A scale for a scale drawing is 17 cm:1 mm. Which is larger, the actual object or the scale drawing?

The probability that exactly 30 drivers out of 600 say they read the newspaper while driving.

To find the probability that exactly 30 out of 600 randomly selected American drivers say they read the newspaper while driving, we can use the binomial probability formula.

The formula is P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where:
- P(X=k) is the probability of getting exactly k successes
- C(n,k) is the number of combinations of n items taken k at a time
- p is the probability of success for each trial
- n is the total number of trials

In this case, the probability of a driver reading the newspaper while driving is given as 5%, or 0.05. So p = 0.05, and the number of trials is 600 (n = 600). We want to find the probability of exactly 30 drivers saying they read the newspaper while driving (k = 30).

Using the formula, the probability is:
P(X=30) = C(600,30) * 0.05^30 * (1-0.05)^(600-30)

Calculating this value will give you the probability that exactly 30 drivers out of 600 say they read the newspaper while driving.

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Answer:

24

Step-by-step explanation:

correct on plato

Answer:

48 portions of salad

Step-by-step explanation:

4 bags spinach = 18 cherry tomatoes = 7.2 lb of chicken

7.2/.75 = 9.6 x 5 = 48

Answer:

Largest: 3

Smallest: 2

Mid-Sized: 1

Step-by-step explanation:

I will be including both an basic explanation of what it is and its proof.

I'm guessing you are either learning about conditional probability at school or preparing for competitions.

Baye's theorem states:

\(P(A|B)=\frac{P(B|A)P(A)}{P(B)}\)

That is the theorem itself and it means that the probability that event A happens given B is true equals the probability event B happens given A is true times the probability event A happens divided by the probability B happens.

That was the basic of the theorem and the proof of this is basically just testing how well you understand what conditional probability is.

\(P(A|B)=\frac{P(AintersectB)}{P(B)}\)

\(P(B|A)=\frac{P(BintersectA)}{P(A)}\)

Now we know that the probably that A and B both happens is the same as the probably that B and A both happens.

Therefore P(A|B) can be seen as P(B|A) multiplied by P(A) and then divided by P(B) which gives the right hand side of the first equation. And this is basically the theorem.

\(P(A|B)=\frac{P(B|A)P(A)}{P(B)}\)

**Note P(B) have to be not equal to 0 because having a 0 in the denominator would make this equation undefined.

If you have any questions or need further explanations please ask me in the comments of the answer, I hope this helped!

Answer:

4≤x>-9

Step-by-step explanation:

Answer: x=-17

Step-by-step explanation: Divide by -1 then add 8 to both sides and get (x+9)^3=-512, and the cube root of -512 is -8, so x+9=-8, and subtracting 9 from both sides we get x=-17 as answer.

The force required to keep a hockey puck sliding at a constant velocity, neglecting ice friction and air resistance, is equal to its weight. The correct option is "equal to its weight."

When a hockey puck is set in motion across a frozen pond and there is no ice friction or air resistance, the only force acting on the puck is its weight, which is the force due to gravity pulling it downward. According to Newton's first law of motion (the law of inertia), an object at a constant velocity will continue to move at that velocity unless acted upon by an external force.

Since the puck is already in motion and we want to maintain its constant velocity, the force required to counteract its weight and keep it sliding is equal to its weight. This is because the weight of an object is the force exerted on it by gravity, and in the absence of other forces, an equal and opposite force is needed to maintain the object's motion without acceleration.

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Answer:

12.16 years

Step-by-step explanation:

Continuous Compounding Formula

\(\large \text{$ \sf A=Pe^{rt} $}\)

where:

Given:

Substitute the given values into the formula and solve for t:

\(\sf \implies 5000=2500e^{0.0570t}\)

\(\sf \implies \dfrac{5000}{2500}=\dfrac{2500e^{0.0570t}}{2500}\)

\(\sf \implies 2=e^{0.0570t}\)

Take natural logs of both sides:

\(\sf \implies \ln 2=\ln e^{0.0570t}\)

\(\textsf{Apply the power law}: \quad \ln x^n=n \ln x\)

\(\sf \implies \ln 2=0.0570t\ln e\)

As ln e = 1:

\(\sf \implies \ln 2=0.0570t\)

\(\sf \implies \dfrac{\ln 2}{0.0570}=\dfrac{0.0570t}{0.0570}\)

\(\sf \implies t=\dfrac{ \ln 2}{0.0570}\)

\(\implies \sf t=12.16047685...\)

Therefore, the time required for the amount to double is 12.16 years (2 d.p.).

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Answer:

I wanna say 8 if its.

y=8x+-8

If thats wrong im sorry

Answer:

8

Step-by-step explanation:

Answer: 185.7 miles

Step-by-step explanation:

To find the total distance, add the smaller distances together.

47.8 + 72 + 65.9 = 185.7

Equivalent equations represent the same mathematical relationship, even if they appear different at first glance.  

1. Analyze the structure: Look for similarities in terms and coefficients. Equivalent expressions will have the same terms and coefficients, even if they are arranged differently.

3. Compare coefficients: If the expressions have the same structure, ensure that the coefficients of corresponding terms are equal. For example, if one expression has 2x and the other has 4x, they are not equivalent.

4. Test values: As a final check, substitute a few values for the variables in the expressions. If the results are the same for all tested values, the expressions are likely equivalent.

Remember that equivalent expressions represent the same mathematical relationship, even if they appear different at first glance.

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Answer:

20

Step-by-step explanation:

4(4)+3(4)-2(4)=20

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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The estimated population of raccoons in town after 9 years is equals to the 135 (round to the nearest whole number).

We have a scientist is studying the population of raccoons in a town.

Initial population of raccoons in town

= 120

Incresing/ growth rate of population of raccoons in town = 1.3% = 0.013

We have to determine the population of raccoons in town after 9 years. Exponential growth function is defined by, y(t) = a × eᵏᵗ

where y(t) = population of raccoons at time "t"

Now, t = 9 years, a = 120 , k = 0.013, then

y(t) = a × eᵏᵗ

=> y(9) = 120 × e⁽⁰·⁰¹³⁾⁹

=> y(9) = 120 × e⁰·¹¹⁷

=> y(9) = 120 × 1.12

=> y(9) = 134.89 ~ 135

Hence, the required population of raccoons in town is 135.

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Complete question :

RACCOONS A scientist is studying the population of raccoons in a town. The population at the beginning of the study was about 120. The scientist discovers that the number of raccoons increases by about 1. 3% each year. Estimate how many raccoons are in the park after 9 years. Use the exponential growth function. Round your answer to the nearest whole number.

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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Answer:

Simplifying -16t2 + 48t + 160 = 0

Reorder the terms: 160 + 48t + -16t2 = 0

Solving 160 + 48t + -16t2 = 0 Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0

Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.

hope it helps.

can u plz take a more clearer photo of the problem and also try to elaborate

The equation that represents the parabola shown on the graph is x² = 6y.

To determine the equation of the parabola with the given information, we can use the standard form of a parabola equation: (x-h)² = 4p(y-k), where (h, k) represents the vertex, and p represents the distance from the vertex to the focus (and also from the vertex to the directrix).

In this case, the vertex is given as (0, 0), and the focus is at (0, 1.5). Since the vertex is at the origin (0, 0), we can directly substitute these values into the equation:

(x-0)² = 4p(y-0)

x² = 4py

We still need to determine the value of p, which is the distance between the vertex and the focus (and the vertex and the directrix). In this case, the directrix is y = -1.5, which means the distance from the vertex (0, 0) to the directrix is 1.5 units. Therefore, p = 1.5.

Substituting the value of p into the equation, we get:

x² = 4(1.5)y

x² = 6y

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Answer:

100n+250t

Step-by-step explanation:

cost of the1 one day pass=100

cost of n one day passes=100n

cost of the 1 three day pass=250

cost of t three day passes=250t

Total sale= 100n+250t

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

To get 7/10 as a decimal you simply divide 7 by 10 which gets you 0.7.

The factorized form of cos(7x) - cos(x) is -2sin(4x)sin(3x). We have proven that cos(A + B) cos(A - B) = -2sin(A)sin(B).

To prove the equation cos(A + B) cos(A - B) = -2sin(A)sin(B), we'll start with the left-hand side (LHS) and manipulate it to show that it is equal to the right-hand side (RHS). LHS: cos(A + B) cos(A - B). Using the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B), we can rewrite the LHS as: LHS = (cos(A)cos(B) - sin(A)sin(B)) cos(A - B)

Now let's use the trigonometric identity cos(A - B) = cos(A)cos(B) + sin(A)sin(B) to substitute the value of cos(A - B) in the above equation: LHS = (cos(A)cos(B) - sin(A)sin(B)) (cos(A)cos(B) + sin(A)sin(B)). Expanding the above equation using the distributive property: LHS = cos^2(A)cos^2(B) - sin^2(A)sin^2(B). Using the trigonometric identity sin^2(x) = 1 - cos^2(x), we can rewrite the LHS further: LHS = cos^2(A)cos^2(B) - (1 - cos^2(A))(1 - cos^2(B))

Expanding the equation: LHS = cos^2(A)cos^2(B) - (1 - cos^2(A) - cos^2(B) + cos^2(A)cos^2(B)). Combining like terms: LHS = 2cos^2(A)cos^2(B) - 1. Now let's simplify the RHS: RHS = -2sin(A)sin(B). Finally, we can see that the LHS is equal to the RHS: LHS = 2cos^2(A)cos^2(B) - 1 = -2sin(A)sin(B) = RHS. Therefore, we have proven that cos(A + B) cos(A - B)= -2sin(A)sin(B). Now, moving on to the second part of the question, which is to factorize cos(7x) - cos(x): cos(7x) - cos(x)

Using the trigonometric identity cos(A) - cos(B) = -2sin((A + B)/2)sin((A - B)/2), we can rewrite the expression as: cos(7x) - cos(x) = -2sin((7x + x)/2)sin((7x - x)/2). Simplifying the equation: cos(7x) - cos(x) = -2sin(8x/2)sin(6x/2). cos(7x) - cos(x) = -2sin(4x)sin(3x). Therefore, the factorized form of cos(7x) - cos(x) is -2sin(4x)sin(3x).

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Answer:

It costs a family 216 dollars to refinish a wood floor. They want to refinish the floor in a larger room. The ratio of length of corresponding sides is 3:4. How much would it cost to finish the floor.

Step-by-step explanation:

Answer:

x = 20

y = 20√2  

Step-by-step explanation:

This is a 45 - 45 - 90° special right triangle

In a 45 - 45 - 90° triangle the legs are congruent and the hypotenuse = leg * √2

If one leg = 20 then the other leg also = 20

Thus, x = 20

If leg = 20

Then hypotenuse = 20 * √2 or 20√2

Thus, y = 20√2  

The total number of flour needed to make a batch of 212 if one batch calls for 234 cups of flour is 49608.

The fundamental concept of making the same number of additions repeatedly is represented by the action of multiplication. The results of multiplying two or more integers are known as the products, and the factors that are used in the multiplication are referred to as the factors.

Given:

The recipe for one batch of dough calls for 234 cups of flour, Thomas is making 212 batches of the recipe,

Calculate the number of cups of flour as shown below,

The number of cups of flour = 234 × 212

The number of cups of flour = 49608

Thus, the total number of flour needed is 49608.

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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