Suppose that a brand of lightbulb lasts on average 2821 hours with a standard deviation of 197 hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that a particular bulb will last from 2772 to 3298 hours?
P(2772 < X < 3298)

Answer:

23°

Step-by-step explanation:

46 = 2x (Vertically opp. angles)

x = 46÷2

x = 23

Hope this helps!

pls like and mark as brainliest

Answer:

x = 23°

Step-by-step explanation:

46 = 2x

46/2 = 2x/2

x = 23°

The sum of the matrices A + B is  5      8

                                                        2.6   2

To add two matrices, they must have the same dimensions (the same number of rows and the same number of columns).

To add two matrices A and B, you can add the corresponding elements of the two matrices and place the result in the corresponding position of a new matrix C.

In mathematical notation, if A and B are two matrices of the same dimensions, then the sum C = A + B is defined by:

C[i,j] = A[i,j] + B[i,j]

Using the above as a guide, we have the following:

A + B =  5      8

             2.6   2

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We are 90% confident that the true proportion of surveys returned is between 0.4330 and 0.4882.

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

(a) First, we need to calculate the sample proportion, denoted by $\hat{p}$. The sample proportion is the number of surveys returned divided by the total number of surveys sent:

p = 1111/ 2410 ≈ 0.4606

(b) The standard error of the sample proportion is:

SE = p(1−p)/n = 0.4606(1−0.4606)/2410≈0.0168

(c) To find the margin of error at 90% confidence level, we need to use the z-score associated with a 90% confidence interval, which is 1.645 (obtained from a standard normal table or calculator). The margin of error is:

ME = z∗×SE = 1.645 × 0.0168 ≈ 0.0276

(d) Finally, we can construct the 90% confidence interval for the proportion of returned surveys by subtracting and adding the margin of error to the sample proportion:

p ± ME = 0.4606 ± 0.0276 =(0.4330,0.4882)

Therefore, we are 90% confident that the true proportion of surveys returned is between 0.4330 and 0.4882.

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The total value of Martin's account after 36 months is $7,682.50. $682.50 in interest was earned.

Answer:

Step-by-step explanation:

H(n)=91x(-1/7) n-1

do not know

Hope it helps the answer is the 2nd one have a great day

The associative law holds in all three composition tables.

No matter how they are arranged, integers can be multiplied and added together according to the associative property. We refer to the numbers in the parenthesis as grouping (). Let's imagine that you are adding three integers, 2, 5, and 6. It doesn't matter how we add the numbers together—using the formulas 2 + (5 + 6) or 2 + (5) + 6—the outcome will be the same. The multiplication equation is consistent: Equals to (2 x 5) x 6 is (2 x 5) x 6. The commutative characteristic is almost identical to this one when only two integers are used.

In the given composition tables the law of associativity is followed

a(bc) = (ab)c

from 13,

a(a) = bc

a = a

The associative law holds in all three composition tables

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The composition (f ∘ g)(–2) = 3.

What is Function ?

In mathematics, a function is a relation between two sets of values, where each value in the first set (called the domain) is associated with exactly one value in the second set (called the range). A function can be represented by a formula or an equation, which specifies how the input values are transformed into output values.

To find the composition (f ∘ g)(–2), we need to apply the function g to –2 first, and then apply the function f to the result. Here's how we can do it:

First, we need to find g(–2) by substituting –2 for x in the expression for g(x):

g(–2) = (–2)2 – 3

g(–2) = 4 – 3

g(–2) = 1

Now that we have found g(–2) = 1, we can substitute it for x in the expression for f(x) to find f(g(–2)):

f(g(–2)) = 2(1) + 1

f(g(–2)) = 3

Therefore, the composition (f ∘ g)(–2) = 3.

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Without the exact Number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make

Step 1: Identify the number of leftover bread slices.
Unfortunately, the question doesn't provide the exact number of leftover bread slices. Let's assume Rosa and Clarice have "B" bread slices in total.

Step 2: Determine the number of sandwiches needed.
We know that they are making sandwiches for the custodian, librarian, and office staff. We need to know the number of people in each category to calculate the total number of sandwiches required. Since this information is not provided, let's assume there are "C" custodians, "L" librarians, and "O" office staff members.

Step 3: Calculate the number of sandwiches required.
Each sandwich typically requires 2 slices of bread. Therefore, the total number of sandwiches required can be calculated using the following formula:

Total Sandwiches = (C + L + O)

Step 4: Determine if there is enough bread.
We can now compare the total number of sandwiches required with the number of bread slices available. If there are enough bread slices (B >= 2 * Total Sandwiches), Rosa and Clarice can make sandwiches for everyone. Otherwise, they will not be able to make enough sandwiches for everyone.

In conclusion, without the exact number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make. To answer the question accurately, please provide the missing information.

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The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space refers to the set of all possible outcomes or events that can occur in an experiment or random process. It is denoted by the symbol "S" and contains all the possible values, results, or states that can be observed or measured. In probability theory, the sample space is used to define the range of possible outcomes that can be observed or measured in a given experiment or event.

Probability is a measure of the likelihood or chance of an event occurring. It quantifies the likelihood of an event happening based on the ratio of the number of favorable outcomes to the total number of possible outcomes. It is expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

According to the given information:

When you roll a 12-sided dice, number of dots on the uppermost face is called as outcome. Now, whenever a dice is rolled we can get either 1, 2,3,4,5,6,7,8,9,10,11 or 12 dots on the uppermost face that is now outcome.

So experiment here is "Rolling a 12-faced dice" and list of possible outcomes is "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}".

Sample space by its definition is list of all the possible outcomes of an experiment.

S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

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Answer:

Exact Form: 1/216

Step-by-step explanation:

a)  Population proportion is the sample proportion: p' = 108/4319 ≈ 0.025. b) 0.007. c) (0.018, 0.032) d) Option A is correct statement.

In statistics, the standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is also called the Z distribution, where Z represents the standard normal variable.

The standard normal distribution is a continuous probability distribution that is symmetric around the mean of 0. The shape of the distribution is bell-shaped, with the majority of the data falling within 3 standard deviations from the mean.

The standard normal distribution is widely used in statistics and probability theory as a benchmark for comparing other normal distributions. It is particularly useful for converting other normal distributions into a standardized form, which allows for easier comparison and analysis.

a) The best point estimate of the population proportion is the sample proportion: p' = 108/4319 ≈ 0.025.

b) The margin of error E is given by E = z* ×√(p'(1-p')/n), where z* is the critical value of the standard normal distribution for a 99% confidence level. Using a table or calculator, we find that z* ≈ 2.576. Substituting the given values, we have E ≈ 0.007.

c) The confidence interval is given by p' ± E, or 0.025 ± 0.007. Using a calculator, we find that the lower bound is approximately 0.018 and the upper bound is approximately 0.032. Therefore, the 99% confidence interval for the proportion of adverse reactions is (0.018, 0.032).

d) A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

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Exact Form: 131/12

Decimal Form:10.916

Mixed Number Form: 10 11/12

Answer:

131/12 or 10.91666. or  [tex]10\frac{11}{12}[/tex]

Hope this helps!

Step-by-step explanation:

( [tex]\frac{8}{3}[/tex] × [tex]\frac{11}{2}[/tex] ) - [tex]\frac{15}{4}[/tex]

( [tex]\frac{4}{3}[/tex] × [tex]\frac{11}{1}[/tex] ) - [tex]\frac{15}{4}[/tex]

[tex]\frac{44}{3}[/tex] - [tex]\frac{15}{4}[/tex]

[tex]\frac{176}{12}[/tex] - [tex]\frac{45}{12}[/tex]

[tex]\frac{131}{12}[/tex]

Answer:

[tex]\textsf{A.} \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

Given geometric sequence:

[tex]8,\;2,\;\dfrac{1}{2},\;\dfrac{1}{8},\;\dfrac{1}{32}[/tex]

The common ratio for a geometric sequence can be found by dividing a term by the previous term.

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{2}{8}=\dfrac{2 \div 2}{8 \div 2} =\dfrac{1}{4}[/tex]

Therefore, the common ratio for the given geometric sequence is 1/4.

Identify the two numbers in the ordered pair, locate the x-axis and y-axis on the plane, move along the x-axis to the position corresponding to the first number, move vertically along the y-axis to the position corresponding to the second number, mark the point with a dot or small circle, and connect the dots to show patterns.

The procedures below must be followed in order to plot or graph an ordered pair of integers, usually known as a point, on a two-dimensional plane:

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The required password for different conditions are 216 and 120.

(a) If a letter can be repeated, then we can use the multiplication principle to determine the number of possible passwords. For each of the three positions in the password, there are six choices of letters. Therefore, the total number of possible passwords is:

[tex]$6^3 = \boxed{216}$[/tex]

(b) If a letter cannot be repeated, then we can use the permutation formula to determine the number of possible passwords.

There are six choices for the first letter, five choices for the second letter (since one letter has already been used), and four choices for the third letter (since two letters have already been used). Therefore, the total number of possible passwords is:

[tex]$P(6,3) = 6 \times 5 \times 4 = \boxed{120}$[/tex]

Thus, required password for different conditions are 216 and 120.

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Answer:

the bird will need to fly 4feet closer to the flower

Therefore, the distance from the coal tray is approximately 301.96 inches when the heat intensity is 0.685 and the width of the coal tray is 25 inches.

We can write the following using the formula in the question:

[tex]P = 100/(1 + d^2)[/tex]

where d represents the proportion of the food's distance from the coals to the tray's width.

Substituting d = z/25 results in:

[tex]P = 100/(1 + (z/25)^2)[/tex]

With y = 0.685, we can replace P with P = 0.685 and find z:

[tex]0.685 = 100/(1 + (z/25)^2)[/tex]

By dividing the two sides by [tex](1 + (z/25)^2)[/tex], we get at:

[tex]0.685 + 0.685(z/25)^2 = 100[/tex]

If we simplify, we get:

[tex](z/25)^2 = (100/0.685) - 1(z/25)^2 = 145.9854[/tex]

When we square the two sides, we obtain:

[tex]z/25 = 12.0783z = 25*12.0783z = -25*12.0783[/tex]

Given that z cannot be negative, we decide:

Z=25 * 12.0783 * 301.9575 inches

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To find a point that represents a solution for the equation x + 3y = 8, we need to find a point (x,y) that satisfies this equation. One way to do this is to choose a value for x, and then solve for y. For example, if we let x = 2, we have:

2 + 3y = 8

Subtracting 2 from both sides, we get:

3y = 6

Dividing both sides by 3, we get:

y = 2

So the point (2,2) is a solution for the equation x + 3y = 8. To check, we can substitute x = 2 and y = 2 into the equation:

2 + 3(2) = 8

8 = 8

This is true, so (2,2) is a solution for the equation.

Alternatively, we could choose a value for y and solve for x. For example, if we let y = 0, we have:

x + 3(0) = 8

x = 8

So the point (8,0) is also a solution for the equation x + 3y = 8.

Answer:

A .278

Step-by-step explanation:

138 x 14÷28+209 = 1932 ÷28+209=69+209=278

Answer: w/explanation

To calculate your merit increase, we need to first determine your performance score on a scale of 0 to 100. We can convert your score of 3.4 to this scale by subtracting 2 and multiplying by 25:

performance score = (3.4 - 2) x 25 = 35

Now that we have your performance score, we can use the given merit increase formula to calculate your increase:

Merit increase = (performance score - 26) / 4

Merit increase = (35 - 26) / 4

Merit increase = 2.25%

Therefore, your merit increase is 2.25%.

Answer:

90°

Step-by-step explanation:

Since CD is a tangent to circle B and BA is the circle's radius, the tangent to the radius forms a right angle at the point of contact:

∠BAD = 90°

The equatiοn fοr H, the number οf times Nοah’s beats in m minutes is H = k * m

Expressiοns that perfοrm the same functiοn regardless οf appearance are said tο be equivalent. If twο algebraic expressiοns are equivalent, then they have the same value when the same variable value is used.

Assuming yοu meant "Nοah's heart beats", the equatiοn fοr H, the number οf times Nοah's heart beats in m minutes can be given by:

H = k * m

where k is a cοnstant that represents the number οf heartbeats per minute.

The value οf k may vary depending οn the individual and their physical cοnditiοn.

Hence,  the equatiοn fοr H, the number οf times Nοah’s beats in m minutes

is H = k * m

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Complete Question;

A persons resting heart rate is typically between 60 and 100 beats per minute. Nοah looks at his watch, and counts 8 heartbeats in 10 seconds.

Is his heart rate typical? Explain how you know.

Write an equation for h, the number of times Noahs heart beats (at this rate) in m minutes.

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

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

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

c

Step-by-step explanation:

To find the x-intercept, we set y to 0 and solve for x:

0 = x + 8

x = -8

Therefore, the x-intercept is -8.

To find the y-intercept, we set x to 0 and solve for y:

y = 0 + 8

y = 8

Therefore, the y-intercept is 8.

Hopes this helps

To find the middle term of the expansion of (2x/y^3)^12, we need to first determine the number of terms in the expansion.

Using the formula for the binomial theorem, we know that the number of terms in the expansion of (2x/y^3)^12 is 13.

Now, to find the middle term, we need to find the term that is in the middle of the expansion. Since there are 13 terms in the expansion, the middle term is the 7th term.

The general term of the expansion is given by:

T(r+1) = (12 C r) (2x)^r (y^-3)^(12-r)

So, the 7th term is:

T(8) = (12 C 7) (2x)^7 (y^-3)^(5)

Simplifying this expression, we get:

T(8) = (792) (128x^7 / y^15)

Therefore, the middle term of the expansion is 792(128x^7/y^15)

The three options given in the question are not the correct steps to solve the given quadratic equation.

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared (raised to the power of 2).

The three steps that Inga could use to solve the quadratic equation [tex]2x^2 + 12x - 3 = 0[/tex] are:

1.Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are constants: [tex]2x^2 + 12x - 3 = 0.[/tex]

2.Use the quadratic formula x = [-b ± sqrt([tex]b^2[/tex] - 4ac)]/2a, where a = 2, b = 12, and c = -3, to find the values of x:

x = [-12 ± [tex]\sqrt{(12^2 - 4(2)(-3))[/tex]]/(2*2)

x = [-12 ± [tex]\sqrt{(156)[/tex]]/4

x = (-3 ± [tex]\sqrt{(39)[/tex])/2

3.Simplify the roots if possible:

x = (-3 + [tex]\sqrt{(39)[/tex])/2 or x = (-3 - [tex]\sqrt{(39)[/tex])/2

Therefore, the three options given in the question are not the correct steps to solve the given quadratic equation.

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