Answer:
Step-by-step explanation:
m= the amount of money the mechanic makes.
h= the amount of money the helper makes.
m=h+5
m+h=114
h+5+h=114
2h+5=114
h=54.50
m=59.5
Helper makes $9 an hour.
Mechanic makes $9.92 an hour.
The earning of helper each earn per hour is 7$ /hr.
To find earning of helper per hour.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and also the properties and manipulation of numbers.
Given that:
let the cost /per hour of helper be x
and that of the mechanic is x+5
now for 6 hour job total earning is
6(x+x+5) = 114
=> 2x+5 = 19
so, 2x = 14 or x = 7
the earning of helper is = 7$ /hr
and earning of mechanic is = 12$/hr
So, the earning of helper each earn per hour is 7$ /hr.
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what are the coordinates of the vertex of the function f(x) = x2 -12x +5?
Answer:
[tex]\huge\boxed{(6;\ -31)}[/tex]
Step-by-step explanation:
METHOD 1:Let: [tex]f(x)=ax^2+bx+c[/tex].
The coordinates of the vertex:
[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]
We have
[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]
Substitute:
[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]
METHOD 2:The vertex form of an equation of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
We have:
[tex]f(x)=x^2-12x+5\to a=1[/tex]
Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
upper box is 0
middle box is 3 and
the downer box is 6
Step-by-step explanation:
Have a nice day
factorize completely (2x+2y) (x-y)+(2x-2y)(x+y)
What are the solutions to the system of equations graphed attached pic
Answer: C
Step-by-step explanation:
For system of equations, the solution is the point or points where the equations intersect. The point they meet signifies that they are the same at the x and y point.
Looking at the graph, we see 2 intersection points. They are (0,-8) and (4,8). Therefore, C is the correct answer.
1. Find the Product of 8.02 and 6.1 and correct your answer to the highest whole number. 2. How many pieces of ribbon each 6cm long can be cut from a roll of ribbon 24m long?
A total of 32/3 strips can be derived from the ribbon.
What is quotients?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
Here, we have,
to determine the number of strips:
From the question, we have the following parameters
Length of a roll of ribbon = 4 meters
Also, from the question;
We have
Length of a piece of ribbon = 5/12 meter
The number of strips of ribbon is the quotient of the Length of a roll of ribbon and the Length of a piece of ribbon
This is represented as
Number of strips = Length of a roll of ribbon/Length of a piece of ribbon
So, we have
Number of strips = (4 )/(5/12)
Evaluate the quotient
Number of strips = 32/3
Hence, the number of strips is 32/3
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complete question:
How many strips of a ribbon can be cut from a roll of ribbon that is 4 4/9 meters long if each piece is 5/12 meters long
1. A mortgage of $200,000 requires payments of $1395.40 per month at 5.7%
compounded quarterly. How long will it take to repay the loan? What amount of interest
does the purchase pay?
Answer:
a) How long will it take to repay the loan?
20 years
b) What amount of interest does the purchase pay?
$134,896
Step-by-step explanation:
a) How long will it take to repay the loan?
In the above question, they are asking you for the Loan duration
The Formula for Loan duration(T) =
ln (- m/(r÷n) × C - m)/In (1 + r/n)
Where:
m = monthly payments = $1395.40
C = Amount of mortgage =$200,000
r = Interest rate = 5.7% = 0.57
n = compounded quarterly = 4
T = ln (- 1395.40/(0.57÷4) × 200,000 - 1395.40)/In (1 + 0.57/4)
T = 20 years.
Therefore, it will take 20 years to repay the Loan.
b) What amount of interest does the purchase pay?
The total number of payments =
Loan duration × Number of months
Number of months = 12 months( because it is monthly payment)
Loan duration = 20 years
Total number of payments = 240 payments.
In the question, we are given the amount paid monthly payment as
$1,395.40
Total amount paid = Monthly payments × Total number of payments
= $1,395.40 × 240
= $334,896
The amount of Interest the purchase pay = $334,896 - $200,000
= $134,896
Chuck has 6$ and he spends 1/5 of his money on candy
Answer:
He spends $1.20 Which means he has $4.80 remaining.
Step-by-step explanation:
1/5 of 6 is 6/1 multiplied by 1/5 and that is 6/5 or 1 1/5
1/5 of a dollar is 20 cents. he has $1.20
6-1.20=4.80.
