Simplify 2/5(14–27)+2^5÷16.

The mean of the sampling distribution of proportion is 0.15

The probability the sample proportion will be within 0.04 of the population proportion is 0.9182

The probability the sample proportion that will be within 0.02 of the population proportion is 0.6157

P(Smokers) in Australia= 15/100=0.15

Sample, n =240

Part a, The mean of the sampling distribution of proportion:

μ₂ = P(Smokers)

    = 0.15

The mean of the sampling distribution of proportion is 0.15

The standard deviation of the sampling distribution of proportion is,

δ [tex]=\sqrt{p\frac{(1-p)}{n} }[/tex]

  [tex]=\sqrt{0.15\frac{(1-0.15)}{240} }[/tex]

 [tex]=0.0230[/tex]

The standard deviation of the sampling distribution of proportion is 0.0230

Part b, The probability the sample proportion will be within +/-0.04 of the population proportion:

To find this, we first, compute the z score then find probability based on standard normal table.

For 0.15-0.04,  p=0.11 and converts to:

   [tex]z=\frac{p-u_{p} }{standard deviation} \\[/tex]

   [tex]=\frac{0.11-0.15}{0.0230}[/tex]

  = -1.74

For 0.15+0.04, p=0.19, and converts to:

    [tex]z=\frac{0.19-0.15}{0.0230}[/tex]

     = 1.74

From the standard normal distribution table, the associated probability for z values and subtracts the probability is,

     [tex]=p(-1.74\leq z\leq 1.74)[/tex]

     [tex]=0.9591-0.0409[/tex]

    [tex]=0.9182[/tex]  

Hence, the probability the sample proportion will be within 0.04 of the population proportion is 0.9182

Part c, the probability the sample proportion will be within 0.02 of the population proportion:

First, compute the z score then find probability based on standard normal table.

For 0.15-0.02, p=0.13, and converts to:

       [tex]=\frac{0.13-0.15}{0.0230}[/tex]

       =-0.87

For 0.15+0.02, p=0.17, this converts to:

    [tex]=\frac{0.17-0.15}{0.0230}[/tex]

    =0.87

From the standard normal distribution table, the associated probability for z values and subtracts the probability is,

    [tex]=p(-0.87\leq z\leq 0.87)[/tex]

   [tex]=0.8079-0.1922[/tex]

   [tex]=0.6187[/tex]

Hence, the probability the sample proportion will be within 0.02 of the population proportion is 0.6157

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The quadratic equation is [tex]-3/5x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]

Quadratic Equation:

A quadratic function is a function of degree two.

The general form of the quadratic equation is

x² + (sum of roots)x + Product of roots.

Given,

Here we have the roots,

[tex]\frac{-1-\sqrt{2} }{3} ,\frac{-1+\sqrt{2} }{3}[/tex]

And the coefficient with x² is equal to -3/5.

Through the given details we have to find the quadratic equation.

To find the equation we have to identify the sum of roots and the product of roots.

So, the sum of roots is,

[tex]= > \frac{-1-\sqrt{2} }{3} +\frac{-1+\sqrt{2} }{3}[/tex]

[tex]= > \frac{-1 }{3} +\frac{-1 }{3}\\= > \frac{-2}{3}[/tex]

Now the product of roots is,

[tex]= > \frac{-1-\sqrt{2} }{3} \times\frac{-1+\sqrt{2} }{3}[/tex]

[tex]= > \frac{1-\sqrt{2}-\sqrt{2}-2 }{3}=\frac{-1-2\sqrt{2} }{3}[/tex]

So, the quadratic equation is,

[tex]= > -3/5x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]

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In the Arabic system, the value of a digit is based on the position of the specific digit.

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On Mondays at noon, the switchboard in a Minneapolis legal firm receives an average of 5.5 incoming calls. Consequently, X's standard deviation is 2.35 calls.

The current personnel can handle up to six calls in an hour, according to experience.

A Poisson distribution with an average number of calls  of 5.5 on Mondays around lunchtime can be used to model the scenario that is being given.

Thus, the following equation represents the standard deviation for the number of calls received, X:

2.35 calls make up the standard deviation of X.

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Answer:

I think options BCDE. There is an angle presented in the picture. There are parallel lines. Also skew lines and line segments.

Step-by-step explanation:

Hope it helps! =D

Answer:

y = - [tex]\frac{1}{5}[/tex] x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (50, - 10) ← 2 points on the line

m = [tex]\frac{-10-0}{50-0}[/tex] = [tex]\frac{-10}{50}[/tex] = - [tex]\frac{1}{5}[/tex]

the line crosses the y- axis at (0, 0 ) ⇒ c = 0

y = - [tex]\frac{1}{5}[/tex] x + 0 , that is

y = - [tex]\frac{1}{5}[/tex] x ← equation of line

Answer:

Try 20.

Step-by-step explanation:

To round 19.5 to the nearest whole number consider the tenths’ value of 19.5, which is 5 and equal or more than 5. Therefore, we have to round up: the whole number part of 19.5, 19, increases by 1 to 20, and the decimal point and all digits (.5) are removed.

19.5 rounded to the nearest whole number = 20

For the exponential function f(x) = 3(0.5)^x, we have that:

An exponential function is modeled according to the rule given below:

[tex]y = ab^x[/tex]

In which the parameters are described as follows:

For this problem, the rule of the exponential function is given by:

y = 3(0.5)^x.

Hence the parameters are:

a = 3, b = 0.5.

Then:

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Answer:

decay; (0,3)

Step-by-step explanation:

Mean time = 142 minutes

One of the the most common expression for the mean of a statistical distribution with random variables is the average of all the terms. The mean of  any given data can be found out by adding all numbers in the data set and then dividing that by the number of values.

First calculate the mid point of the time interval :

(15+17)/2=16

(17+19)/2 = 18

(19+21)/2= 20

(21+23)/2= 22

Multiply each time mid point with respective frequency :

16*5=80

18*12= 216

20*7= 140

22*6= 132

Adding this and dividing by the total number of times that is 4:

= (80+216+140+132)/4

= 568/4

Mean time =142 minutes

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The given distribution is (A) Bimodal skewed as the distribution has 2 humps.

As the given graph has 2 humps, we can conclude that the given distribution is an (A) Bimodal skewed.

Therefore, the given distribution is (A) Bimodal skewed as the distribution has 2 humps.

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Each relationship should be matched with the correct description as follows:

Direct variation can be defined as a type of proportional relationship in which a variable is directly proportional to another variable.

An indirect variation can be defined as a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other.

In conclusion, a joint variation describes a situation in which a variable depends on two other variables which share a directly proportional relationship.

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Answer:

1. 596,681

2. 956,816

3. 96,001

4. 69,596,168

5. 1958

6. 95,596,618

Step-by-step explanation:

1. 500,000 + 90,000 + 6000 + 600 + 80 + 1 = 596,681

2. 900,000 + 50,000 + 6000 + 800 + 10 + 6 = 956,816

3. 90,000 + 6,000 + 0 + 0 + 1 = 96,001

4. 60,000,000 + 9,000,000 + 500,000 + 90,000 + 6.000 + 100 + 60 + 8 = 69,596,168

5. 1,000 + 900 + 50 + 8 = 1958

6. 90,000,000 + 5,000,000 + 500,000 + 90,000 + 6,000 + 600 + 10 + 8 = 95,596,618

I hope this helps!

Answer:

she cannot go on the field trip.

Step-by-step explanation:

Day 1 = 5, done = 3, remaining = 2.

Day 2 = 2 + 5, done = 6, remaining = 1

Day 3 = 1 + 5, done = 2, remaining = 4

Day 4 = 4 + 5, done = 4, remaining = 5

Day 5 = 5 + 5, done = 3, remaining  = 2 + 5

Day 6 = 2 + 5 + 5, done = 7, remaining = 5

Day 7 = 5 + 5, done = 1, remaining = 4 + 5

Day 8 = 4 + 5 + 5, done = 3, remaining = 1 + 5 + 5

Day 9 = 1+ 5+ 5+ 5, done = 2, remaining = 4+5+5

Day 10 = 4+5+5+5, done = 10(maximum assignment done assumed), remaining = 4 + 5

At the end of day 10, she had 9 remaining assignments, so she cannot go on the field trip.

The function's y-intercept is $60.

The equation y = 1/10x+60 can be used to express the function.

y| y 60 is the range.

The equation for the annual cost in dollars, y, based on x, the quantity of game tokens purchased for an arcade member, is represented by the following statements:

A) The function's y-intercept is $60.

B) The equation y = (1/10)x + 60 can be used to express the function.

C) y ≥ 60 is the range.

Typically, the slope-intercept form of the equation of a line is expressed as;

y = mx + c

Where;

the slope is m.

C is the y-intercept.

The input variable or domain is called x.

The output variable or range is called y.

As of right now, we're informed that a single membership costs $60 annually. This is the cost before any input, in this case, the purchase of game tokens.

It follows that the y-value intercept is $60.

According to what we've been told, members can purchase Game tokens for a discounted price of $1 for every 10 tokens. This implies;

y/x = 1/10

Thus, slope = 1/10

Putting this function's equation in slope intercept form now yields

y = (1/10)x + 60

The quantity of game tokens purchased is now limited to a minimum of 0. Thus;

Therefore, Domain; x ≤ 0

The price cannot be less than $60 since x ≤ 0.

Therefore, Range; y ≥ 60

Complete Question: A video game arcade offers a yearly membership with reduced rates for gameplay. A single membership costs $60 per year. Game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens. Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select three answers. The slope of the function is $1.00. The y-intercept of the function is $60. The function can be represented by the equation y = y equals StartFraction 1 Over 10 EndFraction x plus 60.X + 60. The domain is all real numbers. The range is {y| y ≥ 60}.

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The contrapositive statement of "If it does not have four legs, then it is a fish." is  "If it is not a fish, then it has four legs" .Option C

A contrapositive statement is simply defined as a law or rule obtained by contradicting the conclusion and hypothesis of a statement.

It includes the exchange of both the hypothesis and conclusion of a particular conditional statement before negating both the hypothesis and conclusion.

It is also known for the combination of a converse and an inverse statement.

The hypothesis and conclusion are switched or interchanged

A contrapositive statement is represented as;

x y is equivalent to y ~x

Given the statement:

"If it does not have four legs, then it is a fish."

The contrapositive statement would be;

If it is not a fish, then it has four legs.

We can see that the hypothesis and conclusion were interchanged accordingly.

Hence, the statement is "If it is not a fish, then it has four legs"

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Answer: C: If it is not a fish, then it has four legs.

Step-by-step explanation: Hope that helped!

Answer:

n = 29/12 is the simplest form

Step-by-step explanation:

145 ÷ 60 = 29/12

The value of the distance LM in which M is the midpoint between L and N is 64 units.

What is midpoint?

In mathematics. the term midpoint states the middle line of the line segment joining the two sides of the triangle make the third side parallel to the line segment and it also bisect the third side.

According to the question, the point M is the midpoint between L and N. The given parameters are: LM = 12x-8; MN = 14; and LN = 6x + 30

Using standard midpoint property, the distance LN can be written as:

LN = LM + MN ⇒ 6x + 30 = 12x-8 + 14

Taking variables terms one side, we get

6x = 36 ⇒ x = 6

Therefore,

LM = 12x-8 ⇒ 12(6) - 8 = 72 - 8 = 64

Hence, the value of the distance LM in which M is the midpoint between L and N is 64 units.

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Answer:

y = - 4x + 5 ---1

y = 3x - 16 ---2

Substitute 1 into 2:

- 4x + 5 = 3x - 16

7x = 21

x = 3

Substitute x into 1:

y = - 4(3) + 5

= - 7

The total number of voters is 1200, and out of that 720 voters cast their votes.

Let's take total voters = V

The percentage of voters do not cast their votes due to various reasons is 40%.

Therefore, Voters did not cast their votes = (40÷100)V = 0.4V

As 0.4V voters did not cast their votes. To calculate the total number of voters who cast votes, divide (total) by (non-casted-voters):

Voters casted their votes = V  - 0.4V = 0.6V

0.6V = 720

=> V = 1200

The total number of voters is 1200 if 720 voters cast their votes.

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The times that the ball is 34 feet high to the nearest tenth of a second is equal to 4.61 and 0.39 seconds.

In order to determine the time or times for this ball at a height of 34 feet, we would simply substitute the value of the height into the function h(t) as follows;

h(t) = -16t² + 80t + 5

34 = -16t² + 80t + 5

Re-arranging the equation, we have:

16t² - 80t + 34 - 5 = 0

16t² - 80t + 29 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-80)\; \pm \;\sqrt{-80^2 - 4(16)(29)}}{2(16)}\\\\x = \frac{80\; \pm \;\sqrt{6400 - 1856}}{32}\\\\x = \frac{80\; \pm \;\sqrt{4544}}{32}[/tex]

x = (80 ± 8√71)/32

x = (80 + 8√71)/32  and  x = (80 - 8√71)/32

x = 4.61 and 0.39 seconds.

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Answer:

fractions are cross multiplied in two situations:

division:

for e.g what is [tex]\frac{3}{2}[/tex]÷[tex]\frac{7}{5}[/tex]

to solve this expression we cross-multiply fractions:

=15/14

In equation:

for eg [tex]\frac{8x}{7}[/tex] = [tex]\frac{2}{9}[/tex]

to solve this we cross multiply:

8x(9)=2(7)

72x=14

x=14/72

In equation cross multiplication can only be carried out if denominator is same for e.g [tex]\frac{2}{1}[/tex]+ [tex]\frac{8x}{7}[/tex] = [tex]\frac{4}{7}[/tex] cannot be cross multiplied until denominator of 8x and 2 is same

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By cross multiplying, you can simplify the equation and solve for the unknown variable.

Cross multiplication is a technique used when solving equations involving fractions. It is typically used when you have a proportion or an equation with fractions, and you want to eliminate the denominators and solve for the unknown variable.

Cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. This technique is useful for simplifying equations and solving for the unknown variable.

You should cross multiply with fractions when you have an equation in the form:

a/b = c/d

To cross multiply, you would multiply ad (product of the numerators) and bc (product of the denominators) and set them equal:

ad = bc

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Answer:

The length is 6 ft

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

36 = s^2

Take the square root of each side

sqrt(36) = sqrt(s^2)

6 =s

The length is 6 ft

Answer:

6 ft

Step-by-step explanation:

We know that the formula to find the area of a square is :

Area = a² ( length × width)

According to the question they've already given the area of the square as 36ft².

So, to find the the measure of a one side, let the in unknown measure of a side be a.

And now, using the formula let us find the value of a ( length of a one side).

[tex] \sf \: Area = a² \\ \sf 36 = a² \\ \sf \: \sqrt{36} = a \\ \sf6ft = a[/tex]

‌

The standard form of the given equation of the ellipse according to the given properties is [tex]b^{2}[/tex] = ± 4√2.

Here the foci are given which are ( 0,3) and to the eight (0, ±3) and the vertices are (0,13) and  (0, ±1), so we have to find the standard form these values to put these values in a formula which is given below

The formula we are using in this is to form an equation :

[tex]\frac{(x-k)^{2} }{a^{2} }[/tex] + [tex]\frac{(y-k)^{2} }{b^{2} }[/tex] = 1

[tex]\frac{x^{2} }{a^{2} }[/tex] + [tex]\frac{y^{2} }{b^{2} }[/tex] = 1

[tex]\frac{x^{2} }{36}[/tex] + [tex]\frac{y^{2} }{32}[/tex] = 1

After solving the equation given above

we get [tex]b^{2}[/tex] + 4 = 36

Subtract  - 4 on both sides then we get

[tex]b^{2}[/tex]  + 4 - 4 = 36 - 4

[tex]b^{2}[/tex] = 32

[tex]b^{2}[/tex] = ± 4√2

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====================================================

Reason:

The cube root undoes the cubing operation.

It's similar to how the square root undoes squaring.

Your calculator should have a cube root button, or an nth root button. If not, then you can type in 1331^(1/3)

The exponent of 1/3 is the same as a cube root.

The result of 1331^(1/3) is 11

11^3 = 11*11*11 = 1331

Interpretation: You have a box that is 11 cm by 11 cm by 11 cm. The volume is 11^3 = 1331 cubic cm.

As you can see, the cube root is useful if you know the volume and want to work backwards to determine the side length of the cube.

the cube root of 1331 = ∛(11 × 11 × 11) = 11.

The square root of 1331 is 36.48287.

Answer:

m = 1

Step-by-step explanation:

A number is divisible by 3 if the sum of the digits is a multiple of 3

the given number is 2m234 and we are asked to find the smallest m

Adding up known digits gives 2 + 2 + 3 + 4 = 11

The next multiple of 3 is 12

So 11 + m = 12

m = 1

The other possibilities are
m = 4, m = 7

The tree diagram of the outcomes and the number of possibilities is added as an attachment

The given parameters are:

Red balls = 6

Blue balls = 4

This means that the total number of balls is

Total number of balls = Red balls + Blue balls

Substitute the known values in the above equation

So, we have the following equation

Total number of balls = 6 + 4

Evaluate the sum in the above equation

So, we have the following equation

Total number of balls = 10

From the question, we understand that the selection is without replacement, and the number of selections is 2

This means that the sample space in total selections is

{RR, RB, BR, BB}

Where

B represents blue and R represents red

Next, we use the sample space {RR, RB, BR, BB} to make the required tree diagram

See attachment for the tree diagram

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Answer:

Step-by-step explanation:

Use the distance formula.

Distance:

[tex]\Rightarrow \sf{\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}}[/tex]

y₂=(-7)

y₁=(-3)

x₂=4

x₁=8

[tex]\sf{\sqrt{\left(4-8\right)^2+\left(-7-\left(-3\right)\right)^2}}[/tex]

Solve.

Use the order of operations.

PEMDAS stands for:

Do parentheses first.

(4-8)=-4

[tex]\sf{\left(-4\right)^2+\left(-7-\left(-3\right)\right)^2}[/tex]

-7-(-3)=-7+3

-7+3=-4

[tex]\sf{\left(-4\right)^2+\left(-4\right)^2}[/tex]

Do exponents.

[tex]\sf{(-4)^2=4^2=4*4=16}[/tex]

Then, you add.

16+16

[tex]\Rightarrow \boxed{\sf{32}}[/tex]

Therefore, the correct answer is C. 32.

Using percentage we can calculate that 81 students did not take French.

In mathematics, a number or ratio that is expressed as a fraction of 100 is referred to as a percentage. Although the abbreviations "pct" and "pc" are also often used, the percent symbol "%" is the one that is most frequently used. A % is a number that has neither established units of measurement nor dimensions.

The percentage can be calculated by taking the value and dividing it by the total value, then multiplying the result by 100. using the formula (Value/Total Value) × 100% to calculate percentages.

Let the total number of students be x.

Now 91% of this students is equal to 819.

Now using the properties of percentages we can write:

91% of x = 819

or, x = 900

Number of students who did not take French = 900 - 819 = 81

Hence using percentages we can say that 9% or 81 students did not take French.

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The length of line segment FG is 10 units.

So, the length of FG:

So, insert x = 5 in 2x:

Therefore, the length of line segment FG is 10 units.

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