The temperature dropped from 75 degrees to 50 degrees
What was the percent decrease in the temperature?
O 333 %
O
50%
O 663%

In the figure given the value of x is calculated to be

The value of x is solved from using the vertical angle theorem.

According to this theorem, when two straight lines cross, they create two sets of linear pairs with equal angles.

The adjacent angles created by the junction of these two lines are likewise said to be supplementary, or equivalent to 180 degrees.

From this principle,

8x = 2x + 72

8x - 2x = 72

6x = 72

x = 16

The angles marked by 8x is equal to

= 8 * 12

= 96 degrees

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The minimum acceptable rate of 1 sigma of quality production is d) 68.

This corresponds to a 68% acceptance level, which is equivalent to 1 standard deviation in a normal distribution.

A 1 sigma level corresponds to a standard deviation that captures approximately 68% of the data within a normal distribution. This means that if a process is operating at a 1 sigma level, it has a 68% acceptance rate, and the remaining 32% of the data falls outside the acceptable range

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We can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data

First, we can plug in the value of 28 for Age in the regression line equation to get the estimated average number of sick days for an employee who is 28 years old:

Next, we can use the standard error to calculate the margin of error for a 90% confidence interval:

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the estimated average number of sick days:

Confidence interval = 7.079032 ± 2.767462 = (4.31157, 9.84649)

Therefore, we can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data.

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Complete Question:

The estimated regression line and the standard error are given. Sick Days=14.310162−0.2369(Age) se=1.682207 Find the 90% confidence interval for the average number of sick days an employee will take per year, given the employee is 28. Round your answer to two decimal places.

Employee 1 2 3 4 5 6 7 8 9 10

Age 30 50 40 55 30 28 60 25 30 45

Sick Days 7 4 3 2 9 10 0 8 5 2.

Answer:

the answer is 6.8 litres

Step-by-step explanation:

3.4 × 2 = 6.8

The probability that a sample of 130 steady smokers spend between $19 and $21 by using normal probability distribution is 0.897.

The probability distribution that would be symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The formula for normal probability distribution is-

z = (x - μ)/σ

where is the z is the standard normal variate or z-score.

x is the range of the values. ( = 19 to 21)

μ is the mean. (=20)

σ is the standard deviation. (=7)

n is sample size = 130

How likely it is that a sample of 130 regular smokers will spend within $19 and $21?

This is the result of subtracting the pvalue of Z when X = 19 from of the p-value for Z when X = 21.

By central limit theorem;

s = σ/√n

s = 7/√130

s = 0.61

So,

When x = 21

z = (21 - 20)/0.61

z = 1.63  ( p-value of 0.948 taken from z-table)

when x = 19

z = (19 - 20)/ 0.61

z = -1.63 ( p-value of 0.051 taken from z-table)

The probability is 0.948 -  0.051

Probability = 0.897

Therefore, the probability that a sample of 130 steady smokers spend between $19 and $21 is 0.897.

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Answer:

see explanation

Step-by-step explanation:

The perimeter is the sum of the 3 sides , then

2x - 6 + x + 4 + 10 > 50

3x + 8 > 50 ( subtract 8 from both sides )

3x > 42 ( divide both sides by 3 )

x > 14

(4)

The area is calculated by multiplying length and breadth , then

3(4x - 2) < 138 ( divide both sides by 3 )

4x - 2 < 46 ( add 2 to both sides )

4x < 48 ( divide both sides by 4 )

x < 12

Answer:

\(\tt{D. (x-2)² = 16 (y + 1)}\)

Step-by-step explanation:

In order to find the equation of a parabola given its vertex and focus, we can use the standard form equation for a parabola:

\(\boxed{\bold{\tt{(x - h)^2 = 4p(y - k)}}}\)

where (h, k) represents the vertex and p is the distance between the vertex and the focus.

In this case, the vertex is (2, -1) and the focus is (2, 3).

The x-coordinate of the vertex and focus are the same, which tells us that the parabola opens vertically. Therefore, the equation will have the form:

\(\tt{(x - 2)^2 = 4p(y - (-1))}\)

Simplifying further:

\(\tt{(x - 2)^2 = 4p(y + 1)}\)

Now we need to find the value of p, which is the distance between the vertex and the focus.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:

\(\boxed{\bold{\tt{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}\)

Using this formula, we can calculate the distance between the vertex (2, -1) and the focus (2, 3):

\(\boxed{\bold{\tt{Distance = \sqrt{(2- 2)^2 + (3 -(+1))^2}}}}\)

\(\boxed{\bold{\tt{Distance = \sqrt{4^2}}}}\)

Distance 4

Therefore, p = 4. Substituting this value back into the equation, we get:

\(\tt{(x - 2)^2 = 4(4)(y + 1)}\)

\(\tt{(x - 2)^2 = 16(y + 1)}\)

So, the equation of the parabola is\(\tt{ (x - 2)^2 = 16(y + 1)}\)

The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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Step-by-step explanation:

Step 1:  Add 13x to both sides

\(x^2 + 13x = -13x + 13x - 4\)

\(x^2 + 13x = -4\)

Step 2:  Add 4 to both sides

\(x^2 + 13x + 4 = -4 + 4\)

\(x^2 + 13x + 4\)

Step 3:  Use Quadratic Formula

\(x = \frac{ -b \pm \sqrt{ b^2 - 4ac } }{2a}\)

\(x = \frac{ -(13) \pm \sqrt{ 13^2 - 4(1)(4)} } { 2(1)}\)

\(x = \frac{-13 \pm \sqrt{153}}{2}\)

\(x = \frac{-13\pm3\sqrt{17} }{2}\)

Answer:  \(x = \frac{-13\pm3\sqrt{17} }{2}\)

Answer:

-0.3 and - 12.7

Step-by-step explanation:

Rewrite in quadratic form:

x2 + 13x + 4 = 0

The best approximations, given the options, are 0 and - 13

The actual solution is -

The number of miles that Maria ran is 25.6 mile.

From the information given, she runs for 4 hours at a speed of 6.4 miles per hour.

It should be noted that distance is calculated as the speed multiplied by the time taken.

In this case,the distance will be:

= Speed × Time

= 6.4 × 4

= 25.6 miles

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Answer:

V = 135π in3; S = 105π in2

Step-by-step explanation:

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

15,999,999,995

Step-by-step explanation:

16 billion - 5 = 15,999,999,995

The solution to the system of inequalities 4x + y > 8 and x - y < 5

is (2.6, - 2.4).

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, 4x + y is less than 8, x - y is greater than 5.

Therefore, 4x + y > 8 and x - y < 5.

The solution to the system is (2.6, - 2.4).

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For a relative frequency table by rows 4-column table with 2 rows about the breakfast choices of boys and girls. The conclusion is of table is represented by option(b).

We have provided the following information about relative frequency table by rows, tables by row, 4 columns and 2 rows.

Now, we represent the above information into tabular form,

Eat cereal do not eat cereal Total

boys 68.3% 31.7% 100%

girls 69.1% 30.9% 100%

Now, we have to draw conclusion about the relative frequency of these results. From the table, the percentage of girls and boys who eat cereal is exceed from the not. Thus, we cannot say if a person eat cereal for breakfast, then he is a boy. Similarly we cannot know about gender of a person by eats cereal. The right conclusion is that if i am a girl in this group, i am more likely to eat cereal for breakfast than not. Hence, required option is option (b).

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Complete question:

relative frequency table by rows 4-column table with 2 rows. column 1 has entries boys, girls. column 2 is labeled eat cereal with entries 68.3 percent, 69.1 percent. column 3 is labeled do not eat cereal with entries 31.7 percent, 30.9 percent. column 4 is labeled total with entries 100 percent, 100 percent. What conclusion can you draw about the relative frequency of these results?

a) If you are a boy in this group, you are more likely not to eat cereal for breakfast than to eat cereal.

b) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

c) If you eat cereal for breakfast, you are a boy.

d) Knowing if a person eats cereal will help determine gender.

Answer:

B. If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

Step-by-step explanation:

Edge 2023

If x is the largest of the three consecutive integers, then the three consecutive integers can be represented as x-1, x, and x+1.

The sum of these three consecutive integers is:

(x-1) + x + (x+1)

Simplifying the expression, we get:

3x

Therefore, the expression in terms of the given variables that represents the sum of three consecutive integers when x is the largest is 3x.

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Answer:

multiply t from both sides by t, then divide both sides by s.

it should be txy/s = r

Answer:

r =  \(\frac{txy}{s}\)

Step-by-step explanation:

multiply both sides by t

txy = rs

flip the equation

rs = txy

divide both sides by s

\(\frac{rs}{s}\) = \(\frac{txy}{s}\)

r = \(\frac{txy}{s}\)

To calculate the numerator sxx, which is part of a formula for calculating variance or sum of squares, additional information about the dataset or specific formula is needed.

The process involves finding the sum of squares of the data points by subtracting the mean from each data point, squaring the result, and summing up these squared differences. The formula used depends on the statistical method or context. Once sxx is determined, it can be used to compute the variance of the dataset. Variance measures the spread or variability of the data points around the mean and is obtained by dividing sxx by the degrees of freedom (n-1, where n is the sample size).

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Answer:

100

Step-by-step explanation:

5(23-3)

23-3= 20

5 × 20= 100

The value of y when x = 4 is 3.

In this given condition statement, if x is greater than 5, the value of y is 1. If x is less than 5, there is an additional condition.

If x is less than 3, the value of y is 2.

Otherwise, if x is not less than 3, the value of y is 3. Lastly, if x is equal to 5, the value of y is 4.

In the case of x = 4, x is less than 5 but not less than 3.

Therefore, the condition statement within the else condition is satisfied, resulting in the value of y being 3.

This means that when x is equal to 4, the value of y equals 3 as per the given conditions.

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Answer: A teapot.

Step-by-step explanation:

Hello there I hope you are having a great day :)

The Topic Shifting digits:

Shifting digits - Putting a digit in a different place. For a example Take the number 358 you would exchange the number from the hundreds that would equal 838 this meaning that you what to make a bigger number than a small one.

Examples:

1. 358 equal 838

2. 204 equal 402

3. 188 equal 881

You are just making them smaller to a greater number :)

Hopefully that helps you :)

Step-by-step explanation:

this is to make you aware what "power" or "value" is associated with what position in a number.

when I write a number like in the example above

795

then the strongest, most powerful value in the whole number is with the digit in the outmost left position.

the second most powerful with the digit in the next position to the right. and sin on.

and the digit in the outmost right position has the least value.

to make sure that there is no overlap between the positions, every position corresponds to a certain power of 10 level. each position to the left is one level higher, and another level higher and so on.

as we start with 10⁰, the levels go up to number of positions - 1.

3 positions means we go up to 10².

795 = 7×10² + 9×10¹ + 5×10⁰

or

42186 = 4×10⁴ + 2×10³ + 1×10² + 8×10¹ + 6×10⁰

by the way, you know that x⁰ = 1 for any value of x.

if we go into the decimals, then the same principle applies also on the right side of the decimal point. each position further right decreases the exponent of 10 by 1.

23.073 = 2×10¹ + 3×10⁰ + 0×10^-1 + 7×10^-2 + 3×10^-3

it is very important when handling and calculating numbers to stay always very aware of the positions the digits have in the actual number(s). and to combine always only the digits in the right corresponding positions for calculations or comparisons.

bottom line of this exercise above is therefore, if you put a smaller digit into the first position (outmost left), then the number value gets smaller, no matter what you do with the remaining digits in their positions.

and the other way around (bigger digit in the first position makes the number value bigger). it gets smaller or bigger with the associated power of 10.

you can imagine these associated powers of 10 as proponents or "bullies" of the corresponding digits. the bigger the exponent of 10, the stronger and effective the "bully".

on the other end :

even if you put a 9 instead of a 0 into the last (outmost right) position, the number value gets a little bit bigger. it has only the weakest "bully" to "make it heard". it only makes a difference, if the other digits are the same.

e.g.

52760 is smaller than 52769.

but

52770 is bigger than 5276x, no matter what digit you put in for x.

this is what this exercise tries to show you, and the playing around with the numbers should create a "feeling" in you to always think about it, even if it is only sub-consciously.

Answer:

1.1     Solve   x-3y+7  = 0

recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  x-3y+7  = 0 and calculate its properties

Step-by-step explanation:

The anser is in the screenshots

Answer: Solution: (-4, 1)

Step-by-step explanation:

x = 3y - 7

4x + 5y = -11

Substitute x for 3y - 7

4x + 5y = -11

4 (3y - 7) + 5y = -11

12y - 28 + 5y = -11

17y - 28 = -11

Add 28 to both sides

17y = 17

y = 1

x = 3y - 7

x = 3(1) - 7

x = 3 - 7

x = -4

Solution: (-4, 1)

The function f(x) = |x| - 5 is a piecewise function with two different cases: when x is negative and when x is positive.

This means that the function can take on different values depending on whether x is negative or positive.Case 1: x is negativeIf x is negative, then f(x) = -x - 5. To find the range of this function, we can look at the minimum value that f(x) can take on. Since -x is always nonpositive, the smallest value that f(x) can take on is when x = 0, which gives f(0) = -5.

Therefore, the range of f(x) for x negative is given by:r: {f(x) ∈ ℝ | f(x) ≤ -5}Case 2: x is positiveIf x is positive, then f(x) = x - 5. To find the range of this function, we can look at the minimum value that f(x) can take on. Since x is always nonnegative, the smallest value that f(x) can take on is when x = 0, which gives f(0) = -5. Therefore, the range of f(x) for x positive is also given by:r: {f(x) ∈ ℝ | f(x) ≤ -5}Overall, the range of the function f(x) = |x| - 5 is given by:r: {f(x) ∈ ℝ | f(x) ≤ -5}

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The equivalent expression of the perimeter of the regular hexagon is,

⇒ 42x + 24

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

A regular hexagon has six congruent sides.

And, The length of each side is represented by the expression (7x + 4).

Now, We know that;

The sum of all sides of a regular hexagon is called its perimeter.

Hence, We get;

Here, The length of each side is represented by the expression 7x + 4.

So, We get;

The perimeter of Hexagon = 6 × (7x + 4)

                                          = 42x + 24

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Answer:

The answer is the third option! :)

Step-by-step explanation:

Hope you do great:)

The transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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

The functions f(x) and g(x)

Where, we have

f(x) = x²

The translation 6 units left and 4 units up means that

g(x) = f(x + 6) + 4

So, we have

g(x) = (x + 6)² + 4

This means that the transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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The true statement is (a) The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers.

The given parameters are:

\(Pencils = 2400\) --- the pencils needed

The number of pencils the prism can hold is:

\(Prism =60\)

Divide the number of pencils needed by the number of pencils in 1 rectangular prism, to calculate the number of prisms needed (n1)

\(n_1 = \frac{Pencils}{Prism}\)

So, we have:

\(n_1 = \frac{2400}{60}\)

\(n_1 = 40\)

A rectangular prism costs $0.50.

So, the total cost is:

\(Total\ cost = 40 \times 0.50\)

\(Total\ cost = \$20\)

The number of pencils the cylinder can hold is:

\(Cylinder=80\)

Divide the number of pencils needed by the number of pencils in 1 cylinder box, to calculate the number of cylinders needed (n2)

\(n_2 = \frac{Pencils}{Cylinder}\)

So, we have:

\(n_2 = \frac{2400}{80}\)

\(n_2 = 30\)

A cylinder costs $0.75.

So, the total cost is:

\(Total\ cost = 30 \times 0.75\)

\(Total\ cost = $22.5\)

By comparison, the rectangular prism costs $2.5 less than the cylinder

Hence, the true statement is (a)

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Answer:

\(KN\times~JN=LN\times~MN\)

\((x-1)(x+20)=(x+11)(x+2)\)

\(x^2+19x-20-x^2+13x+22\)

\(7x=42\)

\(x=6\)

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

hope it helps...

have a great day!!

Applying exponential properties, we have that the solution to the given expression is:

\(-\frac{125}{343}\)

When a fraction is elevated to the exponent, we apply the exponent to both the numerator and the denominator.

In this problem, we have that:

Negative base with odd exponent, hence the solution is negative and given as follows:

\(-\frac{125}{343}\)

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