A landscaper has 3/4 ton of mulch. She puts 1 1/6 ton of mulch on each flower bed. How many flower beds does she put mulch on?
Find the equations of the tangent line to the curve at the given point. y = 9cos x. (π/3,4.5)
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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Helen makes $66 a day . How much will she make if she works 5 1/2 days ?
What is the area of a sector with a central angle of 2π9 radians and a diameter of 20.6 mm? Use 3.14 for π and round your answer to the nearest hundredth.
Answer:
37.01
Step-by-step explanation:
Sarah has read aloud in class 3 more times than Joel. Sarah has read 9 times. Which equation represents this situation?
A j + 3 = 9
B j − 9 = 3
C 3j = 9
D j − 3 = 9
If $7300 is invested in a savings account for which interest is compounded monthly, and if the $7300 turns into $8600 in 2 years, what is the interest rate of the savings account?
Answer:
8.22%
Step-by-step explanation:
The interest rate of the savings account is 8.22%
What is compound interest formula?[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
What is the formula to find the interest rate?[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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What is the value of x?
#2
a. 71
b. 142
c. 152
d. 76
#3
a. 68
b. 62
c. 112
d. 124
If triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z', what is the ordered pair of X'? (2 points)
Answer:(4,-3)
Step-by-step explanation:
5(2x − 3) = 5
Part A: How many solutions does this equation have?
Part B: What are the solutions to this equation? Show your work.
Please help!!!!:
Mrs. Greenhaus has a six-sided number cube and a spinner. The number cube has the numbers 1 through 6 on its faces, and the spinner has four equal regions with blue, red, yellow, and green each in a different region. This tree diagram represents the outcomes of rolling the number cube and then spinning the spinner.
What is the probability of rolling an even number and landing on blue?
A.1/2
B.7/8
C.1/4
D.1/8
What is 100 + 101 + 102 equal to?
Answer:
111
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
Calculate the median of the data set below. {3, 7, 9, 2, 5, 3, 4, 6, 1, 0} A. 3 B. 3.5 C. 4 D. 10
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
A line of best fit predicts that when x equals 25, y will equal 27.745, but y actually equals 29. What is the residual in this case? A. 1.255 B. -1.255 C. -2.745 D. 2.745
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.
Explanation: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.
Last year, a person wrote 134134 checks. let the random variable x represent the number of checks he wrote in one day, and assume that it has a poisson distribution. what is the mean number of checks written per day? what is the standard deviation? what is the variance?
What would happen to a monthly payment if the interest rate increased
HELP!!!
1. A machine makes bolts that are 12 mm long. The bolts are considered acceptable if they are within 0.2 mm of 12 mm.
a. What is the longest the bolt can be and still be acceptable?
b. What is the shortest the bolt can be and still be acceptable?
true Value Hardware buys 200 snow blowers for $90 each to stock the store for the winter. If True Value sells the 200 snow blowers at $120 each, what is the profit?
At a store, 3 chairs and 4 desks together cost $367.95. The total costof 4 chairs and 6 beds is $$720.72. If the price of the desk is 2 times as much as the price of the chair, what is the total cost of 5 desks and 4 beds?
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.
Explanation: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:
3 chairs and 4 desks cost $367.95 -> 3C + 4D = 367.954 chairs and 6 beds cost $720.72 -> 4C + 6B = 720.72Substitute 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.
Round 9.098 to the nearest tenth.
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:
Identify the tenths place in 9.098, which is 0.1.The digit immediately after the tenths place is 9, which is 5 or higher, so you need to round up.Therefore, when rounding 9.098 to the nearest tenth, the result is 9.1.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
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.
Evaluate the expression 42+6⋅52−33÷32.
Franklin saved money to buy art supplies. He used 1/5 of his savings to buy brushes. He used 1/2 of his savings to buy paint. What fraction of his savings does he have remaining?
Answer is down below
↓↓↓↓↓↓↓↓↓↓↓
bernie and chloe hiked the tremont trail 3 1/2 miles to the end and back then they hiked the wildflower trail 2 3/8 miles how far did they hike
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.
What’s the surface area of a rectangle if it’s 5 by 10 in
A coin is loaded so that the probability of heads is 0.55 and the probability of tails is 0.45. suppose the coin is tossed twice and the results of the tosses are independent. what is the probability of obtaining exactly one head?
There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. a county health office inoculates 83 people. What is the probabythat exactly 10 of them will get the disease at some point their lives?
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
for Owens lemonade recipe, 6 lemons are required to make 5 cups of lemonade?express your answer in simplest form.
plz help
A farmer has 60 bales of hay stored in his barn. He feeds his cows 4 bales each day. Which graph represents the number of bales in the barn, y, after feeding his cows for x days?
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.
Create a Pattern with the rule n-4
A sample is selected from a population with a mean of u=100 and a standard deviation of o-20 what is the expected value of m and the standard error for a sample of n=4