Answer:
(x - 3) inches
Step-by-step explanation:
the ratio of -15 (of the area term) and +5 (of the length term) suggests a term for the width ending in -3. and we need an x in there to get x² for the area.
so, immediate assumption is (x-3) for the width.
let's check
(x+5)(x-3) = x² + 5x - 3x - 15 = x² + 2x - 15
correct.
The probability that a school wins their first game in the national college basketball tournament is related to the rank they have going into the tournament. This can be expressed by the equation y=−6.39x+104 where x is their rank (out of 16) and y is the percent chance they have of winning their first game
According to the model, a school ranked #3 has what probability of winning their first game? Round your answer to the nearest percent.
A. 76%
B. 85%
C. 105%
D. 93%
Answer:
According to the model, a school ranked #3 has 85% probability of winning their first game.
What is the area of parallelogram ABCD?
A)13 square units
B)14 square units
C)15 square units
D)16 square units
Answer:
c 15 square units
Step-by-step explanation:
it is very easy
fine x and y alpha ln trigonometry ln triangles
Step-by-step explanation:
it is easy to get a answer go to web
Find cos(2x) from the given information. tan(x)= 9/8, x in quadrant I
Answer:
cos2x=-17/145
Step-by-step explanation:
Recall cos2x=cos^2x-sin^2x
Or cos2x=cos^2x-(1-cos^2x)*
Or cos2x=2cos^2x-1**
*By a Pythagorean Identity
**Combined like terms
I'm going to use third identity from above because I only have to find cosx or cos^2x to get requested answer for cos2x.
Recall Pythagorean identity 1+tan^2x=sec^2x.
Plug in our tangent valuem...
1+(9/8)^2=sec^2x
1+81/64=sec^2x
145/64=sec^2x
Cosine and secant are reciprocals of each other.
64/145=cos^2x
Now we are ready to plug in and get final answer:
cos2x=2cos^2x-1
cos2x=2(64/145)-1
cos2x=128/145-1
cos2x=-17/145
if a circle’s circumference is decreased by12% what percent is the diameter decreased by?
A) 2√3 %
b) 6 %
C) 12 %
D)24%
Answer:
A) 12%
Step-by-step explanation:
Lets assume a random diameter to work with. I will use a diameter of 10.
Circumference = πD
Circumference = π * 10
Circumference = 31.415
Decreasing the circumference by 12%
31.415 * 0.12 = 3.769
31.415 - 3.769 = 27.64
To find out what percent the diameter is reduced by we will find out the new diameter with the new circumference
Circumference = πD
27.64 = π * D
D = 27.64 / π
New Diameter = 8.8
OldD - NewD
10 - 8.8 = 1.2
1.2/10 = 0.12
The diameter decreased by 12%
The diameter of the circle decreased by 12% due to decrease of circles circumference by 12%.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The diameter is the longest line that can be drawn inside a circle.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
Let's say the diameter of the circle is D
Circumference of circle = πD
12% of Circumference = (12/100) × πD
⇒ 0.12πD
So new circumference will be
πD - 0.12πD = 0.88πD
Now let say new diameter after decreasing circumference is d
Circumference of new circle will be
πd = 0.88πD
d = 0.88D
% decrement = (change/original) × 100
diameter decrease = (D - 0.88D)/D × 100
⇒ 12% hence it will be correct answer.
To learn more about the circle,
https://brainly.com/question/266951
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What is the area of xyz pleae help?
Step-by-step explanation:
here's the answer to your question
Answer:
A = 14 in²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 7 and h = 4 , then
A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 in²
Express the confidence interval in the form of .
Answer:
0.075 - 0.022 < p < 0.075 + 0.022
Do not evaluate each of the math expressions above.
===========================================================
Explanation:
The given confidence interval is in the form (L, U)
L = lower bound = 0.053U = upper bound = 0.097Find the midpoint of L and U to get
(L+U)/2 = (0.053+0.097)/2 = 0.075
This is the value of [tex]\hat{p}[/tex] which is the symbol p-hat or phat (both pronounced the same). It's the sample proportion.
