Five times the lesser of two consecutive numbers is added to three times the greater. the result is 579. find the lesser number

The type of experiment design described in the scenario is: B) Stratified.

In this design, the population is divided into homogeneous groups (in this case, males and females) called strata. Then, within each stratum, participants are randomly assigned to different treatment groups (treatment and control groups).

This approach ensures that each stratum is represented equally in both treatment groups, allowing for comparisons within each group and reducing potential confounding variables.

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Answer:

35

Step-by-step explanation:

The equation can be written as:

p - 10 = 25

To solve for p, we can add 10 to both sides of the equation:

p - 10 + 10 = 25 + 10

Simplifying the left side by canceling out -10 and +10, we get:

p = 35

Therefore, the number we are looking for is 35.

Answer:

nosejgivuguvug7gug7g7g

Step-by-step explanation:

pol

First, we need to define rational numbers

Rational numbers are numbers that can be express as a quotient or fraction

From the question given, The square root of 16 is 4, this can be express as 4/1

Hence, it is a rational number

Therefore the correct option is A

The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

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Answer:

Pauline reflected the original figure over the x-axis:

The coordinates of point B will be (4,3)

Carl reflected the original figure over the y-axis:

The coordinate of points B will be (-4,-3)

When Pauline reflect the original figure over the x-axis, the coordinate of point B' will be (-2, -4). When Carl reflect the original figure over the y-axis, the coordinate of point B' will be (2, 4).

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Mathematics, a reflection over the x-axis is given by this transformation rule:

(x, y)                   →               (x, -y)

Point B = (4, -3) → Point B' = (4, 3)

In Geometry, a reflection over the y-axis of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, the coordinates of point B' after a reflection over the y-axis is as follows:

Point B = (4, -3) → Point B' = (-4, -3)

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Answer:

\( f'(x) = {e}^{x}( \sin x + \cos x ) \)

Step-by-step explanation:

\(f(x) = {e}^{x} \sin x \\ \\ f'(x) = \sin x \frac{d}{dx} {e}^{x} + {e}^{x} \frac{d}{dx} \sin x \\ \\ f'(x) = \sin x \: {e}^{x} +{e}^{x} \cos x \\ \\ f'(x) = {e}^{x}( \sin x + \cos x ) \)

Answer:

  4

Step-by-step explanation:

You want the least positive integer x such that ...

  1/x +9/10 > 4/x

  9/10 > 3/x . . . . subtract 1/x

  3/10 > 1/x . . . . .divide by 3

  x > 10/3 . . . . . multiply by 10x/3

The least positive integer satisfying this requirement is x = 4.

The scale factor for the model of the elephant is 1 : 30 (option A).

A scale drawing is either a smaller or a larger version of an original image. For example, a map is a smaller version of a city, country or area.

A scale factor provides information on the relationship that exists between the scale drawing and the actual image. The scale factor shows the rate of reduction or enlargement of the original image.

Scale factor = actual length of the elephant / length of the elephant in the model

216 / 7.2 = 30

The scale factor is 1 : 30

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The rectangular garden owned by Mr. Franco has an area of 630 square feet, with dimensions of 35 feet by 18 feet.



To find the area of Mr. Franco's rectangular garden, we multiply the length and width of the garden.

Given that the length of the garden is thirty-five feet and the width is eighteen feet, we can use the formula for the area of a rectangle, which is length multiplied by width.

Area = Length × Width

Substituting the given values:

Area = 35 ft × 18 ft

Calculating the product:

Area = 630 square feet

Therefore, the area of Mr. Franco's garden is 630 square feet.

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Answer:

6/6 = to 1

10/2=to 5

2/6= to 1/3 or 0.3333333333

Step-by-step explanation:

6/6 divide by 1

10/2 10 divide by 2

2/6 reduce to 1/3 or o.3333333333

We simplify fractions because doing so always makes them easier to work with or compute.

