Find the explicit formula.
30, 38, 46, 54, ...
an
+
n

Answer:

\((A\cap B)\cap U\)

Step-by-step explanation:

"And" indicates taking the intersection of two sets.

You want numbers that are in all three sets: multiples of 5, multiples of 2, and all 4-digit numbers.

Answer:

0.33=0.33

Step-by-step explanation:

it is answer 0.33=0.33

Answer:

36.598 - 0.001 = 36.597

For a matrix A, the determined matrices are

a) Matrix E₁ is \(E₁ = \begin{bmatrix} \frac{1}{2} & \frac{ - 3}{2} \\ -1 & 3\end{bmatrix} \)

and it's inverse is equals to zero.

b) Matrix E₂ and it's inverse E₂⁻¹ are

\(E₂ = \begin{bmatrix} 1 & -3 \\ - 5& - 1\end{bmatrix} \)

\(E₂⁻¹ = \begin{bmatrix} \frac{ - 1}{16} & \frac{3}{16} \\ \\ \frac{5}{16} & \frac{1}{16} \end{bmatrix}\)

We have a matrix 2×2, A such that

\(A= \begin{bmatrix} 1 & -3 \\ -1 & 3\end{bmatrix}\)

and we have to determine the matrix E₁ with their inverses. Also, matrix E₁ is generated by multiplying the first row of matrix A by 1/2. As we see elements of first row of matrix are 1 and -3.

\(E₁ = \begin{bmatrix} 1 \times \frac{1}{2} & -3 \times \frac{1}{2} \\ -1 & 3\end{bmatrix}

\)

\(E₁ = \begin{bmatrix} \frac{1}{2} & \frac{ - 3}{2} \\ -1 & 3\end{bmatrix} \)

The inverse of A is A⁻¹only when AA⁻¹= A⁻¹A = I.

Steps to determine the inverse of a 2x2 matrix:

Determinant of E₁ = ad - bc , here a =1/2 , b = -3/2 , c= -1 and d = 3. So, |E₁ | = 1/2× 3 - (-3/2)×(-1) = 3/2 - 3/2 = 0 . Thus, Inverse of E₁⁻¹ = 0 .

b) When we multiplies the second row of A by -4 then the elementary matrix E₂ is form. \(E₂ = \begin{bmatrix} 1 & -3 \\ -1 + (- 4)& 3 + ( - 4)\end{bmatrix}\)

\(E₂ = \begin{bmatrix} 1 & -3 \\ - 5& - 1\end{bmatrix}\)

Now, we have determine the Inverse of E₂. The determinant of |E₂| = -1× 1 - (-5)×(-3) = -1 - 15 = -16

So, inverse of matrix is , E₂⁻¹

\(E₂⁻¹ = \frac{1}{16}\begin{bmatrix} - 1 & - ( -3) \\ - ( - 5)& 1\end{bmatrix}\)

\(E₂⁻¹ = \frac{1}{16} \begin{bmatrix} -1 & 3 \\ 5& 1\end{bmatrix}\)

\(E₂⁻¹ = \begin{bmatrix} \frac{ - 1}{16} & \frac{3}{16} \\\\\frac{5}{16} & \frac{1}{16} \end{bmatrix}\)

Hence, we get the required inverse.

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Complete question:

Let A be a 2 x 2 matrix. Given the following descriptions, A = [ 1 -3 ; -1 3]

determine the following elementary matrices and their inverses.

a. The elementary matrix E1 multiplies the first row of A by 1/2 .

b. The elementary matrix E2 adding the second row of A by -4

Answer:

\(59 + 3x < 75\)

Step-by-step explanation:

We know from the question that Fatoumata pays a flat cost of $59 per month and $3 per gigabyte.

If we consider \(x\) to be the number of gigabytes she uses in a month, then her bill every month can be represented by the following expression:

\(59 + 3x\) .

We are told that the bill has to be kept under $75. Therefore:

\(59 + 3x < 75\)

This inequality can be used to solve for \(x\), and so we can use it to find the maximum number of gigabytes she can use while keeping the bill under $75.

The inequality for the maximum number of gigabytes Fatoumata can use while staying within her budget will be equal to $59 + $3(x) < $75.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Price of cell phone plan per month = $59

The price per gigabyte = $3

Then, the equation as per the statement will be,

$59 + $3(x)

Here, x is the number of gigabytes used in a month.

So, the inequality will be,

$59 + $3(x) < $75

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Answer:

21) 130

22) 146

23) 113

24) 150

Step-by-step explanation:

21)

m<BAC = 50

m<BAO = m<CAO = (1/2)m<BAC = (1/2)(50) = 25

A radius intersects a tangent at a right angle, so m<B = 90.

m<BAO + m<B + m<AOB = 180

25 + 90 + m<AOB = 180

m<AOB = 65

m<BOC = 2 × m<AOB = 2 × 65 = 130

22)

m<BAC = 34

m<BAO = m<CAO = (1/2)m<BAC = (1/2)(34) = 17

A radius intersects a tangent at a right angle, so m<B = 90.

m<BAO + m<B + m<AOB = 180

17 + 90 + m<AOB = 180

m<AOB = 73

m<BOC = 2 × m<AOB = 2 × 73 = 146

23)

m<AOB = (1/2)m<BOC = (1/2) × 67 = 33.5

m<BAO + m<B + m<AOB = 180

m<BAO + 90 + 33.5 = 180

m<BAO = 56.5

m<BAC = 2 × m<BAO = 2 × 56.5 = 113

24)

m<AOB = (1/2)m<BOC = (1/2) × 30 = 15

m<BAO + m<B + m<AOB = 180

m<BAO + 90 + 15 = 180

m<BAO = 75

m<BAC = 2 × m<BAO = 2 × 75 = 150

Using the normal distribution, there is a 0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.

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

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

The mean and the standard deviation are given, respectively, by:

\(\mu = 2.5, \sigma = 0.5\).

The probability that a randomly selected cyclist will take between 2.35 and 2.45 hours is the p-value of Z when X = 2.45 subtracted by the p-value of Z when X = 2.35, hence:

X = 2.45:

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

\(Z = \frac{2.45 - 2.5}{0.5}\)

Z = -0.1

Z = -0.1 has a p-value of 0.4602.

X = 2.35:

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

\(Z = \frac{2.35 - 2.5}{0.5}\)

Z = -0.3

Z = -0.3 has a p-value of 0.3821.

0.4602 - 0.3821 = 0.0781.

0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.

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Answer:

23

Step-by-step explanation:

8+15=23

in all, he moved 8 feet to the water, then another 15 feet below the water. this means that he ended up (8+15) feet from where he started.

Answer:

23

Step-by-step explanation:

Answer:

1/16 chance

Step-by-step explanation:

so flipping a tail once is 1/2

so since if we want 4 in a row then multiply 1/2 4 times.

you‘ll get 1/16

so 1/16

________________________________

________________________________

The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is 27/8 square inches or 3 3/8 square inches

From the question, we are to determine the area of the cross-section of the cone

To determine the area of the cross-section of the cone, we will determine the radius of the cross-section.

Let the radius of the cross-section be x and radius of the base of the be r.

The height of the cone is 8 inches and the height of the cone formed from the cross-section is 3 inches

By similar triangle theorem, we can write that

8/r = 3/x

x = (3r)/8

From the given information,

The area of the base is 24 square inches

Thus,

πr² = 24

Therefore, r² = 24/π

The area of the cross-section will be

A = πx²

But, x = (3r)/8

Thus,

A = π [(3r)/8]²

A = π × 3²/8² × r²

A = π × 9/64 × 24/π

A = 27/8 square inches

Hence, the area is 27/8 square inches or 3 3/8 square inches

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y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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Answer: 11/9

Step-by-step explanation:

First, convert two to 18/9. This is still equal to two but this makes it easier to answer the problem, because both of the terms have the same denominator. Now, since both of them have the same denominator, all you need to do is subtract the numerators, and put that over the denominator of 9. 18-7=11. So the answer is 11/9. This is an improper fraction, though you could also make it into a mixed number: 1 and 2/9.

Answer:

11/9

Step-by-step explanation:

Add a one under the 2. So that it becomes 2/1. Now you have the expression, 2/1 - 7/9. To subtract fractions, you need the denominators of the two fractions to be the same. We can put 9 as the common denominator. All you have to do in order for 2/1 to have 9 as its denominator, is to multiply 9 for both the numerator and denominator; 2/1 x 9/9 = 18/9. After that, your new expression would be 18/9 7/9. Just subtract across, 18 - 7 = 11, keep the denominator 9. The answer should be 11/9

1.) The probability that the sample mean will be greater than 48 minutes is 0.9332.

2.) The probability of the sample mean being between 44 and 49 minutes is 0.6687.

3.) The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean.

To solve this problem, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means tends to be approximately normally distributed, regardless of the shape of the original population, when the sample size is large enough.

1.) Probability of sample mean > 48 minutes:

To calculate this probability, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the population mean (μ) is 45 minutes, the population standard deviation (σ) is 12 minutes, and the sample size (n) is 36. We want to find the probability of the sample mean being greater than 48 minutes.

Calculating the z-score:

z = (48 - 45) / (12 / √36) = 3 / 2 = 1.5

Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.5 is approximately 0.9332. Therefore, the probability that the sample mean will be greater than 48 minutes is approximately 0.9332.

