Answer:
r =10
Step-by-step explanation:
5(r + 3) = 3r + 35.
Distribute
5r+15 = 3r+35
Subtract 3r from each side
5r+15-3r = 3r+35-3r
Combine like terms
2r +15 = 35
Subtract 15 from each side
2r+15-15 =35-15
2r = 20
Divide by 2
2r/2 =20/2
r =10
Marlina received her salary on Friday. She spent one-half of her salary on rent and then spent $338 on her electric and water bill. Next, she spent one-half of what was left on her phone bill. After spending $56.00 on gas for her car, Marlina had $102.00 left. How much did Marlin spend on rent?
Answer:
Marlina spent $654 on rent.
Step-by-step explanation:
Let the amount of money Marlina's received for her salary be x.
We know that she spent one-half of her salary on rent and then $338 on her electric and water bill. Therefore, the amount of money she has left can be so far can be represented by:
[tex]\displaystyle x-\frac{1}{2}x-338[/tex]
Next, she spent one-half of what was left on her phone bill. So, we can subtract one-half of the above expression to what we have so far.
[tex]\displaystyle x-\frac{1}{2}x-338-\frac{1}{2}\left(x-\frac{1}{2}x-338\right)[/tex]
Finally, she spent $56 for gas. Thus, we will subtract 56:
[tex]\displaystyle x-\frac{1}{2}x-338-\frac{1}{2}\left(x-\frac{1}{2}x-338\right)-56[/tex]
And we know that after all of the expenses, she will have $102 left. Therefore:
[tex]\displaystyle x-\frac{1}{2}x-338-\frac{1}{2}\left(x-\frac{1}{2}x-338\right)-56=102[/tex]
We want to know how much Marlina spent on rent. So, we can find her salary, since we know the rent is one-half of the salary. To find the salary, we will solve for x.
Distribute:
[tex]\displaystyle x-\frac{1}{2}x-338-\frac{1}{2}x+\frac{1}{4}x+169-56=102[/tex]
Rearrange:
[tex]\displaystyle \left(x-\frac{1}{2}x-\frac{1}{2}x+\frac{1}{4}x\right)+(-338+169-56)=102[/tex]
Combine like terms:
[tex]\displaystyle \frac{1}{4}x-225=102[/tex]
Add 225 to both sides:
[tex]\displaystyle \frac{1}{4}x=327[/tex]
Multiply both sides by 4:
[tex]x=\$ 1308[/tex]
Therefore, Marlina received a total of $1308 for her salary.
We know that she spent half of her salary on rent. Therefore, the amount she spent on rent is:
[tex]\displaystyle r=\frac{1}{2}(1308)=\$ 654[/tex]
Marlina spent a total of $654 on rent.
9514 1404 393
Answer:
$654
Step-by-step explanation:
Let r represent the amount of Marlina's rent. Since that is half her salary, the amount remaining after paying rent is also equal to r. The disposition of that remaining amount is ...
$338 on electric and water (E&W)
(1/2)(r -338) on phone . . . this is half of what is left after paying E&W
$56 on gas
$102 unaccounted
__
The total of these amounts is equal to r, so we have ...
r = 338 + 1/2(r -338) +56 +102
1/2r = 338 -169 +56 +102 = 327 . . . . . eliminate parentheses, subtract 1/2r
r = 2(327) = 654 . . . . . multiply by 2 to get r by itself
Marlina spends $654 on rent.
Joe's employer will reimburse him $0.07 per mile driven. If Joe drives 179.53 miles on a business trip, what is his mileage reimbursement? Round your answer to the nearest cent.
Answer:
$12.27
Step-by-step explanation:
.07 times 179.53 is 12.5671 so rounded to 12.27
The mileage reimbursement for Joe is: $12.27 to the nearest cent.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that Joe's employer will reimburse him $0.07 per mile driven.
If the employer reimburses $0.07 per mile driven, we just need to multiply $0.07 by the number of miles that Joe drives.
So, the mileage reimbursement for Joe is:
0.07 x 179.53 = 12.5671
so rounded to 12.27
Therefore, The mileage reimbursement for Joe is: $12.27 to the nearest cent.
Learn more about the unitary method;
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There are three companies that produce a critical electronic navigation component (ENC) used in the aerospace industry. These companies are Alice Manufacturing, Byte International, and Cognizant Technologies. Alice makes 85% of the ENCs, Byte makes 10%, and Cognizant makes the remaining 5%. The ENCs made by Alice have a 2.5% rate of defects, the ones made by Byte have a 4.0% rate of defects, and the ones made by Cognizant have a 6% rate of defects. If an ENC is randomly selected from the general population of ENCs, the probability that it was made by Alice is _______. If this ENC is later tested and found to be defective, the probability that it was made by Alice is _______.
Answer:
a
[tex]P(A) = 0.85[/tex]
b
[tex]P(A | D) = 0.7522 [/tex]
Step-by-step explanation:
From the question we are told that
The percentage of ENC made by Alice is P(A) 85% = 0.85
The percentage of ENC made by Byte P(B) 10%=0.10
The percentage of ENC made by Cognizant P(C) = 5%= 0.05
The percentage rate of defect of ENC made by Alice is p = 2.5 % = 0.025
The percentage rate of defect of ENC made by Byte is q = 4.0% = 0.04
The percentage rate of defect of ENC made by Cognizant r = 6% =0.06
Generally the probability that a randomly selected ENC will be made by Alice is
[tex]P(A) = 0.85[/tex]
Generally the probability that a randomly selected ENC that was found to be defective will be made by Alice is
[tex]P(A | D) = \frac{P(A) * p}{P(D)}[/tex]
Here
[tex]P(D)[/tex] is the probability that a randomly selected ENC will be defective and this is mathematically represented as
[tex]P(D) = P(A) * p + P(B) * q + P(C) * r[/tex]
=> [tex]P(D) = 085 * 0.025 + 0.10 * 0.040 + 0.05 * 0.06[/tex]
=> [tex]P(D) = 0.02825 [/tex]
So
[tex]P(A | D) = \frac{ 0.85 * 0.025 }{0.02825}[/tex]
=> [tex]P(A | D) = 0.7522 [/tex]
14.
The bar graph shows the enrolment of ALS Community Learning Center in
Barangay Esperanza for calendar years 2014-2018. What year has the least
number of enrollees?
160
140
120
100
80
60
40
20
0
2014
2015
2016
2017
2018
Using the approximation 3.14 for (pie symbol , what is the radius of a circle with a circumference of 59.7
m?
Simplify (-8a-5a-10c)-(2a+10b+20c)
Answer:
-15a-10b-30c
Step-by-step explanation:
(-8a-5a-10c)-(2a+10b+20c)
(-13a-10c)-(2a+10b+20c)
(-13a-10c)-2a-10b-20c
-15a-10b-30c
Answer:
-15a-30c-10b
Step-by-step explanation:
(-8a-5a-10c)-(2a+10b+20c)
(-13a-10c)-2a-10b-20c
-13a-10c-2a-10b-20c
-15a-30c-10b
What is -0.3 x -10/13
Factor X^2 + 7x + 12
Answer:
(x + 3)(x + 4)
Step-by-step explanation:
(x + 3)(x + 4)
x^2 + 3x + 4x + 12
x^2 + 7x +12
Answer:
(x +3) (x+4)
Step-by-step explanation:
I took the test with this question, I hope this helps!
i had 6 cupcakes two days ago, and 9 yesterday. help me continue this pattern. thank you.
Answer:
its adding 3
Step-by-step explanation:
So if you had 6 cupcake two days ago, than yesterday there was 9, so tomorrow you should have 12 cupcake and so on
The requried pattern of cupcakes is given by adding 3 cupcakes each day and the pattern comes out as 6, 9, 12, 15, 18, 21, and so on for the subsequent day.
What is a sequence?The sequence is a pattern of placing the values in a specified manner.
Here,
Assuming that the pattern is to add 3 cupcakes each day, the continuation of the pattern would be:
Two days ago: 6 cupcakes
Yesterday: 9 cupcakes
Today: 12 cupcakes
Tomorrow: 15 cupcakes
Day after tomorrow: 18 cupcakes
In five days: 21 cupcakes
And so on, the pattern would continue adding 3 cupcakes for each subsequent day.
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The given quesiton is incomplete, the complete question s given below,
I had 6 cupcakes two days ago, and 9 yesterday. Assume it to be series. What will be the number of cupcakes that I will have two days from today??
7 is a solution to the equation 3n + 9 = 33. true false
Answer:
No
Step-by-step explanation:
3n+9=33
-9=-9
3n= 24
3n/3=24/3
n=8
Answer:
False
Step-by-step explanation:
Which angles are coreesponding angles?
Answer:
PQN and MNL
Step-by-step explanation:
A corresponding angle is an angle that occupies the same relative position of another angle on a straight line. If they are parallel then they are corresponding.
Mary earns $7.25 an hour. She can determine her salary, s, for the
number of hours she works, h, by using the equation s = 7.25h. Which
statement explains why s is a function of h?
A
For every value of h there is only one value of s.
B.
For some values of h there is more than one value of s.
C.
For some values of s there is more than one value of h.
For every value of s there are two values of h.
D.
Mr. Jones has to invest in three types of stocks, low-risk, medium-risk, and high-risk. He invests according to three principles. The amount invested in low-risk stocks will be at most more than the amount invested in medium-risk stocks. At least will be invested in low- and medium-risk stocks. No more than will be invested in medium- and high-risk stocks. The expected yields are % for low-risk stocks, % for medium-risk stocks, and % for high-risk stocks. How much money should Mr. Jones invest in each type of stock to maximize his total expected yield?
Answer:
Since the numbers are missing, I looked for a similar question:
Mr. Jones has $9000 to invest in three types of stocks: low-risk, medium-risk and high-risk. He invests according to the following rules: the amount invested in low-risk stocks will be at most $1000 more than the amount invested in medium-risk stocks. At least $7000 will be invested in a combination of low- and medium-risk stocks. No more than $7000 will be invested in a combination of medium- and high-risk stocks. The expected annual returns are 6% for low-risk stocks, 7% for medium-risk stocks, and 8% for high-risk stocks. How much should he invest in each type of stock to maximize his total expected yield?
let:
L = low risk stocks
M = medium risk stocks
H = high risk stocks
maximize 0.06L + 0.07M + 0.08H
L + M + H ≤ 9000
L ≥ M + 1000
L + M ≥ 7000
M + H ≤ 7000
using solver, the optimal solution = 4,000L + 3,000M + 2,000H , which yields a maximum profit = $610
Mr. Jones should invest $4,000 in low risk stocks, $3,000 in medium risk stocks and $2,000 in high risk stocks.
Find the slopes of the linear functions.
y = -2x + 7
The slope of the line given by the linear equation is
ty
The slope of the line shown in the graph is
4
-8
4
Answer:
The slope of the line given by the linear equation is -2
The slope of the line shown in the graph is -1
Step-by-step explanation:
The line equation, y = -2x + 7 is written in the slope-intercept form, which is represented by the formula, y = mx + b.
m is the slope, while b is the y-intercept.
Therefore, the slope of the line of the linear equation, y = -2x + 7 is -2.
Find the slope of the line shown in the graph using the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex].
Use the coordinates of any two points on the line. Let's use (0, 5) and (5, 0)
Let,
[tex] (0, 5) = (x_1, y_1) [/tex]
[tex] (5, 0) = (x_2, y_2) [/tex]
[tex] m = \frac{0 - 5}{5 - 0} = \frac{-5}{5} = -1 [/tex]
Therefore:
The slope of the line given by the linear equation is -2
The slope of the line shown in the graph is -1
someone help it’s due in a couple of min
Answer: A $5800
Step-by-step explanation:
His parents cover 9100+ the scholarship for 3300=12400
Valeria is training for a marathon. She jogs the same 15 mile route twice in one week. On Monday, she jogged the route in 1.75 hours. Thursday, she tried to improve her speed. She jogged the same route in 1.63 hours. Her smart watch said her rate on Monday was 8.57 miles per hour. She forgot to set the smart watch to calculate her rate on Thursday. Use the information you have to calculate how fast she was running on Thursday.
Answer:
9.20 miles per hourStep-by-step explanation:
Given data
distance of the route = 15miles
time taken on Monday= 1.75hours
speed= distance./time
speed= 15/1.75
speed= 8.57 miles per hour
her smart watch is correct
time taken on Thursday= 1.63hours
speed= distance./time
speed= 15/1.63
speed= 9.20 miles per hour
she was jogging at 9.20 miles per hour
what is the range of this function?
Answer:
13,13,10,-15
Step-by-step explanation:
What is the answer for number 9
Answer:
y= 2/4x + 16
Step-by-step explanation:
do da math
PLZ HELP I NEED THIS ANSWER IM BEING TIMED
Answer:
The answer is -3. Hope that helped
WILL GIVE BRAINLIEST SO DESPERATE PLS
The life zones on Mount Rainier, a mountain in Washington, can be approximately classified by elevation, as follows.
Low-elevation forest: above 1700 feet to 2500 feet
Mid-elevation forest: above 2500 feet to 4000 feet
Subalpine: above 4000 feet to 6500 feet
Alpine: above 6500 feet to the summit
Write a compound inequality that represents the elevation range h
for each type of plant life.
Answer:
Look down below
Step-by-step explanation:
It's been a little while since I've looked at compound inequalities, so forgive me if this is a bit long.
Let's start with the Low Elevation Forest. Let x represent what is considered the forest. If this is above 1700, x>1700 (which can be rewritten as 1700<x). (Remember, as silly as this may sound, the mouth of the alligator eats the larger part! So the large number has the wide part of the symbol. Remember also that if the sign is < or >, then it includes the number the 'mouth' is facing.) If the forest is up to 2500, you'll generally include 2500 in your equation, so x<2500. This means 1700<x<2500 or x>1700 and x<2500.
Now let's repeat that with the other parts of the question. Mid elevation is x>2500 and x<4000. Subalpine would be x>4000 and x<6500. Alpine is then x>6500 and x< the summit (which is probably the elevation of Mount Rainer in this problem or 14410 feet).
Now we have the question itself. Let's replace x with t for trees for part a. This would mean in the low elevation forest, t>1700 and t<2500 which can be rewritten 1700<t<2500. Now we have flowers in the subalpine AND alpine zones. Let's use f for flowers. If flowers can be in either zone, let's combine them! Because t>4000 and t<6500 in the subalpine level and t>6500 and < the summit (aka 14410 feet), flowers can grow anywhere above 4000 feet. So flowers would be f>4000 and f<14410. Again, you can combine these into: 400<f<14410.
Sorry this is so long, but I hope it helps :)
I NEED HELPPP THIS DUE TODAY!!!! IT IS URGENT!!
Answer:
I t s t o o g r o s s
5 2 4 2 1 1 3 6 1 4 4
Step-by-step explanation:
Im pretty sure that's the answer
What is the ratio of 3 inches to 20 feet
Answer:
1/80
Step-by-step explanation:
Answer:
3 inches is 1/4th of one foot so to 20 ft is 1/80th
Step-by-step explanation:
Remember, 12 in.=1 FT
Hope this helps
;)
James paid $42 for 6 lb of chocolate how much does the chocolate cost per pound
Answer:
7$ gimme brainliest
Step-by-step explanation:
Answer: 7 pounds
Step-by-step explanation:
42/6=7
2b.) What transformation of f(x) does y correspond to?
a.) a verticle translation 4 units down
b.) a verticle translation 4 units up
c.) a horizontal translation 4 units to the left
d.) a horizontal translation 4 units to the right
Answer:
The transformation is " a horizontal translation 4 units to the right " ⇒ (d)
Step-by-step explanation:
Let us revise the translation of a function
If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h) If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - kLet us look at the graph and choose some points on the f(x) and find their images on y
∵ Point (1, 2) lies on f(x)
∵ Point (5, 2) lies on y
∵ Point (3, 8) lies on f(x)
∵ Point (7, 8) lies on y
→ There is no change in the y-coordinates of the points, the change
only in the x-coordinates
∴ The translation is horizontally
∵ 5 - 1 = 4 units ⇒ positive value means to right
∴ f(x) is translated 4 units to the right
∴ The answer is " a horizontal translation 4 units to the right " (d)
is 78 closer to 77.54 or 77.6 closer to 77.54
What does “each point of a line maps to itself” mean? I don’t understand it what it means for it to map to itself.
Brainliest is given if the answer's correct!
A box has a volume of 6750 cubic inches, a length of 25 inches, and a height of 15 inches. What is the width of the box in inches?
Answer:
18 inches
Step-by-step explanation:
Length x width x height = volume
25in x W x 15in = 6750 cubic inches
375 sq inches x W = 6750 cubic inches
W = 18 inches
I need help plzzzzzz
Answer:
...................................
Step-by-step explanation:...................................
how do i check 11z-5=9z+7
Answer:
z= 6
Step-by-step explanation:
You check it by plugging the value, z, into the equation.
11(6)-5=9(6)+7
61=61
Answer:
z=6
Step-by-step explanation:
11z-9z=7+5
2z=12
z=6
A superstar major league baseball player just signed a new deal that pays him a record amount of money. The star has driven in an average of 110 runs over the course of his career, with a standard deviation of 31 runs. An average player at his position drives in 80 runs. What is the probability the superstar bats in fewer runs than an average player next year
Answer:
0.1667
Step-by-step explanation:
Given that:
Average / mean runs (m) = 110 runs
Standard deviation (σ) = 31 runs
Number of runs driven in by an average player in his position = 80
The probability the superstar bats in fewer runs than an average player next year will be the :
P(x < 80)
Zscore = (x - mean) / σ
Zscore = (80 - 110) / 31
Zscore = - 30 / 31
Zscore = - 0.9677419
P(Z < 0.9677419) = 0.1666 ( from z probability calculator)
= 0.1667
