A club’s first meeting was attended by 28 people. Four times as many people went to the first meeting than the second meeting. How many people attended the second meeting?

The correct answer is: χ2 = 2.48, P-value is between 0.10 and 0.15.

First, let's calculate the expected frequencies for each political party affiliation in the sample:

Expected frequency for Democrats: 0.42 x 500 = 210

Expected frequency for Republicans: 0.34 x 500 = 170

Expected frequency for Independents: 0.24 x 500 = 120

Next, we can set up the chi-square test:

χ² = Σ((O - E)² / E)

Where:

O = observed frequency

E = expected frequency

Let's calculate the chi-square test statistic:

χ² = ((200-210)² / 210) + ((187-170)² / 170) + ((113-120)² / 120)

Calculating the above expression gives us:

χ² = (10² / 210) + (17² / 170) + (7² / 120)

χ^2 = 100/210 + 289/170 + 49/120

χ^2 ≈ 0.476 + 1.700 + 0.408

χ^2 ≈ 2.584

The calculated chi-square test statistic is 2.584.

Since we have 3 political party affiliations, the degrees of freedom would be 3 - 1 = 2.

Looking at the chi-square distribution table with 2 degrees of freedom, we find that the P-value for a chi-square test statistic of 2.584 is between 0.10 and 0.15.

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Answer: It will be A that is the best answers

The absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5

The given parameters are:

Minimum = 70 mg/dL

Maximum = 99 mg/dL

Calculate the mean using:

Mean = (Minimum + Maximum)/2

This gives

Mean = (70 + 99)/2

Evaluate

Mean = 84.5

Calculate the range using

Range = Maximum -Minimum

This gives

Range = 99 - 70

Evaluate

Range = 29

The absolute value equation that represents the minimum and maximum normal glucose levels is

|x - Mean| = Range/2

So, we have:

|x - 84.5| = 29/2

Evaluate

|x - 84.5| = 14.5

Hence, the absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5

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The proof that the roots of the equation are equal is shown below

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

(a - b)x² + 5(a + b)x - 2(a - b) = 0

For the roots to be equal, we have

D = 0

The discriminant D is calculated as

(a + b)² - 4 * (a - b) * (a - b) = 0

So, we have

a² + 2ab + b² - 4 * (a² - 2ab + b²) = 0

So, we have

a² + 2ab + b² - 4a² - 8ab - 4b² = 0

This gives

-3a² - 3b²  - 6ab = 0

Divide through by -3

a² + b²  + 2ab = 0

So, we have

(a + b)² = 0

Take the square root

a + b = 0

This gives

a = -b

In other words

a ≠ b

Because a ≠ b, then we can conclude that the roots are equal

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Complete question

If a and b are real and a ≠ b then show that the roots of the equation (a - b)x² + 5(a + b)x - 2(a - b) = 0 are equal

Answer: x=-18

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

\( \huge{ \fbox{ \sf{x = - 18}}}\)

Step-by-step explanation:

\( \text{4(7x + 3) = - 3(2 - 9x)}\)

\( \text{Step \: 1 \: : Distribute \: 4 \: through \: the \: parentheses}\)

\( \hookrightarrow{ \sf{28x + 12 = - 3(2 - 9x)}}\)

\( \text{Step \: 2 \: : Distribute \: - 3 \: through \: the \: parentheses}\)

\(\hookrightarrow{ \sf{28x + 12 = - 6 + 27x}}\)

\( \text{Step \: 3 \: : Move \: 27x \: to \: left \: hand \: side \: and \: change \: its \: sign}\)

\( \hookrightarrow{ \sf{28x - 27x + 12 = - 6}}\)

\( \text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \hookrightarrow{ \sf{28x - 27x = - 6 - 12}}\)

\( \text{step \: 5 \: : Collect \: like \: terms}\)

\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)

\( \hookrightarrow{ \sf{x = - 6 - 12}}\)

\( \text{step \: 6 \: : Calculate}\)

\( \text{ \underline{ Remember!}} : \sf{ \: The \: negative \: integers \: are \: always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}\)

\( \hookrightarrow{ \boxed{ \sf{x = - 18}}}\)

Hope I helped!

Best wishes ! :D

~\( \text{TheAnimeGirl}\)

1) A: It is a function.

B) domain = {1, 2, 3, -2, -4}

C) range = {3, 0, -1, -3, -4}

2) A) Discrete function.

   B) D: {0, 1, 2, 3, 4, 5, 6}

   C) R: {$10, $8.50,  $7, $5.50, $4, $2.50, $1}

A function is a relation that maps elements from the domain into elements from the range, such that each element from the domain can be mapped into only one element from the range.

In the diagram, we can see that each element on the domain (x) is being mapped into only one element of the range (y), so this is a function.

And by looking at the diagram we can see that:

Now let's go to the second problem.

There is a gift card of $10, and we know that each song costs $1.50, then the credit left in the gift card as a function on the number of songs bougth is:

C (x)= $10 - $1.50*x

A) First, this function is discrete, because x can only take whole numbers.

B) The domain is the set of possible values that x can take.

The maximum value that x can take is such that the amoun left on the card is zero, so we solve:

$0 = $10 - $1.50*x

x = $10/$1.50 = 6.7

Rounding down to the nearest whole number:

x = 6

Then the domain (number of songs that can be bought with the gift card) is:

D: {0, 1, 2, 3, 4, 5, 6}

The range is the set of possible values taht C(x) can take, these are:

C(0) = $10

C(1) = $10 - $1.50 = $8.50

C(2) = $10 - $1.50*2 = $7

C(3) = $10 - $1.50*3 = $5.50

C(4) = $10 - $1.50*4 = $4

C(5) = $10 - $1.50*5 = $2.50

C(6) = $10 - $1.50*6 = $1

Then the range is:

R: {$10, $8.50,  $7, $5.50, $4, $2.50, $1}

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The value of ABP is 120°

The value of PQX is 60°

A hexagon, also known as a sexagon, is a six-sided polygon that forms the shape of a cube in geometry. Any simple hexagon has 720° of internal angles in total.

To find their values:

Recall that in a regular hexagon, (6-2) x 180°/ 6 = 120°

Also, (5-2) x 180°/5 = 108°

With these values, we would find that the value of ABP is 120°

<PQX = 120°/2 = 60°

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Answer:

y=4

Step-by-step explanation:

sub point into the general equation

y=mx+c

m=0

x=-2

y=4

4=(0)(-2)+c

c=4

Therefore the equation is y=0x+4

simplified the equation of the line is y=4

(PS if the gradient or slope is 0 then the line is horizontal)

Answer:

y=x+6 I think

Step-by-step explanation:

I have done this problem before so yeah

Hope this helps:)

Answer:

x=28

Step-by-step explanation:

sum of all angles im a triangle = 180°

(2x+5) + (4x+10) + (x-31) = 180

7x=196

x=28

Answer:

x = 28°

Step-by-step explanation:

Sum of a triangle is equal to 180°. Firstly you need to form an equation. Add all the angles which equals to 180°.

2x + 5 + 4x + 10 + x - 31 = 180°

Now simply and find the value of x. Add all the x terms and whole numbers.

7x + 5 + 10 - 31 = 180°

7x + 15 - 31 = 180°

7x - 16 = 180°

7x = 180° + 16

7x = 196

x = 196 ÷ 7

x = 28°

So the angles are:

Angle A = 2x + 5

2 x 28 + 5 = 61°

Angle B = 4x + 10

4 x 28 + 10 = 122°

Angle C = x - 31

28 - 31 = -3°

Answer:

5.96 with the repeating sign over the 6

Step-by-step explanation:

Answer:

6.

Step-by-step explanation:

Convert the decimal to a fraction:

2.33333....  = 2 1/3, so it is:

3 2/3 + 2 1/3

= 3 + 2 + 2/3 + 1/3

= 3 + 2 + 1

= 6.

Answer:

Step-by-step explanation:

5t+6+60+49=180

5t+115=180

5t=65

t=13

Answer:

In a felony case, the purpose of a grand jury is to decide if the evidence warrants prosecution. In a felony case, the purpose of a grand jury is to decide if the evidence warrants prosecution

Answer:

decide if the evidence warrants prosecution

Step-by-step explanation:

To calculate a quantity variance, multiply the standard quantity times the standard price and compare it to the standard quantity allowed times the actual price.

In contrast to range and interquartile range, variance is a measure of dispersion that considers the spread of all data points in a data collection. It is the most commonly used measure of dispersion, along with the standard deviation, which is essentially the square root of the variance. The dispersion between values in a data collection is the most basic definition of variance. Variance is a statistical metric that determines how far one number deviates from the mean and from all other numbers in the collection.

Here,

To compute a quantity variance, multiply the standard amount by the standard price and compare it to the standard quantity permitted multiplied by the real price.

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Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

The measure of arc angle QT is determined as 142 ⁰.

The measure of m∠STR is determined as 23⁰.

The measure of angle subtended by the arc QT is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

The measure of  m∠STR is calculated as;

m∠STR = ¹/₂( arc SR )

m∠STR = ¹/₂ x 46⁰

m∠STR = 23⁰

The measure of arc QT is calculated as;

m∠QST = ¹/₂( arc QT )

arc QT = 2 (m∠QST)

arc QT = 2 x 71⁰

arc QT = 142⁰

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Answer:

y = 2x + 9

Step-by-step explanation:

Y = mx + b indicates slope-intercept equation.

"b" represents y -intercept/beginning.

"mx" represent slope/constant of variation/rate of change

x-intercept represents the end of the graph. (in stories using money its the ending amount).

The y-intercept is always when the x-value is 0. The point of the y-intercept is on the y-axis. The line on the graph starts at the point (0,9). It can be located on the point right above the number labeled under the 9 which is 8. Since the x-value is 0,

The y-intercept is 9.

To find the slope, we have to find two points on the graph to use.

Two points on the graph are:

(1.5, 13) , (2, 14)

Using the slope formula:

y2-y1/x2-x1

Plug in:

14-13/2-1.5

Complete:

1/0.5

divide:

The numbers in 1 divided by 1/2 are labeled below:

1 = whole number

1 = numerator

2 = denominator

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:

1 x 2/1  = 2/1

Thus, the answer to 1 divided by 1/2 in fraction form is:

2/1

To make the answer to 1 divided by 1/2 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

2 / 1 = 2

The answer is rounded to the nearest two decimal points if necessary.

2/1 is an improper fraction and should be written as 2.

So now that we have the y-intercept and slope:

Y-intercept: 9

Slope: 2

Equation: y = 2x + 9

Terms: Linear Equations 8th Grade

Answer:

see below

Step-by-step explanation:

To be arithmetic we have to add the same term each time

1,1,2,3,5,8

1+1 =2  2+1 = 3  3+1 = 4  so it is not arithmetic

20,17,14,11,8,....

Add -3

20+-3 =17   17+-3 = 14  14+-3 = 11   11+-3 = 8

This is an arithmetic sequence

The common difference is -3

The explicit formula is

an = a1+ d(n-1)  where d is the common difference and a1 is the first term

an = 20 -3( n-1)

The recursive formula is

an = an-1 + d  where an-1 is the previous term and d is the common difference

an = an-1  -3

3,7,11, 15

Add 4

3+4=7  7+4=11  11+4=15

This is an arithmetic sequence

The common difference is 4

The explicit formula is

an = a1+ d(n-1)  where d is the common difference and a1 is the first term

an = 3 +4( n-1)

The recursive formula is

an = an-1 + d  where an-1 is the previous term and d is the common difference

an = an-1  +4

Answer:

Answer:

The answer is A. 2.5

-

To determine the recipe conversion factor (RCF), we need to divide the new yield by the original yield.

RCF = new yield / original yield

In this case, the new yield is 25, and the original yield is 10. So we can substitute these values into the formula to get:

RCF = 25 / 10 = 2.5

Therefore, the answer is A. 2.5.

Explanation:

To explain further, the RCF is a conversion factor that allows us to adjust a recipe to make a larger or smaller batch. In this case, the RCF of 2.5 means that we need to multiply all the ingredients in the recipe by 2.5 to make a batch that yields 25 servings, which is 2.5 times the original batch size of 10 servings.

For example, if a recipe calls for 1 cup of flour to make 10 servings and we want to make 25 servings, we can use the RCF of 2.5 to determine how much flour we need:

New amount of flour = Original amount of flour x RCF

New amount of flour = 1 cup x 2.5 = 2.5 cups

Therefore, we need 2.5 cups of flour to make the recipe for 25 servings.

We can use the same formula to adjust the amounts of all the ingredients in the recipe. Once we have calculated the new amounts of all the ingredients, we can follow the original recipe instructions to make a larger batch of the recipe that yields 25 servings.

Hope this helps, if it didn't I'm sorry. If you need more help, ask me! :]

Answer:

a. 95.4

b. UCL = 96.07

LCL = 94.73

c.  Process is in control

Step-by-step explanation:

a. The computation of estimate mean is shown below:-

\(Estimate\ mean = \frac{\Sigma X}{N} \\\\ = \frac{1908.000}{20}\)

= 95.4

b. The computation of Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process is shown below:-

\(UCL = Mean + \frac{3\times \sigma }{\sqrt{Sample\ size} }\)

\(UCL = 95.4 + \frac{3\times (0.5)}{\sqrt{0.5} }\)

= 95.4 + 0.67082

= 96.07

\(UCL = Mean - \frac{3\times \sigma }{\sqrt{Sample\ size} }\)

\(UCL = 95.4 - \frac{3\times (0.5)}{\sqrt{0.5} }\)

= 95.4 - 0.67082

= 94.73

c. The explanation is shown below:-

From the above calculation we can see that the sample lies between LCL AND UCL that is (94.73 ,96.07) ,  

The Process is in control

Answer: 91

Step-by-step explanation: cross multiply.

Answer:

x is 3 y is 52        x is 50, y is 70

Step-by-step explanation:

1

we know y=14x=12x+6 since they are vertical angles, and correlating angles.

14x=12x+6

2x=6

x=3

subsitute x=3

y=14(x)   turns into y=52

x is 3 y is 52

2.

x+20=y  since alternate interior

y+2x+10=180    because they are supplementary

x+20+2x+10=180    subsitute  for y

3x+30=180

3x=150

x=50

50+20=y

70=y

It is given that Hoku is paying the shirt company $880 for shirt design and the first 50 Shirts. So, the fixed price will be $880 for 50 shirts.

Now, for over & above 50 shirts the cost is $12 per shirt.

Now, adding both the amounts to get the total cost of uniform shirts for company. So, the equation for total cost for buying more than 50 uniform shirts becomes y = 12(x-50)+880.

Comparing the above equation with the given equation, the value of p comes out to be 880.

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Solution:

Let's reread the part of the question carefully.

{one more} {than one third the number of dolls than Sally has}

       ↥                                                 ↥                          

       1                                                s/3

This means that Anne has s/3 + 1 dolls, which is 9 dolls.

Hence, the equation that represents the word problem is S/3 + 1 = A.

Answer:

Expand:

x^2+7x-2x-14

Answer:

x^2+5x-14

Step-by-step explanation:

Let x be the number of gallons consumed by the first car.

Then, the number of gallons consumed by the second car is 65-x (since the total gas consumption is 65 gallons).

Using the formula distance = fuel efficiency x gas consumption, we can set up two equations:

First car: distance = 30x

Second car: distance = 20(65-x)

Since the total distance is 1700 miles, we can set up another equation:

Total distance: 30x + 20(65-x) = 1700

Simplifying this equation, we get:

30x + 1300 - 20x = 1700

10x = 400

x = 40

Therefore, the first car consumed 40 gallons and the second car consumed 65-40 = 25 gallons.

Let's assume that the first car traveled x miles and the second car traveled y miles during that week. We can set up two equations based on the given information:

x + y = 1700 (the combined total of miles traveled by both cars)

x/30 + y/20 = 65 (the total gas consumption)

To solve for x and y, we can use the first equation to express one variable in terms of the other. For example, we can solve for y as follows:

y = 1700 - x

Substituting this into the second equation, we get:

x/30 + (1700 - x)/20 = 65

Multiplying both sides by the common denominator 60, we can simplify the equation:

2x + 3(1700 - x) = 3900

2x + 5100 - 3x = 3900

-x = -1200

x = 1200

So the first car traveled 1200 miles during the week. We can use this value to find the second car's mileage:

y = 1700 - x = 1700 - 1200 = 500

Therefore, the second car traveled 500 miles during the week. To find the gallons of gas consumed by each car, we can use the fuel efficiency rates:

Gallons used by first car = 1200 miles / 30 mpg = 40 gallons

Gallons used by second car = 500 miles / 20 mpg = 25 gallons

So the first car consumed 40 gallons of gas and the second car consumed 25 gallons of gas during that week.