Jernel has to figure out the area of her square garage. she knows that one side of the garage is equal to the length of her rabbit pen. the dimensions of the rectangular rabbit pen are 14 by 10. what is the area of the garage?

Answer:

3.5 Liters

Step-by-step explanation:

Since 500 ml is equal to 0.5 liters and there are 7 days in a single week you just need to multiple the number of liters (0.5) by the 7 days to get a total of 3.5 liters

Anneyonghaseyo!!

Radius = 10.5 m

Diameter = 10.5 × 2 = 21 m

Circumference = πd

= 22/7 × 21

= 66 m.

Cost of fencing 1 metre = ₹ 4

Cost of fencing 2 rounds = ?

2 rounds = 2 × circumference

= 2 × 66

= 132 m

Cost of fencing 2 rounds = 132 × 4

= ₹ 528.

________

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂

Answer:

2/3

Step-by-step explanation:

The first person to make me become Brainliest wins the official contest!!! Hurry!

Answer:

I'm not sure but it might be 2/3????? That's just from looking at Spatrickfarley's answer. He deserves Brainliest!

Answer:

Volume of the solid is 377 cm³.

Step-by-step explanation:

Volume of the cylinder = \(\pi r^{2}h\)

Here, r = radius of the cylinder

h = Height of the cylinder

By substituting the values in the formula, (r = 4 cm and h = 10 cm)

Volume of the cylinder = \(\pi (4)^2(10)\)

                                      = 160π

Since one fourth of the cylinder is removed,

Volume of the remaining cylinder = 160π - \(\frac{160\pi }{4}\)

                                                        = 160π - 40π

                                                        = 120π

                                                        = 120(3.14)

                                                        = 376.8 cm³

                                                        ≈ 377 cm³

Volume of the solid is 377 cm³.

Answer:

-6/5

Step-by-step explanation:

The slope is (4 - (-2)) / (-1 - 4) = (4 + 2) / (-5) = 6 / -5 = -6/5.

Answer:

-6/5

Step-by-step explanation:

We can find the slope by using the slope formula

m = (y2-y1)/(x2-x1)

    = (4 - -2)/(-1 -4)

   = (4+2)/ ( -1-4)

   =-6/5

The absolute maximum of g on the interval [-2, 1] is g(1) = 17, and the absolute minimum is g(0) = 10.

Find the absolute maximum and minimum on the interval [−2, 1]?

To find the absolute maximum and minimum of f on the interval [1, 8], we first need to find the critical points of f within that interval. We can do this by finding where the derivative of f is equal to zero or undefined.

Taking the derivative of f, we get:
f'(x) = 1 - 9/x²

Setting f'(x) equal to zero, we get:
1 - 9/x²= 0
Solving for x, we get:
x = ±3

However, since x must be within the interval [1, 8], we can only consider x = 3 as a critical point.

Next, we evaluate f at the endpoints of the interval:
f(1) = 1 + 9/1 = 10
f(8) = 8 + 9/8

Finally, we evaluate f at the critical point:
f(3) = 3 + 9/3 = 6

Therefore, the absolute maximum of f on the interval [1, 8] is f(1) = 10, and the absolute minimum is f(3) = 6.


To find the absolute maximum and minimum of g on the interval [-2, 1], we again need to find the critical points of g within that interval. We can do this by taking the derivative of g:
g'(x) = 3x² + 12x

Setting g'(x) equal to zero, we get:
3x(x+4) = 0
Solving for x, we get:
x = -4 or x = 0

However, since x must be within the interval [-2, 1], we can only consider x = 0 as a critical point.

Next, we evaluate g at the endpoints of the interval:
g(-2) = (-2)³ + 6(-2)² + 10 = 2
g(1) = 1³ + 6(1)² + 10 = 17

Finally, we evaluate g at the critical point:
g(0) = 0³ + 6(0)² + 10 = 10

Therefore, the absolute maximum of g on the interval [-2, 1] is g(1) = 17, and the absolute minimum is g(0) = 10.

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Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For this problem, the parameters are given as follows:

\(\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2\)

The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:

X = 42:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

Z = (42 - 40)/2

Z = 1

Z = 1 has a p-value of 0.8413.

X = 38:

\(Z = \frac{X - \mu}{s}\)

Z = (38 - 40)/2

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

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Answer:

I think it is this but I haven't done factors in a long time

for 21:

1, 3, 7 and 21

for 63

(1, 63), (3, 21) and (7, 9).

hope this helps!

Answer: 7 + 2

Step-by-step explanation:only one solution

Answer:23.4$

Step-by-step explanation:

Answer:

it is the 3rd one on the page

Answer:

77

Step-by-step explanation:

3+2*49-24

3+98-24

101-24

77

Good luck

Answer:

77

Step-by-step explanation

3+2X7^2-4X6

First complete the exponent

3+2X49-4X6

Then multiply

3+2X49-24

Multiply

3+98-24

Calculate the rest of the equation

101-24=77

Therefore the answer is 77.

Please don't be mad if this is incorrect

Also the x's are multiplication symbols and NOT variables

7x9=63/2=31.5

31.5x4= 126

7x7=49

126+49=175

The surface area of the pyramid would be 175cm^2

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is B.

The correct option of the given question is option(c) becomes narrower.

Based on the given information, when the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes narrower. So, the correct answer is option c. becomes narrower.

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When the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes wider.

This is because a higher confidence level implies a narrower interval to provide a higher level of certainty in capturing the true population mean. Conversely, when the confidence level is decreased, the interval needs to be wider to allow for a larger margin of error and account for the reduced confidence requirement.

Widening the interval ensures that the estimate is more conservative and includes a broader range of possible values for the population mean. Therefore, the confidence interval for μ becomes wider as the confidence level is lowered.

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Answer:

-\(3x^{3}\) + \(5x^{2}\) + 4x + 5

Answer:

It would be the fourth choice.

Answer:

a=11

Step-by-step explanation:

⅔a-7=⅓

add 7 to both sides:

⅔a=7⅓

multiply both sides by ³/2 (the reciprocal of ⅔

a=66/6

simplify

a=11

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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The random variable in this case is the z-score of the median of the data set. The z-score measures the number of standard deviations the median is away from the mean of the population.

Since the sample size is 12, the median will be the value that separates the lower 6 values from the upper 6 values in the ordered data set.

To find the random variable, we need to calculate the z-score of the median. The z-score formula is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

However, the exact distribution of the median is complex and depends on the underlying distribution of the population. In this case, we know that the population is normally distributed, but we don't have information about the mean and standard deviation.

To determine the random variable, we need to know the mean and standard deviation of the population. Without that information, it is not possible to calculate the z-score of the median.

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A random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the z-score of the median of the data set. Give the random variable. (Appropriate rounding rules still apply)?

Answer:

260

Step-by-step explanation:

By PEMDAS, we know multiplican comes first. 53*5=265. Then, subtract 5 to get 260.

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Answer:

260

Step-by-step explanation:

the rule is to start with multiplication first 53*5=265 then subtract 5

53 × 5-5= 265-5=260

Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

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Answer: 10 treats per seal, and there are 5 treats left.

Step-by-step explanation:

The zookeeper has 85 treats, and want to divide them into seals, in such a way that the treats left is minimized,

Then we want to find the multiple of  that is closer to 85 (from below)

We know that: 8*10 = 80 is a multiple of 8, and the next one is:

8*11 = 88, but this is larger than 85, so we discard this option.

Then we will divide 80 treats into 8 seals, and we will have:

85 - 80 = 5 treats left.

Then each one of the 8 seals gets:

80/8 =  10 treats.

The deflection angle of light by the white dwarf star is approximately \(\(0.00108 \times 206,265 = 223.03\)\)arcseconds (rounded to two decimal places).

To calculate the deflection angle of light by a white dwarf star, we can use the formula derived from Einstein's theory of general relativity:

\(\[\theta = \frac{4GM}{c^2R}\]\)

where:

\(\(\theta\)\) is the deflection angle of light,

G is the gravitational constant \((\(6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}\)),\)

M is the mass of the white dwarf star,

c is the speed of light in a vacuum \((\(299,792,458 \, \text{m/s}\)),\) and

(R) is the radius of the white dwarf star.

Let's calculate the deflection angle using the given values:

Mass of the white dwarf star, \(\(M = 1.2 \times \text{solar mass}\)\)

Radius of the white dwarf star, \(\(R = 0.0088 \times \text{solar radius}\)\)

We need to convert the solar mass and solar radius to their respective SI units:

\(\(1 \, \text{solar mass} = 1.989 \times 10^{30} \, \text{kg}\)\(1 \, \text{solar radius} = 6.957 \times 10^8 \, \text{m}\)\)

Substituting the values into the formula, we get:

\(\[\theta = \frac{4 \times 6.67430 \times 10^{-11} \times 1.2 \times 1.989 \times 10^{30}}{(299,792,458)^2 \times 0.0088 \times 6.957 \times 10^8}\]\)

Evaluating the above expression, the deflection angle \(\(\theta\)\) is approximately equal to 0.00108 radians.

To convert radians to arcseconds, we use the conversion factor: 1 radian = 206,265 arcseconds.

Therefore, the deflection angle of light by the white dwarf star is approximately \(\(0.00108 \times 206,265 = 223.03\)\)arcseconds (rounded to two decimal places).

Hence, the deflection angle is approximately 223.03 arcseconds.

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The problem involves a set of independent and normally distributed random variables Y₁, Y₂, Y₃, ..., Yₙ with different means and variances. We are asked to find the expected value of the expression E[(Yᵢ - Yₙ)²] for i = 1 to n.

To find E[(Yᵢ - Yₙ)²], we can start by expanding the square term:

(Yᵢ - Yₙ)² = Yᵢ² - 2YᵢYₙ + Yₙ²

Taking the expectation of this expression, we can apply linearity of expectation:

E[(Yᵢ - Yₙ)²] = E[Yᵢ²] - 2E[YᵢYₙ] + E[Yₙ²]

Since Yᵢ and Yₙ are independent, their covariance is zero, and we can simplify the expression further:

E[(Yᵢ - Yₙ)²] = E[Yᵢ²] - 2E[Yᵢ]E[Yₙ] + E[Yₙ²]

Now, we need to evaluate the individual expectations. Given that Yᵢ follows a normal distribution with mean (μ + δᵢ) and variance σ², we have:

E[Yᵢ²] = Var[Yᵢ] + (E[Yᵢ])² = σ² + (μ + δᵢ)²

Similarly, for Yₙ:

E[Yₙ²] = Var[Yₙ] + (E[Yₙ])² = σ² + (μ + δₙ)²

Substituting these values back into the expression, we get:

E[(Yᵢ - Yₙ)²] = σ² + (μ + δᵢ)² - 2(μ + δᵢ)(μ + δₙ) + σ² + (μ + δₙ)²

Simplifying further:

E[(Yᵢ - Yₙ)²] = 2σ² + 2(μ + δᵢ)² - 2(μ + δᵢ)(μ + δₙ)

This is the expected value of the given expression. The proof involves expanding the square term, applying linearity of expectation, and substituting the values of means, variances, and covariances.

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Answer:

Infinitely many solutions

Step-by-step explanation:

-5.9x - 3.7y = -2.1

5.9x + 3.7y = 2.1

If we add these two equations together, -5.9x cancels out 5.9x, -3.7y cancels out 3.7y, and -2.1 cancels out 2.1.

This leaves us with:

0 = 0

Since this is true, that means there are infinite solutions.

\( \tt{}(8 \times 104)(4.5 \times 10 - 1)\)

\(\tt{}(832)(45 - 1)\)

\(\tt{}(832)(44)\)

\(\tt{}832 \times 44\)

\(\tt{}36608\)

Answer:

66

Step-by-step explanation:

Answer:

66 is the correct answer

Step-by-step explanation:

when 7(12)+3(-6)

= 84+(-18)

66

The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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