If
f (x) = 3x +1 and 1-1 = *?
then f-'(7) =
O 22
O-2
02
According to my calculations answer is -2
On Fridays, Jerry stops at Steak & Taco Shack before he goes home. This week
his order was 1 steak sandwich, 2 orders of cheese fries, and 2 taco salads. He was
charged $11.50 before tax. One week ago, his order was 2 steak sandwiches, 3
orders of cheese fries, and 1 taco salad, and he was charged $15.25. Two weeks ago
he ordered 1 steak sandwich, 4 orders of cheese fries, and 1 taco salad, and was
charged $13. How much is 1 steak sandwich? How much is 1 cheese fries? How
much is 1 taco salad?
Answer:
Steak sandwich = x = 4
Cheese fries = y = 1.75
Taco salad = z = 2
Step-by-step explanation:
Let :
Steak sandwich = x
Cheese fries = y
Taco salad = z
This week:
x + 2y + 2z = 11.50 - - - - (1)
Last week :
2x + 3y + z = 15.25 - - - (2)
Two weeks ago :
x + 4y + z = 13 - - - - - (3)
Taking (1) and (2)
x + 2y + 2z = 11.50 ___(1)
2x + 3y + z = 15.25 ___(2)
Multiply (1) by 2 and (2) by 1 and subtract
2x + 4y + 4z = 23
2x + 3y + z = 15.25
_______________
y + 3z = 7.75 - - - - (4)
Taking (2) and (3)
2x + 3y + z = 15.25 - - (2)
x + 4y + z = 13 - - - - - (3)
Multiply (2) by 1 and (3) by 2 and subtract
2x + 3y + z = 15.25
2x + 8y + 2z = 26
______________
-5y - z = - 10.75 - - - - - (5)
Lets solve (4) and (5)
y + 3z = 7.75 - - - - (4) - - - multiply by 5
-5y - z = - 10.75 - - - - - (5) - - - multiply by 1
Then add the result :
5y + 15z = 38.75
-5y - z = - 10.75
____________
14z = 28
z = 28 / 14
z = 2
To find y ; put z = 2 in (4)
y + 3z = 7.75
y + 3(2) = 7.75
y + 6 = 7.75
y = 7.75 - 6
y = 1.75
From equation 3 ;
x + 4y + z = 13 - - - - - (3)
x + 4(1.75) + 2 = 13
x + 7 + 2 = 13
x + 9 = 13
x = 13 - 9
x = 4
Hence,
Steak sandwich = x = 4
Cheese fries = y = 1.75
Taco salad = z = 2
A runner’s distribution of times for running 1,000 meters has a mean of 4.5 minutes with a standard deviation of 0.75 minutes. One of the runner’s times has a z-score of –1.08. Which of the following statements is the best interpretation of this z-score?
This runner’s time was faster than the mean time by 0.75 standard deviations.
This runner’s time was faster than the mean time by 1.08 standard deviations.
This runner’s time was slower than the mean time by 0.75 standard deviations.
This runner’s time was slower than the mean time by 1.08 standard deviations.
Answer:
I believe it is (C).
This runner’s time was slower than the mean time by 0.75 standard deviations.
ED2021
Answer:
B) This runner’s time was faster than the mean time by 1.08 standard deviations.
Step-by-step explanation:
The runner is FASTER because of the negative z score
Correct
Suppose it takes John 27 minutes to run 3 miles. How long would it take him to run 4 kilometers? Round your answer to the nearest minute,
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Answer:
Step-by-step explanation:
4km
[tex]\frac{3 }{27} \frac{miles}{minutes}[/tex] * [tex]\frac{60}{1} \frac{min}{hour}[/tex] * [tex]\frac{1}{.6213} \frac{km}{mile}[/tex]
4km ÷ 10.73 km/hr = .37 hr = 22.3 minutes
Simple geometry please help
Find KL. Round to the nearest hundredth.
Answer:
KL ≈ 1.94
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{JL}{KL}[/tex] = [tex]\frac{1.3}{KL}[/tex] ( multiply both sides by KL )
KL × cos48° = 1.3 ( divide both sides by cos48° )
KL = [tex]\frac{1.3}{cos48}[/tex] ≈ 1.94 ( to the nearest hundredth )
Find the solutions of x^2+30 = 0
please give detailed steps!
Answer:
x= i√30
Step-by-step explanation:
I'm going to go into this under the assumption that you've covered imaginary numbers based on the question. If I'm wrong then sorry about that.
Okay, so first you want to subtract 30 from both sides
x^2=-30
Then you take the square root of each side.
√(x^2)=√-30
x=√-30
Since it's impossible to square a number to get a negative number, you'll end up with an imaginary number. You have to rewrite x=√-30 to get rid of the negative sign under the radical. Rewriting this will also indicate that it's an imaginary number.
Final answer: x = i√30
Farah is x years old. Ibtisam is 3 years younger than Farah. Muna is twice as old as Ibtisam. Write and expression in terms of x, for
(a) Ibtisam's age,
(b) The sum of their three ages, giving your answer in its simplest form.
Answer:
Farah: x
Ibtisam: x-3
Muna: 2(x-3) or 2x-6
Sum of all their ages: 4x-6
Step-by-step explanation:
Farah is x, so we don't need an expression for that.
Ibtisam is 3 years younger than Farah, which means that we need to subtract 3 from Farah, and that would be Ibtisam's age. x-3.
Muna is 2 TIMES Ibtisam's age, so we need to multiply whatever expression taht was used for Ibtisam by 2. Put brackets around the equation with 2 outside: 2(x-3). Solve and you get 4x-6
Now, you have all their ages in expression form, now you need to simplify by adding:
x+x+2x-6
We cannot simplify -6, so we put that aside. Add all the x's and you get 4x, insert the minus 6 at the end:
4x-6
Hope this helps!
--Applepi101
Answer:
a) X -3
b) 4x - 9
Step-by-step explanation:
a) Farah's age is X so Ibtisam will be X - 3 old since he is 3years younger than Farah
b) Farah is X years old
Ibtisam is X - 3 years old
Muna is 2(X -3) since she is 2 times older than Ibtisam.
the sum of Thier ages will be
X + X -3 + 2(x-3)
= 2x - 3 + 2x - 6
= 4x - 9
been stuck on this for a few days now, help on even one would be greatly appreciated!!!
Answer:
-5-9i
Step-by-step explanation:
-1-8i-4-i
-1-4-8i-i
-5-9i
The fraction 64/72 is a
Answer:
proper fraction
Step-by-step explanation:
This is a proper fraction, which has a numerator smaller than the denominator
a mixed number has a whole number in front such as 1 3/5
An improper fraction has a numeration greater than a denominator such as 7/6
drag the numbers to order them from least to greatest
0.19
-2.86
-0.37
0.91
1.46
The larger the negative number the smaller it is:
-2.86, -0.37, 0.19, 0.91, 1.46
Calvin and Jamel each havr cats as pets. Calvin buys cat food in cylindrical can that are 6 centimeters in diameter and 12 centimeters high. Jamel buys cat food in cylindrical can that 12 centimeters in diameter and 6 centimeters high. What is the ratio of the volume of one of Calvin's cans of to the volume of one of Jamel's cans?
Answer:
see below
Step-by-step explanation:
CALVIN
v=[tex]\pi[/tex]× r ² × h
v=3.14 × 3² × 12
v=3.14×9 × 12
v=3.14 × 108
v = 339.12
JAMEL
v=[tex]\pi[/tex] × r ²×h
v=3.14× 6 ² × 6
v=3.14 × 36×6
v=3.14×216
v=678.24
A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?
Answer:
dv = surface area * dh
so
dv/dt = surface area * dh/dt
width at surface = 40 + (80-40)(30/40)
= 40 + 30 = 70 cm = 0.70 m
so
surface area = 9 * .7 = 6.3 m^2
so
.3 m^3/min = 6.3 m^2 * dh/dt
and
dh/dt = .047 meters/min or 4.7 cm/min
Step-by-step explanation:
КУ
11
10
A
9
8
7 구
6
5
4
A А
C
3
B'
2
1
B
C с
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6
A ABC is dilated about the origin./
What scale factor was used to make the image A A'B'C?
Answer:
3
Step-by-step explanation:
The dilation factor is 3
(a+b)2= c+d
answer
answer
Answer:
a+b=c+d/2
i cant understand what answer you want
Given the formula A = 5h (B + b); solve for B.
2
Answer:
B = A/5h - b; You could use
B = (A - 5hb)/5h This just puts everything over a common denominator.
Step-by-step explanation:
A = 5h (B + b) Divide both sides by 5h
A/5h = B + b Subtract b from both sides.
A/5h - b = B
Rearrange to make P the subject, :)..
Answer: [tex]P = \frac{25}{E^2}-Q\\\\[/tex]
Work Shown:
[tex]E = 5\left(\sqrt{\frac{1}{P+Q}}\right)\\\\5\left(\sqrt{\frac{1}{P+Q}}\right) = E\\\\\sqrt{\frac{1}{P+Q}} = \frac{E}{5}\\\\\frac{1}{P+Q} = \left(\frac{E}{5}\right)^2\\\\\frac{1}{P+Q} = \frac{E^2}{25}\\\\P+Q = \frac{25}{E^2}\\\\P = \frac{25}{E^2}-Q\\\\[/tex]
what represent the area of the rectangle in cm^2??
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Answer:
d. 3x² +15x
Step-by-step explanation:
The area is the product of length and width.
A = LW
A = (3x)(x+5) = 3x(x) +3x(5) . . . . use the distributive property
A = 3x² +15x
Answer: D) 3x^2 + 15
==========================================================
Explanation:
Draw a horizontal line to divide the rectangle into two parts (they don't necessarily have to be equal parts). Refer to the diagram below. The upper rectangle is x by 3x. So its area is length*width = x*3x = 3x^2
The lower rectangle is 5 by 3x, so its area is 5*3x = 15x
Combine those two sub-areas back together to get the overall area of 3x^2 + 15x
You could also use the distribution rule
3x*(x+5) = 3x*(x) + 3x*(5) = 3x^2 + 15x
A loaf of bread costs $1.40 and the markup is 30% of the selling price. Find the selling price.
Answer:
The selling price after the markup is $1.82
Step-by-step explanation:
$1.40 * .30 =
Multiply $1.40 times .30 (which is same as 30%)
$1.40 * .30 = $0.42
Add $1.40 and $0.42
= $1.82
Hope this helps.
PLEASE HELP VENN DIAGRAM!
Look at attached for the diagram!!!
In his diagram BH represents the students that have brown hair and W represents the students that are wearing a watch.
Is having brown hair independent of wearing a watch?
Please show some work if possible
Answer:
Yes.
Step-by-step explanation:
Since there is an overlap, that does mean some people with brown hair do wear watches, but not all of them do. Hence it's independent.
what translation was the similarity moved through ?
Simplify: y^-3
a) 3/y
b) - 1/y^3
c) -3y
d) 1/y^3
Answer:
1/y^3
Step-by-step explanation:
We know that a^-b = 1/a^b
y ^-3 = 1/y^3
43% of a sample of 100 visitors to a national park believes that additional funds should be used to preserve endangered species. What is the margin of sampling error for a 95% confidence interval?
A. 9.7%
B. 5.4%
C. 43%
D. 19.4%
Answer:
A. 9.7%
Step-by-step explanation:
margin of error:
z * [tex]\sqrt{\frac{p(1-p)}{N} }[/tex]
n is sample size
z is the z score (for a 95% confidence interval you would use 1.96)
p is the sample proportion
to solve for 'p', remember that if a decimal value is given, use that. but if it is a whole number, then divide that number by the sample size, and substitute it into the formula.
in this case we are given 43% so 0.43.
in the formula :
1.96 * [tex]\sqrt{\frac{0.43(1-0.43)}{100} }[/tex]
if you calculate this you get around 0.09703 this is 9.7%
Margin of error is 9.7% (A)
ρ = 43% which is equal to 0.430
[tex]1 - P = 1 - 0.430 = 0.570[/tex]
The number of sample n = 100
We have to calculate Z at 95% confidence interval
∝ = [tex]1 - 95%[/tex]%
∝ = [tex]1 - 0.95[/tex]
∝ = [tex]0.05[/tex]
∝/2 = 0.025
Z(∝/2) = Z(0.025) = 1.96
Standard error = [tex]\sqrt{ ((1-P)xP / n)}[/tex]
Standard error = [tex]\sqrt{(1-0.43)x0.43 / 100)[/tex]
Standard error = [tex]\sqrt{(0.002451)}[/tex]
Standard error = 0.04950758
Standard error = 0.0495
Margin of error = Z*SE. z = 1.96 and standard error = 0.0495
Margin of error = [tex]1.96x0.0496[/tex]
Margin of error = [tex]0.097216[/tex]
Margin of error = [tex]9.7216%[/tex]%
In conclusion, the margin of sampling error for a 95% confidence interval is 9.7%.
Learn more about margin of sampling error brainly.com/question/3311743
find the length of the arc . round your answers to the nearest tenth PLEASE HURRY
Answer:
10.2
Step-by-step explanation:
Length of arc=(2*pi*r)*(theta/360)
Length of arc=(2*pi*3)*(195/360)=10.2
Can you provide a solution or a formula?
144 x 1.25 = 180
Answer: 144
Answer:
144
Step-by-step explanation:
144 × 1.25 = 180
We add the 1 to .25 to represent the original value plus the 25% increase.
Or you could have divided 180 by 1.25 to find original price.
The point A(−8,−4) is reflected over the origin and its image is point B. What are the coordinates of point b?
