If 2+2=44 and 3+3= 96 and 4+4=168 and 5+5=2510 then what is 6+6=?

Answer:

[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]

And we can use the complement rule and the normal standard distribution or excel and we got:

[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(100,15)[/tex]  

Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]

We select a sample of n = 50 and we want to find the probability that:

[tex]P(\bar X >104)[/tex]

Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}} [/tex]

And using this formula we got:

[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]

And we can use the complement rule and the normal standard distribution or excel and we got:

[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]

Answer:

9

Step-by-step explanation:

In order to round to the nearest ten you must think: what is the nearest multiple of 10. For example, to round 68 to the nearest 10, the nearest whole number is 70, so the answer would be 70. However if you were to round 63 to the nearest 10, to would be 50 since that is the nearest multiple of 10

Answer:9

Step-by-step explanation:

Since the next number is below five you don’t round up it just stays the same

Answer: A) 5/2

B) 10pi for A and 4pi for B

C) 5/2

Step-by-step explanation:

Please find the attached file for the solution

Answer:

(0.3,3)

Step-by-step explanation:

That is the vertex.

Answer:

[tex]15\,\,kg/cm^2[/tex]

Step-by-step explanation:

Given:

The volume of a gas "V" varies inversely with the pressure "P" put on it.

Volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex]

To find:

pressure when volume is 480 [tex]cm^3[/tex]

Solution:

As  of a gas "V" varies inversely with the pressure "P" put on it,

[tex]V=\frac{k}{P}[/tex]

Here, k is a constant

As volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex], put [tex]V=360\,,\,P=20[/tex]

[tex]360=\frac{k}{20}\\k=360\times 20\\=7200[/tex]

So,

[tex]V=\frac{7200}{P}[/tex]

Put [tex]V=480[/tex]

[tex]480=\frac{7200}{P}\\P=\frac{7200}{480}\\=15\,\,kg/cm^2[/tex]

Answer:

Answer:

x=31

Step-by-step explanation:

(x-31)/4=0

multiply each side by 4 so that you have x-31=0.

x-31=0

add 31 to each side.

x=31

Answer:

No, unless you set it equal to zero.

Step-by-step explanation:

(x-31)/4=0

((x-31)/4) times 4 = 0 times 4

x-31=0

x-31 +31 =0 + 31

x=31

Answer:I think it is 226

Step-by-step explanation:

85/2= 42.5 then 268 - 42.5= 225.5 then round it and you get 226

Answer:

A,B and C

Step-by-step explanation:

Answer

a,b,c are the correct answer

Step-by-step explanation:

hope it helps you my luvs

Answer:

20.00+12.76 would give you that sum

Step-by-step explanation:

Answer:

0.00+12.76 would give you that sum

Step-by-step explanation:

Pls BRAINLIEST

Answer: B

Step-by-step explanation:

The reflection transformation in the second figure shows the correct reflection.

There are three types of translations -

Given is a triangle ΔDEF.

Therefore, the reflection transformation in the second figure shows the correct reflection.

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Answer:

Step-by-step explanation:

Answer:

c .54 w/ bar

Step-by-step explanation:

Answer:

g = 8

Step-by-step explanation:

We're going to isolate g to find out what it equals, so we have to divide both sides by 6.

6g=48

__   __

6     6

g = 8

The solution to the equation 6g = 48 is g = 8.

In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical equation:

6g = 48

By dividing both sides of the equation by 6, we have:

g = 48/6

g = 8

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Answer:

1/2

Step-by-step explanation:

Answer:

650

Step-by-step explanation:

2sf= the first two figures

so you count to the first two sf numbers so in this case

it would be 64 then you look at the next one.  But if it is 4 or below  you round or if it is 5 and above you rounded up

in this case the third digit is a 6 so you would round up to 5

answer =650

The number 646.42 can be rounded to two significant figures by increasing the second significant figure up by one because the third figure is 6 which is greater than 5. Therefore, 646.42 becomes 650.

You are requesting to round the number 646.42 to two significant figures (SF). Significant figures are the meaningful digits in a number. For example, in 646.42, there are five significant figures: 6, 4, 6, 4, 2.

To round to two significant figures, we look at the number in the third position, which is another 6. If this number is 5 or greater, we round the second significant figure up. If it is less than 5, we keep the second figure the same. Here, the next number after the two significant figure (6 and 4) is 6, which is more than 5, so you will round 4 up to 5.

Thus, rounded to two significant figures, 646.42 becomes 650.

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Answer:

D

Step-by-step explanation:

2  ( x − 3 )

x  ( x + 1 )

Answer:

ANSWER IS D

Step-by-step explanation:

Answer:

multiply all the numbers

Step-by-step explanation:

Answer:

Option (a).

Step-by-step explanation:

It is given that 3n is an odd number.

We need to find an even number from the given options.

Even numbers: Which are divisible by 2.

Odd numbers: Which are not divisible by 2.

We need know that the numbers are alternatively even and odd.

If we add or subtract 1 from an odd number, we always get an even number.

If we add or subtract 2 from an odd number, we always get an odd number.

3n is an odd number. So,

3n-1 is an odd number.

3n+2 is an even number.

3n+2 is an even number.

3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.

Therefore, the correct option is (a).

The 90% confidence interval = 48.603 < μ < 55.397

Explanation:

Given:

Mean = 52

Standard deviation = 14.6

Sample size, n = 50

Confidence Interval, c = 90%

                                  c = 0.9

Significance level, α = 1 - c

                                  = 1 - 0.9

                                  = 0.1

Critical value, z(α/2) = z(0.05) = 1.645

Critical value = ± 1.645

Margin of error, E = [tex]z(\alpha /2) X \frac{SD}{\sqrt{n} }[/tex]

                             [tex]=1.645 X\frac{14.6}{\sqrt{50} } \\\\= 3.3965[/tex]

Limits of 90% confidence interval are given by:

Lower limit = μ - E

                  = 52 - 3.397

                  = 48.603

Upper limit = μ + E

                  = 52 + 3.397

                  = 55.397

Thus, 90% confidence interval = 48.603 < μ < 55.397

Answer:

[tex]177 \frac{7}{9} cm^2[/tex]

Step-by-step explanation:

Length of the Plastic Sheet= 96cm

Width of the plastic Sheet =70cm

If a square of side x is cut from each corner of the plastic sheet to form the box.

Length of the box=96-2x

Width of the box=70-2x

Height of the box =x

Volume of the box = LWH

Volume=(96-2x)(70-2x)x

The maximum volume of the box is obtained at the point where the derivative is zero.

[tex]V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)[/tex]

Setting the derivative to 0.

[tex]4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}[/tex]

Since we are looking for the minimum value of x,

[tex]x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2[/tex]

We want to find the length of the light beam from the ship to Nicole.

We will see that the solution is 4,585.76 ft.

We can think of this situation as in a right triangle. The adjacent cathetus is the distance between the lighthouse and the ship. The opposite cathetus is the difference in height between Nicole's position and Nick´s position, it is equal to:

250ft - 10ft = 240ft

And the elevation angle is equal to 3°. So we know the angle and the opposite cathetus to this angle, and we want to find the hypotenuse, which is the length of the light beam.

Then we can use the relation:

Sin(θ) = (opposite cathetus)/(hypotenuse)

Solving it for the hypotenuse we get:

hypotenuse = (opposite cathetus)/sin(θ)

Replacing by the values that we know, we get:

hypotenuse = 240ft/sin(3°) = 4,585.76 ft

The length of the line of sight is 4,585.76 ft

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To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We are given the angle of elevation of the light, the height of the cliff, and need to calculate the length of the line of sight.

To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We have a right triangle formed by the line of sight, the height of the cliff, and the distance from the ship to Nicole. We are given the angle of elevation of the light as 3° and the height of the cliff as 250 feet. Let's denote the length of the line of sight as x and the distance from the ship to Nicole as d. Using the tangent function, we can write:

tan(3°) = 250 / d

Simplifying this equation, we have:

d = 250 / tan(3°)

Now we can substitute the value of tangent of 3° and solve for d. Using a calculator, we find that:

d ~ 8424.78 feet

So, the length of the line of sight from the ship to Nicole is approximately 8424.78 feet.

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Answer:

It would take 27.5 minutes the element to decay to 154 grams.

