Jason bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 39 cards left. How many cards did Jason start with ?

According to 10th Amendment it defines the Federal Government only has those powers delegated in the Constitution .

No law establishing a particular religion, forbidding its practice, restricting press or speech freedom, or restricting the right of the people to peacefully assemble and petition the government for redress of grievances may be passed by Congress.

An amendment is a change or improvement that essentially maintains the integrity of the original document. The Bill of Rights is the collective name for the first ten Amendments of the Constitution. It describes Americans' constitutional rights in relation to their government. People are granted civil liberties and rights, such as the freedom of speech, the press, and religion.

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These complex roots can be represented as points on the Argand diagram, where w₁ is at an angle of π/12 from the positive real axis in the counterclockwise direction and w₂ is at an angle of π/12 from the negative real axis in the counterclockwise direction.

i. Expressing z in polar form:

To express z = 1 + i√3 in polar form, we need to find the magnitude (r) and argument (θ) of the complex number. The magnitude r can be found using the formula |z| = √(Re(z)² + Im(z)²), and the argument θ can be found using the formula θ = tan⁻¹(Im(z)/Re(z)).

For z = 1 + i√3, the magnitude is |z| = √(1² + (√3)²) = 2, and the argument is θ = tan⁻¹(√3/1) = π/3.

Therefore, z can be expressed in polar form as z = 2(cos(π/3) + isin(π/3)).

ii. Finding complex roots of w = z¹/²:

To find the complex roots of w = z¹/², we need to take the square root of z and consider both the positive and negative square roots.

Taking the square root of z, we get:

√z = ±√2(cos(π/6) + isin(π/6)).

Therefore, the complex roots of w = z¹/² are:

w₁ = √2(cos(π/12) + isin(π/12)),

w₂ = -√2(cos(π/12) + isin(π/12)).

These complex roots can be represented as points on the Argand diagram, where w₁ is at an angle of π/12 from the positive real axis in the counterclockwise direction and w₂ is at an angle of π/12 from the negative real axis in the counterclockwise direction.

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Answer:

since the rate is the same for both trains, and we know that the distance train A travels plus the distance train B travels equals 562.5 miles, we can use the D(istance) = R(ate) * T(ime) formula to solve this.

Train A:

da = R * 4

Train B:

db = R * 3.5 (using 3.5 instead of 3 and 1/2)

Solve for R:

R * 4 + R * 3.5 = 562.5

7.5 * R = 562.5

R = 75

The trains are traveling at 75 miles per hour.

Step-by-step explanation:

Answer:

speed = distance / time

since they are moving in opposite direction, the time is the sum of the two times = 2 1/2 + 4 = 6 1/2 = 13/2

speed = 585/(13/2) = 90 miles per hour.

Step-by-step explanation:

I hope it helps.

Answer:

50π feet^2

Step-by-step explanation:

area of the circle = 10^2 π = 100π feet^2

A of the sector = 100π/2 = 50π feet^2

The equation of the circle with center (5,-8) containing the point (14,-17) is (x - 5)² + (y + 8)² = 162.

The general equation of a circle with center (h,k) and radius r is given by:

(x - h)² + (y - k)² = r²

Given that:  the center of the circle is (5, -8) and the circle contains the point (14, -17).

We can use these values to find the radius, r, and then substitute them into the equation of a circle to obtain the final answer.

The radius r is simply the distance between the center (5,-8) and the point (14,-17). We can use the distance formula to calculate it:

r = √[ (14 - 5)² + (-17 + 8)²]

r = √[ 81 + 81 ]

r = √162

r = 9√2

Now that we have the value of the radius, we can substitute it into the equation of a circle to obtain the final answer:

(x - 5)² + (y + 8) = (  9√2 )²

(x - 5)² + (y + 8)² = 162

Therefore, the equation of the circle is (x - 5)² + (y + 8)² = 162.

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A) The required population sets are

Population set 1 : Women whose mothers took the drug DES during pregnancy.

Population set 2 : Women whose mothers did not take the drug DES during pregnancy.

B) It is a survay not experiment.

C) The estimate of the number of women out of 1,000 who would be expected to have tissue abnormalities is 16 per 1000 people.

D) The estimate of the number of women out of 1,000 who would be expected to have not tissue abnormalities is 8 per 1000 people.

E) Yes, medical studies often use a relatively large sample to represent the population in the best possible way so that results can be more reliable and can be generalized.

The purpose of a research study is that to uncover something hidden or unknown. Because the study does not use the entire set of data, but it consider sample in an appropriate manner to represent the population as accurately as possible. We have a seven-year medical research study : Women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.

A) Population is defined as the entire group that we want to draw conclusions. In this case, population seta are :

Population set 1 : Women whose mothers took the drug DES during pregnancy.

Population set 2 : Women whose mothers did not take the drug DES during pregnancy.

B) Since, there is no manipulation in the variables has been done, it is not an experiment but a survey.

C.)Consider a sample from population of women whose mothers took the drug DES during pregnancy. Sample size, n = 3980

The number of women who developed tissue abnormalities that might lead to cancer, x = 63

The sample proportion, p = x/n = 63/3980

≈0.0158

A descriptive statistic that used to estimate the number of women out of 1000. So, population who have tissue abnormalities out of 1000,

Required number = 0.0158 ×1000 ≈15.8 ≈ 16

i.e., 16 per 1000 people

D) Now, for the population of women whose mothers did not take the drug DES during pregnancy, the estimate of the number of women out of 1000

1000 who would be expected to have tissue abnormalities can be given as:

Required number ≈ 8 per 1000 people ( because those who took drug have twice the risk).

E) Yes, medical studies often use a relatively large sample to represent the population in the best possible way so that results can be more reliable and can be generalized, which is the main purpose of the medical study.

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The greatest possible number of intersection points for four circles of different sizes is 12.

The greatest possible number of intersection points of four circles of different sizes can be calculated by considering the maximum number of intersection points each pair of circles can have and then summing them up.

When two circles intersect, they can have a maximum of two intersection points. So, if we have four circles, we can find the maximum number of intersection points by considering each pair of circles separately.

For the first circle, it can intersect with the other three circles at most two times each, giving us a total of 2 * 3 = 6 intersection points.

For the second circle, it can intersect with the remaining two circles at most two times each, giving us a total of 2 * 2 = 4 intersection points.

The third circle can intersect with the last remaining circle at most two times, giving us a total of 2 * 1 = 2 intersection points.

Finally, the fourth circle doesn't have any other circle left to intersect with, so it doesn't contribute any additional intersection points.

Now, we can sum up the intersection points from each pair of circles: 6 + 4 + 2 + 0 = 12.

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Ans1wer: 10x^2

Step-by-step explanation:

10x^2+2x^2=12x^2 and -4y-y=-6y

The work done on the chair that weighs 50 N  and lifted to a height of 0.5 m and carried 10 m across the room is 500 joules.

To calculate the work done on the chair, you can use the formula:

Work = Force × Distance × cos(θ)

where:

- Force is the amount of force applied to the chair (in newtons, N)

- Distance is the displacement or distance covered while carrying the chair (in meters, m)

- θ is the angle between the direction of the force and the direction of displacement (if the force is applied vertically upward, then θ = 0°, and the cosine of 0° is 1)

In this case, the force applied to the chair is its weight, which is given as 50 N. The distance covered is 10 m, and the angle between the applied force and the displacement is 0° (since the force is applied vertically upward, perpendicular to the horizontal displacement).

Therefore, the work done on the chair is:

Work = 50 N × 10 m × cos(0°)

     = 50 N × 10 m × 1

     = 500 N·m

The unit for work is the newton-meter (N·m), which is also known as the joule (J). Therefore, the work done on the chair is 500 joules.

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Answer:

The associative property is grouping

Step-by-step explanation:

Answer:

The associative property is the rule that includes grouping of numbers.

Step-by-step explanation:

No, the LDA classifier and the Bayes classifier would not necessarily give similar boundaries when trained on a large amount of training data from an arbitrary distribution.

The LDA (Linear Discriminant Analysis) classifier assumes that the input features are normally distributed and that the class covariances are equal. It finds linear boundaries that maximize the separation between classes based on these assumptions. On the other hand, the Bayes classifier makes decisions based on the class conditional probabilities and prior probabilities of the classes. It can handle arbitrary distributions and does not make assumptions about the class covariances. Therefore, even with a large amount of training data, if the distribution of the data does not conform to the assumptions of LDA (e.g., non-normal distributions or unequal class covariances), the LDA classifier may not give similar boundaries to the Bayes classifier.

The LDA and Bayes classifiers may not give similar boundaries when trained on data from an arbitrary distribution, as the LDA classifier relies on specific assumptions about the data distribution that may not hold true in practice.

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The elevation before the descent is

8.75+1.3=10.05

The elevation before the descent is 10.05

The reduced fraction of 8/12 is 2/3. This means that out of the initial 12 cookies, 8 cookies are left.

To reduce the fraction 8/12, we need to find the greatest common divisor (GCD) of the numerator and denominator, which is the largest number that divides both numbers evenly. In this case, the GCD of 8 and 12 is 4.

Dividing both the numerator and denominator by the GCD, we get:

8 ÷ 4 / 12 ÷ 4 = 2/3

Therefore, the fraction 8/12 is equivalent to 2/3 when reduced.

In conclusion, after reducing the fraction, the fraction of cookies left is 2/3. This means that out of the initial 12 cookies, 4 were sold and there are now 8 cookies remaining.

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The rate at which the candle burn in inch's per hour is 1/4 inches per hour

The rate is how fast the candle burns with the passage of time. It is the height of the candle divided by the time it takes the candle to burin down.

Division is the process of grouping a number into equal parts using another number. The sign used to represent division is ÷. Division is one of the basic mathematical operations.

Rate = height / time it take the candle to burn down

2 / 8 = 1/4 inches per hour

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Answer:

1/4

Step-by-step explanation:

?

Answer:

the top right hand corner

Step-by-step explanation:

Answer:

Probably red ball because it has higher amount

The median of a data set is 12 and the mean is 10, we need to determine the likely skewness of the data. The three options are: the data are skewed to the left, the data are skewed to the right, or the data are symmetrical.

When the median and the mean of a data set are not equal, it indicates that the data are skewed. Skewness refers to the asymmetry of the data distribution. If the median is greater than the mean, it suggests that the data are skewed to the left, also known as a left-skewed or negatively skewed distribution.

In this case, since the median is 12 and the mean is 10, the median is greater than the mean. This indicates that there is a tail on the left side of the distribution, pulling the mean towards lower values. Therefore, the data are most likely skewed to the left.

A left-skewed distribution typically has a long tail on the left side and a cluster of data points towards the right. This means that there are relatively more lower values in the data set compared to higher values.

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The arithmetic mean of the two fractions is 68/35.

The arithmetic mean can be calculated using the mentioned formula -

Arithmetic mean = sum of the numbers / frequency of numbers.

Sum of the fractions = 2/5 + 4/7

Performing division of the two numbers

Sum of the fractions = (14 + 20)/35

Sum of the fractions = 34/35

Arithmetic mean = (34/35)/2

Rewriting the average

Arithmetic mean = (34 × 2)/35

Performing multiplication on Right Hand Side of the equation

Arithmetic mean = 68/35

Hence, the Arithmetic mean is 68/35.

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Answer:

y > 17x - 13

Step-by-step explanation:

We want to write the inequality in slope-intercept form

The general slope intercept form is;

y = mx + b

where m is the slope and b is the y-intercept

So what we have to do to the inequality is to make y the subject

Thus, we have that;

17x -13 < y

Flipping this, we have

y > 17x-13

Arrange the data in ascending order,

The mean is ,

The mean is 98.6.

The median is,

The median is 96.5.u

The mode is the value that appears most often in a set of data values.

The range is determined as the difference between the maximum and minimum value.

Answer:

C

Step-by-step explanation:

x4(x4-5)+5(x4-5)

=x8-5x4+5x4-25

x8-25

The variance of the new dataset is (A²/M²)σ²

To calculate the variance of the new dataset, we first need to find the variance of the original dataset.

We know that the mean of the original dataset is denoted by μ and the standard deviation is denoted by σ.

The variance of the original dataset can be calculated as:

Var(X) = σ²

Now, we need to calculate the value of the transformation for each data point in the original dataset:

Yi = (Axi + B) / M

The mean of the new dataset is:

μ_Y = (Aμ + B) / M

The variance of the new dataset can be calculated as:

Var(Y) = Var[(Axi + B) / M]

Using the property that Var(aX) =\(a^2Var(X),\) we can write:

\(Var(Y) = Var[(Axi) / M] = (A^2/M^2)Var(X)\)

Since we know that Var(X) = σ², we can substitute this value:

Var(Y) = (A²/M²)σ²

Therefore, the variance of the new dataset is (A²/M²)σ²

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14÷3= 4.6666666...

so 4 cookies for each one... with 2 cookies left

Answer:

because if you flip it they will line up

Step-by-step explanation:

Answer:

4.2

Step-by-step explanation:

Because 1/5 has to be converted into the 100 as the denominator and the number you are supposed to have for the numerator so it can be easier and 4 is the whole number so it doesnt need to be in the equation.

1/5

X

20= 20/100  so now all you have to do is make that a decimal since it hasnt got to 100 or past it and you have your answer

The basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.

The basis for the nullspace of the matrix can be found by reducing the augmented matrix to row echelon form and finding the free variables. The free variables correspond to the columns that have a leading entry of 0 and non-zero entries below it, which are the basis vectors for the nullspace.

Using row operations, the augmented matrix can be reduced to:

1  2 -4  5 | 0

0  1 -3  2 | 0

0  0  0  0 | 0

From this, we can see that the free variables are x2 and x4, so the basis for the nullspace is:

-3 x2 + x4

x2

So the basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.

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Answer:

5.40

Step-by-step explanation:

let X represent the price of a 18 minute phone call

X=18 ×1.80

6

= 5.40

Answer:

\(perimetro = \dfrac{(3 + \sqrt{3})m}{2}\)

Step-by-step explanation:

triángulo 30°-60°-90°

\( 1~:~\sqrt{3}~:~2 \)

\( 1m~:~m\sqrt{3}~:~2m \)

\( \dfrac{m}{2}~:~\dfrac{m\sqrt{3}}{2}~:~m \)

\(perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + m\)

\(perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + \dfrac{2m}{2}\)

\(perimetro = \dfrac{m + m\sqrt{3} + 2m}{2}\)

\(perimetro = \dfrac{3m + m\sqrt{3}}{2}\)

\(perimetro = \dfrac{(3 + \sqrt{3})m}{2}\)