2.) Probability of sample mean between 44 and 49 minutes:

To calculate this probability, we need to find the z-scores for both 44 and 49 minutes and then calculate the area between those z-scores.

Calculating the z-scores:

For 44 minutes:

z1 = (44 - 45) / (12 / √36) = -1 / 2 = -0.5

For 49 minutes:

z2 = (49 - 45) / (12 / √36) = 4 / 2 = 2

Using the standard normal distribution table or calculator, we find the probabilities corresponding to z1 and z2:

P(z < -0.5) ≈ 0.3085

P(z < 2) ≈ 0.9772

The probability of the sample mean being between 44 and 49 minutes is approximately P(-0.5 < z < 2) = P(z < 2) - P(z < -0.5) ≈ 0.9772 - 0.3085 = 0.6687.

3.)Conclusion from 100 samples with a mean of 65 minutes:

If 100 samples were collected, and the sample mean was 65 minutes, we would need to assess whether this value is significantly different from the population mean of 45 minutes.

To make this assessment, we can calculate the z-score for the sample mean of 65 minutes:

z = (65 - 45) / (12 / √36) = 20 / 2 = 10

The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean. This is an extremely large deviation, suggesting that the sample mean of 65 minutes is highly unlikely to occur by chance.

Given this, we can conclude that the sample mean of 65 minutes is significantly different from the population mean. It may indicate that there is a systematic difference in the delivery times between the sample and the population, possibly due to factors such as increased demand, traffic, or other external variables

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9n-8=15

Product of n and 9 is 9n

Subtract 8 less than that.

Answer:

The equation cannot be solved because it is undefined. These are the x and y intercepts of the equation y=csc(x) y = csc ( x ) .

Hope this helps! :)

Answer:

There are no intercepts in the graph of csc(x) because the graph never touches the x- or y-axis.

Cosecant is undefined at x = 0 and y = 0.

Answer:

71 degrees

Step-by-step explanation:

Let's close the top part of the picture to make a parallelogram.

A parallelogram's four angles at each corner MUST be equal to 360 degrees.

Another property of a parallelogram is the opposite angles are congruent, meaning they're equal.

So, using these properties, we can now solve for a.

\(360=a+a+109+109\\360=2a+218\\142=2a\\71=a\)

Answer:

a 2,3 2,5 4,5 7,9

Step-by-step explanation:

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. In this case, the height of the cone is the radius of the circle, which is 10 inches, and the radius of the base is half the length of the circumference of the sector, which is (theta/360) * 2 * pi * 10 inches.

We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

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We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

56/25

Step-by-step explanation:

sksksjskskksdidid

Answer:

Option B,

They're similar because two pairs of corresponding angles in the two trapezoids are congruent

Answer:

They're not similar because only one pair of corresponding angles in the two trapezoids is congruent.

Step-by-step explanation:

The tangent from the external point are equal, so the x value is 3 units.

7) The measure of the arc XW is 180-105=75

8) The measure of the arc VWY is 105+75+85 = 265

9) We know that, tangent from the external point are equal

In circle C, AB=AD

26=8x+2

8x=24

x=24/8

x=3 units

10) 9x-3=7x+5

9x-7x=5+3

2x=8

x=8/2

x=4

Therefore, the tangent from the external point are equal, so the x value is 3 units.

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Answer:

Kay has 7 blue balloons

Step-by-step explanation:

if Sal has 5 red balloons and 2 blue balloons and Kay has 5 more blue balloons than Sal the Kay has 7 blue balloons

The number of blue balloons does Kay have is 7.

Given that, Sal has 5 balloons. He has 3 red balloons. The rest are blue.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of blue balloons does Kay have be x.

Number of blue balloons Sal have = 5-3=2

The number of blue balloons does Kay have = Kay has 5 more blue balloons than Sal

⇒ x = 2+5 = 7

Therefore, the number of blue balloons does Kay have is 7.

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Answer:

20

Step-by-step explanation:

Area of a rectangle = l*w

5*4 = 20

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

a(2y - 1)(y + 3)

Step-by-step explanation:

Factor the following:

\( \longrightarrow \) 2ay² + 5ay - 3a

Factor a out of 2ay² + 5ay - 3a:

\( \longrightarrow \) a(2y² + 5y - 3)

The coefficient of y² is 2 and the constant term is -3. The product of 2 and -3 is -6. The factors of -6 which sum to 5 are -1 and 6.

So,

\( \longrightarrow \) a(2y² + (6 - 1)y - 3)

\( \longrightarrow \) a(2y² + 6y - y - 3)

\( \longrightarrow \) a(2y(y + 3) - 1(y + 3))

Factor y + 3 from 2y(y + 3) - 1(y + 3):

\( \longrightarrow \) a(2y - 1)(y + 3)

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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