The length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft
Length of each scarfNumber of friends = 7Total length of scarf = 39.9 ftLength of each scarf = Total length of scarf / Number of friends
= 39.9 ft / 7
= 5.7 ft
Therefore, the length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft
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The graph of the function f(x) is shown below.
-a
If a = 9, then find the value of
3a
f(x) d
-a
f(x) dx =
a
3a
fr f(x) dx.
-a
ROUND YOUR FINAL ANSWER TO 4 DECIMAL PLACES.
2a
3a
The integral of [tex]f(x)[/tex] over the interval [tex][-a,a][/tex] corresponds to the area of a semicircle of radius [tex]a[/tex], so
[tex]\displaystyle \int_{-a}^a f(x) \, dx = \frac{\pi a^2}2[/tex]
The integral over [tex][a,3a][/tex] corresponds to the negative area of a trapezoid with height [tex]a[/tex] and base lengths [tex]2a[/tex] and [tex]a[/tex], so
[tex]\displaystyle \int_a^{3a} f(x) \, dx = -\frac{a(2a+a)}2 = -\frac{3a^2}2[/tex]
Then combining the integrals, we have
[tex]\displaystyle \int_{-a}^{3a} f(x) \, dx = \frac{\pi a^2}2 + \left(-\frac{3a^2}2\right) = \frac{(\pi-3)a^2}2[/tex]
When [tex]a=9[/tex], the integral evaluates to
[tex]\displaystyle \int_{-9}^{27} f(x) \, dx = \frac{(\pi-3)\times81}2 \approx \boxed{5.7345}[/tex][/tex]
Question 2 of 11
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?
If the number of multiple-choice questions is x and the number of short answer questions is y, then:
[tex]x+y=28\\\\3x+5y=100[/tex]
Solve (X+8)=9 absolute value equation PLEASE HELP
Answer:
x = | 1 |
Step-by-step explanation:
how are u in college doing this???
Answer:
1
Step-by-step explanation:
(x+8)=9
x+8=9
x=9-8
x=1
A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
Answer:
the answer is c. the row is chili, the column is no cheese
PLEASE HELP ASAP PLEASEEEEEEE PLEASEEEEEEEEE EASY 20 POINTS
The transformation of a function may involve any change. The function with the graph are given below.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)Right shift by c units: y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)The real graph of the function is f(x)=x², now if the graph of the given function can be found by using the transformation rule as shown above. The function with the graph are given below.
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Which of the following is the balance for a single $2.520 deposit in an account with an APR of 1.16% that compounds interest monthly and is invested for 37 years? Which of the following is the balance for a single $ 2.520 deposit in an account with an APR of 1.16 % that compounds interest monthly and is invested for 37 years ?
Answer:
The balance after 37 years is $3869.99
Step-by-step explanation:
Given:
Principal (P) = $2,520Rate of Interest (R) = 1.16%Time (t) = 37 yearsCompounds Interest Monthly (n) = 12The Amount (A),
A = P (1 + [tex]\frac{R}{100n}[/tex][tex])^{nt}[/tex] if compound n times per year
Amount (A) at 37 years,
A = ($2,520) (1 + [tex]\frac{1.16}{100(12)}[/tex][tex])^{12 x 37}[/tex]
A = ($2,520) (1 + [tex]\frac{1.16}{1,200}[/tex][tex])^{444}[/tex]
A = ($2,520) (1.00096667 [tex])^{444}[/tex]
A = ($2,520) (1.5357)
A = $3869.9944
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Need help please answer!!!
It can be modeled by an exponential function because each time x increases by 1, f(x) is multiplied by 4.
This means the base of the exponential function is 4, and since f(x)=3 when x=0, [tex]f(x)=3(4)^{x}[/tex]
Evaluate the expression. 7^14/7^15 Evaluate the expression . 714 715
Answer:
1/7
Step-by-step explanation:
Alternative Form: 0.142857, 7^-1
one phone company charged 65% of its normal long-distance rate after 5 p.m. A day-rate long-distance call from Houston to Chicago costs 20 cents per minute. How much is an 11-minute call between these two cities after 5 p.m. ?
The cost of 11-minute call between these two cities after 5 p.m is: 142.
CostGiven:
Charges for long distance=65% or .65
Cost=20 cents per minutes
Number of call minutes=11 minutes
Hence:
Cost =20 cents ×11 minutes times 0.65
Cost =143 cents
Therefore the cost of 11-minute call between these two cities after 5 p.m is: 142.
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On January 1, 2021, Princess Corporation leased equipment to King Company. The lease term is 12 years. The first payment of $716,000 was made on January 1, 2021. The equipment cost Princess Corporation $5,188,466. The present value of the lease payments is $5,588,516. The lease is appropriately classified as a sales-type lease. Assuming the interest rate for this lease is 9%, how much interest revenue will Princess record in 2022 on this lease? (Round your answer to the nearest whole dollar amount.)
The amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
Interest revenue
First step
Lease value payments after first payment:
Lease value payments= $5,588,516- $716,000
Lease value payments= $4,872,516
Second step
Lease value payments after second payment:
Lease value payments=$4,872,516+ ($4,872,516×9%) - $716,000
Lease value payments=$4,872,516+$438,526.44-$716,000
Lease value payments=$4,595,042.44
Third step
2022 Interest revenue=$4,643,787.6×9%
2022 Interest revenue=$413,553.8196
2022 Interest revenue=$413,553.82 (Approximately)
Therefore the amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
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Which expression is equivalent to 2x² - x + ?
O A
O
B
C
D
²(x - 2)²
2
IN
2 X-
16
Answer: [tex]2\left(x-\frac{1}{4} \right)^{2}[/tex]
Step-by-step explanation:
[tex]2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}[/tex]
NEED HELP ASAP !!
Which equations are equivalent to 2 + 2 12-x1=1? Check all that apply.
Answer:
[tex]\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5} + \frac{2}{3} |2-x| = \frac{4}{15} \\\\\frac{1}{5}*(\frac{3}{3}) = \frac{3}{15}\\\\\frac{3}{15}-\frac{3}{15} + \frac{2}{3}|2-x| =\frac{4}{15}-\frac{3}{15}\\\\\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
(correct answers only)
A sailfish is swimming after a herring in a straight line at 11.8 m/s and begins to accelerate at 6.39 m/s². How long does it take for the sailfish to reach the herring if it is 55.0 m away?
(unit=s)
According to second equation of kinematics
s=ut+1/2at²55=11.8t+1/2(6.39)t²110=23.6t+6.39t²6.39t²+23.6t-110=0Take positive value
t=2.7sAnswer:
2.7 s (1 d.p.)
Step-by-step explanation:
Use the Constant Acceleration Equations where:
s = displacement in metersu = initial speed in m/sv = final speed in m/sa = acceleration in m/s²t = time in s (seconds)Given:
s = 55 mu = 11.8 m/sa = 6.39 m/s²[tex]\begin{aligned}\text{Using }s & =ut+\dfrac{1}{2}at^2\\\implies 55 & =11.8t+\dfrac{1}{2}(6.39)t^2\end{aligned}[/tex]
Rearrange the equation to equal zero:
[tex]\implies 3.195t^2+11.8t-55=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Use the quadratic equation to solve for t:
[tex]\implies a=3.195, \quad b=11.8, \quad c=-55[/tex]
[tex]\implies t=\dfrac{-11.8 \pm \sqrt{11.8^2-4(3.195)(-55)} }{2(3.195)}[/tex]
[tex]\implies t=2.694780675, -6.388051411[/tex]
As time is positive:
[tex]\implies t=2.694780675... \:\text{s}[/tex]
[tex]\implies t=2.7 \: \text{s (1 d.p.)}[/tex]
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Choose the letter of the equation for
the graph.
The graphed trigonometric function is the one in option a.
Which is the equation of the graph?The key parts that we can see on the graph are:
The midline is y = 1.From this we know that the correct option is either a or b.
at x = 0, f(x) = 0.Now we can evaluate options a and b in x = 0 and see which one is equal to zero.
for a:
y = sin(0 - pi/2) + 1 = sin(-pi/2) + 1 = -1 + 1 = 0
for b:
y = cos(0 + pi/2) + 1 = 0 + 1 = 1
Then we can see that option a is the correct option.
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The repeating decimal z=0.142857142857142857 as fraction
Answer:
[tex] \frac{1}{7} [/tex]
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](-\infty, -1][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Huilan is years 15 younger than Thomas. The sum of their ages is 73 . What is Thomas's age?
thomas age:44
huilan age: 29
Step-by-step explanation:
h = t + 15
t + t + 15 = 73
2t = 73 - 15
2t = 58
t = 29
A pattern has 38 black squares to every 24 red squares. What is the ratio of black squares to red squares?
Step-by-step explanation:
the answer is 38/24 so the final answer is 19/12
Please help it is 10th grade Equations of lines and circles 7. Michael is hanging out in the park and needs to keep his so
a. If Michael is standing at the coordinate (5, 2), and each unit represents a foot, what
equation could be used to show the proper social distance needed?
-6-5 -3-2
12 3456
b. If Jake is standing on the coordinate (1, 1), are the two friends properly distanced?
2
45
Step-by-step explanation:
1) the required equation in common form is:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates, where Michael is standing; r - the social distance;
According to the common form and given coordinates (x₀=-5; y₀=2; r=6) it is possible to make up the required equation:
(x+5)²+(y-2)²=6².
2) if the distance between two friends is:
[tex]d=\sqrt{(-5-1)^2+(2-1)^2}=\sqrt{37}, \ then[/tex]
this distance is longer than social (6 ft). For more info see the attachment.
Can somebody help me
Step-by-step explanation:
first function, f(x) = 5x-3 goes with option B
2nd function, 4- 4x goes with option A
3rd function goes with option D
4th goes with option C
A photographer needs a frame for a 16 x 20 inch picture, such that the total area is 340 in^2. Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?
2x^2 + 36x = 20
2x^2 + 72 = 20
4x^2 + 36x = 20
4x^2 + 72x = 20
twice a number increased by 8 is 20. find the number
Answer:
Answer is 6
Step-by-step explanation:
Let the number be ×
Twice a number is 2×
Twice a number increase by 8 is 2×+8
hence the equivalent will be
2×+8=20
2×=12
×6
Answer:
6
Step-by-step explanation:
Let n be the unknown number.
"Twice a number" means to multiply the number by 2:
⇒ 2n
"Increase by 8" means to add 8:
⇒ 2n + 8
"Is 20" means equals 20:
⇒ 2n + 8 = 20
Therefore, the equation is: 2n + 8 = 20
To solve, subtract 8 from both sides:
⇒ 2n + 8 - 8 = 20 - 8
⇒ 2n = 12
Divide both sides by 2:
⇒ 2n ÷ 2 = 12 ÷ 2
⇒ n = 6
Therefore, the unknown number is 6.
A flower garden is shaped like a circle. Its diameter is 24yd . A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 30yd.
==========================================================
Explanation:
We have two concentric circles. Think of a bulls-eye on a dart board. The inner circle is the garden itself. The outer circle is the garden plus the surrounding pathway. What we're interested in is the area of the outer ring, which is the area of the garden path only.
To find this ring area, we'll need to find the area of each circle.
A = area of the smaller circle
A = pi*r^2
A = pi*12^2
A = 144pi
Notice how I took half of the 24 yard diameter to get the radius of 12 yards.
B = area of the larger circle
B = pi*r^2
B = pi*15^2
B = 225pi
Subtract the two results
C = area of the outer ring, aka the garden path only
C = B - A
C = 225pi - 144pi
C = (225-144)pi
C = 81pi
We're told to use 3.14 in place of pi
C = 81*pi
C = 81*3.14
C = 254.34
The garden path has an area of roughly 254.34 square yards.
1 bag of sand covers 8 square yards.
So we'll need (254.34)/(8) = 31.7925 = 32 bags of sand
A woman bought some large frames for $10 each and some small frames for $4 each at a closeout sale. If she bought 22 frames for $106, find how many of each type she bought.