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Answer:
B(8, 4)
Step-by-step explanation:
Reflection across the origin negates both coordinate values.
(x, y) ⇒ (-x, -y) . . . . . reflection across the origin
A(-8, -4) ⇒ B(8, 4)
An amortized loan of RM60,000 has annual payments for fifteen years, the first occurring exactly one year after the loan is made. The first four payments will be for only half as much as the next five payments, whereas the remaining payments are twice as much as the previous five payments. The annual effective interest rate for the loan is 5%. I If the first four payments are X each, calculate the amount of principal repaid in the eighth payment and the amount of interest in the twelfth payment.
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Answer:
a) RM2256.09 . . . principal paid by 8th payment
b) RM1791.10 . . . . interest paid by 12th payment
Step-by-step explanation:
First of all, we need to find the payments.
The payment amount is the amount that makes the future value of the series of payments equal to the future value of the loan at the given interest rate.
The future value of a single amount is ...
FV = P(1 +r)^n . . . . . where r is the annual rate, and n is the number of years in the future
The future value of a series of payments is ...
FV = P((1 +r)^n -1)/r . . . . . where n is the number of payments of P earning annual rate r
For payments in a series that does not end at the end of the loan, the future value is the product of that of the series and the effect of the accumulation of interest for the remaining time.
__
The first 4 payments will have a future value at the end of the loan period of ...
s1 = X((1 +0.05)^4 -1)/0.05×(1 +0.05)^11 = X(1.05^15 -1.05^11)/0.05
s1 = 7.3717764259X
The next 5 payments will have a future value at the end of the loan period of ...
s2 = 2X((1 +0.05)^5 -1)/0.05×(1 +0.05)^6 = 2X(1.05^11 -1.05^6)/0.05
s2 = 14.8097486997X
The last 6 payments will have a future value at the end of the loan period of ...
s3 = 4X((1 +0.05)^6 -1)/0.05 = 27.20765125X
So, the total future value of the series of payments is ...
payment value = 7.3717764259X +14.8097486997X +27.20765125X
= 49.3891763756X
__
The future value of the loan amount after 15 years is ...
loan value = 60,000(1 +0.05)^15 = 124,735.69
In order for these amounts to be the same, we must have ...
49.3891763756X = 124,735.69
X = 124,735.69/49.3891763756 = 2,525.57
__
At this point, it is convenient to use a spreadsheet to find the interest and principal portions of each of the loan payments. (We find the interest charge to be greater than the payment amount for the first 4 payments. So, the loan balance is increasing during those years.)
In the attached, we have shown the interest on the beginning balance, and the principal that changes the beginning balance to the ending balance after each payment. (That is, the interest portion of the payment is on the row above the payment number.)
The spreadsheet tells us ...
A) the principal repaid in the 8th payment is RM2,256.09
B) the interest paid in the 12th payment is RM1,791.10
_____
Additional comment
The spreadsheet "goal seek" function could be used to find the payment amount that makes the loan balance zero at the end of the term.
We have used rounding to sen (RM0.01) in the calculation of interest payments. The effect of that is that the "goal seek" solution is a payment value of 2525.56707 instead of the 2525.56734 that we calculated above. The value rounded to RM0.01 is the same in each case: 2525.57.
verify sin2θ/1+cos2θ =tanθ
Answer:
LHS.= Sin 2x /( 1 + cos2x )
We have , sin 2x = 2 sinx•cosx
And. cos2x = 2cos^2 x - 1
i.e . 1+ cosx 2x = 2cos^2x
Putting the above results in the LHSwe get,
Sin2x/ ( 1+ cos2x ) =2 sinx•cosx/2cos^2x
=sinx / cosx
= Tanx
.•. sin2x/(1 + cos2x)= tanx
Step-by-step explanation:
28. A boy decided to cut 10 pieces of wood from a length of wood so tha the first piece was 5cm the second 10cm, the third 15cm, the fourth 20cm and so on until he had cut TO pieces, each one 5cm longer than the one he had cut before. What length of the wood did he use? (a) 50cm (b) 55cm (c) 70cm (d) 200cm (e) 275cm
Step-by-step explanation:
he use 50cm length of the wood
8. 15x - 10 = 80
a. X= 2
b. x=4
c. X= 6
Answer:
C
Step-by-step explanation:
15x-10=80
15x=90
x=90/15, x=6
Answer:
x = 6
Step-by-step explanation:
15x - 10 = 80
Add 10 to each side
15x-10+10 = 80+10
15x = 90
Divide each side by 15
15x/15 = 90/15
x = 6
Use distributive property to remove parantheses
9(2/3-3x)
