suppose that three pennies land heads up and you toss the forth penny. What is the probability of landing heads up?

Answer:

y = -30

Option A

Step-by-step explanation:

y = -2x - 10

y = -5x + 20

We just need to substitute the values of y.

We have to equate both the equation.

-2x -10 = -5x + 20

-2x + 5x = 20 + 10

3x = 30

x = 10

Plug x as 10 in any one of the equation

Let's take the first equation

y = -2x  - 10

y = -2(10) - 10

y = -20 -10

y = -30

Answer:

40

Step-by-step explanation:

Answer:40

Step-by-step explanation:

10 for him

5 times 6 is 30

add 10 and 30

you get 40

Answer:

x=-11

Step-by-step explanation:

Steps are in the attachment, but I couldn't include the last step.

The last step is to divide by -2 on both sides.

The final answer then will be x=-11

Answer:

No

Step-by-step explanation:

It could only represent large colleges, not all colleges.  Sampling requires similar characteristics to represent the entire population of testing.

Answer:

1.50

Step-by-step explanation:

7.5 is 1.5 x 5 so, 1 x 1.5 = 1.5

Hence, The probability that the arrival time between vehicles is 10 sec or less and 6 sec is 0.62 and 0.45 respectively.

Simply, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability

The probability that arrival time between vehicles is 10 sec or less.

\(P (X\leq 10) = 1-e^{-\frac{1}{10}*10 } = 1-e^{-1} =1- 0.3679= 0.6231= 0.62\)

The probability that arrival time between vehicles is 6 sec or less.

\(P (X\leq 6) = 1-e^{-\frac{1}{10}*6} = 1-e^{-0.6} =1- 0.54=0.45\)

Hence, The probability that the arrival time between vehicles is 10 sec or less and 6 sec is 0.62 and 0.45 respectively.

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Answer:

17 miles over the course of 3 days

Step-by-step explanation:

the first institution has 441 and the second institution has 189.

We can use algebra to solve the problem. We can start by assigning variables to represent the two institutions:

Let x be the multiplier of the ratio.

Then, we have:

7x is the first institution.

3x is the second institution.

From the problem, we know that the sum of the two institutions is 630:

7x + 3x = 630

Simplifying the left side, we get:

10x = 630

Dividing both sides by 10, we get:

x = 63

Now that we know the value of x, we can find the number of each institution:

First institution = 7x = 7(63) = 441

Second institution = 3x = 3(63) = 189

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The radius of the circle is 17.78 cm.

The formula for calculating the perimeter of a circular sector with angle θ is given by

P = 2rθ

r = P / (2θ)

Substituting in the given values, we have:

r = 64 / (2 x 1.8)

r = 17.78

Therefore, the radius of the circle is 17.78 cm.

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Answer:

48

Step-by-step explanation:

there are 16 cups in a gallon therefore you would multiply 16 times the number of gallons she uses which is 3 so 16 times 3 or you could do 16+16+16 which both would get you 48 so she would need 48 cups to make 3 gallons. hope this helps have a good rest of your night :)❤

Answer:

1.325 x 10 -2

Step-by-step explanation:

That is the answer and I know 100% that it is correct

The measure of the complement of the angle is A) 54.

Given:

The ratio of the measure of the supplement of an angle to that of a complement of the angle is 8:3.

Let x be the angle.

supplement of the angle of x is = 180-x

complement of the angle of x is = 90 -x

180 - x / 90 -x = 8/3

3(180-x) = 8(90-x)

3*180 - 3*x = 8*90 - 8*x

540 - 3x = 720 - 8x

-3x+8x = 720 - 540

5x = 180

divide by 5 on both sides

x = 180/5

x = 36

Complement of the angle = 90 - 36

= 54

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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The area of the floor in the scale drawing will be equal to 150 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Length of the classroom, l = 30 feet and,

The width of the classroom, w = 20 feet.

As per the scale drawing, the length of the classroom, l' = 15 feet

Let the scale width, w' = x feet

As we can see that the original length is twice the scale drawing.

Then, the original width also is twice the scale drawing.

So, w' = 20/2 = 10 feet.

Now, the area of the floor in the scale drawing will be,

A = wl

A = (15)(10)

A = 150 in².  

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The volume of a solid figure with a height of 2 and a square cross-sectional area where the length of the side of a cross-section is x is 2x^2.

To calculate the volume of the solid figure with a height of 2 and a square cross-sectional area, we need to know the length of the side of the cross-section. Let's assume that the length of the side is x.
The cross-sectional area of the figure is the area of the square, which is x^2. The volume of the figure is the product of the cross-sectional area and the height, which is 2x^2.
Therefore, the volume of the solid figure is 2x^2.
It's important to note that the volume of a solid figure is directly proportional to its cross-sectional area. This means that if we increase the cross-sectional area by a factor of 2, the volume will also increase by a factor of 2. This relationship is because the cross-sectional area determines how much material there is to fill up the space. The larger the cross-sectional area, the more material is needed to fill up the same height, resulting in a larger volume.
In conclusion, the volume of a solid figure with a height of 2 and a square cross-sectional area where the length of the side of a cross-section is x is 2x^2.

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Answer: 454.5

Step-by-step explanation:

-2, 20, -200, 2,000 ==> 4 numbers

Mean: (-2+20+(-200)+2000)/4=

(18-200+2000)/4=

(-182+2000)/4

1818/4=454.5

Answer:

a

Step-by-step explanation:

To travel downstream, a boat needs 2 hours while to travel back upstream, it needs 4 hours. The river flows at speed of 3.58  3.58 km/hour

The relation between distance and speed is given by:

distance = speed x travelled time

In the problem, let:

vb = boat speed

v = river speed

Then, when the boat travels downstream:

28.62 = (vb + v) x 2

2vb + 2v = 28.62   ... (Equation 1)

When the boat travels upstream:

28.62 = (vb - v) x 4

Divide both sides by 2:

14.31 = (vb - v) x 2

2vb - 2v = 14.31  ... (Equation 2)

Substract equation 1 by equation 2

2vb + 2v = 28.62

2vb  - 2v = 14.31 _

       4v  = 14.31

          v = 3.58

Hence, the speed of water = 3.58 km/hour

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On solving the provided question we can say that the given equation yield solution as x=27.4 and y= -5/8.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

On solving simultaneously,

x=27.4

y= -5/8

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Answer:

y-7=-13(x-5)

Step-by-step explanation:

y-y1=m(x-x1)

y-7=-13(x-5)

The different ways that the students can elect a president and a vice president will be 13110.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

Given data;

Total no of students =  115

The total number of ways to elect a president = 115

If one person is elected as the president the total number of ways to elect a president  = 114

The different ways that the students can elect a president and a vice president are found as;

⇒ 115 ways × 114 ways

⇒ 13110 ways

Hence the different ways that the students can elect a president and a vice president will be 13110.

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Answer:

t=8

Step-by-step explanation:

Answer:

above sea level

Step-by-step explanation:

Answer:

$10.67

Step-by-step explanation:

Jennifer has a total amount of $80 to buy what she needs

1/5 of the money is spent on sandwich

= 1/5×80

= $16

The amount spent on sandwich is $16

1/6 of the money is spent on tickets to a museum

= 1/6×80

= 0.166×80

= $13.33

The amount spent on tickets is $13.33

1/2 of the money is spent on a book

= 1/2×80

= 0.5×80

= $40

The amount spent on a book is $40

Therefore, to calculate the amount left on her we add the total money spent and subtract it from the original amount of money that she has to spend

= $80-$16+$13.33+$40

= $80-$69.33

= $10.67

Hence the amount of money left on Jennifer is $10.67

Answer:

4:2 or 2:1

Step-by-step explanation:

4 cups of pretzels to 2 cups of bread chips. Simplified it becomes 2:1

The correct option for the range of the piecewise function g(x) is (-∞, +∞).

Thus, option (A) is correct.

In the given piecewise function, g(x), we have two parts:

Part 1: g(x) = \(x^2 - 5\) for x < -3

Part 2: g(x) = 2x for x ≥ -3

For Part 1, the function g(x) = \(x^2 - 5\) represents a downward-opening parabola with the vertex at (-∞, -5)

and, the range extending from -5 to +∞.

So, for x < -3, the range is [-5, +∞).

For Part 2, the function g(x) = 2x represents a linear function with a slope of 2.

As x approaches -3 from the right (x ≥ -3), the function extends from -∞ to +∞.

So, for x ≥ -3, the range is (-∞, +∞).

To find the overall range of the piecewise function, take union of the ranges from both parts.

Thus, the overall range is (-∞, +∞).

Therefore, the range is (-∞, +∞).

Thus, option (A) is correct.

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Answer:

Answer: $17.22 was spent on a pass and $8.94 on lunch for each student and that implies a total of $26.16 was spent on each student

Tell me if wrong. :) Hope it helps!

Step-by-step explanation:

Answer:

Students in her classes At the beginning of the semester, but 13 students withdraw from her classes before Test three. So now she has 150 students. If she has one classes in total, in each class has an equal number of students. How many students are in each class round your answer to the nearest ones? Well, first of all, if she only has one class, then there's 150 students in that class is or class, this is the middle school math teacher signing out.

lazyuser30

Answer:

  x = 11

Step-by-step explanation:

If we assume that points A, B, and C are on the same line with B between A and C, then we have ...

  AB +BC = AC

  (4x +34) +(6x +6) = 150 . . . . use the given expressions

  10x +40 = 150 . . . . . . . . . . . . collect terms

  10x = 110 . . . . . . . . . . . . . . . .  subtract 40; next, divide by 10

  x = 11

If 180 liters of fluid enter the kidneys each day, about 178 liters of fluid will be reabsorbed by the kidneys each day.

The kidneys play a crucial role in filtering and regulating fluid balance in the body. On average, approximately 180 liters of fluid enter the kidneys each day through the process of filtration. However, not all of this fluid is excreted as urine. The majority of it, around 99%, is reabsorbed back into the bloodstream.

The reabsorption process occurs in the renal tubules, where essential substances such as water, electrolytes, and nutrients are selectively transported back into the bloodstream while waste products and excess substances are removed for eventual excretion.

Therefore, out of the initial 180 liters that enter the kidneys, around 178 liters are reabsorbed, leaving only a small amount (approximately 2 liters) to be excreted as urine.

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