Answer:
a). 7
b). -17
c). -2
Step-by-step explanation:
You have to substitute the given x value into the equation.
a). f(3)= 3(3)-2
=9-2
=7
Brian invested his savings in two investment funds. The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit. How much did he invest in Fund B, if both funds together returned a 2% profit?
Answer: Brian invested $16000 in Fund B .
Step-by-step explanation:
Let x be the amount Brian invested in Fund B.
Given, The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit.
i.e. profit on Fund A = 4% of 8000 = 0.04 ×8000 = $320
Profit on Fund B = 1% of x = 0.01x
Together they earn 1% profit, i.e. Combined profit = 2% of (8000+x)
= 0.02(8000+x)
As per question,
Combined profit=Profit on Fund A+Profit on Fund B
[tex]\Rightarrow\ 0.02(8000+x) =320+0.01x\\\\\Rightarrow\ 0.02(8000) +0.02x=320+0.01x\\\\\Rightarrow\ 160+0.02x=320+0.01x\\\\\Rightarrow\ 0.02x-0.01x=320-160\\\\\Rightarrow\ 0.01x=160\\\\\Rightarrow\ x=\dfrac{160}{0.01}\\\\\Rightarrow\ x=16000[/tex]
Hence, Brian invested $16000 in Fund B .
An Aquarium’s dimensions are 3 1/4 ft x 2 ft x 1 3/4. What is the volume of the Aquarium?
Volume = length x width x height
Volume = 3 1/4 x 2 x 1 3/4 = 11 3/8 cubic feet
Answer:
11 3/8 ft^3
Step-by-step explanation:
The volume is given by
V = l*w*h
V = 3 1/4 * 2 * 1 3/4
Change the number to improper fractions
V = (4*3+1)/4 *2 * (4*1+3)/4
= 13/4 *2* 7/4
Rewriting
= 13/1 * 2/4 * 7/4
= 13/1 * 1/2 *7/4
= 91/8
Changing back to a mixed number
8 goes into 91 11 times with 3 left over
11 3/8 ft^3
help with 57, please!!
9514 1404 393
Answer:
a) $554
b) y = 138.50x
c) see attached
Step-by-step explanation:
a) The cost is the product of the number of hours and the cost per hour.
cost = (4 h)($138.50 /h) = $554.00 . . . . for a 4-hour course
__
b) As above, the cost (y) is the product of the number of hours (x) and the cost per hour ($138.50).
y = 138.50x . . . . tuition for x credit hours.
__
c) As in part (b), the tuition is hours times 138.50. That means hours are tuition divided by 138.50.
Examine the table of input (x) and output (y) values below. What is the relationship between the input and output values? Write an equation for this relationship. input (x) –1 0 1 2 3 4 5 output (y) –4 –1 2 5 8 11 14 What do you notice about the relationship between the x and y values?
Answer:
Relationship: As the input increases by 1, the output increases by 3.
Equation: y=3x-1
~Hope this helps~
Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 2 with
these dice. Be sure to reduce.
[?]
Answer:
1/36
Step-by-step explanation:
it is the exact same as if both your dice had the numbers {1,2,3,4,5,6}
you said the SUM of the dice that is indicates the answer of the addition of two (or for that matter more) numbers,... the only numbers that would sum 2 is 1+1,... and because you only have two ones (one per die) the answer is the same as if they where die with normal numbers,...
The probability of rolling a sum of 2 with these dice is 1/36.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
Pair of dice have= {1,2,2,3,3,4}
Now,
The probability of rolling a sum of 2 with two dice is the same as the probability of rolling snake eyes, since the only way to get a sum of 2 is if both dice show a 11. The probability of rolling a 1 on a single die is 1/6, so the probability of rolling a 1 on both dice is (1/6) × (1/6) = 1/3612.
However, in this case, the dice are not standard six-sided dice, but have different numbers on their faces. The first die has {1,2,2,3,3,4} and the second die has {1,3,4,5,6,8}. The probability of rolling a 1 on the first die is still 1/6, but the probability of rolling a 1 on the second die is also 1/6. Therefore, the probability of rolling a sum of 2 with these dice is still (1/6) × (1/6) = 1/36.
This probability cannot be reduced any further, since 1 and 36 have no common factors other than 1.
Therefore, the probability will be 1/36.
Learn more about probability here;
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If $a>0$ and $b>0$, a new operation $\nabla$ is defined as follows:$$a \nabla b = \dfrac{a + b}{1 + ab}.$$For example,$$3 \nabla 6 = \dfrac{3 + 6}{1 + 3 \times 6} = \dfrac{9}{19}.$$For some values of $x$ and $y$, the value of $x \nabla y$ is equal to $\dfrac{x + y}{17}$. How many possible ordered pairs of positive integers $x$ and $y$ are there for which this is true?
This happens when
1 + a b = 17 ==> a b = 16
With a and b both positive integers, and 16 = 2^4, we can have
• a = 1 and b = 16
• a = 2 and b = 8
• a = b = 4
and vice versa. So there are 5 possible ordered pairs.
35\40 = 7\?
a. 5
b. 8
c. 1
d. 4
Answer:
b. 8
Step-by-step explanation:
Simplify the left side by dividing the top and bottom by 5
35/5 = 7
40 /5 = 8
7/8
Hey there!
35/40 = 7/x
Cross Multiply the fraction
35(x) = (7)(40)
→ 35x = 280
DIVIDE 35 to BOTH SIDES
35x/35 = 280/35
CANCEL out: 35/35 because that gives you 1
KEEP: 280/35 because that helps solve for the x-value
→ x = 280/35
x = 8
Therefore, your answer is most likely: 8 (Option B)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1 . 108 kilometers. About how
many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun?
O 5.2. 107 kilometers
O 4.7. 108 kilometers
O 5.2. 108 kilometers
O 5.7. 109 kilometers
or what value of g does the function f(g) = g2 + 3g equal 18?
Answer:
The 2 values that makes the function equal to 18 is 3 and -6
Step-by-step explanation:
First you can convert the quadratic equation from standard form to root form
Step 1: Substitute f(g) = 18
Step 2: Move 18 to the other side to create
0 = g² + 3g - 18
Step 3: Now we rearrange equation from standard form into root form
Step 4: Find what adds to 3 and multiples to -18
-3 and 6 adds to 3 and multiples to -18
Step 5: Now we substitute -3 and 6 into the root equation
0 = (g-3)(g+6)
Step 6: Set the brackets to 0 and solve
g - 3 = 0
g = 3
g + 6 = 0
g = -6
Please give me the correct answer
Answer:
10 centimeters
Step-by-step explanation:
formula for volume of a cylinder = πr² · h
1. Set up the equation
(3.14)(r²)(14) = 4,396
2. Simplify
(43.96)(r²) = 4,396
3. Solve
r² = 100
√r = √100
r = 10
Please help.. Offering 25 points and 5 stars with a thanks
Answer:
2/5
Step-by-step explanation:
There are 2 white and 4 yellow = 6
P(yellow) = yellow /total = 4/6 = 2/3
We keep the ball
Now there are 2 white and 3 yellow = 5
P(yellow) = yellow /total = 3/5
P ( yellow, keep, yellow) = 2/3 * 3/5 = 2/5
We are given 4 yellow balls and 2 white balls. In total, this adds up to 6.
Divide the number of yellow balls to the total number of balls:
4/6 -> 2/3
We are also given 3 yellow and 2 white.
Divide the number of yellow balls to the total number of balls:
3/5
Divide both fractions together:
3/5 * 2/3 = 6/15 = 2/5
Best of Luck!
Someone please help! Thank you
Answer:
Hey there!
We can write a equations here:
3x+y=180
Also, since all of the angles have 3x on the outside, then y must be constant.
3y=180
y=60
Thus, for x, we have 3x+60=180, 3x=120, x=40.
2x+6y
2(40)+6(60)
80+360
440.
Let me know if this helps :)
14. Simplify the expressions
a. 12 - 5y + 21 + y -23
Answer:
10 - 4y
Step-by-step explanation:
Combine like terms. 12, 21 and -23 add up to 10, and -5y + y is -4y.
Then, together, we have 10 - 4y (answer)
Answer:
[tex]\large\boxed{10 - 4y}[/tex]
Step-by-step explanation:
12 - 5y + 21 + y - 23
Combine like terms (add -5y to + y)
12 + 21 - 4y - 23
Add 12 + 21
33 - 4y - 23
Subtract 23 from 33
[tex]\large\boxed{10 - 4y}[/tex]
This is the simplest form of the expression.
Hope this helps :)
Forgot how to do this please help, thank you.
3m + 2x=-3, solve for x
Answer:
[tex]\boxed{x =\frac{-3m-3}{2}}[/tex]
Step-by-step explanation:
[tex]3m + 2x=-3[/tex]
[tex]\sf Subtract \ 3m \ from \ both \ sides.[/tex]
[tex]3m + 2x-3m=-3-3m[/tex]
[tex]2x=-3-3m[/tex]
[tex]\sf Divide \ both \ sides \ by \ 2.[/tex]
[tex]\displaystyle \frac{2x}{2} =\frac{-3-3m}{2}[/tex]
[tex]\displaystyle x =\frac{-3m-3}{2}[/tex]
Answer:
x=\frac{-3-3m}{2}
Step-by-step explanation:
1st step: Subtract 3m from both sides. 3m+2x-3m=-3-3m
2nd step: Simplify. 2x=-3-3m
3rd step: Divide both sides by 2. \frac{2x}{2}=-\frac{3}{2}-\frac{3m}{2}
Final step: Simplify. x=\frac{-3-3m}{2}
The cycling road race through the Adelaide Hills started at 11:50am and the winner
Took 74 minutes. The winner crossed the finishing line at
Find X.
Use angle center circle page for reference.
Explain your answer.
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
Refer to the diagram below for letter names of points.
Using the theorem provided on the second image, we can conclude that [tex]m\angle AOC=2*m\angle ABC=2*100\textdegree = 200\textdegree[/tex]. Keep in mind that this is the reflex [tex]\angle AOC[/tex].
Because [tex]O \in DC[/tex], we know that [tex]DC[/tex] is a diameter by definition, which makes [tex]m\angle DOC = 180\textdegree[/tex].
Using the Angle Addition Postulate, we can write the following equation:
[tex]m\angle AOD+m\angle DOC=m\angle AOC[/tex]
Substituting the measures of each angle into the equation gives us:
[tex]x\textdegree + 180\textdegree = 200\textdegree[/tex]
Solving the equation for [tex]x[/tex] gives us:
[tex]x\textdegree + 180\textdegree = 200\textdegree[/tex]
[tex]x\textdegree + 180\textdegree - 180\textdegree = 200\textdegree - 180\textdegree[/tex] (Subtract [tex]180\textdegree[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]x\textdegree = 20\textdegree \rightarrow \bf x=20[/tex] (Simplify)
Remember that [tex]x=20[/tex], not [tex]20\textdegree[/tex] because the degree symbol was already given in the original expression. Hope this helps!
a submarine is 50 meters below sea level. It goes up 15 meters and down 40 meters. What is the submarines new position relative to sea level
Answer:
-75 m
Step-by-step explanation:
Use sea level as the reference point.
Initially the position is -50 m.
If the submarine goes up 15 m, then its new position is (-50 + 15) m, or -35 m.
If the sub now descends 40 m, its new position is (-35 - 40) m, or -75 m
if y - 1/y =8 then find the value of y^2-1/y^3
Step-by-step explanation:
[tex] {y}^{2} - \frac{1}{ {y}^{3} } [/tex]
factorise out y² ;
[tex] = {y}^{2} (1 - \frac{1}{y} ) \\ \\ = 8 {y}^{2} [/tex]
explain how 6/12 and 4/8 are equal fractions
6/12 and 4/8 are equal fractions, as, when simplified, they share a simplified fraction.
Note that what you do to the denominator, you do to the numerator. Find common denominators for both fractions:
(4/8)/(2/2) = 2/4
(6/12)/(3/3) = 2/4
As you can tell, when they share a common denominator (4), the numerators are the same as well (3).
~
Louis bought 16 cookies at the bakery. He had a
coupon for $7 off his entire purchase. He ended up
paying $13.32. Write an equation to find how much
each cookie originally cost.
Answer:
16x -7 =$13.32
Step-by-step explanation:
$13.32 + $7 = $20.32
$20.32 divided by 16 = $1.27
each cookie cost $1.27
I really hope this help
Answer:- 16x - 7 = 13.32
Also cost of each cookie = $1.27
Explanation:
Let the cost of each cookies be x
ATQ
16x -7 = 13.32
We will mutiply x with 16 because he purchased 16 cookies.
Also he had coupon of $7 which means $7 off which is why -7
And 13.32 is the amount he paid
Now lets solve it
16x - 7 = 13.32
16x = 13.32 + 7
16x = 20.32
x = 20.32/16
x = 1.27
Therefore cost of each cookie is $1.27
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Select the correct answer from the drop-down menu.
If A and Bare independent events, P(Aand B) =
1. P(A)
2.P(B)
3.P(A) * P(B)
4.P(A) + P(B)
Answer:
Step-by-step explanation:
P(A and B)=P(A)*P(B)
The sum of first three terms of an arithmetic series is 21. If the sum of the first two terms is subtracted from the third term then it would be 9. find the three terms of the series. The first and last bra
Answer:
The terms are - 1, 7 and 15.
Step-by-step explanation:
Let the terms be a-d, a, a+d.
ATQ, a-d+a+a+d=21, a=7 and a+d-(a-d+a)=9. 2d-a=9, d=8. The terms are - 1, 7 and 15.
The first three terms will be : -1, 7, 15
We have sum of first three terms of an arithmetic series is 21. It is given that if the sum of the first two terms is subtracted from the third term then it would be 9.
We have to find the three terms of the series.
What is Arithmetic progression or sequence?An arithmetic progression or sequence with common difference [tex]d[/tex] is given as -
a, a + d, a + 2d, a + 3d .....
According to the question -
a + (a + d) + (a + 2d) = 21
3a + 3d = 21
3(a + d)=21
a + d = 7 (Eqn. 1)
(a + 2d) - (a + a + d) = 9
a + 2d - a - a - d = 9
d - a = 9
a = d - 9
Substituting the value of 'a' in Eqn. 1, we get -
d - 9 + d = 7
2d - 9 = 7
2d = 16
d = 8
Therefore -
a = 8 - 9
a = -1
The three terms are -
a = -1
a + d = -1 + 8 = 7
a + 2d = -1 + 2 x 8 = 15
Hence, the first three terms will be - -1, 7, 15
To solve more questions on Arithmetic Sequences and finding the terms, visit the link below -
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Solve for a
5+14a=9a-5 a=
Answer:
-2
Step-by-step explanation:
5+14a=9a-5
+5 +5
10+14a=9a
-9a -9a
10+5a=0
-5a -5a
10= -5a
÷5 ÷5
2= -a
*-1 *-1
-2=a
What number must be subtracted from 25 for the
difference to be 22? Explain your answer. Include a
number line in your explanation.
Answer: 3
Step-by-step explanation:
When you subtract 25 from 22 you get 3 and when you subtract 3 from 25 you 22.
what is the rename of 10/21
Answer: ten Twenty-one
Step-by-step explanation:
10/21
Megan buys condiments in bulk for her restaurant. The company that she orders ketchup from charges $14.78 per gallon for orders less than 8 gallons. For orders of 8 gallons or more, the cost is $11.99 per gallon of ketchup. Which function represents this situation?
side note: f(x)= blank
Answer:
Below
Step-by-step explanation:
● Orders of 8 gallons or more can be modeled as: x》 8
● For each gallons in the situation above the company charges 11.99 per gallon so: 11.99x
● For orders that are less than 8, the comapny charges 14.78 per gallon
● => 14.78x for x < 8
So the function that represent the situation is the second one
rational or irrational? and why
Answer:
rational, simplified number is -0.5
Step-by-step explanation:
(see screenshot)
math help
please. thank you.
Answer:
AC=EG AND BC = FG I THINK IT IS ONLY THIS
Answer:
BC=FG
Step-by-step explanation:
Because BC and FG is congruent side of angle A
hope you understand
Please answer this question now
Answer:
Approximately 439.6 square millimeters.
Step-by-step explanation:
The formula for the surface area of a cone is the following:
[tex]A=\pi r^2+\pi r l[/tex]
Where, r is the radius and l is the slant height.
The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:
[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]
Answer:
292.77
Step-by-step explanation:
πr(r+[tex]\sqrt{h2+r2}[/tex])
13 x 2 = 26
7 x 2 = 14
26 + 14 = 40
[tex]\sqrt{40}[/tex] = 6.32
7 + 6.32 = 13.32
3.14 x 7 = 21.98
21.98 x 13.32 =
292.77
A box contains 20 equal-sized balls, numbered 1 to 20. Two balls are drawn at random simultaneously. What is the probability that the numbers on the two balls will differ by more than 2
Answer:
P = 0,7947 or 79,47%
Step-by-step explanation:
We have 20 balls, the total possible outcomes drawn two balls simultaneously is:
C = m! /n! *( m - n )!
C = 20!/2! *( 20 - 2)!
C= 20*19*18!/ 2* 18!
C = 20*19/2
C = 190
Now the number of successful outcomes x ( those where balls differ by more than 2 is)
x = total numbers of outcomes - 20 ( outcomes differing in 1 ) - 19 (outcomes differing in 2 )
x = 190 - 39
x = 151
Then the probability of drawing tw balls with numbers differing n mr than two is
P = successful outcomes / total outcomes
P = 151/190
P = 0,7947 or 79,47%