Point r is on line segment qs. Given qr =2 and rs = 10, determine he length qs.

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]

The value of first quartile is 34.75.

Q₃ is at the position:

[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]

The value of third quartile is 44.83.

Then the inter-quartile range is:

[tex]IQR = Q_{3}-Q_{1}[/tex]

        [tex]=44.83-34.75\\=10.08[/tex]

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]

                                 [tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]

Thus, the probability that a student scored at most 50 on the examination is 0.89.

Answer:

x=1

Step-by-step explanation:

the line is one unit up from the x axis

Answer:

  b

Step-by-step explanation:

Choice b is the only one that has the first equation properly graphed. The boundary line for that equation will have intercepts that can be found by setting the opposite variable to zero.

  x-intercept = 25/2 = 12.5 (on the positive x-axis)

  y-intercept = 25/5 = 5 (on the positive y-axis)

That is, the boundary line has a shallow negative slope, and is shaded below. Only graph 'b' has such a line.

Answer: x=-150

Step-by-step explanation:

To solve for x, we would need to use our order of operations.

0.3x+18=-27                       [subtract both sides by 18]

0.3x=-45                              [divide both sides by 0.3]

x=-150

Answer:

537.2 ft^2

Step-by-step explanation:

For this problem, we need to find the area of both the inner and outer circle and subtract the area of the outer circle from the area of the inner circle.

The equation for the area of a circle is:

A = πr^2

So we are given the diameters of the circles.  We know that the diameter of a circle is twice the radius.

Let's find the area of the 10ft diameter circle:

A_Little = π(10/2)^2 = π(5)^2 = 25π

Let's find the area of the 28ft diameter circle:

A_Big = π(28/2)^2 = π(14)^2 = 196π

So the area of the big circle excluding the inner circle would be as follows:

196π - 25π = 171π

So 171π in terms of decimals rounded to the nearest tenth would be 537.2.

Cheers.

Area of big remain circle is 536.94 feet²

Given that;

Diameter of big circle = 28 feet

Diameter of small circle = 10 feet

Find:

Area of big remain circle

Computation:

Radius of big circle = 28 / 2 = 14 feet

Radius of small circle = 10 / 2 = 5 feet

Area of big remain circle = π(R1² - R2²)

Area of big remain circle = 3.14(14² - 5²)

Area of big remain circle = 3.14(171)

Area of big remain circle = 536.94 feet²

Find out more information about 'Area of circle'

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I’m thinking the graph should look like this since it starts at (0,10) and $1 for each book which is the x. I apologize if it’s wrong

Answer:

a) 22 pine trees

b) x² = 2² + 0.75²

Step-by-step explanation:

a) The volume of a cube is given as:

Volume of cube = length³

The length of the cube = length of the edges = 3 inches, hence:

Volume of cube = (3 inches)³  = 27 in³

The pine tree is the shape of a cone with diameter of 1.5 inches and a height (h) of 2 inches. The radius (r) = diameter / 2 = 1.5 inches / 2 = 0.75 inches.

The volume of the cone = πr²(h/3) = π × (0.75)² × (2/3) = 1.178 in³

The number of pine trees that the artist can make = Volume of cube / Volume of cone = 27 / 1.178 = 22.9

The number of pine trees that can be made = 22

b) The yam length need to extend from the top of the tree to the base is the same as the slant height of the cone.

Let the yam length be x, therefore:

x² = height² + radius²

x² = 2² + 0.75²

x² = 4 + 0.5625 = 4.5625

x = √4.5625 = 2.136 in

The yam length is 2,136 in

Answer:

area = 2236 in²

Step-by-step explanation:

area of a triangle = 1/2 b h

b = 86

h = 52

plug in values

area = 1/2 * 86 * 52

area = 2236 in²

Going south means you're going in the negative direction along the y axis

Going 4 yards south would be represented as -4 on the y axis number line (this is the vertical number line)

Answer:

Southward translation of the rose garden will move it in the negative y-direction. The integer that represents a change of four yards south is -4.

Step-by-step explanation:

Answer:

3.64

Step-by-step explanation:

Identify the hundredth:

3.642

Check the value of the thousandth:

3.642

2 is less than four, therefore, we will round down.

3.642 ≈ 3.64

Answer:

Step-by-step explanation:

l^2=[(7-V2)/2]^2+(9-V2/2)^2=

49-7V2+2/4+81-9V2+2/4=

49+81+4/4-16V2=

131-16V2=108.4 ft

so l=V108.4≈10.4ft

Answer:

Answer is C

Step-by-step explanation:

This is because Lithium =2.8.1

Sodium=2.8.8.1

Valence electron is the electron located in the last shell

Hope this is correct and helpful

HAVE A GOOD DAY!

12x²y² - 17xy - 40

xy (12xy - 17) - 40

As the x and y are shown in both variables but there is no other common factors. I didn't include the 40 as it didn't share any common factors with all of them.

Answer:

[tex]9y+2y-5y=6y[/tex]

Step-by-step explanation:

So we have the expression:

[tex]9y+2y-5y[/tex]

To simplify, simply combine the like terms. Therefore:

[tex]9y+2y-5y\\=11y-5y\\=6y[/tex]

Further notes:

To understand why we can combine like terms in the first place, we just need to use the distributive property. So we have the expression:

[tex]9y+2y-5y[/tex]

Now, factor out a y from the three terms:

[tex]=y(9+2-5)[/tex]

Do all the operations inside the parenthesis:

[tex]y(9+2-5)\\=y(11-5)\\=y(6)=6y[/tex]

And we moved the y back to the front!

This is the same result as before. When combining like terms, this is what we're essentially doing but without doing the distributive property manually. I hope you understand a bit better on how and why we can combine like terms!

Answer:

6y

Step-by-step explanation:

We are given the expression:

9y+2y-5y

and asked to simplify.

Each term in the expression has the same variable, a "y". Therefore, all three terms are like terms. We can combine the like terms in the expression.

First, factor out a y from each term.

9y+2y-5y

(9+2-5)*y

Solve inside the parentheses first. Add 9 and 2.

(11-5)*y

Subtract 5 from 11.

(6)*y

6y

The expression 9y+2y-5y simplified is 6y.

Answer:

1/ N = 1 / 5 + 1/ 4 - 1/ 3 + 1/12

taking L.C.M

Then,

or, 1/N = 5 + 6 / 20 - 13+ 4 / 12

or, 1/N = 11/ 20 - 7/12

or, 1/N = 14 - 12 / 60

or, 1/N = 2 / 60

NOW,

Do cross multiplication,

60 = 2N

or, 60 / 2 = N

so, N = 30

ANS

Answer: $3.68

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

We are given the equation:

[tex]x+y=2[/tex]

And we subtracted x from both sides to acquire:

[tex]y=2-x[/tex]

Notice that this is the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

If we rearrange our equation, we acquire:

[tex]y = -(1)x+(2)[/tex]

Therefore, m = -1 and b = 2.

In other words, the slope is -1 and the y-intercept is 2.

Answer:

[tex]\Large \boxed{{m=-1, \ b=2}}[/tex]

Step-by-step explanation:

x + y = 2

We need the equation in the form y = mx + b.

m = slope

b = y-intercept

Solve for y by subtracting x from each side.

y = 2 - x

The -x can be written as -1x.

y = 2 - 1x

Rearrange the expression.

y = -1x + 2

The equation is in form y = mx + b.

The slope is -1.

The y-intercept is 2.

Answer:

[tex] \frac{9}{14} [/tex]

Step-by-step explanation:

Evaluate, [tex] -\frac{3}{2} [/tex] ÷ [tex] -\frac{7}{3} [/tex] by first changing the operation from division to multiplication and flipping the fraction by your right upside down.

Thus,

[tex] -\frac{3}{2} * -\frac{3}{7} [/tex]

Negative multiplied by negative = positive

[tex] \frac{3*3}{2*7} = \frac{9}{14} [/tex]

Answer:

f(-3) = -21

Step-by-step explanation:

To find f(-3), we just need to plug x = -3 into f(x) so:

f(-3) = -4 * (-3)² + 15

= -4 * 9 + 15 = -36 + 15 = -21

Answer:

[tex]\Huge \boxed{-21}[/tex]

Step-by-step explanation:

[tex]f(x) = -4x^{2} + 15[/tex]

f(-3), the input is -3 for the function f(x).

The value of x  =  -3

[tex]f(-3) = -4(-3)^{2} + 15[/tex]

Evaluate the expression.

[tex]f(-3) = -4(9)+ 15[/tex]

[tex]f(-3) = -36+ 15[/tex]

[tex]f(-3)=-21[/tex]

The value of f(-3) is -21.

Answer:

Step-by-step explanation:

I am pretty sure your answer is 3

Answer:

2 sides=5 lonely side =7

Step-by-step explanation:

if the full perimeter is 17 and one side is just 7 then you can subtract 7 from 17 and get ten so then you can divide ten by two and get 5 for both sides.

Answer:

one large box equals 15.75kg

one small box equals 13.75kg

Step-by-step explanation:

First, identify your variables:

Let "l" represent the weight of one large box.

Let"s" represent the weight of one small box.

Then, stack the two equations on top of each other:

[tex]5l+3s=120\\7l+9s=234[/tex]

Next, multiply the first equation by 3 so we can use elimination of the "s" variable to find the "l" variable first:

[tex]3(5l+3s=120)\\7l+9s=234\\\\15l+9s=360\\7l+9s=234[/tex]

Now, subtract the two equations to cancel out the s-variable and find the l-variable:

[tex]15l+9s=360\\-(7l+9s=234)\\8l=126\\\frac{8l}{8}=\frac{126}{8}\\l=15.75[/tex]

Then, substitute your l-variable in the original first equation to find the s-variable:

[tex]5l+3s=120\\5(15.75)+3s=120\\78.75+3s=120\\78.85-78.75+3s=120-78.75\\3s=41.25\\\frac{3s}{3}=\frac{41.25}{3}\\s=13.75[/tex]

With all the information that is collected, you find that one large box weighs 15.75kg and one small box weighs 13.75kg.

Answer:

B) skirt 1, white

skirt 1, black

skirt 2, white

skirt 2, black

Step-by-step explanation:

You can wear skirt type 1 in white or black, or skirt type 2 in white or black

B) skirt 1, white

skirt 1, black

skirt 2, white

skirt 2, black

PEMDAS is the order of operation, and is what you follow to solve a expression/equation.

PEMDAS =

Parenthesis

Exponents: This step also includes solving for any roots.

Multiplication

Division

Addition

Subtraction

Answer:

the answer is

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

10:14

Step-by-step explanation:

10lions:14tigers

Answer:

5:7

Step-by-step explanation:

Answer:

12.8 cm^2

Step-by-step explanation:

Angle subtended by the sector=70

Radius of the circle= 21 cm

Area of the sector =[tex]\frac{given angle}{360}[/tex] x [tex]\pi r^{2}[/tex]

                              =    [tex]\frac{70}{360}* \frac{22}{7}*21\\\\\frac{70}{360 } *22*3\\\frac{77}{6}\\ 12.8[/tex]

Answer: 3

Step-by-step explanation:

Given:  A recipe for a pizza that serves 12 people calls for 2 cups of shredded cheese.

12 people = 2 cups of shredded cheese.

Multiply 4 on both sides , we get

48 people = 8 cups of shredded cheese.

So we require 8 cups of shredded cheese  to make pizza for 48 people.

Since, each bag of shredded cheese contains 3 cups.

Then minimum number of bags required = [tex]\dfrac{8}{3}=2.67\approx3[/tex]

Hence, minimum 3 bags required to make pizza for 48 people.

Answer:

Hey there!

The next three terms are: -64, 128, -256.

Let me know if this helps :)

Answer:

-64, 128, -256

Step-by-step explanation:

Times -2 every step

Answer:

I believe it is 48

Step-by-step explanation:

because 4 is two less than 6, and 4 doubled would be 8

Answer:

The ratio of successful events A = 3 to total number of possible combinations of sample space S = 8 is the probability of 2 heads in 3 coin tosses.

Step-by-step explanation:

Answer:   [tex]\dfrac{2}{3}[/tex]

Step-by-step explanation:

Given that there are exactly two heads out of three coins, we have the following possibilities:

H H T

H T H

T H H

Two of the three possible outcomes have two heads in a row.

[tex]\dfrac{\text{Number of "two heads in a row"}}{\text{Number of "exactly two heads"}}=\large\boxed{\dfrac{2}{3}}[/tex]