The base of a triangle is seven less than twice its height. If the area of the triangle is 102 cm2, find the length of the base.

The first number will be \(\frac{11}{2}\) and the second number will be \(-\frac{5}{4}\).

Let the first number be x and the second number be y.

According to the question,

Since seven times the first number plus six times the second number equals 31. So,

\(7x+6y=31.......(1)\)

Similarly,Three times the first number minus ten times the second number is 29.So,

\(3x-10y=29.......(2)\)

Multiplying equation (1) by 3 and equation (2) by 7, we get

\(21x+18y=93\)

\(21x-70y=203\)

Now subtracting both the equations we get,

\(88y=-110\)

\(y=-\dfrac{110}{88}\)

\(y=-\dfrac{5}{4}\)

putting the value of x in equation (1) we get,

\(7x+6\times-\dfrac{5}{4} =31\)

\(7x-\dfrac{15}{2}=31\\\)

\(7x=31+\dfrac{15}{2}\)

\(7x=\dfrac{77}{2}\)

\(x=\dfrac{11}{2}\)

Hence the first number is \(\frac{11}{2}\) and the second number is \(-\frac{5}{4}\).

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Answer:

\(x = \$28.5\)

Step-by-step explanation:

Given

Variation: Direct Proportion

\(3.2m = \$38\)

Required

Determine the cost of 2.4m length

Represent the cost of 2.4m length with x

So, we have:

\(3.2m = \$38\)

and

\(2.4m = x\)

Cross Multiply:

\(3.2m * x = \$38 * 2.4m\)

\(3.2 * x = \$38 * 2.4\)

Solve for x

\(x = \frac{\$38 * 2.4}{3.2}\)

\(x = \frac{\$91.2}{3.2}\)

\(x = \$28.5\)

Hence, the cost of 2.4m length is $28.5

The graph of the function I = √(P/4) is attached accordingly.

The equation I = √(P/4) represents an inverse relationship between the variables I ad P, where I is the current and   P is the power.

As the power P increases, the current I will increase as well, but at a decreasing rate. T his can be seen in the shape of the graph, which is a curve that starts off steep and gradually levels out as P increases.

Conversely, as the power P decreases, the current I will also decrease, but again at a decreasing rate.

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The expression that represents this week's price, in dollars, of a gallon of gasoline is 1.05g.

Given that last week, the price, in dollars, of a gallon of gasoline was g. This week, the price of gasoline per gallon increased by 5%.We are to find which expressions represent this week's price, in dollars, of a gallon of gasoline.

If the price of gasoline per gallon last week was g, and it has increased by 5% this week, then this week's price of gasoline per gallon will be 5% greater than last week's price, which is equal to 1.05 times the price of last week's gasoline per gallon.Therefore, this week's price, in dollars, of a gallon of gasoline is given by the expression 1.05g.

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"The heavens proclaim God's glory; the skies proclaim the work of his hands." They pour forth speech day after day, and unveil knowledge night after night. They have no speech, no words, and no sound is heard from them. Nonetheless, their voice reaches all over the world, and their words reach all the way to the ends of the planet. God has set up a tent for the sun in the heavens. It's like a newlywed emerging from his bedroom, or a champion joyful to run his race. It rises at one end of the heavens and circles back; nothing is bereft of its warmth."

This paraphrase captures the essence of the verses, emphasizing the declaration of God's glory through the beauty and order of the heavens, the continuous revelation of knowledge, and the symbolism of the sun's journey across the sky.

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Answer:

The answer is 452.16 cm³.

Formula to calculate the volume of cone = V = πr²x h/3

Now r = 6 cm and h = 12cm, and value of π = 3.14

By putting the values,

V = (3.14) (6)² (12/3) = (3.14)(36)(4)

Answer:

452.39cm^3

Step-by-step explanation:

Hope this helps :-)

The extent to which the researcher can refer that findings with a sample from which it was drawn is referred to as generalizability.

Generalizability refers to the ability to extrapolate study findings from a sample to the entire population. It also refers to the capacity to apply findings from one study to a similar environment in a different investigation.

Generalizability and transferability are two research traits that are related. When considering generalizability in research, there are two features or dimensions to consider: generalizability as it relates to the specific population on which the research is conducted, and generalizability on a global scale.

Such studies will be easier to generalize if the researcher uses adequate sampling approaches, sample sizes, and exact processes.

In general, a study has strong generalizability when the findings apply to a wide range of persons or situations. The study has weak generalizability if the results can only be applied to a subset of the population or in a very specific circumstance.

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The first and second polygons are exactly the same, the only difference is that the second is bigger! If we look right the first polygon is 4 cm and the second is triple which means that we will have to triple the area of ​​the First polygon to discover the area of ​​the second polygon!

if the first polygon is 4 cm long and the second 12 cm means that the second polygon has three times the area of ​​the first polygon!

\((4 cm.3=12 cm)\\A-10 cm^{2}.3=30 cm^{2}\)

the second polygon has \(30 cm^{2}\)  of area

\(A=30 cm^{2}\)

The median is a statistical measure that represents the middle value of a dataset.

The median is a statistical measure that represents the middle value of a dataset. To find the median, you need to first arrange the data in ascending or descending order, and then find the value that lies exactly in the middle.

The calculation of the median is different depending on whether the dataset has an even or odd number of values.

If the dataset has an odd number of values. Then the median is simply the middle value. If the dataset has an even number of values, then the median is the average of the two middle values.

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Answer:

A        5 StartRoot 3 EndRoot units

Step-by-step explanation:

Answer:

5√3 units

Step-by-step explanation:

edgeee

The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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The number of ways integer points can be assigned to the 12 problems, given that the total points is 100 and each problem is worth at least five points, can be calculated using a combinatorial approach.

To determine the number of ways, we can use the concept of stars and bars, which is a combinatorial technique used to distribute indistinguishable objects into distinguishable groups. In this case, the stars represent the total points (100) and the bars represent the dividers between the problems.

Since each problem is worth at least five points, we can consider a minimum of five points already assigned to each problem. This means we need to distribute the remaining points (100 - 12*5 = 40 points) among the 12 problems.

Using the stars and bars approach, we have 40 stars (representing the remaining points) and 11 bars (representing the dividers between the 12 problems). The number of ways to arrange these stars and bars is equivalent to the number of ways to assign points to the problems.

The answer, therefore, can be calculated using the formula for combinations with repetition: C(n + k - 1, k - 1), where n is the number of stars (40) and k is the number of bars (11).

Hence, the number of ways to assign integer points to the problems is C(40 + 11 - 1, 11 - 1) = C(50, 10).

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Answer:

according to me the ans is 3.

The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The potential ordered outcomes, or sample points, are listed as elements in a set that is used to represent a sample space.

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Answer: The answer is 226.2 feet.

Step-by-step explanation: The formula to find the total surface area of a cylinder is 2\(\pi\) x radius squared x height. If you use the formula you will get 226.19 feet as your answer and I rounded that to 226.2 feet.

UR MOM

Answer:

80

Step-by-step explanation:

v=lwh/3= 5*6*8/3 = 80

The volume of this pyramid in cubic inches is 80 inch³.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

We have,

V = (1/3) (b) (h)

So, the Volume of Pyramid is

= 1/3 x base aera x height

= 1/3  x 5 x 6 x 8

= 5 x 2 x 8

= 80 inch³

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There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

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Step-by-step explanation:

as the graph shows :

4x + 12x = 320

16x = 320

x = 20

Answer:

  h(x) = (x -1)(x -(3 +√2))(x -(3 -√2))

Step-by-step explanation:

The given cubic is said to have 1 as a zero. That means (x -1) is a linear factor of the equation. Dividing the cubic by that using your favorite method gives a quotient that is the quadratic ...

  x^2 -6x +7

We can write this in vertex form by "completing the square":

  (x^2 -6x) +7

  = (x^2 -6x +9) +7 -9 . . . . . add and subtract (-6/2)^2 = 9

  = (x -3)^2 -2

This can be factored as the difference of two squares:

  a² -b² = (a -b)(a +b)

Here we have ...

  a² = (x-3)²   ⇒   a = (x -3)

  b² = 2   ⇒   b = √2

Then the linear factors of the quadratic are ...

  x^2 -6x +7 = ((x -3) -√)((x -3) +√2)

  = (x -(3 +√2))(x -(3 -√2)) . . . . . using the associative property of addition

And the cubic can be factored to linear factors as ...

  h(x) = x^3 -7x^2 +13x -7

  h(x) = (x -1)(x^2 -6x +7)

  h(x) = (x -1)(x -(3 +√2))(x -(3 -√2))

According to given data on unmarried mothers as of 2021, around 25% of American children under 18 are living with a single parent.

The percentage of children born to unmarried mothers does not necessarily indicate the percentage of children living with a single parent, as some unmarried parents may choose to live together and raise their children as a family. Therefore, looking at the percentage of children living with a single parent provides a more accurate representation of the situation.

According to the US Census Bureau's 2020 report, around 25% of American children under 18 live with a single parent. This percentage has increased over the years, with 22% of children living with a single parent in 2000 and 19% in 1980. The reasons for single-parent households vary but can include divorce, separation, death of a spouse, or choice.

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In a hypothesis testing context, before examining the data, one should typically decide whether the alternative hypothesis is one-sided or two-sided. This decision is based on the specific research question and the expected direction of the effect being tested.

It helps determine the appropriate statistical test and the formulation of the null and alternative hypotheses.

