The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.
Part A
Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun.
Express your answer using two significant figures.
Part B
The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.
Express your answer using two significant figures.
Part D
Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?
Express your answer using two significant figures.

Answer:

3√2

Step-by-step explanation:

If you draw the diagonal, you have a 45°45°90° triangle.

The two legs are 3, so the hypotenuse is 3√2

Answer:

Option A.

The heartbeat has a pattern of 60 + (5 x minutes) and linear graphs are straight. The only way the linear graph is straight if there is a pattern.

Step-by-step explanation:

Answer:

Area of the figure = 254.5 cm²

Step-by-step explanation:

Area of rectangle = Length × Width

Area of triangle = 1/2(base × Height)

Dividing the figure into parts for convenience

So,

Rectangle 1  (the uppermost):

4 × 6 = 24 cm²

Rectangle 2 (below rectangle 1):

15 × 8 = 120 cm²

Rectangle 3 (with rectangle 2):

11 × 4 = 44 cm²

Triangle 1 :

1/2(7 × 19) = 133/2 = 66.5 cm²

Now adding up all to get the area of the figure:

Area of the figure = 24 + 120 + 44 + 66.5

Area of the figure = 254.5 cm²

Answer:

Step-by-step explanation:

On the y-axis, graph the point on (0,4). Then from there, go up one, and to the right 4.

Answer:

Unable to read entire question, but see explanation for answer

Step-by-step explanation:

First, you need to find the unit rate per dog. If it takes 3 dogs 10 days to finish 30 pounds of food, then it takes 1 dog 1 day to finish 1 pound of food. I cannot read the entirety of the question because of the cropping, but you can find how much food a single dog eats in that amount of days by just multiplying by the number of days (say, 1 pound in 1 day, or 3 pounds in 3 days). Hope this helps!

Answer:

1

Step-by-step explanation:

took test

Answer:

y= 359 x+1500

Step-by-step explanation:

find the slope  m= (2577-1859)÷(3-1) = 359

y=mx+b

find b : substitute x ,y, and m

get b = 1857 - 359*1 = 1500

Answer:

y= 359 x+1500

Step-by-step explanation:

Answer:

[tex]74.8m[/tex]

Step-by-step explanation:

[tex]A=a^2\\P=4a\\P=4\sqrt{A} \\=4*\sqrt{349.69} \\=74.8m[/tex]

Answer:

The third degree polynomial function = x³ + 27x² + 200x + 300

Step-by-step explanation:

The third-degree polynomial function has zeros −2 and −15.

From the above, we have been given two factors of the polynomial function. Let's derive the factors from the two zeros of the polynomial given.

The two given zeros of the polynomial can be written as:

x= -2

x+2 = 0

(x+2) is a factor of the polynomial

x= -15

x+15 = 0

(x+15) is a factor of the polynomial

So we have two factors of the polynomial (x+2) and (x+15). But since it is a third degree polynomial, we have to find the third factor.

Let (x-b) be the third factor and f(x) represent the third degree polynomial

f(x) = (x-b) (x+2) (x+15)

Expanding (x+2) (x+15) = x² + 2x + 15x + 30

(x+2) (x+15) = x² + 17x + 30

f(x) = (x-b) (x² + 17x + 30)

From the given information, a value of 1,170 is obtained when x=3

f(3) = 1170

Insert 3 for x in f(x)

f(3) = (3-b) (3² + 17(3) + 30)

1170 = (3-b) (9 + 51 + 30)

1170 = (3-b) (90)

1170/90 = 3-b

3-b = 13

b = 3-13 = -10

Insert value of b in f(x)

f(x) = [x-(-10)] (x² + 17x + 30)

f(x) = (x+10) (x² + 17x + 30)

f(x) = x³ + 17x² + 30x + 10x² + 170x + 200x + 300

f(x) = x³ + 27x² + 200x + 300

The third degree polynomial function = x³ + 27x² + 200x + 300

Answer:

Step-by-step explanation:

3/4=24 so 1/4= 24÷3= 8

1/4=8

So to get 4/4 or Cameron's age it is 8×4=32yrs

[tex]answer \\ 32 \: years \: old \\ solution \\ mary's \: age = 24 \\ let \: cameron's \: age \: be \: x \\ given \\ \frac{3}{4} x = 24 \\ or \: x = 24 \times \frac{4}{3} \\ x = 32 \\ hope \: it \: helps[/tex]

Answer:

There is no correlation between age and purchase price

Step-by-step explanation:

In the survey, the researcher found out that a younger customer will not necessarily purchase a lower or higher priced computer thing it is likely true that there might be no correlation between purchase price and age.

It assumes that a younger customer can buy either buy a lower priced computer or can also buy a higher priced if he or she has the money for it.

Answer:

After 121 passes, there will be 11 cups facing up

Step-by-step explanation:

Given that:

Peter initially  lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.

We can have an inequality ; i.e 1 ≤ n ≤  121; if n represents the divisor including n itself for which n  = odd number. Thus at the end of this claim, the cup will be facing up.

On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)

For each divisor on the ith pass of n;

[tex]i \ th \ pass \ = \ n \ \to \ p |n[/tex]  since we are dealing with possibility of having an odds number:

Thus; [tex]p =i[/tex] and [tex]i^2 = n[/tex]  where ; n = perfect square.

Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes

Answer:

[tex] y = \frac{4}{3} - 5[/tex]

Step-by-step explanation:

[tex] - 3y = 15 - 4x \\ - 3y = - 4x + 15 \\ \\ y = \frac{ - 4x + 15}{ - 3} \\ \\ y = \frac{ - 4}{ - 3} x + \frac{15}{ - 3} \\ \\ y = \frac{4}{3} x - 5 \\ which \: is \: in \: slope - intercept \: form.[/tex]

Answer:

s = 4.43

Step-by-step explanation:

Using formula for bigger circle

s =r∅

Where s is the Arc length, r is rdius and ∅ is theta(angle)

8.84=5∅

∅= 8.84/5

Angle = 1.77 radians

So both angles equal to 1.77 radians

Now again

Using formula

s = r∅

Where s is the Arc length, r is rdius and ∅ is theta(angle)

s = (2.5)(1.77)

s ≈ 4.43

Answer:

D

Step-by-step explanation:

In a 30-60-90 triangle, the longer leg is [tex]\sqrt{3}[/tex] times larger than the smaller leg. The length of the shorter leg is therefore:

[tex]\dfrac{18}{\sqrt{3}}= \\\\\\\dfrac{18\sqrt{3}}{3}= \\\\\\6\sqrt{3}[/tex]

Hope this helps!

Answer & Step-by-step explanation:

For this problem we can just set up an equation and equal it to 180.

(2y) + (y + 10) + 50 = 180

Combine like terms.

3y + 60 = 180

Subtract 60 from 180.

3y = 120

Divide 120 by 3.

y = 40

So, the value of y is 40°

Answer:

670

Step-by-step explanation:

2003-814=1189

1189-519=670

Answer: The third number is 670.

Step-by-step explanation:

The sum means three numbers being added up is equal to 2003 so give two of those numbers you have to add them up and subtract it from 2003 to find the third number.

814 + 519 + x = 2003   where x is the third number

1333 + x = 2003

-1333          -1333  

  x = 670   So the third number is 670

Check:  

 814 + 670 + 519 = 2003

     2003 = 2003   so yes again 670 is the third number.

Answer: i did the question i told you the steps

Step-by-step explanation:

From the starting point move three to the left. Then move four down. Then move three times to the left. Lastly move two down.

Answer:

[tex]192ft^2[/tex]

Step-by-step explanation:

The model of a patio was made by

using 1/2 inch square title=4 square feet.

area represented by the 8 *6 model can be calculated as follows;

FIRSTLY, the number of tiles in the 8 *6 model can be calculated by multiplying it i.e

8 *6 model =[tex]48 tiles[/tex]

Hence there are 48 tiles in 8 *6 model

It was given that 1/2 inch square title=4

square feet.

So to calculate the total Area occupied by the 48 tiles

[tex]Area=1/2×48[/tex]

[tex]Area=24inches^2[/tex]

If [tex]1/2inches^2=4ft^2[/tex] ( from the question)

Let X represent [tex]24inches^2[/tex]

Then, [tex]24inches^2=Xft^2[/tex]

Cross multiply

[tex]4×24=X×1/2

X=4×24×2

X=[tex]192ft^2[/tex]

[tex]24inches^2=[tex]192ft^2[/tex]

Therefore, the area represented by the 8 *6 model is [tex]192ft^2[/tex]

Answer:

[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]

[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]

And we can find the probability with this difference:

[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] n = 171[/tex] represent the sample size

[tex]p =0.39[/tex] the proportion of interest

We want to find the following probability:

[tex] P( 0.21 < \hat p < 0.32)[/tex]

We can use the normal approximation for this case since np >10 and n (1-p) >10

For this case we know that the distribution for the sample proportion is given by:

[tex]\hat p \sim N( p , \sqrt{\frac{p (1-p)}{n}} )[/tex]

And we can use the following parameters:

[tex] \mu_{\hat p}= 0.39[/tex]

[tex] \sigma_{\hat p} =\sqrt{\frac{0.39*(1-0.39)}{171}}= 0.0373[/tex]

And we can apply the z score formula given by:

[tex] z = \frac{p \\mu_{\hat p}}{\sigma_{\hat p}}[/tex]

And using this formula we got:

[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]

[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]

And we can find the probability with this difference:

[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]

Answer:

Step-by-step explanation:

The answer is 3x 987 colunm 2

Answer:

The trip will take 36 minutes.

Step-by-step explanation:

This question can be solved using a rule of three.

The boat maintains a constant speed of 15 knots (nautical miles per hour). How many minutes it will take to return to its home port 9 nautical miles away?

So in 60 minutes, 15 nautical miles. How many minutes for 9 nautical miles?

60 minutes - 15 nautical miles

x minutes - 9 nautical miles

[tex]15x = 60*9[/tex]

[tex]x = \frac{60*9}{15}[/tex]

[tex]x = 36[/tex]

The trip will take 36 minutes.

Answer:

0.5 = 50% of bottles have volumes less than 1,007 mL

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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 1007[/tex]

What proportion of bottles have volumes less than 1,007 mL?

This is the pvalue of Z when X = 1007. So

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

[tex]Z = \frac{1007 - 1007}{\sigma}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

0.5 = 50% of bottles have volumes less than 1,007 mL

Answer:

a) The value of absolute minimum value = - 0.3536  

b) which is attained at   [tex]x = \frac{1}{\sqrt{2} }[/tex]  

Step-by-step explanation:

Step(i):-

Given function

                       [tex]f(x) = \frac{-x}{2x^{2} +1}[/tex]     ...(i)

Differentiating equation (i) with respective to 'x'

                     [tex]f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2} }[/tex]   ...(ii)

                    [tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} }[/tex]

Equating Zero

                   [tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]

                 [tex]\frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]

                [tex]2 x^{2}-1 = 0[/tex]

               [tex]2 x^{2} = 1[/tex]

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

             [tex]x = \frac{-1}{\sqrt{2} } , x = \frac{1}{\sqrt{2} }[/tex]

Step(ii):-

Again Differentiating equation (ii) with respective to 'x'

[tex]f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4} }[/tex]

put

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

[tex]f^{ll} (x) > 0[/tex]

The absolute minimum value at   [tex]x = \frac{1}{\sqrt{2} }[/tex]

Step(iii):-

The value of absolute minimum value

                         [tex]f(x) = \frac{-x}{2x^{2} +1}[/tex]

                       [tex]f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}[/tex]

         on calculation we get

The value of absolute minimum value = - 0.3536      

Final answer:-

a) The value of absolute minimum value = - 0.3536  

b) which is attained at   [tex]x = \frac{1}{\sqrt{2} }[/tex]    

In polar coordinates, the inequality changes to

[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]

which is a circle of radius 2 and centered at (2, 0). The set D is then

[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]

The integral is then

[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]

[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]

There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,

[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]

so that the integral is

[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]

[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]

Then invoke another double-angle formula,

[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]

to change the integral to

[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]

[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]

Answer:

odd numbers always end in 1,3,5,7 and 9

odd numbers - 51,23,95,11,67,75,83, and 29

even numbers - 16,32,38,76,62,40 and 80

19p                                  25p                                         16p

9 - 2p , 1 - 1p                   12- 2p, 1- 1p                          5- 2p, 6- 1p

19 - 1p                              10 - 2p, 5- 1p                       6 - 2p, 2- 1p

7- 2p , 5- 1p                    8- 2p, 9- 1p                          4- 2p, 8- 1p

                                       9- 2p, 6- 1p                         6- 2p, 4- 1p

Answer:

LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2

Step-by-step explanation:

Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2

unlike terms 3ad&2bd, 5x&5, -4p&p^2

Step-by-step explanation:

passed

Answer:

Step-by-step explanation:

Answer:

Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.

Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Within what limits do the active minutes for 95% of the people in each group fall

By the Empirical Rule, within 2 standard deviations of the mean.

Mildly obese:

Mean = 373, standard deviation = 61.

373 - 2*61 = 251 minutes

373 + 2*61 = 495 minutes

Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.

Lean people:

Mean = 525, standard deviation = 104

525 - 2*104 = 317 minutes

525 + 2*104 = 733 minutes

Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.

Answer:

61.76 ft^2

Step-by-step explanation:

First find the area of the rectangle without the circle

A = l*w = 14*8 =112

Then find the area of the circle

The diameter is 8 so the radius is 8/2 =4

A = pi r^2 = 3.14 * 16 =50.24

The shaded region is the rectangle minus the circle

112-50.24 =61.76 ft^2