Answer:
[tex]4.80 => Answer[/tex]
Step-by-step explanation:
Use the information given.
1/5 of 6 is equal to 6/5
6/5 = 1.2
Now subtract.
[tex]6-1.2= 4.8[/tex]
So the answer is 4.80 or 4.8
Hope this helps! :)
By: ❤️BrainlyMagic❤️
Brainliest would be appreciated!
Which is the solution to this question 4X equals 32
Answer:
8
Step-by-step explanation:
you would just divide 32 by 4
4x = 32
x = 32/4
x=8
Answer:
[tex]\large\boxed{\sf \ \ \ x=8 \ \ \ }[/tex]
Step-by-step explanation:
Hello
4x=32 we can divide both parts by 4 so
[tex]\dfrac{4x}{4}=\dfrac{32}{4}\\\\<=> x = 8[/tex]
Hope this helps
Write an expression with four terms. Include at least one term with an exponent, one term with a coefficient of 5, one term with three factors, and one constant. Make two of the terms like terms. Include a brief description of each term in the expression.
Answer:
4x^2 + 5x^2 + 4xy
Explanation
You need 2 like terms this could be of the form:
ax^2 + bx^2 + c
1 term with a coefficient of 5, sub in b = 5
ax^2 + 5x^2 + c
1 term with 3 factors, c = 4xy
This would mean it has a factor of 4,x and y.
So final equation is (a could be any value I give it a value of 4 for convenience)
4x^2 + 5x^2 + 4xy
Step-by-step explanation:
Find the surface area of a cylinder with radius 15.8 ft and height 4.4 ft. Use a
calculator. Round to the nearest tenth.
A. 1786.9 ft2
B. 1221.1 ft2
C. 3450.8 ft2
D. 2005.3 ft2
Hey there! I'm happy to help!
First, let's find the area of the two circles that make up the top and bottom of the cylinder. To find the area of a circle, you square the radius multiply it by pi (we will use 3.14)
15.8²=249.64
249.64×3.14=783.8696
Since there are two of these circles we multiply this by 2.
783.8696×2=1567.7392
Now, for the rectangle. To make a cylinder, you take a rectangle and wrap it around the top and bottom circles. One side of this rectangle is the height of the cylinder, and the other is the circumference of the circle (one side wraps all the way around the circle, which is the circumference).
The circumference is the diameter multiplied by 3.14 (pi). The diameter is twice the radius.
15.8×2=31.6
31.6×3.14=99.224
We multiply this by the height.
99.224×4.4=436.5856
Now, we add the areas of the circles and the rectangle.
1567.7392+436.5856=2004.3 (rounded to nearest tenth)
This is closest to D. 2005.3 ft². It is probably a bit off because I used 3.14 instead of actual pi.
Have a wonderful day! :D
Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Evan has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other). A(w) = ___________ b) What width would maximize the area? w = __________ c) What is the maximum area? A = _________ square feet
Answer: A. A=(1000-2w)*w B. 250 feet
C. 125 000 square feet
Step-by-step explanation:
The area of rectangular is A=l*w (1)
From another hand the length of the fence is 2*w+l=1000 (2)
L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.
Express l from (2):
l=1000-2w
Substitude l in (1) by 1000-2w
A=(1000-2w)*w (3) ( Part A. is done !)
Part B.
To find the width w (Wmax) that corresponds to max of area A we have to dind the roots of equation (1000-2w)w=0 ( we get it from (3))
w1=0 1000-2*w2=0
w2=500
Wmax= (w1+w2)/2=(0+500)/2=250 feet
The width that maximize area A is Wmax=250 feet
Part C. Using (3) and the value of Wmax=250 we can write the following:
A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets
Find the sum of the following infinite geometric series
Answer:
[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]
Step-by-step explanation:
Hello,
"Find the sum of the following infinite geometric series"
infinite
We will have to find the limit of something when n tends to [tex]+\infty[/tex]
geometric series
This is a good clue, meaning that each term of the series follows a geometric sequence. Let's check that.
