Match each point of intersection with the system of equations whose solution is at that point. Graph shows 4 lines plotted on a coordinate plane. First line goes through (0, 2) and (2, 0). Second line goes through (1, 1) and (0, minus 1). Third line goes through (minus 4, 0) and (0, 4). Fourth line goes through (minus 3, 3) and (0, minus 3). y = -2x − 3 y = 2x − 1 y = x + 4 y = -x + 2 y = -2x − 3 y = x + 4 y = 2x − 1 y = -x + 2

Answer:

t=0.9

Step-by-step explanation:

Answer:

y=5/4x-11

Step-by-step explanation:

tenemos un punto (4,-6) y una pendiente equal a 5/4.

usa la ecuación y=mx+b (m es la pendiente, b es el y interceptar)

porque sabemos la pendiente es 5/4, ahora mismo la ecuación es:

y=5/4x+b

en el punto, x=4, y=-6

podemos sustituir los números en la fómula para resolver b

-6=4(5/4)+b

-6=5+b

-11=b

entonces,

la ecuación de la recta es y=5/4x-11

(¡lo siento mi español no es perfecto!)

the size of the union of the three sets is: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 3  × 24 million - 3 × 1.4 million + 1.2 million ≈ 69 million

A combination is a way of selecting a subset of objects from a larger set without regard to their order. The formula for the number of combinations of n objects taken r at a time is:
C(n, r) = n! / (r! ×  (n - r)!)
where n! means the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 ×  4 ×  3 ×  2 ×  1 = 120.
To apply this formula to our problem, we first need to count the total number of coins in the pile. Since there are at least 16 of each type, the minimum total is:
16 + 16 + 16 + 16 = 64
But there could be more coins of each type, so the total could be larger than 64. However, we don't need to know the exact number, only that it is large enough to allow us to choose 16 coins from it.
Using the formula for combinations, we can calculate the number of different collections of 16 coins that can be chosen from the pile:
C(64, 16) = 64! / (16! × (64 - 16)!) ≈ 1.1 billion
That's a very large number! It means there are over a billion ways to choose 16 coins from a pile that contains at least 16 of each type.
To answer the second part of the question, we need to count the number of collections that contain at least 3 coins of each type. One way to do this is to use the inclusion-exclusion principle, which says that the number of elements in the union of two or more sets is equal to the sum of their individual sizes minus the sizes of their intersections, plus the sizes of the intersections of all possible pairs, minus the size of the intersection of all three sets, and so on.
In this case, we can consider three sets:
- A: collections with at least 3 pennies
- B: collections with at least 3 nickels
- C: collections with at least 3 dimes
- D: collections with at least 3 quarters
The size of each set can be calculated using combinations:
|A| = C(48, 13) ≈ 24 million
|B| = C(48, 13) ≈ 24 million
|C| = C(48, 13) ≈ 24 million
|D| = C(48, 13) ≈ 24 million
Note that we have to choose 3 coins of each type first, leaving 4 coins to be chosen from the remaining 48 coins.
The size of the intersection of any two sets can be calculated similarly:
|A ∩ B| = C(43, 10) ≈ 1.4 million
|A ∩ C| = C(43, 10) ≈ 1.4 million
|A ∩ D| = C(43, 10) ≈ 1.4 million
|B ∩ C| = C(43, 10) ≈ 1.4 million
|B ∩ D| = C(43, 10) ≈ 1.4 million
|C ∩ D| = C(43, 10) ≈ 1.4 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 43 coins.
The size of the intersection of all three sets can also be calculated:
|A ∩ B ∩ C| = C(38, 7) ≈ 1.2 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 38 coins.

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The range, gaps and outlier of the given data set is 54, 0.5 and 2 and 60.

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals.

The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.

From the given table

Hours                Frequency

15.5-19.5                  25

19.5-24.5                 31

24.5-29.5                44

29.5-34.5                60

34.5-39.5                42

39.5-44.5                30

44.5-49.5                27

49.5-54.5                0

54.5-59.5                0

59.5-64.5                0

64.5-69.5                2

The range is the width that the bars cover along the x-axis.

Now, range is 69-15=54

The gap is 0.5

Outliers are extreme values that stand out greatly from the overall pattern of values in a dataset or graph.

2 and 60

Therefore, the range is 54.

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The inverse Laplace transform of F(s) is given by f(t) = e^(-9t/16) * [(9/8)cos(8t) + (9/16)sin(8t)].

To find the inverse Laplace transform of F(s) = (9-s)/(s^2 + 64), we can use partial fraction decomposition and then refer to a Laplace transform table.

First, we write F(s) as (As + B)/(s^2 + 64) and solve for A and B by equating the numerator of the original function to the numerator of the decomposition.

9-s = (As + B)

When s = 0, 9 = B

When s = i8 or s = -i8, -i16 or i16 = A

Thus, we can write F(s) as F(s) = [(9/i*16)*s + 9/16] / (s^2 + 64)

Now, we can refer to a Laplace transform table to find the inverse transform. Specifically, we can use the formula:

\(L^-1{[(As + B)/(s^2 + a^2)]} = e^(-Bt) * (Acos(at) + (B/a)sin(at))\)

Using this formula with A = 9/i*16, B = 9/16, and a = 8, we get:

f(t) = L^-1{(9-s)/(s^2+64)} = e^(-9t/16) * [(9/8)cos(8t) + (9/16)sin(8t)]

Therefore, the inverse Laplace transform of F(s) is given by f(t) = e^(-9t/16)  [(9/8)cos(8t) + (9/16)sin(8t)].

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Answer:

The area of a circle with diameter 22 is 380.1.

Step-by-step explanation: if this is wrong or incorrect please let me know and sorry if this is wrong

Answer: 380.13yd²

Step-by-step explanation: A=πr2

d=2r

Solving for A

A=1

4πd2=1

4·π·222≈380.13271yd²

Answer:

It lies on the y axis

Step-by-step explanation:

Given

\((0,7)\)

Required

How is it significant?

A coordinate point is represented as \((x,y)\)

In this case, we have that:

\((x,y) = (0,7)\)

i.e.

\(x = 0\)

\(y = 7\)

x being 0 and y being non zero (in this case, 7) implies that the point lies on the y axis

See attachment for point

Answer: It lies on the y axis

Step-by-step explanation:

Answer:

208.16

Step-by-step explanation:

Answer:

208 4/25

Step-by-step explanation:

420 3/50-212 9/10

420 52/50 - 212 9/10

420-212:208

Combine

53/50-- 9/10 : 4/25

Answer 208 + 4/24

or just

208

The vector function r(t) = (8 - 8t)i + (8 - 8t)j + (6 - 6t)k describes the line passing through the point P(8, 8, 6).

In mathematics, the study of lines and their equations is essential in various fields, including geometry and algebra. When given a point and a line, we can determine the equation or a parametric representation of that line.

W are tasked with finding a vector function r(t) that describes the line passing through the point P(8, 8, 6).

To construct the line equation, we can use the point-slope form.

Let's consider the vector equation r(t) = P + tD, where P represents the given point and D is the direction vector of the line.

Since we have a point P(8, 8, 6), we can assign P = 8i + 8j + 6k. To find the direction vector D, we can choose another point on the line and subtract P from it.

Let's choose Q(0, 0, 0) as a convenient point.

Thus, Q - P = -8i - 8j - 6k.

This gives us the direction vector D = -8i - 8j - 6k.

Combining the point P and the direction vector D, we can write the vector function describing the line as r(t) = (8 - 8t)i + (8 - 8t)j + (6 - 6t)k.

In summary, the vector function r(t) = (8 - 8t)i + (8 - 8t)j + (6 - 6t)k describes the line passing through the point P(8, 8, 6).

The equation allows us to represent the line parametrically, enabling further analysis and calculations related to the line's properties and interactions with other mathematical objects.

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Answer:

(10) Person B

(11) Person B

(12) \(P(5\ or\ 6) = 60\%\)

(13) Person B

Step-by-step explanation:

Given

Person A \(\to\) 5 coins (records the outcome of Heads)

Person \(\to\) Rolls 2 dice (recorded the larger number)

Person A

First, we list out the sample space of roll of 5 coins (It is too long, so I added it as an attachment)

Next, we list out all number of heads in each roll (sorted)

\(Head = \{5,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,0\}\)

\(n(Head) = 32\)

Person B

First, we list out the sample space of toss of 2 coins (It is too long, so I added it as an attachment)

Next, we list out the highest in each toss (sorted)

\(Dice = \{2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6\}\)

\(n(Dice) = 30\)

Question 10: Who is likely to get number 5

From person A list of outcomes, the proportion of 5 is:

\(Pr(5) = \frac{n(5)}{n(Head)}\)

\(Pr(5) = \frac{1}{32}\)

\(Pr(5) = 0.03125\)

From person B list of outcomes, the proportion of 5 is:

\(Pr(5) = \frac{n(5)}{n(Dice)}\)

\(Pr(5) = \frac{8}{30}\)

\(Pr(5) = 0.267\)

From the above calculations: \(0.267 > 0.03125\) Hence, person B is more likely to get 5

Question 11: Person with Higher median

For person A

\(Median = \frac{n(Head) + 1}{2}th\)

\(Median = \frac{32 + 1}{2}th\)

\(Median = \frac{33}{2}th\)

\(Median = 16.5th\)

This means that the median is the mean of the 16th and the 17th item

So,

\(Median = \frac{3+2}{2}\)

\(Median = \frac{5}{2}\)

\(Median = 2.5\)

For person B

\(Median = \frac{n(Dice) + 1}{2}th\)

\(Median = \frac{30 + 1}{2}th\)

\(Median = \frac{31}{2}th\)

\(Median = 15.5th\)

This means that the median is the mean of the 15th and the 16th item. So,

\(Median = \frac{5+5}{2}\)

\(Median = \frac{10}{2}\)

\(Median = 5\)

Person B has a greater median of 5

Question 12: Probability that B gets 5 or 6

This is calculated as:

\(P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}\)

From the sample space of person B, we have:

\(n(5\ or\ 6) =n(5) + n(6)\)

\(n(5\ or\ 6) =8+10\)

\(n(5\ or\ 6) = 18\)

So, we have:

\(P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}\)

\(P(5\ or\ 6) = \frac{18}{30}\)

\(P(5\ or\ 6) = 0.60\)

\(P(5\ or\ 6) = 60\%\)

Question 13: Person with higher probability of 3 or more

Person A

\(n(3\ or\ more) = 16\)

So:

\(P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Head)}\)

\(P(3\ or\ more) = \frac{16}{32}\)

\(P(3\ or\ more) = 0.50\)

\(P(3\ or\ more) = 50\%\)

Person B

\(n(3\ or\ more) = 28\)

So:

\(P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Dice)}\)

\(P(3\ or\ more) = \frac{28}{30}\)

\(P(3\ or\ more) = 0.933\)

\(P(3\ or\ more) = 93.3\%\)

By comparison:

\(93.3\% > 50\%\)

Hence, person B has a higher probability of 3 or more

The volume of a right circular cone that has a height of 3.5 ft and a radius of 18.9 ft is given as follows:

1308.6 ft³.

The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.

V = πr²h/3.

The parameters for the cone in this problem are given as follows:

Hence the volume of the cone is given as follows:

V = 3.14 x 18.9² x 3.5/3

V = 1308.6 ft³.

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The 3 cans of peas cost 39 = $27

The 5 bags of flour cost 515 = $75

The 7 packs of milk cost 7*12.50 = $87.50

The total cost of all the items is 27+75+87.50 = $189.50

To calculate the change she received, you subtract the total cost from the amount she had:

change = 200 - 189.50 = $10.50

So Alicia received $10.50 change.

Answer:

85

Step-by-step explanation:

A. The probability of getting 10 or more hits in a week is approximately 0.0131 using the Poisson distribution. B.The probability of getting 20 or more hits in 2 weeks is approximately 0.0175 using the Poisson distribution.

a. The probability that the site gets 10 or more hits in a week is approximately 0.0131.

To calculate this probability, we can use the Poisson distribution, which is commonly used to model the number of events that occur in a fixed interval of time when the events are rare and independent. In this case, the average number of hits per week is given as 5.

Let X be the random variable representing the number of hits in a week. The probability of getting 10 or more hits can be calculated as the complement of the probability of getting less than 10 hits.

Using the Poisson distribution formula, the probability mass function is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

Where λ is the average number of hits per week, and k is the desired number of hits.

To calculate the probability of getting less than 10 hits, we sum the probabilities for k = 0 to 9:

P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)

Using the formula, we substitute λ = 5 and calculate the individual probabilities. Finally, we subtract this sum from 1 to find the probability of getting 10 or more hits:

P(X ≥ 10) = 1 - P(X < 10)

Evaluating this expression, we find that the probability is approximately 0.0131.

b. The probability that the site gets 20 or more hits in 2 weeks is approximately 0.0175.

To calculate this probability, we need to consider the number of hits over a two-week period. The average number of hits per week is still 5, so the average number of hits over two weeks is 10.

Let Y be the random variable representing the number of hits in two weeks. We can again use the Poisson distribution, but this time with λ = 10.

Similar to part a, we calculate the probability of getting less than 20 hits over two weeks:

P(Y < 20) = P(Y = 0) + P(Y = 1) + ... + P(Y = 19)

Using the Poisson distribution formula with λ = 10, we evaluate this sum. Finally, we subtract this sum from 1 to find the probability of getting 20 or more hits:

P(Y ≥ 20) = 1 - P(Y < 20)

Evaluating this expression, we find that the probability is approximately 0.0175.

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Answer:-355/4

Step-by-step explanation:

Answer:

= -355/4

Step-by-step explanation:

= 5/4 + 4(3/4 - 12)(2)

= 5/4 + (-45)(2)

= 5/4 + -90

= -355/3

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

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Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

a. Since we are assuming a uniform probability density function, the probability density function f(x) is constant between a and b. The area under the probability density function must equal 1, so we can set up the equation:

∫a^b f(x) dx = 1

Substituting f(x) = 0.00625 and integrating, we get:

∫a^b 0.00625 dx = 1

0.00625(b - a) = 1

b - a = 160

Since the mean daily discretionary spending is $136, we know that:

(a + b)/2 = 136

Substituting b - a = 160, we get:

a + 80 = 136

a = 56

b = a + 160 = 216

Therefore, the values of a and b for the probability density function are a = 56 and b = 216.

b. The probability of daily discretionary spending between $100 and $200 is the area under the probability density function between $100 and $200. Since the probability density function is constant, this is just the width of the interval (200 - 100 = 100) multiplied by the height of the probability density function (0.00625):

P(100 ≤ x ≤ 200) = (200 - 100)(0.00625) = 0.625

Therefore, the probability that consumers in this group have daily discretionary spending between $100 and $200 is 0.625.

c. The probability of daily discretionary spending of $150 or more is the area under the probability density function to the right of $150. This is just the width of the interval (216 - 150 = 66) multiplied by the height of the probability density function (0.00625):

P(x ≥ 150) = (216 - 150)(0.00625) = 0.4125

Therefore, the probability that consumers in this group have daily discretionary spending of $150 or more is 0.4125.

d. The probability that consumers in this group have daily discretionary spending less than $50 is zero, since the minimum value of x is $56.

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Answer:

2.16 x 10^1

Step-by-step explanation:

(3.6 x 10^5 x 1.5 x 10^-8)/(2.5 x 10^-4)

3.6 x 1.5 = 5.4

10^5 x 10^-8 = 10^(5+-8) = 10^(5-8) = 10^-3

(5.4 x 10^-3) / (2.5 x 10^-4)

5.4 : 2.5 = 2.16

10^-3 : 10^-4 = 10^(-3-(-4) = 10^(-3+4) = 10^1

2.16 x 10^1

The sign that goes in the circle to make the sentence true is >• 4/5+5/8= >1

Let us compare 4/5 and 5/8.

To compare the numbers, we have to get the lowest common multiple (LCM). We can derive the LCM by multiplying the denominators which are 5 and 8. 5×8 = 40

LCM = 40.

Converting 4/5 and 5/8 to fractions with a denominator of 40:

4/5 = 32/40

5/8 = 25/40

= 32/40 + 25/40

= 57/40

= 1.42.

4/5+5/8 = >1

1.42>1

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Joshua scored 65, 80, 85, and 100 on his math tests. 90 score Joshua has to earn on his fifth test to have a mean score of 85

       To calculate the mean score, add up all of the scores and divide by the total number of tests.

       To figure out what score Joshua needs to get on the fifth test, use the formula:

            Total score = mean score × total number of tests

            Total score = 85 × 5

            Total score = 425

  Joshua's total score on all five tests must be 425. He has already earned 330 points from his first four tests (65 + 80 + 85 + 100).

  Therefore, Joshua must earn 95 points on his fifth test (425 - 330 = 95) to achieve a mean score of 85.

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The systems of inequalities given is,

Since he can't sell more than 8 items per day, then from the graph given the best region that should be shaded is region 4.

The volume of the cylnder is  9,728.5 ft³

For a cylinder of radius R and height H, the volume is given by:

V = pi*R^2*H

Where pi = 3.14

Here we know that the height is.

H = (20 + 1/2) ft = 20.5 ft

And the diameter is (1 + 1/5) times the height, then:

D = (1 + 1/5)*(20 + 1/2) ft = (1.2)*(20.5)ft = 24.6ft

And the radius is half of that, so:

R = 12.3ft

Then the volume is:

V = 3.14*(12.3ft)^2*20.5ft = 9,728.5 ft³

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

The number of years for which the money was invested is 5.0 years

From the question, we are to determine how long (in years) the money was invested

From the given information,

Lina invested $7,800 at a simple interest rate of 4.35%

and

She earned $1,696.50 in interest

From the formula for simple interest

I = PRT

Where I is the simple interest

P is the principal

R is the rate

and T is the time in years

From the given information,

I = $1,696.50

P = $7,800

R = 4.35% = 0.0435

Thus,

1696.50 = 7800 × 0.0435 × T

1696.50 = 339.3 × T

T = 1696.50/339.3

T = 5.0 years

Hence, the money was invested for 5.0 years

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Answer: A

Step-by-step explanation:

\(\pi > 3 \implies 5\pi > 15\)

Offering a new product to an established or new market, offering an established product to a new market, or creating a new organization is the entrepreneurial act of new entry.

A new firm, product, or service entering the market is referred to as an entrepreneurial act of new entrance. Finding a market opportunity and creating a special offering that differentiates the company from rivals already in the market are both necessary steps.

A fresh entry can take many different forms, such as the launch of an entirely new good or service that fills a need in the market, the entry into an established market using a unique strategy or business model, or the entry into a new geographic market with an already well-known good or service.

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Answer:

5

Step-by-step explanation:

If a population is decreasing by 8% we can multiply the population by 92% (1-.08)

which means we have the following equation

population=15000(.92)ⁿ

where n is the number of years

we want to know when the population will be 10,000 so we write

10,000=15,000(.92)ⁿ

.66667=.92ⁿ

a rule we have is

\(n=y^x\\log_yn=x\)

which means that

\(.66667=.92^n\\=log_{.92}.66667\)

compute this and get

4.867

round this up to 5

Step-by-step explanation:

A 62.0 kg person in

a rollercoaster moves 29.2 m/s

at the bottom of a curved track

of radius 33.7 m. What is the normal

force acting on the person?

(Unit = N)