Rosita is writing an explicit function for the geometric sequence:
80, 40, 20, 10, \dots80,40,20,10,…80, comma, 40, comma, 20, comma, 10, comma, dots
she comes up with t(n)=160\left( \dfrac12 \right)^nt(n)=160(
2
1
​
)
n
t, left parenthesis, n, right parenthesis, equals, 160, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript.
what domain should rosita use for ttt so it generates the sequence?

Answer: C. 10

Step-by-step explanation:

Ms. Lewis is driving 50mph and is driving a distance of 900 miles. 900/50 is 18, making her total drive 18 hours long. She wants to bring her total driving time down by 3 hours, making it 15 hours. To solve this, divide 900 by 15 (900/15), and you'll get 60. Finally, subtract 60 and 50 (60 - 50), and your answer is 10. Hope this helps.

She should drive 10 miles faster to to reduce her total driving time by 3 hours.

Speed is defined as the distance covered per unit time taken.

Given is that Ms. Lewis plans to drive 900 miles to her vacation destination, driving an average of 50 miles per hour.

Initial time taken to cover the distance -

t{i} = 900/50 = 18 hr

For time taken to be (18 - 3)hrs or 15 hrs, we can write the speed as -

s{f} = 900/15

s{f} = 60 mph

Therefore, She should drive 10 miles faster to to reduce her total driving time by 3 hours.

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Step-by-step explanation:

there are 91 2-digit numbers : 10 ..99

and there are 9 2-digit numbers with identical first and second digit : 11, 22, 33, 44, 55, 66, 77, 88, 99

99 has to be excluded, because there are no 2 2- digit numbers that I can subtract from each other and get 99.

so, e are dealing with 8 possibilities.

88 = 99-11

98-10

77 = 99-22

98-21

97-20

...

78-1

66 = 99-33

98-32

...

67-1

...

11 = 99-88

98-87

...

12-1

all the double- digit numbers are 11 apart. so, by picking 12 numbers, I have to have at least one that I can combine with one of the other 11 to get a double-digit number.

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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Solution :

Given that :

The radius of circle A = 6 cm

The radius of circle C = 4 cm

In circle A

\(\angle EAF = \theta = 140^\circ\)

The length of arc EF = \($2 \pi r \times \frac{\theta}{360^\circ}$\)

                                   \($=2 \times 3.14 \times 6 \times \frac{140^\circ}{360^\circ}$\)

                                    = 14.653 cm

In circle C

\(\angle GCH = \theta = 140^\circ\)

The length of arc GH = \($2 \pi r \times \frac{\theta}{360^\circ}$\)

                                   \($=2 \times 3.14 \times 4 \times \frac{140^\circ}{360^\circ}$\)

                                    = 9.769 cm    

Therefore,

The length of EF is 14.653 cm

The length of GH is 9.769 cm

The length of EF is  1.5 times the length of GH

i.e.                   14.653  = 1.5 x 9.769

                       14.653 = 14.653

Hence proved.

The app costs $11.6, so Jade and Chet will need that much cash.

How to solve equation?

Jade = 8 + 2x

Chet = 4x + 6

Where,

x = $2.50

Amount each earned:

Jade = 8 + 2x

= 8 + 2(2.50)

= 8 + 5

= $13

Chet = 4x + 6

= 4(2.50) + 6

= 10 + 6

= $16

Combined earnings = $13 + $16

= $29

Amount planned to save = 40% of combined earnings

= 40% × $29

= 0.4 × 29

= $11.6

Jade and Chet will therefore need to spend $11.6 to buy the software.

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Answer: Hi there! X = 7 would be your answer

Step-by-step explanation:

Simplify both sides of the equation.

2(3x − 6) = 3(x + 3)

(2) (3x) + (2) (−6)= (3) (x) + (3) (3)

6x + −12 = 3x + 9

6x − 12 = 3x + 9

Subtract 3x from both sides.

6x − 12−3x = 3x + 9−3x

3x − 12 = 9

Add 12 to both sides.

3x − 12+12 = 9+12

3x=21

Divide both sides by 3.

3x/3=21/3

x=7

I hope this helps!!

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hope it helps!:)

Multiply total serves by percentage:

120 x 0.45 = 54

Answer: 54

Answer:

54 Im sure of it. I revised this question by wacthing a video.

Step-by-step explanation:

The data item corresponding to a given z-score, we need the mean and standard deviation of the Distribution. Without this information, it is not possible to determine the specific data item.

To find the data item in a distribution that corresponds to a given z-score, we need to know the mean and standard deviation of the distribution. The formula to convert a z-score to a data value is:

data value = (z-score * standard deviation) + mean

Using this formula, we can find the data item corresponding to the given z-score.

It's important to note that without the mean and standard deviation of the distribution, it is not possible to determine the specific data item corresponding to the z-score.

The z-score represents the number of standard deviations a particular data point is from the mean. A positive z-score indicates a data point above the mean, while a negative z-score indicates a data point below the mean.

To find the specific data item, we would substitute the z-score, mean, and standard deviation into the formula and calculate the corresponding data value. However, since the z-score and the necessary information about the distribution are not provided in your question, it is not possible to provide a specific data item.

In summary, to find the data item corresponding to a given z-score, we need the mean and standard deviation of the distribution. Without this information, it is not possible to determine the specific data item.

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Answer: 5^6

Step-by-step explanation:

First, you have to simplify the numbers so that all of them share the same base. For this problem, the base for all of these numbers would be 5. So now the equation looks like this:

5^2 * 5^1 * 5^3

Next we have to turn all of these numbers into one. Whenever you multiply the numbers, all you have to do is add the exponents together. So now it will look like this:

5^(2+1+3)

Add the numbers up and you get your answer.

5^6

Answer: ≈40.2

Step-by-step explanation:

(2x-1)*(x+1)=90

Distribute

2x^2-1=90

Add 1 to both sides.

2x^2=91

Divide both sides by 2

x^2=45.5

Square both sides.

x≈6.7

Check work by plugging x into both original sides and multiplying them.

(2(6.7)-1)*((6.7)+1)=90

12.4*7.7=95.48

Side lengths are approximately 12.4 and 7.7.

12.4*2=24.8

7.7*2=15.4

24.8+15.4=40.2

Answer:

sorry for being late but it was hard, x=6.5

then perimeter is 39

Step-by-step explanation:

12+12+7.5+7.5=39

Answer:

A: [|8.40−8.96|/8.96]⋅100,

B. 6.25%

Step-by-step explanation:

A.

% error =[ | calculate density - accepted density|/ accepted density]*100%

A: [|8.40−8.96|/8.96]⋅100

B.  |8.40−8.96|/8.96⋅100 = 6.25%

The equivalent expression is 31/8

A fraction is simply defined as the portion representing the part of a whole number, a whole element or a whole variable.

In mathematics, there are different types of fractions, These includes;

From the information given, we have that the expression is written as;

3 1/4 - (-5/8)

expand the bracket, we get;

3 1/4 + 5/8

convert the improper fraction

13/4 + 5/8

Find the LCM

26 + 5/8

31/8

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Among the options given in the question, the following are the properties of the linear correlation coefficient:

The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

If r=−​1, then a perfect negative linear relation exists between the two variables.

Properties of linear correlation coefficient:

Linear correlation coefficient is a value calculated from given data and used to measure the strength of linear relationship between two variables, for instant between x and y variables.

The sign of this coefficient (r) indicates the direction linear relationship will take between x and y. Below are some properties of the linear correlation coefficient:

Now, the properties of the linear correlation coefficient among the given ones in the question are:

b. The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

f. If r=−​1, then a perfect negative linear relation exists between the two variables.

Hence, options b, d and f are correct.

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The missing terms in the sentence are "Inclination" and "Vertical."

Inclination is the angle of tilt below the imaginary horizontal plane oriented 90-degrees to the vertical direction. It refers to the angle at which an object or surface deviates from being perfectly horizontal or flat. It measures the slope or tilt of the object or surface in relation to the vertical direction.

The vertical direction is the imaginary line or axis that points directly up or down, perpendicular to the horizontal plane. It is oriented at a 90-degree angle to the horizontal direction, which is typically considered the direction parallel to the ground or any other reference plane.

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The type of data for the water consumption (liters) by a randomly chosen player on the Celtics roster during a home game would be quantitative continuous data.

This is because the variable, water consumption, is a numerical measurement that can take on any value within a specific range (e.g., 0.5 liters, 1.2 liters, 2.7 liters, etc.), and it can be measured with a high level of precision. The data is continuous because there are no restrictions on the possible values, and it can take on any value within a given range.

what is range?

In statistics, the range refers to the difference between the maximum and minimum values in a dataset. It provides a measure of the spread or variability of the data.

To calculate the range, you simply subtract the minimum value from the maximum value:

Range = Maximum value - Minimum value

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The "transient-solution" for X'' + 8X' + 12X = 15,  X(O) = 2, X'(0) = 2 is X(t) = (-7/8) × \(e^{-6t}\) + (13/8) × \(e^{-2t}\) + 5/4.

In order to find the transient solution of given second-order system, we solve the homogeneous equation associated with it and then find the particular solution for non-homogeneous term.

The homogeneous equation is obtained by setting the right-hand side (RHS) of the equation to zero:

X'' + 8X' + 12X = 0

The characteristic-equation is obtained by assuming a solution of the form X(t) = \(e^{rt}\):

r² + 8r + 12 = 0

(r + 2)(r + 6) = 0

So, the two roots are : r = -2 and r = -6,

The general solution of homogeneous equation is given by:

\(X_{h(t)}\) = C₁ × \(e^{-6t}\) + C₂ × \(e^{-2t}\)

Now, we find the particular-solution for the non-homogeneous term, which is 15. Since 15 is a constant, we assume a constant solution for \(X_{p(t)\):

\(X_{p(t)\) = k

Substituting this into original equation,

We get,

0 + 8 × 0 + 12 × k = 15,

12k = 15

k = 15/12 = 5/4

So, particular solution is \(X_{p(t)\) = 5/4.

The "transient-solution" is sum of homogeneous and particular solutions:

X(t) = \(X_{h(t)\) + \(X_{p(t)\)

X(t) = C₁ × \(e^{-6t}\) + C₂ × \(e^{-2t}\) + 5/4, and

X'(t) = -6C₁ × \(e^{-6t}\) -2C₂ × \(e^{-2t}\) ,

To find the values of C₁ and C₂, we use initial-conditions: X(0) = 2 and X'(0) = 2.

X(0) = C₁ × \(e^{-6\times 0}\) + C₂ × \(e^{-2\times 0}\) + 5/4,
X(0) = C₁ + C₂ + 5/4,

Since X(0) = 2, We have:

C₁ + C₂ + 5/4 = 2      ...Equation(1)

and Since X'(0) = 2, we have:

3C₁ + C₂ = -1     ....Equation(2)

On Solving equation(1) and equation(2),

We get,

C₁ = -7/8  and C₂ = 13/8,

Substituting the values, the transient-solution can be written as :

X(t) = (-7/8) × \(e^{-6t}\) + (13/8) × \(e^{-2t}\) + 5/4.

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The given question is incomplete, the complete question is

For the following second-order system and initial conditions, find the transient solution: X'' + 8X' + 12X = 15,  X(O) = 2, X'(0) = 2.

The height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches. This can be obtained by using the ratio of scale drawing to the real drawing.

Here in the question it is given that,

Thus we can say that, scale of the painting is 2 cm : 7 in

Ratio of scale drawing and real painting is 2 : 7

⇒ Similarly here height of the painting in the scale drawing to the height of the painting in the real drawing will be in the ratio 2 : 7.

We can say that,

2 cm/7 in = x cm/35 in

where x is the height of the painting in the scale drawing

2 cm × 35 in /7 in = x cm

x = 2 × 5 cm

x = 10 cm

Hence the height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches.

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Answer:

8

Step-by-step explanation:

100-3t=76

-3t=-24

t=8

Answer:

t=8

Step-by-step explanation:

100 - 3t = 76

-100        -100

-3t = -24

/-3    /-3

t = 8

Hope this helps!

Answer:

I hope it is correct ✌️

Based on the calculation we know that

The value of x as 7− is 35.

The value of x as 7+ is 35.

Suppose that f( x ) = 7 x − 7. We can complete the following statements by plugging in the values of x and evaluating the function.

As x → 7 − , f ( x ) → 42 − 7 = 35
As x approaches 7 from the left, the function f(x) approaches 35.

As x → 7 + , f ( x ) → 42 − 7 = 35
As x approaches 7 from the right, the function f(x) also approaches 35.

Therefore, the function f(x) = 7x - 7 has a horizontal asymptote at y = 35 as x approaches 7 from both the left and the right.

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Answer:

7920/7

Step-by-step explanation:

( 7 x 40) x 4 = 1120 hours/ 28 days

2 days = 2 x 40/7, because 1 day = 40 hours / 7 days

total: 1120 + 80/7  = 7920/ 7 ≈1131,43 hours

The first term of a sequence along with a recursion formula for the remaining terms is given below: a1 = 1, an+1 = nan/n+3.

We need to write out the first ten terms of the sequence.

Here is the solution;

First term, a1 = 1

Second term, a2 = a1+1 = (a1*n)/(n+3) = (1*n)/(n+3) = n/(n+3)

Third term, a3 = a2+1 = (a2*n)/(n+3) = (n/(n+3)*n)/(n+3) = n²/((n+3)²)

Fourth term, a4 = a3+1 = (a3*n)/(n+3) = (n²/((n+3)²)*n)/(n+3) = n³/((n+3)³)

Similarly, we continue to get the next term as a5 = (n^4)/((n+3)^4)a6 = (n^5)/((n+3)^5)a7 = (n^6)/((n+3)^6)a8 = (n^7)/((n+3)^7)a9 = (n^8)/((n+3)^8)a10 = (n^9)/((n+3)^9)

Thus, the first ten terms of the sequence are: a1 = 1a2 = n/(n+3)a3 = n²/((n+3)²)a4 = n³/((n+3)³)a5 = (n^4)/((n+3)^4)a6 = (n^5)/((n+3)^5)a7 = (n^6)/((n+3)^6)a8 = (n^7)/((n+3)^7)a9 = (n^8)/((n+3)^8)a10 = (n^9)/((n+3)^9)

A recursion formula, also known as a recursive formula or recurrence relation, is a mathematical equation or definition that expresses the terms of a sequence or function in terms of previous terms. It is a way to define a sequence or function recursively, where each term depends on one or more previous terms.

Recursion formulas can also be used to define functions recursively. In this case, the recursion formula expresses the value of the function at a given point in terms of its values at previous points.

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Answer:

rate of change: -3000 feet per minute

the rate of change is showing how many feet the plane descents each minute

The mean of the data set of the people at a birthday party would be 11. The mean absolute deviation would be 5.25

The mean absolute deviation might not be good to use for variation here because there is an outlier of 32.

To find the mean and the mean absolute deviation (MAD) for this data set, we first need to find the mean age.

Mean = (Sum of ages) / (Number of people)

Mean = (7 + 7 + 7 + 8 + 8 + 9 + 10 + 32) / 8

Mean = 88 / 8 = 11

The MAD is the average of the absolute differences between each data point and the mean.

Find the sum of the absolute differences:

4 + 4 + 4 + 3 + 3 + 2 + 1 + 21 = 42

Divide the sum of the absolute differences by the number of data points (8) to get the MAD:

MAD = 42 / 8 = 5.25

The MAD might not be a good measure of the variation in this data set because there is an outlier (32) in the data. The presence of an outlier can significantly impact the MAD, making it seem like there is more variation in the data than there actually is.

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Using the Binomial probability distribution,

The probability that exactly two customers in the sample will default on their payments is 0.31..

We have given that,

4% of total customers a mortgage company default on their payments .

The probability of success i.e number of customers default on their payments (p) = 4%

= 0.04

The probability of failure (q) = 1-p = 1-0.04 = 0.06

Total number of customers in sample (n) = 20

we have to find out the probability that exactly two customers in the sample will default on their payments.

Using the Binomial probability distribution,

P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

the required probability is P(X= 2 )

Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸

=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31

Hence, the required probability is 0.31

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Answer:

NO

Step-by-step explanation:

\(4x^{2} -4x+1=0\\(2x-1)(2x-1)=0\\x=1/2\)

E. 7(1 + 2x) + 10x – 1

Answer:

A, C, D

Step-by-step explanation:

A: 3×2=6

3×4x=12x

C: 5×1=5+1=6

5×2x=10x+2x=12x

D: 7×1=7-1=6

7×2x=14x-2x=12x

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

Given that the sum of the digits is seventeen, we have the equation:

x + y = 17 (equation 1)

The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.

According to the given information, we have the equation:

10y + x = 5x + 30 (equation 2)

To solve the system of equations, we can substitute equation 1 into equation 2:

10(17 - x) + x = 5x + 30

Expanding and simplifying:

170 - 10x + x = 5x + 30

170 - 30 = 5x + 10x - x

140 = 14x

x = 10

Substituting the value of x back into equation 1:

10 + y = 17

y = 7

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

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Answer:

See below

Step-by-step explanation:

20 % is .20 in decimal

   .20 * 25 is tip amount

25 + .20 (25) = $ total