Helen’s age is a multiple of 4. Next year it’ll be a multiple of 3. Helen’s older brother is now 19. How old is Helen now?

Step to step explanation:

Confidence interval for mean, when population standard deviation is unknown:

[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = sample mean

n= sample size

s= sample standard deviation

[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom

We assume the family size is normal distributed.

Given, n= 31 , [tex]\overline{x}=3.1[/tex], s= 1.42 ,

[tex]\alpha=1-0.9=0.10[/tex]

Critical t value for [tex]\alpha/2=0.05[/tex] and degree of 30 freedom

[tex]t_{\alpha/2}[/tex] = 1.697  [By t-table]

The required confidence interval:

[tex]3.1\pm ( 1.697)\dfrac{1.42}{\sqrt{31}}\\\\=3.1\pm0.4328\\\\=(3.1-0.4328,\ 3.1+0.4328)=(2.6672,\ 3.5328)\approx(2.67,\ 3.53)[/tex]

Hence,  the 90% confidence interval for the estimate = (2.67, 3.53)

Answer:

Richard will pay $30.

Step-by-step explanation:

Because "x" is equivalent to the amount of video games he rents, you would replace "x" with 5. Do the math, and you would get 10+20=30! Hope this helps!

Answer:

80 trees have a diameter smaller than 120cm

Step-by-step explanation:

Step 1

To solve this question, we would make use of the Z score formula.

z = x - μ/σ

Where

z = z score

x = Raw score = 120cm

μ = Population mean = 150cm

σ = Population standard deviation = 30cm

Hence,

z =120 - 150/30

z = -1

The z score = -1

Step 2

We find the Probability of the calculated z score using the z score table.

P(z) = P(z = -1) = P(x<120) = 0.15866

Approximately to the nearest hundredth = 0.16

Converting to percentage = 0.16 × 100 = 16%

The percentage of trees with a diameter smaller than 120cm = 16%

Therefore, the number of trees with a diameter smaller than 120cm

= 16% × 500 trees = 80trees

Answer:

the radius of the circle =7

Step-by-step explanation:

the function of a circle:(x – h)^2 + (y – k)^2 = r^2

center(0,0) because the center of a circle is at the origin (h,k)

a line intersect at (0,7)

(0-0)^+7-0)^2=r^2

r^2=49 , r=√49

radius r=7

Answer: 0.06x

Step-by-step explanation:

The given statement:  A number is 30% of 20% of the number x.

The required algebraic expression would be:

30% of 20% of x

[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex]  [we divide a percentage by 100 to convert it into decimal]

[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]

Hence, the required algebraic expression would be :

0.06x

Answer:

THE M ONE

Step-by-step explanation:

IT HAS A DIFFERENT VARIABLE

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

                    ✌ -ZYLYNN JADE ARDENNE

Answer:-8

Step-by-step explanation:

Step-by-step explanation:

Hal is expected to use 0.98, the reason is that 2% of $10,000 will give $200

i.e (2/100)*10,000= $200.

therefore 10,000-200= $9800.

Since the money is decreasing by 2%, we have 100-2= 98% = 0.98

hence when 10,000 is multiplied by 0.98 we have $200 which is 2% of $10,000

Answer:

It's B.

Step-by-step explanation:

I just took the test.

Answer:

x = 22

<a = 88°

<b = 92°

Step-by-step explanation:

To solve for x, <a, and <b, we'd need to recall some of the properties of parallel lines, then apply them in solving this problem.

To find the value of x, recall that consecutive interior angles are supplementary. (5x - 18), and (3x + 22) are consecutive interior angles. Therefore:

[tex] (5x - 18) + (3x + 22) = 180 [/tex]

Solve for x

[tex] 5x - 18 + 3x + 22 = 180 [/tex]

[tex] 5x + 3x - 18 + 22 = 180 [/tex]

[tex] 8x + 4 = 180 [/tex]

Subtract 4 from both sides:

[tex] 8x + 4 - 4 = 180 - 4 [/tex]

[tex] 8x = 176 [/tex]

Divide both sides by 8

[tex] \frac{8x}{8} = \frac{176}{8} [/tex]

[tex] x = 22 [/tex]

=>Find <a:

According to the properties of parallel lines, alternate interior angles are equal. Therefore:

<a = 3x + 22

Plug in the value of x

<a = 3(22) + 22 = 66 + 22

<a = 88°

=>Find <b:

According to the properties of parallel lines, corresponding angles are said to be equal. Therefore,

<b = 5x - 18

Plug in the value of x to find <b

<b = 5(22) - 18

<b = 110 - 18 = 92°

Answer:

810.66 ft²

Step-by-step explanation:

Short answer:

Shaded region:

Answer: 810.66 ft²

I agree.

Answer:

Ok so we have a set of 8 numbers {1,2,...,8}

a) 5 and 8 are picked.The probability here is:

In the first selection we can pick 5 or 8, so we have two possible outcomes out of 8 total outcomes, then the probability for the first selection is:

P = 2/8 = 1/4.

Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8)

Then the probability is:

P = 1/8

The joint probability is equal to the product of the individual probabilities, so here we have:

P = (1/4)*(1/8) = 1/32 = 0.003

b) The numbers match:

In the first selection we can have any outcome, so the probability is:

P = 8/8 = 1

Now, based on the previous outcome, in the second selection we can have only one outcome, so here the probability is:

P = 1/8 = 0.125

The joint probability is p = 1/8

c) The sum is smaller than 4:

The combinations are:

1 - 1

1 - 2

2 - 1

We have 3 combinations, and the total number of possible combinations is:

8 options for the first number and 8 options for the second selection:

8*8  = 64

The probabilty is equal to the number of outcomes that satisfy the sentence divided by the total numberof outcomes:

P = 3/64 = 0.047

Using the probability concept, it is found that there is a:

i. 0.03125 = 3.125% probability that 5 and 8 are picked.

ii. 0.125 = 12.5% probability that both numbers match.

iii. 0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, two integers are chosen from a set of 8, hence, there are [tex]8^2 = 64[/tex] total outcomes.

Item i:

Two outcomes result in 5 and 8 being picked, (5,8) and (8,5), hence:

[tex]p = \frac{2}{64} = 0.03125[/tex]

0.03125 = 3.125% probability that 5 and 8 are picked.

Item ii:

8 outcomes result in both numbers matching, (1,1), (2,2), ..., (8,8), hence:

[tex]p = \frac{8}{64} = 0.125[/tex]

0.125 = 12.5% probability that both numbers match.

Item ii:

Three outcomes result in a sum of less than 2, (1,1), (1,2), (2,1), hence:

[tex]p = \frac{3}{64} = 0.046875[/tex]

0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.

A similar problem is given at https://brainly.com/question/15536019

Answer:

Correlation Coefficient

Step-by-step explanation:

Answer:

z(max) = 650 $

x₁ = 10 units

x₂ = 15 units

Step-by-step explanation:

That is a linear programming problem, we will use a simplex method to solve it

Formulation:

Let´s call  x₁  number of chairs   and x₂ number of tables then :

Item              (in hours)     cutting       assembly      finishing        Profit ($)

Chairs (x₁)                              1                   2                     1                      20

Tables (x₂)                              2                   1                      1                      30

Availability                           40                 42                   25

Objective Function

z  =  20*x₁   +  30x₂   ( to maximize) subject to:

x₁  +  2x₂   ≤  40

2x₁  + x₂    ≤  42

x₁ + x₂     ≤    25

x₁  ,   x₂  >= 0

Using excel or any other software we find:

z(max) = 650

x₁ = 10

x₂ = 15

The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674

Let x represent chairs, and y represent tables

So, the given parameters are:

Cutting:

So, the constraint is:

[tex]\mathbf{x + 2y \le 40}[/tex]

Assembly:

So, the constraint is:

[tex]\mathbf{2x + y \le 42}[/tex]

Finishing:

So, the constraint is:

[tex]\mathbf{x + y \le 25}[/tex]

The unit profit on the items are:

So, the objective function to maximize is:

[tex]\mathbf{Max\ z = 20x + 30y}[/tex]

And the constraints are:

[tex]\mathbf{x + 2y \le 40}[/tex]

[tex]\mathbf{2x + y \le 42}[/tex]

[tex]\mathbf{x + y \le 25}[/tex]

[tex]\mathbf{x,y \ge 0}[/tex]

Using graphical method (see attachment for graph), we have the following feasible points:

[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]

Calculate the objective function using the feasible points.

[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]

[tex]\mathbf{z = 650}[/tex]

[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]

[tex]\mathbf{z = 580}[/tex]

[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]

[tex]\mathbf{z = 673.5}[/tex]

Approximate

[tex]\mathbf{z = 674}[/tex]

Hence, the maximum revenue is 674

Read more about linear programming at:

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The volume of a square pyramid is found by multiplying the area of the base by the height divided by 3.

32 = 4^2 x h/3

32 = 16 x h/3

Multiply both sides by 3

96 = 16 x h

Divide both sides by 16

H = 96/16

H = 6

The height is 6 feet

Answer:

6 ft

Step-by-step explanation:

Volume of the pyramid:

Given

Then, as per formula, we can solve it for h:

Height of the pyramid is 6 ft

Answer:

14 and 9

Step-by-step explanation:

Y values are always the second number in the parenthesis. The X value is the first one. I like to think of Y being dependent on X, so X goes first, then Y.

Answer:

The estimate is  [tex]P__{hat}} \pm E = 0.37 \pm 0.0348[/tex]

Step-by-step explanation:

From the question we are told that  

    The sample size is  n =  522

    The sample proportion of students  would like to talk about school is  [tex]\r p__{hat}} = 0.37[/tex]

  Given that the confidence level is  90 % then the level of significance can be mathematically evaluated as

                  [tex]\alpha = 100 - 90[/tex]

                  [tex]\alpha = 10\%[/tex]

                  [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is  

               [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645[/tex]

Generally the margin of error can be mathematically represented as

               [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }[/tex]

=>            [tex]E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }[/tex]

=>             [tex]E = 0.0348[/tex]

Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is  

                       [tex]P__{hat}} \pm E[/tex]

substituting values

                     [tex]0.37 \pm 0.0348[/tex]

Answer:

5 1/7

Step-by-step explanation:

To find the mean, add up all the numbers and then divide by the number of numbers

(10+ 6+ 9+ 6+ 2+ 0+ 3)/7

The sum of all the numbers is 36 and there are 7 numbers

36/7 =

7 goes into 36  five times with 1 left over

5 1/7

Answer:

5.143

Step-by-step explanation:

Add them all up then divide by the amount of numbers there are.

Answer:

21 wins, table is attached.

Step-by-step explanation:

The ratio of 7 wins to 2 losses is 7:2. A ratio is just saying that every time one value is increased by 7, the other is increased by 2.

So we can fill out the table, in every iteration wins increases by 7 and losses increases by 2.

When we fill this out, we find that when losses is 6, wins is 21, so when you have 2 losses you have 21 wins.

Hope this helped!

Answer:

25

Step-by-step explanation:

150/6

The Unit rate of calories per ounce will be 25 calories per ounce.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Weight of the Greek yogurt container = 6 ounce

Calories per container = 150 calories

The Unit rate of calories per ounce = 150 / 6 = 25

Therefore, the unit rate of calories per ounce will be 25 calories per ounce.

Learn more about the unitary method;

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Answer:

[tex]MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\[/tex]

Step-by-step explanation:

Since the sample size is quite large, we can use the z-distribution.

The margin of error is  given by

[tex]$ MoE = z_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]

Where n is the sample size, s is the sample standard deviation and [tex]z_{\alpha/2}[/tex] is the z-score corresponding to a 90% confidence level.

The z-score corresponding to a 90% confidence level is

Significance level = α = 1 - 0.90= 0.10/2 = 0.05

From the z-table at α = 0.05

z-score = 1.645

[tex]MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\[/tex]

Therefore, the margin of error is 0.776.

Answer:

[tex]\huge\boxed{6}[/tex]

Step-by-step explanation:

[tex]half=\dfrac{1}{2}\\\\quarter=\dfrac{1}{4}\\\\half\ of\ a\ quarter=\dfrac{1}{2}\cdot\dfrac{1}{4}=\dfrac{1\cdot1}{2\cdot4}=\dfrac{1}{8}\\\\\text{Let}\ n-\text{number}\\\\\text{The equation:}\\\\\dfrac{1}{8}n=\dfrac{3}{4}\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup\cdot\dfrac{1}{8\!\!\!\!\diagup}n=8\cdot\dfrac{3}{4}\\\\n=\dfrac{24}{4}\\\\n=6[/tex]

Answer:

  C. Equation

Step-by-step explanation:

An equation generally provides the most specific information about a function. However, it cannot always be used for certain purposes—such as finding a specific inverse function value.

In the case of equations that are infinite series, even evaluating the function can become difficult when the series converges slowly.

Answer:

1) [tex] x= \mu +z\sigma = 1.25 -1.25*0.07= 1.16[/tex]

The best answer woud be:

c. $1.16

2) If we find the z score for the first test we got:

[tex] z=\frac{630-475}{75}= 2.07[/tex]

And for the second test:

[tex] z=\frac{45-32}{6}= 2.17[/tex]

The z score for the second test is greater so then the answer would be:

b. second test

Step-by-step explanation:

For the first question:

For this case we have the following parameters are:

[tex]\mu = 1.25 , \sigma =0.07[/tex]

And we also know that the z score is [tex] z=-1.25[/tex] and we can use the z score formula given by:

[tex] z=\frac{X -\mu}{\sigma}[/tex]

And solving for x we got:

[tex] x= \mu +z\sigma = 1.25 -1.25*0.07= 1.16[/tex]

The best answer woud be:

c. $1.16

For the second question:

First test [tex]\mu = 475, \sigma =75[/tex]

Second test [tex] \mu= 32, \sigma=6[/tex]

630 for the first test and 45 for the second

If we find the z score for the first test we got:

[tex] z=\frac{630-475}{75}= 2.07[/tex]

And for the second test:

[tex] z=\frac{45-32}{6}= 2.17[/tex]

The z score for the second test is greater so then the answer would be:

b. second test

Hi there!

Answer:

Find points for the equation y = 2x + 1 by plugging in x values:

For example, when x = 1, substitute in the value of 'x' into the equation:

y = 2(1) + 1

y = 2 + 1

Solve for the y-value:

y = 3

Repeat this process for multiple points:

X                               Y

-2                              -3

-1                                -1

0                                 1

1                                  3

2                                  5

To get the graph of y = 2x + 1, simply graph these points. :)

Answer:

40

Step-by-step explanation:

20 * 1

= 20

20 * 2

= 40

Answer:

40

Step-by-step explanation:

The first step is to multiply 20 by 1. Whenever you multiply something by 1, it will always stay the same no matter what.

20*1=20

The next step is to multiply by 2. When multiplying anything by two, it is the same as adding the same number to itself. so

20*2=40 or 20+20=40

Hope this helps. Feel free to ask any follow-up questions if you are still confused

Have a great day! :)

Answer:

40 deg

Step-by-step explanation:

The vertical sides of the rectangle are parallel, so the triangle is a right triangle.

The triangle is a right triangle, so the acute angles are complementary.

The bottom right angle of the triangle measures 90 - 50 = 40 deg.

The bottom line and the top side of the rectangle are parallel, so corresponding angles are congruent. x and the 40-deg angle are corresponding angles, so they are congruent.

x = 40 deg.

Answer:

Number is yellow box=3

Step-by-step explanation:

We know this because the way we get that number is subtracting the two numbers above it, which is 8 and 5, which give us 3.

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Thank you,

Have a good day! :)

When you solve this equation using the quadratic formula, you will get [tex]x = \frac{-20\pm \sqrt{400-4k^2}}{2k}[/tex]. The only way for this number to be irrational is for [tex]\sqrt{400-4k^2}[/tex] to be irrational. The square root of any number that is not a perfect square is irrational*, so the solutions of the quadratic are rational if and only if [tex]400-4k^2[/tex] is a perfect square. We can factor out the 4 (which is already a perfect square), which means that [tex]100-k^2[/tex] must be a perfect square. This occurs exactly when k is equal to one of the following:[tex]\sqrt{100},\sqrt{99},\sqrt{96},\sqrt{91},\sqrt{84},\sqrt{75},\sqrt{64},\sqrt{51},\sqrt{36},\sqrt{19}, \sqrt{0}[/tex].

Of these, the only positive integer values of k are: [tex]\sqrt{100}, \sqrt{64}, \sqrt{36}[/tex], or simply 6, 8, and 10.

* This is quite simple to show: Take any rational number, a/b. Without loss of generality, we can assume that a/b is in reduced form, that is, a and b have no common factors. (a/b)^2 is a^2/b^2, and since a and b have no common factors, neither do a^2 and b^2. Therefore, a^2/b^2 cannot be an integer. In the event that a/b is an integer, b would equal 1, and this proof would not hold.

The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, the sequence is -8, -4, 0, 4, 8, ...

a = -8

d = +4

The expression for the nth term will be written as,

an = a + ( n - 1 ) d

= -8 + ( n - 1 ) 4

To know more about arithmetic progression follow

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Answer:

123 domestic stamps

89 foreign stamps

Step-by-step explanation:

Answer:

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

Which equation represents the total number of stamps Malik collected?  

✔ x + y = 212

Which equation represents the difference in the number of foreign and domestic stamps Malik collected?  

✔ x – y = 34

Which system of linear equations represents the situation?  

✔ x – y = 34 and x + y = 212

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

This system of equations models the given information for both stamp types.

x – y = 34

x + y = 212

Solve the system of equations.  

How many foreign stamps does Malik have?

✔ 89  foreign stamps

How many domestic stamps does Malik have?

✔ 123 domestic stamps

Step-by-step explanation:

its right on 2021 edge! :) hope this helps