Solve the question below

Answer:

That video should help you a lot...

Step-by-step explanation:

https://youtu.be/u2L0qWVePfc

Answer:

20

Step-by-step explanation:

just add the 13 to A and B

Answer:

23

Step-by-step explanation:

7-5(1)+3(7)

7-5+21

2+21

23

Answer:

7-5+21 = 23

Step-by-step explanation:

7 - 5p+ 3q

7 - 5(1) + 3(7)

7 - 5 + 21

7 + 16

= 23 hope this helps :)

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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Answer:

Watermelon A weighs 2 kg, watermelon B weighs 4 kg and watermelon C weighs 10 kg.

Step-by-step explanation:

Watermelon A is 2 kg lighter than watermelon B and 5 times lighter than watermelon C. This means that:

A = B - 2

and

A = C / 5 => C = 5A

Watermelons A and C together are 3 times heavier than watermelon B. This means that:

A + C = 3*B = 3B

Put C = 5A:

A + 5A = 3B

6A = 3B

=> B = 6/3 A = 2A

=> A = 2A - 2

=> 2A - A = 2

=> A = 2 kg

B = 2 * 2 = 4 kg

C = 5 * 2 = 10 kg

Therefore, watermelon A weighs 2 kg, watermelon B weighs 4 kg and watermelon C weighs 10 kg.

Answer:

a) \(a = 2\) and \(b = -4\), b) \(c = -10\), c) \(f(-2) = -\frac{5}{3}\), d) \(y = -\frac{5}{2}\).

Step-by-step explanation:

a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:

1) A root of the polynomial at numerator is -2. (Removable discontinuity)

2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.

We analyze each polynomial by factorization and direct comparison to determine the values of \(a\), \(b\) and \(c\).

Denominator

i) \((x+2)\cdot (x-1) = 0\) Given

ii) \(x^{2} + x-2 = 0\) Factorization

iii) \(2\cdot x^{2}+2\cdot x -4 = 0\) Compatibility with multiplication/Cancellative Property/Result

After a quick comparison, we conclude that \(a = 2\) and \(b = -4\)

b) The numerator is analyzed by applying the same approached of the previous item:

Numerator

i) \(c\cdot x - 5\cdot x^{2} = 0\) Given

ii) \(x \cdot (c-5\cdot x) = 0\) Distributive Property

iii) \((-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0\) Distributive and Associative Properties/\((-a)\cdot b = -a\cdot b\)/Result

As we know, this polynomial has \(x = -2\) as one of its roots and therefore, the following identity must be met:

i) \(\left(x -\frac{c}{5}\right) = (x+2)\) Given

ii) \(\frac{c}{5} = -2\) Compatibility with addition/Modulative property/Existence of additive inverse.

iii) \(c = -10\) Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result

The value of \(c\) is -10.

c) We can rewrite the rational function as:

\(f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}\)

After eliminating the removable discontinuity, the function becomes:

\(f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)\)

At \(x = -2\), we find that \(f(-2)\) is:

\(f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right]\)

\(f(-2) = -\frac{5}{3}\)

d) The value of the horizontal asympote is equal to the limit of the rational function tending toward \(\pm \infty\). That is:

\(y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}\) Given

\(y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right]\) Modulative Property

\(y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right]\) Existence of Multiplicative Inverse/Definition of Division

\(y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)\)   \(\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}\)

\(y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)\)   \(\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}\)/\(x^{m}\cdot x^{n} = x^{m+n}\)

\(y = -\frac{5}{2}\) Limit properties/\(\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0\), for \(n \geq 1\)

The horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\).

Using asymptote concepts, it is found that:

a) Building a quadratic equation with leading coefficient 2 and roots 1 and -2, it is found that a = 2, b = -4.

b) c = -10, since the discontinuity at x = -2 is removable, the numerator is 0 when x = -2.

c) Simplifying the function, it is found that at \(x = -2, f(x) = -\frac{5}{3}\).

d) The equation for the horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\)

-------------------------

Item a:

\(2(x - 1)(x - (-2)) = 2(x - 1)(x + 2) = 2(x^2 + x - 2) = 2x^2 + 2x - 4\)

\(2x^2 + ax + b = 2x^2 - 2x - 4\)

Thus a = 2, b = -4.

