not a function.In a circle graph, each value of x is mapped to two values of y, hence it is not a function.Hence a function is given by:
A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).
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One integer is 4 times another. If the product of the two integers is 144, then find the integers.
One possible set of answers is;
Another possible set of answers is:
Find the x-intercept and y-intercept for 8x-9y=15
The x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.
What are the x and y-intercept?Given the equation;
8x - 9y = 15
First, we find the x-intercepts by simply substituting 0 for y and solve for x.
8x - 9y = 15
8x - 9(0) = 15
8x = 15
Divide both sides by 8
8x/8 = 15/8
x = 15/8
Next, we find the y-intercept by substituting 0 for x and solve for y.
8x - 9y = 15
8(0) - 9y = 15
- 9y = 15
Divide both sides by -9
- 9y/(-9) = 15/(-9)
y = -15/9
y = -5/3
We list the intercepts;
x-intercept: ( 15/8, 0 )
y-intercept: ( 0, -5/3 )
Therefore, the x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.
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suppose you are using a=.01 to test the claim than mu is greater than or equal to 32 using a p-value. you are given the sample statistics n=40 , x bar =33.8 and o =4.3. Find the p-value.
0.0040, 0.0211, 0.1030, 0.9960
Using the z-distribution, the p-value for the test is of 0.0040.
What is the test statistic for the z-distribution?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are given as follows:
[tex]\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40[/tex]
Hence the value of the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
z = (33.8 - 32)/(4.3/sqrt(40))
z = 2.65.
What is the p-value?Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.
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solve this equations 3x+4x-8=6(x-3)+x
Answer:
no solutions
Step-by-step explanation:
HELP!!! A,B,or C
Eric was rock climbing. At one point, he stopped and climbed straight down 2 1/2 meters. Then he climbed straight up 6 3/4 meters.Eric was wondering what his change in elevation was after these two moves.
What is the least common multiple of 6x^2+39x-21 and 6x^2+54x+84?
Answer:
B (2nd option)
Step-by-step explanation:
Factor each one.
6x^2+39x-21 is divisible by 3 -> 3(2x^2+13x-7) -> 3(2x-1)(x+7)
6x^2+54x+84 is divisble by 6 -> 6(x^2+9x+14) -> 6(x+2)(x+7)
The greatest common factor is 3(x+7), so taking that out of each polynomial, we have (2x-1) and 2(x+2). The least common multiple is the greatest common factor*(2x-1)*2(x+2) which, simplifying, is 12x^3+102x^2+114x-84, or B.
How many three-digit multiples of 5 have three different digits and an odd tens digit?
I am getting 72. which is wrong
Answer:
68?
Step-by-step explanation:
multiples of 5 end in 5 or 0
_ _ _
last digit has 2 choices ( 5 and 0 )
1,3,5,7,9 are odd
so tens digit has 5 choices but we see that 5 is repeated so we split into more cases
when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40
when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28
40+28=68
a chord subtend an angle of 72⁰ at the center of a circle with radius 24.5m. calculate the perimeter of the minor segment
The perimeter of the minor segment is 77. 4m
How to determine the perimeter
The formula for determining the perimeter of the minor segment is given as;
Perimeter = θ/360 × 2πr + 2r sin θ/2
where;
radius = 24. 5mθ = 72Substitute into the formula;
Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)
Perimeter = 30. 79 + 46. 60
Perimeter = 77. 4 m
Thus, the perimeter of the minor segment is 77. 4m
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Graph the function y=√x+1-4. Which point lies on the graph?
a.) (-2,3)
b.) (1,4)
c.) (-1,-4)
d.) (0,4)
So,some please help me with this question !
=============================================================
Explanation:
Angles EBA and DBC are congruent because of the similar arc marking. Both are x each.
Those angles, along with EBD, combine to form a straight angle of 180 degrees. We consider those angles to be supplementary.
So,
(angleEBA) + (angleEBD) + (angleDBC) = 180
( x ) + (4x+12) + (x) = 180
(x+4x+x) + 12 = 180
6x+12 = 180
6x = 180-12
6x = 168
x = 168/6
x = 28
Angles EBA and DBC are 28 degrees each.
This means angle D = 3x+5 = 3*28+5 = 89
-----------
Then we have one last set of steps to finish things off.
Focus entirely on triangle DBC. The three interior angles add to 180. This is true of any triangle.
D+B+C = 180
89 + 28 + C = 180
117+C = 180
C = 180 - 117
C = 63 degrees
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]
( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )
[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]
[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]
[tex]\qquad❖ \: \sf \:6x = 168[/tex]
[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]
Next,
[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]
( x = 28° )
[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)
When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).
We are required to divide the first expression by second expression.
Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.
Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.
We know that relationship between quotient, divisor, divident and remainder is as under:
Dividend=Divisor*Quotient+Remainder
[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39
Quotient=[tex]x^{2} +8x+19[/tex]
Remainder=39
Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
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What is the solution to this equation?
