The difference of x and 3y is 12, and 5x less 2y is 73. What are the values of x and y?

The correct option regarding the probabilities of the two events when they are independent are given by:

C. The probability of getting a red convertible is 0.10.

If two events, A and B, are independent, the probability of both events happening is the multiplication of the separate probabilities of each event happening, that is.

P(A and B) = P(A) x P(B).

For this problem, the separate probabilities are given by:

Then, for them to be independent, we need that:

P(A and B) = 0.25 x 0.40 = 0.10.

A and B means a red convertible car, hence the correct option is:

C. The probability of getting a red convertible is 0.10.

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Memorizing algebra rules can be challenging, but a few strategies may help: Practice, Mnemonics, Repeat, and Use flashcards.

It's important to note that memorizing rules is not the best approach to understanding the concepts, the best approach is to understand the concepts, and the rules will come naturally.

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The solution to the given Inequality is a > 12 and the graph is as attached.

We are given the Inequality as;

8a - 30 > 66

Now, use addition property of equality to add 30 to both sides to get;

8a - 30 + 30 > 66 + 30

8a > 96

Now, use division property of equality to divide both sides by 8 to get;

8a/8 > 96/8

a > 12

The graph of this is as attached.

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Answer:

\(perimetro = \dfrac{(3 + \sqrt{3})m}{2}\)

Step-by-step explanation:

triángulo 30°-60°-90°

\( 1~:~\sqrt{3}~:~2 \)

\( 1m~:~m\sqrt{3}~:~2m \)

\( \dfrac{m}{2}~:~\dfrac{m\sqrt{3}}{2}~:~m \)

\(perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + m\)

\(perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + \dfrac{2m}{2}\)

\(perimetro = \dfrac{m + m\sqrt{3} + 2m}{2}\)

\(perimetro = \dfrac{3m + m\sqrt{3}}{2}\)

\(perimetro = \dfrac{(3 + \sqrt{3})m}{2}\)

The vertical line that splits the parabola in half is called the "axis of symmetry."

The line of symmetry that divides a parabola in half as "The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola".

A parabola is an approximately U-shaped, mirror-symmetrical plane curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form. A parabola's general equation is written as y = a(x - h)² + k or x = a(y - k)²+ h. Vertex here is indicated by (h, k).

Therefore, The vertical line that splits the parabola in half is called the "axis of symmetry."

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The term that fills in the blank is axis of symmetry.

When graphing a parabola, the vertical line that splits the parabola in half is called the axis of symmetry. The axis of symmetry is a vertical line that passes through the vertex of the parabola. It divides the parabola into two symmetrical halves.

The equation of the axis of symmetry can be found using the formula x = -b/2a, where a and b are coefficients of the quadratic equation in standard form.

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Answer:

1000

Step-by-step explanation:

Okay so let's put T as TOTAL tickets

1800+1500+3T

To make it easier lets do this

3300+3T

total earnings is 5T+1300

So now the problem is this

3300+3T=5T+1300

Lets take away 1300 from both sides

3300-1300 = 2000

1300-1300 = 0

2000+3T=5T

Lets now take 3T from both sides

3T = 3T = 0

5T - 3T = 2T

now we have

2000=2T

Divide both sides by 2

1000=T

The team must sell 1000 tickets to break even

The missing portion that completes the proof are:

1.  Vertical angles are congruent

2. ASA congruence theorem

A proof that can be used in proving some given statement involves some statements on the left column and the corresponding reasons that justify such statements.

Below shows how to prove that triangle CAB and DEB are congruent to each other.

Statement                                Reason                                        

AC║DE                                    Given

AB ≅ EB                                  Given

∠A ≅ ∠E                                  Alternate interior angles are congruent

∠ABC ≅ ∠EBD                        Vertical angles are congruent

ΔCAB ≅ ΔDEB                        ASA congruence theorem

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The missing values of the similar triangles is x = 20/3 and y = 4.5

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔXYZ

Now , the corresponding sides are

15 / 10 = y / 3

Multiply by 3 on both sides , we get

y = 45 / 10

y = 4.5

Now , for the similar triangles , corresponding sides of similar triangles are in the same ratio

And , 2 / 3 = x / 10

Multiply by 10 on both sides , we get

x = 20/3

Hence , the similar triangles are solved

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If It is estimated that only 9/20 of the people who attempt to climb a certain mountain actually reach the summit. If 140 people attempt the​ climb, The number of people that are  expected to reach the​ summit is 63.

