The length of the shadow of a 4 ft stick can be found by comparing its shadow to the shadow of a 32 ft tall building. The building had a shadow 6 ft long. How long would the​ stick's shadow be at that​ time?

[tex]x = 10 - 4y.....(3)[/tex]

I WILL SOVE BY SUBSTITUTION.

[tex]3(10 - 4y) - y = - 9 \\ 30 - 12y - y = - 9 \\ - 13y = -9 - 30 \\ - 13y = - 39 \\ \frac{ - 13y}{ - 13} = \frac{ - 39}{ - 13} \\ y = 3 \\ [/tex]

[tex] x= 10 - 4(3) \\ x = 10 - 12 \\ x = - 2[/tex]

we have (-2,3)

ATTACHED IS THE SOLUTION

The definition of the functions implies that the value of x if f(x) = g(x) is 3

The equations of the functions are given as

f(x) = -2x + 4

g(x) = 2x - 8

This means that, we have the following equation

f(x) = g(x)

Substitute the known values in the above equation

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms in the above equation

So, we have

2x + 2x = 8 + 4

Evaluate the like terms in the above equation

So, we have

4x = 12

Divide both sides by 4

x = 3

Hence, the value of x such that the equations are equal is 3

The graph of the functions can be plotted using a graphing tool

See attachment for the graph of the functions

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The scale factor that was used for the drawing is 1 inch represents [tex]\frac{5}{9}[/tex] feet.

A fraction is a non-integer that has a numerator and a denominator. An example of a fraction is 2/9. 2 is the numerator and 9 is the denominator.

A scale drawing is either a smaller or a bigger version of another image. If the scale used in the drawing is smaller in relation to the dimension of the original image, the scale drawing is a reduced image. If this is not the case, then it is a bigger scale drawing.

The scale drawing is usually reduced at a constant dimensions using a scale factor. In order to determine the scale factor, divide both dimensions provided by 9.

(9 / 9) = (5 / 9)

1 inch = 5/9 feet

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Step-by-step explanation:

equation format: y = mx + b where m is slope and b is the y intercept.

From the points given we find that it is a horizontal line, which means slope or m = 0. So we know so far:

y = 0x + b or y = b

The y-intercept occurs where x = 0. This occurs at y = -7. So the equation for these two points:

EQUATION: y = -7

(Plotted graph attached)

Answer:

Step-by-step explanation:

Given the linear function for the traffic fines:

If a fine comes to $292, substitute f(s)=292 and solve for "s" to find the speed of the person:

Based on the given argument, it is concluded that my friend's reasoning was incorrect.

This refers to the type of function that represents one line on a linear plane in cartesian mathematics.

With this in mind and from the claim of my friend that a line always represents a function, my friend is incorrect because If the line was vertical, then it could not pass through and as such, cannot represent a function.

Therefore, the answer to the question is that my friend is incorrect in his claim about lines and functions.

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Answer:

196 x 3 / 100 = 5,88

Step-by-step explanation:

7% - 4% = 3%

So we need to had 3% t have again 4%

The solution for x in the equation x + 4 = 12 is 8.

Given,

Sum of two numbers is 12

Take the first number as x

Second number is given as 4

We have to find the value of x.

The equation will be like:

x + 4 = 12

Solve for x in the equation.

Add -4 to both sides

x + 4 - 4 = 12 - 4

x = 8

That is, the solution for x in the equation x + 4 = 12 is 8.

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The question is incomplete. Completed question is given below.

The sum of a number and 4 is 12. Find the number.

Notice from the graph that data are mostly to the right.

Answer: Option C The distribution is tailed.

The net sales of Shauna's company when she calculated the sales for her company using the figures is $66700.

The total of a company's net sales is its gross sales less any returns, allowances, and discounts. Externally, net sales calculations are not always obvious. They can frequently be taken into account when calculating top-line revenues that are shown on the income statement.

The total number of units sold is multiplied by the price per unit for the purpose of calculating gross sales. The term "returns" or "sales returns" refers to products that customers have sent back in exchange for reimbursement.

The nets sales based on the information given will be:

Gross sales = $72900

Less: Retuned sales = $3750

Less Discount = $2450

Net sales = $66700

Therefore, the net sale is $66700.

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The equations best represents "y is inversely related to x" is y = k(1/x).

The inverse proportionality can be described as the relationship that exist between two or more quantities whereby when one of the quantities is increasing in value, then the the second quantity will be decreasing in value however there will be a proportionality constant that would be found in the equation.

Considering the chosen option D, we can see that when the value of y is increasing then the value of x will be decreasing, and when the value of x is decreasing , them the value of y will be increasing.

Therefore, option C is correct.

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In a standard normal distribution, the range of values of z is from: D. d. -∞ to ∞.

A z-score is also known as a standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than the data that are far from the mean.

In conclusion, the range of values of z in a standard normal distribution are all real numbers which typically ranges from negative infinity (-∞) to positive infinity (∞).

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Complete Question:

In a standard normal distribution, the range of values of z is from ______.

a. -3.09 to 3.09

b. -1 to 1

c. 0 to 1

d. -∞ to ∞

For the given expressions we will have:

y = exp(x - 4)   →we have a shift of 4 units to the right.

y = exp (x +9)  → we have a shift of 9 units to the left.

y = exp(x) + 7 → we have a shift of 7 units up.

y = exp(x) - 6  → we have a shift of 6 units down.

Remember that the shifts work as follows.

For a function f(x), we define a vertical shift of N units as:

g(x) = f(x) + N

For a function f(x), we define a horizontal shift of N units as:

g(x) = f(x + N)

Then, if we have:

exp(x - 4) we have a shift of 4 units to the right.

exp (x +9) we have a shift of 9 units to the left.

exp(x) + 7 we have a shift of 7 units up.

exp(x) - 6  we have a shift of 6 units down.

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If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm

Consider the width of the rectangle as w

The length of a rectangle is 3 cm less than twice the width of the rectangle

The length of the rectangle = 2w-3

Perimeter of the rectangle = 75 cm

Perimeter of the rectangle =2(l+w)

Where l is the length and w is the width of the rectangle

Substitute the values in the equation

2(2w-3+w) = 75

2(3w-3) = 75

6w-6 = 75

6w = 81

w = 13.5 cm

The length of the rectangle = 2(13.5)-3

=24 cm

Hence, If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm

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Answer: D

Let the unknown value be x.

18 is 50% of ________n can also be written as;

18 = 50% of x

of means multiplication;

18 = 50% * x

18 = 50/100 * x

18 = 50x/100

cross multiply

18 * 100 = 50x

1800 = 50x

Divide both sides by 50

1800/50 = 50x/50

180/5 = x

x = 180/5

x = 36

Hence 18 is 50% of 36

Answer:

Step-by-step explanation:

The probability is represented by the following equation:

Answer:

that would be X=22, i had the same thing today, and got it right :D

Step-by-step explanation:

Using the normal distribution and the binomial distribution, it is found that:

a) 43.25% of 10 year old's cannot go on this ride.

b) There is a 0.7814 = 78.14% probability that at least two of them will be able to ride Batman the Ride.

c) There is a 0.1062 = 10.62% probability that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park.

d) There is a 0.0834 = 8.34% probability that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park.

The z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In the context of this problem, the mean and the standard deviation are given as follows:

[tex]\mu = 55, \sigma = 6[/tex]

For item a, the proportion is the p-value of Z when X = 54, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (54 - 55)/6

Z = -0.17.

Z = -0.17 has a p-value of 0.4325.

Hence the percentage is of 43.25%.

The formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

For item b, the parameters of the binomial distribution are given as follows:

p = 0.5675, n = 4.

Hence:

Hence:

P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3615 + 0.3162 + 0.1037 = 0.7814.

Which is the probability.

For item c, the probability is given as follows:

p x P(X = 0 with n = 2).

Hence:

p = 0.5675 x (0.4325)² = 0.1062.

For item d, the probability is given as follows:

p x P(X = 4 with n = 11). (inverse binomial).

Hence:

0.5675 x (11!)/(5! x 6!) x (0.5675)^4 x (0.4375)^7 = 0.0834.

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Answer:

height = x + 6

Step-by-step explanation:

Volume = length x width x height

V = 10x³ + 67x² + 30x − 72

length = 5x - 4 and width = 2x + 3

So length x width =  (5x - 4 ) x (2x + 3)

Using the FOIL method:

= (5x)(2x) + (5x)(3) + (-4)(2x) + (-4)(3)

= 10x² + 15x - 8x - 12

= 10x² + 7x -12

So to find height, divide Volume by (length x width)

10x³ + 67x² + 30x − 72  ÷ 10x² + 7x -12

Use polynomial long division. See image ( I did the best I could to capture the process)

The answer is x + 6

To verify
Multiply (5x-4) (2x + 3) (x + 6) = 10x³ + 67x² + 30x − 72

SOLUTION

The correct option is A (the first option)

We are asked to find the measure of the angle at the center.

Circle theorem:

The angle at the center of a circle = 2 x Angle at the circumference

The angle at the center of the circle = 2 x = 2 x 91 degrees

=182 degrees

The value for the angle at the center (?) of this circle is

The correct option is A (the first option)

3x + 5y = 15 is the equation of the line in standard form that passes through the point (5,0) and (0,3).

The formula for equation of line is expressed as;

y = mx + b

Where m is the slope and b is the y-intercept.

Given the data in the question;

Point 1 ( 5,0 )

Point 2 ( 0,3 )

First, we determine the slope of the line.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 3 - 0 )/( 0 - 5 )

Slope m = ( 3 )/( -5 )

Slope m = -3/5

Now, we plug the slope and coordinates of one the point into the equation of line to determine the y-intercept b.

y = mx + b

0 = (-3/5)5 + b

Solve for b

0 = -15/5 + b

0 = -3  + b

b = 3

Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (-3/5)x + 3

Convert to standard form; Ax + Bx = C

Multiply each term by 5

y = (-3/5)x + 3

5y = 5(-3/5)x + 5(3)

5y = -3x + 15

Reorder the equation

3x + 5y = 15

Therefore, the equation of the line is in standard form is 3x + 5y = 15.

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Answer:

43%

Step-by-step explanation:

To convert a decimal to a percent, you have to move the decimal over 2 times to the right.

Answer: 0.0625

Step-by-Step Explanation: positive exponents = multiply the number by itself however many times the exponent demands.

negative exponents:  multiply the reciprocal of the base number by itself however many times the exponent demands.

we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.

Total traffic fatalities = 29,757

Alcohol related = 9001

(a) probability that a randomly selected traffic fatality in this year was alcohol related:

P = 9001 / 29,757 = 0.302

(b) probability that a randomly selected traffic fatality in this year was not alcohol related:

P = 1 - 0.302 = 0.698

(c) probability that two randomly selected traffic fatalities in this year were both alcohol related:

P = 0.302 × (9000 / 29756)

P = 0.091

(d)What is the probability that neither of two randomly selected traffic fatalities in this year were alcohol related:

P = 1 - 0.091

P = 0.909

(e)  probability that of two randomly selected traffic fatalities in this year, at least one was alcohol related

P = 0.302 + 0.302 = 0.604

Therefore, we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.

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First graders in an elementary school number 92. We use mode.

Given that,

Determine which statistic would be most appropriate to characterize the middle of the next set of data: the mean, median, or mode.

First graders in an elementary school number 92. The first graders' heights are fairly similar to one another because they are all roughly the same age.

We have to find which statistic—the mean, median, or mode—does the first-graders' height best represent.

First graders in an elementary school number 92.

Depending on which their birthday walls, the first graders might be six, seven and eight on the last day of the second year.

Therefore, We use mode.

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Answer:

  5/9

Step-by-step explanation:

You want the reduced fraction equivalent to the ratio 40L : 72L.

A ratio is reduced by removing the greatest common factor from all parts of the ratio. Here, that factor is 8L.

  40L : 72L = (8L)(5) : (8L)(9) = 5 : 9 = 5/9

The ratio is 5/9.

__

Additional comment

The greatest common factor can be found several ways. The easiest is for you to make use of your knowledge of multiplication tables:

  40 = 5·8

  72 = 9·8

8 is a common factor. Since 5 and 9 have no common factors, 8 is the greatest common factor of 40 and 72.

The part "since  ∠ AMC is a right angle, ∠BMC and ∠CMD will be complementary" and "since  ∠ BMC is a right angle, ∠BMC and ∠AMB will be complementary" , the paragraph proof is incorrect.

We are given that,

∠ AMC and ∠BMC are right angles.

Since,

∠ AMC = ∠ AMB + ∠ BMC

The paragraph part should have been ∠ AMB  and ∠ BMC are complementary angles and,

Since,

∠ BMD = ∠ BMC + ∠ CMD

The paragraph part should have been ∠ CMD  and ∠ BMC are complementary angles instead of the part given in the paragraph proof.

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