Answer:
f(-5) = 22
Step-by-step explanation:
f(x) =-3x+7
Let x = -5
f(-5) =-3*-5+7
= 15 +7
=22
Benjamin’s and David’s ages add up to 36 years. The sum of twice their respective ages also add up to 72 years. Find their ages
Answer:
It can be any two numbers that sum up to 36.
eg:18+18,30+6,15+21
Step-by-step explanation:
Given:
Let Benjamin's age be x and David's age y.
x+y=36
2x+2y=72
Solution:
As twice of 36=72, any two numbers that add up to 36 ,will give a sum of 72 after multiplying them with 2.Therefore ,Benjamin's and David's age can be any set of numbers that sum up to 36.
A jar contains 8 pennies, 5 nickels and 7 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Be very precise with your answers.
a. Find the probability x = 2 cents.
b. Find the probability x = 6 cents.
c. Find the probability x = 10 cents.
d. Find the probability x = 11 cents.
e. Find the probability x = 15 cents.
f. Find the probability x = 20 cents.
g. Find the expected value of x.
Answer:
a. The probability x = 2 cents = 7/22
b. The probability x = 6 cents = 35/66
c. The probability x = 10 cents = 5/33
d. The probability x = 11 cents= 28/33
e. The probability x = 15 cents = 20/33
f. The probability x = 20 cents = 14/33
g. The expected value of x = 5.9
Step-by-step explanation:
This is a binomial probability distribution. The number of trials is known .
a. The probability x = 2 cents.
Probability ( X=2) P( selecting 2 dimes)= 7C2 / 12c2
= 21 / 66 = 7/22
b. The probability x = 6 cents.
Probability ( X=6) P( selecting a nickel and a dime)= 5C1 * 7C1/ 12c2
= 5*7 / 66 = 35/66
c. The probability x = 10 cents.
Probability ( X=10) P( selecting two nickels )= 5C2 / 12c2)
= 10/ 66 = 5/33
d. The probability x = 11 cents.
Probability ( X=11) P( selecting a penny and a dime)= 8C1 * 7C1/ 12c2)
= 8*7 / 66 = 56/66= 28/33
e. The probability x = 15 cents.
Probability ( X=15) P( selecting a penny and a nickel)= 8C1 * 5C1/ 12c2)
= 8*5 / 66 = 40/66= 20/33
f. The probability x = 20 cents.
Probability ( X=20) P( selecting 2 pennies )= 8C2 / 12c2)
= 28 / 66 = 14/33
g. The expected value of x.
E(X) = np
E(X) = 2 * (8C2+ 5C2+ 7C2)/(8+5+7) = 2( 28+10+21)/20
=2(59)/20= 5.9
Whats 18x^3 divided by 7x?????
The image of (-4,6) reflected along the y-axis is
a. (4, -6)
b. (-4,-6)
c. (4, 6)
d. (-4, 6)
Answer:
C(4,6)
Step-by-step explanation:
the x turns into its opposite when reflected across y same thing for y when reflected across x
Answer:
c. (4, 6)
Step-by-step explanation:
The rule of an reflection about the y-axis is: [tex]A(x,y)\rightarrow A'(-x,y)[/tex]
Apply the rule to point (-4, 6):
[tex]\frac{(-4,6)\rightarrow\boxed{(4,6)}}{(x,y)\rightarrow(-x,y)}[/tex]
Option C should be the correct answer.
In the figure below. MN is the arc of a circle with center L. If the length of arc MN is 6π, what is the area of sector LMN?
On a number line, the coordinates of X, Y, Z, and W are −7, −2, 2, and 7, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and
Was is a macroeconomics
Answer:
Macroeconomics is a study that deals with the whole economy and everything pertaining to it.
Step-by-step explanation:
when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.
A taste test asks people from Texas and California which pasta they prefer, brand A or brand B. The table shows the results. A person is randomly selected from those tested. What is the probability that the person is from Texas, given that the person prefers Brand B? PLEASE HELP! I'll name you Brainliest if you're answer is the best!
Answer:
A
Step-by-step explanation:
It would be A because there are 45 people in Texas that prefer brand B. There are 105 people in total that prefer brand B. 45/105 is .42857... so rounded it would be .43, therefore A. I hope this helps.
Answer:
A
Step-by-step explanation:
A soccer ball is made of 32 pieces of leather: white hexagons and black pentagons. Each black piece borders only with white pieces, each white piece borders with three black pieces and three white pieces. How many black pieces are needed to manufacture the ball?
Answer:
24
Step-by-step explanation:
1+3=4
4 divided by 32 is 8
8 white ones
then 8-32 is 24
24 black ones
PLZ HELPPPPPP.
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
A. y=12/x
B. y=12x
C. y=12+x
D. y=12−x
Answer:
B. y=12x
Step-by-step explanation:
x = # of books bought
so then y=12x
Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
Mario invested $5100 at 13%
to be compounded daily. What will be the value of Mario's investment in 2 years? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
Answer:
Amount = $6614 and 19 cent
Step-by-step explanation:
Formula for compound interest is
A= p(1+r/n)^(nt)
Compounded daily
So n= 365*2= 730
T= 2
r= 0.13
P= 5100
A= p(1+r/n)^(nt)
A= 5100(1+0.13/730)^(730*2)
A= 5100(1+1.78082*10^-4)^(1460)
A= 5100(1.000178082)^1460
A= 5100(1.2969)
A= 6614.19
Amount = $6614 and 19 cent
Write an equation perpendicular to the line y=3/2x-2 that goes through (-4,3)
Answer: y=-2/3x-2/3
Step-by-step explanation:
concept to know: two lines that are perpendicular has opposite reciprocal slopes.
y=-2/3x+b
in order to find b or the y-intercept, we need to plug in a point
3=-2/3(-4)+b
3=8/3+b
b=-2/3
y=-2/3x-2/3
Hope this helps!! :)
Robert, a ninth-grader, has just been told, "The reason you’re having so much trouble with division is that you have never mastered compound multiplication. The Math Basic Skills Tests have indicated this quite clearly. We are going to provide you with instruction in multiplication immediately." Robert’s teacher made what kind of decision relative to his skill level?
Answer:
Diagnostic
Step-by-step explanation:
The teacher made a diagnostic decision relative to Roberts skill level. Before she made this decision, she first started with the process of evaluation to know his strength and also establish his weakness. With the knowledge she has gotten she now plans to him with meaningful learning and an efficient curriculum that would help him in mastering multiplication first before division.
A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34, 0.38]. Therefore, there is a probability of 0.98 that the proportion of Drosophola with this mutation is between 0.34 and 0.38. True or False
Answer:
False
Step-by-step explanation:
The 98% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 98% confidence that the proportion of Drosophola with his mutation is between 0.34 and 0.38.
An urn contains 9 red marbles, 6 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Find the probability all three marbles are the same color
Answer:
P(identical colours) = 160/1771 (0.0903 to four decimals)
Step-by-step explanation:
Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)
Choose three without replacement.
Need probability three identical colours.
Use the multiplication rule.
P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253
P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771
P(BBB) = 8/23 * 7/22 * 6/21 = 8/153
Probability of getting identical colours
= P(RRR)+P(WWW)+P(BBB)
= 160/1771 (0.0903 to four decimals)
Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.
-----------------
A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the marbles are chosen is not important, and they are also chosen without replacement, which means that the combination formula is used to find the number of outcomes.-----------------
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
-----------------
The desired outcomes can be:
3 from a set of 9(all red).3 from a set of 6(all white).3 from a set of 8(all blue).Thus:
[tex]D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160[/tex]
-----------------
The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:
[tex]T = C_{23,3} = \frac{23!}{3!20!} = 1771[/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{160}{1771} = 0.0903[/tex]
0.0903 = 9.03% probability all three marbles are the same color.
A similar problem is given at https://brainly.com/question/10896842
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 30 31 64 59 57 33 54 77 56 41 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
mean=502/10=50.2
median=(54+56)2=55
Find x.
A. 21(route)2
B. 7
C.21(route)3/2
D. 21(route)2/2
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the right ΔABD,
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{BD}}{\text{AB}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}[/tex]
BD = [tex]7\sqrt{3}\times \frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{21}{2}[/tex]
Now by applying Cosine rule in the right ΔBDC,
Cos(45)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}[/tex]
x = [tex]\frac{21}{2}\times \sqrt{2}[/tex]
x = [tex]\frac{21\sqrt{2}}{2}[/tex]
Therefore, Option (D) is the correct option.
17. In figure, BAC -859, CA = CB and BD - CD. Find the measure of ZX, Zy and Zz. Give
reasons to support your answer.
A
85°
ب
B
H
V
Answer:
x = 10°, y = 10° and z = 160°
Step-by-step explanation:
Given : m∠BAC = 85°
CA ≅ CB and BD ≅ CD
In the given ΔABC,
Since, CA ≅ CB
Angles opposite to these equal sides will be equal in measure.
m∠BAC ≅ m∠ABC ≅ 85°
Since, sum of interior angles of a triangle = 180°
m∠BAC + m∠ABC + m∠BCA = 180°
85° + 85° + m∠BCA = 180°
m∠BCA = 180° - 170°
m∠BCA = 10°
x = 10°
In ΔBDC,
Since, BD ≅ DC [Given]
Opposite angles to these equal sides will be equal in measure.
Therefore, x° = z° = 10°
Since, x° + y° + z° = 180°
10° + y° + 10° = 180°
y = 180 - 20°
y = 160°
Question
Consider these functions.
f(x) = -9x + 14
g(x)=-3x2
Select the correct answer from each drop-down menu.i
If x = 6, then f(6)
If g(x) -48, then x =
and x =
Submit
Answer:
[tex]\large \boxed{-40, \ 4, \ -4}[/tex]
Step-by-step explanation:
[tex]f(x)=-9x+14[/tex]
[tex]\sf Put \ x \ as \ 6.[/tex]
[tex]f(6)=-9(6)+14[/tex]
[tex]f(6)=-54+14[/tex]
[tex]f(6)=-40[/tex]
[tex]g(x)=-3x^2[/tex]
[tex]\sf Put \ g(x) \ as \ -48.[/tex]
[tex]-48=-3x^2[/tex]
[tex]\displaystyle \frac{-48}{-3} =\frac{-3x^2 }{-3}[/tex]
[tex]16=x^2[/tex]
[tex]\sqrt{16} =\sqrt{x^2 }[/tex]
[tex]x= \pm 4[/tex]
Answer:
F(6) = -9(6) + 14 = -54 + 14. f(6) = -40
G(x) = -48 / g(x) = -3(16) / g(4) = -48
Step-by-step explanation:
For the first one the drop answer is -40
For the second one its 4 then 16
I think because that whats im seeing but these are the right answers :)
An empty swimming pool is to be filled to the top. The pool is shaped like a rectangular prism with length 10m, width 8m , and depth 4m. Suppose water is pumped into the pool at a rate of 16m cubed per hour. How many hours does it take to fill the empty pool?
Answer:
20 hours
Step-by-step explanation:
10*8*4=320 (volume of the pool)
320/16=20 hours
Answer:
20 hours
Step-by-step explanation:
10x8x4 = 320
320 / 16 = 20
it takes 20 hours to fill the empty pool
If SSR is 2592 and SSE is 608, then A. the standard error would be large. B. the coefficient of determination is .23. C. the slope is likely to be insignificant. D. the coefficient of determination is .81.
Answer:
D. the coefficient of determination is .81.
Step-by-step explanation:
SST = SSE + SSR
where
SST is the summation of square total
SSE is the summation of squared error estimate = 608
SSR is the summation of square of residual = 2593
with these in mind we put the values into the formula
= 2592 + 608
=3200
Coefficient of determination = SSR/SST
= 2592/3200
= 0.81
Therefore option D is the correct answer to the question.
Common ratio 2/3, -2, 6
Answer:
The common ratio is - 3Step-by-step explanation:
To find the common ratio between the terms of the sequence divide the previous term by the next term.
That's
[tex] - 2 \div \frac{2}{3} = - 2 \times \frac{3}{2} = - 3[/tex]Or
[tex] \frac{6}{ - 2} = - 3[/tex]Therefore the common ratio of the sequence is - 3
Hope this helps you
Answer:
-3
Step-by-step explanation:
Maria operates a taco truck in her neighborhood. She has created a graph based on her business performance in the previous year. The price she currently sells tacos for is $2.30. Which two statements correctly interpret this graph? Revenue and Cost Functions 1)Maria’s business is incurring losses. 2)Maria’s costs are rising over time. 3)Maria is running a profitable business. 4)Maria’s total revenue exceeds her total profit. 5)Maria’s total profit exceeds her total revenue.
Answer:
3)Maria is running a profitable business.
4)Maria’s total revenue exceeds her total profit.
Step-by-step explanation:
The graph shows variation of revenue and cost with respect to price of product and not with respect to time .
The price of the product is 2.30 . From this graph , we see that at this price revenue exceeds total cost . So maria is running a profitable business .
Total profit can not exceed total revenue as
Total revenue - total cost = total profit .
So total profit will always be less than total revenue .
m+1/4d=7 solve for d
Answer:
d = -4M + 28
Step-by-step explanation:
Find the slope of a line perpendicular to the line defined by the equation 3x-5y=12
Answer:
-5/3
Step-by-step explanation:
Note the slope intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Isolate the variable, y. First, Subtract 3x from both sides:
3x (-3x) - 5y = 12 (-3x)
-5y = -3x + 12
Next, divide -5 from both sides. Remember to divide from all terms within the equation:
(-5y)/-5 = (-3x + 12)/-5
y = (-3x/-5) + (-12/5)
Simplify.
y = (3x/5) - 12/5
y = (3/5)x - 12/5
You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:
Original m = 3/5
Flipped m = -5/3
-5/3 is your perpendicular slope.
Answer:
5
m = - ---- perpendicular slope
3
Step-by-step explanation:
3x - 5y = 12 -------->> convert to y = mx + b
- 5y = - 3x + 12
- 5y = - (3x + 12) --- eliminate the negative
5y = 3x + 12
3x + 12
y = -------------
5
3 12
y = -----x + -----
5 5
the above equation is the form of y = mx + b
where m is the slope and b is the intercept
5
therefore, m = - ---- perpendicular slope
3
If there are 25 students in a class - 11 are guys and 14 are girls what is the probability that one of the students on the class is a guy?
Answer:
0.44
Step-by-step explanation:
11/25 = 0.44 = 44%
Answer:
11/25
Step-by-step explanation:
since there are 25 students, there will be 25 choices, and the 25 will be the denominator
and there are 11 guys so there will be 11 choices of guys and the 11 will go on top
the point p(-3,4) is reflected in the line x +2=0. find the coordinate of the image x
Answer:
(- 1, 4 )
Step-by-step explanation:
The line x + 2 = 0 can be expressed as
x + 2 = 0 ( subtract 2 from both sides )
x = - 2
This is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 2
Thus (- 3, 4 ) is 1 unit to the left of - 2
Under a reflection in the line x = - 2
The x- coordinate will be the same distance from x = - 2 but on the other side while the y- coordinate remains unchanged.
Thus
(- 3, 4 ) → (- 1, 4 )
Find the intersection point for the following liner function f(x)= 2x+3 g(x)=-4x-27
Answer:
( -5,-7)
Step-by-step explanation:
f(x)= 2x+3 g(x)=-4x-27
Set the two functions equal
2x+3 = -4x-27
Add 4x to each side
2x+3+4x = -4x-27+4x
6x+3 = -27
Subtract 3
6x+3 - 3 = -27-3
6x = -30
Divide each side by 6
6x/6 = -30/6
x =-5
Now we need to find the output
f(-5) = 2(-5) +3 = -10+3 = -7
Answer:
Step-by-step explanation:
big burgewr
For an ordered pair (x,y) in a relation, the y element represents the
a.) range
b.) domain
c.) function
d.) input
y represents the range for an ordered pair (x, y). Option A is correct.
For an ordered pair (x, y), What y represents is to determine.
Range of the function is the output value of the function.
Here, in ordered pair (x, y) x represents the values of independent variable terms as domain. And for every value of x their is exist or output values y this set of y values is called as range.
Thus, y represents the range for an ordered pair (x, y).
Learn more about range here:
https://brainly.com/question/17553524
#SPJ1
A TV studio has brought in 8 boy kittens and 9 girl kittens for a cat food commercial. The director is going to choose 11 of these kittens at random to be in the commercial. What is the probability that the director chooses 4 boy kittens and 7 girl kittens? Round your answer to three decimal places.
Answer:
0.204
Step-by-step explanation:
The formula to use to solve this is the combination formula.
Combination formula =
C(n, r) = nCr = n!/r! (n - r)!
Total number of kittens = 8 boy kittens + 9 girl kittens
= 17 kittens
Step 1
We find the probability of choosing 4 boy kittens out of 8 boy kittens
= 8C4 = 8!/4! × (8 - 4)!
= 8C4 = 8! / 4! × 4!
= 8C4 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1)
8C4 = 70
Step 2
We find the probability of choosing 7 girl kittens out of 9 girl kittens
9C7 = 9!/7! × (9 - 7)!
= 9C7 = 9! / 7! × 2!
= 9C7 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (7 × 6 × 5 × 4 × 3 × 2 × 1) × (2 × 1)
9C7 = 36
Step 3
Find the probability of Picking 11 kittens out of 17 kittens
17C11 = 17!/11! × (17 - 11)!
= 17C11 = 17! / 11! × 6!
= 17C11 = 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)
17C11 = 12,376
Step 4
The final step
The probability that the director chooses 4 boy kittens and 7 girl kittens
= 8C4 × 9C7/ 17C11
= 70 × 36/12376
= 2520/12376
= 0.2036199095
Approximately to 3 decimal places = 0.204
Therefore, the probability that the director chooses 4 boy kittens and 7 girl kittens is 0.204