Let x present the expected number of people to reach the summit

Hence,

9  /20 = x  /140

Cross multiply            

20x = 1260

Divide both side by 20x

x = 1260 / 20

x =  63 people

Therefore the number of people are 63 people.

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Answer:

For right angle triangle,

we use Pythagoras theorem that is:

\(c^{2} =a^{2} +b^{2}\)

c = \(\sqrt{a^{2} +b^{2} }\)

For question 1:

c = ?

a = 40

b = 9

putting them in formula,

c = \(\sqrt{40^{2} + 9^{2} }\)

c = 41

For question 2:

c = ?

a = 12

b = 13

putting them in formula,

c = \(\sqrt{12^{2} + 13^{2} }\)

c = approximately 17.69181

For question 3:

c = 35

a = 20

b = ?

putting them in formula,

\(c^{2} =a^{2} +b^{2}\)

\(35^{2} = 20^{2} + b^{2}\)

1225 = 400 + \(b^{2}\)

\(b^{2}\) = 1225 - 400

\(b^{2}\) = 825

\(\sqrt{b^{2} } = \sqrt{825}\)

b = 5 \(\sqrt{33}\)

For question 4:

c = 37

a = 20

b = ?

putting them in formula,

\(c^{2} =a^{2} +b^{2}\)

\(37^{2} = 20^{2} + b^{2}\)

1369 = 400 + \(b^{2}\)

\(b^{2}\) = 1369 - 400

\(b^{2}\) = 969

Taking square root on both sides

b = 31.12

Hope it helps.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{1}{3}}}}}} \)

Step-by-step explanation:

\( \sf{ \frac{2}{3} + ( - \frac{1}{3} )}\)

We know that \( \sf{( + ) \times ( - ) = ( - )}\)

\( \dashrightarrow{ \sf{ \frac{2}{3} - \frac{1}{3}} }\)

While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same.

\( \dashrightarrow{ \sf{ \frac{2 - 1}{3}}} \)

\( \dashrightarrow{ \boxed{ \sf{ \frac{1}{3}}}} \)

Hope I helped!

Best regards! :D

The sum of 2/3 + (-1/3) in fraction form is 1/3 after applying the arithmetic operation, the answer would be 1/3.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The number expression is:

= 2/3 + (-1/3)

= 2/3 - 1/3

Taking 3 as LCM

After simplification:

= (2 - 1)/3

= 1/3

Thus, the sum of 2/3 + (-1/3) in fraction form is 1/3 after applying the arithmetic operation, the answer would be 1/3.

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If baskets B and C are on the same indifference curve and preferences satisfy all four of the basic assumptions in economics, it means that the individual considers both baskets equally preferable and is indifferent between them.

In economics, an indifference curve represents a set of combinations of goods or baskets that provide the same level of utility or satisfaction to an individual. If baskets B and C are on the same indifference curve, it means that the individual derives the same level of satisfaction from both baskets.

The four basic assumptions in economics regarding preferences are completeness, transitivity, more is better, and diminishing marginal rate of substitution. Completeness assumes that individuals can rank any two baskets in terms of preference. Transitivity suggests that if an individual prefers basket A to B and basket B to C, then the individual also prefers basket A to C. The assumption of "more is better" implies that individuals prefer more of a good to less. Diminishing marginal rate of substitution posits that as an individual consumes more of one good, they are willing to give up less of the other good to maintain the same level of satisfaction.

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The complete question is:

Consider the following three market baskets:

Food Clothing

A 6 3

B 8 5

C 5 8

If preferences satisfy all four of the basic assumptions:

A. A is on the same indifference curve as B.

B. B is on the same indifference curve as C.

C. A is preferred to C.

D. B is preferred to A.

E. Both A. and B. are correct.

Answer:

32x = 16 x = 0.5

The actual heart is 0.5 feet or 6 inches.

Step-by-step explanation:

a) the margin of error is 1.675. b) the sample mean is 22.425. c) If the true mean turned out to be 19.45, I would be surprised.

a) The margin of error can be found by taking the difference between the upper limit and the lower limit of the confidence interval and dividing by 2. So, the margin of error is (24.10 - 20.75)/2 = 1.675.

b) The sample mean can be found by taking the average of the upper limit and the lower limit of the confidence interval. So, the sample mean is (24.10 + 20.75)/2 = 22.425.

c) If the true mean turned out to be 19.45, I would be surprised because it falls outside of the 95% confidence interval (20.75, 24.10). This means that there is only a 5% chance that the true mean would fall outside of this interval, so it would be surprising if it did.

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The kinetic energy of the volleyball is 945 joules.

To calculate the kinetic energy of the volleyball, we can use the formula:

Kinetic Energy = 1/2 \(\times\) mass \(\times\) velocity^2

Mass of the volleyball (m) = 2.1 kg

Velocity of the volleyball (v) = 30 m/s

Plugging these values into the formula, we have:

Kinetic Energy = 1/2 \(\times\) 2.1 kg \(\times\) (30 m/s)^2

Simplifying the equation:

Kinetic Energy \(= 1/2 \times 2.1 kg\)  times \(900 m^2/s^2\)

Kinetic Energy \(= 0.5 \times2.1 kg \times 900 m^2/s^2\)

Kinetic Energy = 945 J (joules)

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The formula that expresses the billing rate to a customer who requires an hour of work is $110 + $8.80, which equals $118.80.

To express the billing rate for a customer who requires an hour of work, we can use the given information. The computer technician charges a $30 initial consulting fee and $40 for every half-hour of labour performed. We need to calculate the total cost for one hour of work, including the sales tax.

Calculate the labour cost for one hour. Since the technician charges $40 for every half-hour, the cost for one hour (which is equivalent to two half-hours) would be $40 x 2 = $80.

Add the initial consulting fee to the labour cost. The initial consulting fee is $30.
Calculate the subtotal by adding the labour cost and the initial consulting fee: $80 + $30 = $110.

Add the sales tax. The sales tax is 8% of the subtotal. To calculate the sales tax amount, multiply the subtotal by 8% (or 0.08): $110 x 0.08 = $8.80.

Calculate the total amount to be paid by adding the subtotal and the sales tax: $110 + $8.80 = $118.80.

The formula that expresses the billing rate to a customer who requires an hour of work is $110 + $8.80, which equals $118.80.

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Answer:

p+q = 38/15

Step-by-step explanation:

2/3+p = 1. p = 1 - 2/3

4/5 + q = 3. q = 3 - 4/5

p + q = 1 - 2/3 + 3 - 4/5

-2/3 - 4/5 (common denominator = 15)

4 - 10/15 - 12/15 = 4 - 22/15

4 - 22/15 = (4*15 - 22)/15

= 38/15

The last set should not be the angle of the measurements of triangle ABC i.e. Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees

If we add the three sides of triangle so its total should be 180 degrees

So

= 55 + 65 + 60

= 180

Now

= 60 + 60 + 60

= 180

Now

= 57 + 58 + 65

= 180

And,

= 61 + 57 + 61

= 181

Therefore, The last set should not be the angle of the measurements of triangle ABC i.e. Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees

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Answer: its A

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm pretty

a. Let's check whether the given pairs are in the relation S or not.

Is 2 S 2?

To check if (2, 2) is in S, we need to evaluate the expression:

(1/2) - (1/2) = 1/2 - 1/2 = 0

Since 0 is an integer, (2, 2) is in S.

Is -1 S -1?

To check if (-1, -1) is in S, we need to evaluate the expression:

(1/-1) - (1/-1) = -1 - (-1) = 0

Since 0 is an integer, (-1, -1) is in S.

Is (3, 3) ∈ S?

To check if (3, 3) is in S, we need to evaluate the expression:

(1/3) - (1/3) = 1/3 - 1/3 = 0

Since 0 is an integer, (3, 3) is in S.

Is (3, -3) ∈ S?

To check if (3, -3) is in S, we need to evaluate the expression:

(1/3) - (1/-3) = 1/3 + 1/3 = 2/3

2/3 is not an integer, so (3, -3) is not in S.

b. Set of ordered pairs S:

S = {(x, y) | (1/x) - (1/y) is an integer}

S = {(2, 2), (-1, -1), (3, 3)}

c. Domain and Co-domain of S:

Domain of S: The set of all first components (x-values) of the ordered pairs in S.

Domain of S = {-3, -2, -1, 1, 2, 3}

Co-domain of S: The set of all second components (y-values) of the ordered pairs in S.

Co-domain of S = {-3, -2, -1, 1, 2, 3}

d. Arrow diagram for S:

Domain (C): {-3, -2, -1, 1, 2, 3}

Co-domain (D): {-3, -2, -1, 1, 2, 3}

(2, 2) -----> (0)  // 0 represents an integer

(-1, -1) -----> (0)

(3, 3) -----> (0)

(3, -3) -----> (2/3)  // 2/3 is not an integer

Note: The arrow diagram helps visualize the mapping of elements from the domain to the co-domain based on the relation S. Arrows point from the element in the domain to the result of the expression (integer or not integer) in the co-domain.

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The unknown angles of the right angle triangle is 45 degrees.  

A right angle triangle is a triangle with one angle equals to 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the right triangle has two angle measurements that are equal to each other. The third angle is 90 degrees.

Therefore, let's find the angles measure x, the two other equal angles.

Hence,

x + x + 90 = 180

2x + 90 = 180

subtract 90 from both sides of the equation

2x + 90 = 180

2x + 90 - 90 = 180 - 90

2x = 90

divide both sides by 2

x = 90 / 2

x = 45 degrees

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Answer:

B.2x-5=x+25

Step-by-step explanation:

2x+15=35            x = 10

4/5x=8                x = 10

2x-5=x+25          x = 30

2x+7=27             x = 10

4/3x=x+10/3       x = 10

Answer:

3t

Step-by-step explanation:

The algebraic expression to show the number of tomatoes Tye planted this year is 3t

From the first statement given in the question, we were told that:

From the above statement, we can write the algebraic expression to show the number of tomatoes Tye planted this year. This is shown below:

Number of tomatoes planted this year = 3 × Number of tomatoes planted last year

= 3t

Thus, from the above illustration we can say that the algebraic expression is 3t

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The conclusion that can be drawn from this graph on the long-run frequency of 100 rolls is The long-run frequency of rolling a 3 appears to be about 0.17.

At the 0.17 probability, the proportion of 3s calculated levels off from around the 40th roll to the 100th roll.

This means that the long-run frequency of rolling a 3 is around 0.17 because this was the probability seen for most of the rolls over time.

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Answer:

month 4

Step-by-step explanation:

I took the test

Answer:

Its month 4 on edge.

Step-by-step explanation:

The approximate side length of the square game board is 13 inches.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is side².

We have,

Area of a square game board = Side².

Area of the square = 162 inches²

Now,

Side² = 162 inches²

Side = √162 inches

Side = 12.73 inches

Side = 13 inches

Thus,

The side length of the square game board is 13 inches.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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a) The sampling distribution of p is approximately normal, with a mean of 0.47 and a standard deviation of 0.0158.

The correct option is (A): Approximately normal, 0.47 and 0.0158

b) The probability of obtaining x ≥ 510 individuals with the characteristic is 0.9886.

c) The probability of obtaining x ≤ 440 individuals with the characteristic, P(x ≤ 440) is 0.0446.

(a) The sampling distribution of the proportion (p) can be approximated by a normal distribution using the formula:

σp = √((p * (1 - p)) / n)

where p is the population proportion and n is the sample size.

p = 0.47

n = 1000

σp = √((0.47 * (1 - 0.47)) / 1000)

σp ≈ √(0.2494 / 1000)

σp ≈ √(0.0002494)

σp ≈ 0.0158

(b) The probability of obtaining x ≥ 510 individuals with the characteristic is obtained using the normal distribution and converted to a standard normal distribution by applying the Z-score.

Z = √(x - np) / (np(1-p))

where

x = 510

n = 1000

p = 0.47

Z = (510 - 1000 * 0.47) / √(1000 * 0.47 * (1 - 0.47))

Z = (510 - 470) / √(1000 * 0.47 * 0.53)

Z = 40 / √(249.1)

Z ≈ 2.2678

Using a calculator, the probability corresponding to Z = 2.2678 is approximately 0.9886.

(c) The probability of obtaining x ≤ 440 individuals with the characteristic is obtained using the normal distribution and converted to a standard normal distribution by applying the Z-score.

Z = (440 - 1000 * 0.47) / √(1000 * 0.47 * (1 - 0.47))

Z = (440 - 470) / √(1000 * 0.47 * 0.53)

Z = -30 / √(249.1)

Z ≈ -1.7002

Using a calculator, the probability corresponding to Z = -1.7002 is 0.0446.

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Step-by-step explanation:

D

a triangle is 180°

180-126= 54

Now you have:

56+54+X=180

110+X=180

-110 -110

X=70

Answer:

70 wanna know why add the sides then divide

Step-by-step explanation: