Question in the picture below

There is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.

The null hypothesis is that the true proportion of blocks that contain gold is equal to 0.20. The alternative hypothesis is that the true proportion of blocks that contain gold is less than 0.20.

The test statistic is calculated as follows:

z = (p - p₀) / √(p₀(1-p₀) / n)

The test statistic is equal to -2.00.

The p-value is calculated as follows:

p-value = 2 * P(Z < -2.00)

The p-value is equal to 0.0477.

Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Therefore, there is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.

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Given 20% of the pupils are girls and the rest are boys. So, there are a total of 1785 pupils in the school.

To solve this problem, we can start by using the information that 20% of the pupils are girls to find the total number of girls and boys in the school. If there are a total of x pupils, then 0.2x are girls and 0.8x are boys.

Next, we can use the fact that the ratio of the number of pupils who wear spectacles to those who do not wear spectacles is 1:5 to find the number of pupils who wear spectacles. Let the number of pupils who wear spectacles be y, then 1/6y are girls who wear spectacles and 5/6y are boys who wear spectacles.

We also know that there is an equal number of girls and boys who wear spectacles, so we can write:

1/6y = 5/6y / 4

where 4 is the ratio of boys to girls who wear spectacles.

Solving for y, we get y = 357 * 24 = 8568. Therefore, the total number of pupils in the school is:

x = 0.2x + 0.8x = 1785

Hence, there are 1785 pupils altogether in the school.

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Correct answers -

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

To answer the given questions, let's go step by step:

a. To find the rate of change of water in the pool at t=5 hours, we need to calculate the difference between the rate of water being pumped into the pool and the rate of water leaking from the pool at that specific time.

Rate of change of water in the pool at t=5 hours = P(5) - L(5)

P(5) = 1170 gal/hour (given)

L(5) = [tex]0.3e^5[/tex] gal/hour (given)

Substituting the values into the equation:

Rate of change of water in the pool at t= 5 hours = 1170 - [tex]0.3e^5[/tex]

b. To write an integral expression to calculate the total volume of water in the pool at t=10 hours, we need to integrate the rate of water being pumped into the pool over the time interval [0, 10] and subtract the integral of the rate of water leaking from the pool over the same interval.

Total volume of water in the pool at t=10 hours = ∫[0,10] P(t) - ∫[0,10] L(t) dt

P(t) = 1170 gal/hour (given)

L(t) = [tex]0.3e^t[/tex] gal/hour (given)

Calculating the integrals:

∫[0,10] P(t) dt = ∫[0,10] 1170 dt = 1170t | [0,10] = 1170 × 10 - 1170 × 0 = 11700 gallons

∫[0,10] L(t) dt = ∫[0,10] 0.3[tex]e^t[/tex] dt = 0.3 ∫[0,10] [tex]e^t[/tex]dt = 0.3 ([tex]e^t[/tex]) | [0,10] = 0.3 × ([tex]e^{10} - e^0[/tex]) ≈ 0.3 × (22025 - 1) ≈ 6606.9 gallons

Total volume of water in the pool at t=10 hours = 11700 - 6606.9 ≈ 5093.1 gallons

c. To find the average rate of change of water in the pool over the 10 hours, we need to divide the change in volume by the time interval.

Average rate of change of water in the pool = (Change in volume) / (Time interval)

Change in volume = Total volume of water in the pool at t=10 hours - Initial volume of water in the pool

Change in volume = 5093.1 - 1200 = 3893.1 gallons

Time interval = 10 hours

Average rate of change of water in the pool = 3893.1 / 10 = 389.31 gallons/hour

d. To find the absolute maximum volume of water in the pool over the interval [0,10], we need to find the maximum value of the volume function within that interval.

To determine this, we can find the critical points by setting the derivative of the volume function equal to zero and check the endpoints of the interval.

Since the volume function is not provided, we cannot directly find the absolute maximum volume without additional information.

Final answers-

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

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The better statistics to compare the distribution are given as follows:

A. Mean and standard deviation.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

The standard deviation of a data-set is calculated as square root of the sum of the differences squared between each observation and the mean of the data-set, divided by the cardinality of the data-set.

These two measures should be used as both distributions in this problem are symmetric, meaning that they do not contain outliers.

If the distribution contained outliers, then the median and the IQR should have been used.

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Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.

Let's fix this issue using a set of equations. Assume that x is the quantity of lollipops sold and y is the quantity of fruit snacks sold.

Then we have two equations based on the information given:

x + y = 13.(Total number of fruit snacks and lollipops sold)

1.5x + 1.25y= 18.25 (total amount of money earned)  

To solve for x and y, we can use the substitution method :

x + y = 13 (equation 1)

1.5x + 1.25y = 18.25 (equation 2)

From equation 1, we have x = 13 - y. Substituting this into equation 2, we get:

1.5(13 - y) + 1.25y = 18.25

Simplifying and solving for y, we get

19.5 - 0.25y = 18.25

-0.25y = -1.25

y = 5

Nakeisha therefore sold 5 fruit treats. We may change y = 5 into equation 1 and solve for x to get the quantity of lollipops sold:

x + 5 = 13

x = 8

Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.

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Answer:

25.54

Step-by-step explanation:

SOH CAH TOA

           v            

   Cos 0 = [tex]\frac{adj}{hyp}[/tex]

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

11.

Cos 20° = [tex]\frac{adj}{hyp}[/tex]

Cos 20° = [tex]\frac{24}{x}[/tex]

*Rearrange*

[tex]x[/tex] = [tex]\frac{24}{Cos 20}[/tex]

*Cos 20° = 0.9397*

[tex]x[/tex] = [tex]\frac{24}{0.9397}[/tex]

[tex]x[/tex] = 25.5400659785

Nearest tenth: 25.54

Answer: 6 cups

Step-by-step explanation:

Answer:

The price would be 7.20

Step-by-step explanation:

Answer:

a) It would have taken 1 person 14 days to do this amount of work.

b) It would take 1 person 56 days to finish building this house extension.

We know that 1 person can build a house extension in 70 days. This means that in 1 day, 1 person can do 1/70 of the work. In 7 days, 2 people can do 2 * 7 * 1/70 = 2/10 of the work. This means that 1 person can do 1/10 of the work in 7 days. To finish the remaining 8/10 of the work, 1 person would need 7 * 8 = 56 days.

Step-by-step explanation:

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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Answer:

  322 in²

Step-by-step explanation:

You want the surface area of the rectangular prism with edge lengths 7 in, 14 in, and 3 in.

The surface area can be computed using the formula ...

  A = 2(LW +H(L +W))

  A = 2(7·14 + 3(7 +14)) = 2(98 +63) = 322

The area of the prism is 322 square inches.

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a+c = b+d , because angle c = angle b and a = d

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Angles on parallel lines can be alternate, corresponding or verically opposite to each other. And when they have these properties, the angles are equal to reach other.

b = c , since b+y = 360 and c+y = 360

and also a + x = 180

d + x = 180

therefore a = d

Therefore;

in b+d , we can substitute c for a and b for c

therefore b+d = a+c

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If log 7 equals a and log 8 equals b then log 224 equals: E: none of the above.

Simplify the expression for log (224) by using:

log (ab) = log (a) + log (b) and log (a/b) = log (a) - log (b):

So,

log (224) = log ( 7 × 8 × 4)

= log (7) + log (8) + log (4)

Since log(4) = 0 (since 4 = 2^2)

Simplify

log(224) = log (7) + log (8) + log (4)

= log 7 + log 8

= a + b

Therefore the correct option is E.

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Answer:

6 units right

Step-by-step explanation:

To translate figure P onto figure Q, just translate the figure 6 units to the right.

To find the probability of selecting either a Red or a Brown almond M&M, we need to add their respective probabilities. The probability of selecting either a red or brown almond M&M is 0.2 or 20%.

P(R or Br) = P(R) + P(Br)

From the table given, we know that the probability of selecting a Red almond M&M is 0.1 and the probability of selecting a Brown almond M&M is also 0.1. Therefore,

P(R or Br) = 0.1 + 0.1 = 0.2

So, the probability of selecting either a Red or a Brown almond M&M is 0.2 or 20%.

In summary, to find the probability of selecting either one event or another event, we add their probabilities together. In this case, the probability of selecting a Red or a Brown almond M&M is 0.2 or 20%.

To find the probability of selecting either a red (R) or brown (Br) almond M&M, you can simply add the individual probabilities for each color since they are mutually exclusive events (selecting one does not affect the other).

According to the given probability distribution, the probability of selecting a red M&M (R) is 0.1, and the probability of selecting a brown M&M (Br) is 0.1.

So, to find the probability of selecting either a red or brown M&M (P(R or Br)), you can use the formula:

P(R or Br) = P(R) + P(Br)

Plugging in the given probabilities:

P(R or Br) = 0.1 (for R) + 0.1 (for Br)

P(R or Br) = 0.2

So, the probability of selecting either a red or brown almond M&M is 0.2 or 20%.

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The equation for finding amount of daily pay is bus-driver gets paid $100 each day plus $0.20 per kilometer, "k" is p = 100 + 0.20k.

The equation for finding the amount of daily pay, "p", in the given situation would be : p = 100 + 0.20k,

In this equation, "p" represents the total daily-pay, "100" is the fixed amount paid each day, and

"$0.20" is the rate per kilometer. "k" represents the number of kilometers driven on that day.

To calculate the daily pay, you add the fixed amount of $100 to the product of the rate per kilometer and the number of kilometers driven on that day.

Therefore, the required equation is p = 100 + 0.20k.

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The given question is incomplete, the complete question is

Write an equation for finding the amount of daily pay, p, in the following situation: A bus driver gets paid $100 each day plus $0.20 per kilometer, "k".

Answer:

r≈19.1cm

Step-by-step explanation:

Using the formula

C=2πr

Solving forr

r=C

2π=120

2·π≈19.09859cm

Hope this helps

Answer:

3 ways

Step-by-step explanation:

Using the arrows that they gave us, (which are the directions). The only possible ways are 3. Which I have shown in the screenshot attached below.

If we were to try to do it another time using the directions, it wouldn't work and we would most likely skip a step

Hope I helped!

The first term of an A.P is 14 and the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the A.P is 70/11.

The first term of an A.P is 14. Let the common difference be d. Then the second term of the A.P is given by 14 + d. Similarly, the third term of the A.P is given by 14 + 2d.

The third term of the A.P.Solution:

Sum of the first 5 terms of the A.P can be expressed as:

5/2 [2a + (5 - 1) d] = 5/2 [2(14) + 4d] = 35 + 10d

Sum of the first 10 terms of the A.P can be expressed as:

10/2 [2a + (10 - 1) d] = 10/2 [2(14) + 9d] = 70 + 45d

According to the question, the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. It can be written as follows: 35 + 10d = - (70 + 45d)

Simplifying the above equation, we get:

55d = -105⇒ d = -105/55 = -21/11

Substituting the value of d in 14 + 2d, we get:

14 + 2d = 14 + 2(-21/11) = 14 - 42/11= 112/11 - 42/11= 70/11

Hence, the third term of the A.P is 70/11.

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We can match the terms in the left column to the correct bolded examples as follows:

Sum: 1 + 1 = 2

Difference: 7 - 2 = 5

Term: 2x

Product: 9 * 9 = 81

Factor: 81 ÷ 9 = 9

Quotient: 81 ÷ 9 = 9

Coefficient: 7x - 8y

Variable: 5x + 3

To match the correct expression, an understanding of the mathematical terms is essential. The sum is the addition of terms and in the list, 1 + 1 is an example of a sum. Also, the product is the multiplication of numbers and 9 * 9 = 81 is an example of a product.

Coefficients are numbers that are matched with letters in algebra. A variable is a letter beside a number in an expression. In the option, x is the variable besides 5.

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Answer:

the answer is lateral area

The steps correcting the error;

Step 1: Convert the mixed fraction to improper fractions

Step 2: Find the lowest common  factor

27/8

A fraction can be defined as the part of a whole number, variable or element.

The different types of fractions are;

From the information given, we have that;

10 1/4 - 6 7/8

First, convert the mixed fractions to improper fractions, we have that;

Multiply the numerator of the fraction by the whole number then add the numerator

41/4 - 55/8

Find the LCM

82 - 55 /8

subtract the value

27/8

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The correct statement according to the zero product property is the one in option B.

The zero product property says that if the product of two numbers A and B is zero, then either A or (and) B are equal to zero.

Then if:

(x + 10)*x = 0

Then we have that either:

x = 0

or:

x + 10 = 0

x = -10

Then the correct option is B:

"Either x = 0 or x + 10 =0"

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In the chi-square test expected frequencies represent The frequencies one would expect if the null hypothesis were true

The expected frequencies in the chi-square test represent the frequencies one would expect if the null hypothesis were true. This means that the expected frequencies are calculated based on the assumption that there is no significant difference between the observed and expected frequencies, as suggested by the null hypothesis. The chi-square test compares the observed frequencies with the expected frequencies to determine if there is a significant association or difference between the variables being studied.

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To convert the vertex form of a quadratic equation to standard form, we need to expand the squared term and simplify the expression.

Starting with the vertex form of the equation of a parabola:

y = 2(x - 3)^2 + 5

We can expand the squared term using the square of a binomial formula:

y = 2(x^2 - 6x + 9) + 5

Next, we distribute the coefficient 2:

y = 2x^2 - 12x + 18 + 5

Simplifying the constant terms:

y = 2x^2 - 12x + 23

This is the standard form of the equation of the parabola.

Therefore, the polynomial that passes through the given points is: f(x) = 6 - 38x - 6x^2 + 4x^3 + 3x^4.

To find the polynomial that passes through the given points, we can use the method of interpolation. Since we have five points, we can use a fourth-degree polynomial to fit the data.

Let's assume that the polynomial is of the form:

f(x) = a0 + a1x + a2x^2 + a3x^3 + a4x^4

We can find the coefficients a0, a1, a2, a3, and a4 by substituting the given points into the equation and solving the resulting system of linear equations.

Substituting (-4, 89) into the equation, we get:

89 = a0 - 4a1 + 16a2 - 64a3 + 256a4

Substituting (-3, 7) into the equation, we get:

7 = a0 - 3a1 + 9a2 - 27a3 + 81a4

Substituting (-1, -1) into the equation, we get:

-1 = a0 - a1 + a2 - a3 + a4

Substituting (1, -1) into the equation, we get:

-1 = a0 + a1 + a2 + a3 + a4

Substituting (4, 329) into the equation, we get:

329 = a0 + 4a1 + 16a2 + 64a3 + 256a4

Now we have five linear equations with five unknowns, which we can solve using any method of linear algebra. One possible way is to use matrix inversion. After solving for the coefficients, we get:

a0 = 6

a1 = -38

a2 = -6

a3 = 4

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The area of the trapezium ABCD is 136 square cm

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

The image of the trapezium (see attachment)

The area of the trapezium ABCD is calculated as

Area = 1/2 * Sum of opposite sides * Height

When the given values are substituted in the above equation, we have the following equation

Area = 1/2 * (14 + 20) * 8

Evaluate the sum

Area = 1/2 * 34 * 8

Evaluate the products

Area = 136

Hence, the area of the trapezium ABCD is 136 square cm

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The sum of the x-values where f(x) = g(x) is 3

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

f(x) = 3(2)ˣ

g(x) = 6x

When f(x) = g(x), we have

3(2)ˣ = 6x

Solving for x, we have

x = 1 and x = 2

When these values are added, we have

Sum = 1 + 2

Evaluate

Sum = 3

Hence, the sum of the x-values where f(x) = g(x) is 3

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Answer:

Step-by-step explanation:

The transformation for the function g(x) = 5ˣ - 2 involves a vertical shift downward by 2 units compared to the parent function f(x) = 5ˣ. This is because the constant term (-2) is subtracted from the function. So, the graph of g(x) will be identical to the graph of f(x), except that it will be shifted downward by 2 units. Specifically, the point (0, 1) on the graph of f(x) will be shifted down to (0, -1) on the graph of g(x), and similarly, all other points on the graph will be shifted downward by 2 units.

The measure of arc ZWX is 180 degrees.

Given that WZ and XR are diameters, we know that they are both perpendicular to chord WX. This creates four right angles at point X, and as a result, we have a rectangle formed by the four line segments.

Since WZ and XR are diameters, they each extend from one end of the rectangle to the other. This means that arc ZWX is actually a semicircle, with a measure of 180 degrees.

To see why this is the case, consider that a full circle has a measure of 360 degrees. Since arc ZWX spans exactly half of the circle, it must have a measure of half the circle, or 180 degrees.

In summary, the measure of arc ZWX is 180 degrees. This can be derived from the fact that WZ and XR are diameters, which create a rectangle and a semicircle in the process. While the figure may not be drawn to scale, the relationships between the different line segments and angles remain constant, allowing us to determine the measure of arc ZWX with confidence.

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