For a field trip 5 students rode in cars and
the rest filled ten buses. How many students
were in each bus if 215 students were on the
trip?

Answer:

they are 17 miles away from their campsite.

Step-by-step explanation:

we get the answer by adding the miles traveled north to the miles traveled west, and we get the total number of miles they traveled away from their campsite.

5 + 12 = 17

Answer:

1/2

Step-by-step explanation:

Rise over run. The rise is 4 the run is 8. Simplify.

Answer:

7x+35/2

Step-by-step explanation:

The area of a trapezoid is \(\frac{(b_1+b_2)}{2}\cdot h\), where b1 and b2 are the two bases and h is the height. Because b2 is 5 more than b1, which we will represent as x, we have the two bases as x and x + 5 respectively. Plugging into the equation, we have \(\frac{2x+5}{2}\cdot 7\) .We have this as (x+5/2)(7), which is 7x+35/2

Answer:

a=3

b=2

Step-by-step explanation:

P(x) = ax^2 + bx + 1

P(1)= 6

6= a(1)^2 + b(1) +1

6 = a +b+1

6-1 = a+b

5 = a+b

P(-1) = 2

2 = a( -1)^2 + b(-1) +1

2 = a(1) -b +1

2-1 = a-b

1 = a+b

We have 2 equations and 2 unknowns

Add the two equations together

5 = a+b

1 = a-b

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

6 = 2a

Divide by 2

6/2 = 2a/2

3 =a

Now find b

5 =a+b

5 =3+b

Subtract 3 from each side

5-3 =3+b-3

2=b

Answer:

37/180

Step-by-step explanation:

Reduce this fraction by dividing both sides by 2.  We get 37/180, which cannot be reduced further; 37 and 180 have no common factor.

To determine how many cakes per day Kate should order for this week, we can calculate the expected profit for each possible daily order quantity and choose the one that maximizes profit.

(a) Here are the steps:
1. Calculate the profit for each possible demand, considering the cost of cakes ($10) and the selling price ($18).
2. Multiply the profit by the probability of each demand level.
3. Sum up the expected profits for all demand levels. Doing these calculations for all possible order quantities (1 to 6 cakes), we find that ordering 4 cakes per day maximizes the expected profit for this week.
(b) If the number of cakes next week depends on the number of leftovers at the end of this week, it will not change the estimate for this week. The reason is that we are still maximizing expected profit for this week, and any leftover cakes can be incorporated into next week's order.
(c) If leftover cakes can't be sold later and are dumped at the end of the day, we need to adjust the profit calculations. We still want to maximize the expected profit, but now we have to subtract the cost of unsold cakes. When we redo the calculations with this new information, the optimal order quantity might change, depending on the probabilities and profit margins.
(d) If day-old cakes sell for $12 and two-day-old cakes are donated, we need to adjust our profit calculations again. In this case, we have different selling prices for fresh cakes ($18), day-old cakes ($12), and two-day-old cakes ($0). Using these new prices, we can recalculate the expected profit for each order quantity and choose the one that maximizes the profit.

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a. Kate should order 4 cakes per week taking into consideration the uncertainty of demands.

b. The best strategy is still to order 4 cakes per day for this week and adjust the order for next week based on the leftovers.

c. Kate should order 3 cakes per day for this week to minimize waste.

d. the profit margins change if, day-old cakes sell for $12 and two-day-old cakes are donated.

a. To determine how many cakes per day Kate should order for this week, we need to estimate the number that maximizes her profit while minimizing the risk of having leftover cakes.

We can do this by calculating the expected profit for each possible order quantity and selecting the one that gives the highest profit.
We can calculate the number of cakes by following the steps
1. Multiply the daily demand by its probability, then sum these products to get the expected daily demand:

(1 * .1) + (2 * .2) + (3 * .25) + (4 * .25) + (5 * .15) + (6 * .05) = 3.4 cakes
2. Test different order quantities (from 1 to 6) and calculate the expected profit for each quantity.
3. Select the order quantity with the highest expected profit.

For this problem, Kate should order 4 cakes per day for this week.

b. If the number of cakes next week depends on the number of leftovers at the end of this week, the best strategy is still to order 4 cakes per day for this week and adjust the order for next week based on the leftovers.

c. If leftover cakes can't be sold later and are just dumped at the end of the day, we would want to minimize the risk of leftovers. In this case, Kate should order 3 cakes per day for this week to minimize waste while still maintaining a good probability of selling most of the cakes.

d. If day-old cakes sell for $12 and two-day-old cakes are donated, the profit margins change, and the expected profit calculation should be updated accordingly.

After recalculating, Kate should still order 4 cakes per day for this week, as the order quantity provides the highest expected profit with this new pricing structure.

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The function d/dx (f/g) = 2 gives the value of c as -4.

The denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator, is how the Quotient Rule defines the derivative of a quotient.

Given:

f(x) = 1/2x and g(x) = 1/ (3x + c)

Using Quotient rule

d/ dx (f/g)

= g f' - f g- / g²

So, d/dx ( 3x+c / 2x )

= [3x -1(3x+c)] / 2x²

= -c/ 2x²

Now out x= 1

Also, d/dx (f/g)= 2

-c/ 2 = 2

c= -4.

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Answer:

x = 13

Step-by-step explanation:

→ Remember the amount of degrees a triangle sums to

180°

→ Make an equation

8x - 44 + 8x - 44 + 8x - 44 = 180

→ Simplify

24x - 132 = 180

→ Add 132 to both sides

24x = 312

→ Divide both sides by 24

x = 13

Answer:

16

Step-by-step explanation:

A negative times a negative is a positive. -4^2 is equal to -4 times -4. This would give us 16.

The perimeter of a square is 80 minus 64 y units. Which expression can be used to show the side length of one side of the square?

Answer · 1 vote

Perimeter of the square80-64yA square has 4 sides, so divide the perimeter by 4:(80-64y) / 480 divided by 4 is 2064y divided by 4 is 16yOne side of the ..

Answer:

Its C

Step-by-step explanation:

took the test

answer:

10:03 am

explanation:

9:00 am + 1 hour (60 min) + 3 min = 10:03 am.

Answer:

11.02

Step-by-step explanation:

use a calculator? add the 3 numbers up

Answer:

slope = 3

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (9, 27 )

m = \(\frac{27-3}{9-1}\) = \(\frac{24}{8}\) = 3

\(\mathbb{FINAL\:ANSWER:}\)

\(\huge\boxed{\sf\:Slope=3}}\)

\(\mathbb{SOLUTION\:WITH\:STEPS:}\)

Hi! Hope you are having a nice day!

We are given 2 points that the line passes through, so we can use the slope formula and find the slope.

Slope Formula:

\(\displaystyle\frac{y2-y1}{x2-x1}\)

\(\displaystyle\frac{27-3}{9-1}\)

\(\displaystyle\frac{24}{8}\)

The fraction can be reduced:

\(\displaystyle\frac{3}{1}\)

which is the same as

\(3\)

Hope you could understand everything.

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I see that this is a rate of change time of problem

If andy can run 20 miles in 6 hours, than our goal is to find out how much he runs in a hour

So, we just have to divide 20 by 6.

It's sorta hard to explain

Questions?

Anyhow, the answer is around 3.3 miles per hour

Answer:

3.33 miles

Step-by-step explanation:

We Know

Andy can run 20 miles in 6 hours.

How many miles can he run in 1 hour?

We Take

20 / 6 ≈ 3.33 miles

So, Andy can run about 3.33 miles in 1 hour.

Answer:

1384.74 mm²

Step-by-step explanation:

We Know

Area of circle = r² · π

diameter = 42 mm

radius = 42 / 2 = 21 mm

π = 3.14

We take

21² · 3.14 = 1384.74 mm²

So, the area of the circle is 1384.74 mm²

Answer:

I think they are.

Step-by-step explanation:

Because they are both 39 and 34 degrees so if x and y are the same number they are similar.

Step-by-step explanation:

a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.

b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.

This problem implies more cases to solve as well as the use of other formulas that we can use in the subject of free fall, if we read our exercise again, we will realize that we only have a height of 150 meters from where it is dropped freely a ball. To proceed to resolve, we collect the data.

Data:

h = 150 m

g = 9.8 m/s²

In order to obtain the distance traveled in 4 seconds, we can use the following formula:

\(\bf{\displaystyle h={{v}_{0}}t+\frac{g{{t}^{2}}}{2} }\)

Remember, that as it is a free fall, the initial speed is null, that is, zero. So the formula reduces:

\(\bf{\displaystyle h=\frac{g{{t}^{2}}}{2} }\)

We are going to place the 4 seconds in the “t” of time. Thus:

\(\bf{\displaystyle h=\frac{g{{t}^{2}}}{2}=\frac{\left( 9.8\frac{m}{{{s}^{2}}} \right){{\left( 4s \right)}^{2}}}{2} }\)

Carrying out the indicated operations:

\(\bf{\displaystyle h=\frac{g{{t}^{2}}}{2}=\frac{\left( 9.8\frac{m}{{{s}^{2}}} \right)16{{s}^{2}}}{2}=\frac{156.8m}{2}=78.4m }\)

That is to say that the height at 4 seconds is 78.4 meters.

For the velocity at 4 seconds, we use the following formula:

\(\bf{\displaystyle {{v}_{f}}={{v}_{0}}+gt}\)

Remember, that since there is no initial speed because it is free fall, then the formula is reduced:

\(\bf{\displaystyle {{V}_{f}}=gt }\)

Substituting our data and calculating:

\(\bf{\displaystyle {{v}_{f}}=gt=\left( 9.8\frac{m}{{{s}^{2}}} \right)\left( 4s \right)=39.2\frac{m}{s} }\)

So the speed at 4 seconds is 39.2 m/s.

Although it seems difficult to solve this section, it is not. It's very easy, let's remember that after 4 seconds it has traveled 78.4 meters and that the height from where the ball was dropped is 150 meters, so the difference is the amount that remains to reach the ground, that is:

\(\bf{\displaystyle {{h}_{T}}={{h}_{1}}+{{h}_{2}}}\)

It is as if we had:

\(\bf{\displaystyle 150=78.4+{{h}_{2}} }\)

Clearing "h2" what would be the distance to reach the ground.

\(\bf{\displaystyle {{h}_{2}}=150-78.4=71.6m }\)

In other words, we need to travel 71.6 meters to reach the ground.

There are 25,053,600 different tests of 5 questions each that can be made from Ms. Wood's collection of 25 questions.

To find the number of different tests of 5 questions each that can be made from a set of 25 questions, you can use the combination formula. The combination formula is:

n! / (r! * (n-r)!)

Where n is the total number of items and r is the number of items being chosen at a time.

In this case, n is 25 (the total number of questions) and r is 5 (the number of questions per test). Plugging these values into the formula gives:

25! / (5! * (25-5)!) = 25! / (5! * 20!) = 25 * 24 * 23 * 22 * 21 / (5 * 4 * 3 * 2 * 1) = 25,!053,!600

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Answer:

the length of cube

is 2 mm

Answer:

2m

Step-by-step explanation:

A cube is a 3-dimensional object with all sides of equal length. So, length = breadth = height

Let the side of cube be x.  

Then Volume of cube = x * x * x

So, length (side) of cube is 2m

The most direct way to measure how dispersed a set of scores is, is by using the range. The range is calculated by subtracting the lowest score from the highest score in the dataset, which gives a quick and easy measure of the spread of the scores.

However, the range can be influenced by extreme scores and may not provide a complete picture of the variability. Other measures of variability, such as the standard deviation and variance, take into account the variability of all scores in the dataset and provide a more robust measure of variability.

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Answer:

R = 13 cm, x = 5 cm

Step-by-step explanation:

We can see, that AO = BO = EO

First, we have to find AO from ∆OAD by using the Pythagorean theorem:

\( {ao}^{2} = {ad}^{2} + {x}^{2} \)

\( {ao}^{2} = 144 + {x}^{2} \)

\(ao > 0\)

\(ao = \sqrt{144 + {x}^{2} } \)

Now, let's write that EO = (8 + x)

Since AO = EO, we can write an equation:

\( \sqrt{144 + {x}^{2} } = 8 + x\)

Let's square the whole equation:

\(144 + {x}^{2} = ( {8 + x})^{2} \)

\(144 + {x}^{2} = 64 + 16x + {x}^{2} \)

\( {x}^{2} - {x}^{2} - 16x = 64 - 144\)

\( - 16x = - 80\)

Let's divide both sides of the equation from -16:

\(x = 5\)

OB = 8 + x = 8 + 5 = 13 (radius)

Answer:

20

Step-by-step explanation:

Since Steve is 6 feet tall and his shadow is 9 feet long we can do 9÷6=1.5 then 30÷1.5=20 so 20 is the answer (also I got it right on the test)

The height of the flagpole is 20 feet.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

Given;

The Length of flagpole shadow = 30 ft

The Steve height = 6 ft

The Length of Steve height shadow = 9 ft

The height and shadow length of the two follows the same ratio, just like similar triangles;

The height of flagpole/flagpole shadow length = height of Steve / Steve shadow height

Substituting the values;

h/30 = 6/9

h = 6/9 × 30 = 20 ft

Thus, the Flagpole height is 20 ft.

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Answer:

length is 15

width is 3

Step-by-step explanation:

3 * 5 is 15

3+3+15+15= 36

Answer:

C

Step-by-step explanation:

First, f(x) and g(x) are mirror image over the x-axis. so add a -ve in front.

Second, f(x) is about 2x steeper than g(x), that is its slope is doubled. so add a 2 in front.

Thus, f(x) = -2 g(x)

When we're solving equations, our prime goal is to isolate the variable. We can do this by using inverse operations to combine like terms.

Examples:

\(\sqrt[3]{5x-4}=\sqrt[3]{7x+8}\)

⇒ Here, both sides are being taken to the square root of 3. To remove this, we can raise both sides to the power of 3:

\((\sqrt[3]{5x-4})^3=(\sqrt[3]{7x+8})^3\\5x-4=7x+8\)

⇒ Let's move our x variable to the right side of the equal sign and the numbers to the left side. Start by subtracting 5x from both sides:

\((\sqrt[3]{5x-4})^3-5x=(\sqrt[3]{7x+8})^3\\5x-4=7x+8-5x\\-4=2x+8\)

⇒ Now, subtract 8 from both sides:

\(-4-8=2x+8-8\\-12=2x\)

⇒ Finally, divide both sides by 2 to isolate x:

\(\dfrac{-12}{2}=\dfrac{2x}{2}\\\\-6=x\)

x = -6

Answer:

A

Step-by-step explanation:

EDGE 2019

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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Answer:

I believe the answers are :

5 cm, 9cm, and 15 cm

3 cm, 5 cm, and 10 cm

Step-by-step explanation:

When 2 sides that are not the hypotenuse are added and are less than the hypotentuse, a triangle cannot be formed.

The integral \(∫59/sqrt(1-x^2)\) dx is convergent, and its value is \(59π/a^2\). The substitution x = a sin(t) was used to simplify the integral, and the limits of integration were transformed from -1 to 1 to -π/2 to π/2.

The integral\(∫59/sqrt(1-x^2)\) dx is a definite integral that represents the area under the curve of the function\(59/sqrt(1-x^2)\) between its limits of integration. To determine whether this integral is convergent or divergent, we need to evaluate the integral by using a suitable technique.

We can begin by noting that the integrand is of the form \(f(x) = k/√(a^2-x^2)\), where k and a are constants. This suggests that we should use the substitution x = a sin(t) to simplify the integral.

Making this substitution, we obtain dx = a cos(t) dt and the limits of integration become -π/2 to π/2. The integral now becomes:

\(∫59/sqrt(1-x^2) dx = ∫59/(a cos(t)) a cos(t) dt\)\(= 59∫(1/a^2) dt = 59t/a^2\)

Evaluating the integral from -π/2 to π/2, we obtain:

\(∫59/sqrt(1-x^2) dx\)\(= 59(π/2 - (-π/2))/a^2\)\(= 59π/a^2\)

Since the limits of integration are finite, and the integral has a finite value, we can conclude that the integral is convergent. Evaluating the integral using the substitution x = a sin(t), we obtain the value\(59π/a^2\).

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