9x - 4(x - 2) = x + 20
9x - 4(x - 2) =x + 20
We move all terms to the left:
9x -4(x - 2) - (x + 20) = 0Multiply
9x - 4x -(x + 20) + 8 = 0We get rid of the parentheses.
9x - 4x - x - 20 + 8 = 0We add all the numbers and all the variables.
4x - 12 = 0We move all terms containing x to the left hand side, all other terms to the right hand side
4x=12x = 12/4x = 3the difference between 2 numbers, a and b is 21. the difference of 5 times a and 2 times b is 18. What are the values of a and b?
Answer:
Step-by-step explanation:
a-b=21
5a-2b=18
Using elimination, we have
5a-5b=105
5a-2b=18
So:
3b=-87 so b=-29
Substituting, a=-8
(a,b)=(-8,-29)
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean age of students in a large statistics class is less than 31. A simple random sample of the students has a mean age of 30.4.
Choose the correct answer below.
A.
The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B.
The sample is not unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C.
The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D.
The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
The correct option regarding the sampling is C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
What do you mean sampling?Sampling is a process that is used in statistical analysis in which a predetermined number of observations are taken from a larger population
In this case, since the claim is mean pulse rate of students in a large statistics classes is greater than 72. The sample mean pulse rate was found to be 98.9 then the sample is not unusual if the claim is true. The sample is unusual if claim is false. Therefore there is sufficient evidence to support the claim.
The correct option is C.
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(Subtracting rational coefficients-Mixed numbers)
Simplify by combining like terms:
1/3k - 8 3/4k
[?] ?
_k
?
Answer:
-8 5/12
Step-by-step explanation:
Show Work Please Thank You
Answer:
[tex] \frac{\pi}{4} [/tex]
Step-by-step explanation:
[tex] \sf let \: y = { \tan }^{ - 1} ( \tan \frac{3\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan \frac{3\pi}{4} \\ \\ \sf \hookrightarrow \tan y = \tan(\pi - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan( - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = - \tan \frac{\pi}{4} \\ \\ \boxed {\hookrightarrow{ \bold{y = - \frac{\pi}{4} } } }[/tex]
How many lines can be drawn through points J and K?
Answer:
show the image because we cant answer it if there's no picture or image
Step-by-step explanation:
what is the solution to square root 6x - 3 = 2 square root x?
Answer:
No solution
Step-by-step explanation:
[tex]\sqrt{6x-3}=2\sqrt{x} \\ \\ 6x-3=4x \\ \\ -3=2x \\ \\ x=-\frac{3}{2} [/tex]
However, this would make the right hand side of the equation undefined over the reals, so there is no solution.
Add using fraction strip. 1/2 + 5/2
Answer:
3
Step-by-step explanation:
First we look at our problem 1/2 + 5/2. We can see our denominator is the same so we can add our numerators. 1/2 + 5/2 equals 6/2 = 3.
Answer:
If you add this fraction in fraction strip instead of equivalent fraction method
Step-by-step explanation:
firstly draw 5 1/2 fraction strip
then draw 12 1/4 fraction strip
we taking 1/4 bcoz 1/4 is multiple of 1/2, under 1/2 there is 2 1/4.
The end product will be 12/4
cancel out it 12/4 by 2 ans = 6/2 still we can cancel so cancel out 6/2 by 2 at the end ans will be 3/1 = 3
if you think it wrong then use the equivalent fraction method to see the answer..
1/2 + 5/2
denominators are same so we will take only one denominator and will directly add the numerators
1 + 5 = 6 so
6/2 cancel it the ans will be 3/1 and it's equal to 3.
Please help quick what is the answer thank you
Answer:
y= -3x+4
Step-by-step explanation:
y=mx+c
m= y2-y1 ÷ x2-x1
m= -3
y=-3x+c
7=-3(-1)+c
c=4
y=-3+4
if x is normally distributed with U = 283 and o = 21 find p(x) is greater than 315
The probability that the value of p(x) is greater than 315 is 0.063754
How to determine the probability that the value of p(x) is greater than 315?From the question, the given parameters about the distribution are
Mean value of the set of data = 283Standard deviation value of the set of data = 21The actual data value = 315The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (315 - 283)/21
Evaluate the difference of 315 and 283
z = 32/21
Evaluate the quotient of 32 and 21
z = 1.524
The probability that the value of p(x) is greater than 315 is then calculated as:
P(x > 315) = P(z > 1.524)
From the z table of probabilities, we have;
P(x > 315) = 0.063754
Hence, the probability that the value of p(x) is greater than 315 is 0.063754
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ASAP help me with this ty!
Answer:
96 degrees
Step-by-step explanation:
The angle bisectors splits the two angles mentioned down the middle so the 2 angles are equal to each other.
4x + 4 = 2(x + 13) Distribute the 2
4x + 4 = 2x + 26 Subtract 2x from both sides
2x + 4 = 26 Subtract 4 from both sides
2x = 22 Divide both sides by 2
x = 11 Plug that back into either the right side or the left side of the original equation
4x + 4
4(11) + 4
44 + 4
48. Each angle is 48 degrees. 48 + 48 is 96