Thus, the unknown side length of rectangle for the given area and one side length is found to be 5.5 m.
Explain about the rectangle:Every day, rectangles are all around us. All of these objects—doors in a home, windows in a structure, and books in a library—are rectangles.
A rectangle is a shape having four sides and four right angles (90-degree angles). Given their versatility, rectangles are excellent forms. Rectangles are frequently used in patterns and motifs in brick fireplaces and floor tiles since their right angles blend well with those of other shapes and rectangles.Given that:
area of rectangle 11 m².side length = 2 mArea of rectangle A = length * width
width = area / length
width = 11 / 2
width = 5.5
Thus, the missing side of rectangle for the given area and one side length is found to be 5.5 m.
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Complete question:
Find the unknown side length of the rectangle if its area is 11 m² and one of its side is 2 m.
If f (x) = 2 x + 5 and three-halves are inverse functions of each other and StartFraction 41
The inverse of the function → f(x) = 2x + 5 is → f⁻¹(x) = (x/2) - (5/2).
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace {y} with {x} and vice - versa.Step 2 - Rewrite the equation by solving for {y}.Step 3 - Replace {y} with f⁻¹(x).According to the question, the equation given is as follows
y = f(x) = 2x + 5
y = 2x + 5
Replace 'y' with 'x', we get -
x = 2y + 5
Now, solve for y -
2y = x - 5
y = (x/2) - (5/2)
Replace 'y' with f⁻¹(x) -
f⁻¹(x) = (x/2) - (5/2)
Hence, the inverse of the function → f(x) = 2x + 5 is → f⁻¹(x) = (x/2) - (5/2).
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Need help with top problem. Maybe bottom too
1) The area of a circle circumscribed about a square is 307.7 cm².
2.a.) The angle ACB is 39 degrees.°.
2b.) The value of x is 5.42.
How to determine the area of a circle?We shall find the radius to determine the area of a circle.
First, find the side length of the square:
Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.
Next, find the diagonal of the square, using the Pythagorean theorem:
Diagonal = the diameter of the circumscribed circle.
Diagonal² = side length² + side length²
= 14 cm² + 14 cm²
= 196 cm² + 196 cm²
= 392 cm²
Take the square root of both sides:
Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)
Then, the radius of the circle which is half the diagonal:
Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)
Finally, compute the area of the circle using the formula:
Area = π * Radius²
Area = 3.14 * (9.90 cm)²
Area ≈ 307.7 cm² (rounded to two decimal places)
Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².
2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.
Given that arc AB has a measure of 78°, we can find angle ACB as follows:
Angle ACB = 1/2 * arc AB
= 1/2 * 78°
= 39°
Therefore, the angle ACB is 39 degrees.
2b.) To solve for the value of x, we use the information that the angle ADB = (3x - 12)⁴.
Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:
(3x - 12)⁴ = 78
Solve the equation for x, by taking the fourth root of both sides:
∛∛((3x - 12)⁴) = ∛∛78
Simplify,
3x - 12 = ∛(78)
Isolate x by adding 12 to both sides:
3x - 12 + 12 = ∛(78) + 12
3x = ∛(78) + 12
Finally, divide both sides by 3:
x = (∛(78) + 12) / 3
x = (4.27 +12) / 3
x = 5.42
So, x is 5.42
Therefore,
1) The area of the circle is 154 cm².
2a.) Angle ACB is equal to 102°.
2b.) The value of x is 5.42
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Consider the following hypothesis test: 0 : 12 a : 12 HH A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.32. a. Compute the value of the test statistic. b. Use the t distribution table to compute a range for the p-value. c. At a = 0.05, what is your conclusion? d. What is the rejection rule using the critical value? What is your conclusion?
a) The test statistic is given as t = \(\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}\)= 2.315
b) The pa value will be P = P( t₂₄ > 2.315 ) = 0.015
c) If we compare the p-value and the significance level is given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance
What is a null hypothesis?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
X= represents the sample mean
s = represent the sample standard deviation
n = 25 sample size
\(\mu_o\) = 12 represent the value that we want to test
\(\alpha\) = 0.05 represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
\(p_v\) represent the p-value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 12, the system of hypothesis would be:
Null hypothesis: ≤ 12
Alternative hypothesis: > 12
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better to apply a t-test to compare the actual mean to the reference value, and the statistic is given by:
\(t=\dfrac{X-\mu_o}{\dfrac{\sigma}{\sqrt{n}}}\)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to a specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
\(\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}\)= 2.315
P-value:-
The first step is calculate the degrees of freedom, on this case:
df = n - 1 =25 - 1 = 2
Since is a one side right tailed test the p value would be:
\(p_v\) = P( t₂₄ > 2.315 ) = 0.015
Conclusion
If we compare the p-value and the significance level is given \(\alpha\)= 0.05 we see that \(p_v < \alpha\) so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance.
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Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
Answer:
Your slope is 1/1 or 1 in simplest form
Step-by-step explanation:
Look at attachment below to see drawn line. For further questions just comment below
Hope this helps (:
If an object is dropped from a height of 85 feet, the function h(t) = -16t2 +85 gives the height
of the object after t seconds. Approximately, when will the object hit the ground?
Answer:
Step-by-step explanation: h(t)=-16t2+85
Let h(t)=0 to find when the object will hit the ground
0=-16t2+85
Solve for t=?
We need to get t term on its own
Take 85 from both sides
0-85=-16t2+85-85
-85=-16t2
To get t term on its own
Divide both sides by -16
-85/-16=-16t2/-16
5.3=t2
We have to solve for t squared that means we must take the square root of both sides
the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds
Donna finished 67% of her homework. What fraction of her homework is
completed?
67/10
0.67/100
67/100
67/1000
Answer:
67/100
Step-by-step explanation:
Percent means out of 100.
67% = 67/100
Answer:
67/100
Step-by-step explanation:
When we say Donna has completed 67% of her homework, we are referring to a percentage, which is a way of expressing a part out of 100. In this case, the percentage is 67%.To convert a percentage to a fraction, we can simply write the percentage as a fraction with 100 as the denominator. In this case, since the percentage is 67%, the fraction would be 67/100.\(67\%=\dfrac{67}{100}\)Lindsay Bedford works at the baseball cap shop. She is paid $6.50 per hour plus $0.45 for each cap she embroiders.
How many caps must she embroider to earn at least $85 in an 8-hour day?
Group of answer choices
85
74
110
73
ANSWER - 74
First we must write out our equation
6.50H + .45c= 85.
H represents hours and c represents caps that are embroidered. We know that H(hours,) equals 8 so we can rewrite our equation to look like this.
(6.50 x 8) + (.45 x c) = 85. 6.50 x 8 is 52. Lets subtract 52 from 85. That is 33 dollars. This means 33 dollars must be made from embroidery caps.
Next we will divide 45 cents into 33 dollars until we get our smallest unit. This will tell us how many caps Lindsay embroiders during their eight hour shift. 33 divided by .45 is 73.333_. The three will continue forever, but since you can not make .333 percent of a hat, you have to make a whole to round up to the nearest dollars. Bringing us to our final Answer.
Lindsay will need to make 74 hats during their shift, if the want to make 85 dollars.
HOPE THIS HELPS & GOOD LUCK.
Answer:
74
Step-by-step explanation:
Lindsay wants $85
Lindsay works for 8 hours
$6.50/hour
$0.45/cap
If Lindsay worked for 8-hours (no caps were embroided):
$6.50 x 8 = $52.00
Lindsay wants $85, so she needs:
$85 - $52 = $33 more
Each cap she makes is $0.45, so she needs to make:
$33 ÷ $0.45 = 73.3333 --> 74 caps since 73 is under $33
Therefore Lindsay needs to make 74 caps
----------------------------------------------------------------------------------------------------
General equation:
($6.50 x hrs) + ($0.45 x cap) = total $$
cap = [total $ - ($6.50 x hrs)] ÷ $0.45
PLEASE I NEED HELP the question is,
In the diagram of triangle LAC and triangle DNC below, LA = DN, CA = CN, and DAC is perpendicular to LCN.
a) Prove that triangle LAC = triangle DNC.
b) Describe a sequence of rigid motions that will map triangle LAC onto triangle DNC.
Answer:
1244 DCD
Step-by-step explanation:
help!!
differentiate
\( { {e}^{x} }^{2} log_{10}(2x) \)
Rewrite the function using the change-of-base identity as
\(e^{x^2} \log_{10}(2x) = e^{x^2} \dfrac{\ln(2x)}{\ln(10)}\)
Apply the product rule:
\(\left(e^{x^2} \log_{10}(2x)\right)' = \left(e^{x^2}\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \left(\dfrac{\ln(2x)}{\ln(10)}\right)'\)
Use the chain rule:
\(\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(x^2\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac{(2x)'}{2\ln(10)x}\)
Compute the remaining derivatives:
\(\left(e^{x^2} \log_{10}(2x)\right)' = 2xe^{x^2} \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac2{2\ln(10)x} = e^{x^2}\left(\dfrac{2x\ln(2x)}{\ln(10)} + \dfrac1{\ln(10)x}\right)\)
If you like, you can convert back to base-10 logarithms:
ln(2x) / ln(10) = log₁₀(2x)
1 / ln(10) = ln(e) / ln(10) = log₁₀(e)
Then
\(\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(2x\log_{10}(2x)+\frac{\log_{10}(e)}x\right)\)
What are all prime factorization of 34
if x² = 64, then 1/3 + x⁰
Answer:
4/3 or 1 1/3
Step-by-step explanation:
Finding x
x² = 64x = ±8Substitute in the equation
1/3 + (±8)⁰1/3 + 14/3 or 1 1/3Answer:
\(\huge\boxed{\bf\:\frac{4}{3} }\)
Step-by-step explanation:
If, \(x^{2} = 64\), then,
\(x^{2} = 64\\x = \sqrt{64}\\x = (+/-)8\)
Now, remember that any number when folllowed by exponent 0 will always have its value as 1.
Then,
\(\frac{1}{3} + x^{0} \\ =\frac{1}{3} + (+/-8)^{0} \\= \frac{1}{3} + 1\\=\frac{1}{3} +\frac{3}{3} \:\:\:\: (LCM = 3)\\ \boxed{\bf\:\frac{4}{3} }\)
\(\rule{150pt}{2pt}\)
1.
I Which number line shows the solution to the inequality
-3x - 5 < -2?
A.
B.
C.
D.
-3 -2 -1 0 1
-3 -2 -1 0 1
0++
0 1
3 -2 -1 0
2 3
2 3
2 3
+++
-3 -2 -1 0 1 2 3
which expression is equivalent to 15+8x+3+2x ?a) 28xb) 18 + 10xc) 180xd) 6x + 12
Given the expression:
15 + 8x + 3 + 2x
Let's simplify the expression to find the equivalent expression.
15 + 8x + 3 + 2x
Combine like terms:
15 + 3 + 8x + 2x
= 18 + 10x
Therefore, the equivalent expression
Can someone help me with this problem?
Answer:
875ft squared (2)
Step-by-step explanation:
divide 5 into 35 you get 7
25 is 5 times 5 so you can infer that the measurement for FG would be 5x7
then do 35x25 and thats your answer
Given that f(x) is continuous, ƒ²ƒx)dx =7, ƒ^ƒ(x)dx =−3, and ƒª½‚ƒx)dx = 2.Then (x)dx =I have the multiple choice responses
We are given a set of definite integrals and we are tasked to find the area of the curve from x = 0 to 2.
To do this, we need to recall the adding intervals rules for definite integrals:
\(\int_a^bf(x)dx+\int_b^cf(x)dx=\int_a^cf(x)dx\)Plugging in the given, we have the following equation:
\(\begin{gathered} \int_{-2}^2f(x)dx+\int_0^4f(x)dx-\int_0^2f(x)dx=\int_{-2}^4f(x)dx \\ \\ 7+(-3)-\int_0^2f(x)dx=2 \\ \\ -\int_0^2f(x)dx=-2 \\ \\ \int_0^2f(x)dx=2 \end{gathered}\)The answer is 2.
Pleeeeeeeeeseee help meee!!!
Answer:
y= 44
Step-by-step explanation:
you know 4y so just
×11 and you get 44
find the perimeter of the hallway
Answer: 17x - 39
Step-by-step explanation:
1) Find all sides of the hallway.
P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1
2) Add it together
P= 17x - 39
currently, hayley is one-fifth as old as her brother nathan. 4 years from now 3 times hayleys age will equal nathan's age. how old is nathan now
Find the value of the length x rounded to 1 decimal place.
The diagram is not drawn accurately
Answer:
Give me heart and 5 stars
Step-by-step explanation:
Which polynomial represents the sum below? 8x^2+2x+8 + 3x^3+7x+4
Answer:
\(26 \times21 \frac = 1 > 262 {2}^{2} {?}{?} \)
A sequence of 1 million iid symbols(+1 and +2), Xi, are transmitted through a channel and summed to produce a new random variable W. Assume that the probability of transmitting a +1 is 0.4. Show your work
a) Determine the expected value for W
b) Determine the variance of W
Answer:
E(w) = 1600000
v(w) = 240000
Step-by-step explanation:
given data
sequence = 1 million iid (+1 and +2)
probability of transmitting a +1 = 0.4
solution
sequence will be here as
P{Xi = k } = 0.4 for k = +1
0.6 for k = +2
and define is
x1 + x2 + ................ + X1000000
so for expected value for W
E(w) = E( x1 + x2 + ................ + X1000000 ) ......................1
as per the linear probability of expectation
E(w) = 1000000 ( 0.4 × 1 + 0.6 × 2)
E(w) = 1600000
and
for variance of W
v(w) = V ( x1 + x2 + ................ + X1000000 ) ..........................2
v(w) = V x1 + V x2 + ................ + V X1000000
here also same as that xi are i.e d so cov(xi, xj ) = 0 and i ≠ j
so
v(w) = 1000000 ( v(x) )
v(w) = 1000000 ( 0.24)
v(w) = 240000
Use the discriminant to determine how many and what kind of solutions the quadratic equation 3x^2 + 4x = - 5 has.
A. one real solution
B. two complex (nonreal) solutions
C. no real or complex solutions
D. two real solutions
Pls help!
Answer:
C.
Step-by-step explanation:
The quadratic equation has two complex (nonreal) solutions option (B) is correct.
What is a quadratic equation?Any equation of the form \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)
We have a quadratic equation:
3x² + 4x = - 5
or
3x² + 4x + 5 = 0
D = b² - 4ac
b = 4, a = 3, c = 5
D = (4)² - 4(3)(5)
D = 16 - 60
D= -44
D < 0
Two complexes (nonreal) solutions
Thus, the quadratic equation has two complexes (nonreal) solutions option (B) is correct.
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which choice correctly expresses the number below in scientific notation?
0.000611
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
6.11/104
Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the worst 5% of wait times? Homework Help: 4VE. Determining values from normal distributions based on probabilities (Links to an external site.) (2:42) 4DC. Using normal distributions and probabilities to determine set values DOCX Group of answer choices 29.49 minutes 52.32 minutes 23.92 minutes 46.75 minutes
Answer:
Step-by-step explanation:
waiting times follow a normal distribution with
Mean, \mu=38.12Mean,μ=38.12
Standard\ deviation,\sigma=8.63Standard deviation,σ=8.63
Longer waiting times are worse than shorter waiting times. Hence the worst 20% of wait times are wait times on the right tail of the distribution. The inferred level of confidence is 0.80.
The z value corresponding to the right tail probability of 0.2 is
Z=0.85Z=0.85
But
Z = \frac{x-\mu}{\sigma}Z=
σ
x−μ
x =Z*\sigma +\mux=Z∗σ+μ
=0.85 * 8.63 +38.12 =45.4555=0.85∗8.63+38.12=45.4555
answer:
the shortest wait time that would still be in the worst 20% of wait times is 45.4555 minutes
What is the present value of R13 000 p.a. invested at the beginning of each year for 8years at 10%p.a. compound interest? (NB Use the compound interest tables provided or work to three decimal places only.)
Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:
PV = A *\((1 - (1 + r)^(-n)) / r\)
Where:
PV = Present value
A = Annual payment or cash flow
r = Interest rate per period
n = Number of periods
In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).
Using the formula and substituting the given values, we can calculate the present value:
PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)
Calculating this expression:
PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)
= 13000 * (1 - 0.46318) / 0.10
= 13000 * 0.53682 / 0.10
= 6977.66 / 0.10
= 69776.6
Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
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Mr. hodges wants to build a fence
Answer:
96 feet
Step-by-step explanation: took quiz pls mark brainliest
In December 2018, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon
Assume that the standard deviation price per gallon is $0.05 per gallon and use Chebyshev's Inequality to answer the following
(a) What minimum percentage of gasoline stations had prices within 2 standard deviations of the mean?
(b) What minimum percentage of gasoline stations had prices within 2.5 standard deviations of the mean?
(c) What is the minimum percentage of gasoline stations that had prices between $2.91 and $3.21?
Using Chebyshev's Theorem, it is found that:
a) The minimum percentage is 75%.
b) The minimum percentage is 84%.
c) The minimum percentage is 89%.
By Chebyshev's Theorem, the minimum percentage of measures within k standard deviations of the mean is:
\(P = 100\left(1 - \frac{1}{k^{2}}\right)\)
Item a:
Within 2 standard deviations, hence k = 2, and:
\(P = 100\left(1 - \frac{1}{2^{2}}\right) = 100\left(\frac{3}{4}\right) = 75\)
The minimum percentage is 75%.
Item b:
2.5 standard deviations, hence k = 2.5, and:
\(P = 100\left(1 - \frac{1}{2.5^{2}}\right) = 84\)
The minimum percentage is 84%.
Item c:
3 standard deviations, hence k = 3, and:
\(P = 100\left(1 - \frac{1}{3^{2}}\right) = 89\)
The minimum percentage is 89%.
A similar problem is given at https://brainly.com/question/15050238
une boxes.
Find:
5% of 90 m =
m
25% of 88 kg =
kg
75% of 264 =
Answer:
1) 5% of 90m= 4.5m
2)25% of 88kg = 22kg
3) 75% of 264= 198
Step-by-step explanation:
1) 90m = 100% (divide by 10)
9 = 10% (divide by 2)
4.5 = 5%
2) 88kg = 100% (keep on dividing by 2)
44kg = 50%
22kg=25%
3) 264 = 100%
132 = 50%
66 = 25% (add)
198=75%
40 POINTS PLEASE HELP ASAP YOU CAN SAVE MY LIFE WILL GIVE BRANLIEST
Which expression is equivalent to 8\sqrt(6)
A.\sqrt(14)
B.\sqrt(48)
C.\sqrt(96)
D.\sqrt(384)
Answer:
D. \sqrt(384)
Step-by-step explanation:
All you have to do is to expand the root the way I have done. I hope you understand and rate this answer well.
Don't forget 8 is the same as root(8) * root(8) which will give root(64) and the square root of 64 is 8.