The sum is something like
[tex]\displaystyle \sum_{k=0}^{+\infty} a_k[/tex]
First of all, we need to find an expression for [tex]a_k[/tex]
First term is
[tex]a_0=7[/tex]
Second term is
[tex]a_1=\dfrac{4}{9}\cdot a_0=7*\boxed{\dfrac{4}{9}}=\dfrac{7*4}{9}=\dfrac{28}{9}[/tex]
Then
[tex]a_2=\dfrac{4}{9}\cdot a_1=\dfrac{28}{9}*\boxed{\dfrac{4}{9}}=\dfrac{28*4}{9*9}=\dfrac{112}{81}[/tex]
and...
[tex]a_3=\dfrac{4}{9}\cdot a_2=\dfrac{112}{81}*\boxed{\dfrac{4}{9}}=\dfrac{112*4}{9*81}=\dfrac{448}{729}[/tex]
Ok we are good, we can express any term for k integer
[tex]a_k=a_0\cdot (\dfrac{4}{9})^k[/tex]
So, for n positive integer
[tex]\displaystyle \sum_{k=0}^{n} a_k=\displaystyle \sum_{k=0}^{n} 7\cdot (\dfrac{4}{9})^k=7\cdot \dfrac{1-(\dfrac{4}{9})^{n+1}}{1-\dfrac{4}{9}}=\dfrac{7*9*[1-(\dfrac{4}{9})^{n+1}]}{9-4}=\dfrac{63}{5}\cdot [1-(\dfrac{4}{9})^{n+1}}][/tex]
And the limit of that expression when n tends to [tex]+\infty[/tex] is
[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]
as
[tex]\dfrac{4}{9}<1[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A wire that is 76 feet long needs to be divided into lengths using the ratio 1 to 13. What is the longer length? Round your answer to two decimal places if necessary.
Answer:
70.59 feet
Step-by-step explanation:
There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.
1. Divide 76 by 14
76 ÷ 14 = 5.43
2. Multiply the longer length of 13 parts
5.43 · 13 = 70.59
The longer length of the wire 70.59 feet
There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.
1. Divide 76 by 14
76 ÷ 14 = 5.43
2. Multiply the longer length of 13 parts
5.43 · 13 = 70.59
What is a decimal in numbers?In algebra, a decimal number can be defined as a range whose entire number part and the fractional element are separated by means of a decimal point. The dot in a decimal range is referred to as a decimal point. The digits following the decimal factor show a price smaller than one.
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Find x and y, please solve with steps and leave answers in fraction form, THANK YOU
Answer:
Below
Step-by-step explanation:
Using the proprtionality relation:
● 8/10 =5/x
● (4*2)/(5*2) = 5/x
Simplify using 2
● 4/5 = 5/x
Multiply both sides by 5
● (4/5)*5 = (5/x)*5
● 4 = 25/x
Switch x and 4
● x= 25/4
■■■■■■■■■■■■■■■■■■■■■■■■■
Again use the proportionality relation but this time with y.
● 8/10 =7/y
8/10 = 4/5
● 4/5 = 7/y
Multiply both sides by 5
● (4/5)*5 =(7/y)*5
● 4 = 35/y
Switch 4 and y
● y = 35/4
According to medical data, the ages at which patients have their first knee replacement surgery
follows a normal distribution. The average age for a first knee replacement is 58 years of age, with a
standard deviation of 8.25 years. Therefore, doctors can expect the middle 68% of their knee
replacement surgery patients to be between what ages?
Answer:
The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
Step-by-step explanation:
68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years
So, the ages lies between x₀ + σ and x₀ - σ
So, the ages lie between 58 - 8.25 = 49.75 years
and 58 + 8.25 = 66.25 years
So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
Select the correct answer.
What are the x-intercepts of this function?
g(x) = -0.25x2 – 0.25x + 5
O
(-20,0) and (-4,0)
(4,0) and (20,0)
(5,0) and (-4,0)
(-5,0) and (4,0)
Answer:
[tex]\large \boxed{\sf \ \ (-5,0) \ and \ (4,0) \ \ }[/tex]
Step-by-step explanation:
Hello,
We need to find the zeroes of
[tex]-0.25x^2-0.25x+5=0\\\\\text{*** multiply by -4 ***} \\ \\x^2+x-20=0\\\\\text{*** the sum of the zeroes is -1 and the product -20=-5x4 ***}\\\\x^2+5x-4x-20=x(x+5)-4(x+5)=(x+5)(x-4)=0\\\\x=4 \ or \ x=-5[/tex]
and then g(4)=0 and g(-5)=0
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:(-5,0) (4,0)
I took the test hope it helps you (:
Y is directly proportional to x. Create an equation using k as the constant of proportionality.
Answer:
[tex]y = kx[/tex]
Step-by-step explanation:
y is directly proportional to x.
[tex]y \propto x[/tex]
[tex]y = kx[/tex]
Where k is as the constant of proportionality.
Answer:
y = kx
Step-by-step explanation:
Y is directly proportional to x which means that
=> y ∝ x
=> y = kx
Where k is the constant of proportionality.
Based on historical data, an insurance company estimates that a particular customer has a 2.6% likelihood of having an accident in the next year, with the average insurance payout being $1600.
If the company charges this customer an annual premium of $110, what is the company's expected value of this insurance policy?
Answer: $68.4
Step-by-step explanation:
Given: Annual Premium = $110
Average insurance payout = $1600
Likelihood of having an accident= 2.6% = 0.026 [we divide perecnt by 100 to convert it into decimal]
Then, Expected value = (Annual Premium) - (Likelihood of having an accident) x (Average insurance payout )
= $110 - (0.026) x ($1600)
= $(110-41.6)
= $68.4
Hence, the company's expected value of this insurance policy : $68.4
Find the linear correlation coefficient using only the four points in the lower left corner (for women). Will the four points in the upper right corner (for men) have the same linear correlation coefficient? The correlation coefficient for the points in the lower left corner is requals nothing.
Answer:
Yes, because the four points in the upper right corner from the same pattern as the four points in the lower left corner.
Step-by-step explanation:
The correlation coefficient for the points in the lower left corner equals zero.
The four points in the upper right corner have the same correlation coefficient because the four points in the upper right corner from the same pattern as the four points in the lower left corner.
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on a graph, he notices that his classmates’ times are distributed symmetrically along the x-axis. Which component of data analysis is Ralph observing
Answer:
The overall shape of the data
Step-by-step explanation:
For us to know what shape a data is, it must fulfil 4 conditions
is it symmetrical?the amount of peaks available in the data set.is it uniform? Is it rightly or leftly skewed?From the question, Ralph observed that the classmates time are symmetrical along the x-axis.
Therefore he is observing the shape of the data since one of the conditions have been fulfilled.
Thank you!
Solve of the following equations for x: x – 6 = -2
Answer:
x = 4
Step-by-step explanation:
x - 6 = -2
Add 6 to each side
x-6+6 = -2+6
x = 4
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
[tex]x - 6 = -2[/tex]
Add 6 on both sides of the equation. The [tex]x[/tex] variable should be isolated on one side.
[tex]x - 6 +6= -2+6[/tex]
[tex]x=4[/tex]
The value of [tex]x[/tex] is 4.
Plz help this is an evil question
Answer:
18.9 units of fencing
Step-by-step explanation:
First find the perimeter
P = 2(l+w)
P = 2( 2.5+1.28)
P = 2( 3.78)
P =7.56m
We need 2.5 units of fencing for each meter
Multiply by 2.5
7.56*2.5
18.9 units of fencing
Answer:
Julio needs to purchase 18.9 units of fencing.
Step-by-step explanation:
I meter of the perimeter accounts for 2.5 units of fencing. Respectively 2 meters account for 2 times as much, and 3 meters account for 3 times as much of 2.5 units. Therefore, if we determine the perimeter of this rectangular garden, then we can determine the units of fencing by multiplying by 2.5.
As you can see this is a 2.5 by 1.28 garden. The perimeter would be two times the supposed length, added to two times the width.
2.5 x 2 + 1.28 x 2 = 5 + 2.56 = 7.56 - this is the perimeter. The units of fencing should thus be 7.56 x 2.5 = 18.9 units, or option d.
Solve the formula for the perimeter of a rectangle, with width w and length I,
for the length.
P= 2W + 2/
Answer:
( P -2w) /2 = l
Step-by-step explanation:
P= 2W + 2l
Subtract 2W from each side
P= 2W -2W + 2l
P -2W = 2l
Divide by 2
( P -2w) /2 = l
Answer:
A. [tex]\frac{P - 2w}{2} = l[/tex]
Step-by-step explanation:
Well in,
P = 2w + 2l
to solve for l we need to single it out.
P = 2w + 2l
-2w
P - 2w = 2l
divide everything by 2
[tex]\frac{P - 2w}{2} = l[/tex]
Thus,
the answer is A.
Hope this helps :)
Train passes the first 110 miles in 3 hours, and the next 240 miles at the rate of 60 mph. What was the average speed of the train for the entire trip?
Answer:
50 mph
Step-by-step explanation:
The total distance is 350 miles.
The total time is 3 hr + (240 mi / 60 mph) = 7 hr.
The average speed is 350 mi / 7 hr = 50 mph.
Evelyn is shopping for laundry detergent, and she prefers to get the best unit price she can. At the store, brand A is priced at $54 for 6 loads of laundry and brand B is priced at $63 for 9 loads of laundry
The unit cost of Brand B is less than Brand A, Evelyn for shop for Brand B.
What is the meaning of Unit Price ?Unit price is the price of one(unit) quantity of any substance.
The Brand A detergent costs $54 for 6 loads of laundry
Brand B detergent costs $63 for 9 loads of laundry
The unit price of both the detergent has to be compared to find the best among both
Unit cost for Brand A = 54/6 = $9
1 load of Brand A costs $9
Unit cost of Brand B = $63/9 = $7
1 load of Brand B costs $7
As, the unit cost of Brand B is less than Brand A, Evelyn for shop for Brand B.
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The radius of a conical tent is 5.6 m and the slant height is 12 m. Then the length of canvas required
to make the tent, if the width of canvas is 4 m.
a) 106.6 m
b) 100 m
c) 52.8 m
d) 105.6m
who will answer it first I mark them as the brainlist
Answer:
c) 52.8 m
Step-by-step explanation:
The radius of a conical tent, r = 5.6 m
The slant height = 12 m.
The area of the canvas required to make the tent is equal to the lateral area of the cone.
[tex]\text{Lateral Area of a Cone}= \pi r l\\=\pi \times 5.6 \times 12\\=67.2\pi$ m^2[/tex]
Since the width of the canvas = 4 m
Let the length = l
Area of the canvas = 4l
[tex]4l=67.2\pi$ m^2\\l=67.2\pi \div 4\\l=52.8 m$ (correct to 1 decimal place)[/tex]
The length of the canvas required to make the tent is 52.8m.
Use this scenario for questions 16-20: A city council begins hosting music nights in the park. They want to understand the success of the program, so they record attendance on 4 different nights (n = 4). On average, the city saw an average attendance of 47 (s = 4.7). Other cities that have launched a similar program and have seen an average attendance of μ = 53 (σ = 4.2). Is the city attendance different from other cities that have launched these music programs (alpha = .05)? What would be the hypotheses for this test? (HINT: remember one-tailed and two-tailed tests!).
Answer:
Step-by-step explanation:
To identify the null hypothesis, the null hypothesis is the default statement while the alternative hypothesis is the opposite of the null and always tested against the null hypothesis.
The alternative hypothesis depending on the case study can give rise to a one-tailed or a two-tailed test. The one tailed test includes either less than or greater than option and not both while the two tailed test involves both.
In this case study,
the null hypothesis is u1 (representing the city in particular) = u2 (representing other cities)
The alternative hypothesis is u1 (representing the city in particular) =/ u2 (representing other cities).
This, this test due to its not equal to sign is a two tailed test, the two results might differ maybe with one higher than the other, or lower than the other.
Water leaking from a local reservior at the rate of 500 gallons per hour. A. none of these B. quadratic C. exponential D. linear
Answer:
Linear
The 500 hundred gallons is adding up by the hours. Linear- first difference.
please please please help me. i need to pass, will do anything. ANYTHING!
Answer:
[tex]d \approx 5.8[/tex]
Step-by-step explanation:
Just use the distance formula.
[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]
[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]
[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]
[tex]d=\sqrt{9+25}[/tex]
[tex]d=\sqrt{34[/tex]
[tex]d \approx 5.8[/tex]
Forty percent of all undergraduates at a university are chemistry majors. In a random sample of six students, find the probability that exactly two are chemistry majors. 12. The probability that exactly two are chemistry majors is Type an integer or a decimal. Round to four decimal places as needed.)
Answer:
0.3110
Step-by-step explanation:
This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.
The general formula for a binomial distribution is:
[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]
Where n is the sample size and k is the desired number of successes.
The probability of k=2 in a sample of n =6 is:
[tex]P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110[/tex]
The probability is 0.3110