When Alyssa runs the 400 meter dash, her finishing times are normally distributed
with a mean of 60 seconds and a standard deviation of 2 seconds. Using the empirical
rule, what percentage of races will her finishing time be between 54 and 66 seconds?

Addition of 6q + 1 and q + 11 is 7q + 12

Solution:

Given that, we have to add the given two expressions

Given expressions are:

6q + 1 and q + 11

We have to add both the expressions

Addition of 6q + 1 and q + 11 = 6q + 1 + q + 11

Add the coefficients of same variable. Here "q" is present in two terms

Therefore, add 6q and q

Similarly, add the constants 1 and 11

Thus finally addition is done as:

[tex]6q + 1 + q + 11 = 7q +12[/tex]

Thus addition of 6q + 1 and q + 11 is 7q + 12

Answer:

x = 4 and x = 7

Step-by-step explanation:

Given that the segment in the triangle is parallel to the third side of the triangle and intersects the 2 sides then it divides these 2 sides in proportion, thus

[tex]\frac{x}{12}[/tex] = [tex]\frac{x+1}{15}[/tex] ( cross- multiply )

15x = 12(x + 1) ← distribute

15x = 12x + 12 ( subtract 12x from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

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

[tex]\frac{8}{7}[/tex] = [tex]\frac{16}{2x}[/tex] ( cross-  multiply )

16x = 112 ( divide both sides by 16 )

x = 7

Answer:

x=0

Step-by-step explanation:

-2x+9=9

-2x=9-9

-2x=0

x=0/-2

x=0

Answer:

money spent = number of people *  price of 1 ticket  (direst variation)

 28               = 4 *  price of a ticket

so price of one ticket = 28/4 =  7

Constant of variation is 7

we might write it as m = 7n

Step-by-step explanation:

what does it ask for?

Answer: You might have messed up the question

Here is the answer based on your question

W (Bottled water) = 7/2$

N (Cheese Nachos) = -1/2$

Step-by-step explanation:

2W + 3N = $5.50

3W + 2N = $9.50

Find the common number and subtract them. In order to find isolate the water bottles or nachos. I will do water bottles

15 (2W + 3N = $5.50)

10 (3W + 2N = $9.50)

30w + 45N = $82.5

Minus

30W + 20N = $90

= 25N = -12.5

N = -1/2$

Substitute for N

3W + 2(-1/2) =9.5

3w -1 = 9.5

3w - 10.5

w = 7/2$

The value of [tex]sin100.sin120.sin140.sin160[/tex] is [tex]0.1875[/tex]

Step-by-step explanation:

To find the value of [tex]sin100.sin120.sin140.sin160[/tex], let us find the value of each angle.

The value of [tex]sin100=0.9848[/tex]

The value of [tex]sin120=\frac{\sqrt{3} }{2}[/tex]

The value of [tex]sin140=0.6428[/tex]

The value of [tex]sin160=0.3420[/tex]

Substituting the values of sin, we get,

[tex]sin100.sin120.sin140.sin160=0.9848*\frac{\sqrt{3} }{2} *0.6428*0.3420[/tex]

Multiplying the values of sin, we get,

[tex]sin100.sin120.sin140.sin160=0.1875[/tex]

Thus, the value of [tex]sin100.sin120.sin140.sin160[/tex] is [tex]0.1875[/tex]

The equation of g(x) is g(x) = 6x + 11

Step-by-step explanation:

Let us revise some transformation

∵ f(x) = 2x + 5

∵ The graph of f(x) is stretched vertically by scale factor 3

- That means multiply f(x) by 3

∴ The equation of the new graph is 3(2x + 5)

∵ The new graph is translated 4 units down

- That means subtract 4 from 3(2x + 5)

∴ The equation of g(x) is g(x) = 3(2x + 5) - 4

- Simplify the equation of g(x)

∴ g(x) = 3(2x) + 3(5) - 4

∴ g(x) = 6x + 15 - 4

- Add the like terms in the right hand side

∴ g(x) = 6x + 11

The equation of g(x) is g(x) = 6x + 11

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Answer:

The numbers are 32 , 48

Step-by-step explanation:

Average = 40

Sum of two numbers = 40 * 2 = 80

Let one number =x

Other number = 80 - x

Product of two numbers = GCD * LCM

x*(80-x) = 16*96

80x - x² = 1536

1536 + x² - 80x = 0

x² - 80x + 1536 = 0

x² - 48x - 32x + (-32) * (-48) = 0

x (x -48x) -32 (x -48) =0

(x - 48) ( x - 32) = 0

x - 48 = 0    ; x - 32 = 0

x = 48          ; x = 32

Answer:

48 is 60% of 80.

Answer:

60%

Step-by-step explanation:

48: 80*100 =

(48*100) :80 =

4800:80 = 60

Answer:

The answer is shown in the plotted graph attached with the answer.

Step-by-step explanation:

i) Let y = f(x)

ii) According to the first equation we will consider x = -6, -5, -4, -3, -2, -1, 0, and

   1

Therefore   x   and     y = x + 4         for -6 ≤   x   <  2

iii) y = 6 when x = 2 is the second equation given for the graph

iv)            x                  y = -x + 2        for x > 2 is the third equation given

Answer:

[tex]Width = 2\frac{1}{4}cm[/tex]

[tex]Length=5\frac{5}{12} cm[/tex]

Step-by-step explanation:

Data from the question;

Perimeter of a rectangle is [tex]15\frac{1}{3}[/tex] cm

Length is [tex]3\frac{1}{6}[/tex] cm longer than the width

We are supposed to determine the length and the with of the rectangle;

Assuming, the width x cm

Then, the length is [tex]x+3\frac{1}{6}[/tex] cm

We need to know that the perimeter of a rectangle is given by;

Perimeter = 2 ( length + width)

Therefore;

[tex]15\frac{1}{3}= 2 ( x + (x+3\frac{1}{6}))[/tex]

[tex]15\frac{1}{3}=2(2x+3\frac{1}{6})[/tex]

Thus;

[tex]15\frac{1}{3}=4x+6\frac{1}{3}[/tex]

[tex]4x=9\\x=2\frac{1}{4}[/tex]

Therefore;

[tex]Width = 2\frac{1}{4}cm[/tex]

[tex]Length = x + 3\frac{1}{6}[/tex]

           [tex]=2\frac{1}{4}+3\frac{1}{6}[/tex]

            [tex]=5\frac{5}{12} cm[/tex]

Therefore; the length is [tex]5\frac{5}{12}[/tex] cm while the width is [tex]2\frac{1}{4}[/tex] cm

Answer:

On the blueprint the dimensions are 48 inches by 64 inches.

Step-by-step explanation:

Given:

The scale on blueprint was 1/4 inch = 1 foot.

The actual dimensions of her bedroom are 12 feet by 16 feet.

Now, to find the dimensions on the blueprint.

Let the dimensions on the blueprint be [tex]x[/tex] by [tex]y.[/tex]

As, given the scale on blueprint:

[tex]\frac{1}{4}\ inch=1\ foot[/tex]

So, [tex]\frac{1}{4}\ inch[/tex]  is equivalent to 1 foot.

Thus, [tex]x[/tex] is equivalent to 12 feet.

And, [tex]y[/tex] is equivalent to 16 feet.

Now, solving by cross multiplication method:

[tex]\frac{\frac{1}{4}}{1} = \frac{x}{12}[/tex]

[tex]\frac{4}{1} =\frac{x}{12}[/tex]

By cross multiplying we get:

[tex]48=x[/tex]

[tex]x=48\ inches.[/tex]

Now, again:

[tex]\frac{\frac{1}{4}}{1} =\frac{y}{16}[/tex]

[tex]\frac{4}{1} =\frac{y}{16}[/tex]

By cross multiplying we get:

[tex]64=y[/tex]

[tex]y=64\ inches.[/tex]

Therefore, on the blueprint the dimensions are 48 inches by 64 inches.

Answer:

Step-by-step explanation:

48 and 64

Answer:

x=2

Step-by-step explanation:

x2=64

Divide 2 by 2 and do the same thing to the other side 64 divided by 2. Then that leaves x=32

Answer:

x = 32

Step-by-step explanation:

x2 = x × 2

so x = 32

beacuse 64 ÷ 2 = 32

your welcome

please give me brainliest i just need 1 more!

Answer:

SOmeOne HelP Me WiTh ThIs QuEsTioN pLz

Step-by-step explanation:

The rate of increase in population is r = 12,600 people/year.

We want to find the rate of change in the population of Austin, Texas in the years between 1980 and 1990.

We will assume that this increase in population is modelled with a linear equation, remember that a general linear equation is y = ax + b.

Where the rate of change, or slope, is a.

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂) the slope is given by the formula: m=(y₂-y₁)/(x₂-x₁).

For this case we have two points, these are:

(1980, 346,000)

(1990, 472,000)

Then the slope or rate of change is (472,000-346,000)/(1990-1980)

=12,6000/10

=12,600

Therefore, the rate of increase in population is r = 12,600 people/year.

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The population of Austin, Texas in 1980 was 346,000 people. The population in 1990 was 472,000 people. What is the rate of change of the population with respect to the year for this function?

Answer:

at least two congruent sides

Step-by-step explanation:

give brainliest plz

Answer:

side WA

Step-by-step explanation:

i put sw which was wrong its (side WA) 100% ☺☺☺

Step 1) Place the non-pencil part of the compass at point W and the pencil part at point X. Draw a circle. This circle has a radius of WX.

Step 2) Keep the compass the same width, place the non-pencil part at point X and the pencil part at point W. Draw a circle. This circle has the same radius.

Step 3) The two circles intersect at two other points, A and B. One point is above WX and the other is below. Connecting AB forms the perpendicular bisector.

See the diagram below.

Answer:

The x equal 7

Answer:

X = 7

Step-by-step explanation:

21 = 3x

x = 21/3

= 7

Answer:

  A.)  zero

Step-by-step explanation:

A graph shows the two lines are parallel. Each has a slope of 3. Line A has a y-intercept of +2; Line B has a y-intercept of -2.

There are zero points of intersection.

Ratio is a comparison of two values or two quantities.

Fraction is a another form of ratio.

The first term and the second term in the ratios are important.

It should not be changed.

The first quantity value is in first term and the second quantity value is in second term of the ratio.

Ratio and fractions are same.

Example:

The ratio of male to female in the school is 5 : 6.

5 represents male students and 6 represents female students.

The fraction form of the above ratio is [tex]\frac{5}{6} .[/tex]

Answer:

  16 ft

Step-by-step explanation:

One of the other three sides is 12 ft. After that fence is subtracted from the total, there are 32 ft of fence left for the other two sides of the rectangle. That allows those sides to be 32 ft/2 = 16 ft long.

The rectangle can be 12 ft by 16 ft. The longer dimension is 16 ft.

The longer dimension of the rectangular garden is 16 feet. This is found by understanding the perimeter of a rectangle and subtracting the known side from the total fencing available before dividing the result by 2.

The subject of this question is Mathematics, specifically related to the area and perimeter of rectangles. To find the length or the longer dimension of the rectangular garden, we need to understand the concept of the perimeter of a rectangle. The perimeter is the sum of all sides of the rectangle. Here, the problem provides us with one side of the rectangle to be 12 feet and the sum of the remaining three sides to be 44 feet.

Considering that the rectangular garden has two equal longer sides and two equal shorter sides, we can say the shorter side is 12 feet. Therefore, the combined length of the other two sides (the longer sides) must be 44-12=32 feet. Because these are equal, each one is 32/2 = 16 feet.

Therefore, the longer dimension of the rectangular garden is 16 feet.

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Answer:

Answer: $67.50

Step-by-step explanation:

After 4 weeks, Macy and Robby will have same amount in their accounts.

Step-by-step explanation:

Given,

Amount saved by Macy each week = $12.50

Let,

x be the number of weeks.

M(x) = 12.50x

Amount saved by Robby each week = $7.50

Amount Robby already have = $20

R(x) = 7.50x + 20

For same amount;

M(x) = R(x)

[tex]12.50x=7.50x+20\\12.50x-7.50x=20\\5x=20[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5}=\frac{20}{5}\\x=4[/tex]

After 4 weeks, Macy and Robby will have same amount in their accounts.

Keywords: function, division

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After 4weeks, Macy and Robby will have the same amount in their bank accounts.

To determine after how many weeks Macy and Robby will have the same amount in their bank accounts, we can set up an equation based on their weekly savings and initial amounts.

Let M(t) represent Macy's savings after  t weeks, and R(t) represent Robby's savings after t weeks.

Macy's savings can be expressed as:

M(t) = 12.50t

Robby's saving can be expressed as:

R(t) = 20 + 7.50t

We want to find the number of weeks t such that  M(t) = R(t)

Setting up the equation:

12.50t = 20 + 7.50t

To solve for t, first subtract  7.50t from both sides:

12.50t - 7.50t = 20

5t = 20

Next, divide both sides by 5 to solve for t

[tex]\[ t = \frac{20}{5} \][/tex]

t = 4

Therefore, after 4weeks, Macy and Robby will have the same amount in their bank accounts.

Answer:

0.4

Step-by-step explanation:

you have to divide 2 by 5 that gives you 0.4

Answer: OPTION C.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

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

Whrere "m" is the slope and "b" is the y-intercept.

The line intersects the y-axis when [tex]x=0[/tex], therefore, you can identify from the given table that "b" is:

[tex]b=3[/tex]

Now, in order to find the slope of that line, you can follow these steps:

1. Substitute the value of "b" and the coordinates of any point from the table and into  [tex]y=mx+b[/tex]

2. Solve for "m".

Then, choosing the point (1,1), you get:

[tex]1=m(1)+3\\\\1-3=m\\\\m=-2[/tex]

Therefore, you can determine that the equation of that line in Slope-Intercept form, is:

[tex]y=-2x+3[/tex]

its c are you already dead??

Answer:

Step-by-step explanation:

first shape = 2 pieces

Second shape 12 pieces

Answer:

First Scenario-

2 of the first ones

2 of the third ones

1 of the 5th ones

2 scenario-

2 of the 4th ones

Step-by-step explanation:

i got it right

Answer:

Based on the answers I can see, it'd be all of them.

Step-by-step explanation:

When rounding to the nearest hundred, you round down if the tens are 49 or smaller (e.g. 401 to 400). If the tens are 50 or bigger, you round up (e.g. 351 to 400). I hope that helps you.

Answer: The equation has a slope of 3 and passes through the point (1,-1)

is 3 x-y=4

Step-by-step explanation:

Step 1 :-

An equation having slope 'm' and passing through the point

is [tex]y-y_{1} = m(x-x_{1} )[/tex].......(1)

Step 2:-

Now given equation slope m=3 and given point is (1,-1)

substitute these values in equation(1), we get

[tex]y-(-1)=3(x-1)[/tex]

on simplification, we get

[tex]y+1 = 3 x-3[/tex]

[tex]3 x-y=4[/tex]

Answer:

15.89

Step-by-step explanation:

You would divide 149 by 9 and get 15.88.However this 8 will keep repeating so you have to round it up.