Answer:
Step-by-step explanation:
Because the arcs HI and GJ are the same, that means that the segments HI and GJ are also the same. Therefore,
c + 20 = 2c and
20 = c
Wyatt is making a salad using tomatoes, cucumbers, and carrots. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Wyatt uses:
Ingredient Price per kilogram Amount
Tomatoes 3.30dollars per kilogram 0.3
Cucumbers x dollars per kilogram y kilograms
Carrots z dollars per kilogram 0.20
The total amount Wyatt spends on ingredients is C dollars.
Write an equation that relates x, y, z, and C.
According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:
[tex]C = 0.99 + xy + 0.2z[/tex]
Cost:
0.3 kilograms of tomatoes, at 3.30 dollars per kilogram.
Thus, the cost starts at:
[tex]C = 0.3*3.3 = 0.99[/tex]
y kilograms of cucumbers, at x dollars per kilogram.
Considering this, the cost will now be of:
[tex]C = 0.99 + xy[/tex]
0.2 kilograms of carrots, at z dollars per kilogram:
Now, we have to consider this for the cost, so:
[tex]C = 0.99 + xy + 0.2z[/tex]
A similar example is given at https://brainly.com/question/14544759
in figure , EF=1 and FC=2 What is the length of AC?
Step-by-step explanation:
ae=ec
ec=1+2=3
then ae=3
Answer:
6-most likely (AC=6)
Step-by-step explanation:
Because the 2 sides, AE and EC *look the same. Also you can look at the opposite sides.
*This is what I think
x^ 3 +x^ 2 +4x/x^ 2 +x-2
into partial
fractions
Answer:
x + (4/ x-2) + (2/ x-1)
Step-by-step explanation:
x + (6x/ x^2 + 2x - x -2)
x + (6x/ (x + 2) X (x - 1))
(6x/ (x + 2) X (x - 1))
(A/ x+2) + (B/ x-1)
(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)
6x = Ax + Bx - A + 2B
6x = (A+B)x + (-A+2b)
{0 = -A+2B
{6 = A+B
(A,B) = (4, 2)
(4/ x+2) + (2/ x-1)
x + (4/ x-2) + (2/ x-1)
In the following problem, the ratios are directly proportional. Find the missing variable.
If y1 = 4, x2 = 6, and y2 = 8, what is the value of x1?
Answer:
x1 = 3
Step-by-step explanation:
first set up the proportion (write as fractions):
(y1/x1) = (y2/x2)
then fill in the variables:
4/x1 = 8/6
now cross multiply:
8 • x1 = 6 • 4
simple algebra:
8 • x1 = 24
x1 = 24/8
x1 = 3
If y1 = 4, x2 = 6, and y2 = 8, then the value of x1 is 3 which we can solve using ratios.
In a directly proportional relationship, the ratios between the corresponding values of two variables remain constant. This constant ratio is often referred to as the "proportionality constant."
In this problem, you have two pairs of values: (x1, y1) and (x2, y2). We're given that the ratios are directly proportional, which means:
x1 / y1 = x2 / y2
Plugging in the given values:
x1 / 4 = 6 / 8
Now, cross-multiply to solve for x1:
x1 * 8 = 4 * 6
x1 = 24 / 8
x1 = 3
Therefore, the value of x1 is 3.
Learn more about ratios here:
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Hello Pls help and thanks
Answer:
c.) in the correct answer
factorise m^2 - 12 m + 24
Answer:
(m-6+2root3)(m-6-2root3)
Step-by-step explanation:
m^2 - 12m +36 -12
= (m-6)^2 - 12
= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]
find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x-2y=10
Answer:
(14,2) and (-6/5,-28/5)
Step-by-step explanation:
The distance, d, from two points (x,y) and another point (a,b) can be calculated using
d=sqrt((x-a)^2+(y-b)^2).
Our point (a,b) is (2,7) and d=13.
Making substitutions:
13=sqrt((x-2)^2+(y-7)^2)
We are also given the relation between x and y is given as x-2y=10.
Adding 2y to both sides gives: x=10+2y
Make this insertion into our equation:
13=sqrt((10+2y-2)^2+(y-7)^2)
Simplify inside:
13=sqrt((8+2y)^2+(y-7)^2)
Square both sides:
169=(8+2y)^2+(y-7)^2
Expand binomial squares:
169=64+32y+4y^2+y^2-14y+49
Combine like terms:
169=5y^2+18y+113
Subtract 169 on both sides:
0=5y^2+18y-56
We could try to factor
0=(5y+28)(y-2)
So y=2 or y=-28/5
Recall x=10+2y
So if y=2, then x=10+2(2)=10+4=14.
So if y=-28/5, then x=10+2(-28/5)=10+(-56/5)
=50/5 +-56/5
=-6/5.
So two points satisfying given criteria is
(14,2) and (-6/5,-28/5).
4x + 8 + 3(x - 2) + 3x ,combining liked terms
Answer:
4x+8 +3x - 6 + 3x
10x + 8 - 6
10x + 2
The product of two rational numbers is 47/42 and one of them is -11/21, find the other number
answer:
another number is -47/22
explanation:
let one number be x and the other be y
-11/21 × y = 47/42
y = -47/22
Answer:
- [tex]\frac{47}{22}[/tex]
Step-by-step explanation:
let n be the other number , then
- [tex]\frac{11}{21}[/tex] × n = [tex]\frac{47}{42}[/tex] ( divide both sides by - [tex]\frac{11}{21}[/tex] )
n = [tex]\frac{\frac{47}{42} }{-\frac{11}{21} }[/tex]
= [tex]\frac{47}{42}[/tex] × - [tex]\frac{21}{11}[/tex] ( cancel 21 and 42 )
= [tex]\frac{47}{2}[/tex] × - [tex]\frac{1}{11}[/tex]
= - [tex]\frac{47}{22}[/tex]
What is the smallest number that becomes 600 when rounded to the nearest hundred?
A. 545
B. 550
C. 555
D. 590
Answer:
B. 550
Step-by-step explanation:
550 is the smallest number that becomes 600 when rounded to the nearest hundred
The organic garden at a restaurant is rectangular in shape and has a perimeter of 84 feet. If the length of the garden is 24 ft longer than the width of the garden what is the area of the garden in sq ft
Answer:
297 square feet
Step-by-step explanation:
Let w represent the width of the garden.
Since the length is 24 ft longer than the width, it can be represented by w + 24.
Use the perimeter formula, p = 2l + 2w. Plug in the perimeter and w + 24 as l, then solve for w:
p = 2l + 2w
84 = 2(w + 24) + 2w
84 = 2w + 48 + 2w
84 = 4w + 48
36 = 4w
9 = w
So, the width is 9 ft. Add 24 to this to find the length:
24 + 9 = 33
So, the length is 33 ft.
Find the area of the garden with the formula A = lw:
A = lw
A = (33)(9)
A = 297
The area of the garden is 297 square feet.
A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 8 questions on the survey
Answer:
40320 different surveys would be necessary ...
Step-by-step explanation:
let's start small :
how many are required for 2 questions ?
well, 2 (we can either ask question 1 first and then question 2, or question 2 first and then question 1).
how many for 3 questions ?
well, we have a choice of 3 questions to be asked first. but then for the second and third question we are back in the previous problem of 2 (remaining) questions.
so, we multiply the 3 initial options with the 2 following options. 3×2 = 6
how many for 4 questions ?
well, we have a choice of 4 questions as first question, and then fit the rest we are back in the previous problem of 3 questions. 4×3×2 = 24
you see the pattern ?
yes, that continues as far as we want to go.
for our example the problem was about 8 questions.
so,
8×7×6×5×4×3×2 = 8! = 40320
Why wouldn't you use division to find an equivalent fraction for 7/15
Answer:
This depends whether you want to make the fraction bigger or smaller.
Step-by-step explanation:
If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.
However, if you want to make the fraction bigger, then you would multiply.
Hope this helps! :)
Answer:
Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.
Step-by-step explanation:
How many minutes will the bus take to complete the trip If a bus completes half a trip at 40 km per hour and the other half at 50 20. if the whole trip was 60 k.m. ?
Answer:
The bus will take 81 minutes to complete the trip.
Step-by-step explanation:
To determine how many minutes will the bus take to complete the trip if a bus completes half a trip at 40 km per hour and the other half at 50 km per hour, and the whole trip was 60 km, the following calculation must be performed:
60/2 = 30
30/40 = 3/4 of an hour = 45 minutes
30/50 = 3/5 of an hour = 36 minutes
45 + 36 = 81
Therefore, the bus will take 81 minutes to complete the trip.
△DOG ~△?
Complete the similarity statement and select the theorem that justifies your answer.
**If they are not similar, select "none" for both parts
9514 1404 393
Answer:
nonenoneStep-by-step explanation:
The reduced side ratios, shortest to longest are ...
AC : AT : CT = 8 : 9 : 15
OD : OG : DG = 5 : 6 : 10
These are different ratios, so the triangles are not similar.
*20 points*
how do you get the weighted average from this table?
Answer:
it is
[(2+3+4+6)-2*4]:4=1.75
I THINK
Step-by-step explanation:
[tex]4 + \frac{4}{4 } \: = [/tex]
what is answer
Answer:
5Step-by-step explanation:
[tex]4 + \frac{4}{4} [/tex]
= 4 + 1
= 5 (Ans)
Consider a credit card with a balance of $7000 and an APR of 16.5 %. If you want to make monthly payments in order to pay off the balance in 1 year, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.
9514 1404 393
Answer:
$7641.24
Step-by-step explanation:
The amortization formula tells the payment amount.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where principal P is paid off in t years with n payments per year at interest rat r.
Using the given values, we find ...
A = $7000(0.165/12)/(1 -(1 +0.165/12)^-12) = $7000×0.01375/(1 -1.01375^-12)
A = $636.77
The total of 12 such payments is ...
$636.77 × 12 = $7641.24
You will pay a total of about $7641.24.
_____
Additional comment
Since the payment amount is rounded down, the actual payoff will be slightly more. Usually, the lender will round interest and principal to the nearest cent on each monthly statement. The final payment will likely be a few cents more than the monthly payment shown here.
Finding Perimeter Practice Pages continued Name: 3 A rectangular garden has a width of 90 feet. The perimeter is 500 feet. What is the length of the garden? 500 = (2x) + .......... .........) 500 = 2€ + = 20 = 2 = = € The length of the garden is ................. feet. inchor lona Tell w
Step-by-step explanation:
After putting the values:-
4. Work out the area.
Answer:
90m^2
Step-by-step explanation:
image shows a trapezium,
area of trapezium = h(a+b)/2 = 9(8+12)/2 = 90
Answer:
29
12+8+9 =29
Step-by-step explanation:
additional question
add tose measure
Area of a circle whose circumference is 100ft
Answer:
A≈795.77ft²
Step-by-step explanation:
C=100ft
Area of circle=C^2/4pie
100/4×22/7≈795.77472ft²
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
f(x)g(x) if you find the derivative of two products, you get f(x)g’(x)+f’(x)g(x). Let’s say x^2 = f(x).
(x^2)(g’(x))+2x(g(x)) so it would be your last option, 2x(g(x))+x^2(g’(x))
Mr. Cole packed 20 pounds into a suitcase, and Mrs. Cole packed 23 pounds into the same suitcase. They then had to remove 8 pounds because it was too heavy. How many pounds was their suitcase after making it lighter?
Answer:
35 lbs is the final weight
Step-by-step explanation:
20 +23 = 43 lbs
Then they had to remove 8 lbs
43 - 8 =35
35 lbs is the final weight
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink what fraction of the bouquet is pink? There are 12 roses in a dozen.
A. 5/12
B. 7/12
C. 5/7
D. 7/5
Answer:
7/12
Step-by-step explanation:
There are 12 roses - 5 white = 7 pink
7 pink / 12 total
Twelve residents from the city of Rocklin were randomly selected and asked "How many TVs are in your household?". The following data were obtained: 2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, and 3.
According to Nielsen Media Research the national average is 2.7 TVs per household. Is this sufficient sample evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average of 2.7 TVs per household? Use ! = 5% and assume that the number of TVs in Rocklin households is normally distributed.
Answer:
There isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average .
Step-by-step explanation:
This is a one sample mean test ;
H0 : μ = 2.7
H1 : μ > 2.7
Given the data :
2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3
Sample size, n = 12
The sample mean, xbar = ΣX / n = 33/12 = 2.75
The sample standard deviation, s = 1.215 ( from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.75 - 2.7) ÷ (1.215/√(12))
T = 0.05 / 0.3507402
T = 0.1426
The critical value from Tscore ;
df = 12 - 1 = 11
Critical value = 1.796
Since ; Test statistic < Critical value ;WE fail to reject the Null and conclude that there isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average
Not sure how to do this
8.) It takes Fred 9 minutes to type and spell check 13 pages of a manuscript. Find how long it takes him to type and spell check 60 pages. Round to the nearest whole number. answer: minutes
It will take Fred 42 minutes to type and spell check 60 pages.
Let the first scenario be A.Let the second scenario be B.Let the unknown time be X.Given the following data;
Time taken A = 9 minutesNumber of pages A = 13 pagesNumber of pages B = 60 pagesTime taken B = X minutesTo find how long it takes him to type and spell check 60 pages;
We would use direct proportion to express the work described and solve for the unknown variable (time).
[tex]9 \;minutes : 13 \;pages\\\\X \;minutes : 60 \;pages[/tex]
Cross-multiplying, we have;
[tex]9[/tex] × [tex]60[/tex] [tex]= 13[/tex] × [tex]X[/tex]
[tex]540 = 13X\\\\X = \frac{540}{13}[/tex]
X = 41.54 ≈ 42 minutes
Therefore, it will take Fred 42 minutes to type and spell check 60 pages.
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Janet invests a sum of EUR in an account that offers 3.5% simple interest. After ten years her investment is worth 7425 EUR. How much did she invest?
We need to find the amount of money Janet invested in 10 years to yield 7425 EUR
She invested EUR 21,214.29
Simple interest = P × R × T
Where,
P = principal = ?
R = interest rate = 3.5% = 0.035
T = Time = 10 years
Simple interest = 7425 EUR
Simple interest = P × R × T
7425 = p × 0.035 × 10
7425 = p × 0.35
7425 = 0.35p
Divide both sides by 0.35
P = 7425 / 0.35
= 21,214.285714285
Approximately,
P = EUR 21,214.29
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John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John
buys a new cylindrical propane tank that is twice as wide and half as tall as his
current tank, how much larger will the volume of the new tank be?
Answer:
2 times as large
Step-by-step explanation:
For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128
For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus
V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256
To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in
π * 256 / (π *128) = 2
Please help me solve this question ?
Answer:
Hi,
If you don't know how to derivate, i can show you using
lim (f(x+h)-f(x))/h if h ->0
Step-by-step explanation:
[tex]f(x)=2x^2+3x-2\\\\f'(x)=4x+3\\\\f'(1)=4*1+3=7\\\\f'(3)=4*3+3=15\\\\f'(5)=4*5+3=23\\[/tex]
Step-by-step explanation:
18