Canceling common factors and evaluating the limit, we can finally conclude that the velocity of the ball at t = 2 is as follows. v(2) = lim (-160 + 17)(t - 2) t-2 t2 lim (-160 + 17] t2 = -16 + 17 =

The mean of the data is 4, the median is also 4. The range is 9, with an interquartile range of 2. The standard deviation is 2.14 and the skewness measure is 0.38, indicating a slight positive skew. No outliers are present.

(a) [tex]Mean = (7 + 2 + 6 + 4 + 9 + 4 + 1 + 4 + 2 + 4 + 5 + 2 + 3 + 5 + 2 + 0 + 6 + 7 + 4 + 2) / 20 = 4.[/tex]

[tex]Median = 4[/tex] (after sorting the data)

(b) First quartile (Q1) = 2 (after sorting the data and finding the median of  the lower half)

Third quartile (Q3) = 6 (after sorting the data and finding the median of the upper half)

(c) Range = 9 - 0 = 9

Interquartile Range (IQR) = Q3 - Q1 = 6 - 2 = 4

(d)[tex]Variance = ((7-4)^2 + (2-4)^2 + (6-4)^2 + (4-4)^2 + (9-4)^2 + (4-4)^2 + (1-4)^2 + (4-4)^2 + (2-4)^2 + (4-4)^2 + (5-4)^2 + (2-4)^2 + (3-4)^2 + (5-4)^2 + (2-4)^2 + (0-4)^2 + (6-4)^2 + (7-4)^2 + (4-4)^2 + (2-4)^2) / 20 = 9.05[/tex]

Standard deviation = √Variance = √9.05 = 3.01

(e) Skewness measure = 0. The data are symmetrically distributed (i.e., not skewed to the left or to the right)

(f) Lower limit = 4 - 3.01 x 1.5 = -1.51

Upper limit = 4 + 3.01 x 1.5 = 8.51

Data does not contain outliers as all values are within the lower and upper limits.

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Answer:

Step-by-step explanation:

AB= 20

The x intercept is x = 4 and the y intercept is y = 4.

The intercept of a graph is a point at which the graph crosses either the x-axis or the y-axis. For a graph with an x-intercept, the y-coordinate is 0 and the x-coordinate gives the value at which the graph intersects the x-axis.

For a graph with a y-intercept, the x-coordinate is 0 and the y-coordinate gives the value at which the graph intersects the y-axis. In the context of a line or a linear regression model, the intercept is the value of the dependent variable (y) when the independent variable (x) is 0.

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A linear system is a set of linear equations that can be written in the form ax + by = c, where x and y are variables, a and b are coefficients, and c is a constant.

A linear system is considered homogeneous when all the equations in the system are equal to zero, i.e., they have a constant term of zero. For example, a homogeneous linear system could be:

a linear equation is represented as

2x + 3y = 0

4x - 5y = 0

In this example, both equations are homogeneous because the constant term is equal to zero.

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Answer: Sure! I'd be happy to help you with this.

To find the number of cupcake boxes that fit in the larger box, we need to find the volume of the larger box and divide it by the volume of one cupcake box.

The volume of the larger box is 10.5 x 7 x 7 = 572.5 cubic inches.

The volume of one cupcake box is 3.5 x 3.5 x 3.5 = 42.375 cubic inches.

Dividing the volume of the larger box by the volume of one cupcake box, we get 572.5 / 42.375 = 13.5.

So, 13.5 cupcake boxes will fit in the larger box.

Step-by-step explanation:

Answer: x = 3

Step-by-step explanation: -7 + 9 = 8 - 6

Answer:

y=883

Step-by-step explanation:

The total cost includes $11 per pizza and the delivery fee. A delivery of 5 pizzas costs $58.
11 (dollars per pizza) x 5 (pizzas were delivered) = 55 dollars

58 (total cost) - 55 (total cost for pizza) = 3 (fee)
11x+3=y (Equation)
input the 80 pizzas to the equation
11(80)+3=y
y= 883

Hope this helps! I took a similar question 3 years ago! =)

The number of cakes that Andy, Betty, and Colin have will be 13, 52, and 16, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Andy has x cakes, Betty has 4x cakes, and Colin has x + 3. Then the equation is given as,

0.65(x + 4x + x + 3) = £52.65

Simplify the equation, then we have

0.65(x + 4x + x + 3) = £52.65

6x + 3 = 81

6x = 78

x = 13

Then the number of cakes that Betty has is given as,

4x = 4 (13)

4x = 52

Then the number of cakes that Colin has is given as,

x + 3 = 13 + 3

x + 3 = 16

The number of cakes that Andy, Betty, and Colin have will be 13, 52, and 16, respectively.

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Option (b) is correct. The sample size was not sufficiently large.

The histogram that is shown at the end of the answer shows the results of the simulation. We can clearly see that there are different variations in the population size. There are various reasons which can cause the simulation not to be normal. The main reason for this if the sample size is not big enough. That is because a theory stated that when the sample size taken by a person or researcher is not large or insufficient for the alpha level as well as the analysis one chooses to do, it will limit the statistical power of the study.

Due to the above, we can say that the sample size is not big enough that's why the simulation of the sampling distribution is not approximately normal. So option (b) is correct.

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Your question was incomplete, your most probable question was stated below:
A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation.

Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

(a) The samples were not selected at random.

(b) The sample size was not sufficiently large.

(c) The population distribution was approximately normal.

(d) The samples were selected without replacement.
(e) The sample means were less than the population means.

Answer:

(9.25*0.03)+9.25=9.53

(9.53*0.16)+9.53=11.05

Sales tax was $0.28

Step-by-step explanation:

the CPI to the nearest tenth in 1950 was 24.06.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, a bottle of dishwashing detergent cost $0.31 in 1950 and In 1970, a bottle of dishwashing detergent cost $0.50

Since CPI, Consumer Price Index measures the overall change in consumer prices based on a representative basket of goods and services over time.

The price of dishwashing detergent increased at the same rate as the CPI from 1950 to 1970.

So,

0.50 / 0.31 = CpI for 1970/ CPI for 1950

Since CPI in 1970 is 38.80

CPI in 1950 = 0.62 * 38.80

CPI in 1950 = 24.056

Therefore,  the CPI to the nearest tenth in 1950 was 24.06.

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Complete question:

In 1970, a bottle of dishwashing detergent cost $0.50. To answer each of the parts below, assume that the consumer price index (CPI) was 29.6 in 1960, 38.8 in 1970, and 82.4 in 1980.

If the price of dishwashing detergent increased at the same rate as the CPI from 1970 to 1980, how much did a bottle of dishwashing detergent cost in 1980? By how much did the price of a bottle of dishwashing detergent increase from 1970 to 1980?

The solution is, he have after his birthday total cards 79 cards.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Gil got 4 packages of trading cards.

He already had 75 cards.

so,

he have after his birthday total cards = 75 +4

                                                              = 79 cards

Hence, The solution is, he have after his birthday total cards 79 cards.

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The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed.

When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x² up by 3 units, the graph of the function f(x) = x² + 3 is obtained.

Given that the transformation of the coordinate is x,y ( x+2,y-3). Let the coordinate of the point be ( 2, 2 ).

The translation of the point will be:-

( 2 , 2 ) = ( 2 + 2 , 2 - 3 )

( 2 , 2 ) = ( 4 , -1 )

The graph of the translation of the point is attached with the answer below.

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The value of x is 1.51.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]5^x[/tex] - 4 = 7

[tex]5^x[/tex] = 7 + 4

[tex]5^x[/tex] = 11

Taking logs on both sides.

log [tex]5^x[/tex] = log 11

x log 5 = log 11

x = log 11 / log 5

x = 1.04/0.69

x = 1.51

Thus,

x is 1.51.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{4(2y + 1)}\\\mathsf{= 4(2y) + 4(1)}\\\mathsf{= 8y + 4}\\\mathsf{\rightarrow 4y + 4y + 4}\\\mathsf{\rightarrow 2(4y + 2)}\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{Option\ A. \ 4y + 4y + 4}}\huge\checkmark\\\\\huge\boxed{\mathsf{Option\ B. \ 4y + 4y + 4}}\huge\checkmark\\\\\huge\boxed{\mathsf{Option\ E.\ 8y + 4}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The sum of p, q, and r is 27.

The point of intersection of the lines t1 and t2, (x,y), can be found by using the equation of the lines. The equation of t1 is y=mx+c, where m is the slope, and c is the y-intercept. The equation of t2 is y=mx+c, where m is the slope, and c is the y-intercept.

The equations of t1 and t2 can be written as y= 1/2 x + 1 and y= -1/4 x + 7/2 respectively.

By setting the two equations equal to each other, we can find the x-coordinate of the point of intersection (x,y).

x=2 - 7/4 =4/4 - 7/4 = -3/4

Since x=p−q√r, we can write -3/4 = p−q√r.

Rearranging this equation, we get p+q+r= 4/3 + 7/3 + 4/3 = 27/3 = 9.

Therefore, P+Q+R=27.

Therefore, the sum of p, q, and r is 27.

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Answer:

Marcel's and Stephanie's taxable incomes are less than their annual salaries because they both have a series of tax deductions

Step-by-step explanation:

The graph is attached, the point (2, 3) included in the solution area for the system and (4, 0) is the solution of area for the system.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings.

Each cupcake costs $4, and each piece of fudge costs $2.

4x + 2y ≤ 16

x + y ≥ 4

The graph for system of inequalities is attached.

The point (2, 3) included in the solution area for the system

4(2)+2(3)≤ 16

14≤ 16 is true.

2+3≥ 4 is true.

Point (2, 3) included in the solution area for the system.

From the graph (4, 0) is the solution of area for the system.

Hence, the graph is attached, the point (2, 3) included in the solution area for the system and (4, 0) is the solution of area for the system.

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The greatest common divisor (GCD) of 30 and 36 is 6, which implies they may be divided into six teams of five males and six girls apiece.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.

Here,

To get the greatest number of teams, each team should have the smallest number of players possible. The number of boys and girls should be divisible by the same number to ensure that each team has the same number of boys and girls.

The greatest common divisor (GCD) of 30 and 36 is 6, which means they can be split into 6 teams with 5 boys and 6 girls on each team.

So the greatest number of teams they could have made is 6.

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The 5th edition of Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by John D. Fenton covers a wide range of topics related to the use of Fourier series and boundary value problems to solve various partial differential equations.

The solution to the given differential equation is

[tex]$y(x) = \frac{-1}{2 \pi} \sin(4x)$.[/tex]

One example of a solution, to the ODE differential equation

[tex]$\frac{d^2y}{dx^2} + 4y = 0$[/tex]

with the boundary conditions

[tex]$y(0) = 0$[/tex] and [tex]$y(\pi) = 0$[/tex]

is given by the Fourier series

[tex]$y(x) = A \sin(2x) + B \cos(2x) + C \sin(4x) + D \cos(4x)$[/tex]

Where the constants A, B, C, and D are determined by the boundary conditions.

Using the boundary conditions, we find

[tex]$A = 0$[/tex] and [tex]$B = 0$[/tex]

[tex]$C = \frac{-1}{2 \pi}$[/tex] and [tex]$D = 0$[/tex]

Therefore, the solution to the given differential equation is

[tex]$y(x) = \frac{-1}{2 \pi} \sin(4x)$.[/tex]

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There are 38,400 different ways for Xing to construct a banana split at this ice cream shop if he is allowed to choose between zero and three sprinkled toppings.

a) In order to construct a banana split, Xing needs to select 3 flavors of ice cream, 6 sauces, and 3 sprinkled toppings. Therefore, the formula for the number of ways to construct a banana split is (20 flavors)(6 sauces)(10 toppings)^3. When calculated, this number is 28,800. This means that there are 28,800 different ways for Xing to construct a banana split at this ice cream shop.

b) In this scenario, the formula for the number of ways to construct a banana split is (20 flavors)(6 sauces)(10 toppings)^0 + (20 flavors)(6 sauces)(10 toppings)^1 + (20 flavors)(6 sauces)(10 toppings)^2 + (20 flavors)(6 sauces)(10 toppings)^3. When calculated, this number is 38,400. This means that there are 38,400 different ways for Xing to construct a banana split at this ice cream shop, with the option to choose zero, one, two, or three sprinkled toppings.

Therefore, there are 38,400 different ways for Xing to construct a banana split at this ice cream shop if he is allowed to choose between zero and three sprinkled toppings.

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The market equilibrium on the graph is the point at the middle of the graph where supply and demand intersect.

The market equilibrium has the price of $ 6 and the quantity of 20 units.

The revenue at the equilibrium is $ 120.

The price floor would create a surplus.

The market equilibrium is described as the point where the supply and demand curves intersect. This point has the price of $ 6 and the quantity of 20 units as shown on the graph.

The revenue at this point is:

= 6 x 20

= $ 120

The price floor of $ 8 would mean that the minimum supply would be 30 units and the maximum demand would be 10 units which therefore creates a surplus.

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Answer:

You can use the fact that both the cars were travelling at the same speed so we can take them equal to some variable.

The speed of the cars was 0.8 miles per hour

How to form may you can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

How  to find the speed of the cars?

Supposing that both the cars were travelling with the speed

Let the first car travels  miles

then as second car travels 12 miles extra, thus, distance traveled by second car is  miles.

Using the formula for speed, we have:

For first car:

Distance traveled =  miles

Speed =

Time taken =

Thus,

For second car:

Distance traveled =  miles

Speed =

Time taken =

Thus,

So, we got system of 2 linear equations in two variables.

Using the expression for x from first equation and substituting it in second equation, we get

Substituting this value in first equation to get the value of x

Thus,

The speed of the cars was 0.8 miles per hour

The surface area of Cone is 452.16 unit².

The surface area of a cone is equal to the curved surface area plus the area of the base: π r² + πlr

where r is the radius and l is the slant height.

Given:

Radius= 8 unit

height= 6 unit

slant height, l = √8²+6²= √64+36 =√100= 10units

So, the Surface area of Cone

= πr (l +r)

= 3.14 x 8 ( 10 + 8)

= 25.12 x 18

= 452.16 unit²

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Answer:

t = 9cm

Step-by-step explanation:

area = l*w

2(t-3) = 12

2t - 6 = 12

2t - 6 + 6 = 12 + 6

2t = 16

t = 18/2

t = 9

t = 9cm

Answer:

Rational

Step-by-step explanation:

You will always get a rational number when you add, subtract, multiply, or divide rational numbers with integers.

Hope it helps!

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

The indefinite integral of sin(16x) with respect to x cannot be expressed in terms of elementary functions.

LaTeX, you can display powers using the caret (^) symbol. For example, to display x raised to the power of 2, you would write:

[tex]$x^2$[/tex]

And to display x raised to the power of y, you would write:

[tex]$x^y$[/tex]

To solve this integral, we would typically use numerical or approximate methods, or special functions such as the sine integral or Fresnel integrals.

The indefinite integral of [tex](1 + cos^2(16x))[/tex] with respect to x can be evaluated using the substitution u = cos(16x). The derivative of cos(16x) with respect to x is -16sin(16x), so the integral becomes:

[tex]∫ (1 + cos^2(16x)) dx = ∫ (1 + u^2) du[/tex]

[tex]= 1/3 u^3 + u[/tex]

[tex]= 1/3 cos^3(16x) + cos(16x) + C[/tex]

where C is the constant of integration.

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The domain of the composite function (f o g)(4) for f(x) = 4x - 3 and g(x) = x³ + 2x is equal to -59.

A function is composite when the co-domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function (f - g)(4) as follows:

(f - g) = 4x - 3 - (x³ + 2x)

(f - g) = 4x - 3 - x³ - 2x

(f - g) = 2x - 3 - x³

(f - g)(4) = 2(4) - 3 - (4)³

(f - g)(4) = 8 - 3 - 64

(f - g)(4) = -59

Therefore, the domain of the composite function (f o g)(4) for f(x) = 4x - 3 and g(x) = x³ + 2x is equal to -59.

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Answer:

B.0.85

C.85/100

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3