Let C = {n ∈ Z | n = 6r – 5 for some integer r} and D = {m ∈ Z | m = 3s + 1 for some integer s}.
Prove or disprove each of the following statements.
a. C ⊆ D
b. D ⊆ C

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

A

Step-by-step explanation:

Using the properties of logarithms, we can simplify the expression:

4 log3x + 6 log3y - 7 log3z = log3x^4 + log3y^6 - log3z^7

Now, we can use another property of logarithms, which states that:

loga (mn) = loga m + loga n

Using this property, we can combine the logarithms with addition or subtraction:

log3x^4 + log3y^6 - log3z^7 = log3(x^4 * y^6 / z^7)

Therefore, the simplified form of 4 log3x + 6 log3y - 7 log3z is log3(x^4 * y^6 / z^7).

The congruent reason for the triangles is (b) HL theorem

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

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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The area should be 47.5 CM.

Answer:

Step-by-step explanation:

The figure you see here is a trapezoid.

Area = \(\frac{(a + b)h}{2}\) = \(\frac{(6 + 13)(5)}{2}\) = \(\frac{(19)(5)}{2}\) = \(\frac{95}{2}\) = 47.5 cm

Answer:

a one is right answer

Step-by-step explanation:

h.j.j.k kaoa0

Answer:

24 ounces/ 2 packets = 12 ounces/ packet

Step-by-step explanation:

23 (12 ounces/packet) = 276 ounces of water

The the rate of ounces of water needed for each packet of flavoring would be 12.

Given is the packets of flavoring added to an specific amount of water to make soup.

Now, for 24 ounces of water, 2 packets of flavoring are needed.

Then, for 1 packet of flavoring, (24/2) or 12 ounces of water is needed.

For 5 packets of flavoring, (12 x 5) or 60 ounces of water is needed.

So, the rate of ounces of water needed for each packet of flavoring would be -

r = (60 - 24)/(5 - 2)

r = 36/3

r = 12

r = 12

Therefore, the the rate of ounces of water needed for each packet of flavoring would be 12.

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Example 1:

The pros of Orthographic is that they can show hidden details and all of the connecting parts, they can be annotated to display material and finishes. The pros of Isometric projection is that they dont need many views and it gives accuracy, cons are is created a unorginized apperance by the lack of foreshortening, I would choose Isometric projection because it shows the size of the figure.

Example 2:

Orthographic projection is a good option for showing lots of detail and small things. The limitation is that with all of that detail, they can become quite messy and hard to understand to someone new to them. However, that is one of the pros of Isometric projection. It gives easy detail and is just as good as an Orthographic. Personally, I find Isometric projections easier to interpret.

Answer:

1.44

Step-by-step explanation:

1.63-.19= 1.44

Answer:

\(\Huge \bold{\boxed{\boxed{\text{5\%}}}}\)

Step-by-step explanation:

To calculate the margin of error for the survey, we need to use the formula:

\(\large \text{Margin of error} = \large \text{$\frac{\text{Range of values}}{2}$}\)

The range of values is the difference between the upper and lower bounds of the interval. In this case, the lower bound is 22% and the upper bound is 32%, so the range of values is:

\(\large \text{Range of values = 32\% - 22\% = 10\%}\)

Substituting this value into the formula, we get:

\(\large \text{Margin of error = $\frac{10\%}{2}$ = 5\%}\)

Therefore, the margin of error on the survey is 5%.

Answer:

\(\frac{1}{4^{-4}} = 256\)

Step-by-step explanation:

Given

\(\frac{1}{4^{-4}}\)

Required

Write without the exponent

\(\frac{1}{4^{-4}}\)

Apply the following law of indices

\(\frac{1}{a^m} = a^{-m}\)

So, we have:

\(\frac{1}{4^{-4}} = 4^{-(-4)}\)

Evaluate the bracket

\(\frac{1}{4^{-4}} = 4^4\)

\(\frac{1}{4^{-4}} = 256\)

well, from the end of year 5 to the end of year 6 is only 1 year later, so

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+(\frac{r}{100})(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r\)

The positions of the runners on the number line would be:

B <---(0.9)---(1/2)-D---(0)--A---(3/10)-----(0.6)--C->

Draw a straight line with a ruler or straight edge. This will be the base of your number line. Choose a suitable scale or interval to represent the numbers you want to plot. For example, if you are plotting whole numbers between 0 and 10, you could use a scale where each mark on the line represents one unit (1, 2, 3, etc.).

Label the starting point of your number line with the lowest value you want to plot (in this example, 0). Label each mark on the line with the appropriate number according to your scale. Add any necessary labels, such as a midpoint or endpoints, and any other relevant information.

A is 3/10 mile to the right of the midway point (at position 0), so A's position is 3/10. B is 0.9 mile to the left of the midway point, so B's position is -0.9. C is 0.6 mile to the right of the midway point, so C's position is 0.6. D is 1/2 mile to the left of the midway point, so D's position is -0.5.

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The complete question is:

The local charity race has four runners remaining. The table shows how race's total distance.

Runner - Distance to/from Midway Point

A - 3/10 mile past

B - 0.9 mile before

C - 0.6 mile past

D - I/2 mile before

The midway point is represented by 0 on the number line. Drag each value position of each listed runner

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Ans The answer to the question is ###404 bad gateway Step-by-step explanation:

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

y = -2, 1, 4, 7 (in order)

Step-by-step explanation:

Plug in the value of x into the equation to find y.

For example for -1, plug in x as -1 into the equation.

y = 3(x) +1

y = 3(-1) + 1

y = -2

Similarly plug in the x to find the rest of the values for y.

Answer:

8 Batches

Step-by-step explanation:

Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.

Answer:

area of land purchased =247

The area of the land Rachel purchased is approximately 10,055.64 square feet.

We can start by finding the area of one acre in square feet, which is given as 43,560 square feet.

To find the area of 1/5 acre, we can divide 43,560 by 5, which gives us 8,712 square feet.

Since Rachel's land is in the shape of an isosceles triangle, we need to find the base and height of the triangle in order to calculate its area. Let's call the length of the base "b" and the height "h".

We know that the area of a triangle is given by the formula:

Area = (1/2) x base x height

So, we can rearrange this formula to solve for the height:

height = 2 x Area / base

Now we can substitute in the values we know:

Area = 8,712 square feet

base = unknown

height = unknown

We also know that the triangle is isosceles, which means that two of the sides are equal in length. Let's call the length of one of these sides "s". Then the length of the base can be expressed in terms of s as:

base = 2s

We can use the Pythagorean theorem to find the height in terms of s:

s² + (h)² = (2s)²

s² + h² = 4s²

h² = 3s²

h = s x √(3)

Now we can substitute this expression for the height in terms of s into the formula we derived for the area:

Area = (1/2) x base x height

Area = (1/2) x 2s x s x √(3)

Area = s² x √(3)

We know that the area of the triangle is 1/5 of an acre or 8,712 square feet, so we can set this equal to the expression we just derived for the area and solve for s:

s² x √(3) = 8,712

s² = 8,712 / √(3)

s = √(8,712 / √(3))

Now that we know the length of one of the equal sides of the isosceles triangle, we can find the length of the base by multiplying by 2:

base = 2s

base = 2 x √(8,712 / √(3))

Finally, we can substitute in the values we just found for the base and height into the formula for the area of the triangle:

Area = (1/2) x  base x height

Area = (1/2) x 2 x √(8,712 / √(3)) x √(3) x √(8,712 / √(3))

Area = 2 x 8,712 / √(3)

Area = 17,424 / √(3)

Therefore, the area of the land Rachel purchased is approximately 10,055.64 square feet.

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Answer:

A/( 1+rt) = P

Step-by-step explanation:

A = P ( 1+rt)

Divide each side by ( 1+rt)

A/( 1+rt) = P ( 1+rt)/(1+rt)

A/( 1+rt) = P

The level of the sound with the given properties is 200

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

I0 = 10^-12

I = 10^-8

Also, we have the equation to be

β = 10log(I I0)

Substitute the known values in the above equation, so, we have the following representation

β = 10 * log(10^-12 * 10^-8)

Evaluate

β = -200

Hence, the level of sound is -200

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Complete question

use the following information for determining sound intensity. The level of sound β in decibels, with an intensity of I, is given by β = 10log(I I0), where l0 is an intensity of 10^-12 watt per square meter, corresponding roughly to the faintest sound that can be heard by the human ear find the level of sound β. l = 10^-8 watt per m^2 (quiet radio)

Answer: the next term is -1

Answer:

One of the practical situation of geometric series is : A ball bouncing is an example of a finite geometric sequence. Each time the ball bounces it’s height gets cut down by half. If the ball’s first height is 4 feet, the next time it bounces it’s highest bounce will be at 2 feet, then 1, then 6 inches and so on, until the ball stops bouncing

Answer:

Geometric series are seen in practical situations, most notably in those involving geometric growth or decay. If a series of numbers are formed by percentages, then it can result in a geometric sequence. Ex. compound interest (see below).

Step-by-step explanation:

A geometric series is the result of adding the terms of a geometric sequence. These sequences have a common ratio, r, which is used to find missing terms. The common ratio is found with \(r=\frac{a_n}{a_{n-1}}\). For example, \(a_1(r)=a_2, \mbox{ and } a_2(r)=a_3... \mbox{ etc.}\)

Geometric sequences can be used to model practical situations, and such situation could involve geometric growth or decay.

A geometric sequence can be used to model compound interest. An example of this is \(A = P (1 + \frac{r}{100})^n\) where the common ratio, r, of the series is equal to 1 + r/100 in the compound interest formula above.

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is \((e - 2\sqrt{3} )^2\) = f - 20√3.

Expanding the left side of the equation we have:

\((e - 2\sqrt{3} )^2\) = (e - 2√3)(e - 2√3)

= \(e^2\) - 2e√3 - 2e√3 + 12

= \(e^2\) - 4e√3 + 12

Substituting back in the function

\(e^2\) - 4e√3 + 12 = f - 20√3

\(e^2\) - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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True Statements

It has one face that is a decagon.

It has 11 faces.

It has 20 edges.

False Statements

It has two faces that are decagons.

It has 20 vertices.

Answer:

A. It has one face that is a decagon.

C. It has 11 faces.

D. It has 20 edges.

Step-by-step explanation:got it right in edgenuit y

The measure of the reference angle for the angle A = -319° is 41°

What is Reference Angle?

Every angle is measured from the positive part of the x-axis to its terminal line (the line that determines the end of the angle) traveling counterclockwise. For angles in the first quadrant, i.e., angles less than or equal to 90 degrees, the reference angle is equal to the original angle.

The reference angle is always positive

0° to 90°: reference angle = angle

90° to 180°: reference angle = 180° - angle

180° to 270°: reference angle = angle - 180°

270° to 360°: reference angle = 360° - angle

Given data ,

Let the reference angle be = R

Let the angle be represented as A

Now , the value of A is = -319°

And , The reference angle is always positive

So , the value of A = 319°

So , the angle lies in the first quadrant

Now , the reference angle is calculated by

R = 360° - A

Now , the value of the reference angle R = 360° - 319°

The value of R = 41°

Therefore,  the value of R = 41°

Hence , The measure of the reference angle for the angle A = -319° is 41°

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Answer:

C

Step-by-step explanation:

C is the only answer that doesnt share x-values

The angle addition postulate is the best justification for m∠XPD + m∠DPE = m∠XPE.

An angle bisector is a line segment that divides an angle into two equal parts.

The angle addition postulate states, if a line segment is in between an angle sum of two smaller angles created by the line segment, is equal to the measure of the larger angle.

We have an ∠XPE that is divided by a line segment PD which creates two smaller angles ∠XPD and ∠DPE.

∴ By angle addition postulate m∠XPD + m∠DPE = m∠XPE.

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