T/F : In a 5 by 5. If rankA=4 , then the columns of A form a basis of R5

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The interval of times that represents the middle 99. 7% of his finishing

times in the 400 meter race = (57, 63)

We know that the empirical rule or 68-95-99.7 rule states that for a normal distribution, 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Here, mean (μ) = 60 seconds, standard deviation (σ) = 1 second

To  determine the interval of times that represents the middle 99. 7% of his finishing times in the 400 meter race.

the 99.7% are within three standard deviations would be,

μ ± 3σ

= (60 - 3(1), 60 + 3(1))

= (57, 63)

The required interval is:  (57, 63)

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Answer:

Step-by-step explanation:

Let us represent

First number = x

Second number = y

The sum of two numbers is 50

Hence:

x × y = 50

xy = 50..... Equation 1

x = 50/y

Twice the sum of money the number is 100.

2(x + y) = 100

2x + 2y = 100...... Equation 2

We substitute 50/y for x in Equation 2

2(50/y) + 2y = 100

100/y + 2y = 100

Multiply through by y

100/y × y + 2y × y = 100 × y

100 + 2y² = 100y

Hence:

2y² - 100y + 100

The least possible value for the mode is D=11

Let M be the median

According to the question, the two largest integers are M+2

Let a and b be the two smallest integers such that a<b

Accordingly, the sorted list can be concluded as a,b, M, M+2, M+2

Since the median is 2 greater than their arithmetic mean, we have,

{a+b+M+(M+2)+(M+2)/5 }+2 =M

OR, a+b+14=2M

Note that a+b must be even.

We minimize this sum so that the arithmetic mean, the median, and the unique mode is minimized.

Let a=1 and b=3

from which M=9 and

M+2=11

Therefore, The least possible value for the mode is D=11

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i believe it’s cAnswer:

Step-by-step explanation:

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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To calculate the principal repaid by the 17th monthly payment of $750 on a $22,000 loan at 15% compounded monthly, we need to calculate the monthly interest rate, the remaining balance after 16 payments, and the interest portion of the 17th payment.

The monthly interest rate is calculated by dividing the annual interest rate by the number of compounding periods per year. In this case, it would be 15% / 12 = 1.25%.

The remaining balance after 16 payments can be calculated using the loan balance formula:

\($$B = P(1 + r)^n - (PMT/r)[(1 + r)^n - 1]$$\)

Where B is the remaining balance, P is the initial principal, r is the monthly interest rate, n is the number of payments made, and PMT is the monthly payment amount.

Substituting the values into the formula, we get:

\($$B = 22000(1 + 0.0125)^{16} - (750/0.0125)[(1 + 0.0125)^{16} - 1]$$\)

After calculating this expression, we find that the remaining balance after 16 payments is approximately $17,135.73.

The interest portion of the 17th payment can be calculated by multiplying the remaining balance by the monthly interest rate: $17,135.73 * 0.0125 = $214.20.

Therefore, the principal repaid by the 17th payment is $750 - $214.20 = $535.80.

Answer:

i wanna say 4.16

Step-by-step explanation:

since the total length is 2.6, going from c to where the point would be if it wasn't reflected but rather transformed would be 2.6, doing that again to get to c" would be 2 times, therefore I think it's 4.16

Answer:41,328

Step-by-step explanation:

18+7+11=36 36%

100-36=64 64%

25,200 x 164%=41,328

Answer:

Step-by-step explanation:

Given :-

To Find :-

We can find the slope of the line passing through the points \(( x_1,y_1)\) and \(( x_2,y_2)\)as ,

\(\implies m = \dfrac{ y_2-y_1}{x_2-x_{1}}\)

\(\implies m = \dfrac{ 42-15}{18-7} \\\\\implies \boxed{ m = \dfrac{ 27}{11 }}\)

Hence the slope of the line is 27/11 .

\(\rule{200}2\)

Finding the length of AB :-

\(\implies Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2} \\\\\implies Distance =\sqrt{ (18-7)^2+(42-15)^2 } \\\\\implies Distance =\sqrt{ 11^2 + 27^2 } \\\\\implies Distance =\sqrt{ 121 + 729 } \\\\\implies Distance = \sqrt{ 850} \\\\\implies \boxed{ Distance = 29.15 \ units }\)

Hence the length of AB is 29.15 units .

Answer:

24

Step-by-step explanation:

hope it helps....

it's 100% correct

Answer:

24

Step-by-step explanation:

simplify 48/16

3 = X/8

Multiply both sides by 8

3 × 8 = 24

The total volume of the composite figure is 595.4 cubic inches.

We can decompose the figure into a rectangular prism and a triangular prism.

The volume of the rectangular prism is equal to the product between all the dimensions, so we will get:

V = 9in*6.5in*8in = 468 in³

For the rectangular prism, the volume is 0.5 the product between the dimensions, so here we will get:

V' = 0.5*4.9in*8in*6.5in

V'  =127.4 in³

Then the total volume of the composite figure is:;

volume =  468 in³ + 127.4 in³ = 595.4 in³

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The maximum monthly profit is $420.  To find the maximum monthly profit, we need to find the production level (X) that will maximize the profit.

We can do this by setting the marginal profit equation equal to zero and solving for X:

p'(x) = -0.4x + 20 = 0
0.4x = 20
x = 50

So, the production level that will maximize the profit is 50 widgets per month.

To find the maximum monthly profit, we need to calculate the total monthly revenue and subtract the fixed cost. The total monthly revenue can be calculated as the product of the price per unit and the number of units sold:

p(x) = -0.2x^2 + 20x
p(50) = -0.2(50)^2 + 20(50) = $500

So, the total monthly revenue is $500.

The maximum monthly profit can now be calculated as:

Profit = Total Revenue - Fixed Cost
Profit = $500 - $80
Profit = $420

Therefore, the maximum monthly profit is $420.

So, the answer is $420.

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Answer:

The answer is 8!

Step-by-step explanation:

I took the quiz. Have a great day, hope this helps!

The exact value of tan 120° is -√3. This means that at the angle of 120 degrees, the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle is equal to the negative square root of 3.

To find the exact value of tan 120° using a double-angle identity, we can utilize the tangent double-angle identity, which states:

tan(2θ) = (2tanθ) / (1 - tan^2θ)

In this case, we want to find the value of tan 120°, so we can rewrite it as tan(2 * 60°), since 2θ is equal to 2 * 60°.

Let's substitute θ = 60° into the double-angle identity:

tan(2 * 60°) = (2 * tan 60°) / (1 - tan^2 60°)

We know that the tangent of 60° is equal to the square root of 3 (√3). Therefore, we can substitute tan 60° with √3:

tan(2 * 60°) = (2 * √3) / (1 - (√3)^2)

Now, we simplify the expression further:

tan(2 * 60°) = (2√3) / (1 - 3)

                  = (2√3) / (-2)

                  = -√3

Therefore, the exact value of tan 120° is -√3.

In summary, using the tangent double-angle identity, we found that the exact value of tan 120° is -√3. This means that at the angle of 120 degrees, the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle is equal to the negative square root of 3.

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The value of expression is,

⇒ x ÷ 12

We have to given that;

The algebraic expression is,

⇒ x divided by 12

Hence, We can formulate;

The value of correct expression is,

⇒ x ÷ 12

⇒ x / 12

Thus, The value of expression is,

⇒ x ÷ 12

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The functions are matched with their periods as follows:

The period of a trigonometric function is the smallest positive value of "T" for which the function repeats itself.

Note that to determine the period of a function, we need to identify how the function changes over one cycle. The period can then be obtained by dividing the length of the cycle by the number of complete cycles in the full range of the function.

1) y = - 3 ⁢ tan ⁡ 3 ⁢ x: The period of the tangent function is π/b, where b is the coefficient of x. So, the period of y = - 3 ⁢ tan ⁡ 3 ⁢ x is π/3.

2) y = 6 ⁢ sin ⁡ 3 ⁢ x: The period of the sine function is 2π/b, where b is the coefficient of x. So, the period of y = 6 ⁢ sin ⁡ 3 ⁢ x is 2π/3.

3 )y = - 4 ⁢ cot ⁡ x 4: The period of the cotangent function is π/b, where b is the coefficient of x. So, the period of y = - 4 ⁢ cot ⁡ x 4 is π.

4) y = 2 ⁢ cos ⁡ 2 ⁢ x 3: The period of the cosine function is 2π/b, where b is the coefficient of x. So, the period of y = 2 ⁢ cos ⁡ 2 ⁢ x 3 is 3π.

5 )y = - 2 3 ⁢ sec ⁡ x 5: The period of the secant function is 2π/b, where b is the coefficient of x. So, the period of y = - 2 3 ⁢ sec ⁡ x 5 is 2π/5.

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The description that best fits the definition of the lateral area of a three-dimensional figure is: B. The sum of the areas of its non-bases surfaces.

Lateral area of a three-dimensional figure is defined as the area of the figure excluding the area of its bases.

This implies that the area of the non-bases is not included.

In summary, the best description for the lateral area of a three-dimensional figure is: B. The sum of the areas of its non-bases surfaces.

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The probability that the shuttle will fail to be launched on time, according to its schedule is 18.5%

This can be computed by considering the probability that at least one of the four key devices malfunctions.

Given that each device has a malfunction probability of 0.05, we can calculate the complementary probability of all devices functioning properly and subtract it from 1.

The probability that a single key device malfunctions is 0.05. Since the devices operate independently, the probability that none of them malfunction is the complement of the probability that at least one device malfunctions.

Therefore, the probability of all devices functioning properly is (1 - 0.05) multiplied by itself four times (since there are four devices), which simplifies to 0.95^4. Subtracting this probability from 1 gives us the probability that the shuttle fails to be launched on time, which is 1 - 0.95^4 ≈ 0.185 or approximately 18.5%.

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Answer:

C. 12

hope they help

first mile $2.25 plus $3.50 ×12= $42.00+2.25=44.25

The equation shows a correct trigonometric ratio for angle A in the right triangle  is cos A = 15/17. Option 3

To determine the ratio, we need to know the different trigonometric identities.

These identities are;

The different ratios of these identities are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have that;

Opposite = 8cm

Adjacent = 15cm

Hypotenuse = 17cm

Using the cosine identity, we have;

cos A = 15/17

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The cumulative frequency distribution indicates the total number of data items with values below the class's upper limit.

Cumulative frequency analysis examines how frequently values of a phenomena occur that are less frequent than a reference value. The phenomenon could depend on time or place. Another name for cumulative frequency is frequency of non-exceedance. Each frequency from a frequency distribution table is added to the total of its predecessors to determine the cumulative frequency. Since all frequencies will have previously been added to the prior total, the final result will always be equal to the sum of all observations. The quantity of an element in a set is referred to as the element's frequency. The accumulation of all earlier frequencies up to the present time is another definition for cumulative frequency.

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Answer:

The Formula for Percent Proportion is Parts /whole = percent/100. This formula can be used to find the percent of a given ratio and to find the missing value of a part or a whole.

Answer:

a = 9

Step-by-step explanation:

\(\frac{4}{12}\) = \(\frac{a}{27}\) ( cross- multiply )

12a = 108 ( divide both sides by 12 )

a = 9

Answer:

W=45 degrees

Step-by-step explanation:

We can see that this triangle is an isosceles triangle so the base angles must be equal. So that means angle I and angle K(or w) are equal. The sum of angles in a triangle is 180. So angle J+K+I=180. If we simplify:

2K+J=180

2K+94=180

2K=86

K=43 or w=43

Answer:

  7

Step-by-step explanation:

You want the common difference of the arithmetic sequence that starts ...

  15, 22, 29, ...

The common difference is the difference between a term and the one before. It is "common" because the difference is the same for all successive term pairs.

  22 -15 = 7

  29 -22 = 7

The common difference is 7.

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Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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Answer:

ok

Step-by-step explanation:

1) \(\frac{3}{2} \\\) = 1.5 because the numerator goes int the denominator 1 time and then you ahve left over \(\frac{1}{2}\) which is .5 .

2) \(\frac{5}{2}\) = 2.5 because the 5 goes into the denominator 2 times and then you have left over .5 .

3) \(\frac{1}{4}\) = .25 because a 1 is divided by 4.

4) \(\frac{1}{2}\) = .5 ; a 1 is divided by 2

5) \(\frac{3}{4}\) = .75 because you have .25 x 3 .

6) \(\frac{1}{5}\) = .2 because it is 1 divided by 5

7) 0.04 + 4.1 = 4.14

8) 6.93 - 1.2 = 5.73