45 medals were given out at a band competition. There were 22 bronze medals and 14 silver medals. The rest were gold medals. What percentage of medals were gold medals?

He stands 6 feet tall, and his shadow extends 9 feet. if the building's shadow extends for 322.5 feet.

Now 6/9 = X/322.5

9X = 1935

X = 215ft

The Height of the building = 215ft

Consider an object AB of height h such that its shadow of length s is formed and angle of elevation is θ.

The object AB depicts a right triangle in which ∠ABO = 90o.

Now we know that in trigonometry, the tangent ratio for an angle is equal to the opposite side to that angle divided by its adjacent side.

So, for the angle of elevation θ, we have

=> tan θ = AB/OB

Putting AB = h and OB = s, we get

=> tan θ = h/s

=> s/h = 1/tan θ

=> s = h/tan θ

Learn more about Shadow here:

https://brainly.com/question/15021258

#SPJ4

Answer:

c. t = 18; the Chang family has been driving for 18 hours

Step-by-step explanation:

Given:

D(t) = 2,280 - 60t

Find t when D(t) = 1,200

D(t) = 2,280 - 60t

1200 = 2280 - 60t

Subtract 2280 from both sides of the equation

1200 - 2,280 = 2280 - 60t - 2,280

- 1080 = - 60t

Divide both sides by -60

- 1080 / -60 = - 60t / -60

18 = t

t = 18

This means the Chang family has been driving for 18 hours

c. t = 18; the Chang family has been driving for 18 hours

Answer:

Step-by-step explanation:

The equation that gives total savings y as a function of the number of months x is y = $300x

Given that Mrs. White started saving $300 a month. After 3 months, she had $1200. Now, we need to write an equation that gives total savings y as a function of the number of months x
Let us consider that the total savings Mrs. White saved after x months = y
From the given data, we can see that the amount of saving she does each month = $300
So, at the end of 3 months, she had saved an amount of= $300 × 3 = $900
Total savings after 3 months, y = $1200
Thus, we can say that; the total amount she saves, increases every month by $300$300$300 ×x= $y (total savings)
We can write this equation as the function of total savings y as a function of the number of months
x:y = $300x

Thus, the equation that gives total savings y as a function of the number of months x is y = $300x.

To know more about total savings, click here

https://brainly.com/question/7965246

#SPJ11

Answer:

-3

Step-by-step explanation:

Term:

Term 1 = -3b

Here, b is the variable and (-3) is the coefficient of the variable 'b'.

+12 is called the constant.

Answer:  (-3) is the coefficient.

Answer:

a) 23x

b) 8n

c) -6y

d) -17w

Explanation:

When combining like terms, if there is an addition operator, add both coefficients and carry the variable over. If there is a subtraction operator, subtract both coefficients and carry the variable over. Remember, you can only combine like terms if the variable, and exponent are the same. The addition and subtraction symbols are examples of an operator used in arithmetic. For example, 9x + 14x could be like adding 9 objects and 14 objects together, you have 23 objects total because 9 + 14 = 23. When you add negative numbers, it is like subtracting. When you subtract negative numbers, it is like adding. Negative just means opposite.

a) 9x + 14x = (9+14)x = (23)x = 23x

b) -2n - 10n = (-2+10)n = (8)n = 8n

c) 8y - 14y = (8-14)y = (-6)y = -6y

d) -6w - 11w = (-6-11)w = (-17)w = -17w

Answer:

a: 23x

b: 8n

c: -6y

d: -17w

Step-by-step explanation:

you just add/subtract the numbers then add the variable at the end

The equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

To find the slope of the tangent line to the parabola at the point (1,5), we need to find the derivative of the equation y = 6x - x² and evaluate it at x = 1.

Taking the derivative of y with respect to x:

dy/dx = d(6x - x²)/dx

= 6 - 2x

Now, we can substitute x = 1 into the derivative to find the slope at that point:

slope = 6 - 2(1)

= 6 - 2

= 4

So, the slope of the tangent line to the parabola at the point (1,5) is 4.

To find the equation of the tangent line, we need to use the point-slope form of a line.

The equation is given by:

y - y₁ = m(x - x₁)

Substituting the values we have:

y - 5 = 4(x - 1)

Expanding and simplifying:

y - 5 = 4x - 4

Moving the constant term to the other side:

y = 4x + 1

Therefore, the equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

Learn more about tangent line click;

https://brainly.com/question/23416900

#SPJ4

Complete question =

Find the slope of the tangent line to the parabola at the point (1,5). y = 6x-x². find an equation of the tangent line.

Answer:

I'm pretty sure its -11

Answer:

f(3) = -11

Step-by-step explanation:

Substitute 3 in wherever you see an x:

f(3) = -4 * 3 + 1

f(3) = -12 + 1

f(3) = -11

Answer:

a.y=6

b.-1/8

c.1/2

d.2800

e.-8

f.7.71

Step-by-step explanation:

Answer:

Exact Form:

3√5

Decimal Form:

6.70820393

Step-by-step explanation:

Answer:

Distance = 3√5 or 6.708203932,,,

Step-by-step explanation:

Find the distance between the y-values and x-values which in this case would be 6 and 3. Use the Pythagorean theorem.

\(3^2 + 6^2 = 45\)

Simplify.

\(\sqrt{45} = 3\sqrt{5}\)

The total capacity of pool in gallons is 1625.

Let us assume the water in the pool be x liters. Forming the equation according as per the statement in question -

x + 300 = 80% of total volume - Equation 1

Forming the equation according to second statement -

30% × x = 300

30/100 × x = 300 - Equation 2

Finding the initial volume of water using equation 2-

x = 300×100/30

Cancelling zero and performing division and multiplication to find the initial volume of water

x = 1000 gallons

Now finding the total volume or capacity of pool by keeping the value of x in first equation -

1000 + 300 = 80/100 × total volume

Total volume = 1300×100/80

Performing multiplication and division to find the total capacity of pool

Total capacity of pool = 1625 gallons

Hence, the total capacity of pool in gallons is 1625.

Learn more about calculations on pool capacity -

https://brainly.com/question/1774581

#SPJ4

Answer:

x=-2 y=-5

x=5 x=2

From the given graph, we have that:

The Factor Theorem states that a polynomial function with roots(also called zeros) \(x_1, x_2, \codts, x_n\) is given by the following rule.

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

In a graph, the roots are when the function crosses the x-axis, hence they are given by:

\(x_1 = -2, x_2 = 0, x_3 = 3\)

Hence:

f(x) = ax(x + 2)(x - 3)

f(x) = ax(x² - x - 6)

f(x) = a(x³ - x² - 6x).

When x = 1, y = -6, hence we use it to find the leading coefficient a:

-6 = a(1 - 1 - 6)

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ - x² - 6x.

In a graph, the domain and the range are found as follows:

The function is defined for all real values, and also assume all real values, hence:

Both the domain and the range are all real values.

Hence:

More can be learned about domain and range at https://brainly.com/question/10197594

#SPJ1

Answer:

3

Step-by-step explanation:

4/12 = 1/3 yepppp djdkkdkdd

The solution when solved for b is 14 degrees because angles b and b + 56 are vertically opposite.

When a transversal cuts two parallel lines, some of the angles become congruent.

From the given diagram, the given angles are equal according to the vertical angles theorem.

Both angles are vertically opposite become they meet at a point of intersection.

Hence 5b = b + 56

5b - b = 56

4b = 56

b = 56/4

b = 14

Hence the solution when solved for b is 14 degrees because angles b and b + 56 are vertically opposite.

Learn more on angles here: https://brainly.com/question/16810065

Answer:

Step-by-step explanation:

so just go look it up in google or sum

hope it helps

Step-by-step explanation:

5 - 7x = -44

5 + 44 = 7x

49 = 7x

7x = 49

x = 49/7

x = 7

The equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rectangular track along the walls of the gym and has an area of 7000ft²

Let x be the width of the rectangle.

As the area of track along the walls of the gym is 7000ft²

(x - 12)(3x - 12) = 7000

After simplifying:

3x² - 48x + 6856 = 0

Thus, the equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ1

named width in java with a value of 1.55.

double length = 3.5; double width = 1.55;

Double is a data type in Java that supports storing decimal numbers. It is used to represent values that include a fractional component and is a 64-bit floating-point data type. When exact decimal numbers are required, as in financial or scientific computations, the double data type is frequently utilized. A double's range is roughly  ±\(5.0 \times 10^{-324}\) to ±\(1.7 \times 10^{308\) having a 15–17 decimal digit degree of accuracy.

For example:

double myDouble = 3.14; Alternatively, you may define a double variable without first giving it a value and then give it one later on in your code.

3.5 double length, 1.55 double width;

Learn more about Java

brainly.com/question/29897053

#SPJ4

If the contribution margin from the order is greater than the additional fixed expenses, accepting the special order can result in an increase in operating income.

When evaluating a special sales order, the first step is to calculate the revenue from the order. This is typically based on the selling price and the quantity of units to be sold. Then, the variable expenses directly associated with fulfilling the order, such as direct materials, direct labor, and variable manufacturing overhead, are deducted from the revenue to determine the contribution margin.

Next, the additional fixed expenses that would be incurred if the special order is accepted need to be considered. These expenses are typically costs that are directly related to the production or fulfillment of the order and are not already included in the existing fixed expenses.

To assess the impact of the special order on operating income, the increase (or decrease) in operating income is calculated by subtracting the additional fixed expenses from the contribution margin. If the result is positive, it indicates that accepting the special order would lead to an increase in operating income.

In the given scenario, it is mentioned that Cotton has excess capacity to manufacture the special order. If the incremental analysis shows that the special order would result in a positive increase in operating income, it would be beneficial for Cotton to accept the special sales order.

Learn more about income here :

brainly.com/question/28970926

#SPJ11

The probability of Stephen Curry making exactly three of his next five free throws is 0.3264 or 32.64%.

\(p(x) = nCx * p^x * q^(n-x)\)

where:

n = total number of attempts (5 in this case)

x = desired number of successes (3 in this case)

p = probability of success (0.92 in this case)

q = probability of failure (1 - p, or 0.08 in this case)

Plugging these numbers into the equation gives us:

p(3) = 5C3 * 0.92^3 * 0.08^2 = 0.3264

Stephen Curry is a professional basketball player in the NBA who is known for his incredibly accurate shooting ability. He made 92% of his free throws during the 2018-2019 regular season with the Golden State Warriors. We can calculate the probability of Curry making exactly three of his next five free throws using the binomial probability formula. This formula takes into account the probability of the event (Curry making the free throw) and the number of attempts (five). In this case, the probability of success (Curry making the free throw) is 0.92 and the number of attempts is five. Plugging these numbers into the equation gives us a probability of 0.3264 or 32.64%. This means that Curry has a 32.64% chance of making exactly three of his next five free throws.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

The respective lengths as requested of each triangle are;

x = 7

y = 12

PQ = 29

QR = 29

PS = 32

RS = 32

PT = 25

PR = 50

QT bisects PR and so;

PT = PR (bisected segments)

PQR is an Isosceles triangle where two sides are congruent and so;

PQ = QR

5y - 31 = 2y + 5

3y = 36

y = 12

PRS is an Isosceles triangle where two sides are congruent and so;

PS = RS

4x + 4 = 7x - 17

3x = 21

x = 7

Thus;

PQ = 5(12) - 31 = 29

QR = 2(12) + 5 = 29

PS = 4(7) + 4

PS = 32

RS = 7(7) - 17

RS = 32

PT = 6(7) - 2(12)

PT = 25

PR = 2 * 25

PR = 50

Read more about side length of triangle at; https://brainly.com/question/24597672

#SPJ1

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

The area of the circle is 9π. Then the radius of the circle is given as,

A = π

πr² = π

r² = 1

The center of the circle is at (-7, -15). Then the equation of the circle is given as,

(x + 7)² + (y + 15)² = 1

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

More about the equation of the circle link is given below.

https://brainly.com/question/10618691

#SPJ1

0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.

Explanation:

0>1.

To learn more about Binary string refer to:

https://brainly.com/question/29739112

#SPJ4