A sixth-grade class is painting a mural. To make a darker shade of orange, they use a ratio of 5 ounces of red paint to
3 ounces of yellow paint. Use this ratio to consider the amount of yellow paint needed for each amount of red paint
listed in the table.
Point
Red Paint, x (ounces)
Yellow Paint, y ounces)
A
5
ts
B
15
C
20

The probability of observing heads when tossing either coin is P(h) = 0.5*P(f) + 0.6*P(b), and the probability of observing tails is P(t) = 0.5*P(f) + 0.4*P(b).

Let's denote the probability of observing heads when tossing the fair coin as P(h|f) and the probability of observing tails when tossing the fair coin as P(t|f). Similarly, we can denote the probability of observing heads when tossing the biased coin as P(h|b) and the probability of observing tails when tossing the biased coin as P(t|b).

In this experiment, the probability of tossing the fair coin is P(f) and the probability of tossing the biased coin is P(b). We can calculate the probability of observing heads as:

P(h) = P(h|f)*P(f) + P(h|b)*P(b)

= 0.5*P(f) + 0.6*P(b).

Similarly, the probability of observing tails is:

P(t) = P(t|f)*P(f) + P(t|b)*P(b)

= 0.5*P(f) + 0.4*P(b).

The probability of observing heads when tossing either coin is P(h) = 0.5*P(f) + 0.6*P(b), and the probability of observing tails is P(t) = 0.5*P(f) + 0.4*P(b).

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The probability that a red card is drawn at least once by the third draw is 0.88.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let, a card is drawn from a standard deck of 52 cards and then placed back into the deck.

In a standard 52 card deck the red cards are 26.

So,

P(red) =  n(red cards) / n(total cards)

          = 26 / 52

P(red) = 0.50

Now, X ≈ Bin (n = 3, P = 0.50)

P(X = x) = (n  x) p^x (1 - p)^n-x

(n  x) = \(\frac{n!}{x!(n-x)!}\)

P(X ≥ 1) = 1 - P(X < 1)

            = 1 - P(X = 0)

            = 1- (3  0)(0.5)^0(0.5)^3

            = 1 - 0.125

             = 0.875

P(X ≥ 1)  = 0.88

Hence, the probability that a red card is drawn at least once by the third draw is 0.88.

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Answer:

the process of translating words or text from one language into another.

In Geometry, a translation is a transformation that moves all the points of a figure by the same distance in a given direction.

Let's say you want to translate a triangle by 3 units to the left. You would basically move the entire triangle 3 units to the left without changing the shape.

The equation for the water level in Pensacola as function of time (t) is  \(5 * cos(\pi t/6) + 7\)

As high tide occurred at noon with a water level of 12 feet and the low tide had a water level of 2 feet, we will use cosine function to model the water level as a function of time.

Let us assume time at high tide is t = 0.

The time at the next high tide is t = 12 hours.

We will set up the following equation:

Water Level = A * cos(2π * (t - t0) / T) + C

Given that:

A = (12 - 2) / 2 = 5 feet.

t0 = 0.

T = 12 hours.

C = (12 + 2) / 2 = 7 feet.

The equation for the water level in Pensacola as function of time (t) is:

= 5 * cos(2π * t / 12) + 7.

= 5 * cos(πt/6) + 7

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Answer:

At time, 10 seconds, the mass remaining is 24 grams

At time, 20 seconds, the mass remaining is 12 grams

At time, 30 seconds, the mass remaining is 6 grams

At time, 40 seconds, the mass remaining is 3 grams

At time, 50 seconds, the mass remaining is 1.5 grams

Step-by-step explanation:

Given;

initial mass of the radioactive element  = 48 grams

half life, t = 10 seconds

time of decay (s)                          remaining mass of the  radioactive element

0 ------------------------------------------------- 48 grams

10------------------------------------------------- 24 grams

20 ------------------------------------------------- 12 grams

30 -------------------------------------------------- 6 grams

40 --------------------------------------------------- 3 grams

50 ----------------------------------------------------- 1.5 grams

60------------------------------------------------------0.75 grams

Thus;

At time, 10 seconds, the mass remaining is 24 grams

At time, 20 seconds, the mass remaining is 12 grams

At time, 30 seconds, the mass remaining is 6 grams

At time, 40 seconds, the mass remaining is 3 grams

At time, 50 seconds, the mass remaining is 1.5 grams

Answer:

Step-by-step explanation:

Answer:

33.6

Step-by-step explanation:

2.1 times 16=33.6

Using the numbers 12, 6, 6, the triangle can not be formed.

The given numbers are 12, 6 and 6.

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Here, 6 + 6 = 12 but not greater than 12

Therefore, using the numbers 12, 6, 6, the triangle can not be formed.

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Recall the conversion

1 quarts = 4 cup

Given that there is 15 cups, multiply it by the ratior of quarts to cup, making sure that the cup is in the denominator

Therefore, 15 cups is equivalent to 3 and 3/4 quarts.

Answer:

A

Step-by-step explanation:

The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain

14 → 4

12 →5

10 →6

8 →7

Given the expression:

The angle of the sine and the cosine is the same angle = 67.5°

The given expression is the same as the rule of the sine of the double angle

Where:

so, we will use the sine double-angle to solve the question

So, the answer will be:

So, the answer will be option B) sin 135°

The correct answer is 85 points in each contest

Explanation:

To solve this problem, the first step is to find out how many points Maddie has and then how many points she still needs to get a total of 750 points. Additionally, to do this, the correct process is to multiply the average points by the number of contexts.

In the first five contests, she obtained 68 points average

5 x 68 = 340 points in the first five contests

In the three following contests, she obtained 80 points on average

3 x 80 = 240 points

Now, let's add the points and find how many points she is missing to reach 750 points

340 + 240 = 580

750 - 580 = 170

Finally, let's divide the points missing by 2 because there are still two contests and Madie needs to get the 170 points in these two.

170 ÷ 2 = 85 points

Maddie needs to get 85 points on average to complete her goal of 750 points

Answer:

607 boxes are needed to pack all 14,568 shirts.

Step-by-step explanation:

we need to use division for this to see how many boxes 14,568 shirts will fit in.

14568 / 24 = 607

607 boxes will be needed to pack those shirts.

hope this helped, good luck!

-cheesetoasty

Answer:

A, B, D, E

Step-by-step explanation:

A. congruent by SAS

B. congruent by CPCTC

C. not necessarily true

D. congruent by CPCTC

E. congruent by SAS

F. not necessarily true

Answer: A, B, D, E

Answer:

170.72

Step-by-step explanation:

to find the mean, we must add al the numbers and divide it by n

that is,

164,175,178,166,167,145,176,150,174,162,180,156,173,158,182,184,160,172,186,168,195,169,171,187,170 we have to add al these numbers and divide it by 25

sum- 4628 divided by 25

=170.72

The equation of the new graph is:

f(x) = e^(x-6)

The graphs of the two functions f(x) = e^x and f(x) = e^(x-6) are shown below

From the question, we are to determine the equation of the new graph.

If the graph of the function f(x) = e^x is shifted 6 units to the right, the equation of the new graph can be found by replacing x with (x - 6) in the original equation.

This is because a horizontal shift of a function f(x) to the right by c units can be achieved by replacing x with (x - c) in the equation of the function. So, for the given function, a shift to the right by 6 units would be achieved by replacing x with (x - 6) in the original equation f(x) = e^x.

Therefore, the equation of the new graph is:

f(x) = e^(x-6)

This can also be written as:

f(x) = e^x / e^6

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

9514 1404 393

Answer:

  x = 30

Step-by-step explanation:

In an arithmetic sequence, any given term is the average of the two terms that come before and after. The middle term of this sequence must be ...

  2sin(3x) = (-11 +15)/2

  sin(3x) = 1 . . . . . . . . . . simplify and divide by 2

Then the value of 3x must be 90°, so ...

  x = 90/3 = 30

There is one value of x in the interval [0, 90] that makes this sequence arithmetic: x = 30.

Answer:

linear function

Step-by-step explanation:

straight line then add up

The actual measurement of the length of the colored face of the aquarium is D. 36 inches by 14 inches.

Generally, a scale drawing is described as a drawing that has been reduced or enlarged from its original size to a specified scale.

For instance, the scale of the drawing of the original aquarium is ¹/16.  This implies that the length, width, and height have been scaled down to one-sixteenth of the original size.

Scale drawing = ¹/16 of the original aquarium

Length of the colored face = 2¹/₄ inches

The actual length of the colored face = 36 inches (2¹/₄ inches x 16)

Thus, the actual measurement of the length of the colored face of the aquarium is D. 36 inches by 14 inches.

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Answer:

12

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

x² = 144

If you take the squared value of 12:

= 12² = 12 × 12 = 144

This makes 144 the perfect square of 12.

Therefore, to solve for the value of x, you must take the squared root of x² and 144:

\(\sqrt{x^{2} } = \sqrt{144} = \sqrt{12^{2} }\)

x = 12

Answer:

This comes out to around 25 percent. Simply multiply 40 by 1/4 to get 10 dollars.

Step-by-step explanation:

Answer:

Step-by-step explanation:

40x0.085=3.4

40+3.4= 43.4

43.4x0.18=7.8

43.4+7.8=51.212$

Answer:

i cant see it clearly to give you a propper answer

Answer:

412.92

Step-by-step explanation:

\(A = P(1+\frac{r}{n} )^{nt}\)

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)

Answer:

If the expression is , then the answer is the first option.

If the expression is , then the answer is the third option.

Step-by-step explanation:

Remember that when you have a radical expression in the form , you can rewrite as:

Then:

- If the expression is , then you can rewrite it in the following radical form:

(This form matches with the first option.)

- If the expression is , then you can rewrite it in the following radical form:

(This form matches with the third option).

Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

Hi, the equation you typed is 10c-5

less than is subtraction and the product of two numbers is multiplying them together.

Answer:

52

Step-by-step explanation:

hmm

Answer: C. O $8/hr

Step-by-step explanation:

To solve this, we divide 112 by 14.The answer is 8.

Answer: If the first difference is the same value, the model will be linear. If the second difference is the same value, the model will be quadratic. If the number of times the difference has been taken before finding repeated values exceeds five, the model may be exponential or some other special equation.

Step-by-step explanation: You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference. This table is linear.

select any point of the preimage

I select point A

the coordinates of A (-6,2)

the coordinates of point A'(-4,-2)

that means

the rule of the translation is 2 units to the right and 4 units down

so

(x,y) -------> (x+2,y-4)

the answer is