. Darlene is collecting prize tickets. The equation y = 2x + 1 describes the relationship betweenthe number of days (x) since she began collecting and the number of prize tickets (y) she hascollected. Which statement correctly describes a solution of the equation?A. Darlene has collected 2 prize tickets at the end of 1 day.B. Darlene has collected 4 prize tickets at the end of 9 days.C. Darlene has collected 22 prize tickets at the end of 10 days.D. Darlene has collected 25 prize tickets at the end of 12 days.

The exact value of x is √1156 and it follows the Pythagorean triple

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

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Answer:

x = -2

Step-by-step explanation:

Step 1: Define

f(x) = -x - 5

f(x) = -3

Step 2: Substitute and Evaluate

-3 = -x - 5

2 = -x

x = -2

The calculated value of y when x = 8 is 10.125

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

y varies inversely as the square of x

Mathematically, this can be expressed as

y = k/x²

So, we have

k = x²y

Given that x = 6 when y = -18, we have

k = 6² * -18

So, we have

k = -648

When x = 8, we have

y = -648/8²

Evaluate

y = -10.125

Hence, the value of y is 10.125

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a. This situation would be a binomial experiment if the following conditions are met:

The trials are independent: The selection of one part does not affect the selection of the other.

Each trial has two possible outcomes: In this case, defective or non-defective.

The probability of success (finding a defective part) remains constant for each trial: In this case, the probability is 3% or 0.03.

The number of trials is fixed: We are selecting two parts, so the number of trials is predetermined.

b. Here is a tree diagram representing the two-trial experiment:

          D                ND

        /   \            /   \

       D     ND         D     ND

The branches represent the two trials, with D representing a defective part and ND representing a non-defective part.

c. To find the number of experimental outcomes resulting in exactly one defect, we can observe that there are two outcomes that meet this criterion: D-ND and ND-D. Both represent one defective part and one non-defective part.

d. The probabilities associated with finding no defects, exactly one defect, and two defects can be calculated as follows:

Probability of finding no defects: (1 - probability of finding a defective part) * (1 - probability of finding a defective part) = (1 - 0.03) * (1 - 0.03) = 0.97 * 0.97 = 0.9409.

Probability of finding exactly one defect: (probability of finding a defective part) * (probability of finding a non-defective part) + (probability of finding a non-defective part) * (probability of finding a defective part) = 0.03 * 0.97 + 0.97 * 0.03 = 0.0582.

Probability of finding two defects: (probability of finding a defective part) * (probability of finding a defective part) = 0.03 * 0.03 = 0.0009.

Therefore, the probabilities associated with finding no defects, exactly one defect, and two defects are approximately 0.9409, 0.0582, and 0.0009, respectively.

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Let y = the larger number; and x = the smaler number.

Step 1.

Set up a system of equations:

y - x = 1 eq. 1

3y - 2x = 9 eq 2.

Step 2.

Solve the system by elimination:

1. Multiply eq. 1. by -3:

-3y + 3x = - 3 eq 3.

2. Subtract eq. 2. from eq. 3.:

-3y + 3x = - 3

3y - 2x = 9

_____________

x = 6

3. Substituting x = 6 on eq. 1:

y - x = 1

y - 6 = 1

y = 7

Answer: The larger number is 7.

The fountain will occupy a fraction of 50/173 of the Total area of the courtyard.

Let A be the area of the courtyard and F be the area of the fountain.

We know that the area of the stone-covered part of the courtyard is 246 square feet.

So, the area of the whole courtyard is A = 246 + F square feet.

The fraction of the area of the courtyard occupied by the fountain is given by:

F / A = F / (246 + F)

We can simplify this expression by multiplying the numerator and denominator by the reciprocal of the denominator:

F / A = F / (246 + F) * (1 / (246 + F))

F / A = F / (246 * (246 + F))

F / A = 1 / (246 / F + 1)

We don't know F yet, but we can use the fact that the fountain is rectangular to set up an equation relating the length and width of the fountain:

F = L * W

where L is the length of the fountain and W is the width of the fountain.

