the rate of change of y with respect to x is one-half times the value of y. find an equation for y, given that when x = 0. you get:

The fraction that represents the colored part of each shape is i) ½ ii) 8/9 iii) ½ iv) ¼ v) 3/7 vi) ¼ vii) 1 viii) 4/9 ix) ½ x) 1/2.

Fractions refer to the parts of a whole. A fraction is a ratio between specified parts of a figure to all parts of a figure. The numerator indicates the parts of the whole and the denominator indicates the total number of equal parts. In the given shapes, as everything is equally divided, the fraction of shaded region is equal to the number of shaded parts divided by the number of total parts.

i) The number of shaded regions = 2

The total number of regions = 4

Fraction = 2/4 = 1/2

ii) The number of shaded regions = 8

The total number of regions = 9

Fraction = 8/9

iii) The number of shaded regions = 4

The total number of regions = 8

Fraction = 4/8 = ½

iv) The number of shaded regions = 1

The total number of regions = 4

Fraction = 1/4

v) The number of shaded regions = 3

The total number of regions = 7

Fraction = 3/7

vi) The number of shaded regions = 3

The total number of regions = 12

Fraction = 3/12 = 1/4

vii) The number of shaded regions = 10

The total number of regions = 10

Fraction = 10/10 = 1

viii) The number of shaded regions = 4

The total number of regions = 9

Fraction = 4/9

ix) The number of shaded regions = 4

The total number of regions = 8

Fraction = 4/8 = 1/2

x) The number of shaded regions = 1

The total number of regions = 2

Fraction = 1/2

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Answer:

ABBBB

Step-by-step explanation:

The correct statement is that Joe performed worse than Eric.

To determine which student performed better, we need to compare their standardized scores. Joe's math score of 160 in class A has a mean (μ) of 150 and a standard deviation (σ) of 20. We calculate the z-score for Joe's score as follows:

z = (160 - 150) / 20 = 0.5

On the other hand, Eric's verbal score in class B is 80, with a mean (μ) of 72 and a standard deviation (σ) of 8. The z-score for Eric's score is calculated as:

z = (80 - 72) / 8 = 1

Comparing the z-scores, we find that Eric has a larger standardized score (z = 1) compared to Joe's score (z = 0.5).

This indicates that Eric's score is relatively higher compared to the mean and standard deviation of his class, suggesting better performance.

Therefore, the correct statement is that Joe performed worse than Eric.

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The range of a relation refers to the set of output (y) values that are paired with the input (x) values in the relation. In other words, it is the set of all possible y values that result from plugging in various x values into the relation.

The range can be expressed in various forms, such as a set of points that pair input values with output values or as individual x and y values written in the form (x, y). The range is an important concept in mathematics and is often used to analyze the behavior of functions and other mathematical relationships. Overall, the range of a relation is a long answer that involves understanding the relationship between input and output values and how they relate to each other within the context of the given relation.

The range of a relation is the output (y) values of the relation. In a relation, input values (x) are paired with output values (y). The range specifically refers to the set of all possible output (y) values that result from the input values in the relation.

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7.a) Probability distribution function of X:Let X be the time until the tenth phone call arrives. We can take X to have the exponential distribution with parameter λ = 2/3, as per the Poisson process. As the waiting time for a Poisson process to experience an event follows an exponential distribution, therefore;

f(x) = λ e-λx

= (2/3) e-(2/3)x, x ≥ 0.  b)

Moment generating function, mean and variance of X:

Since X has an exponential distribution, the moment generating function is calculated using the following formula;

M(t) = E(e^(tx))

= ∫0^∞ e^(tx)f(x) dx

M(t) = ∫0^∞ e^(tx) (2/3) e^(-2/3)x dx

M(t) = 2/(2/3 - t), if t < 2/3

The mean and variance of X are:

μ = E(X)

= 1/λ

= 1/(2/3)

= 1.5σ²

= Var(X)

= (1/λ)²

= (1/(2/3))²

= 2.25 c) P(X < 5):P(X < 5)

= ∫0^5 (2/3) e^-(2/3)x dx

= 1 - e^-(10/3) ≈ 0.7681.

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Answer:

6^5 or 7776

Step-by-step explanation:

6^5 because 6 is multiplied with 6, 5 times. So, it is 6^5.

We can also simplify this number.

=> 6 x 6 x 6 x 6 x 6

=> 36 x 36 x 6

=> 36 x 216

=> 7776

Answer:

$8

Step-by-step explanation:

20% of $40

= \(\frac{20}{100}\) × $40

= 0.2 × $40

= $8

$8 is discounted from the regular price

Answer:

$8 off

Step-by-step explanation:

Convert from a percentage to a multiplier by dividing by 100:

\(\frac{20}{100}=0.2\)

Then multiply that by the price:

\(40*0.2=8\)

meaning the item is $8 off.

You can confirm that like so:

\(\frac{8}{40} =0.2\\\)

or 20%

The equation of p(x) after the translation four units up and six units left is given as follows:

q(x) = p(x + 6) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The equation of q(x) after the translation up is given as follows:

q(x) = p(x) + 4.

The equation of q(x) after the translation left is given as follows:

q(x) = p(x + 6) + 4.

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Answer:

f(50) = 31928.24 thousands

Therefore, it means that the US population in year 1850 is 31928.24 thousands

Step-by-step explanation:

Given the function;

f(x)=165.6x^1.345

Where;

f(x) is in thousand and

x is the number of year after 1800

To determine f(50), we will substitute x = 50 into the function of f(x);

f(50)=165.6(50)^1.345

f(50) = 31928.24 thousands

Since f(50) is the US population in year 1800+50 = 1850

Therefore, the US population in year 1850 is 31928.24 thousands

Answer:

270

Step-by-step explanation:

Since you have the value of x as 90

3x=3*90

3x=270

The sequence converges to 1 found using the limit test.

To determine whether the sequence converges or diverges, we have to use the limit test. If the sequence is convergent, we have to find its limit as well.

A sequence is convergent if and only if its limit exists and is finite. It's divergent if it doesn't converge. It's not important whether the limit is positive, negative, or zero. A sequence that increases without bound or decreases without bound diverges.Let's move on to the solution.

To check whether the given sequence converges or diverges, we'll use the limit test.

If an > 0 for n > N, then lim an = 0 → the sequence converges to zero.

If an > 0 for n > N and lim an = L > 0 → the sequence converges to L.

If an > 0 for n > N and liman = ∞ → the sequence diverges to infinity.

If an < 0 for n > N and liman = - ∞ → the sequence diverges to negative infinity.

If an and bn > 0 for n > N, and liman/bn = C > 0 → the sequence converges to C.

an = e−1/√n

Here, n > 0. Also, e is a constant value, so we can rewrite the formula as;

an = e * e^(-1/√n)

Since e is a positive constant, we can ignore it for the limit test.

Now, let's find the limit using the limit test;

\(lim_an = lim e^(-1/√n)\)as n approaches infinity

This can be simplified as;

\(liman = lim 1/e^(1/√n)\)  as n approaches infinity

Since e is a positive constant, it will remain as it is, and we'll work with the other half;

lim 1/e^(1/√n)  as n approaches infinity

We can write

e^(1/√n) as \(e^(1/n^(1/2))\), which means;

\(lim 1/e^(1/√n) = lim 1/e^(1/n^(1/2))\)  as n approaches infinity

Since the power of n in the exponent is increasing as n approaches infinity, the denominator will become too large, resulting in an exponent of zero, which gives 1.e.g.,

1/√1 = 1,

1/√2 = 0.7,

1/√3 = 0.6,

1/√4 = 0.5,

1/√5 = 0.45, ...

Therefore, as n approaches infinity, 1/n^(1/2) approaches zero, and the denominator becomes infinite, causing the fraction to approach zero.

lim_an = lim 1/e^(1/n^(1/2))   as n approaches infinity= 1/1= 1

Therefore, the sequence converges to 1.

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Answer the a person walked 1.344 per 1/12

Step-by-step explanation:

It would equal

6a^2-19a-20

Answer:

6a^2−25a−25 this is the answer to number 5

1) In the context of statistics, the term "normal" is referred to a distribution of the data that follows the characteristic of the Normal distribution: symmetrical and bell shaped.

It was named "normal" distribution because it represents many distributions of measures in nature. But it does not represent what is normal or not in all the possible contexts.

2) If we graph the histogram of the data, we can check if the distribution is normal-like byb looking at those two characteristics: how symmetric is the distribution of the data around the mean (the more symmetric, the closer to the normal distribution) and the shape of the distribution (it should be bell-shaped, with more data around the mean and less on the tails).

The probability of ordering a caramel macchiato or a muffin is 82%.

Let us denote the Probability of ordering a caramel Macchiato as P(C), the Probability of ordering a muffin as P(M), the probability of ordering both a caramel macchiato and a muffin as P(C ∩ M), and the probability of ordering a caramel macchiato or a muffin P(C ∪  M).

It is given that:

P(C)=72%

P(M)=32%

P(C ∩ M)=22%

We need to find P(C ∪  M).

According to the Union Law of probability, the probability of the union of two events A and B is equal to the sum of their individual probabilities minus the probability of their intersection.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

In this case:

P(C ∪ M)=P(C)+P(M)-P(C ∩ M)

Upon substituting the given values;

P(C ∪ M)=72%+32%-22%=82%

Hence, the probability of ordering a caramel macchiato or a muffin =

P(C ∪  M) is 82%.

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Answer:

Slope: -2/3

Y-intercept: 2

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = \(\frac{-5-5}{3-(-2)}\) = \(\frac{-10}{3+2}\) = \(\frac{-10}{5}\) = - 2

Step-by-step explanation:

Aight, so the same intercept

\( - 2y = - 4 - x = = = > \\ y = \frac{1}{2} x + 2\)

m=½

\(y = \frac{1}{2} x + b = = = > \\ now \: let \: us \: replace \: the \: point \\ 1 = \frac{1}{2} ( - 3) + b = = = > \\ \frac{5}{2} = b\)

soooo

\(y = \frac{1}{2} x + \frac{5}{2} \)

Using proportions, Nelly's total pay for last week was of £220.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From Monday to Friday, she worked 17 hours, hence:

On Saturday, she worked 5 hours, and was paid £16 per hour.

Hence her total payment is found as follows:

15 x 8 + 2 x 10 + 5 x 16 = £220.

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Answer:

Answer down below

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A. \(\frac{20-5}{(-2)-(-1)} = \frac{15}{-1} = -15\)

    \(\frac{5-0}{(-1)-0} = \frac{-5}{1} = -5\)

NOT LINEAR

B. \(\frac{(-6)-1}{(-2)-(-1)} = \frac{-7}{-1} = 7\)

    \(\frac{1-2}{(-1)-0} = \frac{-1}{-1} = 1\)

NOT LINEAR

C. \(\frac{9.4-6.2}{(-2)-(-1)} = \frac{3.2}{1} = -3.2\)

   \(\frac{6.2-3}{(-1)-0} = \frac{3.2}{-1} = -3.2\)

   \(\frac{3-(-0.2)}{0-1} = \frac{3.2}{-1} = -3.2\)

LINEAR

\(\left(x-2\right)^{2}+\left(y-4\right)^{2}=25\)

Hope this helps!

The equation of circle is \((x-2)^{2}+(y-4)^{2} =25\)

The equation of circle is given as,

                 \((x-h)^{2}+(y-k)^{2} =r^{2}\)

Where \((h,k)\) is the coordinate of center and r is radius.

From the given figure,

It is observed that, the center of circular pool is (2, 4)

and radius is 5.

substitute the value of center and radius in above equation.

                  \((x-2)^{2}+(y-4)^{2} =5^{2}\\\\(x-2)^{2}+(y-4)^{2} =25\)  

The equation of circle is \((x-2)^{2}+(y-4)^{2} =25\)

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Answer:

2, 3, 4, 5

Step-by-step explanation:

Answer:

I believe 4 of these are correct,

answer choice, 2,3,4and

Step-by-step explanation:

2 and 3 are correct because of the inverse of the parallel theorem and answer choice 4 is just a straight line has an angle of 180. Since angle 3 corresponds to angle 7 also meaning they are congruent. We can say angle 1 and 7 add up to 180. As for answer 5, it is the same side interior thereom

The upper bound for the 98% confidence interval for the difference in true averages number of flowers visited a day between anna's and allen's hummingbirds is 28.77.

To find the upper bound for the 98% confidence interval for the difference in true average numbers of flowers visited a day between Anna's and Allen's hummingbirds, we need to use the following formula:

Upper bound = (x1 - x2) + zα/2 * √(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1^2 and s2^2 are the sample variances, n1 and n2 are the sample sizes, and zα/2 is the critical value from the standard normal distribution for a 98% confidence interval (which is 2.33).

Plugging in the given values, we get:

Upper bound = (220 - 196) + 2.33 * √(47.2/30 + 40.6/30)

Upper bound = 24 + 2.33 * √(2.84 + 1.35)

Upper bound = 24 + 2.33 * √4.19

Upper bound = 24 + 2.33 * 2.046

Upper bound = 28.77

Therefore, the upper bound for the 98% confidence interval for the difference in true average numbers of flowers visited a day between Anna's and Allen's hummingbirds is 28.77 (rounded to 2 decimal places).

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Answer:

43

Step-by-step explanation:

250-35(from Monday)=215

215/5=43

Hope this helps!

The number of equilibrium points for the given nonlinear system is 3.

To find the equilibrium points, we need to set both equations to zero and solve for x and y:

1. x′ = y² − xy = 0
2. y′ = x³y² − x = 0

First, let's look at equation 2. We can factor x out:

x(y²x² - 1) = 0

There are two possibilities:

a. x = 0: Substitute x = 0 in equation 1:

y² - 0 = y² = 0 => y = 0

So, we have one equilibrium point (0, 0).

b. y²x² - 1 = 0: Replacing this in equation 1:

y² - (y²x² - 1)y = 0

Factor out y:

y(y²(1 - x²) - 1) = 0

There are two more possibilities:

i. y = 0: We already considered this case (0, 0).

ii. y²(1 - x²) - 1 = 0: This equation gives us two equilibrium points: (-1, 1) and (1, 1).

Thus, the system has a total of 3 equilibrium points: (0, 0), (-1, 1), and (1, 1).

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