One dinosaur sleps forward out of the pack. He asks, "If there are a total of 200 dinosaurs and only 24 are warriors, whal percent of us are warriors?" He dearly means lo test your intelligence. Can you find the solution (answer)?

Answer:

15x-48.5x+12.40

= -33.2x+12.40

Answer:

Step-by-step explanation:

Product means multiply.

-300

Answer:

86.96%

Step-by-step explanation:

s2 = a2 / n  

a2 =  4.34782608696 if just 1/1 flavour 400/400 was the case.

We are asked to account for 5 flavours 4.34782608696/5

Z test was  0.86956521739 for red candies

s2 = a2/n

a2 = 0.86956521739/1

s2 = 0.86956521739/1  

s2 = 0.87 hundredth place

Percentage  0.86956521739 x 100 = 86.96% to 100th place

Answer:

4

Step-by-step explanation:

Lets plug these points in:

\(\frac{((-2)-10)}{(2-5)} =\frac{-12}{-3} =4\)

Answer:

97% of her laps are completed in less than 134 seconds.

The fastest 5% of her laps are under 125.96 seconds.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 129.71, \sigma = 2.28\)

Find the percent of her laps that are completed in less than 134 seconds.

We have to find the pvalue of Z when X = 134. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{134 - 129.71}{2.28}\)

\(Z = 1.88\)

\(Z = 1.88\) has a pvalue of 0.9699, so 97% of her laps are completed in less than 134 seconds.

The fastest 5% of her laps are under how many seconds?

This is the 5th percentile of times, which is X when Z has a pvalue of 0.05, that is, X when Z = -1.645. So

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.645 = \frac{X - 129.71}{2.28}\)

\(X - 129.71 = -1.645*2.28\)

\(X = 125.96\)

The fastest 5% of her laps are under 125.96 seconds.

Answer:

a. mean = 6.96 , standard deviation = 1.71 b. 0.0641

Step-by-step explanation:

Here is the complete question

According to the Behavioural Risk Factor Surveillance System, 58% of all Americans adhere to a sedentary lifestyle (sedentary means does not exercise).

a. If you selected repeated samples of 12 from the U.S. population, what would be the mean number of individuals per sample who do not exercise regularly? What would be the standard deviation?

b. Suppose you select a sample of 12 individuals and find that 10 of them do not exercise regularly. Assuming that the Surveillance System is correct, what is the probability that you would have obtained results as bad or worse than expected?

Solution

a. Since we can only have two types of outcomes, that is, those who exercise and those who do not exercise, the problem follows a binomial distribution.

Since the probability of those who do not exercise, p = 58 % = 0.58,

the mean of the binomial distribution μ = np where n = sample number = 12

So, μ = 12 × 0.58 = 6.96

The standard deviation of a binomial distribution σ = √(npq) where q = probability that people exercise = 1 - p = 1 - 0.58 = 0.42

So, σ = √(12 × 0.58 × 0.42) = √2.9232 = 1.71

b. To find the worst case, we consider the probability that at best, two exercise. Since two exercise, the probability that at best two exercise is ¹²C₂q²p¹⁰ + ¹²C₁qp¹¹ + ¹²C₀q⁰p¹²

= (12 × 11/2)(0.42)²(0.58)¹⁰ + 12(0.42)(0.58)¹¹ + 1 × (0.42)⁰(0.58)¹²

= 0.05 + 0.0126 + 0.00145

= 0.06405

≅ 0.0641

Answer:

Step-by-step explanation:

Let us assume the question was asked in the year 2020, that is this year

Say that Mr. Green was born in year x

The mathematical expression for his statement is given as

\(x + 2020 - (x + 10 + x + 50) + (2020 - x) = 122\)

Solve for x

x + 2020 + 2020 - x - x - 60 - x = 122

4040- 122- 2x = 0

3918= 2x

divide both sides by 2

3918/2= x

x=1959

He was born in 1959, so now

he is (2020-1959)

=61 years old.

Answer:

Total area = 937.75

Step-by-step explanation:

Area of triangles = ((b*h)/2) * 5

= (12*23/2) * 5

= 138 * 5

Area of triangles = 690

Area of pentagon = a² * √(25 + 10√5) / 4

= 12^2 * √(25 + 10√5) / 4

Area of pentagon = 247.75

Total area = Area of triangles + Area of pentagon

Total area = 937.75

Notice that:

therefore, the interest rate is

which in percent corresponds to:

Given equation of the Circle is ,

\(\sf\implies x^2 + y^2 = 25 \)

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

\(\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2\)

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

\(\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }\)

Hence the point lies within the circle .

Answer:

inside the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 25 ← is in this form

with r = \(\sqrt{25\) = 5

Calculate the distance d from the centre to the point (- 4, 2 ) using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 4, 2)

d= \(\sqrt{(-4-0)^2+(2-0)^2}\)

   = \(\sqrt{(-4)^2+2^2}\)

   = \(\sqrt{16+4}\)

    = \(\sqrt{20}\)

    ≈ 4.5 ( to 1 dec. place )

Since 4.5 is less than the radius of 5

Then (- 4, 2 ) lies inside the circle

Answer: I would need a picture of the exact set up of the question but I think it would go.

T=4b

B= 9

Step-by-step explanation:

The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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Answer:

b & c

Step-by-step explanation:

Answer:

The slope is m=2.145.

The y-intercept is b=-1.33.

Step-by-step explanation:

We have this data:

- The mean and standard deviation for x are 5.43 and 1.12, respectively.

- The mean and standard deviation for y are 10.32 and 2.69, respectively.

- The correlation is 0.893.

We have to calculate the slope and the y-intercept of the least-squares line.

With the given data, we can calculate the slope m as:

\(m=r\;\dfrac{s_y}{s_x}=0.893\;\dfrac{2.69}{1.12}=2.145\)

Then, the y-intercept is calculated as:

\(b=\bar y-m\cdot \bar x=10.32-2.145\cdot 5.43=10.32-11.65=-1.33\)

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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Answer:

0.0548

Step-by-step explanation:

Given that:

Mean (m) life expactancy of product = 14 years

Standard deviation (σ) = 2.5 years

Probability of buying a product which will last more than 18 years ;

x = 18 years

Using empirical formula:

Zscore = (x - mean) / standard deviation

Zscore = (18 - 14) / 2.5

Zscore = 4 /2.5

Zscore = 1.6

Hence ;

P(Z > 1.6)

P(Z > 1.6) = 1 - P(Z < 1.6)

P(Z < 1.6) = 0.9452

P(Z > 1.6) = 1 - 0.9452

P(Z > 1.6) = 0.0548

Hence, probability = 0.0548 OR 5.48%

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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The revenue function derived from the given marginal revenue function is \(R(x) = 1/11)x^{11} - (18/6)x^6 + (12/4)x^4 + 2x + C.\)

A formula means an equation representing the way in which particular items of income behave when plotted on a graph

To get revenue function, we will integrate the marginal revenue function with respect to x.

The integration is the reverse operation of differentiation, so we will integrate each term individually.

Given:

\(MR = x^10 - 18x^5 + 12x^3 + 2\)

Integrating, we have:

\(= \int\limits^a_b {x^10 - 18x^5 + 12x^3 + 2} \, dx \\= (1/11)x^{11} - (18/6)x^6 + (12/4)x^4 + 2x + C.\)

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Answer:

\(y\in (-\infty ,5]\)

Step-by-step explanation:

In this problem, we need to write "Twenty times y is at most 100 in interval notation ".

20 times y means, 20y

Atmost means an inequality which is \(\le\)

ATQ,

\(20\times y\le 100\)

i.e.

\(20y\le 100\\\\y\le 5\)

We can also write it as :

\(y\in (-\infty ,5]\)

Hence, the required interval notation is \(y\in (-\infty ,5]\).

The interval notation is \(\rm y \epsilon (\infty,6]\).

The Interval notation is a method to define a set of numbers between a lower limit and an upper limit by using end-point values.

"Twenty times y is at most 100 in interval notation ".

Here, 20 times y means, 20y at most means an inequality.

Therefore,

The inequality is;

\(\rm 20 \times y\leq 100\\\\20y\leq 100\\\\y \leq \dfrac{100}{20}\\\\y\leq 5\)

Hence, the required interval notation is \(\rm y \epsilon (\infty,6]\).

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The ratio of EG = 36.

Let's assign variables to the lengths of the line segments:

EF = x

FG = 5x

GH = 3x

We know that EH = EF + FG + GH.

Substituting the given values, we have:

54 = x + 5x + 3x

Combining like terms, we get:

54 = 9x

To isolate x, we divide both sides of the equation by 9:

54/9 = x

Simplifying, we find:

6 = x

EF = 6, FG = 5(6) = 30, and GH = 3(6) = 18.

Since EG is the sum of EF and FG, we can calculate it as follows:

EG = EF + FG = 6 + 30

= 36

EG = 36.

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The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Here you go.

The answer is A
II Only

Answer:

4.6

Step-by-step explanation:

Answer - is B 4.6

Explanation - I did the math

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.