We also know that the perimeter of the fountain is 50 feet:

2L + 2W = 50

Simplifying this equation, we get:

L + W = 25

Solving for one variable in terms of the other, we get:

L = 25 - W

Substituting this expression for L into the equation for F, we get:

F = (25 - W) * W

Expanding this expression, we get:

F = 25W - W^2

We also know that the cost of the fountain is $600, which includes installation. So, we can set up another equation relating the cost of the fountain to its dimensions:

1.5LW = 600

Substituting 25 - W for L, we get:

1.5(25 - W)W = 600

Expanding and simplifying this equation, we get:

W^2 - 25W + 400 = 0

Solving this quadratic equation, we get:

W = 20 or W = 5

We reject the solution W = 5 because it implies a negative length for the fountain, which is not physically possible. Therefore, the width of the fountain is W = 20 feet and its length is L = 25 - W = 5 feet.

The area of the fountain is therefore:

F = L * W = 5 * 20 = 100 square feet

The fraction of the area of the courtyard occupied by the fountain is

F / A = 100 / (246 + 100) = 100 / 346 = 50 / 173

So, the fountain will occupy a fraction of 50/173 of the total area of the courtyard.

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Answer:

False

Step-by-step explanation:

I did the E2020 assignment

Answer:

52500

Step-by-step explanation:

first do 5*105 to get 525 then mutiply by 100 to get 52500

Answer:

y = x - 2

Step-by-step explanation:

y = x + b

3 = 5 + b

y = x - 2

We can use the slope intercept form of a line.

y = mx+b where m is the slope and b is the y intercept

y = 1x +b

Substitute the point into the equation

3 = 1*5+b

3 = 5+b

Subtract 5 from each side

3-5 = 5+b-5

-2 =b

y = x-2

Step-by-step explanation:

if you 12kg cost 20 what about 5kg that will be 5kg×20÷12kg= 8.33 when you round of to the nearest hundredth this is the price of 5kg

sorry but i dont think i know how to answer the other question i have done what i only know thankyou

Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

After integration, the required function f is (2x³ - sin (x) + Cx + D).

What is the integration of 'xⁿ' and 'sin (x)'?

\(\int {x^{n} } \, dx = \frac{x^{n+1} }{n+1} + C\\\\\\\int {sinx} \, dx = -cosx + C\)

Given, f''(x) = 12x + sin x

Therefore,

\(\int {f''(x)} \, dx \\\\=\int {f'(x)} \, dx \\\\\\= \int{12x + sin x} \, dx + C\\\\= 6x^{2} - cosx + C\\\)

Again, f'(x) = 6x - cos (x) + C

Therefore,

\(\int {f'(x)} \, dx\\ \\=\int {f(x)} \, dx \\\\= \int {6x^{2} - cosx + C } \, dx \\\\= 2x^{3} - sinx + Cx + D\)

Therefore, the required function is (2x³ - sin (x) + Cx + D).

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Answer:

Step-by-step explanation:

[-5/13] 3/5 +12+13 [-4/5 = - 63/65

Answer:

Distributive property

Step-by-step explanation:

Evan is likely to have 247 points at the end of the regular season. He will surpass the 200-point milestone.

To determine if Evan will reach 200 points during the regular season, we need to calculate the number of points he can potentially score in the remaining three games.

Given his shot chart:

2-Point attempts: 40

2-Point made: 25

3-Point attempts: 31

3-Point made: 13

Free throw attempts: 74

The free throw made: 68

First, let's calculate the total points Evan has scored so far:

2-Point made: 25 * 2 = 50 points

3-Point made: 13 * 3 = 39 points

The free throw made: 68 * 1 = 68 points

Total points scored so far: 50 + 39 + 68 = 157 points

Now, let's calculate the maximum number of points Evan can potentially score in the remaining three games:

2-Point attempts:

3 games * 5 attempts/game * 2 points/attempt = 30 points

3-Point attempts:

3 games * 5 attempts/game * 3 points/attempt = 45 points

Free throw attempts:

3 games * 5 attempts/game * 1 point/attempt = 15 points

Total potential points in the remaining three games:

30 + 45 + 15 = 90 points

Finally, let's calculate the projected total points for the season:

Total points scored so far: 157 points

Total potential points in the remaining three games: 90 points

Projected total points for the season: 157 + 90 = 247 points

Based on his shot chart and the given attempts per game, Evan is likely to have 247 points at the end of the regular season. He will surpass the 200-point milestone.

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Using the z-distribution, the z-statistic would be given as follows:

c) z = -2.63.

At the null hypothesis we test if the means are equal, hence:

\(H_0: \mu_D - \mu_C = 0\)

At the alternative hypothesis, it is tested if they are different, hence:

\(H_1: \mu_D - \mu_C \neq 0\)

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{s}\)

In which \(\mu = 0\) is the value tested at the null hypothesis.

Hence:

\(z = \frac{\overline{x} - \mu}{s}\)

\(z = \frac{-2 - 0}{0.76}\)

z = -2.63.

Hence option B is correct.

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The sampling that would most likely introduce a sampling error is (a) Choosing the first 10 events for the sample

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

The list of options

Also, we have

Tosses = 20

From the list of options, we have

(a) Choosing the first 10 events for the sample

This techique will introduce a sampling error because the selection done by the sampling is not a random selection

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Answer:

Which three questions?

Step-by-step explanation:

I've answered this first question, I guess I need two more...

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

The given expression represents the present value of a series of future cash flows discounted at a rate of 6.5% per year.

Each term in the expression represents a cash flow at a specific time in the future, and the denominator in each term represents the discount factor, which reflects the time value of money.

The first term, $250,000 / (1+0.065)^1, represents a cash flow of $250,000 that will be received in one year.

To determine its present value, we divide it by the discount factor (1+0.065)^1, which reflects the fact that the money will be received one year from now and is, therefore, less valuable than money received today.

Similarly, the second term, $37,500 / (1+0.065)², represents a cash flow of $37,500 that will be received in two years.

To determine its present value, we divide it by the discount factor (1+0.065)²,

which reflects the fact that the money will be received two years from now and is, therefore, less valuable than money received today.

This process is repeated for each term in the expression, representing cash flows that will be received in three, four, five, and six years, respectively.

The sum of these present values represents the total present value of the cash flows or the amount that they are worth today if they are discounted at a rate of 6.5% per year.

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There will be $210.62 in Shawn's savings account at the end of 2 years, hence, option B is correct.

Using the compound interest formula,

A = P(1 + r)ⁿ where amount of money is A in the account after n years, principal (initial deposit) is P, interest rate per year (as a decimal) is r, and  number of years is n. In this case, P = $100, r = 0.035, and n = 2. Plugging these values into the formula, we get,

A = $100(1 + 0.035)²

A = $100(1.072225)

A = $107.22

Therefore, Shawn will have $107.22 in his account at the end of 2 years, which is closest to option B-210.62 (if we assume the deposit is made at the end of each year).

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Answer:

$2600

Step-by-step explanation:

2/100×70000=1400

2/100×60000=1200

1400+1200=2600

9514 1404 393

Answer:

  B.  1/2

Step-by-step explanation:

Maybe you want  the solution to ...

  \(9^x-1=2\)

You can use logarithms, or your knowledge of powers of 3 to solve this.

  \(9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}\)

Using logarithms, the solution looks like ...

  \(x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}\)

Answer:

The population reached a total of 19880 people in 1967.

Step-by-step explanation:

The population in t years after 1951 is given by:

\(P(t) = 130t + 17800\)

Which year the population reached a population of 19880 people.

This is t years after 1951

t is found when \(P(t) = 19880\)

So

\(P(t) = 130t + 17800\)

\(19880 = 130t + 17800\)

\(130t = 2080\)

\(t = \frac{2080}{130}\)

\(t = 16\)

1951 + 16 = 1967

The population reached a total of 19880 people in 1967.

Answer:

16 ounces equals one pound or two cups. Another way to look at the equivalent is that one cup weighs eight ounces and therefore two cups equal 16 ounces and this is the same weight of one pound--16 ounces.

Step-by-step explanation:

Answer:

The null hypothesis is that the mean daily iron intake of the low-income group is equal to or greater than the general population, and the alternative hypothesis is that the mean daily iron intake of the low-income group is less than that of the general population.

H0: μ >= 14.44

Ha: μ < 14.44

(b) We can use a one-tailed t-test to test this hypothesis. With a sample size of 51, degrees of freedom of 50, a sample mean of 12.50, a population mean of 14.44, and a standard deviation of 4.75, we can calculate the t-statistic as follows:

t = (12.50 - 14.44) / (4.75 / sqrt(51)) = -3.16

Using a t-distribution table with 50 degrees of freedom and a significance level of .05, the critical value is -1.677. Since the calculated t-statistic is less than the critical value, we reject the null hypothesis.

Therefore, we can conclude that the mean daily iron intake among the low-income group is significantly lower than that of the general population at a significance level of .05.

(c) The p-value for this test is the probability of obtaining a t-value of -3.16 or more extreme assuming the null hypothesis is true. Using a t-distribution table with 50 degrees of freedom, we find the p-value to be less than .005.

(d) The null hypothesis is that the standard deviation of the low-income group is equal to or greater than that of the general population, and the alternative hypothesis is that the standard deviation of the low-income group is less than that of the general population.

H0: σ >= 5.56

Ha: σ < 5.56

(e) We can use a chi-square test to test this hypothesis. With a sample size of 51, degrees of freedom of 50, and a sample standard deviation of 4.75, we can calculate the chi-square statistic as follows:

chi-square = (n - 1) * s^2 / σ^2 = 50 * 4.75^2 / 5.56^2 = 39.70

Using a chi-square distribution table with 50 degrees of freedom and a significance level of .05, the critical value is 68.67. Since the calculated chi-square statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the standard deviation of daily iron intake among the low-income group is significantly lower than that of the general population at a significance level of .05.

The optimal row strategy =  (7/11, 8/11)

the optimal column strategy =  \(\begin{bmatrix}\frac{3}{11} \\\\\frac{5}{11}\end{bmatrix}\)

and the expected value of the game = 1/11

Let the row player be R and the column player be C.

We know that the expected value of R’s payoff is given by,

\(\begin{bmatrix}p & 1-p\end{bmatrix} \begin{bmatrix}3 & -1 \\-5 & 2 \end{bmatrix} \begin{bmatrix}q\\1-q\end{bmatrix}\\\\=\begin{bmatrix}3p-5+5p & -p+2-2p\end{bmatrix}\begin{bmatrix}q\\1-q\end{bmatrix}\\\\=\begin{bmatrix}8p-5 & -3p+2\end{bmatrix}\begin{bmatrix}q\\1-q\end{bmatrix}\)

= (8p - 5)q  + (-3p + 2)(1 - q)

= 8pq - 5q - 3p + 2 + 3pq - 2q

= 2 + 11pq - 3p - 7q

= 1/11 + 11 (p - 7/11)(q - 3/11)

If R sets p equal to 7/11, then R is guaranteed an expected payoff of 1/11.

If R chooses any other value of p, C can choose a value of q that will make the expression 11 (p - 7/11)(q - 3/11) negative giving a payoff

for R which is less than 1/11.

If R sets p < 7/11 then the expression 11 (p - 7/11)(q - 3/11) is negative as long as q > 3/11.

If p > 7/11 then the expression 11 (p - 7/11)(q - 3/11) is negative as long as q < 3/11.

An expected payoff of 1/11 is the best that R can do if C uses an optimal counterstrategy.

Thus, R’s optimal mixed strategy is (7/11, 8/11)

Similarly C’s best counterstrategy is to set q equal to 3/11 since otherwise R can choose a value of p making the expression 11 (p - 7/11)(q - 3/11) positive to give an expected payoff for R that is greater than 1/11 (thus a payoff for C which is less than -1/11).

Thus C’s optimal strategy is given by \(\begin{bmatrix}\frac{3}{11} \\\\\frac{5}{11}\end{bmatrix}\)

Since the expected pay-off is given by  1/11 + 11 (p - 7/11)(q - 3/11), the value of the game is given by ν = 1/11

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Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A' = (-3, 3 + 3) = (-3, 6)

B' = (0, 7 + 3) = (0, 10)

C' = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).

So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).