Answer:
(d) 9
Step-by-step explanation:
f(x) = 3x + 2
g(x) = - 2x + 1
g(f(x)) = - 2(3x + 2) + 1 = - 6x - 4 + 1 = - 6x - 3
g(f(-2)) = - 6(- 2) - 3 = 9
Suppose that E and f are two events and that P(E and F)=0.3 and P(E)=0.5. What is P(F/E)?
Answer:
[tex]P(F/E) = 0.6[/tex]
Step-by-step explanation:
If we are given two dependent events [tex]A[/tex] and [tex]B[/tex] such that their chances of occurrence or the probabilities of the events are: [tex]P(A)[/tex] and [tex]P(B)[/tex].
Then the conditional probability that the event [tex]B[/tex] will occur given that [tex]A[/tex] has already occurred is given by the following formula:
[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}[/tex]
Here the two events given are [tex]E[/tex] and [tex]F[/tex].
[tex]P(E\ and\ F)\ or\ P(E\cup F) = 0.3[/tex]
and [tex]P(E) = 0.5[/tex]
As per the above formula that we have already discussed, the formula can be written as:
[tex]P(F/E) = \dfrac{P(E \cap F)}{P(E)}\\\Rightarrow P(F/E) = \dfrac{0.3}{0.5}\\\Rightarrow P(F/E) = \dfrac{3}{5}\\\Rightarrow \bold{P(F/E) = 0.6}[/tex]
Jessica has an account with a credit union. Her account earns 2.6% simple interest yearly. Exactly a year and a half ago, she opened her account with $900.
How much interest has she earned so far?
Answer:
$35.1
Step-by-step explanation:
2.6% of 900 = 23.4
Since it's a year and a half you might want to divide by two.
2.6/2 = 1.3
1.3% of 900 = 11.7
add them up,
23.4 + 11.7 = 35.1
It's asking for how much she EARNED not HAS in her bank account in 1.5 years. So include what she earned with interest, do not include the 900 dollars because she didn't earn it with interest, she already had that.
What is the inequality of y-2x<=-3
Use the given x and y values to write a direct variation
equation.
x = 5, y = 25
Answer:
k= 1/5
Step-by-step explanation:
x is proportional to y
x = ky (k is const.)
k = x/y
k= 5/25
k = 1/5
Answer:
Equation of direct variation is : [tex]\mathbf{y=5x}[/tex]
Step-by-step explanation:
We are given: x= 5 and y=25
We need to write equation of direct variation.
The formula for direct variation is: [tex]\mathbf{y=kx}[/tex]
So, if y=25 and x=5, k will be:
[tex]y=kx\\25=k(5)\\k=\frac{25}{5}\\k=5[/tex]
So, equation of direct variation is : [tex]\mathbf{y=5x}[/tex]
The slipe of the line passing through the points (7, 5) and (21, 15) is
Answer:
5/7
Step-by-step explanation:
You find a slope by using the equation y2-y1/x2-x1.
In this case: 15-5/21-7
10/14
5/7
Penny’s bank account showed a balance at the beginning of the month of $180. She
spent $2.50 each day on bus tokens. Write an equation representing the amount A left in
her account after d days.
Answer:
[tex]a=180-2.50d[/tex]
Step-by-step explanation:
If Penny starts with a balance of $180, and [tex]a[/tex] represents the account left in her account after [tex]d[/tex] days. we can start modeling an incomplete equation:
[tex]a=180[/tex]
We are then told that she spends $2.50 each ([tex]d[/tex]) day. This can be represented as:
[tex]2.50d[/tex]
Let's now include the expression into the incomplete equation. Remember that since she is spending, the [tex]2.50d[/tex] will be subtracted from her balance of $180:
[tex]a=180-2.50d[/tex]
In the equation y=kx, which variable is the constant of proportionality?
Answer:the variable k is the constant of proportionality
Step-by-step explanation:
This can be proven when the equation is used to find different values of y. To find these different values, the x variable is substituted for different values while the k value stays the same. hope this helps!!
A recent study has shown that 10% of computer science concentrators suffer from symptoms of Carpal Tunnel Syndrome. Researchers have developed a diagnostic test for this condition and in a recent trial, the test gave a positive result in 96% of the patients who were known to truly have Carpal Tunnel Syndrome.
a) For an initial version of the diagnostic test, the false positive rate (the percentage of people without Carpal Tunnel who incorrectly test positive) was 44%. If a student received a positive result from this test, what would be the posterior probability that they truly have Carpal Tunnel Syndrome?
b) The researchers believe their test will be practically useful if a positive result implies the student has Carpal Tunnel with at least 75% probability. What is the largest possible false positive rate that would achieve this accuracy target?
Answer:
1. 0.1951
2. 3.56%
Step-by-step explanation:
Probability of disease = 0.10
Probability of disease and positive = 0.96
1.
Probability of no disease and positive = 0.44
Probability of disease and positive result = 0.10x0.96/0.10x0.96+0.90x0.44
= 0.096/0.096+0.396
= 0.096/0.492
= 0.1951
2.
Probability of disease false positive result
P(disease|positive result)
= (0.10x0.96/0.10x0.96+0.90xP) >= 0.75
= 0.096/0.096+0.90p >= 0.75
We cross multiply
0.096 >= 0.75(0.096+0.90p)
0.096 >= 0.072 + 0.675p
0.096-0.072 >= 0.675p
0.024 >= 0.675p
P <= 0.03555
Therefore the largest possible false positive rate = 0.0356
= 3.56%
explain why the oppisite of a positive number will always be a negitive number
Answer:
because a positive is over zero and a negative is below zero so from that you can tell that the opposite of any positive will be a negative.
Step-by-step explanation:
The opposite of positive numbers are negative. There are numbers on the right and left side on the number line of zero.
I typed in a detailed "essay" of this but it didn't save. I even put in an example...
Which shows two expressions that are equivalent to (-8)(-12)(2)?
The solution is option C.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
(-8)(-12)(2)
=96*2
=192
so. we get,
It would be c because when you multiply 8 and 12 you get 96 and when you multiply 96x2 you get 192 .
so, therefore your answer is c.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ1
Please help! Not good at math whatsoever!!
Which lines from Natalie Merchant's song "Wonder" most likely inspired R. J. Palacio to give August's mother's great determination in the novel Wonder? O Doctors have come from distant cities just to see me O stand over my bed disbelieving what they're seeing with love, with patience and with faith she'll make her way I'm over your heads how I confound you and astound you
Answer:
C)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The guy above me is correct
Of the 30 girls who tried out for the lacrosse team at Euclid middle school 12 were selected . Of the 40 boys who tried out, 16 were selected. Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls?how do you know?
Answer:
Yes they are the same i know this because for every 10 girls or boys there are 4 who try out for the team. so for every 10 Boys or Girls there are 4 that will try out for the team. For those wondering the ratio is 4:10
Step-by-step explanation:
Answer:
Yes, when simpilfied or written as a fraction they are equal
Step-by-step explanation:
12:30 = [tex]\frac{12}{30\\ \left \\\}[/tex] = [tex]\frac{4}{10\\}[/tex]
16:40 = [tex]\frac{16}{40}[/tex] = [tex]\frac{4}{10}[/tex]
What is 3.761 in expanded form
Answer:
3 + 0.7 + 0.06 + 0.001
Answer:3+ 0.7+ 0.06+ 0.001= 3.761
Step-by-step explanation:
A cell phone tower and a fence are on the same property. the fence is 8 feet tall and has a shadow that measures 14.5 feet. the shadow of the cell phone tower measures 72.5 feet . how tall is the cell phone tower ?
Answer:
40 feets
Step-by-step explanation:
Given that:
Height of fence = 8 feets
Shadow of fence = 14.5 feets
Shadow of cell phone tower = 72.5 feets
Height of cell phone tower = x
Height of fence = shadow of fence
Height of tower = shadow of tower
8 feets= 14.5 feets
x feets = 72.5
Cross multiply :
(14.5 * x) = (72.5 * 8)
14.5x = 580 feets
x = 580/14.5
x = 40 feets
Hence, the height of the cell phone tower is 40 feets
find the sum of 301+73+27 , mentally, using the associative property of addition. Show how you can use the property to group two of the addends. Explain how you found the sum.
Answer:
401
Step-by-step explanation:
301 + 73 + 27
Using the correct order of operations, you would start by adding 301 to 73. Then you'd add 27 to that sum.
Using the associative property of addition, you change the grouping to add 73 and 27 first since that equals 100, and it's easy to add 100 to 301 mentally.
301 + 73 + 27 =
= 301 + (73 + 27)
= 301 + 100
= 410
help help help pls pls ASAP
Answer:
#6 slope is -1/2 and y intercept is 4
#8 slope is 1/3 and y intercept is -2
Step-by-step explanation:
Compare. Select <,>, or=.
8.465? V 8.445
Answer:
8.465>8.445
Step-by-step explanation:
8.465>8.445
So 8.465 is greater than 8.445
A package of 4 pairs of insulated socks costs $26.36. What is the unit price of the pairs of socks?
The unit price is $
per pair of socks
Answer: The unit price is $6.59 per pair of socks
Step-by-step explanation: 26.36. divided by 4 = 6.59
What is the measure of an angle if the measures of its two adjacent supplementary angles add up to 100°?
The answer is not 80 btw
Explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
Answer:
130°
Step-by-step explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
58 students on a bus how many students were fit on a six buses
Answer:
348
Step-by-step explanation:
what’s the value of x?
Answer:
x = -11
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+50 + 72+ x+80 = 180
Combine like terms
2x + 202 = 180
Subtract 202 from each side
2x+202-202 = 180-202
2x =-22
Divide each side by 2
2x/2 = -22/2
x = -11
Plz Help. Euler Equations are hard!
Find the general solution to the following differential equation.
An
2 pie/3
Step-by-step explanation:
which option gives you more snack when spending the same amount of money?
Doritos 4.39 for 11.5 oz
or
cheetos 9.75 for 3.24
Answer:
Spending the same amount of money, Cheetos gives more snacks than Doritos, since with the same money more ounces of the product will be obtained.
Step-by-step explanation:
Given that the Doritos package costs $ 4.39 and contains 11.5 ounces of product, the price of each ounce of said snack comes from the following calculation:
4.39 / 11.5 = X
0.38 = X
Therefore, each ounce of Doritos costs $ 0.38.
In turn, the Cheetos package costs $ 3.24 and contains 9.75 ounces of snacks, so its price per ounce is obtained through the following calculation:
3.24 / 9.75 = X
0.33 = X
Thus, each ounce of Cheetos costs $ 0.33.
Therefore, spending the same amount of money, Cheetos gives more snacks than Doritos, since with the same money more ounces of the product will be obtained.
Which of the following data sets has a range of 40?
a. {40, 10, 20, 100}
C. {40, 10, 20, 50}
b. {40, 10, 20, 80}
d. {40, 10, 20, 40}
Please select the best answer from the choices provided
A
B
С
Answer:
The second answer - 40, 10, 20, 50
Step-by-step explanation:
Range is the difference between the largest and smallest number in a data set. The biggest and smallest numbers in the data set are 50 and 10, respectively. 50 - 10 = 40.
Which statement describes the effect on the parabola f(x)=2x•x-5x+3 when changed to f (x)= 2x•2-5x+1
Answer:
The parabola is translated down 2 units.
Step-by-step explanation:
You have the parabola f(x) = 2x² – 5x + 3
To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:
f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1 Expresion A
The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.
If p> 0 and q> 0, the parabola shifts p units to the right and q units up. If p> 0 and q <0, the parabola shifts p units to the right and q units down. If p <0 and q> 0, the parabola shifts p units to the left and q units up. If p <0 and q <0, the parabola shifts p units to the left and q units down.In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.
This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.
In conclusion, the parabola is translated down 2 units.
Ruth got to the library at 1030 am.
She stayed at the library for 50 minutes.
Then she walked home.
Ruth took 1 1/4 hours to walk home.
(b) At what time did Ruth get home?
Answer:
She got home at 12:35 P.M.
Step-by-step explanation:
She got to the library at 10:30 am.
She spent 50 minutes there
10:30 + 50 mins can be seperated to 30 mins and 20 mins
So, 30 mins goes to 11 and 20 mins more equals 11:20.
She took 1 1/4 hours to get home
1 hour more means 12:20, and since 1/4 of an hour is 15 mins,
12:20 + 15 = 12:35 P.M
hope this helped!
helppppp please I will give brainliest
Answer:
y=1/3x-2
Step-by-step explanation:
Add the two expressions.
3z−4 and 2z + 5
I need it asap please help!
Answer:
3(1)-4=-1 2(1)+5=7
Answer:
5z+1
Step-by-step explanation:
it was simple
Les had $32.00 when he went to the city Market to buy some fresh fruits and vegetables. When he left, he had $23.05. How much money did he spend on food?
Answer:
$8.95
Step-by-step explanation: