Answers
Answer:
8.2
Step-by-step explanation:
Related Questions
2. a chicken farmer also has some cows for a total of 30 animals and the animals have 74 legs in all. how many chickens does the farmer have? 23
Answers
Answer:
23 chickens
Step-by-step explanation:
x + y = 30
We also know that the total number of legs is 74. Each chicken has 2 legs, and each cow has 4 legs, so we can write:
2x + 4y = 74
Now we have two equations with two variables, and we can solve for x (the number of chickens). We can start by solving the first equation for y:
y = 30 - x
Substituting this into the second equation, we get:
2x + 4(30 - x) = 74
Simplifying this equation, we get:
-2x + 120 = 74
Subtracting 120 from both sides, we get:
-2x = -46
Dividing both sides by -2, we get:
x = 23
So, there are 23 chickens.
Answer:
23 chickens
Step-by-step explanation:
Step 1: Set Up a System of Equations
We know that this farmer has some unknown amount of chickens, and some unknown amount of cows. Let's assign a letter to each unknown variable - let the number of chickens be c, and the number of cows be w.
The problem tells us that the farmer has a total of 30 animals (cows and chickens together). Therefore, c + w = 30.
We are then given some information about how many legs the animals have. Recall that a chicken has 2 legs and a cow has 4. Since (we are assuming that) each animal has the "normal" number of legs, we can represent the number of chicken legs as 2c and the number of cow legs as 4w. Since the animals have 74 legs in all, we know that 2c + 4w = 74.
Step 2: Solve the System
We now have the following system of equations:
c + w = 30 (1)
2c + 4w = 74 (2)
The problem is asking us to find the number of chickens, or c. Note that this means we do not have to find the number of cows, or w, so let's manipulate the system to eliminate w, which will make solving for c easier. Solving, we get:
4c + 4w = 120 (3) (Multiply (1) by 4)
2c = 46 (Subtract (2) from (3))
c = 23 (Divide by 2)
Thus, the farmer has 23 chickens.
A cone has a volume of 100x cubic centimeters and a height of 12 centimeters. What is the radius of the base of the
cone in centimeters?
A. 10 cm
B. 5 cm
C. 25 cm
D. Not here
Answers
I’m confused I’m not sure which one it is
Answers
Answer:
A.55
Step-by-step explanation:
Because DE parallel to AC m(<B) common angle So ABC similar to DBEm(<D) = m(<A) = 180 - (60 + 65) =55Consider the tables created using an initial investment of $1,000 and quarterly compounding of interest.
table a represents the function that models the total amount of one investment, a(x), based on the annual interest rate, x, as a percent.
table b represents the function that models the interest rate, r(d), as a percent, based on the total amount at the end of the investment, d.
use the values in the table to verify the relationship between the functions representing the investments. which conclusion can be made?
the functions are inverses because the domain of table a is the same as the range of table b.
the functions are inverses because the range of table a is different from the domain of table b.
the functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (x, y) for the other function.
the functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function.
Answers
Option fourth "The functions are not inverses because, for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function." is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two tables shown in the picture.
Table (A) have values of x and a(x)
Table (B) have values of d and r(d)
As we know if the function has an inverse of it and (x, y) satisfies the function then (y, x) must satisfy the inverse of a function.
Thus, the option fourth "The functions are not inverses because, for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function." is correct.
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does the series converge? if the series does converge, find the sum. (if the quantity diverges, enter diverges.)
Answers
The given series \(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\) is convergence and the sum of the series is 33/28.
In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.
The given series is \(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\).
Firstly we check the convergence of the given series.
When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.
We can write the series as:
\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right\)
As |0.3|<1 and |0.2|<1
Then \(\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n\) is convergent.
So \(\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right\) is also convergent.
\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right\)
Series \(\sum_{n=1}^{\infty}(x)^{n-1}\) converges to 1/x-1 for |x|<1.
\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}\)
\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}\)
\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\) = 10/7 - 1/4
\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\) = 33/28
Hence, the sum of the given series is 33/28.
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The right question is:
Determine whether the series is convergent or divergent.
\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\)
If is is convergent, find the sum. (If the quantity diverges, enter diverges.)
What’s the length for mp
Answers
Hope this helps
Answer: The length of the MP is 13.
Step-by-step explanation: You can count the distance between them.
the 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). what is the margin of error of this confidence interval?
Answers
The margin of error of the 98.4% confidence interval for snapdragons is 3.71.
The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.
The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:
`Margin of error z*(standard deviation/√n`).
The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:
`standard deviation = (range/4) * √n / 1.96`
Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`
Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`
Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`
Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`
Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`
Now that we know the sample size, we can calculate the standard error of the mean:
`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.
The margin of error is `1.96 * 1.89 = 3.71`.
The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.
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a deck of cards is dealt out. what is the probability that the 14th card dealt is an ace? what is the probability that the first ace occurs on the 14th card?
Answers
The probability of picking an ace on any draw is 4/52 or 1/13.
The probability that the 14th card dealt is an ace is 0.002641
We can first calculate the probability of not getting an ace on the first 13 draws, and then find the probability of getting an ace on the 14th draw:
P(No ace on 1st draw) = 48/52
P(No ace on 2nd draw) = 47/51
P(No ace on the 3rd draw) = 46/50
And so on...
P(No ace on the 13th draw) = 36/40.
P(Ace on 14th draw) = 4/39
To find the probability of these independent events, we multiply their probabilities:
P(Ace on 14th draw) = P(No ace in first 13 draws) x P(Ace on 14th draw)
P(Ace on 14th draw) = (48/52) x (47/51) x ... x (4/40) x (4/39)
P(Ace on 14th draw) ≈ 0.002641
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Simplify. Please show work.
Answers
Answer:
Step-by-step explanation:
2(√x+2/2 - 1)² + 4 (√x+2/2 - 1)
2((√x+2/2)² + 1² - 2(√x+2/2)(1)) + 4√x+2/2 - 4
2(x+2/2 + 1 - 2(√x+2/2)) + 4√x+2/2 - 4
x + 2 + 2 - 4√x+2/2 + 4√x+2/2 - 4
x + 4 - 4
x
Answer:
the answer is x
Step-by-step explanation:
The midpoint of AB is MI(-2, -6). If the coordinates of A are (1, -4), what are
the coordinates of B?
Answers
What’s the domain using inequalities for this graph? I’ll give you brainiest
Answers
Answer:
Hi there!
Your answer is:
X is between -4 and +infinity
Step-by-step explanation:
The open circle indicates that it CANNOT be -4, but it has to be greater than it. The arrow indicates that it goes on permanently
Hope this helps
You roll a fair 6-sided die. what is the probability rolling greater than 4
Answers
Answer:
1/3
Step-by-step explanation:
There are 6 possible outcomes when you roll this die: 1,2,3,4,5 and 6. Of these, only 5 and 6 are greater than 4, which is 2 successful outcomes. Probability is successful outcomes/total outcomes = 2/6 = 1/3. Hope this helps!
if your latest test grade and your average test grade on previous exams are equal, your average test grade will:
Answers
If your average test grade from earlier examinations and your most recent test grade is equal, your average test grade will remain constant.
What is average?The average is the ratio created by dividing the total number of figures in a set by the total number of figures.In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.The average can be calculated by dividing the total number of values by the sum of all the numbers. For instance, if your average test grade from earlier examinations and your most recent test grade is equal, your average test grade will not change.Therefore, if your average test grade from earlier examinations and your most recent test grade is equal, your average test grade will remain constant.
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Area of triangle Question 4
Answers
Answer:
3sq units
Step-by-step explanation:
bxh = 2x3=6
6/2=3
for the following situations, would you collect information using a sample or a population? a. to find how many books are published in one week by a famous publishing company. multiple choice 1 sample population b. to test a new drug produced by a biotech company. multiple choice 2 sample population c. to find the number of men and women working in an it company with 600 people. multiple choice 3 population sample d. to estimate the average salary of doctors in california. multiple choice 4 population sample
Answers
We have to solve all of the parts of the given problem using our understanding of a sample and a population. It is given below.
A sample is taken when you want to take data from a specific set and then make observations based on that. A population is, on the other hand, the complete set that you want to make your observations from.
In the given problem -
A. To find how many books are published in one week by a famous publishing company - We are going to use a sample because we need to observe under s set category - one week.
B. To test a new drug produced by a biotech company - We are going to use a population because we need to monitor all individuals who take this drug.
C. To find the number of men and women working in an IT company with 600 people - We use a population here because we are going to use the data of all the people in the company.
D. To estimate the average salary of doctors in California - We use a sample here because the set category is California.
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If sin 30º = cos(3x), then x=_
Answers
Answer:
x = 20º
Step-by-step explanation:
we know that sin x = cos(90-x)
Hence
sin 30º = cos(90 - 30)º
sin 30º = cos 60º
hence sin 30º can be also written as cos 60º
Also, as given
sin 30º = cos(3x)
therefore
cos 60º = cos(3x)
as we have cos on both side then angle for both side will be same
60º = 3x
=> 60º / 3 = x
=> x = 20º
Then x = 20º is answer.
What is the degree of 5x + 3x2 - 4x+1?
3
4
5
6
Answers
Step-by-step explanation:
option A
3 IS CORRECT
HOPE IT HELPS
Answer:
3
Step-by-step explanation:
edge 2021
Solve this problem,
Each month, Megan babysits for a total of 50 hours. How many hours will she spend
babysitting in a year?
hours
Type the correct answer.
Answers
Solve x 3y = 9 3x − 3y = −13 (−1, ten thirds) (1, negative ten thirds) (−1, 3 over 10) (1, negative 3 over 10).
Answers
The solution of the system of equation is x = -1 and y=10/3.
The correct option is A.
Given
The given system of equation is;
\(\rm x + 3y = 9\\\\3x - 3y = -13\)
What is a system of equations?A system of linear equations is a collection of two or more linear equations.
From equation 1
\(\rm x+3y=9\\\\x=9-3y\)
Substitute the value of x in equation 2
\(\rm 3x-3y=-13\\\\3(9-3y)-3y=-13\\\\27-9y-3y=-13\\\\-12y=-13-27\\\\-12y=-40\\\\12y=40\\\\y = \dfrac{40}{12}\\\\y=\dfrac{10}{3}\)
Substitute the value of y in equation 1
\(\rm x+3y=9\\\\ x + 3\dfrac{10}{3}=9\\\\x+10=9\\\\x=9-10\\\\x=-1\)
Hence, the solution of the system of equation is x = -1 and y=10/3.
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Answer:
A
Step-by-step explanation:
Alice's mother wants to wallpaper two adjacent walls in Alice's bedroom. She also wants to put a border along the top of all four walls. The bedroom is 9 ft by 12 ft by 8 ft high. A) If each double roll covers approximately 60 fr and the wallpaper is sold in double rolls only, how many double rolls are needed? B) If the border is sold in rolls of 5 yd each, how many rolls of the border are needed?
Answers
Answer:
A) The number of wallpapers needed to cover the walls is 6 double roll wall papers
B) The number of wall paper border rolls needed is 3 rolls
Step-by-step explanation:
A) The given parameters are;
The dimensions of the room are 9 ft. by 12 ft. by 8 ft. high,
The area one double role wallpaper covers = 60 ft.²
Therefore, we have;
The area of the room wall = 12 × 8 × 2 + 9 × 8 × 2 = 336 ft²
The number of double rolls of wallpaper to be used = Area of wall/(area of wallpaper) = 336/60 = 5.6
Therefore, given that the wall papers are sold in single units, we round up to the next whole number of units to get;
The number of wallpapers needed to cover the walls = 6 double roll wall papers
B) The borders of a wallpaper are installed parallel (and installed along) to the ceiling line
Therefore, the amount of wallpaper border required is given as follows;
Wall paper border length required = 2 × Length of the room + 2 × Width of the room
∴ Wall paper border length required = 2 × 9 ft. + 2 × 12 ft. = 42 ft.
The size of each wall paper border sold = 5 yd. = 15 ft.
Therefore;
The number of wall paper border rolls required = 42 ft./(5 yd.) = 42 ft./(15 ft.) = 2.8 rolls
Therefore, we round up to get the number of wall paper border rolls needed as 3 rolls of wall paper borders.
Write the equation of a line that
passes through the following points
:
Point 2: (0,-8)
Point 1: (-3,0)
Answers
Answer:
\(y = \frac{-8}{3}x - 8\)
Step-by-step explanation:
Solving for the equation of the line with two points:
Let's remind ourself of the slope - intercept formula: \(y = mx + b\)
We first have to find the slope of the line. This is found by using the formula :
\(\frac{y_1 - y_2}{x_1 - x_2}\)
We have to find the change in y (Δy) and divide it by the change in x (Δx)
We then have to plug in a coordinate given to us, and use the point's x and y value to find the y - intercept
Step 1: SlopeLet's use the slope formula
\(\frac{0 - (-8)}{-3 - 0} = \frac{8}{-3}\)
Slope = -8/3
Step 2: Y - InterceptTo find the y - intercept, we'll update our slope - intercept formula with the slope, and plugin a point. Let's use (-3,0)
\(y = \frac{-8}{3}x + b\)
\(0 = \frac{-8}{3}(-3) + b\)
\(0 = \frac{24}{3} + b\)
\(0 = 8 + b\)
\(b = -8\)
Step 3: EquationLet's input our slope and y - intercept to the equation \(y = mx + b\)
Slope = -8/3
Y - Intercept = -8
Equation: \(y = \frac{-8}{3}x - 8\)
-Chetan K
You pay $1.00 to buy a package of paper napkins costing 64¢. How much change will you get back? Give the expression also.
Answers
Answer:
36 back
Step-by-step explanation:
100 - 64 = 36
Answer:
36¢
Step-by-step explanation:
1.00-0.64=0.36
Bob needs $.50 to ride the bus. He has 3 quarters, 5 dimes, and 2 nickels. What is the probability he will pull two quarters in a row from his pocket without replacement? Show work.
Answers
Step 1:
Probability formula
\(\text{Probability of any event = }\frac{n\text{umber of required outcomes}}{n\text{umber of possible outcomes}}\)Step 2:
Number of possible outcomes
Quarters = 3
Dimes = 5
Nickels = 2
Total possible outcomes = 10
Step 3:
\(\begin{gathered} \text{Probability of picking two quarters one after the other without} \\ \text{replacement = }\frac{3}{10}\times\frac{2}{9}=\frac{1}{15}\text{ } \end{gathered}\)Final answer
The probability he will pull two quarters in a row from his pocket without replacement = 1/15
Sean can walk 2 1/4 miles in 2/3 hour.
At this rate, how far can he walk in 1 hour?
Answers
Answer:
3.375 or 3 3/8
Step-by-step explanation:
divide 2 1/4 to get 1 1/8 or 1.125 then multiply by 3 to get 3.375 or 3 3/8
Question 1 a) Loan Amount \( =\$ 300 \) Advance amount \( =\$ 160 \) Remaining Amount To be paid \( =\$ 300-160=\$ 140 \) Time \( =2 \) weeks Calculate interest rate?
Answers
The interest rate in this case is 0%.
To calculate the interest rate for a loan with a loan amount of $300, an advance amount of $160, a remaining amount to be paid of $140, and a time of 2 weeks, follow the steps below:
Step 1: Find the total amount paid
Total amount paid = Advance amount + Remaining amount to be paid
Total amount paid = $160 + $140Total amount paid = $300
Step 2: Find the interest
Interest = Total amount paid - Loan amount
Interest = $300 - $300
Interest = $0
Step 3: Find the interest rate
The interest rate is the percentage of the loan amount that has to be paid as interest.
Hence, the interest rate is 0%.
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Ike Phillips worked 6.7 hours at time-and-a-half pay and 3.4
hours at double-time pay last week. His regular earnings for
the week were $454.80 figured on a regular pay rate of $11.37
an hour.
27. What were Ike's time-and-a-half and double-time pay rates?
28. What amounts did he earn for time-and-a-half and double-time work?
29. What was Ike's total gross pay for the week?
Answers
Working out the different pay rates earned by Ike Phillips :
Time and half pay rate = $17.055Double pay rate = $22.74Time and half earning = $114.2685Double rate earning = $77.316Gross earning = $646.3845Let :
Regular rate = $11.37
Total earning for the week = $454.80
Double pay hours = 3.4
Time and half pay hours = 6.7
Time and half pay rate = 1.5 × regular pay rate = 1.5 × 11.37 = $17.055Double pay rate = 2 × regular pay rate = 2 × 11.37 = $22.74Time and half earning = rate × time = $17.055 × 6.7 = $114.2685 Double rate earning = rate × time = $22.74 × 3.4 = $77.316Gross earning = (regular + time and half + double earning) = $(454.80+114.2685+77.316) = $646.3845Therefore, Ike's gross earning for the week is $646.3845
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what is the measure of angle B ???
Answers
A person jogs 780 meters south and then 360 meters west. What is the direction of the person's resultant vector? Hint: Draw a vector diagram. Ө 0 = [ ? ]° Round your answer to the nearest hundredth.
Answers
Answer:
245.22° (nearest hundredth)
Step-by-step explanation:
To calculate the direction of the jogger's resultant vector, we can draw a vector diagram (see attachment).
The starting point of the person is the origin (0, 0).Given the jogger first jogs 780 m south, draw a vector from the origin south along the y-axis and label it 780 m.Given the jogger then jogs 360 m west, draw a vector from the terminal point of the previous vector in the west direction (to the left) and label it 360 m.Since the two vectors form a right angle, we can use the tangent trigonometric ratio.
\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$ \tan x=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $x$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)
The resultant vector is in quadrant III, since the person jogs south (negative y-direction) and then west (negative x-direction).
As the direction of a resultant vector is measured in an anticlockwise direction from the positive x-axis, we need to subtract the angle found using the tan ratio from 270°.
The angle between the y-axis and the resultant vector can be found using tan x = 360 / 780. Therefore, the expression for the direction of the resultant vector θ is:
\(\theta=270^{\circ}+\arctan \left(\dfrac{360}{780}\right)\)
\(\theta=270^{\circ}-24.7751405...^{\circ}\)
\(\theta=245.22^{\circ}\; \sf (nearest\;hundredth)\)
Therefore, the direction of the plane's resultant vector is approximately 245.22° (measured anticlockwise from the positive x-axis).
Find X both segments are tangents
Answers
Answer:
c
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
2x+10=x+30
so, the answer is 30.
please answer the questions
6. Find the area of the region enclosed by y = 1 X 1 y = x, y ==x, and x > 0. 2
1 7. Find the number a such that the line x = a bisects the area under the curve y x²⁹ 1 ≤ x ≤ 4.
Answers
The area of the region enclosed by the curves y = 1, y = x, y = x^2, and x > 0 is 1/6 square units.
To find the area of the region enclosed by the given curves, we need to determine the points of intersection.
First, we find the intersection points of y = 1 and y = x^2. Setting these equations equal to each other, we have:
1 = x^2
Solving for x, we find x = 1.
Next, we find the intersection points of y = x and y = x^2. Setting these equations equal to each other, we have:
x = x^2
Rearranging the equation, we get x^2 - x = 0. Factoring out an x, we have x(x - 1) = 0. This gives us two solutions: x = 0 and x = 1.
Therefore, the region is bounded by x = 0, x = 1, y = 1, and y = x^2. To find the area of this region, we integrate the difference of the upper and lower curves with respect to x. The integral is given by:
A = ∫[0, 1] (x^2 - 1) dx
Evaluating this integral, we get A = 1/6 square units.
Hence, the area of the region enclosed by the given curves is 1/6 square units.
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