In a preschool, there are 5 students per teacher. There are 10 teachers in the school. How many students are in the school?
2
5
15
50

The base of the ladder is 30 feet from the wall, the top of the ladder is sliding down the wall at a rate of 6 feet per second.

To determine how fast the top of the ladder is sliding down the wall when the base is 30 feet from the wall, we can use the Pythagorean theorem and implicit differentiation.

Step 1: Set up the Pythagorean theorem for the ladder, wall, and ground.
Let x be the distance between the base of the ladder and the wall, and let y be the height of the top of the ladder above the ground. Since the ladder has a length of 50 feet, we have:

\(x^2 + y^2 = 50^2\)

Step 2: Differentiate both sides of the equation with respect to time (t).
Using implicit differentiation, we get:

2x(dx/dt) + 2y(dy/dt) = 0

Step 3: Plug in the given values and solve for dy/dt.
We are given that dx/dt = 8 ft/s (the base is being pulled away from the wall) and x = 30 ft. To find y, plug x = 30 into the Pythagorean theorem equation:

\(30^2 + y^2 = 50^2

y^2 = 50^2 - 30^2\)

y = √(2500 - 900) = √1600 = 40

Now plug in the values of x, y, and dx/dt into the differentiated equation:

2(30)(8) + 2(40)(dy/dt) = 0

Step 4: Solve for dy/dt.
480 + 80(dy/dt) = 0
80(dy/dt) = -480
dy/dt = -480 / 80 = -6

So, when the base of the ladder is 30 feet from the wall, the top of the ladder is sliding down the wall at a rate of 6 feet per second.

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Answer: 43.75 miles per day.

Step-by-step explanation: All you have to do is divide 350 by 8, when you divide you basically just split the number evenly 8 times, which is what 350 divided by 8 is. He will have to drive 43.75 miles a day.

Answer:

The answer is 2/10 and 2/10

(A)

Answer:

By moving the decimal at the end of the number to the correct amount of places for x 10 you move it once to the right for x 100 you move it right twice.

Step-by-step explanation:

The correct total weight of the bags of granola is 8 1/4 pounds.

One thing that can be done to improve Roberto's reasoning is to ensure the accuracy of the calculations.

In his conclusion, Roberto added the weights of the bags of granola (2 1/2, 2 3/4, and 3) and claimed that the total weight was 8 1/4 pounds. However, the sum of these weights does not equal 8 1/4 pounds.

To address this, Roberto should recheck his calculations. Adding mixed numbers involves adding the whole numbers separately and then adding the fractions separately. In this case, 2 1/2 + 2 3/4 + 3 can be calculated as follows:

2 + 2 + 3 = 7 (sum of whole numbers)

1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4 (sum of fractions)

Thus, the correct sum is 7 + 1 1/4 = 8 1/4 pounds.

By double-checking the calculations and providing the accurate sum, Roberto's reasoning would be more precise, reliable, and free from errors.

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The probable question may be:

Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2 1/2+2 3/4+3=8 1/4 pounds.

what is one thing that you could do to Roberto's Reasoning

Answer: 1.68

Step-by-step explanation: Okay, to find this we need to use this formula:

Amount = Part percent * whole number / 100

So, now let's plug in the numbers:

Amount = 14 * 12 / 100

= 168/100

= 1.68

Therefore the amount of gold in the rock is 1.68 oz out of the 12 ounces.

I hope this helped!

Answer: 1.68

Step-by-step explanation: So, if we want to find how much gold is in the rock, it's a good idea to set up a proportion. So, it would be like this:

\(\frac{14}{100} = \frac{?}{12}\)

Now, we would cross-multiply the 12 and the 14, which is 168, and then divide it by 100. That can be found by moving the decimal 2 places left of 168.00. So, that would be 1.68. Therefore, there are 1.68 ounces of gold in the rock. I hope this helped!

Answer: m∠5 = m∠7 = 67°

because a//b => m∠4 + m∠5 = 180°

⇔ 113° + m∠5 = 180°

⇔ m∠5 = 180 - 113 = 67°

because ∠5 and ∠7 are  2 opposing angles

=>  m∠5 = m∠7 = 67°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Angles 4 and 5 are same side interior angles and their measures add up to 180° as per definition:

Angles 5 and 7 are vertical angles and they have equal measure as per definition of vertical angles:

It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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Answer:

is the question  What is 10 percent of 125? = 12.5?

Step-by-step explanation:

if it was here you go

edit:

that is what it is supposed to look like

Answer:

Step-by-step explanation:

What do you need done to this?

125*.10= 12.50

125/.10= 1250

Answer:

∫ cosec²(7-5x) dx =[-cot(7-5x)]/-5 +c

=(1/5)cot(7-5x)+c

note: d/dx(cotx)=- cosecx

The investment of "x" dollars gave him a 15% increase that reach to a total of $1250.

Then x + increase = 1250

Now they tell us that the increase was in fact 25% of the value "x" that he invested. So that increse is: 15% of x , wich in math terms is written in decimal form as: 0.15 * x

Then we replace this in the very first equation we wrote:

x + increase = 1250

x + 0.15 x = 1250

combine the terms with "x":

1.15 x = 1250

solve for x by dividing by 1.15 both sides:

x = 1250 / 1.15

Please notice that any of the equations we have written could be considered as correct answers for the problem. Some are more at the beginning of the reasoning, while the last ones are after we have done some algebraic manipulations to solve for the unknown. But they are all equivalent.

If you are given options to select from, check all those that are like the ones we discussed above.

Answer:

can i have a photo, please?

Step-by-step explanation:

Answer:

V = -5

Step-by-step explanation:

As the paper says, V = m - k.

If you subtract -7 - -2 you get -5 (negative 5)

Hope this helps ^^

Answer:

The question is given below as

Concept:

The question will be solved using the linear pair theorem below

The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.

By applying the principle, we will have that

Hence,

The value of x= 92°

Step 2:

By applying the linear pair theorem, we will also have that

Hence,

The value of z= 92°

Step 3:

By applying the linear pair theorem also, we will have that

Hence,

The value of y= 88°

Answer:

$14 is the answer, hope this helps

Answer:

creo que son 14

Step-by-step explanation:

$4 ---> 2 lbs

X -----> 7 lbs

X = (4*7)/2 ------> X = 14 lbs

Answer:

1,000,000

Step-by-step explanation:

The maturity value due on January 16 is $34,320.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that,

Principal amount ( Starting amount) = $33,000

Rate of interest = 6% = 0.06

The loan is taken in May 17.

There is a time of 8 months in between May 17 and January 16.

Time in years = 8/12 years = 2/3 years

Amount of simple interest = Principal amount × Interest rate × Time

                                            = 33,000 × 0.06 × 2/3

                                            = 1320

Maturity value = Principal amount + Amount of simple interest

                        = $33,000 + $1320

                        = $34,320

Hence the maturity value is $34,320.

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The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer: So, the sales tax on the item is $49.

Step-by-step explanation:

The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:

Sales tax amount = $350 * 14% = $350 * 0.14 = $49

So, the sales tax on the item is $49.

Answer:

1.) 16/20

2.) 15/35

3.) 12/9

4.) 52/60

5.) 9 inches

6.) 24 centimeters

7.) 16 logs

8.) $15.40

9.) 10 miles

10.) 1.5 inches

I hope this is good enough:

Answer:37 number

Step-by-step explanation:

Answer:

It would be three coconuts hope this helped

Step-by-step explanation:

The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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Travis' famous letter, addressed to "The People of Texas and All Americans in the World," in which he passionately appealed for reinforcements and vowed to "never surrender or retreat," has become a symbol of the fortitude and sacrifice displayed by the Texan defenders at the Alamo.

The commander of the Texan forces at the Alamo during the famous battle in 1836 was Colonel William B. Travis. Travis, a lawyer and soldier, was chosen as the leader of the Texan garrison at the Alamo, a former mission turned fortress in San Antonio, Texas. He assumed command of the Texan forces in early 1836 and played a crucial role in the defense of the Alamo against the Mexican army led by General Santa Anna.

Travis and his men, along with notable figures such as James Bowie and Davy Crockett, bravely defended the Alamo against overwhelming odds for thirteen days. Despite their courage and determination, the Texan defenders were ultimately overrun by the Mexican forces on March 6, 1836, and suffered heavy casualties, including the deaths of Travis, Bowie, and Crockett.

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