a laser tag company runs a deal for birthday parties. The cost of a party for 2 hours is $100 plus an additional $15 per person. A birthday $475 last month. How many people attended the party?

Answer:

-3

Step-by-step explanation:

rise/run

\(-\frac{6}{2}\) or \(-\frac{3}{1}\)  which is equal to -3

good luck, hope this helps :)

The number of students in vans are 13 whereas in buses it is 31.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, the School A rented and filled 5 vans and 6 buses with 251 students, and School B rented and filled 6 vans and 14 buses with 512 students.

Let the number of student in vans be v and that of in buses be b, therefore, establishing the system of equations,

5v + 6b = 251.....(i)

6v + 14b = 512....(ii)

Multiplying eq(i) by 6 and eq(ii) by 5

30v + 36b = 1506...(iii)

30v + 70b = 2560....(iv)

Subtracting eq(iii) from (iv)

(30v + 70b = 2560) - (30v + 36b = 1506)

34b = 1054

b = 31

Put b = 31 in eq(i)

5v + 6×31 = 251

5v = 65

v = 13

Hence, the number of students in vans are 13 whereas in buses it is 31.

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Given:

Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.

Total question answered by Steve =  30

Total score = 20 points

To find:

The system of equations for the given problem.

Solution:

Let x be the number of correct answers and y be the number of wrong answers.

Total question answered by Steve =  30

\(x+y=30\)       ...(i)

Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.

Score for 1 correct answer = 4

Score for x correct answer = 4x

Score for 1 wrong answer = -1

Score for y correct answer = -y

Total score = 20 points

\(4x-y=20\)        ...(ii)

The system of equations contains (i) and (ii).

Therefore, the system of equations have two equations \(x+y=30\) and \(4x-y=20\).

1) Todo número entero multiplicado por un múltiplo de 10 hereda los ceros de aquel múltiplo.

2) Si el número es decimal, entonces la coma es desplazada una cantidad de posiciones a la derecha equivalente a esos ceros heredados.

3) 100 kilogramos de frijol cuestan $ 2050.

1) Los casos a realizar sin necesidad de calculadora están correctamente desarrollados, puesto que observan la regla mnemotécnica de que todo número entero multiplicado por un múltiplo de 10 hereda los ceros de aquel múltiplo.

2) De manera semejante a 1), los casos a realizar sin necesidad de calculadora están correctamente desarrollados. Si el número es decimal, entonces la coma es desplazada una cantidad de posiciones a la derecha equivalente a esos ceros heredados.

3) La cantidad total (\(C\)), en pesos, por 100 kilogramos de frijol es igual al precio unitario (\(c\)), en pesos por kilogramo, por la masa comprada (\(m\)), en kilogramos, es decir:

\(C = m\cdot c\) (1)

\(C = 100\,kg\times 20.50\,\frac{\$}{kg}\)

\(C = \$ \,2050\)

100 kilogramos de frijol cuestan $ 2050.

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The cosine function with amplitude 2 and period 6π is given by:

y = 2cos(x/3).

The standard cosine function is given by:

y = Acos(Bx).

In which:

For a cosine function with amplitude 2 and period 6π, we have that A = 2 and B = 1/3, hence:

y = 2cos(x/3).

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Answer:

The speed at the crest of the falls is 32 kilometres (20 miles) per hour (22 miles) per hour.

The water moves at a speed of approximately 8.89 m/s at the crest of Niagara Falls.

It is the conversion of one unit to another unit with its standard conversion.

Examples:

1 hour = 60 minutes

1 minute = 60 seconds

1 km = 1000 m

We have,

To convert km/h to m/s, we need to divide by 3.6.

Now,

1 km/h

= 1000 m/3600 s

= 1/3.6 m/s.

The speed of the Niagara River in m/s.

32 km/h ÷ 3.6

= 8.89 m/s

Therefore,

The water moves at a speed of approximately 8.89 m/s at the crest of Niagara Falls.

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Answer:

When writing a standard number in scientific notation, the first factor must have a value greater than or equal than 1 but less than \(10\).

After changing the smaller exponent (-3) to the larger exponent (-1), its coefficient change to?l A. 0.23.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

From the information, it should be noted that the value was illustrated as:

= 2.3 × 10^-1

= 2.3 × 0.1

= 0.23

Therefore, the correct option is A.

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The limit of (1 + e^(-0.2t/100)) as t approaches infinity is 1. As t approaches infinity, the term e^(-0.2t/100) approaches zero.

To evaluate the limit, we can analyze the behavior of the function (1 + e^(-0.2t/100)) as t approaches infinity. Let's solve it step by step:

1. Examine the exponential term: As t approaches infinity, the term e^(-0.2t/100) approaches zero. This is because the exponent (-0.2t/100) becomes increasingly negative, causing the exponential function to decay rapidly.

2. Analyze the function: The function (1 + e^(-0.2t/100)) consists of a constant term (1) added to the exponential term. Since the exponential term approaches zero, the entire function approaches 1.

3. Apply the limit: As t approaches infinity, the function (1 + e^(-0.2t/100)) approaches 1. This can be observed by considering that the exponential term becomes negligible compared to the constant term.

4. Evaluate the limit: Based on the analysis, we can conclude that:

  lim(t→∞) (1 + e^(-0.2t/100)) = 1.

  Therefore, the limit of (1 + e^(-0.2t/100)) as t approaches infinity is 1.

In conclusion, the limit of (1 + e^(-0.2t/100)) as t approaches infinity is 1.

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If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to widen.

This is because the standard deviation is a measure of the spread of the data, so if it increases, the data points are more spread out from the mean. As a result, the range of values that could reasonably contain the true population parameter (i.e., the confidence interval) needs to be wider to account for the increased variability in the sample.
If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to become wider.
When standard deviation increases, it indicates more variability in the data. As a result, the confidence interval, which is a range of values that estimates the true population parameter with a certain level of confidence, needs to be wider to account for the increased variability. This ensures that the true population parameter is still captured within the interval with the same level of confidence.

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Answer:

make them the same

Step-by-step explanation:

hope this helps

Answer:

The seccond one

Step-by-step explanation:

_

The first one shows 33.3% while the second one shows 20%

I hope this helps!

Answer:

x = 1, y = -4, z = -5

Step-by-step explanation:

Solve the following system:

{x = -4 z - 19 | (equation 1)

{y = z + 5 x - 4 | (equation 2)

{-z - 5 y = 25 | (equation 3)

Express the system in standard form:

{x + 0 y + 4 z = -19 | (equation 1)

{-(5 x) + y - z = -4 | (equation 2)

{0 x - 5 y - z = 25 | (equation 3)

Swap equation 1 with equation 2:

{-(5 x) + y - z = -4 | (equation 1)

{x + 0 y + 4 z = -19 | (equation 2)

{0 x - 5 y - z = 25 | (equation 3)

Add 1/5 × (equation 1) to equation 2:

{-(5 x) + y - z = -4 | (equation 1)

{0 x + y/5 + (19 z)/5 = -99/5 | (equation 2)

{0 x - 5 y - z = 25 | (equation 3)

Multiply equation 2 by 5:

{-(5 x) + y - z = -4 | (equation 1)

{0 x + y + 19 z = -99 | (equation 2)

{0 x - 5 y - z = 25 | (equation 3)

Swap equation 2 with equation 3:

{-(5 x) + y - z = -4 | (equation 1)

{0 x - 5 y - z = 25 | (equation 2)

{0 x + y + 19 z = -99 | (equation 3)

Add 1/5 × (equation 2) to equation 3:

{-(5 x) + y - z = -4 | (equation 1)

{0 x - 5 y - z = 25 | (equation 2)

{0 x + 0 y + (94 z)/5 = -94 | (equation 3)

Multiply equation 3 by 5/94:

{-(5 x) + y - z = -4 | (equation 1)

{0 x - 5 y - z = 25 | (equation 2)

{0 x + 0 y + z = -5 | (equation 3)

Add equation 3 to equation 2:

{-(5 x) + y - z = -4 | (equation 1)

{0 x - 5 y + 0 z = 20 | (equation 2)

{0 x + 0 y + z = -5 | (equation 3)

Divide equation 2 by -5:

{-(5 x) + y - z = -4 | (equation 1)

{0 x + y + 0 z = -4 | (equation 2)

{0 x + 0 y + z = -5 | (equation 3)

Subtract equation 2 from equation 1:

{-(5 x) + 0 y - z = 0 | (equation 1)

{0 x + y + 0 z = -4 | (equation 2)

{0 x + 0 y + z = -5 | (equation 3)

Add equation 3 to equation 1:

{-(5 x) + 0 y + 0 z = -5 | (equation 1)

{0 x + y + 0 z = -4 | (equation 2)

{0 x + 0 y + z = -5 | (equation 3)

Divide equation 1 by -5:

{x + 0 y + 0 z = 1 | (equation 1)

{0 x + y + 0 z = -4 | (equation 2)

{0 x + 0 y + z = -5 | (equation 3)

Collect results:

Answer: {x = 1, y = -4, z = -5

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

see explanation

Step-by-step explanation:

Under a rotation about the origin of 180°

a point (x, y ) → (- x, - y ) , then

A (- 5, - 8 ) → A' (5, 8 )

B (2, - 3 ) → B' (- 2, 3 )

C (- 2, 9 ) → C' (2, - 9 )

Answer:

508.94 in²

Step-by-step explanation:

Magda said the typical measure of orange juice in a full family-size jug is 1 gal in value.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.

The collection of mathematical symbols that emerges from the right arrangement of numbers is known as a mathematical expression and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

The three different types of algebraic expressions are monomial, binomial, and polynomial.

The complete question is : In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer?

a. 2 cups

b. 1 gal

c. 10 gal

d. 10 fl oz

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3) The extra number of feet of coiled tubing Tom needs to run into the well is: 5445 ft

4) The total length of coiled tubing Brendan ran in the wellbore is: 994 ft

5) The distance that the coiled tubing has reached after the first four hours is:  a depth of 16,776 feet in the well.

3) Initial amount of coiled tubing he had after 81 minutes = 9,153 feet

Amount of tubing after another 10 minutes = 10,283 feet

The total tubing required = 15,728 feet.

The extra number of feet of coiled tubing Tom needs to run into the well is: Needed tubing length - Current tubing length

15,728 feet - 10,283 feet = 5,445 feet

4) Speed at which Brendan is running coiled tubing = 99.4 feet per minute.

Coiled tubing inside the wellbore after 8 minutes is: 795.2 feet

Coiled tubing inside the wellbore after 2 more minutes is: 198.8 feet

The total length of coiled tubing Brendan ran in the wellbore is:

Total length = Initial length + Additional length

Total length =  795.2 feet + 198.8 feet

Total Length = 994 feet

5) Rate at which coiled tubing is being run into a 22,000-foot wellbore = 69.9 feet per minute. After the first four hours, we need to determine how deep the coiled tubing has reached.

A time of 4 hours is same as 240 minutes

Thus, the distance covered in the first four hours is:

Distance = Rate * Time

Distance = 69.9 feet/minute * 240 minutes

Distance = 16,776 feet

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The equations represents each graph shown on the coordinate system are:

a) y = 3x + 2

b) y = 2

c) y = 2x - 2

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

We have,

The points where a line passes through them in each given graph:

a) (-1, -1) and (0, 2)

b) (-1, 0) and (2, 0)

c) (0, -2) and (1, 0)

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y₂ - y₁) ÷ (x₂ - x₁)

a)

(-1, -1) and (0, 2)

m = (y₂ - y₁) ÷ (x₂ - x₁)

m = (2 - (-1)) ÷ (0 - (-1))

m = 3 ÷ 1

m = 3

The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.

Since the given line passes through points (0, 2),

y = 3x + b

2 = 3(0) + b

b = 2.

The equation:

y = 3x + 2

b)

(-1, 0) and (2, 0)

m = (y₂ - y₁) ÷ (x₂ - x₁)

m = (0 - 0)  ÷  (2 - (-1))

m = 0

the y-intercept of the line passes through points (0, 2),

y = (0)x + b

2 =  b

b = 2.

The equation:

y = 2

c)

(0, -2) and (1, 0)

m = (0 - (-2)) ÷ (1 - (0))

m = 2 ÷ 1

m = 2

the y-intercept of the line passes through points (0, -2),

y = 2x + b

2 =  2(-2) + b

b = -2.

The equation:

y = 2x - 2

Hence, the equations represents each graph shown on the coordinate system are:

a) y = 3x + 2

b) y = 2

c) y = 2x - 2

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The total number of tickets sold by Diane is 21.

What is a Linear equation?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers and x is a variable. This equation has only one solution.

What is a variable?

Any qualities, quantity, or number that can be measured or counted classifies as a variable.

Here,

Let the tickets sold by Becky = x.

Then, the tickets sold by Diane =3x.

So, the total number of tickets sold by Becky and Diane is = x + 3x = 28

               4x = 28

                 x = 7

The total ticket sold by Diane = 3x = 3*7 = 21

The total ticket sold by Becky = x = 7

Hence, Diane's total ticket for the Fall festival sold is 21.

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Answer:

The slope is 5/6 and the y intercept is -3

Step-by-step explanation:

(a)the area between -1 and 1 is approximately 0.6827 (b) the area between -√3.84146 and √3.84146 is approximately 0.9500.

(a) To track down P(z^2 < 1), we can revamp it as P(- 1 < z < 1) since the square of a standard typical irregular variable is generally certain.

We know that P(-1  z  1) is the same as the area under the standard normal curve between -1 and 1. This is based on the properties of the standard normal distribution.

Using statistical software or looking up the values in the standard normal distribution table, also known as the Z-table, we discover that the range from -1 to 1 is roughly 0.6827.

As a result, P(z2  1)  0.6827.

(b) To track down P(z^2 < 3.84146), we can again modify it as P(- √3.84146 < z < √3.84146) since the square of a standard typical irregular variable is dependably sure.

We can determine the area under the standard normal curve between -√3.84146 and √3.84146 by utilizing the characteristics of the standard normal distribution.

Using statistical software or the standard normal distribution table, we determine that the range between -3.84146 and 3.84146 is approximately 0.9500.

Consequently, P(z2  3.84146)  0.9500.

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Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

Answer:

x=1/7 or 0.14

Step-by-step explanation:

first you distribute: 8-6x+2=x+9

next combine like terms (8 and 2): -6x+10=x+9

then subtract 1x from both sides: -7x+10=9

then subtract 10 from both sides: -7x=-1

divide both sides by -7: x=1/7 or 0.14

As David lifts the mass,

This is the term that is used to refer to the energy that a body has due to the fact that the given body is on motion. The kinetic energy is the energy in motion.

This is the energy that a body would have due to the fact that it is positioned on a gravitational potential field.

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The correct answer is c. 49%.

To calculate the shared variance, we need to square the correlation coefficient.
0.70 squared = 0.49
This means that 49% of the variance is shared variance between the two variables. Therefore, option c is the correct answer.

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If the correlation between variables is 0.70, what percent of the variance is shared varianceis c. 49%.

When the correlation between two variables is 0.70, it means that 49% of the variance is shared variance. This is because the correlation coefficient represents the strength and direction of the linear relationship between two variables, and the coefficient of edterminationd (r-squared) is the proportion of the variance in one variable that can be explained by the variance in the other variable. In this case, the r-squared is 0.70^2, which equals 0.49 or 49%.

Therefore, the answer to the question is that 49% of the variance is shared variance when the correlation between variables is 0.70.


The correct option is c. 49%.

To find the shared variance (also known as the coefficient of determination) between two variables, you need to square the correlation coefficient. In this case, the correlation coefficient is 0.70. When you square 0.70 (0.70 * 0.70), you get 0.49, which represents 49% shared variance.

If the correlation between variables is 0.70, the percent of the variance that is shared variance is 49%.

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Answer:

19,27 cm^2

Step-by-step explanation:

area of triangle = (6 x 3)/ 2 = 9 cm^2

circle area : 3^2 x 3,14 = 28,27 cm^2

area of shaped region = 28,27 - 9 = 19,27 cm^2