The ratio of boys to girls in a group is 7:3. If there are 40 more boys than girls, work out how many girls there are

a) No, a single spray of 10 grams of butter would not be enough to entirely cover the area of 4 slices of toast at 2 meters. The area of 4 slices of toast is larger than the area of 1 slice of toast, meaning that it would require more butter than 10 grams to cover the entire area.

b) A single spray of 10 grams of butter would be enough to cover the area of 8 slices of toast at 3 meters.

c) These changes would affect the amount of butter on each piece of toast in that there would be more butter on each piece with a larger rack and further distance from the "butter gun".

d) At 5 meters from the gun, our up-and-coming chef would be able to spray 16 slices of toast with a single burst of 10 grams of butter. Each piece of toast would also have more butter than it would if it was sprayed at a closer distance.

e) To duplicate the original single-slice toast at 5 meters from the gun, the chef would need to reduce the amount of butter being sprayed. He could do this by simply reducing the distance between the gun and the toast rack.

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Complete question :

A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.

The length of a side must be less than the sum of the other two sides. Here, that means x < 10+13, or x < 23.

In addition, remember that the length of a side must be greater than the difference of the other two sides. That means x > 13 - 10, or x > 3.

Therefore we have two limits for the value of x: 3 and 23.

3 < x < 23

Answer:

5

Step-by-step explanation:

2 + 3 = 5 , theres not much other to say besides for questions like these you can use a calculator :)

Answer:

what is the shape and can I have a pic of what it looks like

C.85 espero ter ajudado

Answer: 14.31

Step-by-step explanation:

Using Law of Sines, we know that

\(\frac{16}{sin(72)} =\frac{PR}{sin(90)}\)

Thus, \(PR=16.8233955878\)

Then, using \(\frac{\alpha }{sin(\alpha)} =2R\),

we know that \(\frac{16.8233955878}{sin(s)} =\frac{16.8233955878}{sin(36)} =28.621670112 = 2R\)

Therefore, \(R = 14.310735056\)

The interval for the graphed function that contains the local maximum is from (negative 0.5, negative 7) to (1.5, 1).

To find the interval for the graphed function that contains the local maximum, we need to use the given minimum and maximum values. The minimum values are (negative 0.5, negative 7) and (2.5, negative 1), and the maximum value is (1.5, 1). We need to determine the x-axis and y-axis crossings. The x-axis crossings are (negative 1, 0), (1, 0), and (3, 0), and the y-axis crossing is (0, negative 6). To find the interval, we need to find the lowest x-coordinate and the highest y-coordinate of the given values. The lowest x-coordinate is (negative 0.5, negative 7) and the highest y-coordinate is (1.5, 1). Thus, the interval for the graphed function that contains the local maximum is from (negative 0.5, negative 7) to (1.5, 1).

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Answer:                          ❁                                ❁                              ✴︎      

28 is the answer (:                                          ❋                                    ❅

Step-by-step explanation:                        ✺                      ✱                      ❅

Mental Math            ✦                                        ✧                               ✶      

First, let's calculate the z-score for the value 2.025 liters using the formula:

z = (x - μ) / σ

Where:

x = the value we want to calculate the probability for (2.025 liters)

μ = the mean of the process (2.050 liters)

σ = the standard deviation of the process (0.020 liters)

Plugging in the values:

z = (2.025 - 2.050) / 0.020

Simplifying:

z= -0.025 / 0.020

z = -1.25

Now, we can look up the probability corresponding to a z-score of -1.25 in the standard normal distribution table or use a calculator.

Using a standard normal distribution table, the probability is approximately 0.1056. This means that the probability of randomly selecting an output from the process that is less than 2.025 liters is approximately 0.1056 or 10.56%.

Alternatively, you can use a calculator or statistical software to find the probability directly by looking up the cumulative distribution function (CDF) of the standard normal distribution at -1.25. The result will also be approximately 0.1056 or 10.56%.

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The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

1,2,3,5

Step-by-step explanation:

Answer:

abce

Step-by-step explanation:

Using the Laplace transform to solve the given integral equation  f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is \(\frac{4(1-2e^-5s)/}{s}\)

explanation is given in the image below:

Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.

The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.

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The probability of picking a dime from the coins in his pocket is 1/13

1 penny = 1 cent

Hence, 100 pennies = $1

1 nickel = 5 cent

20 nickels = $1

1 dime = 10 cent

10 dime = $1

This means that :

Eduardo has :

Total coins = (100 + 20 + 10) = 130 coins

Recall :

Probability = required outcome / Total possible outcomes

P(dime) = number of dimes / total coins

P(dime) = 10 / 130 = 1/13

Hence, the probability of picking a dime = 1/13

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Answer:

0.2

Step-by-step explanation:

5/25

= 20/100

[Multiplying by 4 to make the denominator 100]

= 0.20

[We count the number of zeroes in denominator and move the decimal to the left to the number of places same as the number of zeroes, in numerator. Here there are two zeroes after 1 (in 100, the denominator), so we moved the decimal to the left by two places (20.0 becomes 0.20)

P.S.- This works only when the denominator is something like 10, 100, 1000, 10000 etc.]

= 0.2 [0.20 is simplified as 0.2]

Or simply divide 5 by 25

A picture of the division is attached.

Steps:

1. Since 25 cannot divided 5, we will write a zero and a decimal in the quotient.

2. After this we will add a zero to 5, so that it becomes 50.

3. 50÷25 is 2, so write 2 in the quotient after the decimal.

4. Your answer is 0.2.

Approximately 3.3 inches of rainfall per year.

If central Pennsylvania received only one-third of the usual rainfall in a really dry year, it would be receiving 1/3 * the usual amount of rainfall per year.

In an average year,

     Pennsylvania gets about the same amount of rainfall as a desert, which is typically defined as an area that receives less than 10 inches of precipitation per year.

Therefore, if central Pennsylvania received only one-third of the usual amount of rainfall in a really dry year, it would be receiving,

   1/3 * 10 inches = approximately 3.3 inches of rainfall per year.

This amount of rainfall is significantly less than the average rainfall in Pennsylvania and would qualify as a desert if it persisted over a long period of time.

Hence, Approximately 3.3 inches of rainfall per year.

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Answer: The third option, O 2x²+7x-4

Step-by-step explanation:

     We can use the "FOIL" method. We take the following four sets, multiply them together, then add them for our final answer.

-> first

-> last

-> inner

-> outer

     What does this look like mathematically?

-> first = (2x - 1)(x + 4) = 2x * x = 2x²

-> last = (2x - 1)(x + 4) = -1 * 4 = -4

-> inner = (2x - 1)(x + 4) = -1 * x = -x

-> outer = (2x - 1)(x + 4) = 2x * 4 = 8x

-

2x² - 4 - x + 8x

2x² + 7x - 4

           O 2x²+7x-4

Answer:

\(C. 2x^2+7x-4\)

Step-by-step explanation:

1) Distribute.

\((2x-1)(x+4)\\2x(x+4)-1(x+4)\)

2) Distribute.

\(2x(x+4)-1(x+4)\\2x^2+8x-1(x+4)\)

3) Distribute.

\(2x^2+8x-(x+4)\\2x^2+8x-x-4\)

4) Combine like terms.

\(2x^2+8x-x-4\\2x^2 + 7x - 4\)

To calculate the probability of selecting a boy or a red-haired person as a homeroom representative to student council, we need to find the probability of each event and then use the formula P(A or B) = P(A) + P(B) - P(A and B).

There are 31 students in total (16 girls + 15 boys). The probability of selecting a boy is 15/31.

There are 5 red-haired students (3 girls + 2 boys). The probability of selecting a red-haired person is 5/31.

However, we need to account for the overlap between boys and red-haired students. There are 2 red-haired boys, so the probability of selecting a red-haired boy is 2/31.

Now we can use the formula: P(boy or red-haired) = P(boy) + P(red-haired) - P(boy and red-haired) = (15/31) + (5/31) - (2/31) = 18/31.

So, the probability of selecting a boy or a red-haired person as a homeroom representative to student council is 18/31.

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Answer:

the pyramid is 80 ft² and the rectangular prism is 240 ft²

Step-by-step explanation:

Answer:

??

Step-by-step explanation:

Which equation?

Answer:

D

Step-by-step explanation:

AD≅AB because they are tangent segments from the same point, A

x² + 2 = 11

x² = 9

x = √9 = 3, -3  (two solutions of \(\sqrt{9}\))

Answer:

z=2

Step-by-step explanation:

z^2 - 4z+4 =0

Factor recognizing

a^2 - 2ab - b^2 = (a-b)^2

(z-2)^2 =0

Using  the zero product property

z-2 = 0

z=2

The average weight of the colony over the interval [1,4] is 47.83 newtons

The average value of a function is found by taking the integral of the function over the interval and dividing by the length of the interval.

Given,

\(w(t)=12.5e^{0.5t}\)

The average value of the given function

\(w_{avg} =\frac{1}{b-a}\int\limits^a_b {w(t)} \, dt\)

Here the interval is [1,4]

Therefore, a=1 and b= 4.

Substitute the values of w(t),a and b in the equation

\(w_{avg}= \frac{1}{4-1}\int\limits^4_1 {12.5e^{0.5t} } \, dx \\w_{avg}= \frac{1}{3}\int\limits^4_1 {\frac{25e^{0.5t} }{2} } \, dx\)

Consider,

\(u=\frac{t}{2}\\ \frac{du}{dt}=\frac{1}{2}\\dt=2du\)

Then,

\(w_{avg}= \frac{25}{3}\int\limits^4_1 {e^{u} } \, du\\ w_{avg}= \frac{25}{3}[e^{4/2}-e^{1/2}]\\ w_{avg}= \frac{25}{3}[e^{2}-\sqrt{e}]\\ w_{avg}= \frac{25}{3}[5.74]\\ w_{avg}=47.83\)

Hence, the average weight of the colony over the interval [1,4] is 47.83 newtons

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Answer:

1.8

Step-by-step explanation:

just divide 60 and 32

Answer: Perimeter of given square:40,Area of given square:100

Perimeter of Dilated square:200

Area of Dilated square: 2500

Step-by-step explanation:

The income tax amount of 6% will be equal to $252 on a salary of $4200.

A number or ratio that can be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent implies.

A percentage is a figure or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A percentage is a figure without dimensions and without a standard measurement.

We must divide the value by the overall value to find the percentage, and then multiply the resulting number by 100.

A tax placed on people or organisations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable revenue are typically used to calculate income taxes. Tax rates can change depending on the taxpayer's characteristics and sort of income.

The word "income tax" refers to a category of tax that governments levy on income generated by businesses and people under their jurisdiction.

In this question,

Salary amount= $4200

Income tax= 6%

The amount to be paid in income tax= 6% of $4200

                                                             = (6/100)*4200

                                                             = $252

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691 ounces is approximately equal to 195,340 decigrams.

To convert ounces to decigrams, we need to understand the conversion factors between the two units.

1 ounce is equivalent to 28.3495 grams, and 1 decigram is equal to 0.1 grams.

First, we'll convert ounces to grams using the conversion factor:

691 ounces * 28.3495 grams/ounce = 19,533.9995 grams

Next, we'll convert grams to decigrams using the conversion factor:

19,533.9995 grams * 10 decigrams/gram = 195,339.995 decigrams

Rounding the decigram value to one decimal place, we get:

195,339.995 decigrams ≈ 195,340 decigrams

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154.3325 has two significant figures to maintain consistency with the original data.

To solve the given expression, we'll follow the order of operations (PEMDAS/BODMAS).

Multiply: 111 × 3.3447 = 370.398 (rounded to 3 significant figures).

Divide: 370.398 ÷ 2.4 = 154.3325 (rounded to 4 significant figures).

Significant figures are a way to express the precision of a measurement or calculation result. In this case, the original numbers (111, 3.3447, and 2.4) have varying significant figures.

To ensure the accuracy of the final answer, we round it to the same number of significant figures as the least precise value involved, which is 2.4 with two significant figures. Therefore, the answer, 154.3325 has two significant figures to maintain consistency with the original data.

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