|2w + 12| = |4x|
Hvghvvhvgbvgh

Using the Empirical Rule, the percentages are given as follows:

a) 68%.

b) 5%.

c) 0.15%.

It states that, for a normally distributed random variable, approximately:

For item a, 80 and 120 are within one standard deviation of the mean, hence:

68% of people has an IQ score between 80 and 120.

For item b, the bounds are within two standard deviations of the mean, hence 5% of the observations are outside this interval, that is:

5% of people has an IQ score less than 60 or greater than 140.

For item c, 160 is three standard deviations above the mean. Considering the symmetry of the normal distribution, 0.3/2 = 0.15% of people has an IQ score greater than 160​?.

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The probability that the sum of the 95 values is less than 7450 is 0.1002

Given Data :

An unknown distribution has a

Mean (μ) = 80

Standard Deviation (σ) = 12

Sample Size (n) = 95

is drawn from the population.

∑X ≈ N (95 * 80, [tex]\sqrt{95}[/tex] * 12)

= N (7600, 116.96)

The Probability that the sum of the 95 values is less than 7450 is given as follows :

P(∑x < 7450) = P [(∑x - μ) / s] < [(7450 - 7600) / 116.96

= P(Z < -1.282) = 0.1 (From Z table)

Hence, the probability that the sum of the 95 values is less than 7450 is 0.1002

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In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3

In the graph, we can see a parabola.

We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.

Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:

y = a*(x - h)^2 + k

In the image we can see that the vertex is (2, -3), then:

y = a*(x - 2)^2 - 3

And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:

1 = a*(0 - 2)^2 - 3

1 = a*4 - 3

1 + 3 = a*4

4/4 = a = 1

Then the quadratic equation is y = (x - 2)^2 - 3

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If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].

As per the question statement, we are provided with a mathematical expression in the form of a fraction which goes as [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex].

We are required to calculate an equivalent simplified form of the above mentioned expression.

To solve this question, we simply have to add the fractions in the denominator part and then perform a reciprocal of the overall fraction, and simplify it further in that format only, to obtain our final desired answer. The process is shown below as:

[tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\\=\frac{1}{\frac{(x+3)+(x+2)}{(x+2)(x+3)} } \\=\frac{1}{\frac{(2x+5)}{(x+2)(x+3)} }\\=\frac{(x+2)(x+3)}{(2x+5)} \\=\frac{x^{2}+3x+2x+6 }{2x+5} \\=\frac{x^{2}+5x+6 }{2x+5}[/tex]

Hence, If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].

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Answer:

$2,400,000

Step-by-step explanation:

Just multiply them together

4 x 10¹¹

Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.

400 billion in scientific notation = 4 x 10¹¹

We can complete the sentence as,

My new music player has a capacity of 4 x 10¹¹

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Answer:

$243 is his profit

Step-by-step explanation:

Answer: $4100

Step-by-step explanation:

discount = [tex]\frac{1800}{90}[/tex]×100 = 2000

profit = [tex]\frac{115}{100}[/tex]×2000 = 2300

market price = 2300 + 1800 = 4100

For the linear function x - y = 3, three ordered pairs are given as follows:

Using points (3,0) and (0,-3), the graph of the function is given at the end of the problem.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the function is:

x - y = 3.

In standard notation:

y = x - 3.

Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.

The graph of the function is given at the end of the answer.

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(1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7

From the question, we are to determine the factor by which 1.143 × 10¹ is larger than 9 × 10⁻¹

To determine how many times larger the number is, we will divide 1.143 × 10¹ by 9 × 10⁻¹

Carrying out the division operation

(1.143 × 10¹) ÷ (9 × 10⁻¹)

= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)

= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)

= 0.127 × (10¹ ⁻ ⁽⁻¹⁾)

= 0.127 × (10¹ ⁺ ¹)

= 0.127 × (10²)

= 0.127 × 10²

= 12.7

Hence, (1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7

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Answer:

$10.8

Step-by-step explanation:

First, to determine the price of one cake divide 6.30/7

You will determine one cake costs 90 cents.

So, multiply 0.90 by 12, and you get $10.8

Answer:

31 and 59

Step-by-step explanation:

We can figure this out by putting the words into an equation

"three degrees less than twice the measure of the smaller angle"

we know the smaller angle = x, so:

twice the smaller angle=2x

3 degrees less=-3

you then put those into an equation where they all add up to equal 90 and simplify

x+2x-3=90

3x-3=90

3x=93

x=31

you then plug that into the equation we would have for the second angle:

2x-3

2(31)-3

62-3

59

the first angle would be 31 and the second angle would be 59

:D

The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.

