Answers
Related Questions
What's the diameter of a cirlce eith an area of 615.75?
Answers
πr²=615.75
r²= 615.75*7/22
r=²√196 =14
diameter =2r=2*12 =28
line AB is tangent to circle O at A. The diagram is not drawn to scale.
If AO=21 and BC=14, what is AB?
Answers
BC = 14
OC = radius of the circle = AO = 21
∴ OB = OC + CB = 21 + 14 = 35
Line AB is tangent to circle O at A
∴ AB is perpendicular to AO
∴ Δ OAB is a right triangle at A
Applying Pythagorean theorem
∴ OB² = AO² + AB²
∴ AB² = OB² - AO² = 35² - 21² = 1225 - 441 = 784
∴ AB = √784 = 28
During the first part of a trip, a canoeist travels 96 miles at a certain speed. the canoeist travels 15 miles on the second part of the trip at a speed 5 mph slower. the total time for the trip is 4 hrs. what was the speed on each part of the trip?
Answers
d = r * t
First part of the trip
d = 96 miles
r = ??
t = ??
Second part of the trip
d = 15 miles
r = r - 5
t = 4 - t
Solve for r first.
96/r + 15/(r - 5) = 4 hours multiply through by r and r - 5
96(r - 5) + 15r = 4*(r - 5)(r) Remove the brackets on the left
96r - 480 + 15r = 4*r*(r - 5) Collect like terms on the left.
111r - 480 = 4r(r - 5) Remove the brackets on the right.
111r - 480 = 4r^2 - 20r Bring the left side over to the right side.
0 = 4r^2 - 20r - 111r + 480 Collect like terms.
0 = 4r^2 - 131r + 480
The only way I could do this was to use the quadratic equation.
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]
a = 4
b = - 131
c = 480
[tex]\text{x = }\dfrac{ -(-131) \pm \sqrt{(-131)^{2} - 4*4*480 } }{2*4} [/tex][tex]\text{x = }\dfrac{ 131 \pm \sqrt{(17161) - 7680 } }{8} [/tex]
[tex]\text{x = }\dfrac{ 131 \pm \sqrt{9481 } }{8} [/tex]
[tex]\text{x = }\dfrac{ 131 \pm 97.37 }{8} [/tex]
x = (131 + 97.38)/8
x = 28.55
x = (131 - 97.37)/8
x = 4.20
4.2 isn't going to work because the slower speed has to be larger than 5, otherwise you will get a negative speed (as this solution will give), so 4.20 is an extraneous solution.
r = 28.55 for the first part of the trip and
r = 23.55 for the second part of the trip.
Check.
Let's see if the times add up to 4
d/r = t
96/28.55 = 3.36
15/22.75 = 0.64
The times do = 4, so the rates are correct.
Answers
r1 = 28.55 for the 96 mile trip.
r2 = 23.55 for the 15 mile trip.
WHAT IS THE VALUE OF X
Answers
[tex]\bf \stackrel{(x+4)+1}{(x+5)}(x+4)=\stackrel{(x+1)+11}{(x+12)}(x+1)\implies x^2+9x+20=x^2+13x+12 \\\\\\ 9x+20=13x+12\implies 8=4x\implies \cfrac{8}{4}=x\implies 2=x[/tex]
Iq test scores are normally distributed with a mean of 100 and a standard deviation of 15. find the x-score that corresponds to a z-score of 2.33.
Answers
Answer: 134.95 to be exact
you multiply the zscore with the standard deviation and add the mean
The formula for calculating the z-score:
z = (x - μ) / σ
Where
μ - mean
σ = standard deviation
The x-score that corresponds to a z-score of 2.33 is 134.95.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Iq test scores are normally distributed:
Mean = 100
Standard deviation = 15
z-score = 2.33
The formula for calculating the z-score:
z = (x - μ) / σ
Where
μ - mean
σ = standard deviation
Now,
2.33 = (x - 100) / 15
Multiply 15 on both sides.
2.33 x 15 = x - 100
34.95 = x - 100
Add 100 on both sides.
34.95 + 100 = x
x = 134.95
Thus,
The x-score that corresponds to a z-score of 2.33 is 134.95.
Learn more about mean here:
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Over the past week, 34 baby boys were born at the hospital. this was 54% of all babies born. how many girls were born over the past week? (enter numeric value only. if grounding is necessary, round to the nearest whole number
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Suppose you are headed toward a plateau 70 m high. If the angle of elevation to the top of the plateau is 60 degrees, how far are you from the base of the plateau?
Answers
we know that
in the right triangle ABC
tan 60°=BC/AC----> AC=BC*tan 60°-----> AC=70*tan 60°----> AC=121.24 m
the answer is
121.24 m
To find the distance from the plateau's base, use the tangent function with the given height and angle of elevation.
Explanation:We can use trigonometry to determine the distance from the base of the plateau. The vertical height of the table (opposite side) is 70 m, and the elevation angle to the top of the plateau (theta) is 60 degrees. We can use the tangent function to find the distance (adjacent side) from the table's base: tan(theta) = opposite/contiguous. Solving for the space, we get: adjacent = contrasting/tan(theta). Plugging in the values, the distance from the plateau's base is approximately 40 m.
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Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
A. y = –x + 1
B. 3x − 4y = −4
C. 4x − 3y = −3
D. y – 2 = –(x – 4)
E. y + 2 = (x + 4)
Answers
3x − 4y = 7
-4y = -3x + 7
y = (3/4)x - 7/4
The slope of the given line is 3/4.
The slope of the parallel line is also 3/4.
Now we need the equation of the line that has slope 3/4 and passes through point (-4, -2),
We use the point-slope form of the equation of a line.
y - y1 = m(x - x1)
y - (-2) = (3/4)(x - (-4))
y + 2 = (3/4)(x + 4) <---- check option E. Is the fraction 3/4 not there?
y + 2 = (3/4)x + 3
y = (3/4)x + 1
4y = 3x + 4
3x - 4y = -4 <------ this is choice B.
What is the domain for the piece of the function represented by f(x) = x + 1?
Answers
Answer:
All real numbers
Step-by-step explanation:
The domain of the function represented by f(x) = x + 1 is the all real numbers as there is only addition involved in the function so putting any number as input will not lead the function to infinity.
I NEED UR HELP PLEASE..
Answers
If θ = 30° ; adj = 2 ; hyp = x
Then cos 30° = [tex] \frac{2}{x} [/tex]
⇒ x = [tex] \frac{1}{(cos30)(2)} [/tex]
x = 2.31
Identify the value that is NOT in the range of the piece-wise function.
A. -3
B. 1
C. 3
D. -1
Answers
Since the point (2, 1) is not shaded it is not involved in the answer
The answer is B)1
Hope this helps!
looking at the graph, none of the lines drawn on the graph are at Y= -3
(the lowest dot on the graph is -2)
Find the area of a trapezoid based on the information given below. H=4√2 b1=5√2 b2=3√2
Answers
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
We have:
[tex]b_1=5\sqrt2;\ b_2=3\sqrt2;\ h=4\sqrt2[/tex]
Substitute:
[tex]A=\dfrac{5\sqrt2+3\sqrt2}{2}\cdot4\sqrt2=\dfrac{5\sqrt2}{2}\cdot4\sqrt2=\dfrac{5\cdot4\cdot\sqrt2\cdot\sqrt2}{2}\\\\=\dfrac{20\cdot2}{2}=20[/tex]
Used: [tex]\sqrt{a}\cdot\sqrt{a}=a[/tex]
What is the name of the polygon if the sum of the measures of its interior angles is 1080°?
Answers
Answer:
Octagon
Step-by-step explanation:
It has 8 sides
All ticket for a concert are the same price.
Amy and dan pay £63 altogether for some tickets.
Amy pays 24.50 for 7 tickets.
How many tickets does Dan buy?
Answers
if Amy pays 24.50 for 7 tickets
so
cost each ticket is=24.50/7-----> £3.50
find the total number of tickets=£63/£3.50-----> 18 ticket
let
x-----> amount of tickets purchased by Dan
18=7+x -----> x=18-7-----> x=11
the answer is
11
To determine how many tickets Dan bought, we calculate the price per ticket from Amy's purchase as £3.50 each. Then we subtract Amy's payment from the total to find Dan's payment of £38.50, and finally, we divide Dan's payment by the price per ticket to find that Dan bought 11 tickets.
The question involves finding out how many tickets Dan bought for a concert, using the total amount paid by both Amy and Dan and the price Amy paid for her tickets.
First, we need to find out the price per ticket from the information provided about Amy's purchase:
Amy pays £24.50 for 7 tickets.
To find the price per ticket, we divide £24.50 by 7:
Price per ticket = £24.50 / 7 = £3.50
Next, we use the total amount paid to find out how much Dan spent:
Total amount paid by Amy and Dan = £63
Amount paid by Amy = £24.50
So, the amount paid by Dan = Total amount - Amount paid by Amy
Amount paid by Dan = £63 - £24.50 = £38.50
To find out how many tickets Dan bought, we divide the amount he paid by the price per ticket:
Number of tickets Dan bought = £38.50 / £3.50
Number of tickets Dan bought = 11 tickets
Pratap Puri rowed 14 miles down a river in 2 hours, but the return trip took him 3 and one half hours. Find the rate Pratap can row in still water and find the rate of the current. Let x equals rate Pratap can row in still water and y equals rate of the current. What is the rate that Pratap rows in still water?
Answers
speed down the river is:
speed=distance/time
speed=14/2=7 mi/h
speed up the river is:
speed=(14)/(3.5)=4 mi/hr
thus total speed downstream and upstream will be:
x+y=7...i
x-y=4.......ii
adding the above equations i and ii we get:
2x=11
x=5.5 mi/hr
thus
y=5-5.5=1.5 mi/r
thus the speed in still waters is 5.5 mi/hr
speed of current is 1.5 mi/hr
Final answer:
By establishing equations based on Pratap's rowing times upstream and downstream, we find that Pratap's rowing rate in still water is 5.5 miles per hour.
Explanation:
Finding Pratap's Rowing Rate in Still Water and the Current Rate
To calculate Pratap Puri's rowing rate in still water and the rate of the current, we need to set up two equations based on the information provided. We know that Pratap rowed 14 miles down a river in 2 hours and the return trip took 3 and a half hours.
Step-by-Step Solution
Let x be the rate at which Pratap can row in still water, and y be the rate of the current.
The downstream speed (with the current) is x + y, and the upstream speed (against the current) is x - y.
Using the formula distance = rate × time, for the downstream trip we have 14 = (x + y) × 2, and for the upstream trip 14 = (x - y) × 3.5.
Simplifying both equations gives us: 7 = x + y and 4 = x - y.
To find x, add the two equations to eliminate y, yielding 11 = 2x, or x = 5.5.
Therefore, Pratap's rowing rate in still water is 5.5 miles per hour.
Base your answer to the question on the diagrams shown below.
What is the probability of drawing a red card and then spinning a 1?
Answers
P(Red)×P(Spinning 1)
P(Red)=2/5
P(Spinning 1)=4/8=1/2
Thus:
P(Red)×P(Spinning 1)=1/2×2/5=1/5
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
From the given picture, the total number of cards = 5
The number of red card = 2
Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]
Also, total number of digits on spinner = 8
Number of 1's=4
Thus, the probability of spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]
Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]
Would someone Please answer this question please will be thanked and also will pick brainly!! (please be honest)
Answers
How many ears of corn would equal to 5 pounds?
Answers
Suppose that the measure of the minor arc BD is 172°. Find m BCD. (I need help on all questions in picture)
Answers
the circle is 360 and BD+BCD=360
so BCD=360-172=188
10 - 3(3x - 40) = -9x A)x = -9 B)no solution C)x = 10 D)all real numbers
Answers
10 - 9x + 120 = - 9x You get a bizarre result no matter what you try to do to resolve this. If you say any number will do pick, a number at random for x. Say 10
10 - 90 + 120 = -90 Is this statement true? No. You only need 1 exception but 0 is a popular number to look for answers. Will it work?
10 - 0 + 120 = 0 That doesn't work either.
There is no number you could pick that that would give you anything but 10 + 120 = 0
B <<<<<< No Solution
The matrix below represents the number of minutes four friends spend driving to each others’ homes each week. A row label represents the friend driving and a column label represents the friend being visited.
Answers
Answer:
D - 45
Explanation:
Hope you have a great day!
Yo!!!NEED HELP!!!!WILL GIVE BRAIN!!!!!!!
Answers
Next, we are going to find the possible degree of our function. Remember that the possible degree of a function is the number of x-intercepts.
We can infer from our graph that the function intercepts the x-axis at least 6 times.
We can conclude that the correct answer is: even degrees of 6 or greater.
There was a sample of 200 milligrams of a radioactive substance to start a study. since then, the sample has decayed by 5.4% each year. let t be the number of years since the start of the study. let y be the mass of the sample in milligrams. write an exponential function showing the relationship between y and t .
Answers
y = A * (b) ^ t
Where,
A: initial amount
b: decrease rate
t: time
Substituting values we have:
y = 200 * (0.946) ^ t
Answer:
An exponential function showing the relationship between and and is:
y = 200 * (0.946) ^ t
The exponential function representing the relationship between the mass y of a radioactive sample in milligrams and t years since the start of the study is y = 200(1 - 0.054)^t.
The student is given a starting mass of a radioactive substance and the percentage of the mass that decays each year. To write an exponential function that models this situation, we consider the initial mass, which is 200 milligrams, and the decay rate, which is 5.4% per year. The relationship between the mass y and the time t in years can be represented by the formula y = 200(1 - 0.054)^t.
Using an exponential decay model, we understand that the amount of substance decreases by a certain percentage each year. To account for this, we raise the base (1 - 0.054) to the power of t, representing the number of years, which gives us the factor by which the original mass has reduced.
PLEASE PLEASE HELP ME WITH THESE!!!!
I REALLY NEED HELP AND I WILL AWARD BRAINLIEST FOR WHO IS CORRECT!!!
1. The table below shows the number of cameras sold in each month at the camera shop.
January: 35 cameras were sold
Feb. 21 cameras were sold
Mar. 35 were sold.
April: 55 were sold
May: 73 were sold
Jun. 82 sold
Jul. 85 were sold
Aug. 64 cameras were sold
Sep. 52 sold
Oct. 42 were sold
Nov. 89 were sold
Dec. 125 cameras sold
Use the set of data to answer the question.
The camera shop wants to use the measure of central tendency that expresses how successful they are in selling cameras. Which measure of central tendency should they choose?
A. Mean
B. Interquartile
C. Mode
D. Median
PLEASE HELP PLEASE AND THANK YOU!!!
Answers
Drew ran 5 3/ 8 miles yesterday. Collin ran 8 5/12 miles yesterday. How much farther did Collin run? Choose the correct values to leave your answer as a mixed number. Numbers may be used once or not at all.
Answers
Answer:
The correct answer is 3 1/24
Step-by-step explanation:
because I did all the math
Answer:
3 1/24
Step-by-step explanation:
50 points to answer this for me
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points)
Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points)
Answers
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8-x^-1 intersect are the solutions of the equation 4−x = 8-x^-1.
Part B: Make tables to find the solution to 4−x = 8-x^-1. Take the integer values of x between −3 and 3.
Part C: How can you solve the equation 4−x = 8-x^-1 graphically?
Part A. We have two equations: y = 4-x and y = 8-x^-1
Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when
4-x = 8-x^-1
This is where the two graphs will cross and that is the common point that satisfies both equations.
Part B
see the attached table
the table shows that one of the solutions is in the interval [-1,1]
Part C To solve graphically the equation 4-x = 8-x^-1
We would graph both equations: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
using a graph tool
see the attached figure N 2
the solutions are the points
(-4.24,8.24)
(0.24,3.76)
Part A. We have two equations: y = 4-x and y = 8-x^-1
Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when
4-x = 8-x^-1
This is where the two graphs will cross and that is the common point that satisfies both equations.
Part B
see the attached table
the table shows that one of the solutions is in the interval [-1,1]
Part C To solve graphically the equation 4-x = 8-x^-1
We would graph both equations: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
using a graph tool
see the attached figure N 2
the solutions are the points
(-4.24,8.24) (0.24,3.76)
Write (3n)^3 without exponents
Answers
= (3n)×(3n)×(3n)
= 27 × n × n × n
Answer:
Without exponents, we can write the term as: [tex]27(n)(n)(n)[/tex]
Step-by-step explanation:
The given term is :
[tex](3n)^{3}[/tex]
This can be written as:
[tex](3n)(3n)(3n)[/tex]
= [tex]27n^{3}[/tex]
= [tex]27(n)(n)(n)[/tex]
Hence, without exponents, we can write the term as: [tex]27(n)(n)(n)[/tex]
Whats the distance between points C(0, 4), T(-6, -3)
a √(37)
b √(85)
c √(109)
Answers
[tex]\text{We have:}\\C(0;\ 4);\ T(-6;-3)\\\\\text{substitute coordinates of the points to the formula:}\\\\|CT|=\sqrt{(-6-0)^2+(-3-4)^2}=\sqrt{(-6)^2+(-7)^2}=\sqrt{36+49}=\sqrt{85}[/tex]
[tex]\text{Answer:}\ b.\ \sqrt{85}[/tex]
can someone please solve 5-2x<7
Answers
5 -2x +2x < 7 +2x . . . . . . showing 2x added
5 < 7 +2x . . . . . . . . . . . .. simplified
5 -7 < 7 -7 +2x . . . . . . . . showing 7 subtracted
-2 < 2x . . . . . . . . . . . . . . . simplified
Now, divide by 2
-1 < x
The solution is -1 < x.
If the diameter of a sphere is 12cm, what is its volume to the nearest hundredth