log3 (x-4) =2
log(x+3) 8 =1

Answers

Answer 1

Option three log3 + log(x+4) is the equivalent to the logarithm expression  log3(x+4).

It is given that logarithm expression is log3(x+4).

It is required to simplify the above equation.

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

aᵇ = c

logₐc = b

We have logarithm expression:

log3(x+4)

We know the log property that we can split a logarithm into two logarithms if it contains the product of two numbers ie.

log xy = logx + logy

By using this property we get:

log3(x+4)

= log3 + log(x+4)

Because 3 and (x+4) are two different numbers, not (x+4).

Thus, option three log3 + log(x+4) is the equivalent to the logarithm expression log3(x+4).

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Related Questions

Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 63 people is taken.
Step 2 of 2 : What is the probability that the mean IQ score of people in the sample is less than 98? Round your answer to 4 decimal places, if necessary.

Answers

The probability that the mean IQ score of people in the sample is less than 98 is 0.2533, which is rounded to four decimal places.

What is Probability?

Probability is a branch of mathematics that deals with the likelihood of a certain event or outcome occurring. Probability is based on the concept of counting and measuring the chances of something happening. It can be used to provide insight into how likely a certain outcome is to occur, and can be used to make decisions about the future. Probability can also be used to analyze data, identify patterns, and make predictions.

The probability that the mean IQ score of people in the sample is less than 98 can be calculated using the z-score. The z-score is calculated by subtracting the mean from the given value, 98, and then dividing the difference by the standard deviation, 15.0. This gives a z-score of -0.67.

Using the z-table, the probability of the mean IQ score of people in the sample being less than 98 can be calculated. The probability is 0.2533. Therefore, the probability that the mean IQ score of people in the sample is less than 98 is 0.2533, which is rounded to four decimal places.

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What is the value of A when we rewrite 6^x as A^x/4

Answers

The value of A when we rewrite 6^x as A^x/4 is 3/2

What is an algebraic expression?

An algebraic expression can simply be defined as a mathematical expression that consists of terms, factors, constants, coefficients and variables.

They are also known as expressions made up of arithmetic operations, such as;

AdditionBracketParenthesesDivisionMultiplicationSubtraction

From the information given, we have that;

The function is given as;

6^x

Here, the coefficient or rather the base is 6

To determine the value of A when ^^x is given as A^x/4

The value of A would be;

6/4 = 3/2

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Help me solve this pls

Answers

The calculated approximation of log(15/2) is 0.9

Appomixing the logarithm expression

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

log(10) = 1.1

log(11) = 1.2

log(6) = 0.9

Also, we have

log(15/2)

Applyingthe quotient logarithmic law, we have

log(15/2) = log(15) - log(2)

15 and 2 cannot be derived directly from 10, 11 and 6

So, we solve independently using a calculator

log(15) = 1.2

log(2) = 0.3

Substitute the known values in the above equation, so, we have the following representation

log(15/2) = 1.2 - 0.3

Evaluate

log(15/2) = 0.9

Hence, the approximation is 0.9

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A new company started the year with 3 employees. The company plans to triple the number of employees each year. Drag expressions to complete the table to represent this situation.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Start of Year Number of Employees
1=3
2=?
3 =?
n=?

Answers

If a company starts with 3 employees and plans to triple the number of employees each year, then the number of employees can be represented by the function: f(n) = 3^n

How to find the function to represent this situation?

To find the function to represent this situation we have to consider the information. In this formula we have to incluide the following information:

The number of employees at the end of the n year is equal to 3 raised to the power of n.

where,

n = number of years since the start of the company.

So, for example, if we want to know how many employees the company will have at the end of the second year, we can plug in n = 2 into the function:

f(2) = 3^2 = 9

According to the above, the company will have 9 employees at the end of the second year, and if we want to know how many employees the company will have at the end of the third year, we can plug in n = 3 into the function:

f(3) = 3^3 = 27

So, the company will have 27 employees at the end of the third year.

In general, the formula tells us that the number of employees at the end of the nth year is equal to 3 raised to the power of n.

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In chemistry, the pH
of a solution is a measure of the acidity or alkalinity of a solution. Water has a pH
of 7
and, in general, acids have a pH
less than 7
and alkaline solutions have a pH
greater than 7
. Find the pH
of a solution with a hydronium ion concentration of 7.4×10−3
moles/liter. Round your answer to two decimal places, if necessary.

Answers

The solution has a pH of 2.13, which is a measurement of a solution's acidity or alkalinity.

An aqueous solution's pH is a measure of how basic or acidic it is. The negative logarithm of the concentration of hydronium ions (H₃O⁺) is what this term, which means "power of hydrogen," is defined as. The pH scale goes from 0 to 14, where 0 is the most acidic and 14 is the most basic (or alkaline).

Since the concentration of hydronium and hydroxide ions in a solution with a pH of 7 is equal, this value is regarded as neutral. In contrast to bases, which have a pH above 7, acids have a pH below 7. The difference in the concentration of hydronium ions is represented by each full number on the pH scale.

The pH of a solution can be determined using the formula:

pH = -log[H⁺]

where [H⁺] is the concentration of hydronium ions in moles per liter.

In this case, [H⁺] = 7.4×10⁻³ moles/liter.

Substituting into the formula:

pH = -log(7.4×10⁻³) = 2.13

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Write the equation in standard form for the ellipse with center (0,3), vertex (0,15), and co-vertex (–
10,3).

Answers

Answer:

Step-by-step explanation:

i sorry dont know

A 40-year-old man in the U.S. has a 0.248% risk of dying during the next year . An insurance company charges $260 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar.

Answers

The expected value is calculated by multiplying the probability of each outcome by its corresponding value and then summing up all the values. In this case, the possible outcomes are either the man dies and the insurance company pays out the death benefit of $100,000, or he does not die and the insurance company keeps the premium of $260.

Expected value = (probability of death x death benefit) + (probability of no death x premium)

Expected value = (0.00248 x $100,000) + (0.99752 x $260)

Expected value = $248 + $259.38

Expected value = $507.38

Therefore, the expected value for the person buying the insurance is $507.38, rounded to the nearest dollar.

Given point P (-2, 0). What is the distance of point P from (a) x axis (b) y axis?

Answers

Answer:

Step-by-step explanation:

A math class has 2 girls and 2 boys in the seventh grade and 1 girl and 9 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys?
Write your answer as a fraction in simplest form.

Answers

Answer:

mark me brilliant

Step-by-step explanation:

There are a total of 4+2=6 students in the seventh grade and 9+1=10 students in the eighth grade, so there are a total of 6+10=16 students in the class.

The probability of selecting a boy from the seventh grade is 2/4 = 1/2, and the probability of selecting a boy from the eighth grade is 9/10.

To find the probability of both events happening, we multiply the probabilities:

P(selecting a boy from seventh grade AND selecting a boy from eighth grade) = (1/2) x (9/10) = 9/20.

Therefore, the probability that the students selected for the competition are both boys is 9/20.

Factor the Trinomial
[tex]2a^2+5ab+7b^2[/tex]

Answers

The given trinomial is [tex]2a^2+5ab+7b^2[/tex]. The trinomial can be factored as (2a+7b)(a+b).

What is trinomial?

A trinomial is an algebraic expression consisting of three terms. It can be written in the form ax² + bx + c, where a, b, and c are constants and x is a variable. Trinomials are also used to solve equations, such as quadratic equations.

To factor this trinomial, we will first split the trinomial into two groups. The two groups are (2a, 7b) and (a, b).

Now we will multiply the first terms of both the groups.

We will get 2a × a = 2a².

This is the first term of the trinomial. Now we will multiply the second terms of both the groups.

We will get 7b × b = 7b².

This is the last term of the trinomial. Now we will multiply the first term of the first group and the second term of the second group.

We will get 2a × b = 2ab.

This is the middle term of the trinomial.

Hence, the trinomial can be factored as (2a+7b)(a+b).

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help me please please ​

Answers

Answer:

Step-by-step explanation:

1. -Growth because its increasing

  -asymptote y=0  boundary

  -domain (-∞,+∞)  where does x exist

  -range (0, +∞)    where does y exist

  - y-int (0,2)   plug x into equation or look where it hits y-axis

2.  Decay because its decreasing

   - asymptote y=4

   - domain  (-∞,+∞)

   -range (4, +∞)

   y-int (0,7)

3.  growth

y=-3

domain: (-∞,+∞)

range: (-3, +∞)

(0, -2.25)

4.  decay

y=3

domain  (-∞,+∞)

range (3, ∞)

y-int (0,5)

A genetic experiment with peas resulted in one sample of offspring that consisted of 431 green peas and 152 yellow peas.
a. Construct a 95 ​% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence​ interval, do the results of the experiment appear to contradict the expectation that​ 25% of the offspring peas would be​ yellow?

Answers

The answer  is , (a) the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%).  , (b) we cannot definitively conclude that the results contradict the expectation.

What is Confidence interval?

A confidence interval is a range of values that is used to estimate the true value of an unknown parameter, like a population mean or proportion, based on a sample of data. It is a statistical measure of the precision and reliability of an estimate, and it provides a measure of the uncertainty or margin of error associated with the estimate.

a. To construct  95% confidence interval for percentage of yellow peas, we can use  following formula as :

CI = p ± z*(√((p*(1-p))/n))

Where:

p = proportion of yellow peas = 152/(431+152) = 0.2613

z = z-value for a 95% confidence interval = 1.96 (from standard normal distribution table)

n = sample size = 431+152 = 583

Plugging in the values, we get:

CI = 0.2613 ± 1.96*(√((0.2613*(1-0.2613))/583))

CI = 0.2613 ± 0.0365

CI = (0.2248, 0.2978)

Therefore, the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%).

b. The expected percentage of the yellow peas is 25%. Since the lower limit of the confidence interval is 22.48%, which is less than 25%, it suggests that the actual percentage of yellow peas may be lower than expected. However, since the confidence interval does include 25%, we cannot definitively conclude that the results contradict the expectation.

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I need help with this please

Answers

Answer:

Step-by-step explanation:

X axis come first then the y axis, p needs to start at 3 then go 4 units up and 3 units to the left and then you get (3,4)

Gert's Groceries recorded the total amount of sales each day. Total sales ($) 4,000 5,000 6,000 7,000 8,000 ) What was the median amount of sales each day? 9,000​

Answers

Answer: The median amount of sales each day was $7,000.

Step-by-step explanation:

To find the median amount of sales each day, we need to arrange the sales amounts in order from smallest to largest. Doing so, we get:

4,000 5,000 6,000 7,000 8,000 9,000

Since there are an odd number of values, the median is the middle value, which is 7,000. Therefore, the median amount of sales each day was $7,000.

The middle value of this dataset is 7,000, so the median amount of sales each day is $7,000.

What is the median?

The value that divides the mathematical numbers or expressions in half is known as the median. The midway number of data points is known as the median value. Then, organize the data points in ascending order before calculating the median.

Given information:

Gert's Groceries recorded the total amount of sales each day.

To find the median of a set of data, we need to order the data from least to greatest and then find the middle value(s).

4,000 5,000 6,000 7,000 8,000 9,000

The middle value of this dataset is 7,000, so the median amount of sales each day is $7,000.

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In a certain town, 70% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the standard deviation for the probability distribution.

x P9x)
0 0.0081
1 0.0756
2 0.2646
3 0.4116
4 0.2401

Answers

So, the standard deviation of the probability distribution is approximately 2.780.

To find the standard deviation for the probability distribution, we first need to find the mean (or expected value) of the distribution.

The mean is given by:

μ = ∑(x * P(x))

where x is the number of adults with a college degree and P(x) is the corresponding probability from the table.

μ = (00.0081) + (10.0756) + (20.2646) + (30.4116) + (4*0.2401)

μ = 2.8

So, the mean number of adults with a college degree in a sample of 4 is 2.8.

Next, we can use the formula for the standard deviation of a probability distribution:

σ = √∑[(x - μ)² * P(x)]

where x is the number of adults with a college degree, μ is the mean we just calculated, and P(x) is the corresponding probability from the table.

σ = √ [(0-2.8) ²0.0081 + (1-2.8) ²0.0756 + (2-2.8) ²0.2646 + (3-2.8) ²0.4116 + (4-2.8) ²*0.2401]

σ = √ [7.72404]

σ = 2.780

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What is the value of k if the equation of the line drawn below is 6x + by = k? Step by Step please ​

Answers

Answer:

12

Step-by-step explanation:

a general linear function can be written as

y= mx +b

where "m" is the pendient and "b" it's the point where the funcion has x=0

so u have to solve your ec. for y

[tex]6x + by = k[/tex]

[tex]by = - 6x + k[/tex]

[tex]y = - \frac{6}{b}x + \frac{k}{b} [/tex]

if u see your graph, when x=0 the function's value is 1, so k/b= 1, then k=b

then if we know b , we know k

as I said, m is the pendient, in this case -(6/b) is the pendient

As u may know, the pendient equals tan(alpha)

in this case alpha its the angle between the positive x axis and the function (the big one), we dont have that angle in a triangle to know its tangent, but we have (180-alpha) the littleone, and its tangent is 1/2 (see your graph)

so, for redunction to the first quadrant we have that

[tex] \tan( \alpha ) = - \tan(180 - \alpha ) = - \frac{1}{2} [/tex]

then,

[tex] - \frac{6}{b} = - \frac{1}{2} [/tex]

b=12

k=12

The value of k if the equation of the line drawn is 6x + by = k will be 12.

What is  linear function?

A general linear function can be written as; y= mx +b, where "m" is the pendient and "b" it's the point where the funcion has x=0

Given that;

6x + by = k

by = k - 6x

y = k/b - 6x/b

When x=0 the function's value is 1, thus, k/b= 1, then k=b

In this case -(6/b) is the pendient

The angle between the positive x axis and the function (the big one), we dont have that angle in a triangle to know its tangent, but we have (180-alpha) the littleone, and its tangent is 1/2.

then,

-6/b = -1/2

b=12

k=12

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The table below contains four statements. For which function below are all four statements true? The domain of the function is x ≤ 3. The range of the function is y ≥ 0. The x-intercept of the function is 3. When x decreases, the function increases.

Answers

One of the function that satisfies all four statements is f(x) = 2 - [tex]e^{3-x}[/tex] , for x ≤ 3.

The function that satisfies all four statements is a decreasing function with a horizontal asymptote y = 0 that intersects the x-axis at x = 3. One possible function that satisfies all four statements is:

f(x) = 2 - [tex]e^{3-x}[/tex], for x ≤ 3

Explanation:

Statement 1, The domain of the function is x ≤ 3 because the expression [tex]e^{3-x}[/tex] becomes undefined for x > 3.

Statement 2, The range of the function is y ≥ 0 because the exponential term [tex]e^{3-x}[/tex] is always positive and subtracting it from 2 will always result in a non-negative value.

Statement 3, The x-intercept of the function is 3 because f(3) = 0, which means the graph intersects the x-axis at x = 3.

Statement 4, When x decreases, the function increases because the exponential term [tex]e^{3-x}[/tex] becomes smaller and smaller as x decreases, which causes the entire expression 2 - [tex]e^{3-x}[/tex] to increase.

Correct Question :

Write a function for which all four statements are true.

Statement 1: The domain of the function is x ≤ 3.

Statement 2: The range of the function is y ≥ 0.

Statement 3: The x-intercept of the function is 3.

Statement 4: When x decreases, the function increases.

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List the critical values of the related function. Then solve the inequality
(view photo)

Answers

The critical value is at x = -3/4, and the solution set is  ( -3/4, ∞)

How to find the critical values?

We can define the critical values as the problematic values. For example, we can't divide by zero, so the value of x that makes the denominator equal to zero is a critical value.

4x + 3 = 0

4x = -3

x = -3/4

That is the critical value.

Now let's solve the inequality.

-5/(4x + 3) < 0

That is true as long as the denominator is positive, so:

4x + 3 > 0

x > -3/4

The solutions et is ( -3/4, ∞)

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The equation Negative one-half(x + 1) = (y – 5)2 is represented by which graph? On a coordinate plane, a parabola opens to the left. It goes through (negative 7, negative 3), has a vertex at (1, negative 5), and goes through (negative 7, negative 7). On a coordinate plane, a parabola opens to the right. It goes through (7, 7), has a vertex at (negative 1, 5), and goes through (7, 3). On a coordinate plane, a parabola opens to the right. It goes through (9, negative 3), has a vertex at (1, negative 5), and goes through (9, negative 7). On a coordinate plane, a parabola opens to the left. It goes through (negative 9, 7), has a vertex at (negative 1, 5), and goes through (negative 9, 3).

Answers

The graph of equation 1/2(x+1)=(y – 5)^2 looks like graph of a horizontal parabola.

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

How to graph equation?

one-half(x + 1) = (y – 5)^2, written symbolically, is (1/2)(x - [-1]) = (y – 5)^2

or x + 1 = 2(y – 5)^2.

Because the y term is squared, we know immediately that the graph is a horizontal (not vertical) parabola.  

This equation can be written as

x = 2 - 1

The standard equation of a horizontal parabola with vertex (h, k) is

x = c + h.  Comparing this to the given quadratic:  

we see that k = 5 and h = -1.  This tells us that the vertex of this graph is (-1, 5), and that the graph is stretched horizontally because c = 2 is greater than 1.

To graph this, it's best to make a short table of points, as follows, remembering that y is the independent value and x depends on y through the equation given above.

y    x = 2(y – 5)^2 - 1    (x, y)

0    x = 49                    (49, 0)

2    x = 2(-3)^2 - 1         (17, 2)

1   x = 2(-4)^2 - 1          (31,  1)

vertex (already found) (-1, 5)

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Solve for x assume that all lines which appear tangent are tangent

Answers

Answer:

x = 9

Step-by-step explanation:

The measure of angle M is half of the sum of the big arc minus the little arc it intersects.

We also know ∠M = 4x +4

∠M= 1/2(mArc CK - mArc LN)

Substitute in values

4x +4 = 1/2(15x + 12 - 67)

Combine like terms

4x + 4 = 1/2(15x - 55)

Multiply (what's in side the parenthesis by 1/2)

4x + 4 = 7.5x - 27.5

Isolate the x. Add 27.5 to both sides

4x + 31.5 = 7.5x

Subtract 4x from both sides

31.5 = 3.5x

Divide both sides by 3.5

9 = x

PLEASE HELP FAST!!!!!!
What is the volume of the right pyramid?

Answer options with 5 options
A.
186 and 2-thirds centimeters cubed

B.
84 centimeters cubed

C.
25 centimeters cubed

D.
23 and 1-third centimeters cubed

E.
18 and 2-thirds centimeters cubed

Answers

The volume of the right pyramid is 23 1/3 cm³. The correct option is E,

Given that the length of the side of the right pyramid is 3.75 cm, While the height of the pyramid is 5 cm. Therefore, the volume of the given right pyramid is:

Volume = (1/3) × (side length)² × Height

              = (1/3) × (3.75 cm)² × 5 cm
              = 23.33 cm³

              = 23 1/3 cm³

Hence, the volume is 23 1/3 cm³.

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The complete question must be:

What is the volume of the right pyramid with the base lenght of 3.75 cm and height of 5cm?

A. 186 and 2-thirds centimeters cubed

B. 84 centimeters cubed

C. 25 centimeters cubed

D. 23 and 1-third centimeters cubed

E. 18 and 2-thirds centimeters cubed

Luis Gonzales plays baseball for the Arizona Diamondbacks. After 20 games one season, he had 11 homeruns. Predict how many homeruns he will have after 100 games.

A22
B55
C220
D100

Answers

The number of homeruns Luis Gonzales will have after 100 games can be expected using probability as 55.

Given that,

Luis Gonzales plays baseball for the Arizona Diamondbacks.

Number of games played in a season = 20

Number of games he had homeruns = 11

So there is a chance to get 11 homeruns from 20 games.

Probability of having homeruns = 11/20 = 0.55

If he played 100 games,

Expected number of homeruns he would get = 100 × 0.55 = 55

Hence the expected number of homeruns he has in 100 games is 55.

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I need help figuring out the answers.

Answers

Required true statements are f and d are vertical, d and e supplementary, g and are adjacent, d and g are complementary and f and e are linear pair.

What is the value of d?

Here d is the opposite angle of f.

We know opposite angles are always equal.

So, according to question f = 71° then d = 71°.

Now we need to check given statements are true or false.

1) Given d and f are adjacent.

We know, adjacent angles always have same vertex.

But angle f and d don't have any common vertex.

So, we can say d and f are not adjacent.

2) Given d and e are complementary.

From the picture, sum of d and e is 180°.

We know, sum of two complementary angles is 90° always.

So, this statement is also not true.

3) f and d are vertical.

Vertical angles are always opposite each other where two line cross.

Here it is clear f and d are opposite and they made by two line cross.

So, f and d are vertical is a true statement.

4) d and e supplementary.

Already said sum of d and e is 180°.

We sum of two supplementary angles is 180° always.

So, This is the true statement.

5) Here g and f have common vertex.

So, g and f are adjacent is the true statement.

6) Here value of g is (90-71) = 29°

So, sum of g and d is 90°.

Therefore, g and d are complementary.

7) Here d and g are not opposite.

So, they are not vertical.

8) Linear pair means, two hands of two common line

Here, f and e have two hands of two common line.

So, they are a linear pair.

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Question 9 of 10
Which expression gives the surface area of a sphere with radius r?
OA. TR2²
OB. 43
OC. 42²
OD. 42²

Answers

The expression that gives the surface area of a sphere with radius as r would be =4πr². That is option A.

What is a sphere?

A sphere is defined as the shape whose surface is made up of all the points that are an equal distance from the point that is the shape's center.

The formula that can be used to calculate the surface area of a sphere is given as;

S.A = 4πr²

Since the radius given is in terms of r, therefore, the expression that shows the surface area of a sphere would be = 4πr².

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Which equation has the same missing number 318-100=?

Answers

218 is the answer may I get branliest

If 10 liters of oxygen at stp are heated to 512°c what will be the new volume of gas if the pressure is also increased to 1520 mm of mercury

Answers

To solve this problem, we can use the combined gas law, which relates the pressure, temperature, and volume of a gas:

(P1 × V1)/T1 = (P2 × V2)/T2

where P1, V1, and T1 represent the initial pressure, volume, and temperature of the gas, and P2, V2, and T2 represent the new pressure, volume, and temperature of the gas, respectively.

At STP (standard temperature and pressure), the initial conditions are:

P1 = 1 atm
V1 = 10 L
T1 = 273 K (0°C)

To convert the temperature to Kelvin, we add 273 to the Celsius temperature.

The final conditions are:

P2 = 1520 mmHg
T2 = 512°C + 273 = 785 K

We can now solve for V2:

(P1 × V1)/T1 = (P2 × V2)/T2

(1 atm × 10 L)/(273 K) = (1520 mmHg × V2)/(785 K)

V2 = (1 atm × 10 L × 785 K)/(273 K × 1520 mmHg)

V2 = 9.0 L (rounded to one decimal place)

Therefore, the new volume of the gas is 9.0 liters if 10 liters of oxygen at STP are heated to 512°C and the pressure is also increased to 1520 mmHg.

Please help with question on the Image, Thanks.

Answers

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{d}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ d=\sqrt{ 17^2 - 15^2}\implies d=\sqrt{ 289 - 225 } \implies d=\sqrt{ 64 }\implies d=8 \\\\\\ \stackrel{\textit{radius is half the diameter}}{r=\cfrac{8}{2}}\implies r=4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4\\ h=15 \end{cases}\implies V=\pi (4)^2(15)\implies V\approx 754~cm^3[/tex]

lamar records the high temperature in degrees Fahrenheit for his city over several days in the table​

Answers

Keeping a temperature record can help Lamar and others stay informed about the climate in their area and make informed decisions based on that information.

Lamar has been recording the high temperature in degrees Fahrenheit for his city over several days and has recorded them in a table. It is essential to keep a record of the temperature to track the weather patterns and make predictions about future weather conditions.

By having this data, Lamar can analyze the temperature trends in his city over time. He may notice that certain times of the year tend to be warmer or cooler than others or that some days are unusually hot or cold.

This information can be valuable for planning outdoor activities or making decisions about the best time to travel

To learn more about : temperature

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30 points to whoever answers!!

Answers

Answer:

45.73 square feet.

Step-by-step explanation:

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius.

We can rearrange this formula to solve for r:

r = C / 2π

Plugging in the given value of C = 24 feet, we get:

r = 24 / (2π)

r ≈ 3.819 feet

Now that we know the radius of the circle, we can use the formula for the area of a circle to find the approximate area of the park:

A = πr^2

Plugging in the value of r, we get:

A ≈ π(3.819)^2

A ≈ 45.73 square feet

Therefore, the approximate area of the circular park is 45.73 square feet.

Answer: A = 45.82 ft²

Step-by-step explanation:

Given:

C= 24 ft

Formulas needed:

C=2[tex]\pi[/tex]r    where r is radius

Circumference is the perimeter of the circle.  Length of outside line

and

Area:

A=[tex]\pi r^{2}[/tex]

Area the measurement of the shape or area that you want to cover.

Solution:

C=2[tex]\pi[/tex]r              >substitute C=24     and solve for r

24=2[tex]\pi[/tex]r            > divide both sides by 2[tex]\pi[/tex]

[tex]\frac{24}{2\pi }[/tex]  = r               >use 3.14 for [tex]\pi[/tex]

[tex]\frac{24}{2*3.14}[/tex]  = r          >plug into calculator

r=3.82

Now that we have r   we can solve for A

A=[tex]\pi r^{2}[/tex]

A=(3.14)(3.82)²     >plug into calc

A = 45.82 ft²

Twelve jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 47% are of a minority race. Of the 12 jurors selected, 2 are minorities.
(a) What proportion of the jury described is from a minority race?
(b) If 12 jurors are randomly selected from a population where 47% are minorities, what is the probability that 2 or fewer jurors will be minorities?
(c) What might the lawyer of a defendant from this minority race argue?
(a) The proportion of the jury described that is from a minority race is
(Round to two decimal places as needed.)
(b) The probability that 2 or fewer out of 12 jurors are minorities, assuming that the proportion of the population that are minorities is 47%, is
(Round to four decimal places as needed.)
(c) Choose the correct answer below.
OA. The number of minorities on the jury is unusually low, given the composition of the population from which it came.
B. The number of minorities on the jury is reasonable, given the composition of the population from which it came.
OC. The number of minorities on the jury is unusually high, given the composition of the population from which it came.
OD. The number of minorities on the jury is impossible, given the composition of the population from which it came.
Next

Answers

Step-by-step explanation:

(a) Proportion of minority jurors = 2/12 = 1/6 = 0.1667

(b) Using binomial distribution, P(2 or fewer minorities) = P(0 minorities) + P(1 minority) + P(2 minorities)

P(0 minorities) = (0.53)^12 ≈ 0.005

P(1 minority) = 12C1 (0.47)(0.53)^11 ≈ 0.048

P(2 minorities) = 12C2 (0.47)^2(0.53)^10 ≈ 0.18

P(2 or fewer minorities) ≈ 0.005 + 0.048 + 0.18 ≈ 0.2339

(c) OA. The number of minorities on the jury is unusually low, given the composition of the population from which it came.

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