Answer:
The length is 50 feet and the width is 16 feet
Step-by-step explanation:
Let w represent the width of the room.
If the length is 2 feet longer than 3 times the width, the length can be represented by 3w + 2.
Use the perimeter formula, p = 2l + 2w. Plug in the perimeter and plug in 3w + 2 as l, the length:
p = 2l + 2w
132 = 2(3w + 2) + 2w
Simplify and solve for w:
132 = 6w + 4 + 2w
132 = 8w + 4
128 = 8w
16 = w
So, the width is 16 feet.
Plug in 16 as w into 3w + 2 to solve for the length:
3w + 2
3(16) + 2
48 + 2
= 50
The length is 50 feet and the width is 16 feet
Answer:
width=16feet
length=50feet
Step-by-step explanation:
let width be x and length be 3x+2
perimeter=2(length+width)
132=2(3x+2+x)
132=6x+4+2x
132=8x+4
132-4=8x
128/8=8x/8
16=x
width=16feet
length=16×3+2
length=50feet
If you have two six sided die each labelled one throgh six. Which set of independent events has a higher probability?
Answer : Four sides (1, 2, 3, 4) are less than 5. The probability is 4 out of 6, or 2/3 or 0.6667.
The solution is, the correct answer is B. comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
We will consider all the sets of probabilities, the one with the highest probability is the right answer.
a) You roll an odd number and roll a 5: the probability is calculated thus:
1/6 * 3/6
=0.0833
b) You land on an odd number or you roll a 6: the probability is calculated thus:
3/6 +1/6
= 0.6667
c) You roll a six and roll a 4: the probability is calculated thus:
1/6 * 1/4
= 0.0417
d) You roll a 3 and roll an old number: the probability is calculated thus:
1/6 * 3/6
=0.0833
Now, comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.
Therefore the correct answer is B.
To learn more on probability click:
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APP
A set of quiz scores has a mean of 78 and a standard
deviation of 9. Using a common grading scale where 60
and above is a passing score, what percentage of the
students passed this test?
Explain your answer in terms of the 68-95-99.7 rule.
Answer:
The answer is "There are [tex]97.5\%[/tex] of the students pass in the test ".
Step-by-step explanation:
Since a normally distributed random variable, the practical rule states:
About 68% of the metrics are in the 1 default deviation
About 95% of metrics correspond to 2 standard deviations from the average.
About 3 standard deviations of the average represent 99.7% of the measurement.
We have the following in this problem:
Average of 78, the average 9 default.
Calculating the percentage of students that passed the test.
[tex]Above 60\\\\60 = 78 - 2\times 9[/tex]
Therefore 60 is under the average for two standard deviations.
Its normality test is symmetric, so 50% of such observations are below mean and 50% below mean.
Everything was cleared of the 50 percent above.
Of the 50% below, 95% (within 2 known mean deviations) succeeded.
therefore
[tex]p=0.5+0.5 \times 0.95=0.975[/tex]
Mikita is painting a spherical model of a human cell for a science fair. She uses 452.16 square inches of paint to evenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for the value of π.)
6 in.
12 in.
24 in.
36 in.
Answer:
12
Step-by-step explanation:
Basically you have to divide 3.14 by 452.16 (the formula for area of circle is pi times r squared) and that will get you 144. The square root of 144 is 12 :)
f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).
Answer:
4x-5=4x-5
(f+g) (x)=6x³+3Step-by-step explanation:
If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *
Given:
There is a 65% chance you will make a free throw.
To find:
The percent of the time you will miss.
Solution:
If p is the percent of success and q is the percent of failure, then
[tex]p+q=100\%[/tex]
[tex]q=100\%-p[/tex] ...(i)
It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss. It means we have to find the percent of failure.
Substituting p=65% in (i), we get
[tex]q=100\%-65\%[/tex]
[tex]q=35\%[/tex]
Therefore, there is a 35% chance you will miss the free throw.
(a+b)^2 hihhhhhhhhhhhhhhhhhhhh
Answer:
a^2 + 2ab + b^2
Answered by Gauthmath
A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is Determine the probability that the portion of a claim representing damage to the house is less than 0.2.
Answer:
Please find the complete question in the attachment.
Step-by-step explanation:
The likelihood of the part of claims that is less than 0.05 for all the houses is calculated as:
[tex]P(X < 0.05) = int^{0.05}_{0} int^{1-x}_{0} f(x,y) \ dy\ dx\\\\[/tex]
[tex]= \int^{0.05}_{0} \int^{1-x}_{0} 6(1-x-y) \ dy\ dx\\\\= \int^{0.05}_{0} 6((1-x)-x(1-x)-\frac{(1-x)^2}{2}) \ dx\\\\ = \int^{0.05}_{0} 6(1-2x+x^2-0.5-0.5x^2+x) \ dx\\\\= \int^{0.05}_{0} 6(0.5x^2-x+0.5) \ dx\\\\= 6(0.5\times \frac{0.05^3}{3} -\frac{0.05^2}{2}+0.5 \times 0.05 )\\\\ =0.1426\\\\[/tex]
Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.
a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?
Answer:
[tex](a)\ \frac{dP}{dt} = kP + r[/tex]
[tex](b)\ \frac{dP}{dt} = kP - r[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = kP[/tex]
Solving (a): Differential equation for immigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP + r[/tex]
Solving (b): Differential equation for emigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP - r[/tex]
Rubin grew 9 tomatoes with 6 seed packs. How many seed packs does Rubin need to have a total of 21 tomatoes in his garden?
Answer: 14 seed packs
Step-by-step explanation:
You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.
Determine if the triangles are similar. If they are, state the theorem.
9514 1404 393
Answer:
ΔGHF ~ ΔMLF by AA theorem
Step-by-step explanation:
Answer this please~!!!!
Answer:
12
Step-by-step explanation:
113.04=3.14 x 3^2 x h/3
Select the correct answer.
Simplify the following expression. Classify the resulting polynomial.
3x(x − 3) + (2x + 6)(-x − 3)
quadratic monomial
quadratic binomial
quadratic trinomial
linear binomial
Answer:
quadratic trinomial
Step-by-step explanation:
3x(x − 3) + (2x + 6)(-x − 3)
Distribute
3x^2 -9x + (2x + 6)(-x − 3)
FOIL
3x^2 -9x + -2x^2 -6x -6x -18
Combine like terms
x^2-21x-18
This has 3 terms so it is a trinomial
The highest power of x is 2 so it is quadratic
9514 1404 393
Answer:
x² -21x -18quadratic trinomialStep-by-step explanation:
Eliminating parentheses, we get ...
= (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)
= 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)
= 3x² -9x -2x² -6x -6x -18
= x²(3 -2) +x(-9-6-6) -18
= x² -21x -18
The highest power is 2, so this is a quadratic.
There are 3 terms, so this is a trinomial.
What is the ratio of the area of the inner square to the area of the outer square?
Answer:
Step-by-step explanation:
If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.
First the area of the inner square. Here we go:
Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.
The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.
Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":
[tex]?^2=b^2+(a-b)^2[/tex] and
[tex]?^2=b^2+a^2-2ab+b^2[/tex] and
[tex]?^2=a^2-2ab+2b^2[/tex] so
?, the length of the hypotenuse, is
[tex]?=\sqrt{a^2-2ab+2b^2}[/tex] and now we can use that to find the area of the inner square. The formula for a square's area is
[tex]A=s^2[/tex] so
[tex]A=(\sqrt{a^_2}-2ab+2b^2})^2[/tex] which gives us finally:
[tex]A=a^2-2ab+2b^2[/tex] **
Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is
A = a²
The ratio of the area of the inner to the outer is:
[tex]\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}[/tex] and that does not reduce.
Answer:
A
Step-by-step explanation:
Edmentum
For a standard normal distribution, find:
P(z > -1.6)
Express the probability as a decimal rounded to 4 decimal places.
Answer:
P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960
HELP PLZ<3
An international company has 28,300 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.
Answer:
82991 employees
Step-by-step explanation:
One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that
28300 = 34.1%
If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get
829.912 = 1%
Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get
100% = 82991
Given the exchange rate as K1: HK$1.353, calculate Hong Kong dollar equivalent of K70
Answer:
The Hong Kong dollar equivalent of K70 is HK $ 94.71.
Step-by-step explanation:
Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:
1,353 x 70 = X
94.71 = X
Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.
Find x on this triangle
Answer:
3 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = x/6
6 cos 30 = x
6 ( sqrt(3)/2) = x
3 sqrt(3) =x
can someone help me out with this question???
Answer:
a
Step-by-step explanation:
How many subsets will the sets have? {sheep that have eight legs }
Answer:
256
Step-by-step explanation:
How to find subsets = 2 raise the power n.
N=number of elements in a set.
=2raise the power 8 which is 256.
Please I need a step by step explanation ASAP.
Calculate the perimeter and area of the shape below:
Answer:
38.6 cm
Step-by-step explanation:
add all of the sides up to get your perimeter
In the picture the exponent says 5/3
Answer:
the answer is B
Step-by-step explanation:
[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]
write -8 form of 2 on up and complete other steps
find the value of 'x' in the given figure
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
(2x-20)°+(x+65)°=180°2x-20+x+65=1803x+45=1803x=180-453x=135x=135/3x=45°y _minus 7 equal 10.find y
Answer:
y=17
Step-by-step explanation:
y-7=10
transpose 7
y=10+7
y=17
WILL MAKE BRAINLIEST
Answer:
x=3
Step-by-step explanation:
The ratios need to be the same
AB CB
---------- = ----------
AD ED
3 x
----- = ---------
3+9 12
3 x
----- = ---------
12 12
X must equal 3
What is the common difference in this sequence: 3, 11, 19, 27,35?
1
ОА.1/8
O B. 3
O C. 8
O D. 12
Answer:
8
Step-by-step explanation:
To determine the common difference, take the second term and subtract the first term
11-3 = 8
Check with the other terms in the sequence
19-11= 8
27-19 = 8
35-27=8
The common difference is 8
Answer:
C. 8
Step-by-step explanation:
There is a common difference between them and that’s 8.
3 + 8 = 11
11 + 8 = 19
19 + 8 = 27
27 + 8 = 35
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.
A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters.
Which expression represents the volume of the pyramid?
StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
StartFraction x squared + 2 x squared Over 2 EndFraction cm3
StartFraction x cubed Over 3 EndFraction cm3
StartFraction x cubed + 2 x squared Over 2 EndFraction cm3
Answer:
Hello,
Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
Step-by-step explanation:
[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]
the third of the sum of the cube of x and double of the square of x ( cm³)
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
Area of the square base = x * x = x² cm²
Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)
Volume of pyramid = (x³ + 2x²) / 3
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
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Solve for f(-2)
PLEASE HELPPPPP
Answer:
5/9
Step-by-step explanation:
f(x) = 5 * 3^x
Let x = -2
f(-2) = 5 * 3^-2
We know a^-b = 1/a^b
= 5 * 1/3^2
= 5/9
F(-2) means the value of x is -2
Replace x with -2 and solve:
3^-2 = 1/9
5 x 1/9 = 5/9
Answer: D.5/9
If you make $11.25/hour, how many hours will you need to work to earn $416.25? Please explain how you figured this out.
Answer:
37 hours.
Step-by-step explanation:
Since you need $416.25 start with that. Then divide by $11.25 to see how many hours you need to work. 416.25 divided by 11.25 is 37.
Hii guys if you have time plz help me
Answer:
[tex]5 {x}^{2} + 21 + 5x[/tex]
Step-by-step explanation:
TOTAL AMOUNT earned = Tim money + Melina money
[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]
[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]
[tex] = 5 {x}^{2} + 21 + 5x[/tex]
Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by
The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is
[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]
In this case, we have
x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )
y(t) = 5 - 2t ==> dy/dt = -2
and [a, b] = [0, 2]. The length of the curve is then
[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]
[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]
The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.
[tex]e^2 -\dfrac{1}{e^2 }[/tex]
What is integration?It is the reverse of differentiation.
The parametric equations are given below.
[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]
Then the arc length of the curve will be given as
[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]
Then
[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]
More about the integration link is given below.
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