Answer:
19 small frames and 3 large frames
Step-by-step explanation:
follows the steps in the attached
Another day, another math problem 3
If f(x)=x²+2 and g(x)=x²+5 then the domain of the (fog) (x) is (-∞,∞).
Given the f(x)=x²+2 and g(x)=x²+5
We have to find the domain of the (fog) (x)
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
then,(fog) (x)= (x²+5)²+ 2
=x⁴+25+10x²+2
= x⁴+27+10x²
Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.
So domain (fog) (x)= (-∞,∞).
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Find the principal needed now (the present value) in order to get $10,000 after 15 years, compounded
semiannually at a rate of 5%.
Answer:
10000×(1+5%)^(15×2)=43219.4238
a) Write VW as a column vector.
b) Write WV as a column vector.
c) Write a sentence to explain what you notice about
your answers.
W
V
Answer:
vector VW= w - v
vector WV= v - w
Step-by-step explanation:
there are no figures to solve the question so i'll just write the formula..
vector VW= w - v
vector WV= v - w
In a recent year, 17.7% of all registered doctors were female. If there were 54,400 female registered doctors that year, what was the total number of registered doctors?
Answer:
The total number of registered doctors in this year are 307345.
Step-by-step explanation:
Let the total number of doctors who registered in this year are x
Given that the total number of female doctors in total registered doctors are 54400
According to the question 17.7 percent of the total registered doctors are the female doctors
Hence the total number of registered doctors who are females are 17.7% of x
which is written as 17.7*x÷100
According to the question 17.7x÷100= 54400
as we are given that the total number of female doctors are 54400
now
17.7x = 54400×100
x= 54400×100÷17.7
x= 307344.633 ≈ 307345
Therefore there are 307345 doctors who registered that year.
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1) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches.
a)
What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
b)
If a random sample of twenty-six 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
c)
Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
!) The probability in part (b) is much higher because the mean is larger for the x distribution.
!!) The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
!!!) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
!!!!) The probability in part (b) is much higher because the mean is smaller for the x distribution.
!!!!!) The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
2) Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean = 66 and estimated standard deviation = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
a)
What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
b)
Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
!) The probability distribution of x is approximately normal with x = 66 and x = 45.
!!) The probability distribution of x is approximately normal with x = 66 and x = 22.50.
!!!) The probability distribution of x is approximately normal with x = 66 and x = 31.82.
!!!!) The probability distribution of x is not normal.
c) What is the probability that x < 40? (Round your answer to four decimal places.)
d) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
e) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
f) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?
Yes
NO
g) Explain what this might imply if you were a doctor or a nurse.
!) The more tests a patient completes, the weaker is the evidence for lack of insulin.
!!) The more tests a patient completes, the stronger is the evidence for lack of insulin.
!!!) The more tests a patient completes, the weaker is the evidence for excess insulin.
!!!!) The more tests a patient completes, the stronger is the evidence for excess insulin.
Answer:
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 4 inches.
(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
z1 = (70-71)/4 = -0.25
z2 = (72-71/4 = 0.25
P(70<X<72) = p(-0.25<z<0.25) = 0.1974
Answer: 0.1974
(b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
z1 = (70-71)/(4/sqrt(13)) = -0.9014
z2 = (72-71/(4/sqrt(13)) = 0.9014
P(70<X<72) = p(-0.9014<z<0.9014) = 0.6326
Answer: 0.6326
please mark me the brainiest
Given 2 (x+3) - 4x = x
Prove = 2
Complete the proof. Provide reasons for 1-6 below.
step-by-step explanation:
#1: simplify both sides of the equation.
2(x+3)−4x=x
(2)(x)+(2)(3)+−4x=x
2x+6+−4x=x
(2x+−4x)+(6)=x
−2x+6=x
−2x+6=x
***
#2: subtract x from both sides.
−2x+6−x=x−x
−3x+6=0
***
#3: subtract 6 from both sides.
−3x+6−6=0−6
−3x=−6
***
step 4: divide both sides by -3.
−3x/-3 = -6/-3
solution x = 2