To get the margin of error E, we could do either of the following
E = (U-L)/2 = (0.097-0.053)/2 = 0.022E = U - phat = 0.097 - 0.075 = 0.022E = phat - L = 0.075 - 0.053 = 0.022This value of E represents half the width of the confidence interval. The full width being U-L.
he radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?
Answer:
The bones were 12,485 years old at the time they were discovered.
Step-by-step explanation:
Amount of the element:
The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The radioactive element carbon-14 has a half-life of 5750 years.
This means that [tex]A(5750) = 0.5A(0)[/tex], and we use this to find k. So
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.5A(0) = A(0)e^{-5750k}[/tex]
[tex]e^{-5750k} = 0.5[/tex]
[tex]\ln{e^{-5750k}} = \ln{0.5}[/tex]
[tex]-5750k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{5750}[/tex]
[tex]k = 0.00012054733[/tex]
So
[tex]A(t) = A(0)e^{-0.00012054733t}[/tex]
A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?
Had 100 - 77.8 = 22.2% remaining, so this is t for which:
[tex]A(t) = 0.222A(0)[/tex]
Then
[tex]0.222A(0) = A(0)e^{-0.00012054733t}[/tex]
[tex]e^{-0.00012054733t} = 0.222[/tex]
[tex]\ln{e^{-0.00012054733t}} = \ln{0.222}[/tex]
[tex]-0.00012054733t = \ln{0.222}[/tex]
[tex]t = -\frac{\ln{0.222}}{0.00012054733}[/tex]
[tex]t = 12485[/tex]
The bones were 12,485 years old at the time they were discovered.
13 A traffic roundabout has a circular garden
in the centre and two lanes for traffic
encircling the garden. The diameter of the
garden is 16 metres and each lane is 3 metres
wide. Each lane is to be resurfaced. Calculate
the area to be resurfaced. Answer in square
metres to the nearest whole number.
Answer:
Step-by-step explanation:
The area to be resurfaced is the area of the
whole circle including garden and lanes minus
the area of the garden.
Area of a circle is (pi)r2
radius of garden is (1/2)diameter = 8 m
Garden area: (pi)82 = 64(pi) m2
Diameter of garden plus traffic lanes is
16 + 2(6) because we add 6 m to both sides
of the diameter of the garden.
Full diameter = 16+12 = 28 m
Full radius = 28/2 = 14 m
Full area: (pi)142 = 196(pi) m2
Area to be resurfaced:
196(pi) - 64(pi) = 132(pi) m2 ≅ 415 m2
Write a word description of the set.
{−9, −8, −7, −6, −5, −4, −3, −2, −1}
the set of which one whole numbers,natural numbers, negative integers or integers
greater than__________________.
Answer: negative integers greater than -10
This is because stuff on the number line to the right is larger than stuff on the left. We can say 2 < 7 since 7 is to the right of 2.
Also, -7 < -2 for similar reasoning.
Saying integers greater than -10 excludes this endpoint. We stop once we reach -1 because 0 and anything larger aren't negative integers.
A sequence is defined recursively by the formula f(n+1)=-2f(n). The first term of the sequence is -1.5. What is the next term in the sequence ?
Answer:
next term is 3
Step-by-step explanation:
[tex]f(n+1)=-2f(n)\\\\f(1)=-1.5=-\frac{3}{2}f(2)=-2f(1)=-2*(-\frac{3}{2})=3[/tex]
Answer:
3
Step-by-step explanation:
Took the test and got this right.
A drinking container is shaped like a cone and must hold at least 10 ounces of fluid. The radius of the top of the container is 2.25 inches. The steps for determining the height of the cone-shaped container are shown below.
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Answer:
C. h ≥ 1.9 in
Step-by-step explanation:
As the final step, divide both sides of the inequality by 5.3:
(5.3h)/5.3 ≥ 10/5.3
h ≥ 1.9
4 pts
John makes $2,800 per month and has an opportunity to invest $150 per month at an APR of 4.5% in a 401K plan through work. He plans to retire in 30 years.
Type in the EXACT formula you would use in excel (no spaces) to find the amount in the account after he has invested for 30 years.
Using excel, what is the answer to the formula from the previous part?
How much money will he deposit into the 401K over the 30 years?
How much total interest will he earn on his 401K over the 30 years?
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Answer:
=FV(4.5%/12,30*12,-150,0)$113,907.92$54,000$59,907.92Step-by-step explanation:
We have used the formula shown in Go.ogle Sheets to give the results shown. (We presume Excel has a similar function.)
The result is that the future value of the investment is $113,907.92.
The amount deposited is ($150/mo)(12 mo/yr)(30 yr) = $54,000.
The interest earned is the difference: $113,907.92 -54,000 = $59,907.92.
Use a table of values to graph the function ƒ(x) = x−−√. Choose the correct graph from the options below.
Answer:
B
Step-by-step explanation:
The square root function's graph is graph (b). This makes logical sense, because, when taking the square root (the principal root in particular), a general rule is that both the input and the output must be positive. Moreover, if one were to create a table of values to find points on the graph of the function, each of the points can be found on graph (b).
[tex]f(x)=\sqrt{x}[/tex]
x y
1 1
4 2
9 3
16 4
Therefore graph (B) is the correct answer.
Find the expression that is equivalent to 7(x2 – 5x + 1).
Answer:
7x^2 -35x +7
Step-by-step explanation:
7(x^2 – 5x + 1)
Distribute
7x^2 -7*5x +7*1
7x^2 -35x +7
Which of the following expressions are equivalent to -3x- 6/10
Choose all that apply:
A=3/6x1/10
b=- 3/10x-6
c= none of the above
Answer:
c= none of the above
Step-by-step explanation:
-3x- 6/10
This has two separate terms, a term with a variable
-3x and a term with a constant -6/10
A=3/6x1/10 This has only one term
b=- 3/10x-6 This has a different x term -3/10 which is not -3
c= none of the above
Can I get help it’s EZ points?
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Answer:
maximum: 16minimum: -24Step-by-step explanation:
The attache graph shows the solution region is bounded by lines through the points (-2, 4), (6, 0), and (3, -6).
The solution (x, y) = (-2, 4) gives the maximum value of z: 16.
The solution (x, y) = (3, -6) gives the minimum value of z: -24.
twelve people enter a contest. prizes will be given for first second and third place. how many ways can the prizes be given
Answer:
1320 ways
Step-by-step explanation:
Number of contestants = 12
Positions that are n be awarded = First, Second, Third
Number of contestants who could be first = 12 (all 12 contestants)
Number of contestants who could be second = 11 (all 12 contestants - first)
Number of contestants who could be third = 10 (all 12 contestants - first and second )
The number of ways prices can be given :
(1st * 2nd * 3rd) = 12 * 11 * 10 = 1320 ways
Find the area of the shaded region.
A. 112.5 in²
B. 73.5 in²
C. 122.5 in²
D. 147 in²
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Answer:
B. 73.5 in²
Step-by-step explanation:
The triangle area is half the rectangle area, so the shaded area is also half the rectangle area:
A = 1/2LW = 1/2(21 in)(7 in) = 73.5 in²
Answer:
B.) 73.5 in2
Step-by-step explanation:
I got it correct on founders edtell
What is the value of Z? Z =2^3
the value of Zis 8.
Z =2^3=8
Now we have to,
find the required value of Z.
→ Z = 2^3
→ [Z = 8]
Therefore, value of Z is 8.
Use the figure to find x
Answer:
The value of x is [tex]\frac{7\sqrt{6}}{2}[/tex]
Solution given:
AB=7
BD=x
<BAC=60°
<DBC=45°
In right angled triangle ABC
Tan 60°=opposite/adjacent
Tan 60°=BC/AB
Substitute value
[tex]\sqrt{3}[/tex]=[tex]\frac{BC}{7}[/tex]
BC=[tex]7\sqrt{3}[/tex]
again
In right angled triangle BCD
Using Cos angle
Cos 45=adjacent/hypotenuse
Cos45°=BD/BC
Substituting value
[tex]\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}[/tex]
Doing criss cross multiplication
[tex]\frac{\sqrt{2}}{2}*7\sqrt{3}=x[/tex]
x=[tex]\frac{7\sqrt{6}}{2}[/tex]
Billy's heart rate is 13 beats every 10 seconds. What is his heart rate in beats per MINUTE (bpm)?
Reminder: 1 Minute=60 Seconds
(A)23 bpm
(B)63 bpm
(C)78 bpm
(D)130 bpm
write an expression to represent the sum of 3 and the quotient of a number divided by 6
is absolute value of -998
Answer:
998.
Step-by-step explanation:
Just get rid of the negative sign
Answer:
This should 998 I guess
Step-by-step explanation:
Minus the negative signs
A box of tangerines that weighs 5 pounds costs $4.25.
What is the cost per pound?
Answer:
$0.85
Step-by-step explanation:
$4.25 divided by 5 pounds equals $0.85 per pound.
Answer:
$0.85
Step-by-step explanation:
Find the unit rate.
4.25/5=x/1
Solve for x. X= 4.25/5=0.85
So 1 lb of tangerines costs $0.85.
An office manager booked 55 airline tickets. He booked 6 more tickets on Airline A than Airline B. On Airline C, he booked 5 more than twice as many tickets as on Airline B. How many tickets did he book on each Airline?
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Answer:
A: 17B: 11C: 27Step-by-step explanation:
If we let a, b, c represent tickets booked on airlines A, B, C, respectively, then we have ...
a + b + c = 55
a - b = 6
-2b + c = 5
Using the last two equations to write expressions for a and c, we have ...
a = b +6
c = 5 +2b
These can be substituted into the first equation to give ...
(b +6) +b +(5 +2b) = 55
4b +11 = 55
4b = 44
b = 11
a = b+6 = 17
c = 5 +2b = 27
He booked 17 tickets on Airline A, 11 tickets on Airline B, and 27 tickets on Airline C.
^please answer, thanks in advance ^
Answer:
There is not enough information to determine the mean, the median is 28.
There is not enough information to determine the mean absolute deviation, the interquartile range is 18
Step-by-step explanation:
The box plot given has a skewed distribution, this means that both the mean and median values are not the same. From a box plot, the median value Can be obtained as the point in between the box.
From the box plot given, the marked point in between the box is 28 cm
Hence, Median = 28 cm
The mean cannot be inferred from the skewed box plot.
There is also not enough information to determine the mean absolute deviation ;
The interquartile range:
(Q3 - Q1)
Q3 = upper quartile, the endpoint of the box = 40
Q1 = the starting point of the box = 22
IQR = Q3 - Q1
IQR = 40 - 22 = 18
-4 is a whole number
Answer:
false
Step-by-step explanation:
a whole number is a number that doesnt contain a fraction or negative value
A car travels 1/8 mile in 2/13 minutes. What is the speed in terms of miles per minute?
Answer:
13/16 miles per minute
Step-by-step explanation:
Take the miles and divide by the minutes
1/8 ÷ 2/13
Copy dot flip
1/8 * 13/2
13/16 miles per minute
Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43
Answer: x = (-3,3), y = (-5,5)
Step-by-step explanation:
Add both of the equations together, for [tex]3x^{2}+3y^{2} = 102[/tex]. Now we can divide both sides by 3, getting[tex]x^2+y^2=34[/tex]. we subtract the first equation from our equation we just got, getting [tex]y^2=25[/tex] y= (5,-5). once we plug that in, we get [tex]50+x^2 = 59[/tex], [tex]x^2 = 9[/tex] x = (-3,3)
