A man is four times as old as his son.After 20 years,he will be twice as old as his son.Their present ages are _______ and _______​

Answer:

-3,2,2,5,34

Step-by-step explanation:

Answer:-3,2,2,5,34

Step-by-step explanation:

Answer:

y=26

Step-by-step explanation:

2(3y+7+5)=196-16 do the () first and then subtract 16 from 16

6y+24=180 subtract 24 from both sides

6y=156  divide by 6

y=26

Answer:

26

Step-by-step explanation:

6y+14+10=180

6y=180-24

6y=156

y=26

(i)  \(A^2\) = 7A + 2I, which proves the given equation. (ii)  \(A^{-1\) = (1/2)(A - 7I), which proves the given equation. (iii) The resulting matrix will give us the values of x and y.

(i) To prove that \(A^2 = 7A + 2I\), we need to calculate \(A^2\) and show that it is equal to 7A + 2I.

Given A = [[6, -4], [-2, 1]] and I = [[1, 0], [0, 1]] (the 2x2 identity matrix), we can calculate\(A^2\) as follows:

\(A^2\) = A * A = [[6, -4], [-2, 1]] * [[6, -4], [-2, 1]]
    = [[(6*6) + (-4*-2), (6*-4) + (-4*1)], [(-2*6) + (1*-2), (-2*-4) + (1*1)]]
    = [[36 + 8, -24 - 4], [-12 - 2, 8 + 1]]
    = [[44, -28], [-14, 9]]

Now let's calculate 7A + 2I:

7A + 2I = 7 * [[6, -4], [-2, 1]] + 2 * [[1, 0], [0, 1]]
        = [[7*6, 7*-4], [7*-2, 7*1]] + [[2, 0], [0, 2]]
        = [[42, -28], [-14, 7]] + [[2, 0], [0, 2]]
        = [[44, -28], [-14, 9]]

As we can see, \(A^2\) = 7A + 2I, which proves the given equation.

(ii) To show that \(A^{-1} = (1/2)(A - 7I)\), we need to calculate\(A^{-1\) and show that it is equal to (1/2)(A - 7I).

Given A = [[6, -4], [-2, 1]] and I = [[1, 0], [0, 1]], let's calculate \(A^{-1\):

We can use the formula for the inverse of a 2x2 matrix:
\(A^{-1\) = (1/det(A)) * [[d, -b], [-c, a]], where det(A) is the determinant of A and [a, b, c, d] is the matrix's cofactor.

First, calculate det(A):
det(A) = (6*1) - (-4*-2)
      = 6 - 8
      = -2

Next, calculate the cofactor matrix of A:
[a, b, c, d] = [[6, -4], [-2, 1]]
cofactor(A) = [[d, -b], [-c, a]]
           = [[1, 4], [2, 6]]

Now, calculate\(A^{-1\):
\(A^{-1\) = (1/det(A)) * cofactor(A)
    = (1/-2) * [[1, 4], [2, 6]]
    = [[-1/2, -2], [-1, -3]]

Now, let's calculate (1/2)(A - 7I):

(1/2)(A - 7I) = (1/2) * ([[6, -4], [-2, 1]] - 7 * [[1, 0], [0, 1]])
             = (1/2) * ([[6, -4], [-2, 1]] - [[7, 0], [0, 7]])
             = (1/2) * [[6-7, -4-0], [-2-0, 1-7]]
             = (1/2) * [[-1, -4], [-2, -6]]
             = [[-1/2, -2], [-1, -3]]

As we can see, \(A^{-1\) = (1/2)(A - 7I), which proves the given equation.

(iii) To solve the simultaneous equations using the inverse matrix method, we need to express the equations in matrix form and use the inverse of the coefficient matrix.

The given equations are:
5x + y = 11
3x + 2y = 8

We can rewrite them in matrix form as:
[[5, 1], [3, 2]] * [[x], [y]] = [[11], [8]]

To find the solution, we need to calculate the inverse of the coefficient matrix:
\([[5, 1], [3, 2]]^{-1\)
Let's calculate the inverse:
Given [[a, b], [c, d]], the inverse is:
[[d, -b], [-c, a]] / (ad - bc)

Using the values from the coefficient matrix:
\([[5, 1], [3, 2]]^{-1\) = [[2, -1], [-3, 5]] / (10 - 3)
                   = [[2, -1], [-3, 5]] / 7

Now, we can calculate the solution by multiplying the inverse matrix with the matrix on the right side of the equation:
[[2, -1], [-3, 5]] / 7 * [[11], [8]]

The resulting matrix will give us the values of x and y.

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Lines 'a' and 'c' are parallel lines.

We have to given that,

There are three lines are shown in image.

We know that,

In a parallel line,

If two angles are alternate angles then both are equal to each other.

And, If two angles are corresponding angles then both are equal to each other.

Now, From the given figure,

In lines a and c,

Corresponding angles are 65 degree.

Hence, We can say that,

Lines a and c are parallel lines.

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Answer:

$32.25 - $19 ≤ $ or 13.25 ≤ $

Step-by-step explanation:

Answer:

Step-by-step explanation:

u have to add 9 and 3 to 12 and then divide three by 12 so then the answer is 4 plus 23 squared i lied

Using the concepts of weighting, we got that demographic groups helps in fixing  difference between the levels of different people if there are many or too few people in the sample from that group, compared to the population as a whole.

Demographic segmentation examples actually explain how researchers divide a market into the smaller groups according to age, gender, family income, race and ethnicity, qualification, marital status, nature of the  employment, etc.  

It is an extremely tedious task to the accommodate customers belonging to different demographics and develop the exhaustive marketing plan. Demographic examples ease creating the strategy for a marketer. Thus, they are one of  most commonly implemented marketing segmentation methods compared to the other techniques such as geographic segmentation, behavioral segmentation, or the psychographic segmentation.

Hence, certain demographic groups might end up being under or over-represented means that  there are too many or too few people in the sample from that group, compared to the population as a whole, in that case weighting can therefore potentially helps in fixing the difference in the levels of different people.

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(I) The proportion of times we get a red candy will approach 0.2 as the number of trials increases. (m) The probability of winning at a 'daily number' lottery game is 1/1000 implies that if we play the game repeatedly, the proportion of times we win will approach 1/1000 as the number of plays increases. (n) Saying there is a 30% chance of rain tomorrow indicates that if we observe the occurrence of rainy days over a long period. (o) If 70% of the adult American population wants to retain the penny, then randomly selecting. (p) If we take multiple random samples of 100 people from the adult American population.

(I) The long-run relative frequency definition of probability states that if we repeatedly select M&M candies at random from a large bag, the proportion of times we get a red candy will approach 0.2 as the number of trials increases.

(m) The long-run relative frequency definition of probability states that if we play the 'daily number' lottery game repeatedly, the proportion of times we win will approach 1/1000 as the number of plays increases.

(n) The long-run relative frequency definition of probability states that if we observe the occurrence of rainy days over a long period of time, the proportion of days with rain will approach 30% as the number of days observed increases.

(o) The long-run relative frequency definition of probability states that if we randomly select individuals from the population of adult Americans repeatedly, the proportion of individuals who want to retain the penny will approach 0.70 as the number of selections increases.

(p) The long-run relative frequency definition of probability states that if we take multiple random samples of 100 people from the population of adult Americans, the proportion of samples in which the sample proportion exceeds 0.80 will approach 0.015 as the number of samples increases.

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The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.

What is coefficient of determination?

The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.

R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.

You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:

Dots represent the observations.

The line of best fit, or predictions of the model, is displayed as a black line.

Purple lines represent the deviations (the residuals) between the data and their expected values.

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This is a simple inequality problem involving absolute values.

The given inequality is: $-4 < |x-3|$.We need to find the range of real values of $x$ that satisfy this inequality.
First, let's consider the case when $x-3$ is positive. In this case, the absolute value of $x-3$ is simply $x-3$. So, we can write the inequality as: $-4 < x-3$
Adding $3$ to both sides, we get: $-1 < x$

This means that all values of $x$ greater than $-1$ satisfy the inequality when $x-3$ is positive.
Now, let's consider the case when $x-3$ is negative. In this case, the absolute value of $x-3$ is $-(x-3)$. So, we can write the inequality as: $-4 < -(x-3)$. Expanding the right-hand side, we get: $-4 < -x + 3$

Subtracting $3$ from both sides, we get: $-7 < -x$. Multiplying both sides by $-1$ (which reverses the inequality), we get: $x < 7$.This means that all values of $x$ less than $7$ satisfy the inequality when $x-3$ is negative. Putting both cases together, we have:$x < 7$ or $x > -1$
This is the final answer. We can express it more concisely as:
$-1 < x < 7$

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Answer:

A

Step-by-step explanation:

Answer:

  x = 274 91/107

Step-by-step explanation:

This is called a "two-step linear equation" because it is solved in 2 steps.

Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.

  2.14x -12.18 +12.18 = 576 +12.18

  2.14x = 588.18

__

Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.

  2.14x(1/2.14) = 588.18(1/2.14)

  x = 274.850467... = 274 91/107 . . . the decimal fraction repeats

The solution to the equation is x = 274 91/107.

Answer:

x = 274 91/107

Step-by-step explanation:

Step-by-step explanation:

This is called a "two-step linear equation" because it is solved in 2 steps.

Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.

 2.14x -12.18 +12.18 = 576 +12.18

 2.14x = 588.18

__

Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.

 2.14x(1/2.14) = 588.18(1/2.14)

 x = 274.850467... = 274 91/107 . . . the decimal fraction repeats

The solution to the equation is x = 274 91/107.

Answer:

i will try my best to explain this

Step-by-step explanation:

-(-3) =3 because

how i do it is i move the negative sign to the subtraction sign and together it becomes a plus sign

so it is a positive

You can also look at the screenshots and see for yourself if i didn't explain it very well for you

Answer:

B

Step-by-step explanation:

The solution to a system of equation is when two lines pass and intersect ona specific point. Here we are looking for (0,1).

we can see b intersects on (0,1) so that is out answer.

Answer:

y = 4x - 2

Step-by-step explanation:

Formula: y = mx + b

Parallel means same slope as original and b is -2.

The perimeter of the rectangle in the magnified image is 238cm.

To find the perimeter of the rectangle in the magnified image, we need to determine the dimensions of the magnified rectangle.

Given that 1cm of the image represents 17cm, we can calculate the magnified length and width using the scale factor.

Magnified Length = Length of the original rectangle * Scale Factor

= 3cm * 17

= 51cm

Magnified Width = Width of the original rectangle * Scale Factor

= 4cm * 17

= 68cm

Now, we can calculate the perimeter of the magnified rectangle.

Perimeter of the magnified rectangle = 2 * (Magnified Length + Magnified Width)

= 2 * (51cm + 68cm)

= 2 * 119cm

= 238cm

Therefore, the perimeter of the rectangle in the magnified image is 238cm.

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I’m not sure what you’re asking here

Answer:

the tip is $20 and the food costs $120

Step-by-step explanation:

it says that the bill is 120

when family leaves they spend 140 total

140-120=20

$20 tip

The probability of either of these events occurring (or both), we add the probabilities together: 1/8 + 1/8 = 1/4.

The probability that the first three flips come up heads or the last three flips come up heads (or both) can be calculated by adding the probabilities of these two events occurring separately.

To find the probability of the first three flips coming up heads, we use the formula for the probability of independent events: P(A and B) = P(A) * P(B). Since each flip is independent and has a 1/2 chance of coming up heads, the probability of the first three flips coming up heads is (1/2) * (1/2) * (1/2) = 1/8.

Similarly, the probability of the last three flips coming up heads is also 1/8.

To find the probability of either of these events occurring (or both), we add the probabilities together: 1/8 + 1/8 = 1/4.

Therefore, the correct answer is a. 1/4.

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Answer:

\(\sqrt{170}\)

Step-by-step explanation:

(x2 - x1)^2 + (y2-y1)^2 = c^2

(6 - - 5)^2 + (-3 - 4)^2 = c^2

121 + 49 = c^2

170 = c^2

\(\sqrt{170}\) which is about 13.04

Solution

The population standard deviation is given as

First, we calculate the mean;

Thus, the standard deviation is;

The confidence interval for standard deviation is given by;

Answer:

(1, -4)

Step-by-step explanation:

In this system, multiply the top equation by -4. this will give you

-4x - 12y = 44

4x + 7y = -24

the x values can now cancel out, and add the other values together

-5y = 20

y = -4

now, substitute y = -4 in for one of the starting equations

x + 3(-4) = -11

x - 12 = -11

x = 1

Answer:

2% of 1500 is 30

Step-by-step explanation:

Answer:

2% i think

Step-by-step explanation:

1500 divided by 15 is 100, 30 divided by 15 is 2%

i think thats right

Answer:

-10x

Step-by-step explanation:

Answer:

Use the bodmas rule and do..

Solve in this order

B=bracket

O=of (multiply)

D=divison

M=multiplication

A=addition

S=subtraction

Step-by-step explanation:

U should remember this, it is very important and useful:))

Answer:

Rachael is faster.

you can tell by finding the unit amount.

Step-by-step explanation:

I can tell by finding the unit amount. (miles per minute)

Rachael:

214/15 = 14.2666666667  or about 14.27

Julie:

334/25 = 13.36 miles per minute.

Answer:

  (-3 + 5 i) (1) = (-3 + 5 i)

Step-by-step explanation:

The multiplicative identity property says you can multiply anything by 1 without changing its value. That is demonstrated by the equation above.

Answer:

EDGE2020 is B

The height of the tower from which the rocket was launched is 190 feet and  it takes 6 seconds for the rocket to hit the ground.

The height of the tower from which the rocket was launched, we need to find the value of h(0) in the given function.

Substituting t = 0 into the equation h(t) = -16t² + 65t + 190:

h(0) = -16(0)² + 65(0) + 190

h(0) = 190

Therefore, the height of the tower from which the rocket was launched is 190 feet.

To find the time it takes for the rocket to hit the ground, we need to find the value of t when h(t) = 0.

In other words, we need to solve the equation -16t² + 65t + 190 = 0.

So, 16t²- 65t - 190 = 0.

Using the quadratic formula: t = (-b ± √(b² - 4ac)) / (2a)

where a = -16, b = 65, and c = 190.

t = (65 ± √(65² - 4(16)(-190))) / (2(-16))

t = (65 ± √(4225 + 12160)) / (32)

t = (65 ± √(16385)) / (32)

Since we are looking for the time it takes for the rocket to hit the ground, we only consider the positive value of t.

t = (65 + √(16385)) / (32)

t = 6.031 seconds

Therefore, it takes 6 seconds for the rocket to hit the ground.

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The height of the tower from which the rocket was launched will be 190 feet and it will takes 6 seconds for the rocket to hit the ground.

We are given the height of the tower from which the rocket was launched, we have to find the value of h(0) in the given function.

Substituting t = 0 in h(t) = -16t² + 65t + 190:

h(0) = -16(0)² + 65(0) + 190

h(0) = 190

To determine the time it takes for the rocket to hit the ground,  h(t) = 0.

To solve the equation -16t² + 65t + 190 = 0.

So, 16t²- 65t - 190 = 0.

Using the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

t = (65 ± √(65² - 4(16)(-190))) / (2(-16))

t = (65 ± √(4225 + 12160)) / (32)

t = (65 ± √(16385)) / (32)

t = 6.031 seconds

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Answer:

52

Step-by-step explanation:

Divide 312 by 6 to find the number of events he swam per year

He swam 52 events each year.

Explanation:

You can figure this out by dividing 312 by 6, which would get you 52, the amount of events he swam each year

For the situation where the null hypothesis (H0) is p=0.7 and the alternative hypothesis (HA) is p≠0.7 at α=0.01, we need to find the critical value(s) for z.

a)Since the alternative hypothesis is two-tailed (p≠0.7), we will divide the significance level (α) equally between the two tails. Thus, α/2 = 0.01/2 = 0.005. By looking up the corresponding value in the z-table, we can find the critical value. The critical value for a two-tailed test at α=0.005 is approximately ±2.58.

b) In the scenario where H0: p=0.5 and HA: p>0.5 at α=0.01, we are dealing with a one-tailed test because the alternative hypothesis is p>0.5. To find the critical value for t, we need to determine the value in the t-distribution with (n-1) degrees of freedom that corresponds to an area of α in the upper tail. Since α=0.01 and the degrees of freedom are not given, we cannot provide an exact value. However, if we assume a large sample size (which is often the case with hypothesis testing), we can use the normal distribution approximation and the critical value can be obtained from the z-table. At α=0.01, the critical value for a one-tailed test is approximately 2.33.

c) When H0: μ=20 and HA: μ≠20 at α=0.01, we are conducting a two-tailed test for the population mean. To find the critical value for z, we need to divide the significance level equally between the two tails: α/2 = 0.01/2 = 0.005. By looking up the corresponding value in the z-table, we find that the critical value for a two-tailed test at α=0.005 is approximately ±2.58.

d) In the situation where H0: p=0.7 and HA: p>0.7 at α=0.10 with n=340, we are performing a one-tailed test for the population proportion. To find the critical value for z, we need to determine the value in the standard normal distribution that corresponds to an area of (1-α) in the upper tail. At α=0.10, the critical value is approximately 1.28.

e) For H0: μ=30 and HA: μ<30 at α=0.01 with n=1000, we have a one-tailed test for the population mean. Similar to situation (b), assuming a large sample size, we can approximate the critical value using the z-table. At α=0.01, the critical value for a one-tailed test is approximately -2.33.

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The value of x will be 17 for the given parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite angles of a parallelogram are congruent, which means they have the same measure. This property is known as the parallelogram angle property.

The sum of the two consecutive angles of a parallelogram is 90 degrees.

The value of x will be calculated as,

2x + 3x + 5 = 90

5x + 5 = 90

x + 1 = 18

x = 17

Therefore, the value of x will be 17.

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Answer:

120

Step-by-step explanation:

by using the basic counting rule, there are 5 positions first, then 4, then ,3 and so on down to one. so when you multiply them all together, you get 120. Also i took  a test with the same qeustion, and that was the anwer :)

Answer:

120

Step-by-step explanation:

5 times 4 times 3 times 2 times 1= 120

5 choices for first

1 choice already taken so 4 for the other model

3 for the other

2 for the other

and 1 for the other

=120

Its correct, trust me!