The population P" of a certain city " t" years from now is
given by " P=15,000e^0.04t.
How many years from now will the population be 60,000? Round
to the nearest tenth.

The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation , the zscore of a measure X is given by:

Z = X-u/σ

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean u  and standard deviation s=σ/\(\sqrt{n}\)

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

u= 5.2 ,σ = 0.08 , n= 20 s= 0.0179

Find the interval that contains 95.44 percent of the sample means.

0.5 - (0.9544/2) = 0.0228

Pvalue of 0.0228 when Z = -2.

0.5 + (0.9544/2) = 0.9772

Pvalue of 0.9772 when Z = 2.

So the interval is from X when Z = -2 to X when Z = 2

Z = 2

Z= X-u/σ

By the central Limit Theorem

Z= X-u/s

X= 5.2358

Z = -2

then

X= 5.1642

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Answer:

Weeks is the independent variable and height is the dependent variable.

Step-by-step explanation:

The height of the plant depends on the weeks the plant has been growing. So the height is the dependent variable. Because the number of weeks doesn't depend on anything, the number of weeks is an independent variable.

The probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

The probability of selecting two bottles of each variety when randomly selecting 6 bottles can be calculated using the formula P(A) = n(A) / n(S), where n(A) is the number of possible ways to select two bottles of each variety and n(S) is the total number of possible ways to select 6 bottles. In this case, n(A) is equal to 6! / (2!2!2!) = 90 and n(S) is equal to 6^6 = 46656. So, the probability of selecting two bottles of each variety is P(A) = 90/46656 = 0.0019.

The probability of selecting all bottles of the same variety when randomly selecting 6 bottles can be calculated using the same formula. In this case, n(A) is equal to 6, which is the number of ways to select 6 bottles of the same variety, and n(S) is equal to 46656. So, the probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

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The area of a circle with a radius of 3.5cm rounded to the nearest tenth is 38.5 cm².

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

Area = πr²

Where r is radius and π is constant pi ( π = 3.14 )

From the diagram;

Plug the given value into the above equation and solve for A.

Area = πr²

Area = 3.14 × ( 3.5cm )²

Area = 3.14 × 12.25 cm²

Area = 38.5 cm²

Therefore, the area of the circle is 38.5 cm².

Option B) 38.5 cm² is the correct answer.

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Answer:

84.04, 30.14 and 55.95

Step-by-step explanation:

First you add the ratios together then divide by 170 and mutliply each answer by the answer of 170 divided by the sum of 3.5, 1.25 and 2.33

Answer:

84.04, 30.14 and 55.95

Step-by-step explanation:

→ Add the ratios together

3.5 + 1.25 + 2.33 = 7.08

→ Divide the answer by 170

170 ÷ 7.08 = 24.01129944

→ Multiply the answer by 3.5 , 1.25 , 2.33

3.5 × 24.01129944 = 84.04

1.25 × 24.01129944 = 30.14

2.33 × 24.01129944 = 55.95

Look at picture for solution.

h = height of mountain

theta = angle of elevation

It can be assumed that the mountain will have its highest point at the center of the mountain.

Answer:

Step-by-step explanation:

Let the height is h and distance to the center of mountain is d.

Use tangent to find the value of h:

We get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

We are given the radius of the circle as:

Radius = r = 14 m

We are also given the value of π as:

π = 3.14

We need to find the perimeter and area of the circle.

Perimeter of the circle is given by:

Perimeter = 2 π r

Substituting the values in the formula, we get that:

P = 2 × (3.14) × (14) m

P = 87.92 m.

Area of the circle is given by:

Area = π r²

Substituting the values in the formula, we get that:

Area = (3.14) × (14)²

A = 615.44 m²

Therefore, we get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

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Answer:

x = 6

y° = 125°

Step-by-step explanation:

9x + 1 and 7x + 13 are alternate angles and has same measurement

9x + 1 = 7x + 13

9x - 7x = 13 - 1

2x = 12

x = 6

y° and 7x + 13 are supplementary angles so their sum is 180°

7x + 13 ➡ 7×6 + 13 = 55°

55 + y° = 180 subtract 55 from both sides

y° = 125°

Answer:

E= 36 D=102 F=42

Step-by-step explanation:

E= 36 because of the vertical angles theorem, d =102 because of vertical angles theorem, and finally we have f = 42 because all these angles form a straight angle/line which adds up to 180. So before we knew that d=102 and e=36 so we can add those up and we get 138. Then we subtract 132 from the measure of a straight angle (180 degrees), to get f. SO 180-132 =f=42

The time spent outside by all of the children. The children spent a total of 6 hours outside.

To determine the total time spent outside by all the children, we need to add up the time each child spent outside.

Let's say there are n children, and each child spent a different amount of time outside, which we'll denote by t1, t2, t3, and so on, up to tn. Then, the total time spent outside by all the children is:

Total time = t1 + t2 + t3 + ... + tn

For example, if there are three children who spent 2 hours, 3 hours, and 1 hour outside, respectively, then the total time spent outside is:

Total time = 2 + 3 + 1 = 6 hours

So, the children spent a total of 6 hours outside.

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Answer:

Part A: 1.2 minutes

Part B: 0.83

Part C: 25.2

Answer:

a. 1.2 minutes

b. one lap per 1.2 minutes

c. 25.20 minutes

Step-by-step explanation:

a. do 6 mins/5 laps which gives you 1.2, so 1.2 minutes or 1 minute and 20 seconds

b. uh one lap per 1.2 minutes

c. 25.2 minutes which is approx. 25 minutes and 20 seconds. I reallly hope this helps!

The realized yield that Edward will receive if he sells his $10,000, 5.25% coupon bond at $10,200 is 6.1703%.

Realized yield is the return that an investor receives when he sells his bond in the secondary market. In this case, the bond has been sold at $10,200, which is a premium over the purchase price of $9,400. Realized yield is calculated using the following formula:

Realized Yield = [(Face Value + Total Interest / Selling Price) / Number of Years to Maturity] × 100%,

Where:

Face Value = $10,000

Total Interest = (Coupon Rate × Face Value × Number of Interest Payments) = (5.25% × $10,000 × 10) = $5,250

Selling Price = $10,200

Number of Years to Maturity = 5 years

The number of interest payments per year is 2 because interest is paid semi-annually. Therefore, the number of interest payments for the bond is 5 × 2 = 10. Using the values from above:

Realized Yield = [(10,000 + 5,250 / 10,200) / 5] × 100%

Realized Yield = 6.1703%

Therefore, the realized yield will be 6.1703%.

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To calculate the realized yield, we need to consider the bond's purchase price, sale price, coupon payments, and time period. In this case, the realized yield for Edward's bond is 12.66%.

The realized yield is the return earned by an investor when a bond is sold prior to maturity. To calculate the realized yield, we need to take into account the purchase price, sale price, coupon payments received, and the time period for which the bond was held. In this case, Edward bought a $10,000 bond at $9,400, with a coupon rate of 5.25% and a maturity of 5 years. After 3 years, he sells the bond for $10,200.

To calculate the realized yield, we first need to find the total coupon payments received. Since the coupon is paid semi-annually, there will be 10 coupon payments over the 5-year period. Each coupon payment can be calculated using the formula: Coupon payment = Face value x Coupon rate / 2. So, each coupon payment will be $10,000 x 5.25% / 2 = $262.50.

The total coupon payments received over the 3-year period will be 262.50 x 6 = $1575. Now, we can calculate the realized yield using the formula: Realized yield = (Sale price + Total coupon payments received - Purchase price) / Purchase price x 100.

Inserting the values into the formula, we get: Realized yield = (10,200 + 1,575 - 9,400) / 9,400 x 100 = 12.66%.

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Answer: F. (25 − c) ÷ 4

Step-by-step explanation:

Emma had 25 cookies and gave c cookies to her mom and then divided the rest evenly amongst her 4 friends.

The cookies she shared to her friends are the 25 cookies minus the number of cookies she gave her mom which is:

= 25 - c

This (25 - c) was divided by 4 with each portion given to a friend so the total each friend got was:

= (25 - c) / 4

Answer:

3

Step-by-step explanation:

105/7hrs

15/1hr

15/60min

0.25/per minute

0.25*12

= 3

2u v = 4, where vector u = (1,0,1) and v = (2,2,0) when eu=h1,0,1iandv=h2,2,0i.

To evaluate 2u v, we first need to find the scalar product (dot product) of u and v vector:

u · v = (h1,0,1i) · (h2,2,0i) = 1(0) + 0(2) + 1(2) = 2

Then, we can multiply this result by 2:

2u v = 2(u · v) = 2(2) = 4

Therefore, 2u v = 4.

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Answer:

FE = 9 , DE = 15

Step-by-step explanation:

Δ FDE and Δ HGE are similar , then the ratios of corresponding sides are in proportion , that is

\(\frac{FE}{HE}\) = \(\frac{FD}{HG}\) ( substitute values )

\(\frac{FE}{6}\) = \(\frac{12}{8}\) ( cross- multiply )

8 × FE = 6 × 12 = 72 ( divide both sides by 8 )

FE = 9

and

\(\frac{DE}{GE}\) = \(\frac{FD}{HG}\)

\(\frac{DE}{10}\) = \(\frac{12}{8}\) ( cross- multiply )

8 × DE = 10 × 12 = 120 ( divide both sides by 8 )

DE = 15

The best interpretation of the mean in this situation is: For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

According to the question, the company claims that bowls arrive undamaged in 95 percent of the shipments. Now, the number of shipments with undamaged bowls in 25 randomly selected shipments is represented by the random variable G.

It follows the binomial distribution with a mean of 23.75 shipments and a standard deviation of approximately 1.09 shipments.

Here, the mean is 23.75.

This means that for all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

Hence, the best interpretation of the mean in this situation is: For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

Therefore, the correct option is (e) For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

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Answer:

2.75 cups of sugar

Step-by-step explanation:

Hello!

To find the total amount of sugar Dante needs we need to add the amount need for each recipe

Cookie recipe needs 1.5 cups

Brownie recipe needs 1.25 cups

1.5 + 1.25 = 2.75 cups of sugar

The answer is 2.75 cups of sugar

Hope this helps!

Answer:

the answer is 1.5+1.25=1.75

Step-by-step explanation:

i just added them together

your welcome ( it also depends on how many times he uses the recipes)

Answer:

1: A: 0

2: B: x-intercept

3: A: 0 to 2

Step-by-step explanation:

I just did the assignment on EDGEN and it's 200% correct!

Also, heart and rate if you found this answer helpful! :) (P.S it makes me feel good to know I helped someone today:)  )

The answers that complete the statements are a) zero, b) x - intercept, c) 0 to 2 are the correct statements.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).

For the given situation,

A local business can be modeled as function q(x) = \(x^2 - 4x + 4\)

x is the price of the item in dollars and

q(x) is the number of items produced at that price.

The graph below shows the function q(x).

From the graph, there are zero items produced at a price of $2, because the x-intercept is at (2, 0).

The number of items produced decreases when the price increases from 0 to 2 dollars.

Hence we can conclude that the answers that complete the statements are a) zero, b) x - intercept, c) 0 to 2 are the correct statements.

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Answer:

A coordinate plane with a line passing through (0, negative 4) and (2, 0).

Step-by-step explanation:

rewrite the equation in standard form (Ax+By=C). the equation in standard form is 2x-y=4. to find the intercepts, let one of the values equal 0.

y intercept (let x equal 0)

2x-y=4

2(0)-y=4

-y=4

divide both sides by -1

y=-4

the y intercept is (0,-4)

x intercept (let y equal 0)

2x-y=4

2x-0=4

2x=4

divide both sides by 2

x=2

the x intercept is (2,0)

Answer:

Option C. A coordinate plane with a line passing through (0, negative 4) and (2, 0) or known as the hird graph.

Step-by-step explanation:

EDG

9 minutes is the new standard time for the navigator iii.

What is statistics and example?

If a process improvement has changed the mean observed time for element 6 to 1.50 minutes, then

Element            1    2            3         4             5          6  

Mean obs. Time(t) 1.11   3.1    0.895  1.283333 1.565 1.5  

Normal time       1.0545  1.395 0.93975 1.283333 1.33025 1.65   Sum

Standard time   1.240588 1.641176 1.105588  1.509804 1.565 1.941176

   Sum    9.003333

New standard time = 9 minutes

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5 hours and 30 minutes ya que ambos trabajaran la mitad del trabajo

Answer:

B

Step-by-step explanation:

Have a lovely day! Please let me know if I'm wrong!

Answer:

We want to write the cost equation for the company.

First, we know that:

It cost $20 per box.

There is a fixed cost of $2300.

Then the only variable will be the number of boxes that they make.

Where the number of boxes is the independent variable (the company can decide the number of boxes that they make) and the dependent variable will be the cost (the cost changes as the number of boxes change).

Then we can write the cost equation as:

C(x) = $20*x + $2300.

Where x is our variable, the number of boxes made by the company.

The value(s) of k that make the function continuous over the given interval are k ≥ 0.

To determine the values of k that make the function f(x) continuous over the interval [0, 5] and (5, 10], we need to ensure that the function is defined and has no discontinuities at the endpoints and the transition point.

For the function f(x) = √(kx), the square root function is defined for non-negative values of its argument. Therefore, for the interval [0, 5], we require that kx ≥ 0 for all x in the interval. Since x is non-negative, it follows that k must also be non-negative or k ≥ 0.

For the interval (5, 10], the function is given by f(x) = x + 2, which is a linear function and is continuous for all real values of x. In this case, the value of k does not affect the continuity of the function.

In summary, for the function f(x) = √(kx) to be continuous over the interval [0, 5] and (5, 10], we need k to be non-negative or k ≥ 0.

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The magical profit when 10 pounds of soap is produced is $-105.00.

The cost of producing x pounds of soap is given by the expression: $C(x) = 0.5x^2 + 6x + 100$ dollars.

It is given that the selling price per pound of soap is given by the expression: $S(x) = 12 - 0.15x$ dollars.

So, the revenue obtained by selling x pounds of soap is given by:

$R(x) = S(x) \cdot x = (12 - 0.15x)x = 12x - 0.15x^2$ dollars.

The profit obtained on selling x pounds of soap is given by the difference between the revenue and the cost:

$P(x) = R(x) - C(x)$$P(x) = (12x - 0.15x^2) - (0.5x^2 + 6x + 100)$$P(x)

= -0.65x^2 + 6x - 100$ dollars.

The profit obtained when 10 pounds of soap is produced is given by:

$P(10) = -0.65(10)^2 + 6(10) - 100$$P(10) = -65 + 60 - 100$$P(10) = -105$ dollars.

So, the magical profit when 10 pounds of soap is produced is $-105.00.

In conclusion, the magical profit when 10 pounds of soap is produced is $-105.00.

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In this experiment each time he chack the mold cells there are 8 new cells so the first time he saw 20 cells, then 28 cells then 36 cells and so on.

So in this case the increase of the population is constant so in this case is not an exponential growht, is bether a linear growht

To graph the natural logarithm function, without using a calculator, and using a short table of easy points, we can proceed as follows:

1. We need to remember that the logarithm function is not defined for negative numbers. We cannot find any exponent that raised to a positive number that result in a negative number.

2. The logarithm function is not defined for x = 0. Therefore, we will have an asymptote at x = 0. It is a vertical asymptote, x = 0.

3. The value for ln(1) = 0, and we also know that the value of ln(e) = 1.

We need to remember that e is, approximately, 2.7182818284...

Now, using this information, we will have the following table:

x - values ---------- y-values

Negative values ---- the function is not defined

0 ------------- The function has a vertical asymptote

1 ------------- 0

e (approx. 2.72) ------------ 1

We can see the table of these values in the following drawing:

Now we can sketch a graph of this function as follows:

The domain of the natural logarithm function is, in interval notation:

And the range is (in interval notation too) as follows: