how many solutions if both slopes are the same but the y-intercepts are different

Answer:

Step-by-step explanation:

Can you please include a image?

Thanks!!!

Answer:

The  99%  confidence interval is

                     [tex]37.167< \= x < 44.833[/tex]

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 29[/tex]

  The  sample mean is  [tex]\= x =[/tex]$41

  The  sample standard deviation is  [tex]\sigma =[/tex]$8

   The  level of confidence is [tex]C =[/tex]99%

Given that the confidence level id  99% the level of confidence is evaluated as

        [tex]\alpha = 100 - 99[/tex]

        [tex]\alpha = 1[/tex]%

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is  

      [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

The reason we are obtaining values for  is because  is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while   is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Next we evaluate the margin of error which is mathematically represented as

          [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]

           [tex]MOE = 3.8328[/tex]

The 99% confidence level is constructed as follows

      [tex]\= x - MOE < \= x < \= x + MOE[/tex]

substituting values

    [tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]

     [tex]37.167< \= x < 44.833[/tex]

Answer:  Focus = (-2, 3)

Step-by-step explanation:

[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]

First let's find the vertex. We do that by finding the Axis-Of-Symmetry:

[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]

Then finding the maximum by inputting x = -2 into the given equation:

[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]

The vertex is: (-2, 4)

Now let's find p, which is the distance from the vertex to the focus:

[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]

The vertex is (-2, 4) and p = -1

The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)

Answer:

3¾

Step-by-step explanation:

Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.

Formula for geometric sequence:

[tex] a^n = a ( n-1 ) * r [/tex]

Given:

First term, a1 = 30

ratio, r = ½

Required:

Find the fourth term

Where, the first term, a¹ = 30

Second term: a² = 30 * ½ = 15

Third term: a³ = 15 * ½ = 7.5

Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾

Therfore the fourth term of the geometric sequence is 3¾

Answer:

f(x)= 8(0.5)^x

Step-by-step explanation:

As you can see on the graph there are two specific points labeled:

(0,8) and (1,4)

The 8 would be the initial value and starting point of the "design"

A is always the initial value so replace that.

Then proceed to divide 4 by 8 to figure out the percentage change its 0.5

leave x as it is

Answer:

a)  [tex]\frac{2}{3} \,\frac{lb}{bread}[/tex]

b)  [tex]1\frac{1}{4} \,\frac{in}{domino}[/tex]

Step-by-step explanation:

Part a:

every 4 lbs of flour, she makes 6 loaves of bread. this as a rate in simplest fraction form is:

[tex]\frac{4}{6} \,\frac{lb}{bread} = \frac{2}{3} \,\frac{lb}{bread}[/tex]

Part b:

every 10 inches , 8 dominoes can be placed. then the rate can be written as:

[tex]\frac{10}{8} \,\frac{in}{domino} = \frac{5}{4} \,\frac{in}{domino} =1\frac{1}{4} \,\frac{in}{domino}[/tex]

Answer:

[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points

[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]

Substitute:

[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

We can use the slope formula since we have 2 points

m = ( y2-y1)/(x2-x1)

    = (9-3)/( 7 - -5)

    = (9-3) /( 7+5)

   = 6/ 12

  = 1/2

Answer: options 2,3and 6

Answer:

option

2-Twelve students answered Mr. Chiu’s question.

3-Three people studied for two hours.

6-Four people studied for four or more hours.

Step-by-step explanation:

hope this helps:)

An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.

An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.

To find the outlier for the given data set follow the given steps.

Step one: The first step is to find the quartiles for the data set.

For this data set, the quartiles are:

Q1 = 45.5

Q3 = 62.5

Step Two: Find the Interquartile Range

The interquartile range is the difference between the first and third quartiles.

IQR = Q3 - Q1

IQR = 45.5 - 62.5

IQR = 17

Step Three:

The next step is to set up a fence beyond the first and third quartiles using the interquartile range.

Lower Fence = Q1 - (1.5 × IQR)

Lower Fence = 45.5 - (1.5 × 17)

Lower Fence = 20

Upper Fence = Q3 + (1.5 × IQR)

Upper Fence = 62.5 + (1.5 × 17)

Upper Fence = 88

Step Four: Find the Outliers

Any numbers in the data that are above or below the fences are outliers.

Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.

Learn more about Outlier:

https://brainly.com/question/26958242

#SPJ2

Hey there! I'm happy to help!

Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.

10x+50y=1080

x+y=28

We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.

x+y=28

Subtract x from both sides.

y=28-x

Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.

10x+50(28-x)=1080

We use distributive property to undo the parentheses.

10x+1400-50x=1080

We combine like terms.

-40x+1400=1080

We subtract 1400 from both sides.

-40x=-320

We divide both sides by -40.

x=8

Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.

Have a wonderful day! :D

Answer:

2π radians

Step-by-step explanation:

Answer:

Step-by-step explanation:

First , let us rewrite the given equation into y= mx+b format

.y= -x +7

Slope is -1

Slope of the line perpendicular to the given equation is -(-1) ie., 1

Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b

1 = -1 +b

2 = b

Equation of the line perpendicular to the given equation and passing through (-1,1) is

y=x +2

Answer:

C. μ = 3.60

Step-by-step explanation:

Two tables have been attached to this response.

One of the tables contains the given data and distribution with two columns: Houses Sold and Probability

The other table contains the analysis of the data with additional columns: Frequency and Fx

=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,

When the number of houses sold = 0

F = P(0) x Total number of houses sold

F = 0.24 x 28 = 6.72

When the number of houses sold = 1

F = P(1) x Total number of houses sold

F = 0.01 x 28 = 0.28

=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,

When the number of houses sold = 0

Fx = F * x

F = 6.72 x 0 = 0

Now to get the mean, μ we use the relation;

μ = ∑Fx / ∑F

Where;

∑Fx = summation of the items in the Fx column = 100.8

∑F = summation of the items in the Frequency column = 28

μ = 100.8 / 28

μ = 3.60

Therefore, the mean of the given probability distribution is 3.60

The mean of the discrete probability distribution is given by:

C. μ = 3.60

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:

[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]

Hence option C is correct.

More can be learned about the mean of discrete distributions at https://brainly.com/question/24855677

Answer:

-5 < x < 0

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

14(z + 3) = 14z + 21

Expand brackets.

14z + 42 = 14z + 21

Subtract 14z on both sides.

42 = 21

There are no solutions.

Answer:

No solution

Step-by-step explanation:

First, We have to simplify the right side.

Distribute 14, 14z+42.

Now the equation stands as 14z+42=14z+21

Subtract 14z from both sides,

this makes it 42=21.

We know when the solution is #=#, our answer is no solution.

Answer:

k ≥ 24

Step-by-step explanation:

ᵏ⁄₄ ≥ 6

Multiply each side by 4

ᵏ⁄₄ *4 ≥ 6*4

k ≥ 24

Answer:

k≥24

Step-by-step explanation:

k/4≥6

Use the multiplication property of equality by multiplying both sides by 4 to get

k≥24

If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem

Thank you

Answer:

8.5cm

Step-by-step explanation:

convert 3.4metres to cm that is by multiplying by 100

3.4×100=340cm

1rep 40

?rep 340

that is 340/40

=8.5cm

Answer:

8.5 cm

Step-by-step explanation:

Scale = 1:40

Length of the room = 3.4 meters

3.4 meters =3.4 X 100 =340 cm

Since 1 unit on the diagram represents 40 units

The length of the diagram

[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]

The length of the room on the diagram is 8.5 cm.

Answer:  see below

Step-by-step explanation:

1) Foci is plural for Focus.  Since a hyperbola has two focus points, they are referred to as foci.  The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

    a)  does the hyperbola open up or to the right?

    b)  what is the center (h, k) of the hyperbola?

    c)  What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]

Answer:

792

Step-by-step explanation:

The first three composite numbers are 4,  6 ,8

so 4^3+6^3+8^3=64+216+512=792

Answer:

Time taken by Stephen = 162 seconds

Step-by-step explanation:

Stephan gathered data which fits in the line of best fit,

y = -2.1x + 565.6

Where x represents the age (in months)

And y represents the time (in seconds) taken by Stephen to run two laps on the track.

Time taken to run 2 laps at the age of 192 months,

By substituting x = 192 months,

y = -2.1(192) + 565.6

  = -403.2 + 565.6

  = 162.4 seconds

  ≈ 162 seconds

Therefore, time taken by Stephen to cover 2 laps was 162 seconds when he was 192 months old.

Answer:

[tex]\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0[/tex]

[tex]\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

38.68 cm

Step-by-step explanation:

Perimeter of an equilateral triangle : P = 3a

Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]

a = side length

The area is given, solve for a.

[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a = 12.894839[/tex]

The side length is 12.894839 centimeters.

Find the perimeter.

P = 3a

P = 3(12.894839)

P = 38.684517 ≈ 38.68

The perimeter is 38.68 centimeters.

According to the given situation, the computation of two number in a given ratio is shown below:-

We assume the numbers is x and y

Given that

[tex]\frac{x}{y} = \frac{3}{1}[/tex]

x = 3y

and

[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]

With the help of above formula we will put the value and be able to find the values of x and y

x - y = 6

3y - y = 6

2y = 6

y = 3

x = 3y = 9

x = 9, y = 3

Therefore the correct answer is x = 9 where as y = 3

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

(11π/9 )ft/s

Step by step Explanation

Let us denote the height as h ft

But we were told that The diameter of the base of the cone is approximately three times the altitude, then

Let us denote the diameter = 3h ft, and the radius is 3h/2

The volume of the cone is

V = (1/3)π r^2 h

Then if we substitute the values we have

= (1/3)π (9h^2/4)(h) = (3/4)π h^3

dV/dt = (9/4)π h^2 dh/dt

We were given as 22feet and rate of 8 cubic feet per minute

h = 22

dV/dt = 8

8= (9/4)π (22) dh/dt

= 11π/9ft/s

Therefore, the rate is the height of the pile changing when the pile is 22 feet is

11π/9ft/s

Answer:

Step-by-step explanation:

Let, present age of son be 'x'

present age of father be 'y'

y = 4x→ equation ( i )

After five years,

Son's age = x + 5

father's age = y + 5

According to Question,

[tex]y + 5 = 3(x + 5)[/tex]

Put the value of y from equation ( i )

[tex]4x + 5 = 3(x + 5)[/tex]

Distribute 3 through the parentheses

[tex]4x + 5 = 3x + 15[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S. and change its sign

[tex]4x - 3x = 15 - 5[/tex]

Collect like terms

[tex]x = 15 - 5[/tex]

Calculate the difference

[tex]x = 10[/tex]

Now, put the value of X in equation ( i ) in order to find the present age of father

[tex]y = 4x[/tex]

plug the value of X

[tex] = 4 \times 10[/tex]

Calculate the product

[tex] = 40[/tex]

Therefore,

Present age of son = 10

present age of father = 40

Hope this helps..

Best regards!!

Answer:

3057.6 cm³

Step-by-step explanation:

You have a cylinder and a rectangular prism.  Solve for the area of each separately.

Cylinder

The formula for volume of a cylinder is V = πr²h.  The radius is 7, and the height is 7.

V = πr²h

V = π(7)²(7)

V = π(49)(7)

V = 343π

V = 1077.57 cm³

Rectangular Prism

The formula for volume of a rectangular prism is V = lwh.  The length is 20, the width is 11, and the height is 9.

V = lwh

V = (20)(11)(9)

V = (220)(9)

V = 1980 cm³

Add the areas of the two shapes.

1077.57 cm³ + 1980 cm³ = 3057.57 cm³

Round to the nearest tenth.

3057.57 cm³ ≈ 3057.6 cm³

Answer:

Step-by-step explanation:

The surface area of a cone is:

● Sa = Pi*r^2 +Pi*r*l

r is the radius and l is the slant heigth

The diameter of this cone is 12 inches so the radius is 6 (12/2=6).

●Sa = Pi*36 +Pi*6*10

●Sa = 301.59 in^2

Answer:

pi (6) * 10+ pi ( 6)^2

Step-by-step explanation:

The surface area of a cone is given by

SA =  pi rl +pi r^2  where r is the radius and l is the slant height

We know the diameter is 12 so the radius is 12/2 = 6

SA =  pi (6) * 10+ pi ( 6)^2

Answer:

a) Mean = 4.55

   Median = 4.7

   Mode = 1.9

b) S =  2.3952

   CV = 52.64 %

   Range = 6.3

c) Yes, since the average and median values are both over "acceptable" ranges.

Step-by-step explanation:

Explanation is provided in the attached document.

Answer:

x1= -4, x2 = 7

Step-by-step explanation:

Move expression to the left-hand side:

1/4x-3/4-7/x=0

Write all the numerators above a common denominator:

x^2 - 3x - 28 /4x =0

When the quotient of expressions equal 0, the numerator has to be 0

x^2 + 4x - 7x - 28 = 0

x(x+4) - 7(x+4) =0

(x+4) × (x-7) =0

Separate into possible cases:

x+4=0

x-7=0

Answer: -9

Step-by-step explanation: