Identify an equation in point-slope form for the line perpendicular to
y= - 1/3x - 6 that passes through (-1,5).

O A. y + 1 = 3(x - 5)
O B. y + 5 = 1/3(x - 1)
O C. y - 5 = 3(x + 1)
O D. y - 5 = - 1/3(x + 1)

Full Question

Of the cartons produced by a​ company, 10​% have a​ puncture, 6​% have a smashed​ corner, and 0.4​% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing​ ____%. ​(Type an integer or a decimal. Do not​ round.)

Answer:

[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]

Step-by-step explanation:

Given

[tex]Puncture\ Corner = 10\%[/tex]

[tex]Smashed\ Corner = 6\%[/tex]

[tex]Punctured\ and\ Smashed\ Corner = 0.4\%[/tex]

Required

[tex]P(Punctured\ or\ Smashed\ Corner)[/tex]

For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;

[tex]P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)[/tex]

Substitute:

10% for P(Puncture Corner),

6% for P(Smashed Corner) and

0.4% for P(Punctured and Smashed Corner)

[tex]P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%[/tex]

[tex]P(Punctured\ or\ Smashed\ Corner) = 15.6\%[/tex]

Convert % to fraction

[tex]P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}[/tex]

Convert to decimal

[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]

Using Venn probabilities, it is found that:

In this problem, the events are:

The "or" probability is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Then:

[tex]P(A \cup B) = 0.1 + 0.06 - 0.004 = 0.156[/tex]

The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.

To learn more about Venn probabilities, you can check https://brainly.com/question/25698611

Answer:

[tex]\boxed{195}[/tex]

Step-by-step explanation:

The fruit flies grows geometrically.

[tex]125=80k^2[/tex]

Find the value of k.

[tex]\sqrt{\frac{125}{80} } =k[/tex]

[tex]1.25=k[/tex]

[tex]P=80(1.25)^t[/tex]

[tex]t[/tex] is number of days.

[tex]P=80(1.25)^4[/tex]

[tex]P=195[/tex]

Answer:

5/(1/3)

Step-by-step explanation:

She has 5 granola bars and gives 1/3 of one to each of her friends. To find how many friends she can give it to, divide 5 by 1/3. You would get a total of 15 friends that you can give granola bars to. The question is asking for an expression so the expression would be 5/(1/3) or 5*3

Answer:

1/3 x = 5

x=15

Step-by-step explanation:

You’re multiplying 1/3 times the number of friends (x), and then multiplying both sides by the reciprocal to solve for x

Answer:

a

  The null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

The Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

b

     [tex]\sigma_{\= x} = 0.8944[/tex]

c

   [tex]t = -2.236[/tex]

d

  Yes the  mean population is  significantly less than 21.

Step-by-step explanation:

From the question we are given

           a set of  data  

                               20  18  17  22  18

       The confidence level is 90%

       The  sample  size  is  n =  5  

Generally the mean of the sample  is  mathematically evaluated as

        [tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]

       [tex]\= x = 19[/tex]

The standard deviation is evaluated as

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

         [tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]

         [tex]\sigma = 2[/tex]

Now the confidence level is given as  90 %  hence the level of significance can be evaluated as

         [tex]\alpha = 100 - 90[/tex]

        [tex]\alpha = 10[/tex]%

         [tex]\alpha =0.10[/tex]

Now the null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

the Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

The  standard error of mean is mathematically evaluated as

         [tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]

substituting values

         [tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]

        [tex]\sigma_{\= x} = 0.8944[/tex]

The test statistic is  evaluated as  

              [tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

              [tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]

              [tex]t = -2.236[/tex]

The  critical value of the level of significance is  obtained from the critical value table for z values as  

                   [tex]z_{0.10} = 1.28[/tex]

Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected

Answer:

x=1

y=1

Step-by-step explanation:

Please look at the image below for solutions⬇️

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.

Point form

(x, 2-x)

Answer:

Since the transformation is made by shifting the function right, it is a horizontal transformation.

Answer:

$0.558

Step-by-step explanation:

The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:

Then our expected value can be calculated as:

[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]

Answer:

Side length: 3 cm.

Surface area: 54 cm squared.

Step-by-step explanation:

The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.

So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.

There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.

Hope this helps!

Answer:

13 2/5

Step-by-step explanation:

a = 2 and b = -3

so the question asks whats.... a^3 - b^3/5

First we plug in the values of a and b

(2)^3 - (-3)^3 /5

Now we solve the ones in paranthesis first

(2)^3 = 8 because 2×2×2 and

-(-3)^3 forget about the - outside the parenthesis so

(-3)^3 = (-27) because (-3)×(-3)×(-3)

now we put it back together

8 -(-27)/5

the two minus become plus so

8 + 27/5

Now we solve it like fractions

8 and 27/5

simplify

13 and 2/5

Hope that helps!

Answer:

3.87

Step-by-step explanation:

The computation is shown below:

Data provided in the question

mean distance = [tex]\bar x[/tex] = 188 meters

Standard deviaton = [tex]\sigma = 14[/tex]

Hits drivers = 15

The distance = 174 meters

H_0: μ≤174;

H_a: μ>174

Based  on the above information, the test statistic z-score is

[tex]z = \frac{\bar x - \mu }{\sigma / \sqrt{n} } \\\\ = \frac{188 - 174}{\ 14 / \sqrt{15} }[/tex]

= 3.87

Hence, the test statistic is 3.87

Note:

We take the μ≤174 instead of μ=174;

Answer:

95% confidensce interval of the mean (two-tail) =  [132.2, 139.2]

Step-by-step explanation:

Given:

N = size of sample = 61

m = sample mean = 135.7

s = sample standard deviation 13.7

Need 95% confidence interval

Solution.

alpha (95% confidence interval) = 0.05

(1-alpha/2) = 0.975   [two sided]

Equation for confidence interval of the mean

= m +/- t(1-alpha/2,N-1) * s / sqrt(N)

= 135.7 +/- 2.0003 * 13.7 / sqrt(60)

= [132.16, 139.24]

Answer:

k = [tex]\frac{980a}{b}[/tex]

Step-by-step explanation:

Fisherman noticed a stretch in the spring = 'b' centimetres

Weight of the fish = a kilograms

If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,

F = kΔx

Where k = spring constant

Δx = stretch in the spring

F = weight applied

F = mg

Here 'm' = mass of the fish

g = gravitational constant

F = a(9.8)

  = 9.8a

Δx = b centimetres = 0.01b meters

Therefore, 9.8a = k(0.01b)

k = [tex]\frac{9.8a}{0.01b}[/tex]

k = [tex]\frac{980a}{b}[/tex]

Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]

Answer:

See below.

Step-by-step explanation:

So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.

Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.

Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.

Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:

In other words, we will have:

[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.

Let's determine n first. We know that f(0)=64, thus:

[tex]f(0)=64=4(-2)^3\cdot n[/tex]

[tex]64=-32n, n=-2[/tex]

Now, let's expand:

Expand:

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

[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]

[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]

[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]

This is the simplest it can get.

Answer:

it opens up

goes up 4 but doesn't move left or right

Answer:

123 domestic stamps

89 foreign stamps

Step-by-step explanation:

Answer:

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

Which equation represents the total number of stamps Malik collected?  

✔ x + y = 212

Which equation represents the difference in the number of foreign and domestic stamps Malik collected?  

✔ x – y = 34

Which system of linear equations represents the situation?  

✔ x – y = 34 and x + y = 212

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

This system of equations models the given information for both stamp types.

x – y = 34

x + y = 212

Solve the system of equations.  

How many foreign stamps does Malik have?

✔ 89  foreign stamps

How many domestic stamps does Malik have?

✔ 123 domestic stamps

Step-by-step explanation:

its right on 2021 edge! :) hope this helps

Answer:

if you're just reflecting the point over the y-axis it just becomes (8,10)

Answer: (8, 10)

Explanation and Example:

I have a trick that I use. I'm not sure if it will make sense to you but I'll explain it. When the question asks you to reflect over the x-axis, then keep the x in (x,y) the same and just flip the sign for the y. If the question asks you to reflect over the y-axis, then keep y the same and flip the sign for x.

Reflect over x-axis:

(-2, 6) -----> (-2, -6)

Reflect over y-axis:

(-4, -8) -----> (4, -8)

Answer:  C

Step-by-step explanation:

h · k(x) = 2(3x - 5)(-2x + 1)

           = (6x - 10)(-2x + 1)

           = -12x² + 6x + 20x - 10

           = -12x² + 26x - 10

Answer:

C

Step-by-step explanation:

h(x) × k(x)

= 2(3x - 5)(- 2x + 1) ← expand factors using FOIL

= 2(- 6x² + 3x + 10x - 5)

= 2(- 6x² + 13x - 5) ← distribute parenthesis by 2

= - 12x² + 26x - 10 → C

Answer:

see explanation

Step-by-step explanation:

differentiate using the power rule.

[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus

[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1

x = 5 → 2(5) - 1 = 10 - 1 = 9

To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero

2x - 1 = 0 , then

2x = 1 and

x = [tex]\frac{1}{2}[/tex]

Answer:

x+2y=12-------(1)

x-2y=3---------(2)

Adding equations 1 and 2

we get

2x=18

x=9

Equation 1

9+2y=15

2y=15-9

2y=6

y=3

The solution of the given system is x=9, y=3

Step-by-step explanation

Answer:

-3.5 meters per second

Step-by-step explanation:

Take the distance and divide by the time

-17.5 meters/ 5 seconds

-3.5 meters per second

Answer:

-3.5 m/s

Step-by-step explanation:

Rate of the anchor =  [tex]\frac{distance}{time}[/tex]

[tex]\frac{-17.5}{5}[/tex]

-3.5 meters per second.

Step-by-step explanation:

im sorry but i need more info or a picture or something to actually anwser the question...

Answer:

C) y = x + 5

Step-by-step explanation

Add 5 to both sides

Answer: m = - 2200

Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.

The year a car is bought and its price means:

f(0) = 31,500

Five years later, the price is $20,500, i.e.:

f(5) = 20,500

With these two pairs of value, slope is calculated as:

[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]

[tex]m = \frac{20500-31500}{5-0}[/tex]

[tex]m = \frac{- 1100}{5}[/tex]

m = - 2200

The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where l is the length

w is the width

The length of the rectangle is 2 feet longer than the width is written as

l = 2 + w

Perimeter = 20feet

So we have

20 = 2( 2 + w ) + 2w

20 = 4 + 2w + 2w

4w = 16

Divide both sides by 4

w = 4

Substitute w = 4 into l = 2 + w

That's

l = 2 + 4

l = 6

Hope this helps you

Answer:

w = 4 and L = 10

Step-by-step explanation:

perimeter of a rectangle = 2(l+w)

p = 20

L = 2 + w

w = ?

20 = 2(2 + w + w)

20 = 2(2 + 2w)

20/2 = 2 + 2w

10 = 2 + 2w

10 - 2 = 2w

8 = 2w

w = 8/2 = 4

L = w + 2

L = 4 +2 = 6

w = 4 and L = 10

Answer:

8n6

step by step explanation.

Answer:

680

Step-by-step explanation:

add 1342+89 to get 1431

then add -295+-456 to get -751

then subtract 751 from 1431 to get 680

Step-by-step explanation:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer: $951,064.06 would be your answer.

Step-by-step explanation: Hope that helped!

Answer:

  148°

Step-by-step explanation:

The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.

  arc QN = 2(74°) = 148°

_____

Comment on the question and answer

Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.

__

We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.

Answer:

148

Step-by-step explanation:

Edge 2020

Step-by-step explanation:

I'm not sure what your answers are, but you can only square 3 and -3 to get 9.

Answer:

3, -3

Step-by-step explanation:

3*3 = 9

-3 * -3 = 9

These are the only two numbers that square to 9

Answer:

45

Step-by-step explanation:

Both angles (2x+45) and x together form a straight angle which measures 180 degrees.

Together should make you think of adding the angle measurements.

So we have that (2x+45)+x should be 180 degrees.

The equation we want to solve is:

(2x+45)+x=180

2x+45+x=180

(2x+x)+45=180

3x+45=180

3x=180-45

3x=135

x=135/3

x=45

Let's confirm that x is 45.

(2x+45) with x=45:

(2*45+45)

(3*45)

135

So (2x+45)+x at x=45 gives us:

135+45

180

Answer has been confirmed.

Answer:

[tex]\boxed{x = 45}[/tex]

Step-by-step explanation:

=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)

=> [tex]3x+45 = 180[/tex]

Subtracting 45 to both sides

=> 3x = 180-45

=> 3x = 135

Dividing both sides by 3

=> x = 45