What is probability?

These generalities have been given a self-evident fine formalization in probability proposition, which is used extensively in areas of study similar to statistics, mathematics, wisdom, finance, gambling, artificial intelligence, etc.

P(sugar | oatmeal) = (7/25)(6/24) = 0.07

The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.

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Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail

We are told in the question that

Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.

From the question, the length of the Tremont Trail = 3 1/2 miles

Hence, the distance (how far )Linda has walked =

3/4 of 3 1/2 miles

= 3/4 × 3 1/2 miles

= 3/4 × 7/2 miles

= 21/8 miles

= 2 5/8 miles or 2.625 miles

Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.

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The function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -

(y - 4) - |x - 3| = 0

The modulus function can be written as follows -

|x| =  x  [for x ≥ 0]  

|x| = - x [for x < 0]

Given that a function f(x) = |x| which is shifted down by 4 units and right by 3 units. Therefore, we can write -

y = f(x) = |x|

Change in y - coordinate = y + 4.

Change in x - coordinate = x - 3.

We will plot the graph of h(x) after the doing the given changes in the coordinates.

Now, we have -

y = |x|

y - |x| = 0

Change in y - coordinate can be written as -

(y + 4) - |x| = 0

Change in x - coordinate can be written as -

(y - 4) - |x - 3| = 0

Now, the graph of both f(x) and and h(x) is attached at the end.

Therefore, the function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -

(y - 4) - |x - 3| = 0

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Answer:

i think is 7/12

because if 4/7 chose pasta,1/5 chose pizza then we add 7+5=12 then we sudstract 12-4-1 = 7.

hope that helps

The interval notation is { 5/ 2 < x > 0 }

Given the inequalities;

To determine the value of x, we have;

2x - 1 < 4

collect like terms

2x < 4 + 1

2x < 5

Make 'x' the subject

x < 5/ 2

−5x −3 > −3

collect like terms

-5x > -3 + 3

-5x > 0

x > 0

Thus, the interval notation is { 5/ 2 < x > 0 }

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The required cost is $ 101.22.

This problem can be solved by unitary method.

Given that monthly cost of customer if he uses 410 minutes is $71.

So, cost per minute = [tex]\frac{71}{410}[/tex]

                               =$ 0.17

And if the customer uses 720 minutes then the cost is $118.

So, cost per minute is = [tex]\frac{118}{720}[/tex]

                                   =0.16

Now if he uses 687 minutes then for 410 minutes cost incurred will be

= 410 × 0.17

= $ 69.7

And for next 197 minutes cost incurred will be = 197 × 0.16

                                                                         = $ 31.52

Total cost for 687 minutes = $(69.7 + 31.52)

                                         = $ 101.22

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There is a difference between the expressions -x/y and -x/-y

The expressions are given as:

-x/y and -x/-y

When the expression -x/-y is evaluated, we have:

-x/-y = x/y

This means that

-x/y = -x/y

-x/-y = x/y

When the above expressions are compared, we can see that both expressions are not equal

Hence, there is a difference between the expressions -x/y and -x/-y

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The total amount of each ingredient are as follows;

Pears = 1/2 pound

Grapes = 3/8 pounds

Pineapple = 3/4 pounds

Oranges = 3/8 pounds

We are given the amounts of fruits as;

4 pounds of pears

3 pounds of grapes

6 pounds of pineapple

3 pounds of oranges

Now, total pounds of fruits = 4 + 3 + 6 + 3 = 16 fruits

Ratio of pears = 4/16 = 1/4

Ratio of grapes = 3/16

Ratio of pineapple = 6/16 = 3/8

Ratio of oranges = 3/16

Thus. amount of each ingredient required are;

Pears = 1/4 * 2 = 1/2 pound

Grapes = 3/16 * 2 = 3/8 pounds

Pineapple = 3/8 * 2 = 3/4 pounds

Oranges = 3/16 * 2 = 3/8 pounds

Thus, the total amount of each ingredient are as follows;

Pears = 1/4 * 2 = 1/2 pound

Grapes = 3/16 * 2 = 3/8 pounds

Pineapple = 3/8 * 2 = 3/4 pounds

Oranges = 3/16 * 2 = 3/8 pounds

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The probability that both of the boxes one would select had the decoder ring is 9.9%.

Given, the store manger gives the surety that 19 out of 59 boxes on the shelf have the secret decoder ring.

The boxes on the shelf which have a different gift inside is = 40 boxes.

If one randomly selects two boxes from the shelf to purchase, the probability that both of them have the secret decoder ring = ?

You can imagine that someone used invisible link to label each box with a number, and knows that boxes number 1 through 19 have decoder rings, while boxes number 20 through 59 have other gifts.

There are 59×58/2

= 3422/2

= 1711 possible sets of two boxes that one could select, but there are only 19 × 19/2

= 342/2

= 171 possible sets of two boxes with decoder rings.

The fraction of possible pairs of boxes where both boxes have the secret decoder ring is:

= 171/1711

= 0.099 = 9.9%

Hence there is 9.9% probability that both of the boxes one might select had a decoder ring.

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(a) The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) The slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec². The slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Both are walking at a velocity of 7.2 ft/sec at t=8 sec.

What is velocity?

(a) For Alicia,

m=(Δv/Δt)=(8-4)/(10-0)=4/10=0.4

f(t)=0.4t+4

for Damon,

m=(Δv/Δt)=(9-0)/(10-0)=9/10=0.9

g(t)=0.9t

The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) Value and meaning of the slope is

m for Alicia =0.4

Slope is determined (Δv/Δt)=(8-4)/(10-0)=4/10=0.4 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec².

m for Damon=0.9

Slope is determined (Δv/Δt)=(9-0)/(10-0)=9/10=0.9 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Value and meaning of the average rate of change on the interval:

the average rate of change of Δ on the interval [4,8] =

[tex]\frac{Velocity\ at\ 8\ sec - Velocity\ at\ 4\ sec}{Time\ interval\ (8-4)\ sec}[/tex]

=(7.2-3.6)/(8-4)=(3.6/4)=0.9 ft/sec²

So, Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Let both are walking with the same velocity at t sec.

So, Let's equate their velocities

0.4t+4=0.9t

t=4/0.5 = 8 sec

The velocity of Alicia at 8 sec = 0.4(8)+4 = 7.2 ft/sec

The velocity of Damon at 8 sec = 0.9(8) = 7.2 ft/sec

So, both are walking at a velocity of 7.2 ft/sec at t=8 sec.

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Answer:

Only one equation fits all the information on the table which is:

y = 1/6x

Answer:

y = 1/6x

Step-by-step explanation:

To find the equation, let's see if each option works by plugging in x into each equation.

y = –1/4x

Plug -6 into x

y = –1/4(-6)

y = 1.5

y = –1/4x doesn't work because we didn't get -1.

y = 6x

Plug -6 into x

y = 6(-6)

y = -36

y = 6x doesn't work because we didn't get -1.

y = 1/6x

Plug 1/6x into x

y = 1/6(-6)

y = -1

Let's see if the other x values work.

Plug 0 into x

y = 1/6(0)

y = 0

Plug 12 into x

y = 1/6(12)

y = 2

y = 1/6x works.

y = –2x

Plug -6 into x

y = –2(-6)

y = 12

y = -2x doesn't work because we didn't get -1.

y = 1/6x is the only linear equation that worked and got all y values, so that is your answer.

Hope that helped and have a lovely rest of your day!

The length and width of rectangle is 10 feet and 4.5 feet.

This problem is related to the area and perimeter of plane figures. We have to find the dimensions of the rectangle using the data given.

Given, the length is 1 feet more than twice the width.

Let the width be a feet.

So, length = (2a+1) feet

Now according to question,

   [tex](2a+1)(a)=45\\[/tex]

⇒ [tex]2a^{2} +a-45=0[/tex]

On solving the above quadratic equation we get a=4.5 feet.

So, length = 10 feet.

The dimension of rectangle is 10 feet × 4.5 feet.

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the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps

Step-by-step explanation:

15 * 3 = 45

45 + 15 = 60

Answer: I just points so rate this a 10

Step-by-step explanation:

Answer:

owi4w85e963696w95witote5iw47e

The equation  equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4. Option E

This is further explained below.

Generally,   the equations equivalence is  mathematically given as

-2m - 5m - 8 = 3 + (-7) + m

Therefore

-7m - 8 = 3 + (-7) + m

When we write the equation such that the variable appears on the right-hand side first, we get the following:

-7m - 8 = m - 4

In conclusion, The equation  equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4.

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Answer:

 I think the answer is 9.920 please be careful with your answer I think it 9.920 because it says nine hundred and ninety two thousands so therefor the decimal need to be in between 9 and 9 I hope you get this correct!

step-by-step explanation: