1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

Answer:

? = 5

Step-by-step explanation:

Recall: when 2 transversal lines cuts across 3 parallel lines, the parallel lines are divided proportionally by the transversals.

Therefore:

?/10 = 3/6

Cross multiply

?*6 = 3*10

?*6 = 30

Divide both sides by 6

? = 30/6

? = 5

Answer:

3/56

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome.

Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.

The total number of marbles in the box

= 1 + 3 + 2 + 2

= 8 marbles

The probability that the first marble is white and the second marble is blue

= 3/8 * 1/7

= 3/56

Answer:

y = 1/3x - 7/3

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - (-3) / 4 - (-2)

2/6

= 1/3

y = 1/3x + b

-1 = 1/3(4) + b

-1 = 4/3 + b

-7/3 = b

Answer:

299.88 mi. !!!!!

you just multiple all of them together to get the area!!!

Answer:

A

Step-by-step explanation:

Given that the cones are similar then corresponding dimensions are in proportion, that is

[tex]\frac{12}{2}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )

12x = 6 ( divide both sides by 12 )

x = 0.5 → A

Answer:

[tex] \frac{(3) ^{2} + 3}{3 - 1} [/tex]

[tex] \frac{9 + 3}{3 - 1} [/tex]

[tex] \frac{12}{2} [/tex]

= 6

Answer:

The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

Step-by-step explanation:

According to the given information, vector stands in the 4th Quadrant ([tex]x > 0[/tex], [tex]y < 0[/tex]) and direction of the vector ([tex]\theta[/tex]) in sexagesimal degrees, is determined by following definition:

[tex]\theta = 360^{\circ} - \tan^{-1} \left(\frac{|y|}{|x|} \right)\pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

Please notice that angle represents a function with a periodicity of 360°.

If we know that [tex]x = 4[/tex] and [tex]y = -3[/tex], then the direction of the vector is:

[tex]\theta = 360^{\circ}-\tan^{-1}\left(\frac{|-3|}{|4|} \right)\pm 360\cdot i[/tex]

[tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex]

The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

Answer:

8x-3

Step-by-step explanation:

Average of 2 numbers means add the two numbers and divide by 2

(y+z)/2 = 5x

Let z = 2x+3

(y+2x+3)/2 = 5x

Multiply each side by 2

y+2x+3 = 10x

Subtract 2x from each side

y+3 = 10x-2x

y+3 = 8x

Subtract 3

y = 8x-3

The other number is 8x-3

Answer:

JK=12

KI=16

Step-by-step explanation:

[tex]K\in\ [JI]\ \Rightarrow\ |JK|+| KI |=|KI|\\\\x^2-4x+3x-2=28\\\\\Longleftrightarrow\ x^2-x-30=0\\\\\\\Longleftrightarrow\ x^2+5x-6x-30=0\\\\\\\Longleftrightarrow\ x(x+5)-6(x+5)=0\\\\\\\Longleftrightarrow\ (x+5)(x-6)=0\\\\x=-5\ (excluded)\ or\x=6\\\\\\\Longleftrightarrow\ \\|JK|=x^2-4x=6^2-4*6=36-24=12\\|KI|=3x-2=3*6-2=18-2=16\\\\Proof: 12+16=28\\[/tex]

Answer:

Step-by-step explanation:

Hello!

          2          4              5          ∟ 70

        -2           1                                 3, 5

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

                      3              5        0

                      3              5       0

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

                     0                0        0

Answer:

0

Step-by-step explanation:

Answer:

152 / 370

Step-by-step explanation:

Total number of people

152+218 = 370

P( own a dog) = people said yes / total

                       = 152 / 370

Answer:

10th term

Step-by-step explanation:

The equation of the arithmetic sequence is an=-7+(n-1)*1=-8+n, plugging in 2 and solving for n we have

2=-8+n, n=10

Answer:

4y+x-3=0

Step-by-step explanation:

The equation is y=mx+b

1) Use the coordinates from the first point

(-1,1)

1= -m+b

2) Use the coordinates frm the second point

(-5,2) (y=mx+b, use x=-5, y=2)

2=-5m+b

You have the system of equations

1=-m+b (multiply by -1)  -1= m-b

2=-5m+b

Add the first equation (multiplied by -1) and the second one

-1+2= m-b-5m+b

1= -4m

m=-0.25

2=1.25+b

b=0.75

y=-0.25x+0.75

4y= -x+3

4y+x-3=0

Answer:

0

2

-1

Step-by-step explanation:

from f(0) we find that

y = mx - 1

from f(-1) we find that the equation is

y = -3x - 1

1)

inverse f(x) :

x = -3y - 1

y = -(x + 1) / 3           x = -1

y = -(-1 + 1) / 3

y = 0

2)

y also equal to 0 since x = -1

3)

f^-1(2) = -(2+1) / 3

          = -3/3

          = -1

f(-1) =  2

Answer:

3

Step-by-step explanation:

The general formula of the series is 3072/(-2)^(n-1). A11=3072/(-2)^10=3

Answer:

Step-by-step explanation:

3 times 8= 24 • 24 = 576 - 1 =575

or

3•8=24•2=48-1=47

not sure

Answer:

The answer is [tex]x=\frac{4(+-)\sqrt{19} }{3}[/tex] in exact form or [tex]x=2.7863[/tex], [tex]x=-0.1196[/tex] in decimal form.

Step-by-step explanation:

To solve this equation, start by moving all expression to the left side of the equation, which will include subtracting [tex]3x^2[/tex] and adding 1 to both sides of the equation. The equation will look like [tex]8x-3x^2+1=0[/tex].

Then, use the quadratic formula to find the solutions to the equation. The quadratic formula looks like [tex]\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex].

For this problem, the quadratic variables are as follows:

[tex]a=-3\\b=8\\c=1[/tex]

The next step is to substitute the values [tex]a=-3[/tex], [tex]b=8[/tex], and [tex]c=1[/tex] into the quadratic formula and solve for x. The quadratic formula will look like [tex]\frac{-8(+-)\sqrt{8^2-4(-3)(1)} }{2*-3}[/tex]. To simplify the equation, start by simplifying the numerator, which will look like [tex]x=\frac{-8(+-)2\sqrt{19} }{2*-3}[/tex]. Then, multiply 2 by -3 and simplify the equation, which will look like [tex]x=\frac{4(+-)\sqrt{19} }{3}[/tex]. The final answer is [tex]x=\frac{4(+-)\sqrt{19} }{3}[/tex] in exact form. In decimal form, the final answer is [tex]x=2.7863[/tex], [tex]x=-0.1196[/tex].

Answer:

3

Step-by-step explanation:

3 - 3/x

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

1 - 1/x

Multiply the top and bottom by x

x(3 - 3/x)

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

x(1 - 1/x)

3x -3

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

x-1

Factor the numerator

3(x-1)

-------

x-1

Cancel like terms

3

-----

1

3

Answer:

a. 0.4129 = 41.29% of the bank's Visa cardholders pay more than 29 dollars in interest.

b. 0.1867 = 18.67% of the bank's Visa cardholders pay more than 35 dollars in interest.

c. 0.0742 = 7.42% of the bank's Visa cardholders pay less than 14 dollars in interest.

d. An interest payment of $35.2 is exceeded by only 18% of the bank's Visa cardholders.

Step-by-step explanation:

Normal Probability Distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

Mean of 27 dollars and a standard deviation of 9 dollars.

This means that [tex]\mu = 27, \sigma = 9[/tex]

A. What proportion of the bank's Visa cardholders pay more than 29 dollars in interest?

This is 1 subtracted by the p-value of Z when X = 29, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{29 - 27}{9}[/tex]

[tex]Z = 0.22[/tex]

[tex]Z = 0.22[/tex] has a p-value of 0.5871.

1 - 0.5871 = 0.4129

0.4129 = 41.29% of the bank's Visa cardholders pay more than 29 dollars in interest.

B. What proportion of the bank's Visa cardholders pay more than 35 dollars in interest?

This is 1 subtracted by the p-value of Z when X = 35, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 27}{9}[/tex]

[tex]Z = 0.89[/tex]

[tex]Z = 0.89[/tex] has a p-value of 0.8133.

1 - 0.8133 = 0.1867

0.1867 = 18.67% of the bank's Visa cardholders pay more than 35 dollars in interest.

C. What proportion of the bank's Visa cardholders pay less than 14 dollars in interest?

This is the p-value of Z when X = 14. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14 - 27}{9}[/tex]

[tex]Z = -1.445[/tex]

[tex]Z = -1.445[/tex] has a p-value of 0.0742.

0.0742 = 7.42% of the bank's Visa cardholders pay less than 14 dollars in interest.

D. What interest payment is exceeded by only 18% of the bank's Visa cardholders?

This is the 100 - 18 = 82nd percentile, which is X when Z has a p-value of 0.82, so X when Z = 0.915.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.915 = \frac{X - 27}{9}[/tex]

[tex]X - 27 = 0.915*9[/tex]

[tex]X = 35.2[/tex]

An interest payment of $35.2 is exceeded by only 18% of the bank's Visa cardholders.

Answer:

$500

Step-by-step explanation:

Intrest = P. A * Intrest Rate * Time

Time = 1 year, Intrest Rate = 9%, P. A. is what we need to find, Intrest is 45

45=x*9/100*1, x=500

Answer:

500

Step-by-step explanation:

I = PRT  where I is the interest, P is the amount invested, R is the rate and T is the time

We want 1 year at 9% to get 45 dollars in interest

45 = P ( .09) (1)

45 = .09P

Divide each side by .09

45/ .09 = P

500 =P

Answer:

0.40905 - 0.10204 = .30701 = 30.7 %

Step-by-step explanation:

0.23 0.40905

1.27 0.10204

Answer:

Step-by-step explanation:

Answer:

machine fed copies = 25, hand fed copies = 55

Step-by-step explanation:

let machine fed = x, hand fed = y

0.08x+0.2y = 13 (1)

x+y = 80

x= 80-y (2)

sub (2) into (1)

0.08(80-y)+0.2y=13

6.4-0.08y+0.2y=13

0.12y=6.6

y = 55

sub y=55 into eqn 2

x = 80-55 = 25

Answer:

(3 × 25)/5 marbles can go in each bag

Explanation:

Number of bags Regina has = 3

Number of marbles in each bag = 25

So, total number of marbles = 3 × 25

Number of marbles in each bag, if divided equally into 5 bags = (3 × 25)/5

Further:

Solving the expression,

(3 × 25)/5

= 75/5

= 15

So, the each bag has 15 marbles if they are equally divided into 5 bags.

Answer:

(25 x 3) / 5

Step-by-step explanation:

you have to do 25 x 3 to get the total amount of marbles. Then you have to divide that by the amount of bags.

Hi ;-)

[tex]x=7 \ and \ y=3\\\\y-y:1+x=3-3:1+7=3-3+7=0+7=\boxed7[/tex]

Step-by-step explanation:

the graph will be compressed vertically

A quadratic a function has a form of,

[tex]f(x)=ax^2+bx+c,a\neq0[/tex]

The first function has a term [tex]x^3[/tex] which doesn't fit the profile of a quadratic function. The highest exponent on x inside a quadratic function can be 2, but here we have 3 so this is not a quadratic function, but rather a cubic function.

The second function fits the form of a quadratic function perfectly.

The third function is a bit tricky. While technically the third function could be considered quadratic if the leading term would be something like [tex]0x^2[/tex] and we did't even see it written out because multiplying with 0. But when we specified the form of a quadratic function, we strictly said that the number before [tex]x^2[/tex] aka [tex]a[/tex] cannot equal to zero. So the last function is not a quadratic function but rather a linear function.

Hope this helps :)

Step-by-step explanation:

f(x) = 4x² + x - 3

[tex]f(x) = 4x {}^{2} + 3 - 2[/tex]

r3t40 is correct

Answer:

Hypotenuse=10 miles.

Short leg=6 miles.

Step-by-step explanation: