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To find the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company, we can use the following formula: CI = X ± Zα/2 * (σ/√n).

Where:

X = sample mean = 325.5 mg
σ = sample standard deviation = 10.3 mg
n = sample size = 80
Zα/2 = the critical value of the standard normal distribution corresponding to a 90% confidence level, which is 1.645.

Plugging in the values, we get:

CI = 325.5 ± 1.645 * (10.3/√80)
CI = 325.5 ± 2.38
CI = (323.12, 327.88)

Therefore, we can say with 90% confidence that the mean amount of drug in all the pills manufactured by the company is between 323.12 mg and 327.88 mg.


1. Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size:
SE = 10.3 mg / √80 ≈ 1.15 mg

2. Find the critical value (z) for a 90% confidence interval using a standard normal distribution table or calculator. In this case, the critical value is approximately 1.645.

3. Calculate the margin of error (ME) by multiplying the critical value (z) by the standard error (SE):
ME = 1.645 × 1.15 mg ≈ 1.89 mg

4. Determine the confidence interval by adding and subtracting the margin of error from the sample mean:
Lower Limit = 325.5 mg - 1.89 mg ≈ 323.61 mg
Upper Limit = 325.5 mg + 1.89 mg ≈ 327.39 mg

Thus, the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company is approximately 323.61 mg to 327.39 mg.

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Answer: 4,12

Step-by-step explanation:

Bowl-O-Rama:

y = 2 + 2.50x

Bowling Pinz:

y = 4 + 2x

When you graph this, the solution is (4, 12). This represents that when you play 4 games for either company, both the prices will be the same, $12.

Answer:

$18.00

Step-by-step explanation:

Bowl-O-Rama: $4.50 times 4

Bowling Pinz: $6.00 times 3

The value οf x is 3

A variety οf issues are resοlved by algebraic calculatiοns that treat variables like explicit integers in a single cοmputatiοn. The quadratic fοrmula, fοr instance, can be used tο sοlve any quadratic equatiοn by exchanging the variables in the quadratic fοrmula fοr the numerical values οf the cοefficients in the equatiοn.

A variable in mathematical lοgic is either a symbοl fοr an undefined term οf the theοry (a meta-variable), οr it is a fundamental οbject οf the theοry that is changed withοut cοnsidering any pοtential intuitive meaning.

Given

8x+17 = 41

Sοlving fοr variable 'x'

Add '-17' tο each side.

17 + -17 + 8x = 41 + -17

Or, 8x=24

Divide each side by '8'

Or, x=3

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The composite function N(T(t)) = 20082.The time when the bacteria count reaches 20082 is approximately 30.28 hours.

To find the composite function N(T(t)), we need to substitute the expression for T(t) into the function N(T).

Given:

N(T) = 307² - 112T + 75

T(t) = 3t + 1.7

Substituting T(t) into N(T), we get:

N(T(t)) = 307² - 112(3t + 1.7) + 75

Simplifying:

N(T(t)) = 307² - 336t - 190.4 + 75

N(T(t)) = 307² - 336t - 115.4

Now let's find the time when the bacteria count reaches 20082.

N(T(t)) = 20082

307² - 336t - 115.4 = 20082

Taking 115.4 to the other side:

\(307^2\) - 336t = 20082 + 115.4

307² - 336t = 20197.4

336t = 307² - 20197.4

Dividing by 336:

t = (307² - 20197.4) / 336

Calculating the value of t:

t ≈ 30.28

Therefore, the time when the bacteria count reaches 20082 is approximately 30.28 hours.

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Answer:

Step-by-step explanation:

f(x) = 9x - 25/5

f(x) = 9x - 5

f(6) = 9*6 - 5

f(6) = 54 - 5

f(6) = 49

=================

You might mean

f(x) = (9x - 25)/5

f(6) = (9*6 - 25) / 5

f(6) = (54 - 25) / 5

f(6) = 29/5

f(6) = 5.8

Moral: please use brackets to clarify the question.

Answer:

y = x+5 This equation satisfies all the four sets of x and y values 1.When x = 5,y = x+5 = 5+5 = 10 2.When x = 10,y = x+5 = 10+5 = 15 3.When x =15,y = x+5 = 15+5 = 20 4.When x = 20,y = x+5 = 20+5 = 25 Hence,

Step-by-step explanation:

F(a, b, c, d) is a function defined as the sum of the product of the elements in sets {0, 2, 3, 10, 15} and the elements in set {7, 9, 11}.

The function F(a, b, c, d) represents a mathematical expression where a, b, c, and d are variables. The function calculates the sum of two terms. The first term, m(0,2,3,10,15), represents the product of the elements in the set {0, 2, 3, 10, 15} multiplied by an unknown coefficient m. The second term, d(7,9,11), represents the product of the elements in the set {7, 9, 11} multiplied by the variable d.

To evaluate the function, you would substitute specific values for a, b, c, and d. For example, if a = 1, b = 2, c = 3, and d = 4, the function would become F(1, 2, 3, 4) = m(0,2,3,10,15) + 4(7,9,11).

The function F(a, b, c, d) can be considered as a mathematical expression that combines two terms to obtain a result. The first term, m(0,2,3,10,15), involves an unknown coefficient m and the product of the elements in the set {0, 2, 3, 10, 15}. This means that each element in the set is multiplied by m and then added together. The second term, d(7,9,11), involves the variable d and the product of the elements in the set {7, 9, 11}. Similarly, each element in this set is multiplied by d and then added together.

The function F(a, b, c, d) is a general expression that can be evaluated by substituting specific values for a, b, c, and d. For instance, if a = 1, b = 2, c = 3, and d = 4, the function becomes F(1, 2, 3, 4) = m(0,2,3,10,15) + 4(7,9,11). This means that the elements in the first set are multiplied by m, while the elements in the second set are multiplied by 4. The resulting products are then summed to obtain the final value of the function.

In summary, F(a, b, c, d) is a mathematical function that involves the multiplication and addition of elements from two sets, with coefficients m and d, respectively. By substituting specific values, the function can be evaluated to obtain a numerical result.

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Answer:

4

Step-by-step explanation:

18 + 18 = 36

So you got 36 cuz you times by two so you times the same for x

which is

2 x 2 = 4

Answer:

4

Step-by-step explanation:

We can set up a proportion.

18:2 = 36: x

If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4

Answer:

11.5652173913

Step-by-step explanation:

You might have to round

switch the variables

x = -y + 6

x - 6 = -y

-x + 6 = y

The difference between deductive reasoning and inductive reasoning lies in their underlying principles and the way they draw conclusions.

Deductive reasoning is a logical process that starts with a set of premises or assumptions and uses rules of inference to reach a valid and certain conclusion. It operates from the general to the specific. In deductive reasoning, if the premises are true and the logical rules are applied correctly, the conclusion is necessarily true. It is a reliable method for establishing truth and is commonly used in mathematics and formal logic. Deductive reasoning allows us to make precise and conclusive arguments based on logical relationships between statements.

Inductive reasoning, on the other hand, is a process of drawing general conclusions based on specific observations or evidence. It operates from the specific to the general. Inductive reasoning involves making probabilistic or likely conclusions rather than absolute certainties. It relies on patterns, trends, and past experiences to make generalizations and predictions about future events or situations. Inductive reasoning is commonly used in scientific research, empirical investigations, and everyday decision-making. It allows us to make educated guesses and formulate hypotheses based on observed patterns or evidence.

Both deductive reasoning and inductive reasoning play crucial roles in the study of logic.

Deductive reasoning is important in logic because it allows us to establish the validity and soundness of logical arguments. It ensures that our conclusions are logically derived from the premises, preserving truth and consistency. Deductive reasoning is the foundation of formal logic systems, providing a framework for analyzing and evaluating logical structures and arguments. It helps us identify valid deductive arguments and detect logical fallacies or inconsistencies.

Inductive reasoning, on the other hand, is vital for hypothesis generation, scientific inquiry, and empirical investigations. It enables us to make generalizations and predictions based on observed patterns and evidence. Inductive reasoning allows us to make probabilistic claims and draw conclusions about the likelihood or probability of certain events or phenomena. It is essential for forming scientific theories and developing models that explain real-world phenomena.

In summary, deductive reasoning focuses on certainty and truth preservation, while inductive reasoning deals with probability and generalization based on observed evidence. Both types of reasoning are valuable tools in logic, each serving different purposes and contributing to our understanding of the world.

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Answer:

the answer is one and only 28

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42\(x_{0}\) in which \(x_{0}\) is the initial population.

Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.

We are required to find the number of bacteria present after 10 weeks.

let the number of bacteria present at t is x.

So,

dx/dt∝x

dx/dt=kx

1/x dx=k dt

Now integrate both sides.

\(\int\limits {1/x} \, dx\)=\(\int\limits{k} \, dt\)

log x=kt+log c----------1

Put t=0

log \(x_{0}\)=0 +log c    (\(x_{0}\) shows the population in beginning)

Cancelling log from both sides.

c=\(x_{0}\)

So put c=\(x_{0}\) in 1

log x=kt+log \(x_{0}\)

log x=log \(e^{kt}\)+log \(x_{0}\)

log x=log \(e^{kt}x_{0}\)

x=\(e^{kt}x_{0}\)

We have been given that the population triples in a week so we have to put the value of x=2\(x_{0}\) and t=1 to get the value of k.

2\(x_{0}\)=\(e^{k} x_{0}\)

2=\(e^{k}\)

log 2=k

We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.

x=\(e^{20log 2}\)\(x_{0}\)

x=\(e^{0.30*2}\)\(x_{0}\)

x=\(e^{6}x_{0}\)

x=403.42\(x_{0}\)

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42\(x_{0}\) in which \(x_{0}\) is the initial population.

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The given question is incomplete as the question incudes the following:

Calculate the population after 20 weeks.

Answer:

brainliest please

Step-by-step explanation:

116

SOLUTION

Given the question, the following are the steps to solve the problem

Step 1: Write out the question

Step 2: Solve the expression in the first bracket

Step 3: Calculate the tangent of the result in step 2

Hence, the result from the evaluation of tan(sin^-1)(7/9) is approximately 1.2374

The correct rows in the inequalities are

The rows are given as:

-3x - 4 < x + 4  ⇒ -3x < x

2(x - 5) + 1 ≤ 5  ⇒ 2(x - 5) ≤ 4

-4x ≥ -24  ⇒ x ≤ 6

x = 2y and 2x + 2y > 60  ⇒ 6y > 60

y + 2 ≤ 4 - x and 4 - x ≤ 3y  ⇒ y + 2 ≤ 3y

To determine the correct rows, we simply solve each inequality.

This is done as follows:

-3x - 4 < x + 4

Collect like terms

-3x - x < 4 + 4

Evaluate the like terms

-4x < 8

Divide by -4

x > -2

This means that:

-3x - 4 < x + 4  ⇒ -3x < x is false.

2(x - 5) + 1 ≤ 5  

Subtract 1 from both sides

2(x - 5) ≤ 4

This means that:

2(x - 5) + 1 ≤ 5   ⇒ 2(x - 5) ≤ 4 is true.

-4x ≥ -24  

Divide through by -4

x ≤ 6

This means that:

-4x ≥ -24  ⇒ x ≤ 6 is true.

x = 2y and 2x + 2y > 60

Substitute 2y or x in 2x + 2y > 60

2(2y) + 2y > 60

Evaluate the product

4y + 2y > 60

Evaluate the like terms

6y > 60

This means that:

x = 2y and 2x + 2y > 60  ⇒ 6y > 60 is true.

y + 2 ≤ 4 - x and 4 - x ≤ 3y

We have:

y + 2 ≤ 4 - x and 4 - x ≤ 3y

This can be rewritten as:

y + 2 ≤ 3y

This means that:

y + 2 ≤ 4 - x and 4 - x ≤ 3y  ⇒ y + 2 ≤ 3y is true

Hence, the correct rows are 2, 3, 4 and 5

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Answer:

2 pairs of jeans

Step-by-step explanation:

1) Subtract the cost of the t-shirt

   As we are given the information that she will only be buying one t-shirt it

   means that we can get rid of the price of it...

   $80-$9 = $72

2) Find the number of jeans

   Knowing that we have $72 left we have figure out how many jeans she

   can buy by dividing 72 by 34...

   $72 ÷ $34 = 2

Hope this helps, have a great day!

Answer:

10.20°

Step-by-step explanation:

Given that:

Grade = 18% ; rise = 18ft

For every 100 feets, plane roses 18%

The question can be solved using Pythagoras rule :

Tangent θ = opposite / Adjacent

Tan θ = 18 / 100

Tan θ = 0.18

θ = tan^-1(0.18)

θ = 10.203973

θ = 10.20°

Answer:

its  a)

Step-by-step explanation:

This answer is a) because 8/3 radio drink mix is a)

                     Hope this helps .  ;D

The angles that make the trigonometric statements true using the relationship of sine and cosine for the value of the angle is 45°.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The angles that make the trigonometric statements true.

Let the angle be x. Then we have

sin(x) = cos(B)

sin(B) = cos(x)

If they are equal then we can apply the sine and cosine relationship.

\(\rm sin (90 - \theta) = cos \ \theta\\\\\rm cos (90 - \theta) = sin \ \theta\)

Then sin x can be written as cos (90 – B). Then we have

cos(90 – B) = cos(B)

       90 – B = B

                B = 45

Similarly, cos x can be written as sin (90 – B). Then we have

sin(90 – B) = sin(B)

      90 – B = B

               B = 45

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Answer:

Both fill in the blanks are A

Step-by-step explanation:

Correct on edge

the distance to the town is approximately 14 km.

To find the distance to the town, we need to use the formula:

Distance = Speed * Time

Given information:

Walking speed = 3.5 km/h

Resting time = 45 minutes = 45/60 = 0.75 hours

Riding speed = 7.5 km/h

Total time spent = 6 hours 37 minutes = 6 37/60 = 397/60

Let's break down the time spent into different components:

Time spent walking to the town:

Time1 = Distance / Walking speed = Distance / 3.5 km/h

Time spent resting in the town:

Resting time = 0.75 hours

Time spent riding back from the town:

Time2 = Distance / Riding speed = Distance / 7.5 km/h

Total time equation:

Time1 + Resting time + Time2 = Total time

(Distance / 3.5) + 0.75 + (Distance / 7.5) = 397/60

After solving

Distance = 14

Therefore, the distance to the town is approximately 14 km.

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The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Answer:

54 °F

Step-by-step explanation:

I think the answer would be 54 °F because it dropped 6 degrees every hour and it happened for 9 hours. So you would multiply 6 times 9. Your answer would be 54. I hope this is correct if it isn't then I am truly sorry.

The perimeter of the rectangle is given as;

the breadth is also given as;

Recall that the formula for the perimeter of a restangle is;

where,

l is the length and b is the breadth

So, let us substitute the values of P and b into the formula;

Now, let us solve for l;

Therefore the length of the of the rectangle is 9cm

In the question given that :he​ reasoned, the probability of rolling a nine must be one eleventh but bob is wrong because the probability is 1/36 which is not equal to 1/11

From the question, we have the information available is:

Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11, 12.

and, there are 11​ outcomes, he​ reasoned, the probability of rolling a nine must be one eleventh.

To write the what is wrong with  Bob's reasoning.

Now, According to the question:

In the probability:

He rolled 11 times:

So, we can represent the \(w_2\) is the outcome with the sum of pints in two die are 2.

Then the probability is:

\(P(w_2 = 2) = (\frac{1}{6} ).(\frac{1}{6} )=\frac{1}{36}\neq \frac{1}{11}\)

So, in the question given that :he​ reasoned, the probability of rolling a nine must be one eleventh but bob is wrong because the probability is 1/36 which is not equal to 1/11.

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To solve this problem, we have to use the combination formula

Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have

Remember that factorials are solved by multiplying the number in a reversal way, as follows

The specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

For a two-tailed hypothesis test, an appropriate null hypothesis indicating that the population correlation is equal to zero would be:

H₀: ρ = 0

where ρ represents the population correlation coefficient.

This null hypothesis states that there is no significant correlation between the two variables being analyzed.

In a two-tailed hypothesis test, the alternative hypothesis would be that there is a significant correlation, either positive or negative, between the two variables:

Hₐ: ρ ≠ 0

This alternative hypothesis states that there is a significant correlation between the two variables, but does not specify the direction of the correlation.

It's important to note that the specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

Additionally, the choice of null and alternative hypotheses will affect the statistical power of the test, which is the probability of correctly rejecting the null hypothesis when it is false.

Hence, the specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

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Complete Question:

For a two-tailed hypothesis test, which of the following would be an appropriate null hypothesis indicating that the population correlation is equal to o?

A. H₀: 1 = 2, B. H₀ : M₁ = M₂ C. H₀: O = 0  

D. None of the options above are correct.

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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The correct response is c. 8√2 . The length of the diagonal if the side of the square is 8√2.

A polygon's opposed vertices (or corners) are connected by a line segment known as a diagonal. Or to put it another way, a diagonal is a line segment joining two polygonal vertices that are not neighbouring. With the exception of the figure's edges, it connects a polygon's vertices. For instance, a diagonal line or movement runs slopingly from one corner of a square to the other corner. a type of straight line called a diagonal. Straight up, down, or across are not possible on a diagonal line. It is a line that joins the corners of a form at two points. Instead of running straight up or across, a diagonal is formed by a straight line that is positioned at an angle.

Right isosceles triangles with both legs 8 feet long would make up each half.

The hypotenuse that both of those triangles would share is the diagonal.

We must determine the hypotenuse's length, d, in feet.

According to the Pythagorean theorem, the lengths of the legs' squares sum up to the length of the hypotenuse's square, so

\(8^{2} +8^{2} =8\sqrt{2}\)

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A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8ft? Leave your answer in simplest radical form.

a. 16√8

b. 2√8

c. 8√2

d. 4