The height of a flare is given by the equation h(t)= -0.5t² +16t+22 where h is the height of the flare in metres and is the time the flare has been in the air in seconds. How long will the flare be in the air if it fizzles out at a height of 10 m above ground?

The mistake that Rafael made is interchanging the y-values with the x-values.

The real slope of the line is 25.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (100 - 50)/(4 - 2)

Slope, m = 50/2

Slope, m = 25.

Read more on slope here: brainly.com/question/3493733

#SPJ1

Applying the definition of variation, we have:

1. When x = 36, y = 6.

2. When x = 1, y = 27.

3. It takes 3 seconds for the object to fall 144 feet.

4. Length of a string that vibrates 64 times per second is 48 inches.

Inverse variation is a type of relationship between two variables in which one variable increases while the other decreases, or vice versa, in a way that the product of the two variables remains constant.

In other words, if we have two variables x and y that are inversely proportional, we can write:

x × y = k, where k is a constant.

1. We are given that y varies directly as the square root of x. This means that we can write:

y = k√x

where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 16, y = 4:

4 = k√16

4 = 4k

k = 1

Now we can use this value of k to find y when x = 36:

y = 1√36

y = 6

Therefore, when x = 36, y = 6.

2. We are given that y varies inversely with the cube of x. This means that we can write:

y = k/x³

where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 3, y = 1:

1 = k/3³

1 = k/27

k = 27

Now we can use this value of k to find y when x = 1:

y = 27/1³

y = 27

Therefore, when x = 1, y = 27.

3. We are given that the distance that an object falls varies directly with the square of the time, t, of the fall. This means that we can write:

d = kt²

where d is the distance, k is a constant of proportionality, and t is the time. To find the value of k, we can use the given information that when t = 1, d = 16:

16 = k(1)²

16 = k

k = 16

Now we can use this value of k to find the time it takes for the object to fall 144 feet:

144 = 16t²

9 = t²

t = 3

Therefore, it takes 3 seconds for the object to fall 144 feet.

4. We are given that the rate of vibration of a string under constant tension varies inversely with the length of the string. This means that we can write:

r = k/L

where r is the rate of vibration, L is the length of the string, and k is a constant of proportionality.

To find the value of k, we can use the given information that when L = 24 inches, r = 128 vibrations per second:

128 = k/24

k = 3072

Now we can use this value of k to find the length of a string that vibrates 64 times per second:

64 = 3072/L

L = 48 inches

Therefore, the length of a string that vibrates 64 times per second is 48 inches.

Learn more about inverse variation on:

https://brainly.com/question/13998680

#SPJ1

We can rewrite 3.1672 × 10¹² as 3.1672 × 10² The correct option is A

First we first express it as a number between 1 and 10 multiplied by a power of 10. In this case, 316.72 can be expressed as:

3.1672 × 10¹² (since we move the decimal point 2 places to the right to get to 31672)

However, in scientific notation, the exponent should represent the number of places the decimal point is moved. Since we moved the decimal point to the right, the exponent should be negative.

Therefore, we can rewrite 3.1672 × 10¹² as:

3.1672 × 10²

So, the answer is (A).

Learn more about scientific notation here : brainly.com/question/30567686

#SPJ1

The probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu is: 0.087.

This is a binomial distribution problem, where n = 55 and the probability of success (i.e. a person subscribing to Hulu) is p = 0.41.

The probability mass function of a binomial distribution is:

P(X = x) = (nCx) * p^x * (1-p)^(n-x)

where nCx is the binomial coefficient (i.e. the number of ways to choose x items from n items).

So, in this case, we want to find P(X = 20):

P(X = 20) = (55C20) * 0.41^20 * (1-0.41)^(55-20)

P(X = 20) ≈ 0.087

Therefore, the probability that in a random sample of 55 18 to 29-year-olds, 20 will say they currently have a subscription to Hulu is approximately 0.087or 8.7%.

Learn more about probability here:https://brainly.com/question/24756209

#SPJ1

The point in which f(x) have a horizontal tangent are (-7 + √46)/3, (-7 - √46)/3

To find the values of x where the graph of f(x) has a horizontal tangent, we need to find where the derivative of f(x) is equal to zero (since the derivative gives the slope of the tangent line).

First, we find the derivative of f(x):

f'(x) = 3x² + 14x + 1

Next, we set f'(x) equal to zero and solve for x:

3x² + 14x + 1 = 0

Using the quadratic formula, we get:

x = (-14 ± √(14² - 431)) / (2*3)

x = (-14 ± √(184)) / 6

x = (-14 ± 2√46) / 6

Simplifying:

x = (-7 ± √46) / 3

Therefore, the values of x where the graph of f(x) has a horizontal tangent are (-7 + √46)/3 and (-7 - √46)/3.

Learn more on horizontal tangent here;

https://brainly.com/question/29001364

#SPJ1

The percent of the bottle of apple juice is 40%.

An element of a whole number is a fraction. There are many different kinds of fractions. Three-quarters, for instance, is a fraction.

A decimal point separates a fractional component from an integral component to form a decimal. In the decimal 2.5, for instance, the fractional portion comes after the decimal point and is followed by the integer 2, which is put before it.

Per cent simply means one in a hundred. Hence, it is a number with a fractional representation that has a denominator of 100. As a result, fractions of a whole number are also described using percentages.

Given that, 80-ounce bottle of apple juice contains 32 ounces of water.

Thus,

% of water = (32 / 80) * 100 = 40%

Hence, the percent of the bottle of apple juice is 40%.

Learn more about decimals here:

https://brainly.com/question/29765582

#SPJ1

Answer:

82.28

this was really easy,

An equation for a rational function with the given characteristics is found as:  f(X) = a(x+4)(x) / (x+2)(x-4).

As x = -2 and X = 4 have vertical asymptotes, the denominator will contain the equations (x+2) and (x-4)

The terms (x+4) and 1 will be in the numerator since the x intercepts are (-4,0) , respectively (x-0).

Our current formula is f(X) = a(x+4)(x) / (x+2)(x-4)

We examine the horizontal asymptote to determine the value of A.

The limit of a function as x -> infinity would be - 3 since the horizontal asymptote reflects what the function looks like as x approaches infinity.

Thus,  an equation for a rational function with the given characteristics is found as:  f(X) = a(x+4)(x) / (x+2)(x-4)

Know more about rational function

https://brainly.com/question/19044037

#SPJ9

After making the minimum payment of $125, the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

If the minimum monthly payment of $125 is made, we can calculate the new balance, unpaid balance, and interest charge as follows:

The interest rate per month is (18% per year) / 12 = 1.5% per month.

First, we calculate the interest charge for the month on the unpaid balance:

Interest charge = (1.5% per month) x ($5000 unpaid balance)

Interest charge = $75

Next, we subtract the minimum payment from the unpaid balance to get the new unpaid balance:

Unpaid balance = $5000 - $125

Unpaid balance= $4875

Then, we add the interest charge to the new unpaid balance to get the new balance:

New balance = $4875 + $75

New balance = $4950

Finally, we can calculate the purchasing power as the credit limit minus the new balance:

Purchasing power = $5000 - $4950

Purchasing power = $50

Therefore the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

Learn more about purchasing power here:https://brainly.com/question/28199500

#SPJ1

On solving the provided question, we can say that Given that you have already waited for 10 minutes, the inequality that you will have to wait another six minutes or longer is around 0.0183.

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.  

Applying the exponential distribution's memoryless characteristic, we have:

P(Y ≥ 6 | Y > 10) = P(Y ≥ 16)

= 1 - P(Y < 16)

= 1 - F(16) (16)

where F(t) is the exponential distribution's cumulative distribution function (CDF) with a mean of 4 minutes.

F(t) = 1 - e(-t/) yields the CDF of an exponential distribution with mean, where t 0. As a result, we have:

[tex]P(Y \geq 6 | Y > 10) = 1 - F(16) (16)\\= 1 - (1 - e^(-16/4))\\= e^(-4) (-4)\\≈ 0.0183[/tex]

Given that you have already waited for 10 minutes, the likelihood that you will have to wait another six minutes or longer is around 0.0183.

To know more about inequality visit:

https://brainly.com/question/29914203

#SPJ1

Answer:

w = 6in, l = 10in

Step-by-step explanation:

Area of a rectangle is [tex]A=l*w[/tex]

and [tex]l = 4 + w[/tex]

We can solve for length and width by substituting these values for the equation.

[tex]60in^2=(4+w)*w[/tex]

[tex]60in^2=4w+w^2[/tex]

[tex]0 = w^2 + 4w + 60in^2[/tex]

factor out the equation.

[tex]0= (w+10)(w-6)[/tex]

therefore w = 6in (tossing out the negative solution)

which means

[tex]l = 4 + w[/tex]

[tex]l = 6in + 4[/tex]

l = [tex]10in[/tex]

Hope this helps!
Brainliest is much appreciated!

Using set theory, the element in each of the set are, A - B = {3, 5}, (A - B)^c = {2, 4, 6, 7, 8, 9, 10, 11}, U - (A - B)^c = {3, 5}, (A \cup B)^c = {2, 4, 6} and (A^c U B^c)^c = {7, 9, 11}.

The given sets are:

U = {2,3,4,5,6,7,8,9,10,11}

A = {3,5,7,9,11}

B = {7,8,9,10,11}

We can use these sets to find the following:

1. A - B: The elements in set A that are not in set B are {3, 5}.

2. (A - B)^c: The complement of set A - B in U contains all the elements in U that are not in A - B. These elements are {2, 4, 6, 7, 8, 9, 10, 11}.

3. U - (A - B)^c: This set contains all the elements in U that are not in the complement of A - B. These elements are {3, 5}.

4. (A U B)^c: This set contains all the elements in U that are not in the union of sets A and B. The union of A and B is {3, 5, 7, 8, 9, 10, 11}, so the complement is {2, 4, 6}.

5. (A^c U B^c)^c: This set contains all the elements in U that are in neither the complement of set A nor the complement of set B. The complement of set A is {2, 4, 6, 8, 10} and the complement of set B is {2, 3, 4, 5, 6}. The union of these two sets is {2, 3, 4, 5, 6, 8, 10}, so the complement of this set in U is {7, 9, 11}.

Learn more on set theory here;

https://brainly.com/question/13458417

#SPJ1

The correct statement regarding the relative minimums of each function is given as follows:

The minimum of h(x) is farther left and down from the minimums of f(x) and g(x).

The function f(x) is defined as follows:

f(x)= √x.

It has a relative minimum at (0,0), which is one the first quadrant.

The function g(x) is defined as follows:

√x-3+1

It is a translation of 3 units right and 1 unit up of f(x), hence the minimum has coordinates (3,1), which is on the first quadrant.

The function h(x) is defined as follows:

h(x)= √x+1-2

It is a translation of 1 unit left and 2 units down of f(x), hence the minimum has coordinates (-1, -2), which is on the third quadrant.

The third quadrant is farther left and down from the first quadrant.

More can be learned about translation at https://brainly.com/question/30958512

#SPJ1

Answer:

61,770

Step-by-step explanation:

6.177 x [tex]10^{4}[/tex]

[tex]10^{4}[/tex] = 10,000

6.177 x 10,000 = 61,770

So, the answer is 61,770

Using Pythagoras theorem, we can find the length of the missing side to be 10 units.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, also referred to as the Pythagorean theorem.

The Pythagorean Theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of its other two sides.

In the given triangle, the base is given as:

b = 6 units.

height, h = 8 units.

Let the missing side be = x.

Now as per the Pythagoras theorem,

x² = 8² + 6²

⇒ x² = 64 + 36

⇒ x² = 100

⇒ x = 10.

Therefore, the length of the missing side of the triangle here is 10 units.

To know more about Pythagoras theorem, visit:

https://brainly.com/question/343682

#SPJ1

Answer:

Step-by-step explanation:

[tex]S=40R+20[/tex]

The correct function equivalent to the original function V = 40,000(0.64) is V = 40,000(0.64)ⁿ.

Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.

Here,

The original function V = 40,000(0.64) models the value, V, of a $40,000 car after t years, where the car depreciates at a rate of 36% per year. The expression 0.64 represents the remaining value of the car after one year, which is obtained by subtracting 36% from 100% (i.e., 100% - 36% = 64%).

To find an equivalent function, we need to simplify 0.64. We can write 0.64 as 0.8², since 0.8 multiplied by itself gives 0.64.

So, V = 40,000(0.64) is equivalent to V = 40,000(0.8²), which simplifies to V = 40,000(0.64). This means that both expressions represent the same function that models the value of the car after t years, given that the car depreciates at a rate of 36% per year.

To know more about percent,

https://brainly.com/question/29172752

#SPJ1

Therefore , the solution of the given problem of equation comes out to be spot A's coordinates are (80,-20).

In mathematical formulas, it is common to use the same variable term to guarantee agreement between two claims. Mathematical assertions, also known as equations expression, are employed to convey the equality of numerous academic figures. In this case, the normalise method adds b + 6 using the data of y + 6 rather than splitting 12 into two parts.

Here,

Let (a,b) represent the location of point A. Consequently, the inclination of the line through (0,0) and (a,b) is

=> m = (b - 0) / (a - 0) Equals b / a

This line being parallel to the initial road gives us:

=>  m = -1/4

Therefore:

=>  b / a = -1/4

=>  b = -a/4

=>  √[(a - 0)² + (-a/4 - 0)²] = √(17a²/16)

From (a,-a/4) to (85,0), the distance is:

=>  √[(85 - a)² + (0 - (-a/4))²] = √[(85 - a)² + (a/4)²]

These two separations are equal, so we can put them at the same value and find a:

=>  √[(85 - a)² + (a/4)²] = √(17a²/16)

When we square both edges, we obtain:

=>  (85 - a)² + (a/4)² = 17a²/16

=>  16(85 - a)² + a² = 17a²

=>  16(7225 - 170a + a²) + a² = 17a²

=>  115600 - 2720a + 17a² + a² = 17a²

=>  18a² - 2720a + 115600 = 0

=> 9a² - 1360a + 57800 = 0

=>  a = (1360 ± √(1360² - 4957800)) / (2*9)

=>  a = (1360 ± √(307600)) / 18

=>  a = (1360 ± 560) / 18

=>  a = 80 or a = 40/9

Point A's y-coordinate is:

=> b = -a/4 = -80/4 = -20

Consequently, spot A's coordinates are (80,-20).

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

We can cοnclude that the expοnential functiοn represented by the given table is [tex]y = 3(0.5)^x[/tex]

An expοnential functiοn is a mathematical functiοn οf the fοrm [tex]f(x) = ab^x[/tex], where a and b are cοnstants and b is greater than 0 and nοt equal tο 1. It is a type οf mathematical mοdel that describes a prοcess where a quantity grοws οr decays at a rate prοpοrtiοnal tο its current value οver time οr space.

An expοnential functiοn has the fοrm:

[tex]\mathrm y = ab^x[/tex]

where "a" is the initial value οf the functiοn, and "b" is the grοwth factοr οr base οf the functiοn.

Tο find the equatiοn οf the expοnential functiοn represented by the given table, we can use the first twο data pοints tο determine the values οf "a" and "b", and then check if the remaining data pοints fit the functiοn.

Using the first data pοint (0, 3), we get:

[tex]3 = ab^0[/tex]

3 = a

Using the secοnd data pοint (1, 1.5), we get:

[tex]1.5 = ab^1[/tex]

1.5 = 3b

b = 0.5

Therefοre, the equatiοn οf the expοnential functiοn represented by the given table is:

[tex]y = 3(0.5)^x[/tex]

We can check the remaining data pοints tο see if they fit the functiοn:

Fοr [tex]x = 2, y = 3(0.5)^2 = 0.75[/tex]

Fοr[tex]x = 3, y = 3(0.5)^3 = 0.375[/tex]

Since all the data pοints fit the equatiοn, we can cοnclude that the expοnential functiοn represented by the given table is:

[tex]y = 3(0.5)^x[/tex]

To learn more about Exponential Functions

https://brainly.com/question/28596571

#SPJ1

To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.

A factor is a number or expression that divides another number or expression evenly without a remainder.

To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.

To determine this factor, we divide the desired number of rolls (30) by the original number of rolls (12):

2.5 = 30/12

To find the amounts of each ingredient needed to make 30 rolls, we multiply the original amounts by 2.5:

Yeast: 1/4 oz x 2.5 = 0.625 oz (or about 0.63 oz)

Warm water: 1 cup x 2.5 = 2.5 cups

Molasses: 3 tbsp x 2.5 = 7.5 tbsp (or about 1/2 cup + 1 tbsp)

Powdered milk: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)

Egg yolk: 1 beaten yolk x 2.5 = 2.5 beaten yolks (or about 2 yolks)

Egg white: 1 beaten white x 2.5 = 2.5 beaten whites (or about 2 whites)

Bread flour: 3 1/2 cups x 2.5 = 8.75 cups (or about 8 3/4 cups)

Butter: 6 tbsp x 2.5 = 15 tbsp (or about 1 cup - 1 tbsp)

Salt: 1 tsp x 2.5 = 2.5 tsp (or about 2 1/2 tsp)

Whole wheat flour: 1/2 cup x 2.5 = 1.25 cups (or about 1 1/4 cups)

Raisins: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)

To make 30 rolls, you will need 0.625 oz (or about 0.63 oz) of yeast.

To make 30 rolls, you will need 0.83 cups (or about 3/4 cup + 1 tbsp) of powdered milk.

To make 30 rolls, you will need 15 tbsp (or about 1 cup - 1 tbsp) of butter.

To make 30 rolls, you will need 8.75 cups (or about 8 3/4 cups) of bread flour, which is 8.75 - 1.25 = 7.5 cups more than the 1.25 cups of whole wheat flour needed.

If you put in 3/8 cup of water instead of the 1/4 cup called for in the original recipe, you have added an extra 3/8 - 1/4 = 1/8 cup of water, or 2 tablespoons of water.

To know more about factor visit:

https://brainly.com/question/29014674

#SPJ1

Answer:

[tex]A=\frac{4}{6} *600 = 400\\B=\frac{2}{6} *600 = 200[/tex]

Answer:

the scale factor = 3

Step-by-step explanation:

the question is basically saying: how did (12,-4) jump to (36,-12)

we can make d represent the scale factor used to get (12,-4) to (36,-12)

so,

12d = 36

-4d = -12

all there's left to do is to simply solve for d, which is 3

Answer: -5 1/4

Step-by-step explanation:

After answering the final question incorrectly, Sandra's score will be -5 1/4 in fraction form, and -5.25 in decimal form. This is because every time Sandra gets a question wrong her grade goes down by -3/4 points. And -4 1/2 minus -3/4 is -5 1/4. I hope this helped. If not, let me know and I can try to reword it.

Answer: b

Step-by-step explanation:

To determine the distance of the foot of the ladder from the wall, we can use trigonometry. Let's call the distance we want to find "x".

First, let's draw a diagram:

          |\

          | \

   20   |  \ x

          |   \

          |____\

           40°

In this diagram, the ladder is the hypotenuse of a right triangle, and the distance we want to find ("x") is one of the legs. The other leg is the height of the ladder on the wall, which we don't need to know in order to solve the problem.

We can use the trigonometric function for the sine of an angle to relate the angle of elevation to the distance "x" and the length of the ladder:

sin(40°) = x / 20

To solve for "x", we can multiply both sides by 20:

20 sin(40°) = x

Using a calculator, we can evaluate the sine of 40 degrees to get:

20 sin(40°) ≈ 12.85

So the distance of the foot of the ladder from the wall is approximately 12.85 meters, rounded to two decimal places.

Answer: -1/2

Step-by-step explanation:

To find the slope: rise/run

starting from the point (0,2), you go up 1 to reach the line

Therefore 1 is your rise.

Then go right 2 units and you hit the line again.

Therefore the slope is 1/2.

But the linear line is going downwards, so it is a negative slope

Therefore your final answer is:

-1/2

Answer: 14 dollars.

Step-by-step explanation:

You (1) + your four friends (4) is 5.

5 times a number is 70.

5x=70

70/5=14

x=14

So, Jane's hourly rate is $6.00 per hour.

In mathematics, division is a basic arithmetic operation that involves splitting a number or quantity into equal parts or groups. It is the inverse operation of multiplication, where we find out how many times one number (the divisor) can fit into another number (the dividend) without leaving any remainder.

Here,

However, we can calculate her hourly rate by dividing her total earnings by the number of hours she worked.

From the payroll information provided, Jane earned $120.00 for 20 hours of work. Therefore, her hourly rate would be:

Hourly rate = Total earnings / Number of hours worked

Hourly rate = $120.00 / 20 hours

Hourly rate = $6.00 per hour

To know more about division,

https://brainly.com/question/28598725

#SPJ1