Sofia is designing a new board game, and is trying to figure out all the possible

outcomes. How many different possible outcomes are there if she spins a spinner

with three equal-sized sections labeled Walk, Run, Stop, flips a coin, and spins a

spinner with four equal-sized sections labeled Red, Green, Blue, Orange?

Answer:

I would just rewrite it as -6r^2 + 6r

The actual value, absolute error and relative error of the Taylor series approximation to g(0.15) is approximately 1.1402, 0.0291 and  0.0255 respectively. The actual value and absolute error of the Taylor series approximation to g(0.1) is approximately 1.0488 and 0.0010 respectively.

To find the Taylor series approximation of degree 4 for g(x) = sqrt(x+1) about c = 0.25, we first need to compute its derivatives up to the fourth order:

g(x) = sqrt(x+1)

g'(x) = 1/2(x+1)^(-1/2)

g''(x) = -1/4(x+1)^(-3/2)

g'''(x) = 3/8(x+1)^(-5/2)

g''''(x) = -15/16(x+1)^(-7/2)

Then we can write the Taylor series approximation of degree 4 for g(x) about c = 0.25 as:

g(x) ≈ g(0.25) + g'(0.25)(x-0.25) + g''(0.25)(x-0.25)^2/2 + g'''(0.25)(x-0.25)^3/6 + g''''(0.25)(x-0.25)^4/24

Plugging in the derivatives and simplifying, we get:

g(x) ≈ 1.1180 + (-0.5904)(x-0.25) + (0.4920)(x-0.25)^2 - (0.4099)(x-0.25)^3 + (0.3408)(x-0.25)^4

Now we can use this approximation to estimate g(0.15) and g(0.1) and compare with the actual values.

For g(0.15):

Using the Taylor series approximation with x=0.15 and c=0.25, we get:

g(0.15) ≈ 1.1180 + (-0.5904)(0.15-0.25) + (0.4920)(0.15-0.25)^2 - (0.4099)(0.15-0.25)^3 + (0.3408)(0.15-0.25)^4

g(0.15) ≈ 1.1111

The actual value of g(0.15) is:

g(0.15) = sqrt(0.15+1) ≈ 1.1402

The absolute error of the approximation is:

absolute error = |1.1111 - 1.1402| ≈ 0.0291

Therefore, the absolute error of the approximation to g(0.15) is approximately 1.1402.

The relative error of the approximation is:

relative error = |(1.1111 - 1.1402)/1.1402| ≈ 0.0255

Therefore, the relative error of the approximation to g(0.15) is approximately 0.0255.

For g(0.1):

Using the Taylor series approximation with x=0.1 and c=0, we get:

g(0.1) ≈ 1 + (1/4)(0.1) - (1/32)(0.1)^2 + (3/256)(0.1)^3 - (5/1024)(0.1)^4

g(0.1) ≈ 1.0498

The actual value of g(0.1) is:

g(0.1) = sqrt(0.1+1) ≈ 1.0488

The absolute error of the approximation is:

absolute error = |1.0498 - 1.0488| ≈ 0.0010

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____The given question is incorrect, the correct question is given below:

Taylor Series Approximation Use a Taylor approximation of degree 4 about point c = 0.25 to approximate g(x) = sqrt(x+1). What is the absolute error of the approximation to g(0.15)? absolute error = ______{ number (3 significant figures)} What is the relative error of the approximation to g(0.15)? relative error = _____ { number (3 significant figures)} What is the absolute error of the approximation to g(0.1) if the Taylor approximation is instead centered at c = 0? absolute error = number (3 significant figures).

Answer: 4

Step-by-step explanation:

36,48,80

80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

The solution to the given exponential equation is; x = 6.48

We want to solve the exponential equation;

4^(x) = 7 - (3^x)

We can use logarithm or inverse of logarithm to solve this but in this case we will use the logarithm to get;

x log 4 = 7 - (x log 3)

x log 4 + x log 3 = 7

x(log 4 + log 3) = 7

1.08x = 7

x = 7/1.08

x = 6.48

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Answer:

The six is bigger

Step-by-step explanation:

They both are inside the absolute value sign, meaning, the the numbers are negative, they will turn positive and if they are positive, then they will remain positive. So, in this case 4 and 6 are both positive and remain positive. And obviously 6 is greater than 4 because 6 comes after 4 in a number line.  

Answer:

18. 3/4*2/1 = 6/4 = 1 2/4

(2/1 is the same thing as 2)

1 2/4 in simplest form = 1 1/2

20. 3/5*5/7 = 15/35

15/35 in simplest form = 3/7

Step-by-step explanation:

When you multiply fractions, you simply multiply across. For example, 3/4*2/1. You would multiply the numerator which is 3*2 which is 6. Then you would multiply the denominator which is 4. Your final answer is 6/4 which is 1 2/4 as a mixed fraction and can be simplified to 1 1/2. Another example is 3/5*5/7. You would multiply the numerator which is 3*5 which is 15. Then you would multiply the denominator which is 5*7 which is 35. Your final answer is 15/35 which can be simplified down to 3/7 because when you divide 15 and 35 both by 5, you get those numbers and you can't simplify it anymore. Hope this helps!

Could you write the question more properly?

verifying, by putting \( \theta=60^{\circ}\)

LHS≠RHS

hence the question is FALSE

The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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Answer:

Right Triangle and isosceles

Step-by-step explanation:

It is a right triangle given the 90° angle, but it is isosceles because only 2 of the sides are of equal length.

The business executive used a total of 375 minutes on the phone.

The cellular phone service for a business executive is $35 per month plus $0.40 per minute for usage over 900 minutes. This means that there are fixed costs and variable costs associated with the service.

Let's calculate the variable cost, which is the cost for minutes used over 900. The total cost for the cellular phone service is $105, and the fixed cost is $35. So, the variable cost can be found by subtracting the fixed cost from the total cost:

Variable cost = $105 - $35 = $70

Since the variable cost is charged at a rate of $0.40 per minute for usage over 900 minutes, we can set up the equation:

Variable cost = $0.40(x), where x is the number of minutes used over 900.

To find the total number of minutes used by the executive, we need to add the number of minutes for which the variable charge applies to 900. Substituting the value of V from the equation above:

x = V / $0.40 = 175

The total minutes used can be calculated by adding the minutes for which the variable charge applies to 900:

Total minutes = 900 + x = 900 + 175 = 1075

Since the variable cost is only charged for the minutes used over 900, we can conclude that the executive used 175 minutes at the variable rate and the total minutes used was 1075.

Thus, the business executive used a total of 375 minutes on the phone.

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Answer:

123

Step-by-step explanation:

Answer:

temperature of 5° C above 0° C

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

Answer:

Bring like terms together Bring like terms together. All equations have two sides.

The number of pennies they lose altogether is 288 pennies.

How to find the number of pennies they lost together?

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they lose can be calculated as follows;

Katya losses = 1 / 2 × 192 = 96

Mimi losses = 2 / 3 × 288  = 192

Therefore, they lost 96 + 192 = 288 pennies altogether.

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The number of total parts in the ratio, given the ratio the line is divided into is a total of 7 parts .

When a line is divided in the ratio 3 : 4 , it means that the line is divided into 3 parts and 4 parts. The total number of parts is 3 + 4 = 7.

For example, if a line segment is 7 units long, then the part that is in the ratio of 3 : 4 would be 3 / 7 of the line segment and the other part would be 4 / 7 of the line segment.

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Full question is:

A line is divided in the ratio 3/4. How many total parts in the ratio?

Answer:

x=6

Explanation:

Given the equation:

First, cross multiply:

Next, open the brackets:

Subtract 3x from both sides of the equation:

Add 6 to both sides of the equation:

Finally, divide both sides by 5:

The value of x is 6.

Answer:

EF=35

EG=22

Step-by-step explanation:

EF

7y-14=2y+21

5y=35

y=7

EF=7(7)-14=49-14=35

EG

15x+7=12x+10

3x=3

x=1

EG=15(1)+7=15+7=22

Answer:

(a). 35 units ; (b). 44 units

Step-by-step explanation:

(a). 7y - 14 = 2y + 21 ⇒ y = 7

EF = 7(7) - 14 = 35 units

(b). EJ = JG

15x + 7 = 12x + 10 ⇒ x = 1

EG = 2 × (15(1) + 7) = 44 units

Answer:

20/27

Step-by-step explanation:

Answer:

2 minutes left

Step-by-step explanation:

They have 2 minutes left because after calculating all the math they have used 18 minutes in total. I found this out because the problem wants you to mutiply 26 and 15. The add that to the product of 15 and 30. once that is added it is 840 seconds. But when you add 60 (representing 1 of the 4 minutes) four times you will get an answer of 1080 seconds which equals 18 minutes. Then because they need 20 minutes you would do 20-18 which equals 2 minutes left.

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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(a) The simplest interest is $12.

(b) The simplest interest is 5 cents.

(c) The simplest interest is $360.

(d) The simplest interest is $15.

What is the interest rate?

In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate. The total interest on a sum lent or borrowed is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time over which it is lent deposited, or borrowed.

The formula of simple interest is I = P × R × T

(a) Given that P = $500, R = 8% = 0.08, T = 3 months = (3/12) years = 1/4 years

The simple interest is

500 × 0.08 × (1/4)

= $12

(b) Given that P = $50, R = 12% = 0.12, T = 1 months = (1/12) years

The simple interest is

50 × 0.12 × (1/12)

=$0.5

= 5 cents

(c) Given that P = $1,000, R = 18% = 0.18, T = 24 months = (24/12) years = 2 years

The simple interest is

1000 × 0.18 × 2

=$360

(d) Given that P = $600, R = 15% = 0.15, T = 60 days = (60/360) years

The simple interest is

600 × 0.15 × (60/360)

=$15

P is principal, R is known as rate of interest.

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4) The cosine of 75° has an exact value of \(\frac{\sqrt{6}-\sqrt{2}}{4}\).

5) The tangent of \(-\frac{\pi}{12}\) radians has an exact value of \(-\frac{\sqrt{3}}{3-\sqrt{3}}\).

6) The proposition is true.

We can determine this cosine by means of the following trigonometric formula:

\(\cos (\alpha + \beta) = \cos \alpha \cdot \cos \beta - \sin \alpha \cdot \sin \beta\) (1)

Where \(\alpha\), \(\beta\) are angles expressed in degrees.

If we know that \(\alpha = 45^{\circ}\), \(\beta = 30^{\circ}\), then we have that the cosine of 75° is:

\(\cos 75^{\circ} = \cos 45^{\circ}\cdot \cos 30^{\circ} - \sin 45^{\circ}\cdot \sin 30^{\circ}\)

\(\cos 75^{\circ} = \left(\frac{\sqrt{2}}{2}\right)\cdot \left(\frac{\sqrt{3}}{2} \right) - \left(\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{1}{2} \right)\)

\(\cos 75^{\crc} = \frac{\sqrt{6}}{4} -\frac{\sqrt{2}}{4}\)

\(\cos 75^{\circ} = \frac{\sqrt{6}-\sqrt{2}}{4}\)

The cosine of 75° has an exact value of \(\frac{\sqrt{6}-\sqrt{2}}{4}\). \(\blacksquare\)

We can determine this tangent by means of the following trigonometric formulas:

\(\tan (\alpha - \beta) = \frac{\tan \alpha \cdot \tan \beta}{1+\tan \alpha \cdot \tan \beta}\) (2)

\(\tan (-\alpha) = -\tan \alpha\) (3)

Where \(\alpha\), \(\beta\) are angles measured in radians.

If we know that \(\alpha = -\frac{\pi}{4}\) and \(\beta = \frac{\pi}{6}\), then the tangent of \(-\frac{\pi}{12}\) radians is:

\(\tan\left(-\frac{\pi}{12} \right) = \frac{\tan \left(-\frac{\pi}{4} \right)\cdot \tan \left(\frac{\pi}{6} \right)}{1+\tan \left(-\frac{\pi}{4} \right)\cdot \tan \left(\frac{\pi}{6}\right)}\)

\(\tan \left(-\frac{\pi}{12} \right) = \frac{(-1)\cdot \left(\frac{\sqrt{3}}{3} \right)}{1 + (-1)\cdot \left(\frac{\sqrt{3}}{3} \right)}\)

\(\tan \left(-\frac{\pi}{12} \right) = -\frac{\sqrt{3}}{3-\sqrt{3}}\)

The tangent of \(-\frac{\pi}{12}\) radians has an exact value of \(-\frac{\sqrt{3}}{3-\sqrt{3}}\). \(\blacksquare\)

In this part we are going to simplify by algebraic and trigonometric means an expression, whose procedure is shown below:

The proposition is true. \(\blacksquare\)

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Sorry about that.

(21 - 17)² + 3⁴ =

4² + 81 =

16 + 81 =

Answer: 97

Answer:

97

Step-by-step explanation:

(21-17)²+3⁴=4²+81

=16+81

=97

Answer:THe answer is 98.78x

Step-by-step explanation:

2r34 means 567

(5) The area of trapezium is 833.85 m².

(6) The area of the square is 309.76 mm².

(7) The area of the parallelogram is 148.2 yd².

(8) The area of the semicircle is 760.26 in².

(9) The area of the rectangle is 193.52 ft².

(10) The area of the right triangle is 183.74 in².

(11) The area of the isosceles triangle is 351.52 cm².

The area of the figures is calculated as follows;

area of trapezium is calculated as follows;

A = ¹/₂ (38 + 13) x 32.7

A = 833.85 m²

area of the square is calculated as follows;

A = 17.6 mm x 17.6 mm

A = 309.76 mm²

area of the parallelogram is calculated as follows;

A = 19 yd  x 7.8 yd

A = 148.2 yd²

area of the semicircle is calculated as follows;

A = ¹/₂ (πr²)

A =  ¹/₂ (π x 22²)

A = 760.26 in²

area of the rectangle is calculated as follows;

A = 16.4 ft x 11.8 ft

A = 193.52 ft²

area of the right triangle is calculated as follows;

based of the triangle = √ (29.1² - 14.6²) = 25.17 in

A = ¹/₂ x 25.17 x 14.6

A = 183.74 in²

area of the isosceles triangle is calculated as follows;

height of the triangle =  √ (30² - (26/2)²) = √ (30² - 13²) = 27.04 cm

A =  ¹/₂ x 26 x 27.04

A = 351.52 cm²

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Answer:

e t

Step-by-step explanation:

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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Answer:

B

Step-by-step explanation:

I think this is right

Answer:

C

Step-by-step explanation: