Suppose family incomes in a town are normally distributed with a mean of P25000 and a standard deviation of P6000 per month. What is the probability that a family has an income between P14,000 and P32,500?

The division expression is (x² - 9x + 14)/(x - 5) = x - 4 - (6/(x - 5))

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

(x² - 9x + 14)/(x - 5)

Using a long division setup, we have

x - 5 | x² - 9x + 14

The division is carried out as follows

         x  - 4

x - 5 | x² - 9x + 14

         x² - 5x

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

               -4x + 14

               -4x + 20

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

                            -6

So, we have

Quotient = x - 4

Remainder = -6

Hence, the quotient is x - 4 and the remainder is -6

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Answer:

12

Step-by-step explanation:

The odds in favor of drawing a 7 are 1 to 12.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

There are four 7s in a deck of 52 cards, so the probability of drawing a 7 is 4/52, which simplifies to 1/13. The odds in favor of drawing a 7 are the ratio of the probability of drawing a 7 to the probability of not drawing a 7, which is:

(1/13) : (12/13

We can simplify this ratio by dividing both terms by the greatest common factor, which is 1:

(1/13) : (12/13) = 1 : 12

Therefore, the odds in favor of drawing a 7 are 1 to 12.

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Answer:

\( \boxed{efficiency, \gamma = 74.93 \%}\)

Step-by-step explanation:

\( efficiency, \: \gamma = \frac{1500 - 376}{1500} \times 100 \\ \gamma = \frac{1124}{1500} \times 100 = 74.93 \\

efficiency, \gamma = 74.93 \%\)

The relationship between the variables in the table is a direct variation.

A function that models the relationship is y = 3x.

In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:

y = kx

Where:

Under direct variation, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, the constant of proportionality (variation) can be calculated as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 9/3 = 27/9 = 39/13 = 60/20

Constant of proportionality (k) = 3.

Therefore, the required function is given by;

y = kx

y = 3x

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Answer:

Step-by-step explanation:] Answer would be 400%

New value - Original Cost

         Original value

= 20 - 4/4

= 16/4

= 4 x 100

= 400%

The detailed answer of this question is:

P(X > 100 | X > 50)=0.455

Given that X follows an exponential distribution, we know that the probability density function (PDF) of X is given by:

f(x) = λe^(-λx) for x ≥ 0

where λ is the rate parameter of the distribution.

We are given that P(X < 50) = 0.25. Using the cumulative distribution function (CDF) of X, we can write:

P(X < 50) = 1 - e^(-λ*50) = 0.25

Solving this equation for λ, we get:

λ = -ln(0.75)/50 ≈ 0.0278

Now, we are asked to find P(X > 100 | X > 50). Using the definition of conditional probability, we can write:

P(X > 100 | X > 50) = P(X > 100 and X > 50) / P(X > 50)

= P(X > 100) / P(X > 50)

= e^(-λ100) / e^(-λ50)

= e^(-λ*50)

Substituting the value of λ, we get:

P(X > 100 | X > 50) = e^(-0.0278*50) ≈ 0.455

Therefore, the probability that a high-risk driver will have an accident after 100 days given that they have not had an accident for the first 50 days is approximately 0.455.

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Answer:

8

Step-by-step explanation:

Substitute the values in the expression, we have:

\(\displaystyle{|-1-3|+4}\)

Evaluate:

\(\displaystyle{|-4|+4}\)

Any real numbers in the absolute sign will always be evaluated as positive values. Thus:

\(\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}\)

Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.

The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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The inequality that represents the value of x is (b)  x > 80

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

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

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

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Answer:

\(x\leq -20\)

values ranging from minus infinity to negative 20

Step-by-step explanation:

we write the inequality associated with the text in terms of the unknown number "x" as:

\(\frac{3}{4} x-2\leq -17\)

then, we solve for "x" by adding 2 to both sides, and then isolating "x" on the left as shown below:

\(\frac{3}{4} x-2\leq -17\\\frac{3}{4} x\leq -17+2\\\frac{3}{4} x\leq -15\\3\,x\leq -60\\x\leq -\frac{60}{3} \\x\leq -20\)

then, the range of x-values is from minus infinity to negative 20

The solution of the system of equations is c = 10 and d = 7.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

A system of equations,

c+d=17  {equation 1}

c-d=-3  {equation 2}

Adding both the equation,

we get,

c + d + c - d = 17 + 3

2c = 20

Divide by 2,

we get,

c = 10 and d = 7.

Therefore, c = 10 and d = 7.

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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If 7 in every 9 packets of crisps in a box are salt and vinegar, then 9-7 = 2 packets of crisps in a box are plain.

If there are 63 packets of salt and vinegar in the box, then 63 packets / 7 = 9 groups of 9 packets in the box.

So, 9 groups * 2 plain crisps = 18 packets of plain crisps in the box.

Your Welcome :) Hope you have a great day!

Answer:

14

Step-by-step explanation:

9/9 - 7/9 = 2/9

2 in every 9 packets of ceisps in a box are plain crisps.

Then:

63*2/9 = 126/9

= 14

Due to its neighbouring perpendicular sides and opposite parallel and equal-length sides, the quadrilateral ABCD is a rectangle.

a) The opposite sides are parallel and equal.

b) The opposite angles are equal.

c) The consecutive or adjacent angles are supplementary.

d) If any one of the angles is a right angle, then all the other angles will be at right angle.

e) The two diagonals bisect each other.

4. To find the area of a parallelogram, you can follow these steps:

Measure the length of the base of the parallelogram. Let's call this measurement "b".

Measure the height of the parallelogram. Let's call this measurement "h".

Multiply the base length "b" by the height "h" to get the area of the parallelogram.

Therefore, the formula to calculate the area of a parallelogram is:

Area = base length (b) \(*\) height (h)

In symbols, this can be written as:

\(A = b \times h\)

Alternatively, if the length of both adjacent sides is known, you can use the formula:

A = base length (b) \(*\) the length of adjacent \(side (a) * sin\)(θ)

where theta is the angle between the base and adjacent side.

5.  the given vertices on a coordinate plane and see what kind of figure they form.

The figure formed by the vertices A, B, C, and D is a quadrilateral. To determine the precise classification of the quadrilateral, we can use its properties.

To determine if the parallelogram is a rhombus, rectangle, or square, we need to check if the diagonals bisect each other and if the adjacent sides are perpendicular. We can find the midpoint of AC and BD as:

Midpoint of AC:  \(((2 + 8)/2, (3 + 7)/2) = (5, 5)\)

Midpoint of BD: \(((7 + 3)/2, (2 + 8)/2) = (5, 5)\)

The diagonals AC and BD intersect at the midpoint \((5,5)\), so they bisect each other.

We can also find the slopes of adjacent sides AB and BC, and we find that they are:

AB: \(-1/5\)

BC: \(5\)

The product of their slopes is \(-1\), so the adjacent sides are perpendicular.

Therefore, the quadrilateral ABCD is a rectangle, because it has opposite sides that are parallel and equal in length, and adjacent sides that are perpendicular.

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer:

1. 4 Degrees Celsius

2. -3 Degrees Celsius

3. 6 Degrees Celsius

4. -1.5 Degrees Celsius

Step-by-step explanation:

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer:

5x(−7yz+4y+3)

Step-by-step explanation:

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

first: Definitions

mean: the average or the most common value in a collection of numbers

(So u add all numbers and then divide the answer by how much numbers there were)

median: Is middle value.

(example:   4, 5, 6) (The median will be the middle which is 5) (But if there are even amount of numbers like this:      4, 5, 6, 7) (Then you will get the two middle numbers which in this case are 5 and 6 you add them and then divide by 2.)

standard deviation:  measures the spread of the data about the mean value

Step-by-step explanation:

Now lets get to problem!

we have numbers:

24, 20, 16, 18, 18, 26, 22

the mean will be: 144 (remember now you have to divide by 7 because there are 7 numbers.)

So it would be 20.57

Now the median:

(Since there are 7 numbers you just find the number in the middle and that would be ur median.)

24, 20, 16, 18, 18, 26, 22

median answer: 18

Like we said: The sample standard deviation measures the spread of a data distribution of the sample. It is usually used to estimate the population standard deviation

So the standard deviation will be: 3.6

I hope this helps  :)

Answer:

What is the answer to I love my pet / ages 5-6

What is the answer to I love my pet: aww, u mean it?

ages 5-6: goo goo ga ga

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

The solution to the given inequality is\($$x \leq-6$$\)

\($$3 x+5 \leq-13$$\)

Move 5 to the right side

\($$3 x \leq-18$$\)

Divide both sides by 3

\($\frac{3 x}{3} \leq \frac{-18}{3}$\)

Simplify

\($$x \leq-6$$\)

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The required graph is attached below.

Given that,

Quarterback Susie has a bad attitude and often gets fined for bad sportsmanship.

And the table of cost is given,

Cost of fine       Number of fines

    1                              1

    2                             4

    3                              1

We know that,

A graph is a form of figure used to show accumulated data. This data might be quantitative or qualitative, which means that graphs can be utilized for a variety of purposes.

This is why there are numerous sorts of graphs, such as bar graphs, line graphs, area graphs, pictographs, and others.

To plot this data,

Label number 0, 1 , 2, 3, 4... on a number line

Which represents the cost of fine in thousands of dollars.

And plot the graph according to the given data.

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Answer:

2x ( -3x + 14)

Step-by-step explanation:

Distribution property is used in a format like a ( b + c ). To simplify these kinds of expressions, we multiply the outside term by each of the inside terms. So in this instance, a ( b + c ) is equal to ab + ac.

3x ( 2x - 8 ) + 4x

Let's use what we learned above, and multiply the outside term (-3x) by each of the inside terms.

-3x · 2x + (-3x) · (-8) +4x

Simplify by multiplication:

-6x² + 24x +4x

Finally, we add:

-6x² +28x

Now, to simplify further, we can look for terms that show up in numbers.

We can see that the variable x is present in each of the terms, so we can factor that out, removing it from the term as follows:

x ( -6x + 28)

We can look and see that 2 is also a common factor between the two terms, so we can take that out too.

2x ( -3x + 14)

This is the most simplified it can get.

Answer:

\(f(x) = 3 {x}^{2} + 5x - 8\)

\(f(x + h) = 3 ({x + h})^{2} + 5(x + h) \\ = {3x}^{2} + {3h}^{2} + 6xh + 5x + 5h - 8 \\ \)

answer will be 6x+5

Answer: i think 6

Step-by-step explanation:

Answer:

2/10

Step-by-step explanation:

-5+7=2, since the denominator stays the same.

2/10, simplified is 1/5

Answer:

2/10 or 1/5

Step-by-step explanation:

Because -5/10 and 7/10 both have 10 as the denominator we don't have to do anything about that, so you just add and simplify.

If you need me to go through it in depth let me know, but I hope that helps!

Have a great day!