Find three consecutive integers such that twice the sum of the first is 11 more than three times the largest

Answer:

The required number is 7

Step-by-step explanation:

Let a number = x

We are given the condition: five more than three times a number is 26

We need to find the number.

Writing the condition in mathematical form:

five more than three times a number is 26: \(3x+5=26\)

Now, solving this equation we can find x, the number

\(3x+5=26\\\)

Subtract 5 from both sides

\(3x+5-5=26-5\\3x=21\)

Divide both sides by 3

\(\frac{3x}{3}=\frac{21}{3}\\x=7\)

So, we get: x = 7

The required number is 7

Answer:

The answer should be "12,000"

12 x 103 = 1,236

1,236 x 10 = 12,360

Step-by-step explanation:

The dimension of the box is 50in by 10in by 15in

The volume of an object is the quantity of substance it contains.

The formula for calculating the volume of the box is expressed as:

V = lwh

where:

Given the following parameters

length = 5w
height = w + 5

Substiute

7500 = 5w(w)(w+5)
7500 = 5w²(w+5)
1500 = w³+5w²
w³+5w² - 1500 = 0

Factorize to determine the width

On factorizing, the width of the box is 10 inches

Recall that:

l = 5w
l = 5(10)

l = 50inches

Get the height

h = w + 5
h = 10 + 5
h = 15inches

Hence the dimension of the box is 50in by 10in by 15in

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Answer:

(1, 36)

Step-by-step explanation:

Degrees of freedom for the F-test of the two way ANOVA

Here, we use a two factors, independent measures ANOVA, where, factor \(A\) has 2 level and a factor \(B\) also has 2 levels.

So, here,

\($k_1$\) = number of levels of A = 2

\(k_2\) = number of levels of B = 2

And n = sample size in each treatment condition = 10

So we have,

\(d_1\) = df of the main effect A = (\($k_1$\) - 1) = 2 - 1 = 1

\(d_2\) = df of the main effect A = (\($k_2$\) - 1) = 2 - 1 = 1

\(d_3\) = df of interaction effect (A x B) = (\($k_1$\) - 1)(\($k_2$\) - 1)

                                                        = (2-1)(2-1)

                                                         = 1

And \(d_4\) = df of within variation (i.e. error variation) = \($k_1k_2(n-1)$\)

                                                                                 = 2 x 2 x (10 - 1)

                                                                                  = 36

So, the df value for the F-ratio evaluating the main effect of factors-A is

=  (\(d_1, d_4\))

= (1, 36)

Answer:She incorrectly factored out the value of a.

Step-by-step explanation:

In solving a quadratic equation by completing the square method, the value a is not factored out. Rather, the steps involved are:

Divide through all the terms by a

Move the term c/a to the right had side

Complete the square on both sides using the value of b/2

Obtain the values of x

Answer: B. She subtracted the wrong value to maintain balance after completing the square.

If there had been a 2% decrease in total receipts, the new deficit would be $361.08 billion.

If there had been a 2% decrease in total receipts, the new total receipts would be:

New total receipts = $2154 billion - (2% of $2154 billion)

New total receipts = $2154 billion - $43.08 billion

New total receipts = $2110.92 billion

The total outlays would remain the same at $2472 billion.

So, the new deficit would be:

New deficit = New total outlays - New total receipts

New deficit = $2472 billion - $2110.92 billion

New deficit = $361.08 billion

Therefore, if there had been a 2% decrease in total receipts, the new deficit would be $361.08 billion.

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The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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Answer:

15%

Step-by-step explanation:

hope i helped!! please follow ❤❤

Answer:

15%

Step-by-step explanation:

anything out of 100 and is 2 digits will be the same number.

example: 72/100 = 72%

btw: can you give me Brainliest?

Answer:

Step-by-step explanation:4/3 inch increase per year

Answer:

243 as a power of 3

= 3^5

=243

Answer:

Step-by-step explanation:

The angle of a line is 180 degrees. A right angle is 90 degrees, and the given angle is 55 degrees. All you have to do is add 90 and 55, and subtract that sum from 180.

Answer:

Always

Step-by-step explanation:

Answer:

0.351

0.352

Step-by-step explanation:

you can go even smaller by a digit

for example:

0.35111111111111111111... is still between 0.35 and 0.36

there are so many possibilities by the way...

Answer:

2

Step-by-step explanation:

subtract 3 from the 3 and 3 from 11 which would give you 8 then you would divide the 4 from 4a which would leave you with just a and then divided 4 by 8which would give you 2 so its a=2

Answer:

15%

Step-by-step explanation:

move the decimal 2 places because you're dividing by 10

Using the vertical line test, the graph that represents a function is: Graph C.

A simple test we can carry out quickly to determine if a graph represents a function is the vertical line test.

Using the vertical line test, a vertical line is drawn across the curve in the given plane. If the vertical line intersect the curve more than once, it is not a function, but if it intersects the curve at just exactly one point, then the graph represents a function.

If we draw a vertical line across each of the given graphs, only the graph in option C will be intersected at exactly only one point.

Therefore, graph C represents a function.

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Answer:

27 fl oz.

Step-by-step explanation:

According to the information, the null hypothesis is that 70% or fewer of the instructor's students have improved their driving distance by at least 20 yards. The alternative hypothesis is that more than 70% of the instructor's students have improved their driving distance by at least 20 yards. Based on the data provided, we can evaluate whether the instructor's claim is valid.

Accordign to the information we have to consider that the null hypothesis states that 70% or fewer of the instructor's students have improved their driving distance by at least 20 yards, while the alternative hypothesis suggests that more than 70% have seen such improvement.

According to the above, the claim's validity is assessed by comparing the observed data with the expected outcome under the null hypothesis. In this case, 138 out of 180 viewers reported an improvement. Statistical tests can be conducted to determine if this observed proportion significantly differs from the hypothesized proportion of 70% or fewer.

To conclude, if the test results reject the null hypothesis, there is evidence to support the claim; otherwise, the claim cannot be validated.

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No, the instructor's claim is NOT valid. See   the explanation below.

To   test the hypothesis, we can use a z- test.

z = (p - p₀) / σ

Where

σ = √(p₀(1 - p₀) / n)

where:

Since p  =138/180

= 0.7667.

p₀=0.7. The sample size is n=180.

z = (0.7667 - 0.7) / √(0.7(1 - 0.7) / 180)

= 1.95277604597

≈ 1.92

Since the p-value for a z-score of 1.92 is 0.054, we can reject the null hypothesis.

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The value of 'x' and 'y' in the given circle and triangle are 30 and 12 respectively.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given information we can form,

x² = 18² + 24². (As tangent is always perpendicular to the radius).

x² = 900.

x = 30.

Now, y = x - radius.

y = 30 - 18.

y = 12.

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Answer:

The height of the tree to the nearest foot is 75.

Step-by-step explanation:

The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.

tangent = opposite/adjacent

\(\frac{tan(59)}{1} = \frac{h}{45}\)

h = tan(59) * 45

h ≈ 74.89

To the nearest foot, 74.89 is 75 ft.

The correct answer is (D) AB is 4 x 4, BA is 2 x 2.

What is order of a matrix?

The order of a matrix refers to the number of rows and columns in the matrix. If a matrix has m rows and n columns, we say that it is an m x n matrix. The order of the matrix is written as "m x n".

In general, if A is an m x n matrix and B is an n x p matrix, then the product AB is an m x p matrix and the product BA is an n x n matrix.

In this case, A is a 4 x 2 matrix and B is a 2 x 4 matrix. Therefore, the product AB is a 4 x 4 matrix, and the product BA is a 2 x 2 matrix.

So the answer is (D) AB is 4 x 4, BA is 2 x 2.

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Answer:

y = -1/2x+3

Step-by-step explanation:

We have y = 2x-9

This is in slope intercept form

y = mx+b  where m is the slope

The slope is 2

We want a line that is perpendicular

Perpendicular lines have slopes that are negative reciprocals

The slope is -1/2

The equation of the new line is

y = -1/2x+b

Substituting the point into the equation

5 = -1/2(-4)+b

5 = 2+b

5 -2=b

3=b

y = -1/2x+3

Answer:

y = -1/2x + 3

Step-by-step explanation:

We know that if two lines are perpendicular to each other the multiplication of the slopes of those 2 lines equals -1.

m₁ × m₂ = -1

Given that, the slope of one line is 2 (m₁). Now, let us find the slope of the other line (m₂) using the above formula.

2 × m₂ = -1

2m₂ = -1

Divide both sides by 2.

m₂ = -1/2

And now let us find the value of the y-intercept ( c in the formula y = mx + c) using the given coordinate.

( -4 , 5 )⇒ ( x , y ).

Let us find it now.

y = mx + c

5 = -1/2x × -4 + c

5 = 2 + c

5 - 2 = c

3 = c

And now let us write the equation for the new line.

y = m x + c

y = -1/2x + 3

The value on simplifying the fraction expression 5/6 - 7/12 is obtained as 1/4.

What is a fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

The fraction expression is given as 5/6 - 7/12.

5/6 - 7/12

First take the LCM of the denominator -

LCM = 12

Now, multiply 2 by 5 in first fraction numerator, as 6 multiplied by 2 is 12 (LCM) -

10/12 - 7/12

Now, use the arithmetic operation of subtraction -

(10 - 7)/12

3/12

Divide numerator and denominator by 3 -

1/4

Therefore, the final value as a fraction is obtained as 1/4.

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Answer:

Step-by-step explanation:

1755*39= 68445

68445/39=1755

68445/1755=39

Answer:

  (c)  20%

Step-by-step explanation:

You want the percent error in an estimate of 240, when the actual count was 200.

The percent error can be found by ...

  error = (estimate/actual -1) × 100%

  error = (240/200 -1) × 100%

  error = (1.2 -1) × 100% = 20%

The error in the estimate was 20%.

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The factored trinomial expression is (5p + 2)(2p - 1)

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

10p^2-p-2

To factor the trinomial 10p^2 - p - 2, we can use the method of finding two numbers that multiply to -20p^2 and add to -p.

We can use these numbers to write the trinomial as a product of two binomials:

So, we have

10p^2 - p - 2 = 10p^2 - 5p + 4p - 2

Factorize

10p^2 - p - 2 = 5p(2p - 1) + 2(2p - 1)

This gives

10p^2 - p - 2 = (5p + 2)(2p - 1)

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The histogram doesn't support Alfonso's claim and the correct option is 5: No, the distribution is skewed to the left with a mean age greater than 36.

What is a histogram?

A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram.

Consider the given histogram at the photo below. It is an left-skew histogram, since it has a long tail to the left side.

We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.

For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.

1. midpoint = 32, probability= 0.03

2. midpoint = 33, probability = 0.04

3. midpoint = 34, probability = 0.05

4. midpoint = 35, probability = 0.1

5. midpoint = 36, probability =0.11

6. midpoint = 37, probability = 0.13

7. midpoint = 38, probability = 0.2

8. midpoint = 39, probability = 0.09

So, it is obtained that -

μ = 0.03 · 32 + 0.04 · 33 + 0.05 · 34 + 0.10 · 35 + 0.11 · 36 + 0.13 · 37 + 0.25 · 38 + 0.20 · 39 + 0.09 · 40

μ = 37.15

Therefore, this histogram is left-skewed with mean greater than 36.

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Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

We have,

To determine if the die is balanced, we can perform a chi-square test of goodness of fit.

The null hypothesis is that the die is balanced, and the alternative hypothesis is that the die is not balanced.

First, let's calculate the expected frequencies for each outcome assuming the die is balanced. Since there are 180 tosses in total, each outcome is expected to have an equal probability of 1/6.

Expected frequency for each outcome

= (Total tosses) x (Probability of each outcome)

Expected frequency for each outcome = (180) x (1/6)

Expected frequency for each outcome = 30

Now, we can calculate the chi-square test statistic using the formula:

χ² = Σ [(Observed frequency - Expected frequency)² / Expected frequency]

Let's calculate the chi-square test statistic:

χ² = [(28 - 30)² / 30] + [(36 - 30)² / 30] + [(36 - 30)² / 30] + [(30 - 30)² / 30] + [(27 - 30)² / 30] + [(23 - 30)² / 30]

χ² = [(-2)² / 30] + [(6)² / 30] + [(6)² / 30] + [(0)² / 30] + [(-3)² / 30] + [(7)² / 30]

χ² = 4/30 + 36/30 + 36/30 + 0/30 + 9/30 + 49/30

χ² = 134/30

χ² ≈ 4.467

Next, we need to compare the calculated chi-square value to the critical chi-square value at a significance level of 0.01 and degrees of freedom equal to the number of outcomes minus 1 (6 - 1 = 5).

Looking up the critical chi-square value in a chi-square distribution table with 5 degrees of freedom and a significance level of 0.01, we find it to be approximately 15.086.

Since the calculated chi-square value (4.467) is less than the critical chi-square value (15.086), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the die is not balanced at a 0.01 level of significance.

Thus,

Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

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