A woman bought a bag of rice 5700 naira and in 3 weeks later, she could only buy 2/4 of the bags for 5700 naira. Find the percentage?

Given that a circle is inscribed in an isosceles trapezoid with bases of 8 cm and 2 cm. We need to find the probability that a randomly selected point inside the trapezoid lies on the circle.

The isosceles trapezoid is shown below: [asy] draw((0,0)--(8,0)--(3,5)--(1,5)--cycle); draw((1,5)--(1,0)); draw((3,5)--(3,0)); draw((0,0)--(1,5)); draw((8,0)--(3,5)); draw(circle((2.88,2.38),2.38)); label("$8$",(4,0),S); label("$2$",(1.5,5),N); [/asy]Let ABCD be the isosceles trapezoid,

where AB = 8 cm, DC = 2 cm, and AD = BC.

Since the circle is inscribed in the trapezoid, we can use the following formula:2s = AB + DC = 8 + 2 = 10 cm

Where s is the semi-perimeter of the trapezoid. Also, let O be the center of the circle. We can draw lines OA, OB, OC, and OD as shown below: [asy] draw((0,0)--(8,0)--(3,5)--(1,5)--cycle); draw((1,5)--(1,0)); draw((3,5)--(3,0)); draw((0,0)--(1,5)); draw((8,0)--(3,5)); draw(circle((2.88,2.38),2.38)); label("$A$",(0,0),SW); label("$B$",(8,0),SE); label("$C$",(3,5),N); label("$D$",(1,5),N); label("$O$",(2.88,2.38),N); label("$8$",(4,0),S); label("$2$",(1.5,5),N); draw((0,0)--(2.88,2.38)--(8,0)--cycle); label("$s$",(3,0),S); label("$s$",(1.44,2.38),E); [/asy]Since O is the center of the circle, we have:OA = OB = OC = OD = rwhere r is the radius of the circle.

Also, we have:s = OA + OB + AB/2 + DC/2s = 2r + 2s/2s = r + 5 cmWe can solve for r:r + 5 cm = 10 cmr = 5 cmNow that we know the radius of the circle, we can find the area of the trapezoid and the area of the circle.

Then, we can find the probability that a randomly selected point inside the trapezoid lies on the circle as follows:Area of trapezoid = (AB + DC)/2 × height= (8 + 2)/2 × 5= 25 cm²Area of circle = πr²= π(5)²= 25π cm²Therefore, the probability that a randomly selected point inside the trapezoid lies on the circle is:

Area of circle/Area of trapezoid= 25π/25= π/1= π

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The probability that a randomly selected point inside the trapezoid lies on the circle is 0.399 or 39.9%. Therefore, option (A) is the correct answer.

The circle is inscribed in an isosceles trapezoid with bases of 8 cm and 2 cm.

Inscribed Circle of an Isosceles Trapezoid

Therefore, the length of the parallel sides (AB and CD) is equal.

Let the length of the parallel sides be ‘a’. Then, OB = OD = r (let)

It is also given that the lengths of the parallel sides of the trapezoid are 8 cm and 2 cm.

Then, its height is given by:

h = AB - CD / 2 = (8 - 2) / 2 = 3 cm

Therefore, the length of the base BC of the right-angled triangle is equal to ‘3’.

Then, the length of the other side (AC) can be given as:

AC = sqrt((AB - BC)² + h²) = sqrt((8 - 3)² + 3²) = sqrt(34) cm

The area of the trapezoid can be calculated as follows:

Area of the trapezoid = 1/2 (sum of the parallel sides) x (height)A = 1/2 (8 + 2) x 3A = 15 sq. cm.

The area of the circle can be given by:

Area of the circle = πr²πr² = A / 2πr² = 15 / (2 x π)

Therefore, r² = 2.39

r = sqrt(2.39) sq. cm.

Now, the probability that a randomly selected point inside the trapezoid lies on the circle can be calculated by dividing the area of the circle by the area of the trapezoid:

P (point inside the trapezoid lies on the circle) = Area of the circle / Area of the trapezoid

P = πr² / 15

P = π (2.39) / 15

P = 0.399 or 39.9%

The probability that a randomly selected point inside the trapezoid lies on the circle is 0.399 or 39.9%.

Therefore, option (A) is the correct answer.

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Answer:

4+4−8

Step-by-step explanation:

Answer:

none of these

Step-by-step explanation:

There are 3 boys walking

There are a total of 20 people

3/20 = 0.15

That is 15 percent, therefore none of these answers.

Step-by-step explanation:

any has at least one mode

Main answer: An orthogonal basis for the given span H is {x1, x2-x1, x3 - (x1 + x2 - x1)} which simplifies to {x1, x2-x1, x3-x2}.

Supporting explanation: Given, x₁ = 0, x₂ = 1, x₃ = √3The span of H is the set of all linear combinations of x1, x2 and x3.So, we have to find an orthogonal basis for H using the Gram-Schmidt process. Let's start with the first vector x1 = [0, 0, 0]The second vector x2 is the projection of x2 onto the subspace perpendicular to x1. x2 is already perpendicular to x1 so x2-x1 = x2. So, the second vector is x2 = [0, 1, 0].The third vector x3 is the projection of x3 onto the subspace perpendicular to x1 and x2. x3 is not perpendicular to x1 and x2, so we subtract the projections of x3 onto x1 and x2 from x3. Projection of x3 onto x1:projx₁(x₃) = x₁ [(x₁ . x₃)/(x₁ . x₁)] = [0, 0, 0]Projection of x3 onto x2:projx₂(x₃) = x₂ [(x₂ . x₃)/(x₂ . x₂)] = [0, √3/3, 0]Therefore, x3 - projx₁(x₃) - projx₂(x₃) = [0, √3/3, √3]So, the orthogonal basis for H is {x1, x2-x1, x3 - (x1 + x2 - x1)} which simplifies to {x1, x2-x1, x3-x2}.

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Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:

x_(t) = 146t + 24yt + 3

y_(t) = (876t + 21) / ((-144) - 10t)

To solve the given linear system of differential equations, let's rewrite the system in a more standard form:

dx/dt = 146 + 24y

dy/dt = 12x + 20y

We'll use the initial conditions x_(0) = 3 and y_(0) = 3 to find the specific solution.

To solve the system, we can use the method of integrating factors.

Solve the first equation:

dx/dt = 146 + 24y

Rearrange the equation to isolate dx/dt:

dx = (146 + 24y) dt

Integrate both sides with respect to x:

∫dx = ∫(146 + 24y) dt

x = 146t + 24yt + C_(1) ---(1)

Solve the second equation:

dy/dt = 12x + 20y

Rearrange the equation to isolate dy/dt:

dy = (12x + 20y) dt

Integrate both sides with respect to y:

∫dy = ∫(12x + 20y) dt

y = 6x + 10yt + C_(2) ---(2)

Now, we'll apply the initial conditions x_(0) = 3 and y_(0) = 3 to find the values of C_(1) and C_(2).

From equation (1), when t = 0, x = 3:

3 = 146(0) + 24(3)(0) + C_(1)

C_(1) = 3

From equation (2), when t = 0, y = 3:

3 = 6(0) + 10(3)(0) + C_(2)

C_(2) = 3

Now, substituting the values of C_(1) and C_(2) back into equations (1) and (2), we get:

x = 146t + 24yt + 3

y = 6x + 10yt + 3

Simplifying further:

x = 146t + 24yt + 3

y = 6(146t + 24yt + 3) + 10yt + 3

x = 146t + 24yt + 3

y = 876t + 144y + 18 + 10yt + 3

x = 146t + 24yt + 3

y - 154y - 10yt = 876t + 18 + 3

(-144y) - 10yt = 876t + 21

y = (876t + 21) / (-144 - 10t)

Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:

x_(t) = 146t + 24yt + 3

y_(t) = (876t + 21) / ((-144) - 10t)

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Answer:

150 cm squared

Step-by-step explanation:

I guess that's the answer if I'm wrong you can tell me right away so that I can try another method thank you.

X/2= 87.2

to find X:

87.2 X 2= 174.4

therefore X is 174.4

Answer:

$30.99

Step-by-step explanation:

The formula for simple interest is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.

I = (30)(0.033)(1)

I = 0.99

Then add that to the amount deposited ($30) and you're done.

30 + 0.99 = $30.99

Please let me know if you have questions.

The answer is $29.01

Question:

A population consists  1, 2, 4, 5, 8. Draw all possible samples of size 2  without replacement from this population.

Verify that the sample mean is an unbiased estimate of the population mean.  

Answer:

[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]

[tex]\hat p = \frac{3}{5}[/tex] --- proportion of evens

The sample mean is an unbiased estimate of the population mean.

Step-by-step explanation:

Given

[tex]Numbers: 1, 2, 4, 5, 8[/tex]

Solving (a): All possible samples of 2 (W.O.R)

W.O.R means without replacement

So, we have:

[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]

Solving (b): The sampling distribution of the proportion of even numbers

This is calculated as:

[tex]\hat p = \frac{n(Even)}{Total}[/tex]

The even samples are:

[tex]Even = \{2,4,8\}[/tex]

[tex]n(Even) = 3[/tex]

So, we have:

[tex]\hat p = \frac{3}{5}[/tex]

Solving (c): To verify

[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]

Calculate the mean of each samples

[tex]Sample\ means = \{1.5,2.5,3,4.5,3,3.5,5,4.5,6,6.5\}[/tex]

Calculate the mean of the sample means

[tex]\bar x = \frac{1.5 + 2.5 +3 + 4.5 + 4 + 3.5 + 5 + 4.5 + 6 + 6.5}{10}[/tex]

[tex]\bar x = \frac{40}{10}[/tex]

[tex]\bar x = 4[/tex]

Calculate the population mean:

[tex]Numbers: 1, 2, 4, 5, 8[/tex]

[tex]\mu = \frac{1 +2+4+5+8}{5}[/tex]

[tex]\mu = \frac{20}{5}[/tex]

[tex]\mu = 4[/tex]

[tex]\bar x = \mu = 4[/tex]

This implies that [tex]\bar x[/tex] is an unbiased estimate of the [tex]\mu[/tex]

Correct Question:

He counts 18 female students, 16 male students, and 6 teachers. There are

720 people in the auditorium. Consider the probability of selecting one person

at random from the auditorium.

Which of these statements are true?

Choose all that apply.

A:  The probability of selecting a teacher is 6%.

B : The probability of selecting a student is 85%.

C : The probability of selecting a male student is 32%.

D : The probability of selecting a female student is 45%.

Step-by-step explanation:

Option B  and D are correct because

The total number of people in one cross section = 18 + 16 + 6 = 40.

A = The probability of selecting a teacher is = (6/40)x100 = 15 % not equal to 6 %

B = The probability of selecting a male student is = (34/40)x100 = 85%

C = The probability of selecting a male student is = (16/40)x100 = 40 % not equal to 32 %

D : The probability of selecting a female student is = (18/40)x100= 45%

Answer:

Dominos is the better deal.

Answer: ±√2

Step-by-step explanation: A fraction is undefined when its denominator is =0 or undefined. so we need to get 2/3x²-6=0 or undefined. so we can also do 3x^2-6=0. Solving yields ±√2!

Answer:

m ÷ 7

Step-by-step explanation:

"Quotient" means you're dividing, so this just means you're dividing m by 7.

Answer:

[tex](g*f)(x) = 34[/tex]

Step-by-step explanation:

For sake of clarity, [tex](g * f)(x) = g(f(x))[/tex]

First, find [tex]f(1)[/tex]

[tex]f(1) = 2(1)^2 - 2(1) - 4\\f(1) = 2-2-4 \\f(1)=-4[/tex]

Then, take what you got for [tex]f(1)[/tex] and plug that into [tex]g(x)[/tex].  In this case, [tex]f(1) = -4[/tex]

[tex]g(-4) = -5(-4) + 14\\g(-4)= 20 + 14\\g(-4) = 34[/tex]

Please make sure to mark brainliest if this satisfies your

Answer:

Yield per share = 7.68% (Approx.)

Step-by-step explanation:

Given:

Dividend paid = $4.15

Price per dividend = $54

Find:

Yield per share

Computation:

Yield per share = [Dividend paid / Price per dividend]100

Yield per share = [4.15 / 54]100

Yield per share = [0.0768]100

Yield per share = 7.68% (Approx.)

Answer:

25

Step-by-step explanation:

First, plug -5 in for a, -(-5)^2. We treat the negative on the outside of the paranthese as a -1 so we do -1 times -5 and we get 5. Then we square 5 and get 25.

Answer:

Range = [0, ∞)

Step-by-step explanation:

Range is the y-values

For this question y starts at 0 and just continually goes up so:

Range = [0, ∞)

Answer: You want to calculate the interest on $380 at 5.3% interest per year after .5 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $380.00.

r is the interest rate, 5.3% per year, or in decimal form, 5.3/100=0.053.

t is the time involved, 0.5....year(s) time periods.

So, t is 0.5....year time periods.

To find the simple interest, we multiply 380 × 0.053 × 0.5 to get your answer.

Step-by-step explanation:

After considering the given data we conclude that the new point generated is (2,3), under the condition that g(x) is transformed by [tex]-g[4(x+2)][/tex].

To evaluate the new point after the transformation of point (2,-3) by -g[4(x+2)], we can stage x=2 and g(x)=-3 into the expression [tex]-g[4(x+2)][/tex]and apply  simplification to get the new y-coordinate. Then, we can combine the new x-coordinate x=2 with the new y-coordinate to get the new point.
Stage x=2 and g(x)=-3 into [tex]-g[4(x+2)]:[/tex]
[tex]-g[4(2+2)] = -g = -(-3) = 3[/tex]
The new y-coordinate is 3.
The new point is (2,3).
Hence, the new point after the transformation of point (2,-3) by [tex]-g[4(x+2)][/tex] is (2,3).
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The probability that the selected individual has children in public schools AND favors the school tax is 0.32

The probability that the selected individual favors the school tax AND has children in public schools is 0.32.

The probability that the selected individual favors the school tax AND does NOT have children in public schools is 0.2.

The probability that the selected individual favors the school tax AND is over 56 years old is 0.15.

The probability that the selected individual favors the school tax AND is 18-25 years old is 0.45.

Based on the given information, the probability of event F (the selected individual favors the school tax) is 0.54, as 54% of the respondents are in favor of the tax. The probability of event C (the selected individual has children in public schools) is 0.59, as the approval rating rises to 59% for those with children in public schools. The probability of event O (the selected individual is over 56 years old) is 0.37, as only 37% of those over age 56 said they would vote for the tax. The probability of event Y (the selected individual is 18-25 years old) is 0.71, as 71% of 18- to 25-year-olds said they would vote for the tax.

Using these probabilities, we can estimate the values of the following probabilities:

(1) P(CF) is the probability that the selected individual has children in public schools AND favors the school tax. Based on the given information, we can multiply the probabilities of events C and F: P(CF) = 0.59 * 0.54 = 0.318, or approximately 0.32.

(ii) P(FIC) is the probability that the selected individual favors the school tax AND has children in public schools. This is the same as P(CF), so P(FIC) = 0.32.

(iii) P(FIN) is the probability that the selected individual favors the school tax AND does NOT have children in public schools. To calculate this, we can use the fact that the approval rating falls to 44% for those with no children in public schools. So, P(FIN) = 0.44 * (1 - 0.59) = 0.18, or approximately 0.2.

(iv) P(FTO) is the probability that the selected individual favors the school tax AND is over 56 years old. To calculate this, we can use the fact that the approval rating for those over 56 years old is only 37%. So, P(FTO) = 0.37 * (1 - 0.59) = 0.1523, or approximately 0.15.

(v) P(FY) is the probability that the selected individual favors the school tax AND is 18-25 years old. To calculate this, we can use the fact that the approval rating for those 18-25 years old is 71%. So, P(FY) = 0.71 * (1 - 0.37) = 0.4477, or approximately 0.45.

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Answer:

 Forgot picture?

Step-by-step explanation:

Answer:

You can get your grade up by studying, getting a tutor, paying attention in class, taking good notes, asking questions, and cheating (i don't recommend this one :/)

Answer:

YOU DO IT X 2

Step-by-step explanation:

Step-by-step explanation:

the correct answer is exponent because 6 is its power.

hope this answer will help u.

have a great time.

The calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.

Hence, the claim that the proportion is at least 34% is rejected.

Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.

Null hypothesis:

H0: p ≥ 0.34

Alternative hypothesis:

Ha: p < 0.34

where:p = proportion of Littleton fathers who do not help with childcare

Here, the level of significance, α = 0.05

Level of significance = α = 0.05

The test statistics for a proportion is given as z-test.  

The formula for calculating z-score for a proportion is: z = (p - P) / sqrt[P(1 - P) / n]

where:

P = Population proportion

p = Sample proportion

n = Sample size

The calculated value of z-statistics can be compared with the critical value of z-score from the standard normal distribution table at a particular level of significance.

If the calculated value of z is greater than the critical value of z, then we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Calculating the z-statistic:

Here, Sample size n = 225

Sample proportion

p = 97/225

= 0.4311

Population proportion

P = 0.34z

= (p - P) / sqrt[P(1 - P) / n]z

= (0.4311 - 0.34) / sqrt[(0.34)(0.66) / 225]z

= 2.80

Since the alternative hypothesis is one-tailed (Ha: p < 0.34), the critical value of z at α = 0.05 can be found as follows:

The critical value of z = zα

= -1.645

Since the calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.

Hence, the claim that the proportion is at least 34% is rejected.

Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.

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Answer:

389.19 m²

Step-by-step explanation:

The surface area of the box = area of the two equal triangles + area of the 3 different rectangles

✔️Area of the two equal triangles:

Area = 2(½*base*height)

base = 7 m

height = 8 m

Area of the two triangles = 2(½*7*8) = 56 m²

✔️Area of rectangle 1:

Area = Length*Width

L = 13 m

W = 7 m

Area of rectangle 1 = 13*7 = 91 m²

✔️Area of rectangle 2:

L = 13 m

W = 8 m

Area of rectangle 2 = 13*8 = 104 m²

✔️Area of rectangle 3:

L = 13 m

W = 10.63 m

Area of rectangle 3 = 13*10.63 = 138.19 m²

✅Surface Area of the box = 56 + 91 + 104 + 138.19 = 389.19 m²

Answer:

here,hope this helps : )

Step-by-step explanation:

Answer: A= 32

a (Base) 6

b (Base) 10

h (Height) 4

Step-by-step explanation: A=a+b

2h=6+10

2·4=32    I really hoped this helped