-------------------------

Item b:

\(-2c - 5(-2)^2 = 0\)

\(-2c - 20 = 0\)

\(2c = -20\)

\(c = -\frac{20}{2}\)

\(c = -10\)

-------------------------

Item c:

With the coefficients, the function is:

\(f(x) = \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \frac{-5x(x + 2)}{2(x - 1)(x + 2)} = -\frac{5x}{2(x - 1)}\)

At x = -2:

\(-\frac{5(-2)}{2(-2 - 1)} = -\frac{-10}{-6} = -(\frac{5}{3}) = -\frac{5}{3}\)

Thus, simplifying the function, it is found that at \(x = -2, f(x) = -\frac{5}{3}\)

-------------------------

Item d:

The horizontal asymptote of a function is:

\(y = \lim_{x \rightarrow \infty} f(x)\)

Thus:

\(y = \lim_{x \rightarrow \infty} \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \lim_{x \rightarrow \infty} \frac{-5x^2}{2x^2} = \lim_{x \rightarrow \infty} -\frac{5}{2} = -\frac{5}{2}\)

The equation for the horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\)

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The height of the ball will be 16.94 feet. Then the baseball travels over the fence.

Given that:

Distance at time t, x = 140t

Height at time t, y = 3.1 + 40t − 16t²

Height, h = 10 feet

Distance, x = 320 feet

The time is calculated as,

320 = 140t

t = 320/140

t = 16/7

The height at t = 16/7 is calculated as,

y = 3.1 + 40(16/7) − 16(16/7)²

y = 3.1 + 97.43 - 83.59

y = 16.94 feet

y > 10 feet

The height of the ball will be 16.94 feet. Then the baseball travels over the fence.

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The values of p1 and p2 are not dependent on each other. So: the values of p1 and p2 cannot be less than 0; and these values cannot be greater than 1.

The expected values of p1 and p2 is between 0 and 1 (inclusive)

p1 and p2 can be vastly different from 0.66

p1 and p2 can be similar or different

The concept is probability

Given that:

proportion of group 1

proportion of group 2

The expected values of p1 and p2

Because p1 and p2 are proportions, the values of p1 and p2 cannot be less than 0; and these values cannot be greater than 1.

So, the expected values are:

Will p1 and p2 be different from p

As explained earlier, the expected values of p1 and p2 can take any value between 0 and 1.

The values of p1 and p2 are independent of .

So, p1 or p2 can be vastly different from

Similar or different values in p1 and p2

Recall that: the expected values are:

Both values are independent of each other.

So, it will not be surprising, if both values are similar or different.

The statistical concept

When terms like proportions and selections are used as used in this question, the statistical concept is probability.

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(a) The monopolist's profit-maximizing quantity is 50 units, and the price is $100 per unit.

(b) To achieve the allocatively efficient quantity, the government should set the price at $60 per unit.

(c) Producing the allocatively efficient quantity may not be economically feasible for the monopolist as the price is lower than the average total cost of production.

(d) To have the monopolist earn zero economic profit, the government should set the price at $80 per unit.

(e) The deadweight loss will decrease compared to that of the unregulated monopolist.

(a) The profit-maximizing quantity is where marginal revenue equals marginal cost, which occurs at 50 units, and the corresponding price is $100 per unit. At this quantity, the monopolist's total revenue is $5000, and its total cost is $2500, resulting in a profit of $2500.

(b) To achieve allocative efficiency, the government should set the price at the point where the demand curve intersects the marginal cost curve, which is at 70 units and a price of $60 per unit. At this quantity, the price is equal to the marginal cost, and society maximizes its total surplus.

(c) Producing the allocatively efficient quantity may not be economically feasible for the monopolist because the price of $60 per unit is lower than the average total cost of production, which is $75 per unit. Thus, the monopolist will incur losses if it produces at this quantity.

(d) To regulate the monopolist to earn zero economic profit, the government should set the price at the point where the demand curve intersects the average total cost curve, which is at 80 units and a price of $80 per unit. At this quantity, the price is equal to the average total cost, and the monopolist earns zero economic profit.

(e) The deadweight loss will decrease compared to that of the unregulated monopolist because the allocatively efficient quantity is being produced. However, there may still be some deadweight loss due to the difference between the price and the average total cost.

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The conditional probabilities are as follows: P(B | C) = 0.295, P(C | B) = 0.371, P(A | B) = 0.371, P(B | A) = 0.333, P(A | C) = 0.273, and P(C | A) = 0.308. These probabilities represent the likelihood of one event occurring given that another event has already occurred.

To determine the conditional probabilities, we can use the formula:

P(X|Y) = P(X ∩ Y) / P(Y)

where X and Y are events.

1. P(B | C):

P(B | C) = P(B ∩ C) / P(C)

P(B ∩ C) = P(B n C) = 0.13

P(C) = 0.44

P(B | C) = 0.13 / 0.44 = 0.295

2. P(C | B):

P(C | B) = P(C ∩ B) / P(B)

P(C ∩ B) = P(B n C) = 0.13

P(B) = 0.35

P(C | B) = 0.13 / 0.35 = 0.371

3. P(A | B):

P(A | B) = P(A ∩ B) / P(B)

P(A ∩ B) = P(A n B) = 0.13

P(B) = 0.35

P(A | B) = 0.13 / 0.35 = 0.371

4. P(B | A):

P(B | A) = P(B ∩ A) / P(A)

P(B ∩ A) = P(A n B) = 0.13

P(A) = 0.39

P(B | A) = 0.13 / 0.39 = 0.333

5. P(A | C):

P(A | C) = P(A ∩ C) / P(C)

P(A ∩ C) = P(A n C) = 0.12

P(C) = 0.44

P(A | C) = 0.12 / 0.44 = 0.273

6. P(C | A):

P(C | A) = P(C ∩ A) / P(A)

P(C ∩ A) = P(A n C) = 0.12

P(A) = 0.39

P(C | A) = 0.12 / 0.39 = 0.308

Therefore, the conditional probabilities are:

P(B | C) = 0.295

P(C | B) = 0.371

P(A | B) = 0.371

P(B | A) = 0.333

P(A | C) = 0.273

P(C | A) = 0.308

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The value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

GH² = IH × JI {secant tangent segments}

JI = 12 - IH, we shall represent IH with x so that;

8² = x(12 - x)

64 = 12x - x²

x² - 12x + 64 = 0 {rearrange to get a quadratic equation}

with the quadratic formula;

x = [12 + √(-112)]/2 or x = = [12 - √(-112)]/2

√(-112) = 4i√7 {where i = √(-1)}

so;

x = (6 + 2i√7) or x = (6 - 2i√7)

Therefore, the value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)

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Answer:

8 - (2/x

hope it is helpful

Answer:

13

Step-by-step explanation:

Put n as 4

\(3(4)+1=12+1=13\)

Hope this helps :)

X is the total number of cakes she made. From the question, we know there are two kinds of cakes; those she sold and those she didn't. So;

X= number of sold cakes + number of cakes not sold

Here, the number of sold cakes is 15, and the number of cakes left is 4. So,

X= number of sold cakes + number of cakes not sold= 15+4=20

So, the total number of cakes is 20

To conduct a hypothesis test to determine if there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode, we can follow these steps:

1. Define the null hypothesis (H0) and alternative hypothesis (Ha):
  - Null hypothesis (H0): The true percentage of those in the first group who suffer a second episode is the same as the true percentage of those in the second group who suffer a second episode.
  - Alternative hypothesis (Ha): The true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode.

2. Determine the significance level: The significance level is given as 0.1, which means we need to find evidence that is strong enough to reject the null hypothesis with a 10% chance of making a Type I error (incorrectly rejecting a true null hypothesis).

3. Calculate the test statistic: We need to compare the observed proportions in both groups to determine if they are significantly different. The test statistic used for this situation is the z-test for comparing proportions.

4. Calculate the test statistic value: The formula for the z-test for comparing proportions is:
  - Test statistic value = (p1 - p2) / √((p * (1 - p)) * ((1/n1) + (1/n2)))
  - where p1 and p2 are the observed proportions of second episode occurrences in the first and second groups respectively, n1 and n2 are the sizes of the first and second groups respectively, and p is the pooled proportion calculated as (x1 + x2) / (n1 + n2), where x1 and x2 are the number of second episode occurrences in the first and second groups respectively.

5. Determine the critical value(s): The critical value(s) depend on the significance level and the type of test (one-tailed or two-tailed). Since the alternative hypothesis is two-tailed, we will find the critical values for a two-tailed test with a 0.1 significance level.

6. Compare the test statistic value with the critical value(s): If the absolute value of the test statistic value is greater than the critical value(s), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

7. Draw a conclusion: Based on the results of the hypothesis test, we can draw a conclusion regarding whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode.

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Answer:

(-3, 2)

I'm pretty sure.

If 40% of the population is , the probability that both randomly selected people are  is 16%. However, without knowing the percentage of the population that is , we cannot calculate the exact probability.

To find the probability that both randomly selected people are , we need to know the percentage of the population that is . Let's assume that the percentage of the population that is  is 40%.

To calculate the probability that both randomly selected people are , we multiply the probability of the first person being  (40%) by the probability of the second person being  (also 40%). Since the events are independent, we can multiply the probabilities together.

Probability of the first person being  = 40%
Probability of the second person being  = 40%

Probability that both people are  = Probability of the first person being  * Probability of the second person being
= 0.4 * 0.4
= 0.16 (or 16%)

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Answer:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Company A will charge $ 37 less than Company B

Part C:

Company A will charge $ 65 less than Company B

Step-by-step explanation:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Renting a car for 6 days

Company A:

35 * 6 + 15 = 210 + 15 = $ 225

Company B:

42 * 6 + 10 = 252 + 10 = $ 262

Company A will charge $ 37 less than Company B

Part C:

Renting a car for 10 days

Company A:

35 * 10 + 15 = 350 + 15 = $ 365

Company B:

42 * 10 + 10 = 420 + 10 = $ 430

Company A will charge $ 65 less than Company B

Answer:

hypotenuse = 6.3

Step-by-step explanation:

here 6 and 2 are the legs of the triangle . we are asked to find hypotenuse (longest side)

using pythagoras theorem

a^2 + b^2 = c^2

6^2 + 2^2 = c^2

36 + 4 = c^2

40 = c^2

\(\sqrt{40}\) = c

6.32 = c

6.3 = c

We are given the dot-plots of sixth-grade test scores and seventh-grade test scores.

Let us first find the median of the two test scores.

Recall that the median is the value that divides the distribution into two equal halves.

Sixth Grade Geograph Test Scores:

From the dot-plot, we see that 11 is the median test score since it divides the distribution into two equal halves.

Median = 11

Seventh Grade Geograph Test Scores:

From the dot-plot we see that 13 is the median test score since it divides the distribution into two equal halves.

Median = 13

Therefore, the median score of the seventh-grade class is 2 points greater than the median score of the sixth-grade class.

Now let us find the interquartile range which is given by

Seventh Grade Geograph Test Scores:

The upper quartile is given by

At the 10th position, we have a test score of 13

The lower quartile is given by

At the 3rd position, we have a test score of 11

So, the interquartile range is

Sixth Grade Geograph Test Scores

The upper quartile is given by

At the 9th position, we have a test score of 10

The lower quartile is given by

At the 3rd position, we have a test score of 8

So, the interquartile range is

So, the IQR is the same as the difference between medians.

Therefore, the median score of the seventh-grade class is 2 points greater than the median score of the sixth-grade class. The difference is the same as the IQR

Hence, the correct answer is option B

Answer:

\(x=35\)

Step-by-step explanation:

Set the two equations equal:

\(4x+7=6x-63\)

Add 63 to both sides:

\(4x+70=6x\)

Subtract 4x from both sides:

\(70=2x\)

Divide both sides by 2:

\(x=35\)

Answer:

65

Step-by-step explanation:

Triangles are 180 degrees in total. If you add the degrees that are known, 62 and 53, you get 115. Then you would do 180-115, which is 65. 65 would be the value of x. Hope this helps!

Answer:

the 4th one is the answer

Step-by-step explanation:

Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

Answer:

The value of the snack bar is $ 2 and that of the magazine subscription is 25 $

Step-by-step explanation:

We have a system of two equations and two unknowns, which would be the following:

let "x" be the cost of the snack bar

Let "y" be the cost of the magazine subscription

16 * x + 4 * y = 132

20 * x + 6 * y = 190 => y = (190 - 20 * x) / 6

replacing:

16 * x + 4 * (190 - 20 * x) / 6 = 132

16 * x + 126.66 - 13.33 * x = 132

2.66 * x = 132 - 126.66

x = 5.34 / 2.66

x = 2

for "y":

y = (190 - 20 * 2) / 6

y = 25

Which means that the value of the snack bar is $ 2 and that of the magazine subscription is 25 $

Answer: 7

Step-by-step explanation:

If you draw it out, you can visually tell it's 5 units, but you can also tell by looking at the two distinct y values, -2 and 5. The distance between them is 7 units, as you take the absolute value of both of them, then add to get 7.

The rate of change of concentration with respect to time at t=12 minutes is -1/1029 units/m in.

So, the correct answer is A.

To find the rate of change of concentration with respect to time at t=12 minutes, we need to take the derivative of the equation C(t) = 1/6(4t +1)^-1/2 with respect to time.

This will give us the instantaneous rate of change of concentration at t=12 minutes.

The derivative of C(t) is given by -1/12(4t+1)^-3/2(4), which simplifies to -2/(3(4t+1)^3/2).

Plugging in t=12 minutes, we get -2/(3(4(12)+1)^3/2), which simplifies to -1/1029 units/m in.

Hence the answer of the question is A.

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