Find the value of z and
simplify completely.

Answer: -x + y = 8

Step-by-step explanation:

So first you are going to want to find the slope of the equation. The equation for that it (y2 - y1)/(x2 - x1) = (10 - 7)/(2 - -1) and that equals 1. So your slope will be 1.

Now you have half of your equation complete, currently it looks like, y = x + b. So we have to find the y intercept. You can do that by plugging in a pair of coordinates into the current equation and solve for b.

Lets plug in (2,10)

10 = 2 + b

10 - 2 = b

b = 8

So now you have your equation in slope intercept form, y = x + 8. Just move the x over to the left side and there is your answer.

-x + y = 8

Answer:

a) 15.52mm

b) 25.8275mm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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, or the area to the left side of the curve. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, that is, the area to the right side of the curve.

A) What wing-span has an area of 0.1005 on it left side under the standard normal curve?

This is X when Z has a pvalue of 0.1005. So it is X when Z = -1.28.

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

[tex]-1.28 = \frac{X - 20}{3.5}[/tex]

[tex]X - 20 = -1.28*3.5[/tex]

[tex]X = 15.52[/tex]

This wing-span is 15.52mm.

B) What wing-span has an area of 0.0480 on it right side under the standard normal curve?

This is X when Z has a pvalue of 1 - 0.0480 = 0.9520. So this is X when Z = 1.665.

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

[tex]1.665 = \frac{X - 20}{3.5}[/tex]

[tex]X - 20 = 1.665*3.5[/tex]

[tex]X = 25.8275[/tex]

This wing-span is 25.8275mm.

Answer:

x = 20º

Step-by-step explanation:

we know that  sin x = cos(90-x)

Hence

sin 30º = cos(90 - 30)º

sin 30º = cos 60º

hence sin 30º can be also written as cos 60º

Also, as given

sin 30º = cos(3x)

therefore

cos 60º =  cos(3x)

as we have cos on both side then angle for both side will be same

60º =  3x

=> 60º / 3 = x

=> x = 20º

Then  x = 20º is answer.

Answer:

2(L+W)H

Step-by-step explanation:

Surface area= 2(L+W)H

Answer:

D

Step-by-step explanation:

The mean is the average summing all values together and dividing by the number of values been investigated.

Hence since no values exist between 201-350 that means the mean can not be there.

Answer:

The relative frequency of the class 201 - 350 is 0.

Step-by-step explanation:

-6(4 + 5v) - 3 = -57

Use distributive properties

-24 -30V -3 = -57

Combine like terms

-27 -30v = -57

Add 27 to both sides

-30v = -30

Divide both sides by -30

V=1

Answer:

v = 1

Step-by-step explanation:

-6(4 + 5v) - 3 = -57

Add 3 to each side

-6(4 + 5v) - 3+3 = -57+3

-6(4 + 5v)  = -54  

Divide by -6 on each side

-6(4 + 5v)  / -6 = -54/-6

4+5v = 9

Subtract 4 from each side

4+5v-4 = 9-4

5v = 5

Divide each side by 5

5v/5 = 5/5

v =1

Answer:

when both bottom numbers on a fraction are the same at the lowest form

Step-by-step explanation:

example: 2/4 + 6/8 the common denomenator is 8 as both numbers go into it and you only have to times by 2 so answer would be 10/8 which is also 1 2/8

Answer:

True

Step-by-step explanation:

Logic: if 3+4 =7 then 4+3 also = 7 or 3*4 =12 then 4*3 is also 12 etc.

Answer:

Yes it is

Step-by-step explanation:

Each x value is represented by exactly one y value.

Answer:

Any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.

Step-by-step explanation:

Interpreting Box Plots

A box plot is used to present the 5-Number summary of a set of data.

The 5-Number summary consists of the following in their order of appearance on the box plot.

In the box plot, the following rules applies

Using these, we interpret the given box plot

A left whisker extends from 1 to 6.

The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12.

The right whisker extends from 16 to 19.

Therefore any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.

Answer:

a) Not replaced

Yelllow marker First - Then Blue Marker  =

(1/10)(1/9)  =  1/90

b) Replaced

(1/10) (1/10)  = 1/100

Answer   "C"

Step-by-step explanation:

Answer:

Yes,she had enough

½pound=8ounces

she needs a total of 24ounces

Step-by-step explanation:

She had enough because ½pound is 8ounces thus 16ounces+8ounces add up to 24ounces.

Answer:

Yes,she had enough

½pound=8ounces    she needs a total of 24ounces

Step-by-step explanation:

Answer:

12 meters

Step-by-step explanation:

Looking at the problem we can see that it typifies a right angled triangle. The rope running from the top of the flagpole to the hook on the ground is the hypotenuse of the triangle. Let us call this hypotenuse c. Let the distance between the hook and the foot of the flagpole be b. Let the height of the flagpole be a.

From Pythagoras theorem;

c^2 = a^2 + b^2

a^2= c^2 - b^2

a= √c^2-b^2

From the question

c= 13 metres

b= 5 metres

a= the unknown

a= √c^2-b^2

a= √(13)^2 - (5)^2

a= √169 - 25

a= √144

a= 12 meters

Answer:

The flagpole  12 meters tall

Step-by-step explanation:

Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long

∵ The hook is 5 meters from the flag pole

∵ The flagpole and the ground ⊥ to each other

By using Pythagoras theorem:

hypothenus side is 13m

base is 5m

how tall is the flagpole is x

[tex]13^2=x^2+5^2\\\\169=x^2+25\\\\x^2=169-25\\\\x^2=144\\\\x=12m[/tex]

The flagpole  12 meters tall

-11/10

Step-by-step explanation:

so first get the x on one side of the equal sign and the numbers on the other.

x+2 4/5 = 3 1/6

- 2 4/5 - 2 4/5

x= -11/10

Answer:

Left side simplifies to (-2/3)^1 and the right side simplifies to (-2/3)^(-n) which means 1 = -n so n = -1.

Answer:

A

Step-by-step explanation:

Because B corresponds with 80 and a line segment is 180 degrees b + a =180 and a would be 100.

Answer:

1st graph: m = -1/2. (m is the slope)

2nd graph: m = 3/2.

3rd graph: Midpoint = (1/2, 1/2)

Step-by-step explanation:

1st graph:

Find the slope by looking for two points on the line. Use the formula [tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

We can derive the points (-3, 0) and (1, -2). Plug these into the equation above.

[tex]m= \frac{-2-0}{1-(-3)}[/tex]

Simplify this, giving you: m = -1/2.

2nd graph:

Use the same formula as stated above. From this graph, you can plug in the points (-1, 1) and (1, 4)

[tex]m = \frac{4-1}{1-(-1)}[/tex]

Simplifying gets you: m = 3/2.

3rd graph:

To find the midpoint, use the formula: [tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex]

Plug in the end-points of the graph, or (-3, 2) and (4, -1).

You get:

[tex](\frac{-3+4}{2}, \frac{2-1}{2})[/tex]

Simplify:

Midpoint = (1/2, 1/2)

Answer:

If you are talking about the amount of money, it is $664,285.71

If not then lmk

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

AB + BC = AB

3x+5  + 2x+8 = 88

Combine like terms

5x +13 = 88

Subtract 13 from each side

5x+13-13 = 88-13

5x = 75

Divide each side by 5

5x/5 = 75/5

x = 15

Answer:

15

Step-by-step explanation:

AB + BC = AB

3x + 5 + 2x + 8 = 88

5x + 13 = 88

5x = 88 - 13

= 75/5

= 15

Hope this helps!

Answer:

The rocket reached its maximum height at 1.25 seconds.

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

Reading off the graph:

y-intercept  = (0, 2.5)

x-intercept = (3.5, 0)

Answer:

9b-8

Step-by-step explanation:

6b+5b-2b-8

11b-2b-8

9b-8

Answer:

As per BODMAS rule: 3 x 5 x 7 + 7 = 105 + 7 = 112. 112 is an even number and is therefore a composite number

Step-by-step explanation:

you need to do BODMAS so

3 x 5 x 7 = 105

then add 7 so there for 112

112 is an even number and therefore a composite number

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer

Make a tally table and line plot to show the data.

Time (in hours)              Tally      Total

[tex]\frac{1}{4}[/tex]                                         //             2

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

[tex]\frac{3}{4}[/tex]                                       ///              3

1                                      ////              4

Hope it will find you well.

The percent decrease is found by using the formula (original price - new price)/(original price). The percent decrease is then (2.49 - 1.99)/2.49 = 0.20 = 20%. A percent increase is found by using the formula (new price - original price)/(original price). The percent increase is then (2.49 - 1.99)/1.99 = 0.25 = 25%. The percents of change are not the same. The percent increase is greater.

Answer:

2.49-1.99= 0.5

0.5 divided by2.49 times 100 is about 20% decrease

1.99-2.49+0.5 also so it is also a 25 percent increase

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

The height of the platform is when t=0

h(0) = -4(0)^2 + 75(0) +20

        =20

The height of the platform is 20

Answer:

aₙ=23 - 8n

Step-by-step explanation:

15, 7, -1,....

AP with the first term of 15 and common difference  -8

aₙ=a₁+(n-1)d= 15+(n-1)*(-8)= 15 -8n +8= 23 - 8n

aₙ=23 - 8n

Answer:

1947 units^2

Step-by-step explanation:

you can split it up into different sections of rectangles.

the first one is 25x39= 975

The second section is the connector which you do

43-25=18

and you do 39-27=12 and then

you multiple 18x12 which equals 216

and the final section you do 24+12=36

and 36x21=756

and finally you add them all up to equal 1947 units^2

Answer:

Third option correct

Step-by-step explanation:

The diagonal is the distance between 2 of the vertices, and to end.

So the option we shall choose will contain 2 of the vertices in a distance between points equation.

Mathematically, the distance between two points is given by;

D = √(x2-x1)^2 + (y2-y1)^2

The correct option is the third option.

This is because it takes into consideration two of the vertices which are points A and point C

Answer: c the third one

Step-by-step explanation: