Can you please help I don’t understand

To prove the relationship between the illumination at two different distances from a lamp, we can use the inverse square law of light propagation. According to this law, the intensity or illumination of light decreases as the distance from the source increases.

The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:

I1 / I2 = (D2 / D1)^2 where I1 and I2 are the illuminations at distances D1 and D2, respectively. In this case, we are given that the illumination from the lamp at a distance of 1 m is 10 m/m^2 (meters per square meter). Let's assume that the illumination at a distance of 0.5 m is I2.

Using the inverse square law, we can write the equation as:

10 / I2 = (1 / 0.5)^2

Simplifying the equation, we have:

10 / I2 = 4

Cross-multiplying, we get:

I2 = 10 / 4 = 2.5 m/m^2

Therefore, we have proven that the illumination at a point 0.5 m away from the lamp is 2.5 m/m^2, not 40 m/m^2 as stated in the question. It seems there may be an error or inconsistency in the given values.

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Answer:

x=4

y=1

Step-by-step explanation:

4x=7y+9

4x+y=17

7y+9+y=17

8y=17-9

8y=8

y=1

so

4x=7*1+9

4x=16

x=16/4

x=4

The area of a 2D form is the amount of space within its perimeter. The correct option is D.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the L block will be the sum of the area of A and B. Therefore, the area can be written as,

Area of L block = Area of A + Area of B

                          = (7×2) units² + (1 × 5) units²

                          = 14units² + 5units²

                          = 19units²

Hence, the correct option is D.

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Answer:

Step-by-step explanation:

amama

Answer:

x = 70

Step-by-step explanation:

Answer:

Step-by-step explanation:

b/c we know that the inside angles of a triangle add to 180

180 = 38 + x + x + 2

180 = 40 + 2x

140 = 2x

70 = x

Answer:

\(2*2^1^/^4\)

(≈2.378)

Step-by-step explanation:

we know that:

\(a^x*a^y=a^x^+^y\)

[this is the same as multiplying any exponents]

3/4 + 1/2 = 1 + 1/4

if [\(a^x*a^y=a^x^+^y\)], then [\(a^x^+^y=a^x*a^y\)] must also be true

so,

\(2^1^+^1^/^4=2^1*2^1^/^4\\\)

= \(2*2^1^/^4\)

(\(2^1^/^4 = 1.189207115\))

1.189207115 · 2 = 2.37841423001

(rounded to 2.378)

Answer:

\(2*2^1^/^4\)

(2.37841)

Explanation:

3/4 + 1/2 = 1 + 1/4

= \(2*2^1^/^4\)

(\(2^1^/^4 = 1.189207115\))

(2)(1.189207115) = 2.37841423001

For the given equations of the demand and supply of goods , the elasticity of supply will be (a) 5/4 .

The Elasticity of supply is defined as a measure of responsiveness of the quantity of a good or service supplied to changes in its price. It is the degree to which the quantity supplied of a product or service changes when there is a change in its price.

We know that the elasticity of supply curve is the same as the slope of supply curve because it represents the proportion of change in price that will change the quantity supplied.

The equation for the supply curve is given to be :  S = -5 + (5/4)p ,

So , the slope of Supply curve is given in the equation is 5/4 .

Therefore , The  Elasticity Of Supply is 5/4 , the correct option is (a) .

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The given question is incomplete , the complete question is

Suppose that the supply and demand of a good are given by the following equations:

Demand = 75 - (3/4)p and Supply = -5 + (5/4)p ,

What is the elasticity of supply?

(a) 5/4

(b) 10/9

(c) 3/4

(d) 11/8

Answer:

: Marked price of dinner set = $480. Discount = 18% of $480 = 0.18 × 480 = $86.40.

| Must include: 7Step-by-step explanation:

Answer:

Step-by-step explanation:

The real answer would 28%

Recall that the order of the operations PEMDAS

1. Parenthesis

2. Exponents.

3. Multiplication.

4. Division.

5. Addition.

6. Subtraction.

1. Given expression is

Multiply 3 and 5, we get

Divide 6 by 2, we get

Subtract 3 from 8, we get

Add 5 and 15, we get

The answer is

2.Given expression is

Multiply 7 and 3, we get

Divide 15 by 5, we get

Subtract 3 from 21, we get

The answer is

3. Given expression is

First, we need to solve inside the parenthesis, divide 12 by 2, we get

Add 1 and 6, we get

Solve exponent.

Multiply 2 and 49, we get

Add 8 and 98, we get

The answer is

Answer:

m=7

Step-by-step explanation:

subract 35 from both sides to isolate the variable. Then you should be left with 5m=35. From there, divide both sides to isolate the variable even more, and you should be left with m=35/5 which is 7.

Answer: m=7

Step-by-step explanation:

\(5m+35=70\)

subtract 35 on both sides

\(5m+35-35=70-35\)

\(5m=35\)

divide 5 on both sides

\(35/5=7\)

\(m=7\)

The probability of getting a green marble first and a red marble second exists 5/26.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given: Red marbles = 3

Green marbles = 10

So, the total marbles = 3 + 10 = 13

Probability = Favorable outcomes  / Total outcomes

Since, here replacement is not allowed,

Therefore, the probability of getting a green marble and a red marble

= first red and second green + first green second red

= 3/13 × 10/12+ 10/13 × 3/12

= 2 × 3/13 × 10/12

= 30/78

= 5/13

The probability of getting a green marble first and a red marble second

= 10/13 × 3/12

= 30/156

= 5/26

Therefore, the probability of getting a green marble first and a red marble second exists 5/26.

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Answer:

more classmates like hip-hop

step-by-step explanation:

percentages (%) are out of 100

classmates: 62% of 80 is the same thing as

\( \frac{62}{100} \times 80 = 50 \: rounded \: up\)

relatives: 70% of 60 is the same thing as

\( \frac{70}{100} \times 60 = 42\)

we can clearly see that more classmates like hip-hop

The height (in inches) of a triangle with an area of 720 square inches and base of 32 inches is 45 inches.

The height of a triangle can be found using the formula for the area of a triangle: A = (1/2)bh, where A is the area, b is the base, and h is the height.

In this case, we are given the area (720 square inches) and the base (32 inches) and are asked to find the height.

First, we can plug in the given values into the formula:

720 = (1/2)(32)(h)

Next, we can simplify the equation by multiplying both sides by 2:

1440 = 32h

Finally, we can solve for the height by dividing both sides by 32:

h = 45 inches

Therefore, the height of the triangle is 45 inches.

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Answer:

Multiply the denominator of the fractional part by the whole number, and add the result to the numerator.

Step-by-step explanation:

You can add or subtract mixed numbers by turning them to improper fractions first. Improper fractions are fractions where the numerator is greater than the denominator.

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Answer:

61.5%

Step-by-step explanation:

The percent of his money that he spent on the pair of shoes is \(\frac{36.90}{60} \cdot 100% = 61.5%\)

Answer:

x = 5

Step-by-step explanation:

4x - 3(2x - 1) = 7x - 42 ← distribute and simplify left side

4x - 6x + 3 = 7x - 42

- 2x + 3 = 7x - 42 ( subtract 7x from both sides )

- 9x + 3 = - 42 ( subtract 3 from both sides )

- 9x = - 45 ( divide both sides by - 9 )

x = 5

Answer:

it's the first one

Step-by-step explanation:

you'd get each output (y) when you subtract 4 from whatever x is

The indefinite integral is: ∫(1/(x^2+1))dx = ln|x^2 + 1| + c, where c is the constant of integration

To find the indefinite integral by making a change of variables, we can use the substitution method. Let u be the denominator of the integrand, so we can write:

∫(1/(x^2+1))dx = ∫(1/u) * (du/dx) dx

To find du/dx, we differentiate both sides of u = x^2 + 1 with respect to x:

du/dx = 2x

Substituting this into our integral, we get:

∫(1/u) * (du/dx) dx = ∫(1/u) * (2x) dx

Now we can make a change of variables by letting f(u) = ln|u|. Using the chain rule, we have:

df/du = 1/u

Substituting this into our integral, we get:

∫(1/u) * (2x) dx = 2∫(df/du) * x dx

Integrating with respect to x, we get:

2∫(df/du) * x dx = x * ln|u| + c

Substituting u = x^2 + 1, we get:

x * ln|u| + c = x * ln|x^2 + 1| + c

Therefore, the indefinite integral is:

∫(1/(x^2+1))dx = ln|x^2 + 1| + c, where c is the constant of integration.

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Answer:

(x-9)(x+2)

Step-by-step explanation:

x^2-7x-18

What 2 numbers multiply to -18 and add to -7

-9*2 = -18

-9+2 = -7

(x-9)(x+2)

Answer:

Below.

Step-by-step explanation:

x^2 - 7x - 18

-9 * 2 = -18 and -9 +2 = -7 so the factors are:

(x - 9)(x + 2)

Answer:

The semi-circles form an entire circle with a diameter of 74.

The radius is 37

The area of the rectangle is 95 x 74 = 7030

The area of the circle is 3.142 x 37*37 = 4298.66

The total area is 11328.66

Answer:

\( (\frac{{m}^{2} }{4} )\pi\)

Step-by-step explanation:

we can find the radius from the diameter by dividing the diameter by 2 (radius is half the diameter)

the formula for the area of a circle is r²π (with r being radius) but since we must use diameter we have to replace r with (m/2)

this gives us our new formula of (m/2)²π, which simplifies to (m²/4)π

that is the answer

- kan academy advance

Answer:

Step-by-step explanation:

Answer:

67 miles per hour

Step-by-step explanation:

We can set up a proportion to find how many miles per hour this person travels:

268/4

=67

So, the rate is 67 miles per hour.

Hope this helps :)

— driving 268 miles in 4 hours is a total rate of 67 miles per hour

why???

268/4 = 67

The statement is true that 95% of all possible sample means will fall above 76.71.

We know that the sample mean can be calculated using the formula;

\($\bar{X}=\frac{\sum X}{n}$\).

Given that the mean is 80 and the variance is 400 for the population and the sample size is 100. The standard deviation of the population is given by the formula;

σ = √400

= 20.

The standard error of the mean can be calculated using the formula;

SE = σ/√n

= 20/10

= 2

Substituting the values in the formula to get the sampling distribution of the mean;

\($Z=\frac{\bar{X}-\mu}{SE}$\)

where \($\bar{X}$\) is the sample mean, μ is the population mean, and SE is the standard error of the mean.

The sampling distribution of the mean will have the mean equal to the population mean and standard deviation equal to the standard error of the mean.

Therefore,

\(Z=\frac{76.71-80}{2}\\=-1.645$.\)

The probability of the Z-value being less than -1.645 is 0.05. Since the Z-value is less than 0.05, we can conclude that 95% of all possible sample means will fall above 76.71.

Conclusion: Therefore, the statement is true that 95% of all possible sample means will fall above 76.71.

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a. The z-score for a blood pressure reading of 140 is 1.22.

b. The proportion of the population suffering from high blood pressure (reading above 140) is 0.1112.

c. The proportion of the population with systolic blood pressure in the range from 104 to 140 is 0.7185.

To solve the problem, we need to use the standard normal distribution since we know the mean and standard deviation of the population.

a. The z-score for a blood pressure reading of 140 is calculated as:

z = (140 - 118) / 18 = 1.22

Therefore, the z-score for a blood pressure reading of 140 is 1.22 (rounded to two decimal places).

b. To find the proportion of the population suffering from high blood pressure, we need to calculate the area under the standard normal distribution curve to the right of z = 1.22 (since we are interested in readings above 140). Using a standard normal distribution table or calculator, we find that the area to the right of 1.22 is 0.1112.

Therefore, the proportion of the population suffering from high blood pressure (reading above 140) is 0.1112.

c. To find the proportion of the population with systolic blood pressure in the range from 104 to 140, we need to calculate the area under the standard normal distribution curve between z = (104 - 118) / 18 = -0.78 and z = (140 - 118) / 18 = 1.22. Using a standard normal distribution table or calculator, we find that the area between -0.78 and 1.22 is 0.7185.

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