The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.944 g and a standard deviation of 0.324 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. In what range would you expect to find the middle 70% of amounts of nicotine in these cigarettes (assuming the mean has not changed)

Answer:

1. a. Please find attached, the diagram for the first circle with radius = 3 cm

b. Please find attached, the diagram for the second circle with diameter = 3 cm

2. The similarities are;

a) Both circles can be described by a point and a radius or a diameter

The differences are;

a) The length of the radiuses are different for the two circles (3 cm and 1.5 cm)

b) The circumferences of the two circles are different

c) The area covered by the two circles are different

3. The circumference of the circle with radius equal to 3 cm is larger than the circumference of the circle with diameter equal to 3 cm

4. The circumference to diameter ratio of the circle with radius  = 3 cm is π

The circumference to diameter ratio of the circle with diameter  = 3 cm is π

Both circles have equal circumference to diameter ratio given that the circumference = π × The diameter

Step-by-step explanation:

1. a. The radius length of the first circle = 3 cm

The diagram for the first circle with radius 3 cm is attached

b. The diameter length of the second circle = 3 cm

The diagram for the second circle with diameter 3 cm is attached

2. The similarities are;

a) Both circles can be described by a point and a radius or a diameter

The differences are;

a) The length of the radiuses are different for the two circles (3 cm and 1.5 cm)

b) The circumferences of the two circles are different

c) The area covered by the two circles are different

3. The circumference of the circle with radius equal to 3 cm is 2 × π × 3 = 6·π cm

The circumference of the circle with diameter equal to 3 cm is π × 3 = 3·π cm

Therefore, the circumference of the circle with radius equal to 3 cm is larger than the circumference of the circle with diameter equal to 3 cm

4. The circumference to diameter ratio of the circle with radius = 3 cm is 6·π cm/(2 × 3 cm) = π

The circumference to diameter ratio of the circle with diameter = 3 cm is 3·π cm/(3 cm) = π.

Both circles have equal circumference to diameter ratio given that the circumference = π × The diameter.

The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.

In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.

In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.

Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.

Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.

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Answer:

These are paralell because they are even to eachother

Step-by-step explanation:

perpendicular means that they are like a plus sign

and intersecting means they intersect at some point.

Answer:

The answers is They are parallel because they are even and there is no difference between the two.

Hope This Helps!!!!! :)

Answer:

Step-by-step explanation:

1. the 125g

b. 100ml for 1.79

Answer:

-3 - 1 = 4/9(-5 - 4)

Step-by-step Explanation:

Point-Slope form uses the formula y-y1=m(x-x1).

m is the slope, which they gave you, so you can substitute it into the formula:

y - y1 = 4/9(x - x1).

They also gave you a first point (-5, -3) So you can substitute the x and y of those into the formula as well.

-3 - y1 = 4/9(-5 - x1)

y1 and x1 are for another point. By drawing a graph and then using the rise and run of the slope (up 4 and over 9), you can get another point (as shown in the picture).

Substitute the x and y values of that point into the equation as well and you have your answer:

-3 - 1 = 4/9(-5 - 4)

Answer:

$7.2

Step-by-step explanation:

First, look at the discount. It's 40%.

Next, I look at the price. It's $12.

100-40 is 60.

60/100 (60%) times 12 is equivalent to 7.2. Enjoy :D

Answer:

Row n ---> 27th term is 27.

Row T ---> 27th term is 80.

Step-by-step explanation:

To find the 27th term for the top row, row n, you will use this formula:

an = a1 + f × (n-1)

The first number = 1

The common difference (f) = 1

a27 = 1 + 1 × (27-1)

a27 = 1 + 27 - 1

a27 = 28 - 1

a27 = 27

So, the 27th term is 27.

We will do the same for the row T.

an = a1 + f × (n-1)

The first number = 2

The common difference (f) = 3

a27 = 2 + 3 × (27-1)

a27 = 2 + 81 - 3

a27 = 83 - 3

a27 = 80

So, the 27th term is 80.

Explanation

Add the components of the vectors

u+v = (4,2) + (-3,2)

u+v = (4+(-3),  2+2)

u+v = (1,4)

Then to evaluate the length of vector u = (a,b), we use this formula

|u| = sqrt(a^2+b^2)

Which is derived from the pythagorean theorem. We're looking for the hypotenuse of the right triangle formed. In this case a = 1 and b = 4.

So,

|u+v| = sqrt(1^2 + 4^2)

|u+v| = sqrt(17)

Answer:

The amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Step-by-step explanation:

The given function is:

f(t) = -1/2(4t - 2π)

We can rewrite this function in the form:

f(t) = A cos(B(t - C)) + D

where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Comparing this with the given function, we can see that:

A = 1/2

B = 4

C = π/2

D = 0

Therefore, the amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Note that the negative sign in front of the function does not affect the amplitude, period, or phase shift. It simply reflects the function across the x-axis.

Given that det(A) = 5, the determinant of 2(adj A) is 200.

To find the determinant of 2(adj A), we need to understand the properties of the adjugate matrix and the determinant.

First, let's define some terms:

A is a 3 x 3 matrix.

adj(A) represents the adjugate matrix of A, which is obtained by taking the transpose of the cofactor matrix of A.

det(A) is the determinant of matrix A.

We are given that det(A) = 5. This means that the determinant of matrix A is equal to 5.

To find the determinant of 2(adj A), we can use the following property of determinants:

det(kA) = k^n * det(A), where k is a scalar and A is an n x n matrix.

In this case, k = 2 and A = adj(A), which is a 3 x 3 matrix. Therefore, we have:

det(2(adj A)) = (2^3) * det(adj A).

Since adj(A) is a matrix obtained by taking the transpose of the cofactor matrix of A, multiplying it by 2 will simply multiply each element of the cofactor matrix by 2. Hence, the determinant of adj(A) will also be multiplied by 2^3 = 8.

Therefore, we can write:

det(2(adj A)) = (2^3) * det(adj A) = 8 * det(adj A).

We know that det(adj A) is equal to the determinant of A raised to the power of (n-1), where n is the dimension of the matrix. In this case, n = 3, so we have:

det(adj A) = det(A)^(n-1) = det(A)^2 = 5^2 = 25.

Substituting this back into our equation, we get:

det(2(adj A)) = 8 * det(adj A) = 8 * 25 = 200.

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Answer:

3.44

Step-by-step explanation:

3*16=48+7=55     55/16=3.4375

Answer:

3.44

Step-by-step explanation:

  3.4375 rounded to the nearst hundredth is 3.44

The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Answer:

-42(x - 2) and -6(7x - 14)

Step-by-step explanation:

If one half-life of U-236 is 23 million years then it will take 45.5 or approximately 46 million years to decay. Then the correct option is A.

Half-life is the time interval that is needed to decay the atomic nuclei of a radioactive sample.

A sample contains 16.75 g of the radioisotope U-236 and 50.25 g of its daughter isotope, Th-232.

Initially, the whole sample is consisting the radioisotope. Then the initial total mass will be

m₀ = 16.75 + 50.25

m₀ = 67 g

Now we also know that the half-life is 23 million years. Then we have

\(m = m_oe^{- \lambda t}\)

Then put the value

\(\begin{aligned} 16.75 &= 67 e^{- \lambda t}\\\\0.254 &= e^{- \lambda t}\\\\\lambda t &= 1.37\\\\\dfrac{ln2}{23 \rm \ million \ years } \times t &= 1.37\\\\t &= 45.5 \ \rm million\ years \end{aligned}\)

If one half-life of U-236 is 23 million years then it will take 45.5 or approximately 46 million years to decay. Then the correct option is A.

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Answer:

a. 46 million years

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

h(x) = 3 – 3/x

h(3) = 3 – 3/3

h(3) = 0/3

h(3) = 0

i hope this helped

Answer:

Clockwise from upper left: 3, 3, 9, 12

Step-by-step explanation:

Put the number in the left colloum in for x in the equation above

Answer:

The question gives you an equation and the x variable, so plug the value of x into the equation.

Row 2, x=1

\(y=3x^{2} \)

\(y=3(1)^{2}\)

y=3

\(y=3^{x} \)

\(y=3^{1} \)

y=3

Row 3, x=2

\(y=3x^{2} \)

\(y=3(2)^{2} \)

y=12

\(y=3^{x} \)

\(y=3^{2} \)

y=9

The slope of a line perpendicular to line j include the following: C. -7/3.

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

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

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 4)/(3 + 4)

Slope (m) = 3/7

In Mathematics, a condition that must be true for two lines to be perpendicular include the following:

m₁ × m₂ = -1

3/7 × m₂ = -1

m₂ = -7/3

Slope, m₂ of perpendicular line = -7/3

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Answer:

15.3 m/s

Step-by-step explanation:1) Find the gravitational potential energy using the equation :

     \(PE_g=mgh\)

    \(PE_g=2.5(12)(9.8)\\PE_g=294\)

2) Then use the equation for kinetic energy to solve for the velocity:

     \(KE=\frac{1}{2} mv^{2}\)

     \(294=\frac{1}{2}(2.5)(v^2)\\235.2=v^2\\\sqrt{235.2} =v\\15.3 m/s=v\)

Answer:

57.5

Step-by-step explanation:

First you would have to multiply following PEMDAS so

(1/4)(2)

=0.5

Then subtract 58 and 0.5

58-0.5

=57.5

and thats your answer

Answer:

57.5 or 57 1/2

Step-by-step explanation:

1. Start with 1/4*2 due to the ”order of operation rules”. You then get 1/2.

2. Then, continue to do 58-1/2 to get 57.5 or 57 1/2

the shortest side is 6 centimeters and the length of each of the other sides is 12 centimeters each.

Let x represent the length of the shortest side of the triangle.

Two sides of the triangle are each twice as long as the shortest side. This means that the length of the two sides would be 2x.

The perimeter of a triangle is the sum of each side of the triangle.

The puzzle piece in the shape of a triangle has perimeter 30 centimeters. This means that

x + 2x + 2x = 30

5x = 30

x = 30/5

x = 6

The length of each of the two sides is

2x = 2 × 6 = 12

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The description that accurately explains how a fair decision can be made in this situation is:

"If the product of the spins is 2, pale lilac will be used. If the product is 4, mellow sage will be used. If the product is 12, seafoam blue will be used. If the product is 1, 6, or 36, totally taupe will be used."

Decision-making based on random outcomes refers to a process where choices or actions are determined by the result of a random event or chance. This approach is often used in situations where there is uncertainty or when all available options are perceived to have similar values or consequences.

The decision on which paint color to use is based on the product of the outcomes from spinning the spinner twice. Each outcome corresponds to a specific number on the spinner. By multiplying the two outcomes together, we obtain the product.

According to the given description, specific products are associated with each paint color. For example, if the product of the spins is 2, the color pale lilac will be used. If the product is 4, mellow sage will be used. If the product is 12, seafoam blue will be used. And if the product is 1, 6, or 36, totally taupe will be used.

This approach ensures a fair decision-making process based on the random outcomes of spinning the spinner.

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Answer:

The answer is 1.788

Step-by-step explanation:

The factor of independent variable that were in the study will be 2.

It should be noted that an independent variable is the variable that the experimenter changes in order to test the dependent variable.

In this case, if a 2 x 3 factorial design with between subjects variables was carried out with 8 subjects per cell, the independent variable factor is 2.

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Answer:

It should be \(15*10^{4}\).

Step-by-step explanation:

\(300=3*10^{2}\\500=5*10^{2}\\\\300*500=(3*10^{2})*(5*10^{2})=(3*5)*10^{(2+2)}=15*10^{4}=1.5*10^{5}\)

Answer: 1.5 x 10^5

Step-by-step explanation:

The first step is to re-arrange the factors like this :

5 x 3 x 10^2 x 10^2

Since

5 x 3 = 15

and the index law

10^a x 10^b = 10^a + ^b

gives us

10^2 x 10^2 = 10^2 + ^2 = 10^4

then we can rewrite the product like this :

5 x 3 x 10^2 x 10^2 = 15 x 10^4

Finally, we need to convert this into scientific notation :

15 x 10^4 = 1.5 x 10^5  

So the final answer is

1.5 x 10^5

Answer:

7/5 or 1.4

Step-by-step explanation:

1. Cross multiply. 5(2x-1)= 3(3)

2. Simplify and add 5. 10x -5= 9.     10x = 14

3. Divide by 10. 10x/10 = 14/10

X= 14/10= 7/5 or 1.4

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Answer: C.5

Step-by-step explanation:

There are 66,960 number of ways to set up a batting order of 9 players from among the 12 players on the baseball team.

To determine the number of ways to set up a batting order of 9 players from among the 12 players on a baseball team, we can use the concept of permutations.

Since the order matters in a batting order, we can use the formula for permutations.

The number of permutations of selecting 9 players from a pool of 12 players is given by:

P(12, 9) = 12! / (12 - 9)!

Calculating this, we have:

P(12, 9) = 12! / 3!

= (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4) / (3 * 2 * 1)

= 12 * 11 * 10 * 3 * 7 * 2

= 66,960

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Answer:

\(\huge\boxed{xy = 2}\)

Step-by-step explanation:

=> \(\sf (x+y)^2 = x^2 + y^2 + 2xy\)

Given that \(\sf x + y = 3 , x^2 + y^2 = 5\)

=> \(\sf (3)^2 = 5 + 2xy\)

=> \(9 = 5 + 2xy\)

=> \(9-5 = 2xy\)

=> \(4 = 2xy\)

Dividing both sides by 2

=> 2 = xy

OR

=> xy = 2

Answer:

5

Step-by-step explanation:

it's an f(x) equation and -6 is in the place of x

so you go to where x is -6 on the graph

and then you see it's where y is 5

so the answer is 5

(sorry if this doesn't make sense!)