Please help with this math problem

Answer:

y=2/3x-11/3

Step-by-step explanation:

First, find the slope.

m= y2-y1/x2-x1

-3+5/1+2 = 2/3

Slope is 2/3

Now, pick one of the coordinates and use that and the slope to put it in point-slope form.

Point slope form: y-y1=m(x-x1)

Let's use (1,-3)

y+3=2/3(x-1)

Distribute 2/3 to (x-1) and simplify to get the equation in slope-intercept form.

y+3=2/3x-2/3

y=2/3x-11/3

Answer:

y=2/3x-11/3

Step-by-step explanation:

use slope formula and slope intercept form. y=mx+b

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

\(\frac{a}{4} = \frac{13}{20}\)

Step-by-step explanation:

GIVEN :-

TO FIND :-

SOLUTION :-

To find the value of  \(\frac{a}{4}\) , just put a = 2.6 there in the expression.

\(=> \frac{a}{4} = \frac{2.6}{4} = \frac{\frac{26}{10} }{4} = \frac{26}{40}\)

Reducing the fraction gives - \(\frac{13}{20}\)

In decimal form , it is - \(0.65\)

Answer:

b = 3/4

Step-by-step explanation:

\(\frac{1}{2}x + b=\frac{1}{4} (2x+3)\)

Distribute.

\(\frac{1}{2}x + b=\frac{1}{2} x+\frac{3}{4}\)

Subtract 1/2x from both sides to isolate the b.

\(b=\frac{1}{2} x+\frac{3}{4}-\frac{1}{2}x\)

1/2x and -1/2x cancel each other out.

\(b=\frac{3}{4}\)

So b = 3/4

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06\)

Answer:

Z<-3 is the anwser to this question, good luck !

Multiply through by LCM, 4

\( \frac{ - 3z - 1}{2} \times 4 > \: \: \: \frac{4}{1} \times 4\)

\(2( - 3z - 1) > 16\)

\( - 6z - 2 > 16\)

\( - 6z > 16 + 2\)

\( - 6z > 18\)

\( \frac{ - 6z}{ - 6} < \frac{18}{ - 6} \)

\(z < - 3\)

Answer:

Step-by-step explanation:

This is a straight forward division problem.

12/(5/8).

The rule for division of fractions is: invert the denominator and multiply.

For this problem: 12/(5/8) = 12 * 8/5 = 96/5.

Based on the information, the answer is A). While wages have increased, spending power has mostly remained the same since 2000.

The fact that the cost of living has also increased, eating up much of the gains from wage growth. In addition, many Americans are now working multiple jobs, which can leave them with less time and energy to spend money on discretionary items.

According to the Bureau of Labor Statistics, the average hourly wage for all workers in the United States increased by 16.3% between 2000 and 2021. However, the Consumer Price Index (CPI), which measures the cost of a basket of goods and services, increased by 26.5% over the same period. This means that the purchasing power of the average worker has actually declined by 10.2% since 2000.

The rise of the gig economy has also contributed to the decline in spending power. Many Americans are now working multiple jobs, often in low-wage industries such as food service and retail.

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While wages have increased, spending power

a)has mostly remained the same since 2000

b) as wages go up, so does spending power

c) the spending power of men is less than the spending power of the overall population

d) the wages of women have increased faster than the wages of men

The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:

612 dollars

Step-by-step explanation:

From the given information:

Amount of the total mixture = 6000 pounds

Also, for each batch, there needs to be at least 25% bluegrass seed.

It implies that:

In 6000 pounds, there are (25×6000)/100 = 1500 pounds of bluegrass seed.

The remaining amount of (6000 - 1500 = 4500)pounds will be for rye and Bermuda.

Suppose the amount of rye seeds = x pounds

while that of Bermuda is (4500 - x) pounds

Then, since the amount of Bermuda contains no more than 2/3 of that of rye.

The equation can be written as:

\(( 4500 - x) = \dfrac{2x}{3}\)

13500 - 3x = 2x

13500 = 5x

\(x = \dfrac{13500}{5}\)

x = 2700

Now, the amount of rye seed = 2700 pounds

while that of Bermuda seed = 4500 - 2700 = 1800 pounds

However, For Bluegrass, we are told that the cost of 1 pound is 12 cents.

So, the cost of 1500 bluegrass seeds = 12 × 1500 = 18000 cents

For rye seed; cost of 1 pound = 14 cents

the cost of 2700 rye seeds = 14 × 2700 = 37800 cents

For Bermuda seed; cost of 1 pound = 3 cents

the cost of 1800 rye seeds = 3 × 1800 = 5400 cents

The total amount = (18000 + 37800 + 5400) = 61200 cents

Recall that:

100 cents = 1 dollars

61200 cents = x dollars

x = 61200 cents/100 cents

x = 612 dollars

Thus, the minimum cost is 612 dollars.

Answer:

hold on

Step-by-step explanation:

do you have options?

So on solving the provided question we can say we can plotting data by x = 0.83; y = 0.79; z = 0.83

Here, we have,

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables.

Diagrams created by hand or on a computer are also acceptable.

Move 2 units to the right after starting at the origin before going 3 units up.

The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points.

The pink dot with the letter P thus stands for 2.3.

Before creating a line chart, you need first generate a number line for each value in your data collection.

Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

x = 0.83

y = 0.79

z = 0.83

xa = 0.85

ya = 0.85

za = 0.85

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Answer:

Step-by-step explanation:

d

Supplementary angles are angles that have a sum of 180 degrees. They are formed on a straight line.

Looking at the given diagram, we can notice how angle SUV and SUT are supplementary angles. We know this because they form the straight line, VT.

We are given angle SUT, which is 58 degrees.

Because angles SUV and SUT have a sum of 180 degrees, we can solve for angle SUV by subtracting 58 from 180:

180 - 58 = 122

Therefore, angle SUV is 122 degrees.

122 degrees

Answer:

Angle SUV = 180 - 58

= 122° (adjacent angles on a straight line)

Full question attached

Answer:

Option C: because the percent of children compared differ too much

Explanation:

Sample Proportion of students from Montessori = students that participated from Montessori /total number of students assigned to Montessori

=30/54= 0.56

Sample proportion of students from other schools = students that participated I'm the study /total number of students assigned to other schools

=25/112

=0.22

We observe that there is a large difference(0.56-0.22) between the two sample proportions hence the bias

Answer:se

Step-by-step explanation:

Answer:

A) 0.5

B) 10

Step-by-step explanation:

A) First, you need to Combine Like Terms on the right side of the =

98-248 = -150

Now, you need to Isolate the variable by getting rid of the -178. What you do to one side, you must do the the other.

56a-178(+178) = -150(+178)

56a = 28

Finally, you must remove that 56 on the a. Since it stands for 56 x a, you must do the same you did with the -178 except with Division.

56a/56 = 28/56

a = 0.5

B) Combine Like terms

640+70 = 710

Isolate the variable

710(-20) = 69y+20(=20)

690 = 69y

Remove the 69 with division

690/69 = 69y/69

10 = y

Answer: Anything that is 1202 or larger

In other words, \(m \ge 1202\)

So we could have m = 1202, or m = 1203, or m = 1204, etc.

===============================================

Explanation:

The monthly bill is at least $109.14, since this is the lowest amount she has been charged.

\(\text{monthly bill} \ge 109.14\\\\0.07m+25 \ge 109.14\\\\0.07m \ge 109.14-25\\\\0.07m \ge 84.14\\\\m \ge \frac{84.14}{0.07}\\\\m \ge 1202\\\\\)

This says that the least number of minutes Martina has used is 1202 minutes.

So if m was a whole number, then m could be selected from the set {1202, 1203, 1204, ...}

Side note: 1202 minutes = 1202/60 = 20.033 hours approximately.

Answer: x = 50

Step-by-step explanation:

In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.

The members of a possible set C are {6, 9, 12}

The universal set is the set that contains all other sets. Given the following sets

ξ = {x:x is an integer, 2 ≤ x ≤ 14}

B = {x:x is a prime number}

A = {x:x is a multiple of 3}

The sets B and A are:

B = {2, 3, 5, 7, 11}

A = {3, 6, 9, 12}

If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.

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we find the probability corresponding to z = -0.4, which is 0.3446, and the probability corresponding to z = 0.5, which is 0.1915. To find the probability between these two values, we subtract the smaller probability from the larger one. So, p(-0.4 < z < 0.5) = 0.3446 - 0.1915 = 0.1531.

To answer these questions, we need to make a sketch of the normal distribution and use the unit normal tables to determine the appropriate probability.

1. p(z > 2.1)

First, we sketch the normal distribution and shade the area to the right of 2.1. This area represents the probability we are seeking.

Using the unit normal tables, we find the probability corresponding to z = 2.1, which is 0.4821. However, since we are looking for the probability to the right of 2.1, we need to subtract this value from 1 to get the correct probability. So, p(z > 2.1) = 1 - 0.4821 = 0.5179.

2. p(z > -3.4)

Again, we sketch the normal distribution and shade the area to the right of -3.4.

Using the unit normal tables, we find the probability corresponding to z = -3.4, which is 0.0003. However, since we are looking for the probability to the right of -3.4, we need to subtract this value from 1 to get the correct probability. So, p(z > -3.4) = 1 - 0.0003 = 0.9997.

3. p(z < 1.3)

This time, we sketch the normal distribution and shade the area to the left of 1.3.

Using the unit normal tables, we find the probability corresponding to z = 1.3, which is 0.4032. So, p(z < 1.3) = 0.4032.

4. p(0.9 < z < 1.9)

For this question, we sketch the normal distribution and shade the area between 0.9 and 1.9.

