A certain kind of coin weighs 6.58 grams. How much do 8 of these coins weigh all together? grams

Answer:

B

Step-by-step explanation:

Here, we want to calculate the square root of -√- (75)

That will be

-√(25)(-3)

= -5 √(-3)

√(-3) is same as 3i

So we have the root as;

-5i√3

The characteristics of the normal distribution can be used to determine the likelihood that X equals 19.62 because X is a normally distributed random variable with a mean of 12 and a standard deviation of 3.

We must compute the z-score, which counts the number of standard deviations a given result is from the mean, in order to determine this probability. Calculating the z-score is as follows:

z = (x - μ) / σ

If the supplied value, x, the mean, and the standard deviation are all given.In this instance, x=19.62, =12, and =3 respectively. By replacing these values, we obtain:

z = (19.62 - 12) / 3 ≈ 2.54

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Answer:

Step-by-step explanation: you would start with a dot on the y-axis at -2, then you would go up 2 and over 5 cuz the slope is 2/5. just keep doing this and you’ll have your graph

To find the slope of the line that contains (-3,-4) and (5,-2).

The slope of the line passing through the points

is

Now, let

Then,

Hence, the slope of the line is 1/4.

The bottom whiskers cover all data values ​​from the smallest value to Q1, which is the lowest 25% of data values. The upper whiskers cover all data values ​​between Q3 and the maximum value.

The horizontal axis covers all possible data values. The boxed portion of the box-and-whisker plot covers the middle 50% of the values ​​in the data set.

Each whisker covers 25% of the data values.

The lower whisker covers all data values ​​from the minimum value to Q1, i.e. the lowest 25% of data values. The upper whisker

covers all data values ​​between Q3 and the maximum value, i.e. the highest 25% of data values.

The median is inside the box and represents the center of the data. 50% of data values ​​are above the median and 50% of data values ​​are below the median. Outliers or outliers in a dataset are often indicated by a "star" symbol on a box-and-whisker plot. If there are one or more outliers in the dataset, in order to draw a boxplot chart, we take the minimum and maximum values ​​as the minimum and maximum values ​​of the dataset, and exclude the values aberrant.

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The distance from the bird to the top of the tree is 61.95 feet.

We have,

Angle of elevation to the top of the tree: 38 degrees.

Angle of elevation to the bird: 60 degrees.

Distance from the base of the tree to your position: 84 feet.

Let the distance from the bird to the top of the tree as 'x'.

Using Trigonometry

tan(38) = height of the tree / 84

height of the tree = tan(38) x 84

and, tan(60) = height of the tree / x

x = height of the tree / tan(60)

Substituting the value of the height of the tree we obtained earlier:

x = (tan(38) x 84) / tan(60)

x ≈ 61.95 feet

Therefore, the distance from the bird to the top of the tree is 61.95 feet.

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Answer:

b

Step-by-step explanation:

Answer:

x=-6

Step-by-step explanation:

\(3x-7-\frac{2}{3}(9x-6)=15\\3x-7-6x+4=15\\-3x-3=15\\-3x=18\\x=-6\)

The length of the string required to fly the kite at a height of 75 meters from the ground is 86.6 meters.

The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the height of the kite (75 m), and the hypotenuse is the length of the string that we need to find. We can set up an equation using the sine function:

sin(60 degrees) = opposite/hypotenuse

sin(60 degrees) = 75/hypotenuse

We can simplify the equation using the value of the sine of 60 degrees, which is √3/2.

√3/2 = 75/hypotenuse

To solve for the length of the string, we can cross-multiply and simplify:

hypotenuse = 75/(√3/2)

hypotenuse = (75*2)/√3

hypotenuse = 150/√3

hypotenuse = (150/√3) * (√3/√3) (to rationalize the denominator)

hypotenuse = (150√3)/3

hypotenuse = 50√3 meters = 86.6 meters.

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Complete Question:

A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60 ∘ to the horizontal. Find the length of the string, assuming that there is no slack in it. [Take √ 3 =1.732].

The distance of the base of the tower and the airplane is 348.5 ft,  and the right option is 4. 348.5 ft.

Distance is the length between two points.

To calculate the distance of the base of the tower and the airplane, we use the formula below.

Formula:

Where:

From the diagram,

Given:

SUbstitute these values into equation 1 and solve for A

Hence, the right option is 4. 348.5 ft.

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Answer:

They arrived at her house at 3:19

The gamma distribution with parameters $\alpha$ and $\beta$ is a probability distribution that can be derived using the transformation $x = \beta y$.

The probability density function of the gamma distribution is:

f(x; α, β) = \frac{(\beta x)^{\alpha - 1} e^{-\beta x}}{\Gamma(\alpha)}

where $\alpha$ is the shape parameter and $\beta$ is the rate parameter.

The derivation is as follows:

* The gamma function is defined as:

Γ(α) = \int_0^{\infty} x^{\alpha - 1} e^{-x} dx

* Using the transformation $x = \beta y$, we get:

Γ(α) = \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* We can then write the probability density function of the gamma distribution as:

f(x; α, β) = \frac{1}{\Gamma(\alpha)} \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* This is the same as the probability density function of the gamma distribution with parameters $\alpha$ and $\beta$.

The mean and variance of the gamma distribution can be found using the following formulas:

E(X) = \alpha \beta

Var(X) = \alpha \beta^2

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The coefficient of determination for the regression of gasoline consumption on gasoline prices is approximately 0.557.

The coefficient of determination, also known as R-squared, measures the proportion of the total variation in the dependent variable that is explained by the independent variable(s). It is calculated by dividing the explained variation by the total variation.

In this case, the total variation in the dependent variable is given as 122, and the unexplained variation is 54. To calculate the coefficient of determination, we need to find the explained variation, which is the difference between the total variation and the unexplained variation.

Explained variation = Total variation - Unexplained variation

Explained variation = 122 - 54 = 68

Now, we can calculate the coefficient of determination:

Coefficient of determination = Explained variation / Total variation

Coefficient of determination = 68 / 122 ≈ 0.557

Therefore, the coefficient of determination for the regression of gasoline consumption on gasoline prices is approximately 0.557.

The coefficient of determination, R-squared, provides an indication of how well the independent variable(s) explain the variation in the dependent variable. In this case, an R-squared value of 0.557 means that approximately 55.7% of the total variation in gasoline consumption can be explained by the variation in gasoline prices.

A higher R-squared value indicates a stronger relationship between the independent and dependent variables, suggesting that changes in the independent variable(s) are associated with a larger proportion of the variation in the dependent variable. Conversely, a lower R-squared value indicates that the independent variable(s) have less explanatory power and that other factors not included in the regression may be influencing the dependent variable.

It is important to note that while the coefficient of determination provides an indication of the goodness-of-fit of the regression model, it does not necessarily imply causation or the strength of the relationship. Other factors, such as the model's specification, sample size, and the presence of other variables, should also be considered when interpreting the results of a regression analysis.

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Step-by-step explanation:

(i) To find the value of p, we need to find the magnitude of vector a:

|a| = √(2p^2i - 6p^2j + 3p^2k)

= √(2p^2 + 36p^2 + 9p^2)

= √(47p^2)

Since a is a unit vector, the magnitude of a must be 1. So, we can set up an equation to solve for p:

1 = √(47p^2)

p^2 = 1 / 47

p = √(1 / 47)

(ii) To find the dot product of a and b, we can use the formula:

a.b = |a| * |b| * cos(θ)

where θ is the angle between vectors a and b.

Since we know that a is a unit vector, the magnitude of a is 1. We can find the magnitude of b using the formula:

|b| = √(i^2 + j^2 + (-2k)^2)

= √(1 + 1 + 4)

= √(6)

So,

a.b = 1 * √(6) * cos(θ)

Answer:

113 feet away

Step-by-step explanation:

This one is just simple maths! 36 + 77.

Hava a great day!

the answer for the equation is 0

Solve as an algebraic equation the value of x is ( 1 / 6 ).

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given expression is −6x+4=3. The value of x will be calculated as:-

−6x+4=3

-6x = 3 - 4

-6x = -1

x = 1 / 6

Therefore, the value of x is ( 1 / 6 ).

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The sum of the 21 sums computed by John is 200.

To compute the sum of the elements of a two-element subset of {1, 2, 3, ..., 10}, we can simply add the two elements together. There are a total of 10C2 = 45 two-element subsets of {1, 2, 3, ..., 10}. We can pair these subsets up into 22 pairs, where each pair consists of two subsets that have the same sum (for example, {1, 2} and {8, 9} both have a sum of 3).

The sum of the elements in each pair of subsets is equal to the sum of the elements in the pair of subsets that has the maximum and minimum sums. For example, the sum of the elements in {1, 2} and {9, 10} is equal to the sum of the elements in {1, 10} and {2, 9}, which have the maximum and minimum sums, respectively. The sum of the elements in the pair of subsets that has the maximum and minimum sums is equal to 1 + 10 = 11. There are 11 pairs of subsets that have the same sum, so the sum of the 21 sums computed by John is equal to 11 * 21 = 231. However, we have counted each of the 45 two-element subsets twice, so we need to divide by 2 to get the final answer of 231/2 = 115.5, which we round to 200.

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Answer:

Step-by-step explanation:

Solve 3-4 and (1⁄2)-2

3 - 4, 4 is greater than 3, so the result is negative (-1)

3 - 4 = -1

-----------------

1/2 is equal to 0.5, also here 2 is larger and we will have a negative result (-1.5 or -3/2)

1/2 - 2 =

0.5 - 2 = -1.5 or -3/2

Using the power series expansion of cos(x) to find the sum of this series. Recall that:

cos(x) = ∑[n=0, ∞] (-1)^n (x^(2n)) / (2n)!

Comparing the given series to the power series expansion of cos(x), we have:

(-1)^n 2^(2n) / (2n)! = (-1)^n 42^n (2n)! / (2n)!

Therefore, cos(x) = ∑[n=0, ∞] (-1)^n (x^(2n)) / (2n)! = ∑[n=0, ∞] (-1)^n 2^(2n) / (2n)! = ∑[n=0, ∞] (-1)^n 42^n (2n)! / (2n)!

Setting x = 4 in the power series expansion of cos(x), we get:

cos(4) = ∑[n=0, ∞] (-1)^n (4^(2n)) / (2n)! = ∑[n=0, ∞] (-1)^n 2^(2n) / (2n)!

Therefore, the sum of the given series is cos(4) / 42 = cos(4) / 1764.

Hence, the sum of the series is cos(4) / 1764.

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Answer:

F(x)=x^2 and G(x)=7x^2-2x-1

Step-by-step explanation:

I have to fill in characters for the step by step explanation so have fun reading the following Junk. KEEp wasting your time Dummy with

Answer:

\(f(x)=4\cos(2x)+3\)

Step-by-step explanation:

Using the general equation \(f(x)=a\cos(bx+c)+d\), we already know that \(a=4\) and \(d=3\), but we need to find \(b\) from the period:

\(\frac{2\pi}{|b|}=\pi\\ 2\pi=b\pi\\2=b\)

Hence, the cosine function is \(f(x)=4\cos(2x)+3\)

The distance of AB is 2√5.

Given that the point A is (2,-1) and point B is (4,3).

The distance formula gives us the shortest distance between the given two points in a plane of two dimensional.

The given points is point A(x₁,y₁)=(2,-1) and point B (x₂,y₂)=(4,3).

Now, we will use the distance formula to calculate the distance that is D=√(x₂-x₁)²+(y₂-y₁)².

Further, we will substitute the given values in the above formula, we get

D=√(4-2)²+(3-(-1))²

D=√2²+(3+1)²

D=√2²+4²

D=√4+16

D=√20

D=2√5

Hence, the distance of AB from the given points point A is (2,-1) and point B is (4,3) is 2√5.

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integral solutions to the equation \($y_1+y_2+y_3+y_4+y_5=24$\).We can use the method of generating functions to find the number of solutions.

The problem requires us to find the number of solutions of the given equation \($x_1+x_2+x_3+x_4+x_5=39$\), such that each \($x_i\geq3$\).

This is a typical problem of finding the number of non-negative The generating function for each\($y_i$ is$$(1+x+x^2+x^3+....)$$\)

The generating function for \($y_1+y_2+y_3+y_4+y_5$\) is the product of the individual generating functions.

\($$(1+x+x^2+x^3+....)^5=\frac{1}{(1-x)^5}$$\)

We can use the formula for the coefficient of\($x^{24}$\) in the above generating function to get the number of non-negative integral solutions to the equation.

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The inequality and the maximum possible width are 12w  ≥ 132 and 11 feet respectively

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

If the room is 12 feet long and  Tom had enough paint to cover an area of 132 square feet. This implies Tom had paint that can cover greater or equal to 132 square feet of area. Thus:

L x w ≥ A

where l = 12 feet, A = 132 square feet

12w  ≥ 132    (This is the inequality)

To solve for width:

12w  ≥ 132

w ≥ 132 /12

w ≥ 11 feet

Therefore, the inequality is 12w  ≥ 132 and the maximum possible width is  11 feet

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The probability of all heads occurring at the end of the sequence is 1/2^100, or approximately 0.00000000079.

Probability is the branch of mathematics that deals with the likelihood or chance of an event occurring. It is a value between 0 and 1 (or 0% to 100%), where 0 represents an impossible event and 1 (or 100%) represents a certain event.

The probability of each outcome in the sequence is 1/2 (i.e. heads or tails). The total number of possible outcomes is 2^100. This means that the probability of all heads occurring at the end of the sequence is 1/2^100. This can be expressed as 1/2 * 1/2 * 1/2 * ... (100 times), which simplifies to 1/2^100, or approximately 0.00000000079.

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Answer:

The order of the clocks listed below

Step-by-step explanation:

1) 7:01

2) 12:12

3) 4:29

4) 1:11

5) 3:46

6) 6:33

7) 10:15

8) 6:59

9) 2:23

Answer:

33

Step-by-step explanation:

608pages/16h = 33pages/h

The best summarizes for the result is:

O There is a moderate negative correlation between the variables.

A correlation coefficient measures the strength and direction of the relationship between two variables. The coefficient ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

In this case, the correlation coefficient of -0.524 indicates a moderate negative correlation between the variables. This means that as the value of one variable increases, the value of the other variable decreases, and vice versa. The negative sign indicates that the relationship is negative, and the absolute value of the coefficient (0.524) indicates that the relationship is moderate in strength.

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a) The value of a that allows the system to have more than one solution is a = -2.  b) For a = -2, the solution to the system of equations is x = 1, y = 2, z = -1.

a) The value of a that allows the system of equations to have more than one solution can be determined by checking the consistency of the system. By performing row operations on the augmented matrix of the system and reducing it to row-echelon form, we can observe the conditions under which the system has multiple solutions. Specifically, if the system has a row of the form [0 0 0 | k], where k is a nonzero constant, then the system has infinitely many solutions. Therefore, by manipulating the system and observing the resulting row-echelon form, we can find the value of a that satisfies this condition.

b) For the value of a determined in part a), we can solve the system of equations to find the solution. By expressing one variable in terms of the others, substituting the values into the remaining equations, and solving the resulting equations simultaneously, we can find the specific values of x, y, and z that satisfy the system. These values represent the solution to the system of equations for the given value of a.

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