Select the zero that satisfies the given equation 2 + 3(2x + 1) = 3(× + 2)?

Answer:

C. 4(x + y)

Step-by-step explanation:

Use the distributive property.

4(x + y) = 4x + 4y

Answer:

C. 4(x + y)

Step-by-step explanation:

If you multiply this answer out (4 times x and 4 times y) it is the equivalent to 4x + 4y.

Answer:

h=11x3

Step-by-step explanation:

just answered it for someone else 30 minutes ago

Answer:

Possible

Step-by-step explanation:

The rule for triangle side lengths is that the two shortest sides must add up to the longest side so it is possible because

3+7 = 10

Two short sides = The longest side

Answer:

possible

Step-by-step explanation:

3+7= 10

The statement that can be deduced to confirm parallel lines based on the given information is: a) AD ||  DC

When two lines are intersected by a transversal, the angles formed at the intersection can provide information about the relationship between the lines. In this case, we are given the information that the measure of angle 3 (m<3) is equal to the measure of angle b (m<b).

According to the property of corresponding angles, when two parallel lines are intersected by a transversal, the corresponding angles formed at the intersection are congruent. In other words, if the measure of angle 3 is equal to the measure of angle b, it indicates that lines AD and DC are parallel.

By observing that the measures of angle 3 and angle b are equal, we can deduce that line segment AD is parallel to line segment DC.

This conclusion is based on the fact that the corresponding angles formed by the transversal (in this case, line AB) cutting the two lines (AD and DC) are congruent, indicating parallelism between the lines.

Therefore, the statement "AD || DC" can be deduced from the given information about the measures of angle 3 and angle b.

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The complete question is:

Using the information given, select the statement that can be deduced to confirm parallel lines.

When m<3 = m<b, which of the following statements is correct?

a) AD || DC

b) AB || BC

c) None

35x + 65y = 815 and x + 7 = y are the system of equations that can be used to find the number of boxes.

What is an algebra?

One of the many different mathematical disciplines is algebra. Algebra is, broadly stated, the study of mathematical symbols and the guidelines for applying those symbols to formulas.

Given,

The weight of each small box = 35 pounds
The weight of each large box = 65pounds
The total weight of the boxes = 815pounds
There were7 times as many small boxes shipped as large boxes
Let 'x' be the number of small boxes and 'y' be the number of large boxes
The weight of 'x' small boxes = 35x pounds
The weight of 'y' large boxes = 65y pounds
The total weight of the two types of  boxes together = 35x+65y

Since the total weight of the boxes is 815 pounds, we have
35x+65y = 815---------------------(1)

Since 7 more small boxes =   large boxes, hence we have,
x + 7 = y ------------------------(2)
Solving both the equations we get,

x = 3.95 or 4
and, y = 10.95 or 11

The number of large boxes shipped = 11

The number of small boxes shipped  = 4

∴ The number of small boxes shipped = 4 and the number of large boxes shipped = 11.

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Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

This is an example of a theoretical probability.

Theoretical probability is calculated based on the possible outcomes and their likelihood without conducting any experiments or observations. In this case, the probability of getting a tail on the coin is 1/2 (since there are 2 sides) and the probability of getting a 2 on the six-sided die is 1/6 (since there are 6 sides).

To find the combined probability, you multiply the individual probabilities: (1/2) * (1/6) = 1/12, which equals approximately 8.3%.

This is an example of a theoretical probability, as it is based on the assumption of a fair six-sided die and a fair coin. The probability of getting a tail on the coin is 0.5, and the probability of rolling a 2 on the die is 1/6.

Multiplying these probabilities gives a theoretical probability of 0.5 ×1/6 = 1/12, which is equivalent to 8.3% (rounded to one decimal place).

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Answer:

D

Step-by-step explanation:

Think of how you might express a line in a formula, there are many ways to do it but the only form the answers have is in the slope intercept form or

y=mx + b

Only B, D, and E fit this form so A and C can now be eliminated.

where m is the slope of a line and b is the y intercept of the line.

Here we see that the y intercept (or where the line hits the y-axis) is 0 so it should not have any constant b. This means it should be of the form

y = mx.

Finally, to find the slope m we use the rise over run of the slope of the line which can be put algebraically as

\(\frac{y_2-y_1}{x_2-x_1}\)

Where two points (x2, y2) and (x1, y1) are essentially being subtracted to give a slope. x2 and y2 are to the right of x1 and y1 to give the slope going from left to right.

On the graph we can see that the points with whole numbers are (0,0) (3,2), and (4,6). So we know that our answer must have x2 y2 and x1 y1 as whole numbers because those are the only options in our answers.

Although B uses the points (3,2) and (4,6) it subtracts them backwards with (3,2) as (x2,y2) instead of them acting as (x1,y1). This gives the slope from right to left which we do not want.

E puts x in the top part of the equation in the form  \(\frac{x_2-x_1}{y_2-y_1}\) which is not the formula used to find slope which is why E is incorrect.

From this, we figure out that the only answer that has one of the options of the form \(\frac{y_2-y_1}{x_2-x_1}\) is answer D because it has the points (4,6) and (0,0) in the right order.

Answer:

b) 22

Step-by-step explanation:

180 = (4x+12) + (3x+14)

180 = 7x + 26

7x = 154

x=22

The most reasonable interpretation is c) there is a 0.60 probability that it will rain somewhere in the author's region at some point during the day.

The statement from Weather.com indicates that there is a chance of rain for the author's home region.The statement does not provide any information on the duration of the rain or how much of the region will be affected.

The use of the word "chance" suggests that there is a probability involved.Option a. assumes that 60% of the region will get rain, which is not supported by the statement.

Option b. assumes that it will rain for 60% of the day, which is also not supported by the statement.Option c. correctly reflects the probability aspect of the statement, indicating that there is a 0.60 probability that it will rain somewhere in the region at some point during the day.

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Answer:

(72-40) = 8 x (9-5)

Step-by-step explanation:

GCF = 8

(72-40) = 8 x (9-5)

For the estimator s_0 to be unbiased, the condition is that the coefficient of y, denoted as d, should be equal to zero.

3a) To determine when s_0 is an unbiased estimator of y, we need to calculate its expected value E(s_0) and check if it equals y.

The estimator s_0 is given by s_0 = c + dy. We want to find the values of c and d such that E(s_0) = E(c + dy) = y.

Taking the expectation of s_0, we have:

E(s_0) = E(c + dy) = c + dE(y)

Since E(y) = μ, where μ represents the population mean, we can rewrite the equation as:

E(s_0) = c + d*μ

For s_0 to be an unbiased estimator, E(s_0) should be equal to the true population parameter y. Therefore, we require:

c + d*μ = y

This equation implies that c should be equal to y minus d multiplied by μ:

c = y - d*μ

Substituting this value of c back into the expression for s_0, we get:

s_0 = (y - dμ) + dy = (1 + d)y - dμ

To make s_0 an unbiased estimator, we need the coefficient of y, (1 + d), to be equal to zero:

1 + d = 0

d = -1

Therefore, the condition for s_0 to be an unbiased estimator is that d = -1.

3b) With d = -1, we substitute this value back into the expression for s_0:

s_0 = (-1)*y + y = y

This means that the estimator s_0, now a function of c only, simplifies to y, which is the true population parameter.

The variance of s_0 in terms of σ^2 and d can be calculated as follows:

Var(s_0) = Var((-1)y + y) = Var(0y) = 0*Var(y) = 0

Therefore, the variance of s_0 is zero when d = -1.

Intuition: When d = -1, the estimator s_0 becomes a constant y. Since a constant has no variability, the variance of s_0 becomes zero, which means the estimator perfectly estimates the true population parameter without any uncertainty.

3c) When Var(y1) = σ1^2 and Var(y2) = σ2^2 are unequal, we can find the value of d that minimizes the variance expression for s_0.

The variance of s_0 in terms of σ1^2, σ2^2, and d is given by:

Var(s_0) = Var((1 + d)y - dμ) = [(1 + d)^2 * σ1^2] + [(-d)^2 * σ2^2]

Expanding and simplifying the expression, we get:

Var(s_0) = (1 + 2d + d^2) * σ1^2 + d^2 * σ2^2

To find the value of d that minimizes the variance, we differentiate the expression with respect to d and set it equal to zero:

d(Var(s_0))/dd = 2σ1^2 + 2d * σ1^2 - 2d * σ2^2 = 0

Simplifying further, we have:

2σ1^2 + 2d * (σ1^2 - σ2^2) = 0

Dividing both sides by 2 and rearranging, we find:

d = -σ1^2 / (σ1^2 - σ2^2)

Therefore, the value of d that minimizes the variance expression is -σ1^2 / (σ1^2 - σ2^2).

Intuition: The value of d that minimizes the variance depends on the relative sizes of σ1^2 and σ2^2. When σ1^2 is much larger than σ2^2, the denominator σ1^2 - σ2^2 becomes positive, and d will be a negative value. On the other hand, when σ2^2 is larger than σ1^2, the denominator becomes negative, and d will be a positive value. This adjustment in d helps balance the contribution of y1 and y2 to the estimator, considering their respective variances.

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Answer:

value if x is -21.25.

...............

Answer:

AAS

Step-by-step explanation:

Answer:

3/10? I'm pretty sure thats the easiest way to write it without doing to much work.

Answer:

write 30% as it's fraction, as simply as possible​

Step-by-step explanation:

Analysis of variance (ANOVA) is a statistical tool used to test for equality of means across multiple groups or populations. This test helps to determine whether the observed differences between the means of different groups are statistically significant or simply due to chance.

ANOVA calculates the variation or deviation in the means of different groups by comparing the variance within the groups to the variance between the groups.

In ANOVA, the population is the entire group of individuals or objects that are being studied. For example, if we are comparing the means of three different age groups, the population would be all individuals in those three age groups.

ANOVA looks at the variance between these groups and within each group to determine if there is a statistically significant difference in means.

When conducting an ANOVA, standard deviations, variances, and means are all important measures of central tendency and variability. Standard deviations and variances are used to calculate the within-group variation and between-group variation.

Proportions, on the other hand, are not used in ANOVA as this test is specifically designed for continuous data, such as means.

Overall, ANOVA is a useful tool for analyzing differences in means across multiple populations.

By calculating the deviation or variation between and within groups, it can help researchers determine whether observed differences are statistically significant or not.

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There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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To ensures the function is continuous at x = 4, g(4) is equal to 136,

To define g(4) such that the function is continuous at x = 4, we need to find the value of g(4) that makes the function continuous at that point.

The given function is defined as: f(x) = 2x - 32, for x < 4 , f(x) = 9x^2 - 8, for x ≥ 4. To make the function continuous at x = 4, we set g(4) equal to the value of the function at that point. g(4) = f(4)

Since 4 is equal to or greater than 4, we use the second part of the function:

g(4) = 9(4)^2 - 8

g(4) = 9(16) - 8

g(4) = 144 - 8

g(4) = 136

Therefore, g(4) is equal to 136, which ensures the function is continuous at x = 4.

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The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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Twelve horses will take 18 hours to consume 36 bales of hay.

Given,Six horses eat 12 bales of hay in 12 hours We need to find,

Let's assume that 1 horse will eat 1 bale of hay in x hours.

As we know,6 horses will eat 12 bales of hay in 12 hours.

Now we can find x as follows:

For 1 horse, 1 bale of hay is consumed in x hours

So, for 6 horses, 6 bales of hay will be consumed in x hours.

Then,6 horses consume 12 bales of hay in 12 hours6 horses consume 6 bales of hay in 6 hours1 horse consumes 1 bale of hay in 6 hours

Now we have to find how many hours will 12 horses take to eat 36 bales of hay.

If 1 horse eats 1 bale of hay in 6 hours, then 12 horses will consume 12 bales of hay in 6 hours.

Therefore, 12 horses will consume 36 bales of hay in 18 hours.

So, the answer is: Twelve horses will take 18 hours to consume 36 bales of hay.

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4. f(x,y) is homogeneous of degree 2.

5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:

A function is said to be homogeneous of degree k, if it satisfies the condition:

f(tx,ty) = \(t^k\)f(x,y)

We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:

f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)

Hence f(x,y) is homogeneous of degree 2.

5. Which of the following functions f(x,y) are homothetic? Explain.

(a) f(x,y)=\((xy)^2\)+1

(b) f(x,y)=\(x^2+y^3\)

Let us first understand the meaning of homothetic transformation.

A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.

Let’s now find out whether the given functions are homothetic or not.

(a) f(x,y)=\((xy)^2\)+1

In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:

f(x,y) = g(h(x,y))

where g is a strictly monotonic function and h is a homogeneous function with degree 1

We have

f(x,y) = \((xy)^2\)+1

Let’s assume g(x) = x - 1, then g(x+1) = x

Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)

Now, we have

g(h(x,y)) = h(x,y) - 1 = (xy) - 1

Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

(b) f(x,y)=\(x^2+y^3\)

We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.

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In linear equation , the car y's price changes the most.

What are a definition and an example of a linear equation?

According to the question

a)  Car x : £ 10320  ≈  £ 10300        10320 - 10300 = 20

    Car y  : £ 15430 ≈ £ 15400          15430 - 15400 = 30

    Car z   :  £ 17490 ≈  £ 17500        17490 - 17500  = 10

                   10 < 20 < 30

so the car y's price changes the most.

b) this car's price change £ 30

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Answer:

Step-by-step explanation:

12. all angles are the same size.

all ik sry

Answer:

113.04 square inches

Step-by-step explanation:

The diameter of the circle is 12 inches, so the radius is (1/2) * 12 = 6 inches. The area of this circle is approximately 3.14(6^2) = 3.14 * 36 = 113.04 square inches.

For the given scenario: the Probability of making both shots are A. 0.64 and B. 0.72

a) If a player makes 80% of his foul shots, the probability of making a single foul shot is 0.8. Since the two shots are considered independent events, the probability of making both shots is the product of the individual probabilities.

Therefore, the probability of making both shots is 0.8 * 0.8 = 0.64.

To calculate the probability of making exactly one shot, we need to consider two scenarios: making the first shot and missing the second, or missing the first shot and making the second. Each scenario has a probability of 0.8 * 0.2 = 0.16.

Therefore, the probability of making exactly one shot is 0.16 + 0.16 = 0.32.

Similarly, the probability of missing both shots is 0.2 * 0.2 = 0.04.

b) In this case, the outcome of the second shot depends on the outcome of the first shot. If the player makes the first shot (with a probability of 0.8), the probability of making the second shot is 0.9.

Therefore, the probability of making both shots is 0.8 * 0.9 = 0.72.

If the player misses the first shot (with a probability of 0.2), the probability of making the second shot is 0.7.

Therefore, the probability of making exactly one shot is 0.2 * 0.7 = 0.14.

Since there are only two possible outcomes (making both shots or making exactly one shot), the probability of neither shot being made is 1 - (0.72 + 0.14) = 0.14.

Therefore, for the given scenario:

a) Probability of making both shots: 0.64

  Probability of making exactly one shot: 0.32

  Probability of missing both shots: 0.04

b) Probability of making both shots: 0.72

  Probability of making exactly one shot: 0.14

  Probability of missing both shots: 0.14

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Answer:

60

Step-by-step explanation:

30% of total boxes at the store is equal to 18

so

\((30 \div 100 ) \times x = 18 \\ x = 18 \times( 100 \div 30) = \\ 18 \times (10 \div 3) = \\ 6 \times 10 = 60\)

The 18 boxes of cereal Isaac purchased. This represents 30% of all the boxes in the store then total boxes of cereal at the store exists 60.

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. To exstimate a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

The total no of boxes =  y × 100/x

Given x = 30%

y = 18 boxes

Total boxes at the store = 18 × 100/30 = 60

Therefore, the total boxes of cereal at the store exists 60.

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The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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The probability of spinning a yellow on the spinner in the diagram is 1/8.

Probability is the ratio of the required outcome to the total possible outcome. It gives a measure of how probable a certain item or event can be obtained from a series of events.

Mathematically,

Probability = Required outcome / Total possible outcomes

Here ,

Total possible outcomes = 8

Required outcome = Yellow segment = 1

Probability(Yellow ) = 1/8

Hence, probability of spinning a yellow is 1/8.

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she receives 15 rupees as the balance , The price of one apple is 27 rupees.

Let x represent the price of one apple. The equation for the given problem can be written as follows:

5x + 15 = 150

In this equation, 5x represents the total cost of 5 apples, and 15 represents the balance received by Alan. The equation states that the sum of the total cost and the balance should be equal to the amount paid by Alan, which is 150 rupees.

To solve the equation, we can first subtract 15 from both sides to isolate the term 5x:

5x = 150 - 15

5x = 135

Next, we can divide both sides by 5 to solve for x:

x = 135 / 5

x = 27

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