Are the expressions 1/2(4c+8) + 3c-2 and 4c+2(0.5c+1) equivalent?

Answer:

Find the slope (1,3), (5,5): m = 0.5

Find the slope (0,-1), (2,3): m = 2

Find the slope (2,-3), (5,-4): m = -1/3

Step-by-step explanation:

m = y2-y1/x2-x1

Answer: 2, 1, -1/3

Step-by-step explanation:

y2-y1/x2-x1

5-3 = 2

5-4=1

2

It will take 10 days for 1023 students to know the secret.

We can start by using the formula for exponential growth: n = 2^k

where n is the number of students who know the secret and k is the number of days.

On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.

We want to find k when n = 1023, so we can solve for k:

1023 = 2^k

log2 1023 = k

k = 10

So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.

Therefore, It will take 10 days for 1023 students to know the secret.

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It will take 10 days for 1023 students to know the secret.

We can start by using the formula for exponential growth: n = 2^k

where n is the number of students who know the secret and k is the number of days.

On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.

We want to find k when n = 1023, so we can solve for k:

1023 = 2^k

log2 (1023) = k

k = 10

So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.

Therefore, It will take 10 days for 1023 students to know the secret.

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The factors of quadratic function x²-12x + 36 are (x -6) and (x - 6).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A quadratic function:

x²-12x + 36.

To factorize the quadratic function:

x²-12x + 36,

= x²-6x -6x + 36

= x(x - 6) -6(x - 6)

= (x -6) (x - 6)

Therefore, the factors are (x -6) and (x - 6).

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To determine if the club should increase the budget for the indoor rock climbing facility, the usage data of members must be analyzed. The best measure of center to use in this scenario would be the mean, as it gives a clear average of the usage data.

If the average usage of the members is at least two times per week (8 times per month), the club can consider increasing the budget.

However, if the data is inconclusive, it could mean that the sample size is too small or there is too much variability in the data, making it difficult to accurately determine the average usage. In this case, additional data or further analysis may be needed to make a clear decision.

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Answer:

Mixed Number: 11 1/4

Decimal: 11.25

Step-by-step explanation:

Answer:

[tex] \red {\boxed{\tt{ 11\frac{14}{56} }}}[/tex]

Step-by-step explanation:

[tex] \tt4 \frac{3}{8} \times 2 \frac{4}{7} \\ \\ \tt \frac{8 \times 4 + 2}{8} \times \frac{7 \times 2 + 4}{7} \\ \\ \tt \frac{35}{8} \times \frac{18}{7} \\ \\ \tt{ \frac{35 \times 18}{8 \times 7} } \\ \\ \tt {\frac{630}{56}} \\ \\ \tt{ 11\frac{14}{56} }[/tex]

The variable "Gallons of water in a swimming pool" is a quantitative variable.

Quantitative variables are variables that are numerical and can be measured on a scale, such as height, weight, or time. In this case, the number of gallons of water in a swimming pool can be measured and can take any value within a range, such as 0 to 100,000 gallons. Therefore, "Gallons of water in a swimming pool" is a quantitative variable.

In contrast, qualitative variables are variables that describe an attribute or characteristic of a person, place, or thing, and they do not have a numerical value. Examples of qualitative variables include hair color, religious affiliation, or nationality.

"

Complete question

Determine whether the variable is qualitative or quantitative. explain your reasoning.

Variable: Gallons of water in a swimming pool

"

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Answer:

below

Step-by-step explanation:

Interest = prt       p = principle = 500   r = rate in decimal = .12   t = years

            = 500 ( .12)(4) = 240 dollars

Answer:

y = 10x + 60

Step-by-step explanation:

Hope this will help on your test.

The piece of cardboard needed will be 44 by 44 inches.

The volume of a square box can be defined as the space occupied by the square box or the cube, It is equal to the cube of the length of the side of the square box.

The formula for the volume is V = s³

The volume will be L*W*H

We are cutting 3 inches from each corner, so the length and width will each be x-6.

The height will be 4.

4332 = 4* (x - 6)* (x - 6)

1444= (x - 6)²

38 = x-6

x=44 inches.

The piece of cardboard needed will be 44 by 44 inches.

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Large pizzas are 14 inches in diameter and will offer approximately 10 slices.

What is meant by diameter?

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The probability of getting omeone is  25.3%

Find the probability of getting omeone in the 18-21 age bracket or omeone who repond?

Define the two events

A = someone is in the 18-21 age bracket

B = the person does not respond

Based on the table, we have

n(A) = number of people in set A = 76

n(B) = 31

n(A and B) = 11

So,

n(A or B) = n(A) + n(B) - n(A and B)

n(A or B) = 76+31-11

n(A or B) = 96

We have 96 people in the age 18-21 bracket, they didn't respond, or both.

Divide this over the 379 people surveyed

96/379 = 0.253 = 25.3%

Answer: 25.3%

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A linear growth function has a positive constant slope, whereas an exponential growth function has a positive rising slope.

Explanation and response: Exponents are not permitted in a linear equation. Because the link between the two variables does not vary at a constant pace, the exponents in an equation generate a nonlinear graph. Linear functions have a constant rate of change per unit interval. Over equal intervals, an exponential function changes by a similar ratio.

The exponential function is another sort of nonlinear function.A nonlinear function in which the independent variable equals the function’s exponent, as in… The independent variable in these functions is an exponent in the equation. Exponential functions are shown as straight lines on semilog paper. Semi-log paper contains two axes: one arithmetic and one logarithmic. The exponential constant in the equation is given by the slope of the line (m).

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the term for the given Table is given below:

Mathematics is all about theorems. A rigorous proof is a specific form of logical argument that has been used to demonstrate the truth of a claim, which is what a theorem is.

A. Definition refers to a statement that exactly defines the object, thing, or everything.

B. Postulate or axiom is a statement that is accepted as true in order to initiate an argument.

C. Common notion is the statement that helps to understand the common sense of the subject.

D. Theorem is a statement that shows proof on the basis of previously made statements.

E. Corollary is a statement that acts as a small proof that has already been proven.

Therefore, the correct matching for the given terms will be:

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Complete question:

Explain the main parts and uses of two kinds of proofs. March the word with the right definition.

A. Definition

B. Postulate(axiom)

C. Common notion

D. Theorem

E. Corollary

1. A statement that is assumed to be true without proof

2. A statement that has already been proven to be true

3. A statement that tells exactly what something is or means

4. A statement that makes sense based on another statement that has already been proven

5. A statement that is not officially defined but that is understood to be common sense.

Help pls :3

The equation of the each of the lines in slope-intercept form are:

5. y = -1/3x + 3.

6. y = 2x - 2

7. y = -8/3x + 4.

8. y = -2x + 1.

The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

5. Slope (m) = rise/run = -1/3

y-intercept (b) = 3

The equation is: y = -1/3x + 3.

6. Slope (m) = rise/run = 2/1 = 2

y-intercept (b) = -2

The equation is: y = 2x - 2

7. Slope (m) = rise/run = -8/3

y-intercept (b) = 4

The equation is: y = -8/3x + 4.

8. Slope (m) = rise/run = -2/1 = -2

y-intercept (b) = 1

The equation is: y = -2x + 1.

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Probability that a teacher prefer projector & is female candidate is =

Total Female prefer whiteboard/Total people = 28/75 = 0.373

Given that the information below:

Male people prefer projector - 22

Female people prefer projector - 28

Total people prefer projector - 50

Male people prefer Whiteboard - 10

Female people prefer whiteboard - 15

Total people prefer whiteboard - 25

Total number of Male people - 32

Tota lnumber of  Female people - 43

Total number of people - 75

Here the solution given below :

Probability that a teacher prefer projector & is female candidate is =

Total Female prefer whiteboard/Total people = 28/75 = 0.373

The correct option of this question is  B) 0.373. Explation is given above.

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Crater Lake National Park in Oregon is renowned for its spectacular scenery and pristine natural beauty. The park contains an impressive 155 miles of trails, which is significantly more than its 33 miles of shoreline.

The abundant trails within the park provide visitors with an opportunity to explore the area on foot, discovering the unique beauty and landscape that has captivated viewers for centuries.

The trails range from short, easy hikes to more difficult, challenging hikes. Many of the trails lead to breathtaking views of the lake, or to the top of the dormant volcano, Mount Mazama.

The trails are well-maintained and very well-marked, so visitors can confidently and safely make their way around the park. There are also several trails that feature interpretive signs to provide visitors with educational information about the area’s flora, fauna, and geology.

Using the trails, visitors can explore Crater Lake National Park’s many wonders, such as the stunning

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The correct 2-variable equation that models how many feet Nick can run is: 25x = m,

Hence, option (d) is correct choice.

As per the data given,

We have,

Nick can run at a speed of 25 feet per second.

We need to convert the above statement in 2-variable equation models

We can write it as:

Distance covered by Nick will be:

25x = m

where x is the time in seconds that Nick runs and

m is the distance in feet that Nick runs.

The equation represents the relationship between time and distance using the constant speed of 25 feet per second.

The distance travelled is equal to the speed multiplied by the time.

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Answer: C- 96

Step-by-step explanation:

The statement that accurately describes unimodal distribution is

" A distribution in which one value is more frequent than other values"

What is unimodal distribution ?

One distinct peak or most frequent value characterises a distribution as unimodal. The values start out climbing, reaching a single high, and then starting to fall. The "mode" in "unimodal" refers to the local maximum on a chart, not the most frequent value in a data set (although they are closely related).

In a graph, one peak will correspond to one mode (one common number), therefore conceptually they are the same thing. There is no list of numbers to go to when attempting to determine if a graph represents a unimodal distribution or not.

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Answer:

tan K = 4/3

Step-by-step explanation:

Tangent is a ratio. The side marked 32 is opposite from angle K. And the side marked 24 is adjacent to (next to) angle K.

Tangent K is the ratio:

opposite/adjacent

tan K = opp/adj

fill in the given side lengths

tan K = 32/24

simplify, both numbers are divisible by 8

tan K = 4/3

The mean of this sampling distribution is 70.9, which is less than the value of the population median of  73, therefore, the sample median is a biased estimator of the population median.

The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

A statistic used to estimate a parameter is an unbiased estimator if the mean of its sampling distribution is equal to the value of the parameter being estimated.

We obtained the following data from part (a) of this problem,

Sample 1: 64, 65, 73, and median is 65.

Sample 2: 64, 65, 74, and median is 65.

Sample 3: 64, 65, 76, and median is 65.

Sample 4: 64, 73, 74, and median is 73.

Sample 5: 64, 73, 76, and median is 73.

Sample 6: 64, 74, 76, and median is 74.

Sample 7: 65, 73, 74, and median is 73.

Sample 8: 65, 73, 76, and median is 73.

Sample 9: 65, 74, 76, and median is 74.

Sample 10: 73, 74, 76, and median is 74.

Let us calculate the mean of this sampling distribution,

μ(median) = ( 65+65+65+73+73+73+73+74+74+74)/10

μ(median) = 709/10

μ(median) = 70.9

The mean of the sampling distribution is found to be equal to 70.9.

(b) 70.9, which is less than the value of the population median of

73, therefore, the sample median is a biased estimator of the population median.

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Answer:The distance between the two points (4, 9) and (7, 5) can be calculated using the distance formula:

√((7 - 4)^2 + (5 - 9)^2) = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.

Step-by-step explanation:

So the length of JL is equal to the square root of the expression in the parentheses.

Given,

Based on the information given,

The triangle JLK is a right triangle with JL being the hypotenuse.

Since the angle between IJ and JL is half the angle between JI and JK,

we know that JL is also the perpendicular bisector of IK.

By using the Pythagorean theorem, we can find the length of JL:

[tex](JL)^2 = (2x + 5)^2 + (3x)^2[/tex]

Expanding and simplifying the right side:

[tex]JL^2 = 4x^2 + 20x + 25 + 9x^2[/tex]

[tex]JL^2 = 13x^2 + 20x + 25[/tex]

Taking the square root of both sides:

[tex]JL = \sqrt{(13x^2 + 20x + 25)}[/tex]

So the length of JL is equal to the square root of the expression in the parentheses.

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-8,215 in decimal form.  1101 0010 0011 0111 is a signed binary representation of -8,215 in decimal form.

The binary number 1101 0010 0011 0111 is a signed binary representation of -8,215 in decimal form. To convert this number to decimal, the first bit is the sign bit. This bit is 1, indicating that the number is negative. The remaining 14 bits represent the magnitude of the number. To convert to decimal, each bit is multiplied by two to the corresponding power of two, beginning with the least significant bit. The least significant bit is 2^0 or 1. The next bit is 2^1 or 2 and so on. The value of the number can then be determined by adding the values of each bit together. 1101 0010 0011 0111 = -1 + 2 + 8 + 16 + 32 + 64 + 512 + 1024 + 4096 = -8,215.

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The growth factor in the function is 5.

An exponential function with the form A(t) = [tex]C a^t[/tex], where a > 0

When t = 0, the function's initial value is represented by the number C, and the growth (or decay) factor is represented by the number a.

If a > 1, the function represents growth; If 0 < a < 1, the function represents decay.

Given:

y = 4 x [tex]5^7\\[/tex]

we know the general form of Exponential function

g(x) = [tex]ab^x[/tex]

where a is the initial amount

b is the growth or decay factor

and, x is the time

Now, comparing to the given function

Initial amount= 4

Growth factor = 5

time = 7

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The discounted prices are given as follows:

5) Soccer ball: $7.46.

6) Leather jacket: $202.31.

7) Board game: $15.83.

8) Baseball cap: $11.43.

9) Wooden key: $15.12.

10) Phone charger: $13.30.

The discounted prices are obtained applying the proportions in the context of this problem, multiplying the original price by the decimal equivalent of the discounted price.

Hence the discounted prices are obtained as follows:

5) Soccer ball: 10.65 x (1 - 0.3) = $7.46.

6) Leather jacket: 216.95 x (1 - 0.0675) = $202.31.

7) Board game: 17.69 x (1 - 0.105) = $15.83.

8) Baseball cap: 13.45 x (1 - 0.15) = $11.43.

9) Wooden key: 16.75 x (1 - 0.0975) = $15.12.

10) Phone charger: 15.65 x (1 - 0.15) = $13.30.

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She ran faster on Thursday running at 7.5 mph which is 0.3 mph faster than 7.2 mph speed on Wednesday

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Speed is the ratio of total distance travelled to total time taken. It is given by the equation:

Speed = distance / time

1 hour = 60 minutes

She ran 6 miles in 50 minutes.

50 minutes = 50 min * 1 hr per 60 min = 5/6 hr

Speed on Wednesday = distance / time = 6 miles / (5/6)hr = 7.2 mph

She ran 4 miles in 32 minutes.

32 minutes = 32 min * 1 hr per 60 min = 8/15 hr

Speed on Thursday = distance / time = 4 miles / (8/15)hr = 7.5 mph

Difference in speed = 7.5 mph - 7.2 mph = 0.3 mph

She ran faster on Thursday

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The change that will ensure that the code segment functions as intended is "Removing lines 5-8

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Answer: An argument is a value passed to a function. A parameter variable is a variable local to the function which receives the argument.

Step-by-step explanation:

The term "argument" refers to the values that are specified inside a function when the function is invoked. The variables that are defined when the function is declared, however, are referred to as parameters.

What is Function?

A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

The term "argument" refers to the values that are specified inside a function when the function is invoked. The variables that are defined when the function is declared, however, are referred to as parameters.

argument:

These are employed in function call statements in order to transfer value from the calling function to the receiving function.

Also called as Actual Parameters, they are.

Each argument is always assigned to the parameter specified in the function specification during the call.

Parameter:

These are utilised in the called function's function header to obtain the value from the parameters.

When a function is called, arguments are passed as values to local variables known as parameters.

Formal Parameters is another name for them.

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