The computation of the p-value and the decision of whether or not to reject the null hypothesis are made after examining the data and conducting the statistical analysis. The p-value is a measure of the strength of the evidence against the null hypothesis, and it is compared to a predetermined significance level to make a decision. If the p-value is below the significance level, the null hypothesis is typically rejected in favor of the alternative hypothesis.

Therefore, the correct answer is (c) decided whether the alternative hypothesis is one-sided or two-sided.

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a. The probability that a patient experiences relief is 0.9.

b. The probability that at least 10 patients experience relief is 0.9988 (rounded to four decimal places)

c. The probability that at most 7 experience relief is 0.0007 (rounded to four decimal places)

d. The average number of patients who experience relief is 1.14 (rounded to two decimal places)

e. The probability that none of the 15 patients experience relief is 1.0E-15 (rounded to scientific notation)

a. The probability that a patient experiences relief is 0.9. The probability that all 15 experience relief is given by:

P(all 15 experience relief) = (0.9)^15 = 0.2059 (rounded to four decimal places)

b. The probability that at least 10 patients experience relief can be calculated by adding the probabilities of 10, 11, 12, 13, 14, and 15 patients experiencing relief:

P(at least 10 experience relief) = P(10) + P(11) + P(12) + P(13) + P(14) + P(15)

where P(k) represents the probability that k patients experience relief. Each P(k) can be calculated using the binomial probability formula:

P(k) = (15 choose k) * 0.9^k * 0.1^(15-k)

Using a calculator or software, we can find:

P(at least 10 experience relief) = 0.9988 (rounded to four decimal places)

c. The probability that at most 7 patients experience relief is the same as the probability that 8 or fewer patients experience relief. We can use the complement rule to calculate this probability:

P(at most 7 experience relief) = 1 - P(more than 7 experience relief)

To find P(more than 7 experience relief), we can add the probabilities of 8, 9, ..., 15 patients experiencing relief:

P(more than 7 experience relief) = P(8) + P(9) + ... + P(15)

Again, each P(k) can be calculated using the binomial probability formula. Using a calculator or software, we can find:

P(at most 7 experience relief) = 0.0007 (rounded to four decimal places)

d. The average number of patients who experience relief is given by the expected value of a binomial distribution:

E(X) = np

where X is the number of patients who experience relief, n is the sample size (15), and p is the probability of success (0.9). Thus,

E(X) = 15 * 0.9 = 13.5

The standard deviation of a binomial distribution is given by the square root of the variance:

s = sqrt(np*(1-p))

Thus,

s = sqrt(150.90.1) = 1.14 (rounded to two decimal places)

e. The probability that none of the 15 patients experience relief is given by:

P(none experience relief) = 0.1^15 = 1.0E-15 (rounded to scientific notation)

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Answer:

115

Step-by-step explanation:

When two angles are supplementary, their measures must add up to 180 degrees. Therefore, if we call the other angle x:

x+65=180

x=180-65=115 degrees

Hope this helps!

Answer:

None of them

Step-by-step explanation:

Supplementary angles have 180 degrees

50+65=115

40+65=105

130+65=185

310+65=375

The largest possible number of red socks in the drawer that is consistent with this data is 990.

To solve the given question, we will form equations according to the given data including a known and an unknown variable.

Let r be the number of socks that are red, and t be the total number of socks.

We get,

2(r(r-1)+(t-r)(t-r-1))=t(t-1)

Expanding the left hand side and the right hand side

we get,

4r^2-4rt+2t^2-2t = t^2-t

moving the terms, we will get that

4r^2-4rt+t^2 = t

We notice that the left side is a perfect square.

(2r-t)^2 = t

Thus t is a perfect square.

And, the higher t is, the higher r will be. So, we should set

t = 44^2

= 1936

we see, 2r-1936 = 44

We will use the positive root, to get that

2r-1936 = 44,

2r = 1980

r = 990

Therefore, we can conclude that the largest possible number of red socks in the drawer that is consistent with this data is 990.

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The correct option is A) No, because the center of a distribution and the spread are not related

The standard deviation is a measure of the spread or dispersion of a set of data. It is not directly related to the mean or average of the data.

The standard deviation is calculated based on the deviations of each data point from the mean, taking into account how many data points there are.

The mean does not affect the calculation of the standard deviation, as the formula for standard deviation is based solely on the data itself and not on any summary statistics like the mean.

The value of the standard deviation can remain the same even if the mean changes, and conversely, the mean can change without affecting the standard deviation.

Thus, option A) No, because the center of a distribution and the spread are not related is correct.

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Step-by-step explanation:

no her answer is lxb this answer is right for you

Answer:

3,404 gallons

Step-by-step explanation:

68,080/20=3,404

could you maybe put the multiple choice list so someone can help :))