Which expression is equivalent to to the equivalent -1/2(-3/2x+6x+1)-3x

Final answer:

Bernie and Chloe hiked a total of 9 3/8 miles after completing the round trip on Tremont Trail and the Wildflower Trail.

Explanation:

Bernie and Chloe hiked the Tremont Trail which was 3 1/2 miles to the end and back, meaning they hiked 7 miles on this trail (since they had to return). After that, they hiked the Wildflower Trail, which was 2 3/8 miles long. To find out the total distance they hiked, you would add these two distances together.

The total distance for the Tremont Trail (to the end and back):
3 1/2 miles to the end + 3 1/2 miles back = 7 miles

The total distance for the Wildflower Trail:
2 3/8 miles

Adding both distances gives us:
7 miles (Tremont Trail) + 2 3/8 miles (Wildflower Trail) = 9 3/8 miles

Therefore, Bernie and Chloe hiked a total of 9 3/8 miles.

Final answer:

To round 9.098 to the nearest tenth, we round up because the hundredths digit is 9, resulting in 9.1.

Explanation:

Rounding 9.098 to the nearest tenth:

Answer: 0.021

Step-by-step explanation:

Given : The probability that a person inoculated with a particular vaccine will get the disease anyway. : p= 20%=0.20

The total people inoculates : n= 83

The binomial probability formula :-

[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex]

Now, the probability that exactly 10 of them will get the disease at some point their lives :-

[tex]P(X)=^{83}C_{10}(0.2)^{10}(0.8)^{73}\\\\=\dfrac{83!}{10!(83-10)!}(0.2)^{10}(0.8)^{73}=0.0209841759622\approx0.021[/tex]

Hence, the probability that exactly 10 of them will get the disease at some point their lives =0.021

Answer:

8.22%

Step-by-step explanation:

The interest rate of the savings account is 8.22%

[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]

where, A : Amount

P = Principal amount

r = Annual interest rate as a decimal

R = Annual interest rate as a percent

r = R/100

n = number of compounding periods per unit of time

t = time in decimal years

[tex]r=n[(\frac{A}{P} )^{\frac{1}{nt} }-1][/tex]

For given question,

the principal amount (P) = $7300

the amount (A) = $8600

period (t) = 2

n = 12 (since it's monthly compounding)

To find 'r'

Using the formula of rate of interest,

[tex]\Rightarrow r=n[(\frac{A}{P} )^{\frac{1}{nt} }-1]\\\\\Rightarrow r=12\times [(\frac{8600}{7300} )^{\frac{1}{12\times 2} }-1]\\\\\Rightarrow r=12\times [(1.18)^{\frac{1}{24} }-1]\\\\\Rightarrow \bold{r=0.0822}[/tex]

The rate of interest in percentage form,

[tex]\Rightarrow R=r\times 100\\\\\Rightarrow R=0.0822\times 100\\\\\Rightarrow \bold{R=8.22\%}[/tex]

Therefore, the interest rate of the savings account is 8.22%

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Answer:

The median of the data set is 3.5 ⇒ answer (B)

Step-by-step explanation:

* Lats talk about the median of the data

- The median is the middle value of the arranged data

- You must to arrange the data at first to find the median

- The number of data is very important when you find the median

- If the number of data odd (1 , 3 , 5 , 7 , .....), then the median

 will be the middle one of the data

* Ex: if the number of data is 13, then the median will be the 7th on

∵ 13 ÷ 2 = 6.5, then there are 6 numbers before and 6 number after

∴ The median is the 7th one

- If the number of data even (2 , 4 , 6 , 8 , .....), then there is no

 middle on, we will find two numbers on the middle.

 So we take the average of them

* Ex: if the number of data is 12, then the median will be the

        average of the  6th and 7th numbers

* Lets use this conditions in our problem

- The data are 3 , 7 , 9 , 2 , 5 , 3 , 4 , 6 , 1 , 0

- At first arrange the data

* 0 , 1 , 2 , 3 , 3 , 4 , 5 , 6 , 7 , 9

- The number of data is 10

∵ 10 ÷ 2 = 5

∴ The median will be the average of the 5th and 6th numbers

∵ The 5th number is 3 and the 6th number is 4

∴ The median = (3 + 4)/2 = 3.5

* The median of the data set is 3.5

Answer:

c

Step-by-step explanation:

got it right on edge

Answer:(4,-3)

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

Answer:

The required equation is [tex]y=-4x+60[/tex]  and graph of this equation is shown below.

Step-by-step explanation:

Let y be the number of bales in the barn after feeding his cows for x days.

It is given that a farmer has 60 bales of hay stored in his barn.

Initial number of bales = 60

He feeds his cows 4 bales each day. It means number of bales decrease by 4 bales per day.

Slope = -4

The slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept or initial value.

Substitute m=-4 and b=60 in the above equation.

[tex]y=-4x+60[/tex]

The y-intercept of the graph is 60.

The table of values is shown below

   x               y

   0             60

  15              0

Plot these these points on coordinate plane and connect them by a straight line.

The required graph is shown below.

Answer:

The correct option is A.

Step-by-step explanation:

From the given information it is clear that at x=25, the predicted value of y is 27.745 and the actually value is 29.

Predicted value = 27.745

Observed value = 29

The formula for residual is

Residual = Observed value - predicted value

[tex]Residual=y-\hat{y}[/tex]

[tex]Residual=29-27.745[/tex]

[tex]Residual=1.255[/tex]

The residual in this case is 1.255, therefore option A is correct.

The residual is 1.255.

The residual is the difference between the actual y-value and the predicted y-value for a given x-value. In this case, the predicted y-value when x equals 25 is 27.745, but the actual y-value is 29. Therefore, the residual is calculated by subtracting the predicted value from the actual value: 29 - 27.745 = 1.255. So, the answer is A. 1.255.

Answer:

37.01

Step-by-step explanation:

The equation of the tangent line to the curve is

y = -9 ( √3 / 2 )x + [ ( 3π√3 + 9 ) / 2 ]

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the curve be y = 9 cos ( x )

To find the equation of the tangent line to the curve y , take the derivative of y , we get

dy / dx = 9 ( - sin ( x ) )

dy / dx = -9 sin ( x )

So , y' = -9 sin ( x )

when x = π/3

Now plug in your value for x into y'

-9 sin ( π/3 ) = -9 ( √3 / 2 )

This is the slope of the tangent line at x = π/3

And , To find the equation of the tangent line, we need a value for y. Simply plug your x value into the original equation for y

So ,

y = 9 cos x

y = 9 cos ( π / 3 )

y = 9 ( 1/2 )

y = 9/2

Now use point slope form to find the equation of the tangent line

y - y₁ = m ( x - x₁ )

Substituting the values in the equations , we get

y - 9/2 = -9 ( √3 / 2 ) ( x - π/3 )

On simplifying the equation , we get

y - 9/2 = -9 ( √3 / 2 )x + 9 ( √3 / 2 ) ( π/3 )

Adding 9/2 on both sides of the equation , we get

y = -9 ( √3 / 2 )x + [ ( 3π√3 + 9 ) / 2 ]

Hence , the equation is y = -9 ( √3 / 2 )x + [ ( 3π√3 + 9 ) / 2 ]

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The negative sign indicates a decrease in the number of members. Therefore, the percentage change of -25% means that the number of members decreased by 25%. To summarize, the percentage change in the number of members from last year to this year is 25% decrease.

To find the percentage change in the number of members from last year to this year, we'll use the formula for percentage change:

[tex]\[ \text{Percentage change} = \left( \frac{\text{New value} - \text{Old value}}{\text{Old value}} \right) \times 100\% \][/tex]

Given that last year the chess club had 20 members and this year it has 15 members, we can plug these values into the formula:

[tex]\[ \text{Percentage change} = \left( \frac{15 - 20}{20} \right) \times 100\% \][/tex]

[tex]\[ \text{Percentage change} = \left( \frac{-5}{20} \right) \times 100\% \][/tex]

[tex]\[ \text{Percentage change} = -\frac{1}{4} \times 100\% \][/tex]

[tex]\[ \text{Percentage change} = -25\% \][/tex]

The negative sign indicates a decrease in the number of members. Therefore, the percentage change of -25% means that the number of members decreased by 25%.

To summarize, the percentage change in the number of members from last year to this year is 25% decrease.

The complete question is:

Last year the chess club had 20 members. This year the club has 15 members. Find the percentage of change and state whether the percent of change is an increase or decrease.

Answer is down below

↓↓↓↓↓↓↓↓↓↓↓

After creating equations based on the given costs and solving for the price of chairs, desks, and beds, we find that the total cost for 5 desks and 4 beds is $725.78.

To solve this problem, we will start by setting up two equations based on the information given about the prices of chairs, desks, and beds. Let's denote the cost of one chair as C, the cost of one desk as D, and the cost of one bed as B. According to the problem, the desk costs 2 times as much as the chair, so we have D = 2C.

Now, we can create equations based on the total costs provided:

Substitute the value of D from D = 2C into the first equation:

3C + 4(2C) = 367.95 -> 11C = 367.95 -> C = 33.45

With the cost of a chair found, we can find the cost of a desk:

D = 2C = 2(33.45) = 66.90

Now, to find the cost of a bed, we use the second equation and substitute values for C:

4C + 6B = 720.72 -> 4(33.45) + 6B = 720.72 -> 133.80 + 6B = 720.72 -> 6B = 586.92 -> B = 97.82

Finally, we calculate the total cost of 5 desks and 4 beds:

5D + 4B = 5(66.90) + 4(97.82) = 334.50 + 391.28 = 725.78

The total cost of 5 desks and 4 beds is $725.78.