Answer:
314.16 m
Step-by-step explanation:
The distance across the track is 100 metres. This means that the diameter is 100 m.
The track is circular, so, we need the circumference.
The circumference of a circle is given as:
C = πD
where D = diameter
Therefore, the circumference of the track is:
C = π * 100 = 314.16 m
She walked a distance of 314.16 m
Francesca has a garden at home. She has 3 rows of tomato with 8 plants . She also have 5 rows of zucchini plants with 6 plants in each row. Write a numerical expression for the total number of plants in Francesca garden
Answer:
54 plants
Step-by-step explanation:
3rows of tomatoes with 8 plants each
=3×8=24
5 rows of zucchini plants with 6 plants each
=5×6
=30
Total number of plants in Francesca garden
=24 tomatoes+30 zucchini
=54 plants
Determine the attributes of the hyperbola represented by this equation:
(y-21)^2/20^2-(x+20)^2/21^2=1
The vertices are A: (-41,21) and (1,21), B: (-20,0) and (-20,42), C: (-20,1) and (-20,41), D: (20,1) and (20,41).
The foci are A; (-50,21) and (10,21), B: (-20,-8) and (-20, 50), C: (-20,-10) and (-20,52), D; (20,-8) and (20,42)
Answer: The above answer is correct.
1. C
2. B
Step-by-step explanation: I got this right on Edmentum.
The vertices of the hyperbola will be (–20, 41) and (–20, 1). Then the correct option is C. The foci of the hyperbola will be (–20, 50) and (–20, –8). Then the correct option is B.
What is a hyperbola?The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
The equation of the hyperbola is given below.
[tex]\rm \dfrac{(y-21)^2}{20^2}-\dfrac{(x+20)^2}{21^2}=1[/tex]
The vertices (h, k + a), (h, k – a) are the two bending points of the hyperbola with center (h, k).
The center of the hyperbola will be at (-20, 21).
The value of a and b will be 20 and 21, respectively.
Then the vertices of the hyperbola will be
(–20, 21 + 20) and (–20, 21 – 20)
(–20, 41) and (–20, 1)
Then the correct option is C.
The foci (h, k + c), (h, k – c) are the two bending points of the hyperbola with center (h, k).
c² = a² + b²
c² = 20² + 21²
c = 29
Then the foci of the hyperbola will be
(–20, 21 + 29) and (–20, 21 – 29)
(–20, 50) and (–20, –8)
Then the correct option is B.
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What is the volume of the cylinder shown below?
Answer: V=1008π units³
Step-by-step explanation:
The formula for volume is [tex]V=\pi r^2h[/tex]. We can plug in our values to find volume.
[tex]V=\pi (12)^2(7)[/tex]
[tex]V=1008\pi[/tex]
write the recurring decimal 0.4 as a fraction in its simplest form.
Answer:
2/5
Step-by-step explanation:
0.4 = 4/10 which in simplest form is 2/5
Answer:
2/5
Step-by-step explanation:
A health club surveyed 175 members about which types of equipment they had used in the past month. Of the 175 members, 117 had used treadmills, 89 had used stationary bikes, and 53 had used both types of equipment. Some members had used neither type of equipment. Of the 175 members, how many had used treadmills, stationary bikes, or both?
Answer:
153 members
Step-by-step explanation:
Given;
117 had used treadmills
N(A) = 117
89 had used stationary bikes
N(B) = 89
53 had used both types of equipment
N(A∩B) = 53
The number of members that had used treadmills, stationary bikes, or both is;
N(A or B) = N(A) + N(B) - N(A∩B)
N(A or B) = 117 + 89 - 53
N(A or B) = 153
The number of members that had used treadmills, stationary bikes, or both is 153
În figura 2 este reprezentat un triunghi ABC, dreptunghic în A, cu BC=32 cm și BD=8 cm, unde AD perpendicular pe BC, D apartine de BC. Punctul M este mijlocul laturii AC.
a) Arătați că AB=16 cm.
b) Calculați aria patrulaterului ABDM.
c) Demonstrati că, dacă N este punctul de intersecție a drepturilor AB și DM, atunci segmentele MN și AC sunt concurente.
Answer:
..........................
Mastery Test
What is the y-value when x equals -16?
y = -200 - 12(x)
The average number of acres burned by forest and range fires in a county is 4,500 acres per year, with a standard deviation of 780 acres. The distribution of the number of acres burned is normal. What is the probability that between 3,000 and 4,800 acres will be burned in any given year? Round your answer to four decimal places.
Answer:
0.6206
Step-by-step explanation:
We would be using the Z score probability to answer this question
The formula to find the is given as :
is z = (x-μ)/σ,
x = observed value
μ = mean or average value
σ = Standard deviation
To find the probability that between 3,000 and 4,800 acres will be burned in any given year
Step 1
Find the probability that that between 3,000 will be burned in any given year
z = (x-μ)/σ,
x = observed value = 3000
μ = mean or average value = 4500
σ = Standard deviation = 780
z = (3000- 4500)/780
z = -1.92308
Step 2
Find the probability that that between 4,800 will be burned in any given year
z = (x-μ)/σ,
x = observed value = 4800
μ = mean or average value = 4500
σ = Standard deviation = 780
z = (4800- 4500)/780
z =0.38462
Step 3
Using the Z score normal distribution table:
= P(Z <0.38462) - P(Z < - 1.92308)
= P(-1.92308 < Z < 0.38462)
Using the Z score normal distribution table:
P(z) -1.92308 = 0.02743
P(z) 0.38462 = 0.64803
Therefore, the probability that between 3,000 and 4,800 acres will be burned in any given year
0.64803 - 0.02743
= 0.6206
Answer: 0.6225
Step-by-step explanation:
$P\left(3,000<X<4,800\right)=0.6225
The mean is μ=4500 and the standard deviation is σ=780. Because the probability between two values is to be calculated, subtract the probability of the lower value from the higher value. In this case, you have to use the NORMDIST function twice.
1. Open Excel and click on any empty cell. Click Insert function, fx.
2. Search for NORMDIST in the search for a function dialog box and click GO.
3. Make sure NORMDIST is on top in select a function. Then click OK.
4. In the function arguments of the NORMDIST function, enter 4800 for X, 4500 for mean, 780 for Standard_dev, and TRUE for Cumulative, all for the higher value of X. Thus, the answer, rounded to four decimal places, is 0.6497.
5. Click on any other empty cell. Click Insert function, fx.
6. Search for NORMDIST in the search for a function dialog box and click GO.
7. Make sure NORMDIST is on top in select a function. Then click OK.
8. In the function arguments of the NORMDIST function, enter 3000 for X, 4500 for mean, 780 for Standard_dev, and TRUE for Cumulative, all for the lower value of X. Thus, the answer, rounded to four decimal places, is 0.0272.
Now subtract: 0.6497−0.0272=0.6225. Thus, the probability that between 3,000 and 4,800 acres will be burned in any given year is 0.6225.
A tent guy line supports one of the upright tent poles. It runs from the top of the pole to a peg in the ground two and a half metres away from the base of the pole. If the guy line is 359cm long, how tall is the upright tent pole? Give your answer in centimetres correct to the nearest centimetre.
Answer:
258 cm
Step-by-step explanation:
Given:
Distance from the base of the pole to the base of a tent guy line is [tex]2\frac{1}{2}[/tex]
Length of a tent guy line is 359 cm
To find: Height of the upright tent pole
Solution:
Let AB denotes the pole and AC denotes a tent guy line.
According to Pythagoras theorem, in a right angled triangle, square of hypotenuse is equal to sum of squares of other two sides.
[tex]AC^2=AB^2+BC^2[/tex]
[tex]AC=359 cm\\AB=x\\BC=2\frac{1}{2}\,m=\frac{5}{2}\,m=\frac{5}{2}\times 100=250\,cm[/tex]
Therefore,
[tex](359)^2=x^2+(250)^2\\128881=x^2+62500\\128881-62500=x^2\\66381=x^2\\x=257.6\,cm\approx 258\,cm[/tex]
Please answer correctly !!!!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
B
Step-by-step explanation:
These lines are parallel so they have no solutions
Answer:
Infinite Solutions
Step-by-step explanation:
When graphed, the lines overlap with each other. This means that the system has an infinite number of solutions.
Simplify: (2x-3)(4x+1)
Answer:
[tex]8x^2-10x-3[/tex]
Step-by-step explanation:
[tex](2x-3)(4x+1)[/tex]
[tex]2x(4x+1)-3(4x+1)[/tex]
[tex]8x^2+2x-12x-3[/tex]
[tex]8x^2-10x-3[/tex]
5Y+8 -ly-8-8y-1"
Your answer
Answer:
[tex]-4y-1[/tex]
Step-by-step explanation:
[tex](5y+-y+-8y)+(8+-8+-1)[/tex]
[tex]-4y-1[/tex]
Answer:
5y + 8 - 1y - 8 - 8y - 1
variables = -4y
numbers = -1
-4y - 1 is the answerthe scale on the map started as 1 : 100 000 on the map jennifer estimates that the distance to her destination is 8cm if she is correct in her estimate how many kilometers is it to her destination
Answer:
8km
Step-by-step explanation:
1:100000
8 : x
x = the distance travelled in cm = 8 x 100000 = 800000cm
convert cm to km = 800000/100000 = 8km
Hope this helps.
Good Luck
Will crown brainiest the first answer
Answer:
2
Step-by-step explanation:
10a² : 5a² = 10 : 5 = 2
Two sandboxes with the same area are shown. The equation represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter. 2.72 meters 3.06 meters 9.16 meters 10.18 meters
Answer:
C
Step-by-step explanation:
9.16 meters
The length of sandbox 2 is 9.16 meters.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
Given Two sandboxes with the same area,
area of sand box 1 = 25 m²
area of sand box 2 = w(3w+1) = 25
25 = w(3w + 1)
3w² + w - 25 = 0
w = 2.7248 (round to 2.72 m)
length is (3w + 1) = 3(2.72) + 1 = 9.16 m
Hence the length is 9.16 meters.
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the complete Question is,
Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter. and area of sandbox 1 ia 25 m².
50 POINTS!! Are the sums rational or irrational?
Answer:
rational
irrational
irrational
rational
rational
irrational
Step-by-step explanation:
sqrt(16) + (-21/5) = 4 + (-21/5) = 4+(-4 1/5)= rational both can be written as fractions
pi +24 irrational pi is irrational
sqrt(8) + pi = 2 sqrt(2) + pi irrational because both are irrational
sqrt(4) +5 = 2+5 = 7 rational
sqrt(36) + cuberoot(27) =6+3 = 9 rational
3/4+ sqrt(27) = 3/4 + 3sqrt(3) = irrational sqrt(3) is irrational
Answer:
rational
irrational
irrational
rational
rational
irrational
Step-by-step explanation:
√16 = 4 is rational.
-21/5 is rational it can be expressed as a fraction.
[tex]\pi[/tex] is irrational.
√4 = 2 is rational.
5 is a rational number.
√36 = 6 is rational.
∛27 = 3 is rational.
3/4 is rational.
√27 is irrational.
Hy it
Use the work shown below to solve.
The solution is k =
À Ý
N 0
1. Identify the operation in the equation.
2. Use inverse operations to solve.
Subtraction property of equality
3/8 = k + 11
3/2 - 1 1 2 = k + 11 2 - 17
- Addition property of equality
§ + (-2) =k+ 11 + (-1)
Nola
Answer:
-4
Step-by-step explanation:
i just did it..
Answer:
The correct answer is -4
Step-by-step explanation:
I hope this helps you.
Can someone help me with my homework please!
Answer:
(-1, 4)
Step-by-step explanation:
In the figure attached,
Ordered pair representing point P is (3, 4) [parallel to y-axis]
If this point has been reflected across a line x = 1
New point after reflection across x = 1 will be,
P(3, 4) → P'(-1, 4)
Since point P and P' will be equidistant from the line (x = 1), so the x ordinate of P' will be = 3 - 4 = -1
And y-ordinates of point P' will be same as y = 4
Which graph is defined by f(x) = |x2 − x − 2|? A. graph A B. graph B C. graph C D. graph D
Answer:
Step-by-step explanation:
When the question comes with answer choices, please share them. In this case it sounds like there were four graphs from which to choose.
f(x) = |x^2 − x − 2| is always zero or greater, due to the absolute value function.
x^2 − x − 2 = 0 factors to (x - 2)(x + 1) = 0, so the zeros of f(x) are {-1, 2}.
Plot x-intercepts {-1, 2}. The axis of symmetry is the vertical line x = 1/2, which is precisely halfway between the x-intercepts. If we now choose the test number x = 0, we find the value of f(0) to be |-2}, which tells us that the y-intercept is (0, |-2|), or (0, 2), so we have a parabolic curve opening down between x = -1 and x = 2 and touching (but not crossing) the x-axis at those x-values. To the left of x = -1 the curve increases steadily from y = 0 in Quadrant II; to the right of x = 2, the curve increases steadily from y = 0 in Quadrant I.
The graph for the given function is plotted below.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=|x²-x-2|.
Graph the absolute value using the vertex and a few selected points.
Put x= -2, -1, 0 and 1 in the given function, we get
When x=0
y= |0-0-2|
y=0
When x=1
y=|1-1-2|
y=2
When x=-2
y=|4+2-2|
y=2
Now, plot points (-2, 4), (-1, 0), (0, 2) and (1, 2) on graph
Therefore, the graph for the given function is plotted below.
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Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t squared, where t is time in seconds. The height of a certain tower is 986 feet. How long would it take an object to fall to the ground from the top of the building?
Answer: t = 7.85seconds
Step-by-step explanation:
Given that :
Height of tower = 986 Feets
Function s(t) = 16t^2
To find the time t 8 in Seconds taken for an object to fall to the ground from the top of the building
16t^2 = 986
t^2 = 986/16
t ^2 = 61.625
Take the square root of both sides
t = sqrt(61.625)
t = 7.85seconds
Answer:
7.85sec
Step-by-step explanation:
Given that,
s(t)=16t squared, where t is time in seconds. The height of a certain tower is 986 feet.
s(t) = 16t²
so when s = 986feet
16t² = 986 feet
t² = 986 / 16
t² = 61.625
t = √61.625
t= 7.85 seconds
Aaron buys 2 t-shirts for $10.50 each, a 3-pack of socks for $7.95, what is the total cost of Aaron’s purchases?
Answer:
10.50+10.50+7.95=$28.95
3y+4/2-6y = -2/5
solve please help me with this answer please
Answer:
[tex]\frac{3y+4}{2-6y} = -\frac{2}{5} \\y=-8[/tex]
Answer:
y = -8
Step-by-step explanation:
Rule => [tex]\frac{x}{y} = \frac{a}{b} , x.b = y.a[/tex][tex]\frac{3y+4}{2-6y} = \frac{-2}{5}[/tex]
Rule => [tex]-\frac{x}{y} = \frac{-x}{y} = \frac{x}{-y}[/tex]5 ( 3y + 4) = -2 ( 2 - 6y)
15y + 20 = -4 + 12y
15y - 12y + 20 = -4 + 12y -12y
3y + 20 = -4
3y + 20 - 20 = -4 -20
3y = -24
y = -8
Hope this helps ^-^
simplify: x-1/5(x-1)squared
Answer:
[tex]\frac{1}{5x-5}[/tex]
Step-by-step explanation:
=> [tex]\frac{x-1}{5(x-1)^2}[/tex]
=> [tex]\frac{x-1}{5(x-1)(x-1)}[/tex]
Cancelling (x-1)
=> [tex]\frac{1}{5(x-1)}[/tex]
=> [tex]\frac{1}{5x-5}[/tex]
The simplified form of the expression (x-1)/5(x-1)² is 1/(5x-5).
The given expression is (x-1)/5(x-1)²
To simplify the expression (x-1)/5(x-1)², we can first cancel out the common factor of (x-1) in the numerator and denominator:
(x-1)/(5(x-1)²) = 1/[5(x-1)]
The expression simplifies to 1 divided by 5 times (x-1), which can be written as:
1/(5x-5)
So, the simplified form of (x-1)/[5(x-1)²] is 1/(5x-5).
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Kirby is packing granola bars for a field trip. He already packed 2 bags
with 5 granola bars in each bag. He has 10 more granola bars to pack.
How many granola bars will Kirby pack in all?
granola
bars
Answer:
i need help
Step-by-step explanation:
On a coordinate plane, a v-shaped line crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and the x-axis at (2, 0). What is the domain of the function on the graph?
Answer:
b
Step-by-step explanation:
i did the test and I got the answer right here after being corrected so yah.
Answer:
All real numbers
Step-by-step explanation:
6-x=5x+30
what is x
Answer:
x = -4
Step-by-step explanation:
6 -x = 5x + 30
6 - 30 = 5x + x
-24 = 6x
divide both sides by 6 to get x = -4
Answer:
[tex]=-4[/tex]
Step-by-step explanation:
[tex]6-x=5x+30\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\6-x-6=5x+30-6\\\mathrm{Simplify}\\-x=5x+24\\\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}\\-x-5x=5x+24-5x\\Simplify\\-6x=24\\\mathrm{Divide\:both\:sides\:by\:}-6\\\frac{-6x}{-6}=\frac{24}{-6}\\Simplify\\\frac{-6x}{-6}=\frac{24}{-6}\\\mathrm{Simplify\:}\frac{-6x}{-6}:\quad x\\\frac{-6x}{-6}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{6x}{6}\\\mathrm{Divide\:the\:numbers:}\:\frac{6}{6}=1\\=x[/tex]
[tex]\mathrm{Simplify\:}\frac{24}{-6}:\quad -4\\\frac{24}{-6}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{6}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{6}=4\\=-4\\[/tex]
Check all that apply to determine the following conversion.
4 km = ? mm
•Move the decimal place over 6 until to the right
• Move the decimal place over 6 units to the left
•Divide 4 km by 1’000’000 to calculate mm
• Multiply 4km by 1’000’000 to calculate mm
• Add 1’000’000 to calculate mm
• Move the decimal place 6 units left, then 2 units to the right
Answer:
4 km -> 400,000 mm
put a decimal point at the end of 4 and move it to the left 6 times because we know that 1 km is equal to 100,000 and it has zeros.
hence, it is proven that 4 km is equal to 4000,000.
Which equation represents the relationship between the x-values 0, 2, 4, 6, 10and the y-values 4, 16, 28, 40, 64in the table
Answer:
y = 8x +4
Step-by-step explanation:
i need the right answer to this question please and how you got it!!!
Answer:
a) 1 and 7 = congruent
b) 2 and 5 = supplementary
c) 4 and 6 = congruent
d) 3 and 8 = supplementary
Step-by-step explanation:
Congruent angles are the same, but in different forms. So they might be flipped around, but they are still the same angle and they have the same number of degrees.
Supplementary angles are 2 angles that add up to 180 degrees.
For example, you know that 2 + 3 = 180 degrees, because its sitting on a straight line, and so they are supplementary. They have been cut unevenly which makes 2>3. Same goes for all the other pairs of angles. Using this, you can determine which ones are supplementary and congruent.
So, even though they haven't given you exact values for each of the angles, just by looking at the shape, you can often tell very easily what kind they are:
*acute angles = angles that are less than 90 degrees
*obtuse angles = angles more than 90 degrees, but less than 180 degrees.
a) 1 and 7 have the same shape. Both are acute angles, just flipped upside down.
b) 2 and 5 are complementary. 5 is an acute angle, like 1 and 7. 2 is an obtuse angle, like 6 and 8. If you look at it closely, you can tell that they add up to 180 degrees.
c) 4 and 6 are congruent. They are both obtuse angles.
d) 3 and 8 are supplementary. 3 is an acute angle and 8 is obtuse.
Hope this helped : )
Please help! Correct answer only, please! Given matrix A and B both have dimensions 2 x 2 and are the inverse of one another what should be the following product? A · B A. B. C. D.
Answer:
Option B.
Step-by-step explanation:
Let the two matrix A and [tex]A^{-1}[/tex] are,
A = [tex]\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}[/tex] and [tex]A^{-1}[/tex] = [tex]\frac{1}{(-1)}[/tex][tex]\begin{bmatrix}2 &-3\\-3 & 4\end{bmatrix}[/tex]
Therefore, [tex]A^{-1}[/tex] = [tex]\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}[/tex]
Now [tex]A.A^{-1}[/tex] = [tex]\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}.\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}(-8+9) & (12-12)\\(-6+6) & (9-8)\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}[/tex]
Therefore, Option (B) will be the answer.