Step-by-step explanation:

The decay equation:

[tex]\frac {dN}{dt}\propto -N[/tex]

[tex]\Rightarrow \R\frac {dN}{dt}=-\lambda N[/tex]

[tex]\Rightarrow \frac {dN}N=-\lambda dt[/tex]

Integrating both sides

[tex]\Rightarrow \int \frac {dN}N=\int-\lambda dt[/tex]

[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]

When t=0, N=[tex]N_0[/tex] = initial amount

[tex]ln|N_0|=-\lambda .0+c[/tex]

[tex]\Rightarrow c=ln|N_0|[/tex]

[tex]ln|N|=-\lambda t+ln|N_0|[/tex]

[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex]

Decay equation:              

                    [tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

Given that, the half life of of element X is 11 minutes.

For half life, [tex]N=\frac12 N_0[/tex],  t= 11 min.

[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11[/tex]

[tex]\Rightarrow ln|\frac12}|=-\lambda . 11[/tex]

[tex]\Rightarrow -\lambda . 11=ln|\frac12}|[/tex]

[tex]\Rightarrow \lambda =\frac{ln|\frac12|}{-11}[/tex]

[tex]\Rightarrow \lambda =\frac{ln|2|}{11}[/tex]                [ [tex]ln|\frac12|=ln|1|-ln|2|=-ln|2|[/tex] , since ln|1|=0]

N=154 grams, [tex]N_0[/tex] = 870 grams, t=?

[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t[/tex]

[tex]\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}[/tex]

      =27.5 minutes

It would take 27.5 minutes the element to decay to 154 grams.

Answer:

60.6 minutes

Step-by-step explanation:

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

Answer:

f(4) = -11

If g(x) = 2 then x = 0

Step-by-step explanation:

here it asks to determine graphically, so we need to use the provided graph:

f(4) = -11 ( just notice the y-coordinate of the point of x-coordination 4)

If g(x) = 2 then x = 0 (just notice the x-coordinate of the point of y-coordination 2)

The rate of the passenger train is 100 miles per hour.

Given:

1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.

2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.

We can set up equations based on the distances traveled and the rates:

1. For the passenger train:

[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]

Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]

So, the rate of the passenger train is 100 miles per hour.

Answer:

(1) The coefficient of x in this expression is -10.

(2) The value of the expression for x = 15 is -9.

Step-by-step explanation:

(1)

A coefficient is a numerical value that is placed before a variable or is multiplied by the variable in an algebraic equation.

For example, in the algebraic equation 4x² + 5y the coefficient of variable y is 5.

The expression given is:

1 - 10 x + 4 y

The coefficient of x in this expression is -10.

(2)

The expression provided is:

[tex]f(x)=\frac{1}{5}x - 12[/tex]

Compute the value of the expression for x = 15 as follows:

[tex]f(x)=\frac{1}{5}x - 12\\=(\frac{1}{5}\times 15) - 12\\=3-12\\=-9[/tex]

Thus, the value of the expression for x = 15 is -9.

Answer:

y = 1/3

Step-by-step explanation:

Answer:

140 individuals were surveyed

42 people are planning on going to the mountains

Step-by-step explanation:

The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.

If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:

[tex]21=n*0.15\\n=140\ individuals[/tex]

140 individuals were surveyed

Since 30% responded "the mountains", the number of people planning on going to the mountains is:

[tex]m = 140*0.30\\m=42\ people[/tex]

42 people are planning on going to the mountains

Answer:

12

Step-by-step explanation:

f(x)=3x+9

f(12) = 3*12 +9

       36+9

        45

f(8) = 3*8+9

     =24+9

     = 33

f(12) - f(8) = 45-33

                    12

Answer:

1.84ft

Step-by-step explanation:

From the figure attached,

AB = Height of the window = 15ft

Let the distance between the base of the housr and the fence 'C' = xft

If the angle of depression = 7°

Then angle of elevation of the top of the fence from the house = 7°

Now from right triangle ABC,

tan7° = x/15

x = tan7°×15

x = 0.1227×15

x = 1.84ft

Therefore, distance of the house from the fence is 1.84ft

Answer: ACE

The radius of the cone is 9 units

The height of the cone is 12 units

The volume of the cone is represented by the expression 1/3 pie (9)2(12)

Step-by-step explanation: