Write −0.258 as a fraction in simplest form.

Answer:

\(4\sqrt{17}\)

Step-by-step explanation:

We remember the distance formula. Given two points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\), the distance between them is \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\).

Aha! We can plug in these two points into the distance formula!.

We get \(\sqrt{(-8-8)^2+(5-1)^2}=\sqrt{(-16)^2+4^2}=\sqrt{256+16}=\sqrt{272}=4\sqrt{17}\).

Therefore, the answer is \(\boxed{4\sqrt{17}}\) and we're done!

Answer:

option d has the value of 24

Step-by-step explanation:

Permutation test is used to synthesize the population distribution of the statistic of interest for hypothesis testing of mean, median, and quartiles

An estimation of the population distribution—the distribution from which our observations originated—is the goal of a permutation test. We can then calculate how uncommon our observed values are in comparison to the population.

I find the permutation test to be more natural, and it only relies on the assumption of random assignment of treatment groups.

In a permutation test, you compare the observed test statistic to the distribution of values

you get when the treatment group assignments are shuffled/randomized/permuted.

The null hypothesis that two distinct groups originate from the same distribution is tested using permutation tests, also known as exact tests, randomization tests, or re-randomization tests. A permutation test can be used for hypothesis testing or significance testing (including A/B testing) without requiring any presumptions to be made about the distribution of the samples, such as that the samples must be normally distributed.

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Answer:

range =18-2

=16

mean=(n+1)/2

=6+1/2

=3.5

Step-by-step explanation:

range =largest value subtract by smallest value

Answer:

− 7 2 − 33

Explanation:

Step 1 ) Subtract the numbers

*Note* A common technique for simplifying algebraic expressions. When combining like terms, such as 2x and 3x, we add their coefficients. For example, 2x + 3x = (2+3)x = 5x.

− 58 + 23 − 14 − 56

−58 −33 −14  

Step 2)  Combine the like terms.

*Note* To combine like terms, we have to add the coefficients and keep the variables the same. We add like terms to make one term.

−58a −33 −14a

−72 −33

(What do you mean simplified fractions? You listed whole numbers)

Hey there!

-58a + 23 - 14a - 56

COMBINE the LIKE TERMS

= (-58a - 14a) + (23 - 56)

= -72a - 33

Therefore, your answer should be:

-72a - 33

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:  10 goes up top, 7 in the bottom

Reason: It's standard convention that the terms multiply to the number up top, and add to the thing down below. Search out "factor diamond method" to get more examples how the diagram is set up.

The two mystery numbers are 2 and 5

This is found through trial and error.

The value of x for GT is 6.5 .

What is the congruence of triangles?
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

Given, ΔGET ≅ ΔABS
Following the statement that corresponding sides of congruent triangles are congruent, we have:
GE = AB, ET = BS and GT = AS -(i)
AB = 10, BS = 13, AS = 18, GT = 4x - 8 -(ii)
Comparing (i) and (ii) we have, 4x - 8 = 18 ⇒ 4x = 26 ⇒ x = 26/4 = 6.5
Thus, the value of x for GT is 6.5 .

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The probability there is at least one pair is therefore 1−p.

acc to our question-

hence,The probability there is at least one pair is therefore 1−p.

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Answer:The coefficient in this expression is 3.

Step-by-step explanation:

What is a Coefficient?

By definition, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic.

What is a variable?

A variable is a symbol that represents a mathematical object. So for example, 9p + 2. In this equation, the variable would be the letter "p."

a. Rafael deposited £62.10 in the account at the start.

b. The annual interest rate on Rafael's account is approximately 3.66%.

a) To calculate how much money Rafael deposited in the account, we need to find the difference between the two amounts.

Amount after 6 years - Amount after 5 years = £1752.60 - £1690.50 = £62.10

b) To work out the annual interest rate on the account, we can use the simple interest formula:

I = Prt

where I is the interest earned, P is the principal amount (i.e., the amount deposited by Rafael), r is the annual interest rate, and t is the time period in years.

We know that Rafael's account pays simple interest, so the annual interest rate remains constant over the years.

Let's represent the annual interest rate by x.

Using the formula, we can write:

£62.10 = P * x * 1, as the interest rate is per annum.

Simplifying the equation:

£62.10 = Px

x = £62.10 / P

The interest rate is equal to £62.10 divided by the amount Rafael deposited.

Substituting the value of P, we get:

x = £62.10 / £1690.50 ≈ 0.0366 or 3.66% (to 1 d.p.)

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To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).

To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.

Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).

To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).

Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.

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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.

To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:

1. τ(mn) = τ(m)τ(n)

2. σ(mn) = σ(m)σ(n)

Let's start with property 1:

1. τ(mn) = τ(m)τ(n)

If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.

Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).

Now let's move on to property 2:

2. σ(mn) = σ(m)σ(n)

Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.

Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.

Hence, we can conclude that σ(mn) = σ(m)σ(n).

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Answer:The value of x must be 7 units.

Step-by-step explanation:

hope this helps

The equation of the osculating plane is (-1/3)(x-0) + (1/3)(y+1) + (2/3)(z-8 π) = 0.

First, we find the point on the curve at

\(t = 2\pi\)

\(x = sin(2(2\pi)) = 0 \\

y = -cos(2(2\pi)) = -1 \\

z = 4(2\pi) = 8\pi\)

So the point on the curve is

\( (0, -1, 8\pi)\)

To find the normal plane, we take the cross product of the partial derivatives:

\(r_t = (2cos(2t), 2sin(2t), 4) \\

r_t(2\pi) = (2cos(4\pi), 2sin(4\pi), 4) = (2, 0, 4) \\

r_tt = (-4sin(2t), 4cos(2t), 0) \\

r_tt(2\pi) = (0, -4, 0) \\

n = r_t × r_tt = (-16, -8, -8)\)

So the equation of the normal plane is

\(-16(x-0) - 8(y+1) - 8(z-8\pi) = 0.\)

To find the osculating plane, we first find the unit tangent and unit normal vectors:

\(T = r_t / ||r_t|| = ( \frac{1}{2})cos(2t)i + ( \frac{1}{2}) sin(2t)j + ( \frac{1}{4})k \\

N = n / ||n|| = ( \frac{2}{3})cos(2t)i + ( \frac{1}{3})sin(2t)j + ( \frac{1}{3})k\)

Then the binormal vector is B = T × N, which is

\(( \frac{ - 1}{3})sin(2t)i + ( \frac{1}{3} )cos(2t)j + ( \frac{2}{3} )k\)

Finally, the equation of the osculating plane is

\(( \frac{ - 1}{3})(x-0) + ( \frac{1}{3})(y+1) + ( \frac{2}{3})(z-8\pi) = 0\)

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$7.20 was taken off the price.

The price would now be $4.80

Answer: $7.2

Step-by-step explanation:

First, you must find 60% of $12 which is $7.2. Then, you must subtract $12 - $7.2 which is $4.8. $12 - $4.8 is 7.2.

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Solution for What is 12.5 percent of 40:

12.5 percent *40 =

(12.5:100)*40 =

(12.5*40):100 =

500:100 = 5

Now we have: 12.5 percent of 40 = 5

Question: What is 12.5 percent of 40?

Percentage solution with steps:

Step 1: Our output value is 40.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$40=100\%$.

Step 4: Similarly, $x=12.5\%$.

Step 5: This results in a pair of simple equations:

$40=100\%(1)$.

$x=12.5\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{40}{x}=\frac{100\%}{12.5\%}$

Step 7: Again, the reciprocal of both sides gives

$\frac{x}{40}=\frac{12.5}{100}$

$\Rightarrow x=5$

Therefore, $12.5\%$ of $40$ is $5$

Answer:

9π ft² or approximately 28.26 ft²

Step-by-step explanation:

The area of a circle is A=πr².

Plug 3 in for the radius.

A=π(3²)

A=9π ft²,

or using 3.14 for pi,

Approximately 28.26 ft².

The first term in the series is 336. The second term is obtained by subtracting 4 from the first term; subtract 4 from that to get the third term; and so on. Then the n-th term in the series is

336 - 4 (n - 1)

or

340 - 4n

The last term in this series is 4, so we solve for n :

340 - 4n = 4

336 = 4n

n = 336/4 = 84

The sum of the series is then

\(\displaystyle\sum_{n=1}^{84}(340-4n) = 340\sum_{n=1}^{84}1 - 4 \sum_{n=1}^{84}n\)

Recall that

\(\displaystyle \sum_{n=1}^{N} 1 = N\)

\(\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2\)

Then the sum we want is

\(\displaystyle\sum_{n=1}^{84}(340-4n) = 340\times84 - 4\times\frac{84\times85}2 = \boxed{14,280}\)

Answer: 35 square units.

Step-by-step explanation:

- In this question you need to substitute in the given values to the triangle to fulfill the equation for the area of triangle.

Area of a triangle = \(\frac{1}{2}\) x base x height.

The base was 'x', which was 14 units.

The height was 'h', which was given as 5 units.

Substitute these into the equation.

Answer:

$0.40

Step-by-step explanation:

5.60/14 = .40

The mean per capita income in thousands of dollars with 99% confidence interval and sample size of 1417 is equal to CI = (23.7, 24.3).

Construct the 99% confidence interval for the mean per capita income, use the formula,

CI = x ± Z× (σ / √n)

where

x is the sample mean,

σ is the population standard deviation,

n is the sample size,

Z is the z-score corresponding to the desired level of confidence.

Using attached z-score table,

For a 99% confidence interval, the corresponding z-score is 2.58

Substituting the given values, we get,

⇒CI = 24 ± 2.58 × (5.1 / √1417)

Simplifying the expression inside the parentheses, we get,

⇒CI = 24 ± 0.349

⇒CI = (23.7, 24.3)

Rounding to one decimal place, the confidence interval is (23.7, 24.3) thousands of dollars.

Therefore, the 99% confidence interval for the mean per capita income is CI = (23.7, 24.3).

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Answer:

36 ounces

Step-by-step explanation:

1 lb = 16oz

So just multiply 2 lb by 16 to get 32.

Then you can multiply 16 by 0.25 (a.k.a 1/4) OR divide 16 by 4

You get 4 ounces

Finally, add 32 and 4 to get your total of 36 ounces.

5 more than a number is greater or equal to 27

The "number" can be represented as x.

\(\boxed{x+5\geq 27}\)

The required,
(a) it would cost Mandla R72.19 if he used 8.75 kl of water.
(b) it would cost Mandla R115.50 if he used 14 kl of water.

The table can be set up as follows:

Number of kilolitres used Tariff per kilolitre (RO/kl)

Less than 6                           R7.50/kl

6 - 10                                    R8.25/kl

More than 10                              R8.25/kl

a) Mandla used 8.75 kl of water, which falls in the second category of 6-10 kl. The cost per kilolitre for this category is R8.25. Therefore, the total cost for Mandla would be:

8.75 kl x R8.25/kl = R72.19

So it would cost Mandla R72.19 if he used 8.75 kl of water.

b) Mandla used 14 kl of water, which falls in the third category of more than 10 kl. The cost per kilolitre for this category is also R8.25. Therefore, the total cost for Mandla would be:

14 kl x R8.25/kl = R115.50

So it would cost Mandla R115.50 if he used 14 kl of water.

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Answers: 36

Step-by-step explanation:

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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