Using the unit normal tables, we find the probability corresponding to z = 0.9, which is 0.3159, and the probability corresponding to z = 1.9, which is 0.4713. To find the probability between these two values, we subtract the smaller probability from the larger one. So, p(0.9 < z < 1.9) = 0.4713 - 0.3159 = 0.1554.

5. p(-0.4 < z < 0.5)

Finally, we sketch the normal distribution and shade the area between -0.4 and 0.5.

Using the unit normal tables, we find the probability corresponding to z = -0.4, which is 0.3446, and the probability corresponding to z = 0.5, which is 0.1915. To find the probability between these two values, we subtract the smaller probability from the larger one. So, p(-0.4 < z < 0.5) = 0.3446 - 0.1915 = 0.1531.

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Answer:

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Step-by-step explanation:

For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.

To find the probability of damage on a parachute, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability of a parachute having damage.

The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that \(\mu = 185, \sigma = 32\)

Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of  Z when X = 100. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{100 - 185}{32}\)

\(Z = -2.66\)

\(Z = -2.66\) has a p-value of 0.0039.

What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

0.0039 probability of a parachute having damage, which means that \(p = 0.0039\)

5 parachutes, which means that \(n = 5\)

This probability is:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807\)

Then

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193\)

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Answer:

solution: \(Sn= \frac{a_{1} (1-q^{n} )}{(1-q)} = \frac{1(1-4^{n}) }{1-4} = \frac{4^{n}-1 }{3}\)

Step-by-step explanation:

Answer:

∠ABC = 32

∠DBC = 42

Step-by-step explanation:

∠ABD = ∠ABC + ∠DBC

74 = 5x - 3 + 5x + 7

= 5x + 5x + 7 - 3

74 = 10x + 4

74 - 4 = 10x

70 = 10x

x = 70 / 10

x = 7

∠ABC = 5x - 3

= 5 ( 7 ) - 3

= 35 - 3

∠ABC = 32

∠ABD = ∠ABC + ∠DBC

∠DBC = ∠ABD - ∠ABC

= 74 - 32

∠DBC = 42

Answer:

\(\frac{f(x+h)-f(x)}{h}\)\(=2x - h\)

Step-by-step explanation:

Given

\(f(x) = 8 - x^2\)

Required

Determine: \(\frac{f(x+h)-f(x)}{h}\)

First, we calculate f(x + h)

\(f(x) = 8 - x^2\)

\(f(x+h) = 8 - (x+h)^2\)

\(f(x+h) =8- x^2-2xh-h^2\)

So, we have:

\(\frac{f(x+h)-f(x)}{h}\) \(= \frac{8- x^2-2xh-h^2 - 8 + x^2}{h}\)

\(\frac{f(x+h)-f(x)}{h}\) \(= \frac{8 - 8 + x^2- x^2-2xh-h^2}{h}\)

\(\frac{f(x+h)-f(x)}{h}\) \(= \frac{-2xh-h^2}{h}\)

\(\frac{f(x+h)-f(x)}{h}\)\(=2x - h\)

Answer:

(C) 13/6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

Function Notation

Exponential Properties: \(\sqrt[n]{x} = x^\frac{1}{n}\)

Calculus

The definition of a derivative is the slope of the tangent line.

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

f(x) = ∛x

Tangent Line Point (8, 2)

Find approximation of f(10)

Step 2: Differentiate

Step 3: Find Equation of Tangent Line

Tangent Point (8, 2)

Find instantaneous slope

This is our slope of the tangent line at (8, 2)

Find instantaneous equation

Step 4: Find Approximation

Evaluation f(10)

Here we see that the approximation would be 13/6 using the tangent line approximation (calculus). Therefore, C is the correct answer.

Let t be the number of minutes that have passed since water started being added to the two pools. The total amount of water in the first pool after t minutes is 707 + 18.25t liters, and the total amount of water in the second pool after t minutes is 43.5t liters. We are looking for the value of t that makes these two quantities equal, which represents the time when the two pools have the same amount of water.

We can set the two quantities equal to each other and solve for t to find the value of t that makes the two pools have the same amount of water:

707 + 18.25t = 43.5t

707 = 25.75t

t = 27.5

Therefore, after 27.5 minutes, the two pools will have the same amount of water.

To find the amount of water that will be in each pool when they have the same amount of water, we can substitute the value of t that we found above into the expressions for the total amount of water in each pool:

First pool: 707 + 18.25 * 27.5 = 707 + 501.875 = 1208.875

Second pool: 43.5 * 27.5 = 1208.875

Therefore, when the two pools have the same amount of water, each pool will have 1208.875 liters of water.

The number the spinner is most likely to land on is 2

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

The spinner

From the spinner, we have the number that covers the largest area to be 2

i.e.

Largest area = 2

This means that the number it is most likely to land on is 2 and it has the highest probability

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Answer:

* 27x=9 * x=9/27 ithink so srry if you get wrong

Step-by-step explanation: