Which equation represents a line that has a slope of 4 and passes through the point (3,-8)?

Answer:

Given two events A and B of a sample set :-

P[A] = 0.20  

P[not B]=0.40

[tex]P[B/A]=0.25[/tex]

To find P[A or B]:

[tex]P[A or B] = P[A] + P[B] - P[A \cap B][/tex]                ......[1]

Calculate for [tex]P[B][/tex] and [tex]P[A \cap B][/tex]

P[B] = 1- P[not B]

Substitute the value P[not B] we get;

P[B] = 1-0.40 = 0.60      

[tex]P[A \cap B] = P[B/A] \cdot P[A][/tex]

Substitute the given values we get;

[tex]P[A \cap B] = 0.25 \cdot 0.20 = 0.05[/tex]

Then;

[tex]P[A or B] = 0.20+0.60-0.05 = 0.80-0.05 =0.75[/tex]

Therefore, the value of P[A or B] is, 0.75.

The probability of P(A∪B) is 0.35.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Given

     P(A) = 0.20

     P(B) = 0.40

P(A∩B) = 0.25

The probability of P(A∪B).

We know the formula

P(A∪B) = P(A) + P(B) - (A∩B)

P(A∪B) = 0.20 + 0.40 - 0.25

P(A∪B) = 0.60 - 0.25

P(A∪B) = 0.35

Thus the probability of P(A∪B) is 0.35.

More about the probability link is given below.

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Answer:

1.  P ( tails) = 1/2

2.P (number greater than 4)   = 1/3

3.  P (2 die sum to 8) = 5/36

Step-by-step explanation:

A coin only has 2 possibilities, head or tails, and they are equally likely

So the probability of getting a tails is 1/2

P ( tails) = 1/2

A die has the numbers 1,2,3,4,5,6 .  There are 2 numbers greater than 4.  They are 5 and 6.  So there are 2 of the 6 choices that work.

P (number greater than 4)  = 2/6  = 1/3

See the dice chart

There are 36 possibilities when you roll the die.

There are 5 that sum to 8

P (2 die sum to 8) = 5/36

Answer:

Guy above is correct

Step-by-step explanation:

Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right by h units, then

 the new function g(x) = f(x - h)  

- If the function f(x) translated horizontally to the left by h units, then

 the new function g(x) = f(x + h)  

- If the function f(x) translated vertically up by k units, then the new

 function g(x) = f(x) + k  

- If the function f(x) translated vertically down by k units, then the

 new function g(x) = f(x) – k  

- A vertical stretching is the stretching of the graph away from the

 x-axis  

- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically  

 stretched by multiplying each of its y-coordinates by k.  

- A vertical compression is the squeezing of the graph toward  

 the x-axis.  

- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)

 vertically compressed by multiplying each of its y-coordinates by k.  

* Lets solve the problem

∵ f(x) = sin(x)

∵ f(x) is stretching vertically by a factor of 4

∴ f(x) multiplied by 4

∵ f(x) is shifting 3 units to the right

∴ We will change x to (x - 3)

∵ The new function is g(x)

∴ g(x) = 4 sin(x - 3)

- The attached graph for more understand

f(x) is the red graph

g(x) is the blue graph

Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

The given function is:

f(x) = sin(x)

Stretching by a factor of 4:

A vertical stretch or compression of f(x) can be expressed as:

cf(x), where c is any constant

if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.

Since, given function is being stretched by a factor of 4, the transformed function will become:

4f(x)

Shifting by 3 units right:

A shift of f(x) to right can be obtained by subtracting c from every occurrence of x in f(x) , where c is the number of units f(x) is being shifted in right direction. Since in this case f(x) is shifted 3 units to right, the transformed function will be:

f(x - 3)

Applying both the transformations to f(x), we get g(x) as:

g(x) = 4 f(x - 3)

g(x) = 4 sin(x - 3)

Answer: 5, 3, [tex]\dfrac{1}{6}[/tex], D

Step-by-step explanation:

-5 < 0 so f(-5) = | -5 | = 5

-3 < 0 so f(-3) = | -3 | = 3

6 > 0 so f(6) = [tex]\dfrac{1}{6}[/tex]

graph D (since x can equal zero)

[tex]f(x)=x^3+3x^2-10x-24\\\\y-intercept\ for\ x=0:\\\\f(0)=0^3+3(0)^2-10(0)-24=-24[/tex]

Answer:

The attached image shows he graph for given function.

Step-by-step explanation:

We are given the following expression in the question:

[tex]f(x) = x^3 + 3x^2-10x-24[/tex]

The zeroes of the given function can be calculated as:

[tex]x^3 + 3x^2-10x-24 = 0\\x = -4, x = -2, x=3[/tex]

Thus,the graph for the given function passes through the x-axis on the points (-4,0), (-2,0) and (3,0).

The function crosses the y-axis at the point (0,24)

The attached image shows the graph for given function.

Thus, the second option is the correct graph for given function.

4. -3

5. 3

4. For x > -2, the value of a is the slope of the line. The line goes down 3 units for each 1 to the right, so the slope is -3/1 = -3. Then a = -3.

___

5. The ordered pair (h, k) is typically used to name the point to which a function is translated. The vertex of the function f(x) = |x| is (0, 0). When it is translated to (h, k), the function becomes ...

... q(x) = |x -h| +k

If the new vertex is (3, 0), then h = 3 and k = 0. This is consistent with the equation shown. (k = 0 means q(x) = |x -h|.)

Answer:

45/63

Step-by-step explanation:

6 3/10=63/10,    4  1/2=45/10,

(45/10)/(63/10)=45/63

Answer:

HELLO :

f(4) = -1/2(4)+5 = -2+5=3

Answer:

-1< x< 3  x is an integer

Step-by-step explanation:

There are the dots on the number line.  Three points are represented

x= 0,1,2

We want an inequality

-1< x< 3  x is an integer

Answer:

a. -2, even mult. and 1, odd mult.

b.[tex](x+2)^2(x-1)[/tex]

c. Odd degree of 3 or higher, likely higher due to the turns in the graph.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -2,1

We can write them in intercept or factored form as (x-1) and (x+2).  

Because the graph never crosses the x-axis at x=-2 the zero has an even multiplicity of at least 2.  The opposite is true for x=1 because it crosses. Therefore it has an odd multiplicity of at least 1.

The graph is a sideways s shape and ends up so is positive.  

This means the function has a degree of 3 or higher with the degree being odd.

Answer:

Sorry if this isnt helpful: Im just going off stuff i learned to see if this will help you at all. Im only in 7th so.. Sorry in advance!!

Step-by-step explanation:

To find the rate, you need to create a unit rate table thing, like this:

5/3 = ?/1 To do this, you would need to divide 5 by 3 and 3 by 3 to get y and x. You get: 1.666 continued. Rounded, about 1.7 . so your unit rate for part A is 1.7/1. You would do the same thing. 2/3 = ?/1. I will let you solve that :)))

Finished A! Now B:

To compare, we use the butterfly method! so 1.7/1 o ?1. cross multiply, and whichever number is bigger comes on top. Then you would explain why that number is bigger. BAM

Answer:

The answer is A. 1 1/2

Step-by-step explanation:

You have 3 5/12  - 2 1/3

1/3 of 12 is 4.

So change 2 1/3 to 2 4/12

3 5/12 - 2 4/12 = 1 1/2

I hope this helps!

Cheers, July.

Answer:i cant see it good

Step-by-step explanation:

Let S = spoon

Let K = knife

1 knife is thee times the cost of a spoon, so it would be 3S

Now you have 9S + 12K = 82.80

We can replace the K with 3S:

9S +12(3S) = 82.80

Simplify the left side:

9S + 36S = 82.80

Add:

45S = 82.80

Divide both sides by 45"

S = 82.80 / 45

S = 1.84

One spoon cost $1.84

We know one knife cost 3 times as much, so multiply the cost of a spoon by 3:

Knife = 1.84 x 3 = $5.52

Answer:

1.84 x 3 = $5.52

QUESTION 34

We want to find the variance of [tex]82,44,67,52,120[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{82+44+67+52+120}{5}[/tex]

[tex]\bar X =\frac{365}{5}[/tex]

[tex]\Rightarrow \bar X =73[/tex]

This means that,

[tex]\sigma^2=\frac{(82-73)^2+(44-73)^2+(67-73)^2+(52-73)^2+(52-73)^2+(120-73)^2}{5}[/tex]

This gives us,

[tex]\sigma^2=\frac{(9)^2+(-29)^2+(-6)^2+(-21)^2+(47)^2}{5}[/tex]

[tex]\sigma^2=\frac{81+841+36+441+2209}{5}[/tex]

[tex]\sigma^2=\frac{3608}{5}[/tex]

[tex]\sigma^2=721.6[/tex]

QUESTION 35

We want to find the variance of [tex]10,12,15,18,11,13,14,16,19,20[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{10+12+15+18+11+13+14+16+19+20}{10}[/tex]

[tex]\bar X =\frac{148}{10}[/tex]

[tex]\fRightarrow \bar X =14.8[/tex]

This means that,

[tex]\sigma^2 =\frac{(10-14.8)^2+(12-14.8)^2+(15-14.8)^2+(18-14.8)^2+(11-14.8)^2+(13-14.8)^2+(14-14.8)^2+(16-14.8)^2+(19-14.8)^2+(20-14.8)^2}{10}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-4.8)^2+(-2.8)^2+(0.2)^2+(3.2)^2+(-3.8)^2+(-1.8)^2+(-0.8)^2+(1.2)^2+(4.2)^2+(5.2)^2}{10}[/tex]

[tex]\sigma^2=\frac{23.04+7.84+0.04+10.24+14.44+3.24+0.64+1.44+17.64+27.04}{10}[/tex]

[tex]\sigma^2=\frac{105.6}{10}[/tex]

[tex]\sigma^2=10.56[/tex]

QUESTION 36

We want to find the variance of [tex]100,140,130,180,80,160[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{100+140+130+180+80+160}{6}[/tex]

[tex]\bar X =\frac{790}{6}[/tex]

[tex]\Rightarrow \bar X =131.67[/tex]

This means that,

[tex]\sigma^2=\frac{(100-131.6667)^2+(140-131.6667)^2+(130-131.6667)^2+(180-131.6667)^2+(80-131.6667)^2+(160-131.6667)^2}{6}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-31.6667)^2+(8.3333)^2+(-0.6667)^2+(48.3333)^2+(-51.6667)^2+(28.3333)^2}{6}[/tex]

[tex]\sigma^2=\frac{10325}{9}[/tex]

[tex]\sigma^2=1147.22[/tex]

To find the variance of a set of data, find the mean, subtract the mean from each data point, square the differences, and find the average of the squared differences. The standard deviation is the square root of the variance.

To find the variance of a set of data, follow these steps:

For the data set 82, 44, 67, 52, 120 (Question 34), the mean is 73, the squared differences are 81, 841, 36, 441, and 1849, and the average of the squared differences is 631.20, rounding to two decimal places.

For the data set 10, 12, 15, 18, 11, 13, 14, 16, 19, 20 (Question 35), the mean is 14.8, the squared differences are 23.04, 4.84, 0.64, 8.84, 12.96, 3.24, 1.44, 2.56, 19.36, and 29.16, and the average of the squared differences is 10.10, rounding to two decimal places.

To find the standard deviation of a set of data, take the square root of the variance. For the data set 100, 140, 130, 180, 80, 160 (Question 36), the variance is 9300, and the standard deviation is 96.49, rounding to two decimal places.

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Answer:

Approx. 48 cm

Step-by-step explanation:

The two horizontal sides of this parallelogram have length 12 cm each.

The length of one slanting side can be estimated by (eye:  the base of the triangle partially outlined with a dashed line is approx. 3 cm.  Then, using the Pyth. Thm., we estimate the hypotenuse of this triangle to be

sqrt(3^2 + 10^2), or sqrt(109), which is approx. 10.45.

Thus, the estimated perimeter is

P = 2L + 2W, which, here, is

P = 2(12 cm) + 2(10.45 cm), or 44.9 cm.

The fourth answer, 48 cm, is the one closest to this estimated 44.9 cm.

Answer:

n = 9 is the value in the replacement set is a solution to the equation [tex]3(n+7)=48[/tex]

Step-by-step explanation:

Given an equation: [tex]3(n+7)=48[/tex]                      .....[1]

Replacement set: {8, 9, 10}

For n = 8

Substitute in equation [1], we get;

[tex]3(8+7)=48[/tex]  

[tex]3(15)=48[/tex]

[tex]45=48[/tex]           False.

Similarly, For n = 9

Substitute in equation [1], we get;

[tex]3(9+7)=48[/tex]  

[tex]3(16)=48[/tex]

[tex]48=48[/tex]           True.

for n = 10

Substitute in equation [1], we get;

[tex]3(10+7)=48[/tex]  

[tex]3(17)=48[/tex]

[tex]51=48[/tex]           False.

Therefore, the value in the replacement set is a solution to this equation [tex]3(n+7)=48[/tex] is, 9

Answer:

9

Step-by-step explanation:

Answer:

64.5A

Step-by-step explanation:

Answer:

[tex]12\frac{1}{2}[/tex] hours.  

Step-by-step explanation:

We have been given that Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M.

Let us find the number of hours between 8:00 am to 1:00 pm.

There are 4 hours between 8:00 am to 12 noon and 1 hour from noon to 1:00 pm. So the total number of hours between 8:00 am to 1:00 pm is 5 hours.

Now let us find total number of hours worked by Phyllis Doran by adding 7 1/2 and 5.

[tex]\text{The total number of hours Doran worked}=7\frac{1}{2}+5[/tex]

[tex]\text{The total number of hours Doran worked}=12\frac{1}{2}[/tex]

Therefore, the total number of hours worked by Phyllis Doran is [tex]12\frac{1}{2}[/tex] hours.

Answer:

D

Step-by-step explanation:

An inequality is an expression which means more than one number is a solution. We graph the solutions on a number line to show all possible values. We graph using circles and arrows.

This is a filled in circle on -2 so this is [tex]\leq or \geq[/tex]. This means only answers C and D are options.

Answer D points to the right.

Answer:

The answer is D

Step-by-step explanation:

MrsStrong was correct!!!! Thank you

Answer: 173

Step-by-step explanation: 173 x 3 = 519. 520-173 = 347

Answer:

32 houses will have a pool

Step-by-step explanation:

40% of 80 is 32

Answer:

Step-by-step explanation:

If ΔABC and ΔDEF are similar, then

AB is proportional to DE

BC is proportional to EF

CA is proportional to FD

and

angles A and D are congruent

angles B and E are congruent

angles C and F are congruent

Answer:

B.)Segment BC is proportional to segment EF, and angles A and D are congruent.

Step-by-step explanation:

The x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.

To find the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4, we can use the slope formula:

slope = (change in y) / (change in x)

Given that the slope is -4 and the two points are (x, -9) and (0, 1), we can plug the values into the slope formula:

-4 = (-9 - 1) / (x - 0)

Now, simplify the equation:

-4 = -10 / x

Now, cross-multiply:

-4x = -10

Now, solve for x by dividing both sides by -4:

x = -10 / -4

x = 5/2

So, the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.

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Answer:

25

Step-by-step explanation:

There are 100 capsules and she can only buy 1/4

Multiply 100 * 1/4

100 * 1/4 =

100/4

25

We can check  by  calculating how many she leaves at the store

100 * 3/4 =

300 /4 = 75

The ones she bought , plus the ones she left behind should be 100 capsules

25+ 75 = 100

100 = 100

Check

Answer:

150 feet

Step-by-step explanation:

in order to find the solution we have to take the L.C.M of 25 and 30

L.C.M of 25 and 30 is 150

so after 150 feet , they will both fall down

Answer: They will both fall down after 150 feet.

Step-by-step explanation:

Hi, to answer this question we have to find the least common multiple (LCM)

of 30 and 25:

To obtain the multiple of a number we have to multiply that number by another number (not zero) in the multiplication table order (by 1,by 2,by 3,etc)

30,60,90,120,150

25,50,75,100,125,150

The LCM is a number that appears on both lists, and is the smallest.

They will both fall down after 150 feet.

Feel free to ask for more if needed or if you did not understand something.