A survey was conducted by sampling 400 persons who were questioned re- garding union membership and attitude toward decreased national spending on social wel- fare programs. The cross-tabulated frequency counts are presented. Support Indifferent Opposed Total 112 36 28 176 Union Nonunion 84 68 72 224 Total 196 104 100 400 Can these observed differences be explained by chance or are attitude and membership status associated?

Uncle Makhosi needs approximately 1.56 kilograms of butter.

To determine the amount of butter in kilograms, we'll use the conversion rate of 1 kg = 2.25 pounds.

First, we need to convert 3 and a half pounds to a decimal form. Since half a pound is equal to 0.5 pounds, we can express 3 and a half pounds as 3.5 pounds.

Next, we'll use the conversion rate to calculate the equivalent weight of 3.5 pounds in kilograms:

3.5 pounds * (1 kg / 2.25 pounds) = 1.56 kilograms (rounded to two decimal places).

To summarize, based on the given conversion rate of 1 kg = 2.25 pounds, Uncle Makhosi requires approximately 1.56 kilograms of butter to fulfill his 3 and a half pound requirement. This conversion can be useful when dealing with different units of measurement, allowing us to easily switch between kilograms and pounds.

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If a caterer can purchase 4 cartons of Sprite for $10, then the cost of a single carton is $ 2.50 per carton.

The cost of a single carton of Sprite which is also called the unit cost of the cartons of Sprite can be determined as follows.

1. You are given that the caterer can purchase 4 cartons of Sprite for $10.

2. Divide the total cost by the number of cartons to find the cost per carton.

The cost of a single carton of Sprite is $10 / 4 cartons = $2.50 per carton.

Hence, the cost of a single carton if four cartons of Sprite cost $10 is $2.50 per carton.

Note: The question is incomplete. The complete question probably is: A caterer can purchase 4 cartons of Sprite for $10, what is the cost of a single cartons.

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Answer:

Step-by-step explanation:

y=(x+5)(x+4)=x²+5x+4x+20=x²+9x+20=x²+9x+(9/2)²-(9/2)²+20

\(y=(x+\frac{9}{2} )^2-\frac{81}{4} +20\\y=(x+\frac{9}{2})^2-\frac{81}{4}+\frac{80}{4}\\y=(x+\frac{9}{2})^2-\frac{1}{4}\)

vertex is (9/2,-1/4) or(4.5,-0.25)

The equation of the line is in point-slope form, which means it is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the point we are given is (-9,3), so (x1, y1) = (-9, 3). We can then calculate the slope of the line using the following formula:

m = (y2 - y1)/(x2 - x1)

In this case, the points (-9,3) and (-4,-4) give us y2 = -4 and y1 = 3, x2 = -4 and x1 = -9. Substituting these values into the slope formula, we get:

m = (-4 - 3)/(-4 - (-9)) = -7/5

Therefore, the slope of the line is -7/5. We can now plug this value and the point (-9,3) into the point-slope form equation to get the final equation:

y - 3 = (-7/5)(x - (-9))

The point-slope form equation of a line is a very useful way to write the equation of a line when you only know one point on the line and the slope of the line. The equation is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

To use the point-slope form equation, we first need to find the slope of the line. We can do this using the following formula:

m = (y2 - y1)/(x2 - x1)

In this case, the points (-9,3) and (-4,-4) give us y2 = -4 and y1 = 3, x2 = -4 and x1 = -9. Substituting these values into the slope formula, we get:

m = (-4 - 3)/(-4 - (-9)) = -7/5

Once we have the slope of the line, we can plug it and the point (-9,3) into the point-slope form equation to get the final equation:

y - 3 = (-7/5)(x - (-9))

This equation can be used to find the y-coordinate of any point on the line, given the x-coordinate. For example, if we want to find the y-coordinate of the point on the line with an x-coordinate of 0, we can plug x = 0 into the equation and solve for y:

y - 3 = (-7/5)(0 - (-9))

y - 3 = -7/5 * 9

y - 3 = -63/5

y = -60/5

y = -12

Therefore, the point on the line with an x-coordinate of 0 has a y-coordinate of -12.

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Answer:

1)d

2)

6)b

7)d,c,b,a

8)a,b

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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Given:

The length of the rectangle = \(y^2+3y+7\)

Width of the rectangle = \(y-3\)

To find:

How much longer is the length?

Solution:

We need to find the difference between length and width of the rectangle.

\(Difference=Length-Width\)

\(Difference=y^2+3y+7-(y-3)\)

\(Difference=y^2+3y+7-y+3\)

\(Difference=y^2+(3y-y)+(7+3)\)

\(Difference=y^2+2y+10\)

Therefore, the length of the rectangle is \(y^2+2y+10\) much longer than the width.

Answer:

9

Step-by-step explanation:

so we know that its a right triangle and 8 and \(\sqrt{17}\) are not the hypotenuse.

the equation for this is \(a^{2}\)+\(b^{2}\)=\(c^{2}\) with c being the hypotenuse.

\(8^{2}\)+\(\sqrt{17} ^{2}\)=\(c^{2}\)

64+17=\(c^{2}\)

81=c

\(\sqrt{81}\)=c

9=c

Answer:

Step-by-step explanation:

To make the use of Pythagoras's theorem clear

\(C^{2}\) = \(A^{2}\) + \(B^{2}\)

where C is they hypotenuse or Hyp

A is one side often called  the Adjacent side

B is the other side often called the Opposite side

when A = 8

and B = \(\sqrt{17}\)

then

\(C^{2}\)  = \(8^{2}\) + \(\sqrt{17} ^{2}\)

\(C^{2}\) = 64 + 17

\(C^{2}\) = 81

C = \(\sqrt{81}\)

C = 9

Answer:

a

Step-by-step explanation:

Answer:

NO!

Step-by-step explanation:

An input can't have more than one output, but output can have multiple inputs.

Answer:

it is a (1 , 1.5)

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

It's ( 1 , 1.5 ) because the lines are both

intersecting each other at that point.

Hope this helps! <3

Answer:

The missing exponent is 5

Step-by-step explanation:

Answer:

x = 27

Step-by-step explanation:

Hello There!

The first thing we want to do is find the measure of arc AD

remember the circumference of a circle in degrees is 360

so to find the measure of arc AD we subtract the given arc measures (97 and 112) from 360

360 - 112 - 97 = 151

so arc AD = 151

now to find x

if you didnt know an included angle formed by tangent lines is equal to one half of its major arc minus its minor arc

For this problem to be more specific ∠B = 1 half of (arc AD - arc AC)

Now what we want to do is plug in the known information and solve for angle B

∠B = 1/2 ( 151 - 97 )

151 - 97 =54

54/2=27

so we can conclude that x = 27

Answer:

8 dragons in your dream

Step-by-step explanation

4 dragons in 14 h x 2 =8 dragons in total

(Hippity hoppity now your dreams are reality.)

Answer:

number 2. A
number 3. C

number 4. B

Step-by-step explanation:

if the answer's are correct then comment or like

Problem 3

Answer: 4 compounding periods per year

In other words, the money is being compounded quarterly

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

Explanation:

The compound interest formula is

\(A = P*(1+\frac{r}{n})^{n*t}\\\\\)

The variables are

In this case, we have

So,

\(A = P*(1+\frac{r}{n})^{n*t}\\\\104,070.70 = 100,000*(1+\frac{0.02}{n})^{8}\\\\(1+\frac{0.02}{n})^{8} = \frac{104,070.70}{100,000}\\\\(1+\frac{0.02}{n})^{8} = 1.040707\\\\1+\frac{0.02}{n} = (1.040707)^{1/8}\\\\1+\frac{0.02}{n} \approx 1.0049999946977\\\\n+0.02 \approx 1.0049999946977n\\\\0.02 \approx 1.0049999946977n-n\\\\0.02 \approx 0.0049999946977n\\\\n \approx \frac{0.02}{0.0049999946977}\\\\n \approx 4.0000042418445\\\\n \approx 4\)

So it appears that we're compounding the money n = 4 times a year (aka quarterly) and doing so for 8/4 = 2 years.

Note how,

\(A = P*(1+\frac{r}{n})^{n*t}\\\\A = 100,000*(1+\frac{0.02}{4})^{4*2}\\\\A = 100,000*(1.005)^{8}\\\\A \approx 104,070.704392543\\\\A \approx 104,070.70\\\\\)

which helps confirm the answer.

The standard deviation of returns is 0.0665 when a person is holding stock and there are three possible outcomes.

To calculate the expected return, we multiply the probability of each state by its corresponding return and sum them up:

Expected return = (20% * 18%) + (55% * 9%) + (25% * -5%)

Expected return = 0.20 * 0.18 + 0.55 * 0.09 + 0.25 * (-0.05)

Expected return = 0.036 + 0.0495 - 0.0125

Expected return = 0.073

The expected return is 7.30%.

To calculate the standard deviation of returns, we need to find the variance first. The variance is calculated as the weighted sum of squared deviations from the expected return:

Variance = (20% * (18% - 7.30%)^2) + (55% * (9% - 7.30%)^2) + (25% * (-5% - 7.30%)^2)

Variance = 0.20 * (0.1077)^2 + 0.55 * (0.0177)^2 + 0.25 * (-0.123)^2

Variance = 0.00232 + 0.000173 + 0.001903

Variance = 0.004423

The standard deviation is the square root of the variance:

Standard deviation = √(0.004423)

Standard deviation = 0.0665

Therefore, the value obtained is 0.0665.

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Answer:

Triangles B and C

Step-by-step explanation:

Im not 100% sure i cant really explain because i did this in my head sorry im 60% sure its right sorry its my bad if you get it wrong

Triangles A and B are similar because they have the same equal pair of corresponding angles. Thus, the correct answer is option (D).

As per the shown figure, In triangles A and B have:

Same angle = 67°

Same angle = 23°

Same angle = 90°°

As we know that similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

Here, triangles A and B have corresponding angles that are the same.

Thus, triangles A and B are similar.

Therefore, the correct answer is an option (D).

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The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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An equation that models the parabola formed when a cross-section is taken through the reflector’s central axis is y= 1/12(x-0)^2+0

This answer works as an upward parabola

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.

The formula for a vertical parabola is y=1/4p(x-h)^2+k

In this problem, it is given that the vertex is at the origin (0,0) and the focus (the bulb), is 3 centimeters away from the vertex.

Now, you know the values of the variables. Fill in the values

FROM THE FORMULA:

1/4p turns into 1/12 since p is 3.

(x-h)^2+k turns into (x-0)^2+0, since h and k were the values of the vertex which was 0,0

once all the variables are given values (except x and y) you have made your equation!

The answer is y=1/12(x-0)^2+0

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Answer:

The range of this quadratic function is

-infinity < y ≤ 2.

Answer:

What is a polynomial?

  - In mathematics, a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables

What is a rational function?

- In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.

Are all polynomials rational functions?

.A function that cannot be written in the form of a polynomial, so no they are not all functions.

The length of the shorter leg will be 2.5 feet and the length of the longer leg is 4.5 feet.

The Pythagoras theorem will be used in calculating the lengths.

This will be:

a = First leg = x

b = Second leg = x + 4

c = Hypothenuse = 7

In this case, the values will be substituted into the formula given below:

a² + b² = c²

x² + (x + 4)² = 7²

x² + x² + 8x + + 16 = 49

Collect like terms

2x² + 8x + 16 - 49

2x² + 8x - 33

By using the quadratic formula, the value of x will be 2.5. This is the shorter leg. The Longer leg will be: 2.5 + 4 = 6.5 feet

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Using an exponential function, it is found that 242.5 mg of radium will be left after the 40 days.

The exponential function for the amount of a decaying substance is modeled by:

\(A(t) = A(0)e^{-kt}\)

In which:

In this problem, the half-life is of 100 days, hence:

\(A(100) = 0.5A(0)\)

Which is used to find k.

\(A(t) = A(0)e^{-kt}\)

\(0.5A(0) = A(0)e^{-100k}\)

\(e^{-100k} = 0.5\)

\(\ln{e^{-100k}} = \ln{0.5}\)

\(-100k = \ln{0.5}\)

\(k = -\frac{\ln{0.5}}{100}\)

\(k = 0.0069314718\)

Then, the equation is:

\(A(t) = A(0)e^{-0.0069314718t}\)

He started with 320 mg of radium, hence \(A(0) = 320\), and the equation is:

\(A(t) = 320e^{-0.0069314718t}\)

After 40 days, the amount left is:

\(A(40) = 320e^{-0.0069314718(40)} = 242.5\)

242.5 mg of radium will be left after the 40 days.

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the amount of juice left in Luna's glass is 1/2.

We have been given that Luna mixes 3/4 cup of orange juice with 3/8 cup of cranberry juice.

First of all, let us find the total amount of juice Luna had by adding the amount of orange juice to amount of cranberry juice.

Total amount of juice Luna had = 3/4 + 3/8

                                                 = 9/8

Since Luna gave 5/8 cup of juice to Mags, so let us subtract amount of juice given to Mags from the total amount of juice to find the amount of juice left in Luna's glass.

Hence, Amount of juice left in Luma glass is,

= 9/8 - 5/8

= 4/8

= 1/2

Therefore, the amount of juice left in Luna's glass is 1/2.

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