A fraction is a piece of the entire. The number is shown as a quotient in mathematics, where the numerator and denominator are split. Both are integers in a straightforward fraction. A fraction appears in a complex fraction's numerator or denominator. The numerator of a valid fraction is smaller than the denominator. A fraction is a mathematical concept that denotes a component of a whole or, more generally, any number of equal parts. As employed in conversational English, a fraction—such as one-half, eight-fifths, and three-quarters—indicates the number of components of a particular size. With fractions, smaller portions of a whole are represented. The whole may be made up of one thing or several things. In any case, they collectively constitute what is referred to as a whole.

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Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the engineer's claim. Hence, the engineer's claim is false.

To answer this question, we need to conduct a hypothesis test with a significance level of α = 0.05. The null hypothesis (H0) is that the true mean commute time is equal to or greater than 25 minutes, while the alternative hypothesis (Ha) is that the true mean commute time is less than 25 minutes. We can use a one-sample t-test to test this hypothesis, where the test statistic is calculated as:
t = (sample mean - hypothesized mean) / (standard deviation/sqrt (sample size))
t = (24.6 - 25) / (13 / sqrt(1923))
t = -1.53

Using a t-distribution table with degrees of freedom (df) equal to the sample size minus 1 (df = 1922), we find that the p-value for this test is 0.064. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the engineer's claim that the mean commute time is less than 25 minutes. The deviation from the hypothesized mean is -0.4 which is less than 1 standard deviation, hence we cannot say with confidence that the mean commute time is less than 25 minutes.

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The given problem states that x and y vary inversely, and by using the given values, an equation is formed (x * y = 9) which can be used to find y when x = 3 (y = 3).

Since x and y vary inversely, we can write the equation as x * y = k, where k is a constant.

Using the given values x = 1 and y = 9, we can substitute them into the equation to find the value of k:

1 * 9 = k

k = 9

Therefore, the equation relating x and y is x * y = 9.

To find y when x = 3, we substitute x = 3 into the equation:

3 * y = 9

y = 9 / 3

y = 3

So, when x = 3, y = 3.

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Answer:

it is actually 35

Step-by-step explanation:

This is because the plot is accelerating not decreasing also like if you think peter griffin is in! EPIC

Answer:

Negative Correlation

Step-by-step explanation:

Since the points are approximately lined up in a linear line pointing toward the bottom right, the slope of the best fit line would be a negative value. So the scatter plot shows a negative correlation.

The Hall's Marriage Theorem holds, and there exists a perfect matching of the men and women on the island so that everyone is matched with someone they are willing to marry.

The Hall's Marriage Theorem.

Let there be m men and w women on the island.

It is possible to match them so that everyone is matched with someone they are willing to marry.

First, we need to prove that for any subset S of men on the island, the number of women that they are collectively willing to marry is at least |S|k.

Let S be any subset of men on the island.

Since every man is willing to marry exactly k women, the number of women that any single man is willing to marry is k.

The number of women that S collectively is willing to marry is at least |S|k.

Next, we need to prove that for any subset T of women on the island, the number of men that they are collectively willing to marry is at least |T|k.

Let T be any subset of women on the island.

Since every woman is willing to marry exactly k men, the number of men that any single woman is willing to marry is k.

The number of men that T collectively is willing to marry is at least |T|k.

Now, we need to show that the Hall's Marriage Theorem holds.

That is, we need to show that for any subset S of men on the island, the number of women that they are collectively willing to marry is at least |S|, and for any subset T of women on the island, the number of men that they are collectively willing to marry is at least |T|.

Suppose, for the sake of contradiction, that there exists a subset S of men on the island such that the number of women that they are collectively willing to marry is less than |S|.

Then, by the first proof, the number of women that they are collectively willing to marry is at least |S|k. Since |S|k < |S|, this leads to a contradiction.

Similarly, suppose there exists a subset T of women on the island such that the number of men that they are collectively willing to marry is less than |T|.

Then, by the second proof, the number of men that they are collectively willing to marry is at least |T|k. Since |T|k < |T|, this leads to a contradiction.

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When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.

We can simplify  the Boolean function F = xy'z' + xy'z+ w'xy +   w'x'y' + w'xy using the following Boolean Algebra rules.

Absorption - x + xy = x

Commutativity -  xy = yx

Associativity - x(yz) = (xy)z

Distributivity - x(y + z) = xy + xz

Using the above , we   have

F = xy'z' + xy'z+ w'xy + w'x'y' +   w'xy

= xy'(z + z') + w'xy(x + x')

= xy' +  w'xy

= (x' + y)(x' + y')  + w'xy

= x' + y' + w'xy

This means that the simplified expression is F = x' + y' + w'xy.

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Answer:

yes

Step-by-step explanation:

Even after 5 minutes, it will still take Darnell 27 more minutes to get home. If Hector can make it in 24 minutes, then he can catch up to Darnell before he gets home.

y = 4/3x +5 is the equation of the line that passes through the point (-3, 1) and has a slope of 4/3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us use point-slope formula  y-y₁ = m(x-x₁) with point (-3,1) and slope m of 4/3.

Plug in the values

y-1 =4/3(x-(-3))

y-1 = 4/3(x+3)

Apply distributive property

y-1 =4/3x +4

Add 1 on both sides

y = 4/3x +5

Hence, y = 4/3x +5 is the equation of the line that passes through the point (-3, 1) and has a slope of 4/3.

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Answer:

x = 8√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to solve for the missing length.

Step 2: Identify Variables

Leg a = 8

Leg b = 8

Hypotenuse c = x

Step 3: Solve for x

Answer:

m=-3/5

Step-by-step explanation:

Answer:6283.19 cm cubed, assuming pi is 3.14 or it's 2000 pi

Step-by-step explanation:

V=pi r squared times h over 3

Answer:

The answer is around 6283.19

Step-by-step explanation:

I know this because the formula of the cone is V=πr^2h/3 so substituded the known value to get this answer.

Pi equal 3.14

Answer:

x=17/1/7, y=8/4/7

Step-by-step explanation:

x:

30/30+x=14/22

420+14x=660

14x+240

x=17/1/7

y:

14/22=15/15+y

210+14y=330

14y=120

y=8/4/7

Answer:

x = \(17\frac{1}{7}\)

y = \(8\frac{4}{7}\)

Step-by-step explanation:

1. Lines DE and AC are parallel.

Therefore, by the Triangle Proportionality Theorem:

\(\frac{SideBD}{SideAD} = \frac{SideBE}{SideEC}\)
= \(\frac{30}{x} = \frac{15}{y}\)

Rearranging:

\(\frac{30}{15} = \frac{x}{y}\)

\(2 = \frac{x}{y}\)

Cross-multiplication is applied:

\((x)(1) = (2)(y)\)

\(x = 2y\) —-(equation i)

2. ΔBDE and ΔBAC are similar triangles

Which means:

\(\frac{SideBD}{SideDE} = \frac{SideBA}{SideAC}\)

\(\frac{30}{14} = \frac{30 + x}{22}\)

Cross-multiplication is applied

\((14)(30 + x) = (30)(22)\)

\(420 + 14x= 660\)

\(14x = 660 - 420\)

\(14x = 240\)

\(x = \frac{240}{14}\)

Reduce the numerator and denominator by the Highest Common Factor (2):

∴x = \(\frac{120}{7}\)

     =\(17\frac{1}{7}\)

Substitute the value of x in (equation i) to solve for y:

\(\frac{120}{7} = 2y\)

\(y = \frac{120}{7(2)}\)

∴y = \(\frac{60}{7}\)

    = \(8\frac{4}{7}\)

The slope of the line containing the points A(-8,6) and B(11,2) is given as follows:

m = -0.2105.

The angle of the line is given as follows:

θ = -11.89º.

The two points on the line are given as follows:

A(-8,6) and B(11,2).

Given two points, the slope is obtained by the division of the change in y by the change in x, hence:

m = (2 - 6)/(11 + 8)

m = -0.2105.

The slope represents the tangent of the angle, hence the angle is the arc tangent of the slope, thus:

θ = arctan(-0.2105)

θ = -11.89º.

The problem asks for the slope and for the angle of the line containing points A and B.

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