Answer:
They complete the hill in 8 hours
Step-by-step explanation:
Equations:
Let's call the variables:
Aran can make build the ant hill in A hours
Beatrice can make build the ant hill in B hours
Charlie can make build the ant hill in C hours
In one hour, Aran makes 1/A of the ant hill.
In one hour, Beatrice makes 1/B of the ant hill.
In one hour, Charlie makes 1/C of the ant hill.
Aran and Beatrice build it in 10 hours, thus:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}=\frac{1}{10}\qquad\qquad[1][/tex]
Similarly:
[tex]\displaystyle \frac{1}{A}+\frac{1}{C}=\frac{1}{12}\qquad\qquad[2][/tex]
[tex]\displaystyle \frac{1}{B}+\frac{1}{C}=\frac{1}{15}\qquad\qquad[3][/tex]
We need to find the time taken for the three ants to build the anthill:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=[/tex]
Adding [1], [2], and [3]:
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}[/tex]
Adding the fractions (LCM=60):
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6}{60}+\frac{5}{60}+\frac{4}{60}[/tex]
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}[/tex]
Dividing by 2:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}[/tex]
All ants together make 1/8 of the hill, thus they complete the hill in 8 hours
The scatter plot shows the test scores of a group of students who studied for different amounts of time in a week. A graph shows Hours Spent Studying on x axis and Test Score on y axis .The graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 100 at increments of 10. The ordered pairs 0, 21 and 0.8, 32 and 1.2,35 and 1.5,39 and 2.1, 42 and 2.3,45 and 2.5,49 and 2.7, 50 and 3, 67 and 4.6, 56 and 5, 69 and 5.3,70 and 5.7,74 and 6.4,78 and 7.2,80 and 7.5,84 and 8.5,88 and 8.7,92 and 9.5,96 are shown on the graph. What will most likely happen to the test scores of students if the number of hours they study increases? Test scores will increase because the graph shows a negative association. Test scores will increase because the graph shows a positive association. Test scores will decrease because the graph shows a positive association. Test scores will decrease because the graph shows a negative association.
Answer:
Test scores will increase because the graph shows a positive association.
Step-by-step explanation:
Since it is going upwards to the right instead of going downwards and for the people who steady more hours they get better scores on there test.
btw i just took it and got it right
From given scatter plot, if the number of hours they study increases then the test scores will increase because the graph shows a positive association.
What is scatter plot?"A type of data representation that shows the relationship between two numerical variables. "
What is positive association?"When the values of one variable tend to increase as the values of the other variable increase, then two variable have positive association."
What is negative association?"When the values of one variable tend to decrease as the values of the other variable increase, then two variable have negative association."
For given question,
The scatter plot shows the test scores of a group of students who studied for different amounts of time in a week.
A scatter plot shows Hours Spent Studying on x axis and Test Score on y axis .
Also we have been given the ordered pairs
(0, 21), (0.8, 32), (1.2, 35), (1.5, 39), (2.1, 42), (2.3, 45) and (2.5, 49) and (2.7, 50) and (3, 67) and (4.6, 56) and (5, 69) and (5.3, 70) and (5.7, 74) and (6.4, 78) and (7.2, 80) and (7.5, 84) and (8.5, 88) and (8.7, 92) and (9.5, 96)
From the given data points of scatter plot,
as x - value increases, y - value also increases.
This means, if the number of hours they study increases, the test scores will increase.
Here, the values of one variable tend to increase as the values of the other variable increase.
This means, there is positive association in variables Hours Spent Studying and Test Scores.
Therefore, from given scatter plot, if the number of hours they study increases then the test scores will increase because the graph shows a positive association.
Learn more about the positive association here:
https://brainly.com/question/858660
#SPJ2
Bethany is working her way through school. She works two part-time jobs for a total of 30 hours a week. Job A pays $5.90 per hour, and Job B pays $7.20 per hour. How many hours did she work at each job the week that she made $193.90.
Answer:
13 hours at Job B, and 17 hours at Job A.
Step-by-step explanation:
13×7.20= 93.60
17×5.90=100.30
100.30+93.60= 193.90
PLEASE HELP ;-; Ill GIVE BRAINLY
What is the solution to the following system of equations? Explain how you know.
Answer:
-3,1
Step-by-step explanation:
When you are doing Systems Of Equations using a graph, the point where the lines intersect is your answer
homework 1 relations domain range and functions 3-8
Answer:
Step-by-step explanation:
Domain - Set of x-values
Range - Set of y-values
3). Since, x values vary from x = -6 to x = 5,
Domain of the graph = [-6, 5]
Since, y-values vary from y = -2 to y = 3
Range of the graph = [-2, 3]
4). Domain of the graph = [-3, 3]
Range of the graph = [-6, 5]
5). Domain of the graph = (-∞, ∞)
Range of the graph = (-∞, ∞)
6). Domain of the graph = (-∞, 4]
Range of the graph = (-∞, ∞)
7). Domain of the graph = (-∞, ∞)
Range of the graph = [-1, 5]
8) Domain of the graph = [-1, 5)
Range of the graph = [-3, 3)
Answer:
Step-by-step explanation:
Jonas is buying fencing to surround his garden. If his garden has a perimeter of 36 feet, and fencing costs
$10.00 a yard, how much money will he need for the fencing?
Answer:
Step-by-step explanation:
$120
5 ^ 3 + 1/2 ^ 2.
I need help.
Answer:
125.25
Step-by-step explanation:
5 cube =125
1/2=0.5
0.5 squared =0.25
125+0.25=125.25
5
After simplifying the expressions on each side of an equation, you observed that the coefficients of x and the constants
on each side of the equal sign were the same. What kind of solution(s) do you expect for this equation?
No solution
Infinitely many solutions
One unique solution
T
Answer:
The solution has infinitely many solutions.
Step-by-step explanation:
Correct option is - The solution has infinitely many solutions.
The expression is of the form -
ax + b = ax + b
In the expression , any value of x will satisfy
So, we get infinitely many solution
For example -
for x = 1
a(1) + b = a(1) + b
⇒ a + b = a + b
satisfied.
for x = 2
a(2) + b = a(2) + b
⇒ 2a + b = 2a + b
satisfied.
Hereon, for any value of x , it satisfies.
Solve the following equation.
4x - 2 = 22-8x
Answer:
x = 2
Step-by-step explanation:
4x - 2 = 22 - 8x
Move all variables to a single side by adding 8x to both sides of the equation.
4x + 8x - 2 = 22 - 8x + 8x
12x - 2 = 22
Add 2 to both sides to move the constants to one side.
12x - 2 + 2 = 22 + 2
12x = 24
Divide both sides by 12 to isolate the x.
12x / 12 = 24 / 12
x = 2
Answer:
x = 2
Step-by-step explanation:
Add 2 to both sides.
4x - 2 +2 = 22 - 8x + 2
Simplify.
4x=-8+24
Add 8x to both sides.
4x+8x= -8x + 24 + 8x
Simplify.
12x = 24
Divide both sides by 12.
12x/12 = 24/12
Simplfy.
x = 2
hope this helps! :)
Show the work for the answer
x=³√27
x = 3
Answer:
x = 3
Step-by-step explanation:
Given that,
[tex]x=\sqrt[3]{27}[/tex]
We need to show work to solve it.
We know that,
27 = 3×3×3
or
27 = (3³)
So,
[tex]x=\sqrt[3]{3\times 3\times 3}\\\\=(3^3)^{\dfrac{1}{3}}\\\\x=3[/tex]
Hence, this is the required solution.
Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now. Assuming (a) interest at an annual rate of 5% compounded annually, or (b) interest at an annual rate of 6% compounded continuously, which option should she choose under the consideration of cash value only?
A) If the interest is at the annual rate of 5%, compounded annually, then the present value of the five installments is $______. B) If the interest is at the annual rate of 6%, compounded continuously, then the present value of the five installments is $______.
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.
First, we determine the value of the 5 installments using a 5% annual compounded rate.
We calculate the future value, and then the present value:
FV= {A*[(1+i)^n-1]}/i
A= annual payments
FV= {60,000*[(1.05^5) - 1]} / 0.05
FV= $331.537.88
PV= FV/(1+i)^n
PV= $259,768.60
At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.
Now, if the annual rate is 6% continuously compounded.
First, we need to calculate the effective interest rate:
r= e^i - 1
r= effective inerest rate
r= e^0.06 - 1
r= 0.0618
FV= {60,000*[(1.0618^5) - 1]} / 0.0618
FV= 339,443.23
PV= 339,443.23/1.0618^5
PV= $251,509.01
At an annual rate of 6% compounded continuously, she should choose the $255,000.
what is the answer i need help
Answer:
90/100
Step-by-step explanation:
both equal 0.9
Answer:
[tex]\frac{90}{100\\}[/tex]
Step-by-step explanation:
[tex]\frac{9}{10}[/tex] equals [tex]\frac{90}{100\\}[/tex]
By multiplying the numerator and denominator of [tex]\frac{9}{10}[/tex] by 10, we get [tex]\frac{90}{100\\}[/tex] .
9 x 10 = 90
10 x 10 = 100
) A cyclist travels a distance of 90 miles in 5 hours. What was her average speed? 2) How far along a motorway would you travel if you drove at 70 mph for 4 hours? 3) I drive to Bude in Cornwall from Sheffield in about 6 hours. The distance from Sheffield to Bude is 315 miles. What is my average speed? 4) The distance from Leeds to London is 210 miles. The train travels at an average speed of 90 mph. If I catch the 9.30 am train in London, at what time should I expect to arrive in Leeds? 5) How long will an athlete take to run 2000 m at an average speed of 4 metres per second? 6) The distance between Sheffield and Land’s End is 420 miles. a) What is the average speed of a journey from Sheffield to Land’s End that takes 8 hours 45 minutes? b) If Sam covered the distance at an average speed of 63 mph, how long would it take him?
sum of two numbers is 35 and the difference is 15
Answer
IM not too sure
Step-by-step explanation:
Not too sure sorry kid
Answer:
25 and 10 are the numbers
Step-by-step explanation:
What is the probability of spinning a number greater than 5 on a spinner numbered 1-8 and tossing a tail on a coin
Answer:
3/16
Step-by-step explanation:
P(6,7,8 and 'T') = 3/8 x 1/2 = 3/16
Answer:
12/64
Step-by-step explanation:
We have numbers 1-8 = /8
We have the numbers 6, 7, 8 on the spinner = 3/8
We have the event it doesn't get over 8 too = 8/8-3/8 = 5/8
To use if the question has two events for spinner.
We toss a coin = H or T = 1/2
We convert a 3/8 and 1/2 to same HCF = 4/8 = ( 2x 4 = 8)
3/8 x 4/8 = 12/64
Draw the proble. give me steps. Please
Answer:
I cant draw 4 u sry
Answer:
A. c = 3.5h + 15
Step-by-step explanation:
I can't exactly draw the problem BUT I can still help.
C represents the cost altogether but we do not know how much the total cost would be.
So we're paying $15 as a fee, no more from that.
Next, there's another fee that costs $3.50 per hour but since we wouldn't know how long we would use the kayak, hours would represent h.
Now, c = 3.5h + 15.
(In other words, the cost to rent a kayak would be $3.5 PLUS the additonal 15 one time cost.)
Jennifer is saving money to buy a bike. The bike costs $258. She has $125 saved, and each week she adds $19 to her savings.
How long will it take her to save enough money to buy the bike?
It will take her___
weeks to save for the bike.
Answer:
7 weeks
Step-by-step explanation:
Answer:
7 weeks
Step-by-step explanation:
A line passes through the point (-2, 7) and has a slope of -5.
What is the value of a if the point (a, 2) is also on the line?
a. -7
b.-1
c.1
D.7
I NEED ANSWERS SOON
Answer:
[tex]\boxed{a = 3}[/tex]
Step-by-step explanation:
[tex] (using \: the \: points : (2, \: 7) = ( x_{1}, \: y_{1}\: \: ) \\ hence : (a, \: 2) = ( x_{2}, \: y_{2}\: \: ) \\ but \: m = \frac{ y_{2} -y_{1} }{x_{2} - x_{1}} = \frac{2 - 7}{a - 2} \\ - 5 = \frac{2 - 7}{a - 2} \\ - 5(a - 2) = 2 - 7 \\ - 5a + 10 = 2 - 7 \\ - 5a = - 5 - 10 \\ - 5a = - 15 \\ a = \frac{ - 15}{ - 5} \\ \boxed{a = 3}[/tex]
X-4/x-3 is less than 2x-1/2
Answer:
yes
Step-by-step explanation:
yes
The equation S = 50 + 45w represents the savings, S, after w weeks working and
depositing (putting in) money into a savings account at the bank.
Determine whether there is a proportional relationship between S and w.
Explain your reasoning.
Answer:
yes
Step-by-step explanation:
50 can be the initial money in the account and she can be depositing 45 dollars every (w) weeks and it will show her (S) savings
Ill mark brainliest please answer!
Answer:
Step-by-step explanation:
You can change radicals to fractional exponents and vice versa. The 1/2 power means square root. The 1/3 power means the cubed root. etc etc
A:) [tex](81)^\frac{1}{2} =\sqrt{81} =9[/tex]
B:) [tex](125)^\frac{1}{3} =\sqrt[3]{125} =5[/tex]
C:) [tex](49)^\frac{3}{2}=\sqrt{(49)^3} =343[/tex]
D:) [tex](8)^\frac{5}{3}=\sqrt[3]{(8)^5}=32[/tex]
HELP ASAP PLEASE! GIVING AWAY 30 POINTS AND BRAINLIEST!
Answer:
DB!
Step-by-step explanation:
Question a: 3+3+2+2 = 10 dinners
Question b: 15-30 and 30-45, because most people choose that range.
Hope I helped!
Answer:
a) 10 b) 2-3 dollars
Step-by-step explanation:
a) 3+3+2+2
b) (2+2+3+3)/2 equal 2.5 mean, range between them is 2 to 3
MNOP is a trapezoid with bases MN and OP. If MN = 25 and OP = 23, what is the length of the midsegment of MNOP?
Answer:
24
Step-by-step explanation:
you can get the answer from the attachment
The midsegment of a trapezoid divides the trapezoid into equal parts.
The length of the midsegment of MNOP is 24
The lengths of the base are given as:
[tex]\mathbf{MN = 25}[/tex]
[tex]\mathbf{OP = 23}[/tex]
Let the midsegment be x.
So, we have:
[tex]\mathbf{x=\frac{1}{2}(MN + OP)}[/tex]
Substitute values for MN and OP
[tex]\mathbf{x=\frac{1}{2}(25 + 23)}[/tex]
[tex]\mathbf{x=\frac{1}{2}(48)}[/tex]
[tex]\mathbf{x=24}[/tex]
Hence, the midsegment of MNOP is 24
Read more about midsegments of trapezoids at:
https://brainly.com/question/7511906
11 + 5 + 52 x 12 – 10 =
(11 + 5) + 52 x (12 - 10) =
The Fabric storage box below is shaped like a rectangular prism how much fabric is needed to cover the exterior of the box
Answer:
2952 square centimeters are needed to cover the exterior of the box.
Step-by-step explanation:
We need to cover five external faces of the box. The surface area formula ([tex]A_{s}[/tex]), measured in square centimeters, is derived from surface area formula for parallelpiped:
[tex]A_{s} = w\cdot l + 2\cdot w\cdot h + 2\cdot l \cdot h[/tex] (1)
Where:
[tex]w[/tex] - Width, measured in centimeters.
[tex]l[/tex] - Length, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
If we know that [tex]w = 36\,cm[/tex], [tex]l = 23\,cm[/tex] and [tex]h = 18\,cm[/tex], then the outer surface area of the storage is:
[tex]A_{s} = (36\,cm)\cdot (23\,cm)+2\cdot (36\,cm)\cdot (18\,cm)+2\cdot (23\,cm)\cdot (18\,cm)[/tex]
[tex]A_{s} = 2952\,cm^{2}[/tex]
2952 square centimeters are needed to cover the exterior of the box.
A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6 days. Its average brightness is 3.5 and the brightness changes by /-0.25. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days: B(t)=4.2 +0.45sin(2pit/4.4)
A) Find the rate of change of the brightness after t days.
B) Find the rate of increase after one day.
Answer:
a) The rate of change of the brightness after t days is [tex]B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}[/tex]
b) The rate of increase after one day is of 0.0915.
Step-by-step explanation:
The brightness after t days is given by:
[tex]B(t) = 4.2 + 0.45\sin{(\frac{2\pi t}{4.4})} = 4.2 + 0.45\sin{(0.4545\pi t)}[/tex]
A) Find the rate of change of the brightness after t days.
This is [tex]B^{\prime}(t)[/tex]
The derivative of a constant is 0, the derivative of [tex]\sin{at}[/tex] is [tex]a\cos{at}[/tex]
So, in this case, we have that:
[tex]B^{\prime}(t) = 0.45*0.4545\pi\cos{(0.4545\pi t)} = 0.204525\pi\cos{(0.4545\pi t)}[/tex]
The rate of change of the brightness after t days is [tex]B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}[/tex]
B) Find the rate of increase after one day.
This is [tex]B^{\prime}(1)[/tex]. So
[tex]B^{\prime}(1) = 0.204525\pi\cos{(0.4545\pi)} = 0.0915[/tex]
The rate of increase after one day is of 0.0915.
What is the difference between 100 and 33?
Answer:
67
Step-by-step explanation:
100 - 33 = 67
The difference between 100 and 33 is 67.
The answer is 67 if you go to your calculator app and do 67+33 it equals 100
Which of the following are accurate factors of 3x2 – 75 when multiplied together? Select the two correct answers. (2 poin
03(x - 5)
(x + 5)
O (3x + 5)
(-5)
Answer:
First and last
Step-by-step explanation:
The ratio of boys to girls in Mr. Lee's Geography class is 3 to 5. If there are a total of 32 students in the class, how many of them are girls?
The area (A) of a rectangle varies jointly as the length (l) and the width (w), and whose A = 60 sq. cm when l = 4 cm and w = 3 cm. What is the area of rectangle if the length is 6 cm and whose width is 3 cm?
Answer:
The area is 90 sq. cm
Step-by-step explanation:
Given
The variation can be represented as:
[tex]A\ \alpha\ l * w[/tex]
Area = 60, when l = 4 and w = 3
Required
Find Area, when l = 6 and w = 3
Represent the variation as an equation
[tex]A = k(l * w)[/tex]
Where k is the constant of variation.
Substitute 60 for A, 4 for l and 3 for w
[tex]60 = k * (4 * 3)[/tex]
[tex]60 = k * 12[/tex]
Make k the subject
[tex]\frac{60}{12} = k[/tex]
[tex]5=k[/tex]
[tex]k=5[/tex]
To get the value of Area when l = 6 and w = 3.
Substitute 5 for k, 6 for l and 3 for w in [tex]A = k(l * w)[/tex]
[tex]A = 5 * 6 * 3[/tex]
[tex]A = 90[/tex]
The area is 90 sq. cm
2. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD and (iv) AC.
Answer:
The answer is below.
Step-by-step explanation:
A square is a quadrilateral (has four sides and four angles) in which all the sides are equal. Also all the angle of a square are equal and measure 90°. The diagonals of a square are equal.
In square ABCD:
AB = BC = CD = AC
Given that P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b.
a) In triangle ABP:
BC = AB (all sides of a triangle are equal)
BP = 1/2 (BC) = 1/2(AB) = 0.5AB
Using Pythagoras theorem:
AB² + BP² = AP²
substituting:
AB² + (0.5AB)² = a²
AB² + 0.25AB² = a²
1.25AB² = a²
AB² = a² / 1.25
AB² = 0.8a²
AB = √(0.8a²)
AB = a√0.8
b) In triangle ADQ:
AD = CD (all sides of a triangle are equal)
DQ = 1/2 (CD) = 1/2(AD) = 0.5AD
Using Pythagoras theorem:
AD² + DQ² = AQ²
substituting:
AD² + (0.5AD)² = b²
AD² + 0.25AD² = b²
1.25AD² = b²
AD² = b² / 1.25
AD² = 0.8b²
AD = √(0.8b²)
AD = b√0.8
c) In triangle ABD, Using Pythagoras theorem:
AB² + AD² = BD²
Substituting:
0.8a² + 0.8b² = BD²
But AB = AD (all sides of a triangle are equal). Hence AB = AD = 0.8a² = 0.8b²
BD = √(0.8a² + 0.8b²)
BD = √(1.6a²) 0.8a² = 0.8b²
BD = a√1.6
D) AC = AD (diagonal are equal)
AC = √(0.8a² + 0.8b²)
AC = √(1.6b²) 0.8a² = 0.8b²
AC = b√1.6