Sasha is playing a game with two friends. Using the spinner pictured, one friend spun a one, and the other friend spun a four. Sasha needs to spin a number higher than both friends in order to win the game, and she wants to calculate her probability of winning. How many desired outcomes should Sasha use in her probability calculation

The limit lim f(x) as x approaches 2 does not exist, as the function approaches different values from the left and right sides of x=2.

The limit of a function at a particular point is the value that the function approaches as the input approaches that point. To find the limit lim f(x) as x approaches 2, we look at the behavior of the function as x gets closer and closer to 2.

From the graph of the function f, we can see that as x approaches 2 from the left side, the function approaches a value close to 1. However, as x approaches 2 from the right side, the function approaches a value close to 3. Since the function approaches different values from the left and right sides of x=2, the limit does not exist.

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The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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The age of Walter at the end of year 1999 will be equal to 55 years.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

Let's assume respective age of Walter and Walter's grandmother is x and y years respectively.

In 1994 , age of Walter was  :

x = y / 2

or y = 2x

It is also given that the sum of years they were born is 3838.

The year Walter was born = (1994 - x)

The year Walter's grandmother was born :

= (1994 - y)

= 1994 - 2x                                  (∵ y = 2x)

So , we can write an equation to find out Walter's age which is :

1994 - x + 1994 - 2x = 3838

3988 - 3x = 3838

3x = 3988 - 3838

x = 150 / 3

x = 50 years

or the age of Walter in 1994 is 50 years.

At end of 1999 Walter's age will be:

= 50 + 5.

= 55 years

Therefore , the age of Walter at the end of year 1999 will be equal to 55 years.

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The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)

=\(\sqrt{14400+10201-24240(0.34)}\)

=\(\sqrt{24601-8246}\)

\(\sqrt{16355}\)

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

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We know that an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.

For an experiment to be considered verifiable, several things should be done. Firstly, the experiment should be designed in a way that allows others to replicate it and obtain the same results. This means that all procedures, materials, and variables used should be clearly documented and made available to others.

Secondly, the experiment should be conducted in a controlled environment, where all external factors that could influence the results are minimized or eliminated.

Thirdly, the data obtained from the experiment should be analyzed and interpreted objectively, without any bias or preconceived notions. Finally, the results should be subjected to peer review and scrutiny by experts in the relevant field to ensure that they are valid and reliable.

By following these steps, an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.

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Let's simplify step-by-step.

9r+5−15

=9r+5+−15

Combine Like Terms:

=9r+5+−15

=(9r)+(5+−15)

=9r+−10

Answer:

=9r−10

Answer:

(19)(-8i)

Step-by-step explanation:

(2 - 6i)(8 + i)(9 - 3i)

(2 + 8 + 9)(-6i + i - 31)

(19)(-8i)

To help account for variability, the pollster used a simple random sample.

Sampling is the selection of a subset (a statistical sample) of people from within a statistical population in statistics, assurance, and survey procedures. the population's characteristics that were sampled. Obtaining samples that are typical of the population being researched is the objective of statisticians.

In situations where it is not practical to evaluate the complete population, sampling offers insights and is more cost-effective and time-efficient than doing so.

Each observation gives a number for one or more characteristics of certain things or people, including their size, location, color, or weight.

In survey sampling, especially in stratified sampling, ratings can be added to the results to take into consideration the sample design. The practice is guided by conclusions from statistical theory and probability theory.

Since 1000 people are randomly selected , hence we can say that the preference is simple random sample.

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Regression Equation y is 379.9996 ⋅1.04^x . Regression analysis is a set of statistical processes used in statistical modelling to estimate the relationships between a dependent variable and one or more independent variables.

Regression analysis is a set of statistical processes used in statistical modelling to estimate the relationships between a dependent variable and one or more independent variables.

Linear regression is the most common type of regression analysis, in which the line that best fits the data according to a specific mathematical criterion is found. The ordinary least squares method, for example, computes the unique line that minimises the sum of squared differences between the true data and that line.

This allows the researcher to estimate the conditional expectation of the dependent variable when the independent variables take on a given set of values for specific mathematical reasons. Less common types of regression employ slightly different procedures to estimate alternative location parameters or the conditional expectation across a larger set of non-linear models.

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Answer:

24 is correct answer

Step-by-step explanation:

its a 5:15 ratio, you are finding 8:x

8/5=1.6-> 1.6 x a5 = 24

Answer:

24 plates

Step-by-step explanation:

If she can wash 15 dishes in 5 minutes you just need to figure out how many dished she can washe in 1 minute. so you are gonna divide 15 by 5 and get 3 because 3 times 5 equals 15. so then that means she can wash 3 plates in 1 minute. so if she washed 15 in 5 in 6 minutes she can wash 18 and in 7 minutes she can wash 21 and in 8 minutes she can wash 24. Your just adding 3 to the 15 for every minute.

Answer:

228mm^2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

keep change flip

   3         -       -2

3 + 2

The possible error in this case is a Type I error, which occurs when we reject the null hypothesis when it is actually true, and conclude that the proportion is less than 0.12 when it is actually 0.12 or greater.

In hypothesis testing, a Type I error occurs when we reject the null hypothesis when it is actually true, while a Type II error occurs when we fail to reject the null hypothesis when it is actually false.

In this case, we rejected the null hypothesis that the proportion of Americans who support federal spending cuts to Medicaid is 0.12, in favor of the alternative hypothesis that the proportion is less than 0.12. The p-value was 0.026, which is less than the 5% level of significance.

Since we rejected the null hypothesis, there is a possibility of a Type I error. However, we cannot determine the probability of a Type II error without knowing the actual proportion of Americans who support federal spending cuts to Medicaid this year.

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Answer:

x = 149, cars and 51 motorcyles

Step-by-step explanation:

4x + 2(200-x) = 698

2x = 298 x = 149, cars and 51 motorcyles

Given:

The equation of the curve is:

\(y=x^{\frac{5}{2}}\)

To find:

The gradient of the given curve at the point where \(x = 4\).

Solution:

We have,

\(y=x^{\frac{5}{2}}\)

Differentiate with respect to x.

\(y'=\dfrac{5}{2}x^{\frac{5}{2}-1}\)       \([\because \dfrac{d}{dx}x^n=nx^{n-1}]\)

\(y'=\dfrac{5}{2}x^{\frac{3}{2}}\)

Substituting \(x=4\), we get

\(y'=\dfrac{5}{2}(4)^{\frac{3}{2}}\)

\(y'=\dfrac{5}{2}(2^2)^{\frac{3}{2}}\)

Using properties of exponents, we get

\(y'=\dfrac{5}{2}(2)^{2\times \frac{3}{2}}\)         \([\because (a^m)^n=a^{mn}]\)

\(y'=\dfrac{5}{2}(2)^{3}\)

\(y'=\dfrac{5}{2}(8)\)

\(y'=20\)

Therefore, the gradient of the given curve at the point where \(x = 4\) is 20.

The solution to the implicit

differentiation

of cos(xy) = 8 + sin(y) is dy/dx = -x(cos(xy))/(sin(y) + 8cos(xy)).

To find dy/dx by implicit differentiation, we start by differentiating both sides with respect to x. Using the chain rule, we get -sin(xy)(y + xy') = 0 + cos(y)y'. Solving for y', we get

dy/dx = -x(cos(xy))/(sin(y) + 8cos(xy)).

This is the solution to the problem.

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The exact values of the trigonometric functions of a vector are listed below:

sin θ = - 7√58 / 58

cos θ = - 3√58 / 58

tan θ = 7 / 3

cot θ = 3 / 7

sec θ = - √58 / 3

csc θ = - √58 / 7

In this problem we find the coordinates of the terminal end of a vector, whose trigonometric functions are now defined:

P(x, y) = (x, y)

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = y / √(x² + y²)

If we know that x = - 3 and y = - 7, then the exact values of the trigonometric functions are, respectively:

sin θ = - 7 / √[(- 3)² + (- 7)²]

sin θ = - 7 / √58

sin θ = - 7√58 / 58

cos θ = - 3√58 / 58

tan θ = 7 / 3

cot θ = 3 / 7

sec θ = - √58 / 3

csc θ = - √58 / 7

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By using standard deviation, it can be concluded that

The given estimate of standard deviation = 3 is not true

What is Standard Deviation?

At first, it is important to know about variance.

Variance is the sum of the square of deviation from mean divided by the total number of observations. Standard Deviation is the square root of variance.

Highest number = 40 and lowest number  = 22

Range = 40 - 22 =18

Standard deviation = \(18 \div 4\)

Standard deviation = 4.5

So the above statement is false

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Answer:

t = 36 minutes

Step-by-step explanation:

Given that,

Distance Andrea drive from home, d = 21 miles

The speed of Andrea, v = 35 mph

We need to find how many minutes will it take er to get to work. Let the time is t. We know that,

speed = distance/time

\(v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{21}{35}\\\\t=0.6\ h\)

or

t = 36 min

So, the required time is 36 minutes.  

The weight of Sugar Syrup is 42 grams

What is Weight?

The amount or quantity of bulk or heaviness; the weight of something. Physics. In an area of constant gravitational acceleration, mass is typically used as a measure of mass since the force of gravity acting on a body is equal to the body's mass times the local acceleration of gravity.

First calculate the mass

Adding * grams of water

= 5/5+x

= 0.12

⇒ 5 = 012x ( x + 5)

⇒ 5 = 012x + 0.6

= 4.4/0.12

= 37grams

Total mass of these two materials will be

= 5 + 37

= 42 grams

weight of Sugar Syrup will be

x = 5 / 0.12

= 42 grams

The weight of Sugar Syrup is 42 grams

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Answer:

25

Step-by-step explanation:

That is the answer, 25

Answer:

44

Step-by-step explanation:

1. substitute variables with their constants

(-9)(-3) - (-3)(8) - 7

2. multiply all like terms

(27) - (-24) - 7

3. Combine all like terms

27 + 24 - 7

51 - 7

= 44

Answer:

44

Step-by-step explanation:

Evaluate z x - x y - 7 where x = -3, y = 8 and z = -9:

z x - x y - 7 = -9 (-3) - -3×8 - 7

Hint: | Multiply -9 and -3 together.

-9 (-3) = 27:

27 - -3×8 - 7

Hint: | Multiply -1 and -3 together.

-(-3) = 3:

27 + 3×8 - 7

Hint: | Multiply 3 and 8 together.

3×8 = 24:

27 + 24 - 7

Hint: | Evaluate 27 + 24 using long addition.

| 1 |  

| 2 | 7

+ | 2 | 4

| 5 | 1:

51 - 7

Hint: | Subtract 7 from 51.

| 4 | 11

| 5 | 1

- | | 7

| 4 | 4:

Answer: 44

Answer:

Test-retest

Step-by-step explanation:

Based on the information given it is an example of TEST-RETEST.

TEST-RETEST is a relibility test that is been conducted on a group of people twice but on a different day or different time reason been that once the group of people write the test ,they will be ask to come back and retake the same test a week later in order to assess whether the test results they wrote earlier on and the new test results they newly rewrite a week later are the same or for the sole aim of assessing the reliability of the new test they rewrite and the old test they wrote earlier.

Example a group of students may write a test on Friday in which the same group of students will be ask to come back and rewrite the same test the following Friday which inturn makes the students to write the same test twice.

Therefore this is an example of which type of reliability TEST-RETEST.

Therefore, the maximum volume of the box is 112 cubic units, and the dimensions of the box that give us the maximum volume are: Length = 14 units, Width = 4 units ,Height = 2 units

To maximize the volume of the box, we need to find the dimensions that maximize the volume of the box. Let's assume that squares of side length x are cut out of each corner of the cardboard. Then, the dimensions of the box can be expressed as:

Length = 18 - 2x

Width = 8 - 2x

Height = x

The volume of the box is given by the product of these dimensions:

\(V(x) = (18 - 2x)(8 - 2x)(x)\)

Expanding this equation, we get:

\(V(x) = 4x^3 - 52x^2 + 144x\)

To find the maximum volume, we need to take the derivative of V(x) and set it equal to zero:

\(V'(x) = 12x^2 - 104x + 144 = 0\)

Solving this quadratic equation, we get:

x = 2 or x = 6

We need to check both solutions to see which one gives us the maximum volume.

When x = 2, the dimensions of the box are:

Length = 18 - 2(2) = 14

Width = 8 - 2(2) = 4

Height = 2

The volume of the box is:

V(2) = (14)(4)(2) = 112

When x = 6, the dimensions of the box are:

Length = 18 - 2(6) = 6

Width = 8 - 2(6) = -4 (negative, so this solution is not possible)

Height = 6

Therefore, the maximum volume of the box is 112 cubic units, and the dimensions of the box that give us the maximum volume are:

Length = 14 units

Width = 4 units

Height = 2 units.

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To find the absolute value of an equation, you set up two separate equations representing the positive and negative cases, solve each equation, and check the solutions by substituting them back into the original equation.

Finding the absolute value of an equation involves determining the magnitude or distance of a number or expression from zero on the number line. The absolute value function is denoted by the symbol "|" surrounding the number or expression. The absolute value function always returns a positive value or zero, regardless of the sign of the number or expression inside it. Here's how you can find the absolute value of an equation:

Identify the number or expression inside the absolute value notation.

For example, consider the equation |x - 5| = 3.

Set up two separate equations.

The first equation represents the positive case:

x - 5 = 3

The second equation represents the negative case:

-(x - 5) = 3

Solve each equation separately.

Solve the first equation:

x - 5 = 3

x = 3 + 5

x = 8

Solve the second equation:

-(x - 5) = 3

-x + 5 = 3

-x = 3 - 5

-x = -2

x = 2 (multiply both sides by -1 to remove the negative sign)

Check the solutions.

Substitute the found values of x back into the original equation to ensure they satisfy the absolute value condition.

For |x - 5| = 3:

When x = 8: |8 - 5| = 3 (True)

When x = 2: |2 - 5| = |-3| = 3 (True)

State the solutions.

The solutions to the equation |x - 5| = 3 are x = 8 and x = 2.

In summary, to find the absolute value of an equation, you set up two separate equations representing the positive and negative cases, solve each equation, and check the solutions by substituting them back into the original equation.

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The ordered triplet (x, y, z) or the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7 is (-170/127, -89/127, 282/127).

Start with the first equation:

x + 3y + 2z = 1

Isolate x by subtracting 3y and 2z from both sides:

x = 1 - 3y - 2z

Substitute this expression of x into the second equation:

0.3x + y + 5z = 10

Substitute the value of x found in step 2 into this equation:

0.3(1 - 3y - 2z) + y + 5z = 10

0.3 -0.9y -0.6z + y + 5z = 10

0.1y + 4.4z = 9.7

y + 44z = 97

Solve for y by isolating it:

y = 97 - 44z

Substitute this expression of y into the first equation:

x + 3(97 - 44z) + 2z = 1

x + 291 - 132z + 2z = 1

Solve for x:

x = 130z - 290

Substitute this expression of x into the third equation:

-2(130z - 290) - 3(97 - 44z) + z = 7

-260z + 580 - 291 + 132z + z = 7

Solve for z:

127z = 282

z = 282/127

Substitute this value of z into the expression of y:

y = 97 - 44(282/127)

= -89/ 127

Substitute the values of z into the expression of x:

x = 130(282/127) - 290

= - 170/ 127

So the solution of the system of equations is: x = -170/127, y = -89/127, z = 282/127.

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Answer:

Its an institution

Step-by-step explanation:

A college is not a region, state or country. It is an institution.

After 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.

To find the concentration of sugar in the tank after 12 minutes, we need to consider the amount of sugar and water added during that time period.

The tank initially contains 100 gallons of water with 5 pounds of sugar mixed in. Over the course of 12 minutes, the tap pours in 10 gallons per minute of water and 1 pound per minute of sugar.

After 12 minutes, the total amount of water added is 10 gallons/minute * 12 minutes = 120 gallons. The total amount of sugar added is 1 pound/minute * 12 minutes = 12 pounds.

Therefore, the final volume of water in the tank is 100 gallons (initial) + 120 gallons (added) = 220 gallons.

To find the concentration of sugar in the tank after 12 minutes, we divide the total amount of sugar (5 pounds initial + 12 pounds added) by the final volume of water (220 gallons):

Concentration of sugar = (Total amount of sugar) / (Final volume of water)

= (5 pounds + 12 pounds) / 220 gallons

= 17 pounds / 220 gallons

Simplifying the expression, we get:

Concentration of sugar = 0.0773 pounds/gallon

Therefore, after 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.

It's important to note that in this scenario, we assume perfect mixing of the sugar and water in the tank. Also, the concentration of sugar may vary over time as more water and sugar are added.

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