Noah made 12 \text{ kg}12 kg of trail mix for his family's hiking trip. His family ate 8600 \text{ g}8600 g of the trail mix on the hiking trip. How many grams of trail mix did Noah have left?

Answer:

It is 80

Step-by-step explanation:

This because of when we divided the number 400 by 15 we got 26.6' an infinite number this is how many times the survey 12/15 was taken then if we then times this by 3 we get 80 which is the amount of people who prefer their own dinner

Answer:

[tex]\sqrt{85}  or 9.22[/tex]

Step-by-step explanation:

You need to remember the following equation:

[tex]a^{2} + b^{2} = c^{2}[/tex]

Where a and b is the lengths of the two sides and c is the hypotenuse.

So simply plug these values into this:

[tex]6^{2} + 7^{2} = h^{2}[/tex]

36 + 49 = h^2

36 + 49 = 85

So the hypotenuse is the square root of 85:

[tex]\sqrt{85}  = 9.22[/tex]

The slope-intercept form of the line passing through the point (7, -2) and parallel to the line y = -8x - 4 is y = -8x + 54. The required answer is y = -8x + 54.

To find the slope-intercept form of a line parallel to the given line, we need to determine the slope of the given line first.

The given line has a slope of -8 since it is in the form y = mx + b, where m represents the slope.

Since the line we are looking for is parallel to the given line, it will have the same slope of -8.

Now, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (7, -2) with a slope of -8:

y - y1 = m(x - x1)

Substituting the values of the point and slope:

y - (-2) = -8(x - 7)

Simplifying:

y + 2 = -8x + 56

Rearranging the equation to the slope-intercept form:

y = -8x + 54

Therefore, the slope-intercept form of the line passing through the point (7, -2) and parallel to the line y = -8x - 4 is y = -8x + 54. The required answer is y = -8x + 54.

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Answer:

The balance after 15 year is  $831.25 .

Step-by-step explanation:

Formula

[tex]Amount = P (1 + r)^{t}[/tex]

Where P is the principle and r is the rate of interest in the decimal form and t is the time.

As given

Caiden earned $475 from mowing lawns last summer.

He deposited this money in an account that pays an interest rate of 3.8% compounded annually.

Here

P = $475

3.8% is written in the decimal form.

[tex]= \frac{3.8}{100}[/tex]

= 0.038

r = 0.038

t = 15 years

Put in the formula

[tex]Amount = 475 (1 + 0.038)^{15}[/tex]

[tex]Amount = 475 (1.038)^{15}[/tex]

[tex]Amount = 475\times 1.75(Approx)[/tex]

Amount = $831.25

Therefore the balance after 15 year is  $831.25 .

Caiden will have approximately $850.91 in his account after 15 years of interest compounded annually at a rate of 3.8%.

In this problem, we're dealing with compound interest, not simple interest. The formula to calculate compound interest is: A = P (1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest; P is the principal amount (the initial money); r is the annual interest rate (in decimal); n is the number of times that interest is compounded per year; and t is the time the money is invested for in years. In this case, P equals $475, r equals 3.8/100 or 0.038 (transforming percentage to decimal), n is 1 (because the interest is compounded annually), and t is 15 years. Substituting these values into the formula gives: A = $475 (1 + 0.038/1)^(1*15). Calculate the bracketed part first, resulting in a figure around 1.038 and raise it to the power of 15, so we get a value around 1.7914. Multiply this by the initial amount of $475 to get the final balance after 15 years which will be approximately $850.91. Hence, Caiden will have $850.91 in his account after 15 years.

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Answer:

l = 20.5 cm

h = 17.5 cm

w =  9.5 cm

Step-by-step explanation:

Conditions

l+w =30     Solving for w     30 - l = w

h = l-3

V = l*w*h

Substituting in

V = l * (30-l) * (l-3)

   = (30l-l^2) (l-3)

   = 30 l^2 - l^3 - 90l + 3l^2

Combining like terms

Step-by-step solution

-l^3 + 33 l^2 - 90 l

To find the maximum we need to take the first derivative and then set it equal to zero

-3l^2 + 66l -90 = 0

Factor out a -3

-3 (l^2 -22l +30) =0

Using my calculator and the quadratic formula

l = 11 - sqrt(91)

l = 11 + sqrt(91)

l = 1.5 or 20.5  approximately

If l = 1. then

h= l-3   would be negative  so

l = 20.5

h = l-3

h = 17.5 approximately

w = 30-l = 9.5 approximately

Answer:

y = 0x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = 0 and c = 9, hence

y = 0x + 9

The equation of a horizontal line is normally written as y = 9

with the x- term omitted

The equation of a line with a slope of 0 and a y-intercept of 9 is y = 9, which represents a horizontal line on the graph.

The student is asking about the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Given that the slope (m) is 0, and the y-intercept (b) is 9, the equation of the line is simply y = 0x + 9. Since any number multiplied by zero is zero, this simplifies to y = 9.

Therefore, the equation of the line with a slope of 0 and a y-intercept of 9 in slope-intercept form is y = 9. This represents a horizontal line that crosses the y-axis at 9.

Answer: length = 7 c, and width = 6 cm

Step-by-step explanation:

Choose a graph from the list of graph, like in the picture.

I hope this helps, sorry for my messy handwriting. If you have any questions feel free to ask me!

Plug the coordinates of the point in the equation and solve for b:

[tex] y=bx-2 \iff -3=4b-2 \iff 4b=-1 \iff b=-\dfrac{1}{4} [/tex]

Answer:

Step-by-step explanation:

Subtract the 680 from 960, then divide the product by 52000 to get the answer

Answer:

A F(x)=30x

Step-by-step explanation:

just plug number in to the equations to see which one matches

Answer: [tex]f(x)=30\cdot2^{2x}[/tex]

Step-by-step explanation:

Given: A wildlife preservation group records the number of squirrels in a city park.

The first count recorded = 30 squirrels.

A second count of 60 squirrels is recorded six months later, and 120 squirrels are counted at the end of one year.

The growth rate of squirrel=[tex]\frac{120}{30}=4=2^2[/tex]

The exponential growth equation is given by :-

[tex]y=Ab^n[/tex], where A is the initial amount , b is the growth rate and n is the time period.

If the growth rate remains constant, then the function represents the number of squirrels after x years is given by :-

[tex]f(x)=30\cdot(2^2)^x=30\cdot2^{2x}[/tex]

Answer: p = -2w + 20

Step-by-step explanation:

If the student had 20 pencils but now has 18 pencils, he uses pencils at a rate of 2 per week.  So, m = -2  (negative because he is decreasing the amount of pencils).  The student started with 20 pencils so b = 20

Use the y = mx + b but replace "y" with "p" and replace "x" with "w" and input the m and b as stated above:

             p = -2w + 20

Answer: Zoe is closer to the actual product because 6.80 is closer to 6.8493 than 6.90 mathematically. Another way to estimate 6.8493 is to round to the nearest hundredth place: 6.85

Zoe will have an estimate closer to the actual product.

To determine who will have an estimate closer to the actual product, we can compare the rounding methods used by Zoe and Andrew. Zoe rounded 6 * 8493 to 6 * 8000, while Andrew rounded 6 * 8493 + 6 * 9000. In this case, Andrew's estimate will be closer to the actual product because he considered additional terms in his calculation.

Another way to estimate 6 * 8493 that would give a better estimate is to round each term separately before multiplying. For example, rounding 6 to 10 and 8493 to 8500, the estimate would be 10 * 8500 = 85,000.

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Answer:

13 miles

Step-by-step explanation:

Write and solve an equation involving this information, using x as the distance traveled, in miles:

Cost(x) = $6.75 = $3.50 + ($0.25/mile)x

First, subtract $3.50 from both sides, obtaining:  $3.25 = ($.25/mile)x.

Next, divide both sides by $0.25/mile:

        $3.25

x = ------------------ = 13 miles

      $0.25/mile

The length of the taxi ride was 13 miles.

Answer:

Thus; Jupiter travels at 480 miles/m and in 6 minutes, it will travel 2880 miles.

Step-by-step explanation:

First to convert it you need to multiply 8 miles per second by 60 seconds because there are 60 seconds in a minute:

 8 miles    x    60 s 

1 second        1 min

The unit of seconds will cancel out so you will get 480 miles/ min

To get how far it travels in 6 min you need to multiply the speed by 6 minutes

480 miles   x  6 min = 2880

  1 min

The unit of minutes will cancel out to get 2880 miles

Answer:

Step-by-step explanation:

Applying BODMAS here;

We first solve what is in the brackets:

9x - 81 -3 = -8x - 16

We then put the like terms together:

9x + 8x = -16 + 81 + 3

We then do the addition:

17x = -16 + 84

We then do the subtraction:

17x = 68

Simplifying this gives:

x = [tex]\frac{68}{17}[/tex] = 4

C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.

The advantage of experimental probability over theoretical probability is that option C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Experimental probability is the probability where the probability of something is found by real experiments.

This is not computed by assuming or calculation.

Theoretical probability is the probability where the probability of something is found theoretically.

The probability is found using formulas and calculation.

So, it is not always possible to calculate theoretical probability in complex situations.

But experimental probability can be found in any case using experiments.

Hence the correct option is C.

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Answer: 11.6 units.

Step-by-step explanation:

1. Plot the points as you can see in the graph attached.

2. As you can see, the lenght TA is 3 units.

3. Apply the formula for calculate the distance between two points, to calculate the length TP and TA. The formula is:

[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

4. Therefore, you have:

[tex]TP=\sqrt{(1-3)^{2}+(4-0)^{2}}=4.47units[/tex]

[tex]AP=\sqrt{(4-3)^{2}+(4-0)^{2}}=4.12units[/tex]

5. The perimeter is the sum of the the lenght of each side, therefore:

[tex]Perimeter=3units+4.47units+4.12units\\Perimeter=11.59units[/tex]

6. To the nearest tenth unit:

[tex]Perimeter=11.6units[/tex]

Answer: Probability that a student chosen at random likes science given that he or she likes art is 58%

Step-by-step explanation:

Since we have given that

Probability that a student who likes art and science = 21%

Probability that a student who likes art = 36%

According to question,

we need to find the probability that a student chosen at random likes science given that he or she likes art.

So, we will use "Conditional Probability":

P(A) = 0.36

P(S ∩ A) = 0.21

[tex]P(S\mid A)=\frac{P(S\cap A)}{P(A)}\\\\P(S\mid A)=\frac{0.21}{0.36}\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%[/tex]

Hence, Probability that a student chosen at random likes science given that he or she likes art is 58%.

Answer: The triangle mentioned here is an acute angled triangle.

Step-by-step explanation: x+x+10+2x-6=180°(angle sum prop. of triangles)

               =                             4x+4=180°

               =                             4x=174°

               =                             x=44°

therefore, x=44°

                 ,x+10=44+10=54°

                 ,2x-6=2(44)-6=82°

Answer:

Given the function:

f(x) = the quantity of x squared plus 3x minus 4 , all over x plus 4

i,e

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

or

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

or

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

or

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

⇒y= f(x) = x -1                 ......[1]

Find the x-intercepts and y-intercepts for the equation [1] ;

y-intercepts defined as the graph crosses the y-axis;

substitute x =0 to solve for y;

y = 0-1 = -1

y = -1

x-intercepts defined as the graph crosses the x-axis;

substitute y =0 to solve for x;

0 = x-1

or

x = 1

Plot these points (0 , -1) and (1, 0) on the graph for the given function as shown below.

Answer: [tex]10(512 – c) + 5c = 3,570[/tex]

Step-by-step explanation:

Given : The number of student tickets sold is represented by c.

For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each.

The sellers collected $3,570 from 512 tickets sold.

Since , the total tickets sold = 512

Therefore , the number of adults ticket = [tex]512-c[/tex]

Now, cost of total child tickets : [tex]5c[/tex]

Cost of total adult tickets = [tex]10(512 – c)[/tex]

Now, according to the cost of the tickets , we have the following equation :-

[tex]10(512 – c) + 5c = 3,570[/tex]

Answer:

9 hours

Step-by-step explanation:

First off we need to subtract 17 from 71 in order to get rid of the initial cost. This will lead us to 54. The last thing we need to do is divide that by 6 since you pay 6 hours per hour. Mike paid 71 dollars to rent a bike for 9 hours.

Answer:

13.0 units

Step-by-step explanation:

To find the distance between two points, we use the formula

d = sqrt( (y2-y1)^2+ (x2-x1)^2)

    sqrt((-3--10)^2 + (-12--1)^2)

    sqrt( (-3+10)^2 + (-12+1)^2)

    sqrt( (7^2  + (-11)^2)

   sqrt( 49+121)

   sqrt( 170)

 13.038

Rounding to the nearest tenth

13.0

Answer:

90 days

Step-by-step explanation:

That = 3240 / 36

= 90 days

Answer:

90 days

Step-by-step explanation:

Hello, I think I can help you with this

You can easily solve this by using a simple rule of three.

Step one

Define

if the drives an average 36 miles per day,the how many days(x)  will it take to drive 3240 miles :it is

1 day ⇔ 36 miles

x days ⇔ 3240  miles

the relation is

[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\[/tex]

Step two

solve for x

[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\\\x=\frac{1\ day*3240\ miles}{36\ miles}\\x=90\ days\\[/tex]

90 days

Have a great day.