Answer:
a) 39 meters
b) t = 1.8 seconds
Step-by-step explanation:
a)
To find the starting height of the riders, we just need to use the value of t = 0 in the equation of h(t):
h(0) = -9.8*0^2 - 5*0 + 39
h(0) = 39 meters
b)
To find when the height will be equal 0, we just need to use the value of h(t) = 0 and then find the value of t:
0 = -9.8*t^2 - 5*t + 39
Delta = b^2 - 4ac = 25 + 4*39*9.8 = 1553.8
sqrt(Delta) = 39.418
t1 = (5 + 39.418)/(-2*9.8) = -2.2662 s (A negative value for the time is not suitable for the problem)
t2 = (5 - 39.418)/(-2*9.8) = 1.756 s
Rounding to nearest tenth, we have t = 1.8 s
There are ten dogs at the dog park on a busy Saturday. Two of them are Corgis. What is the probability that a randomly selected dog is a Corgi? Type your answer as a fraction in simplest form.
Answer: 1/5
Step-by-step explanation:
From the question, there are ten dogs at the dog park on a busy Saturday and two of the dogs are Corgis. The probability that a randomly selected dog is a Corgi will be the number of Corgis divided by the total number of dogs. This will be:
Probability (Corgi) = Number of Corgis/total number of dogs.
Probability (Corgi) = 2/10
= 1/5
If you are given a paper which has lines which are the length of a needle apart, and then you repeated drop that needle onto the paper, the probability that the needle with cut the line is:
Answer:
The correct option is;
[tex]\frac{1}{\pi }[/tex]
Step-by-step explanation:
Here we have that
[tex]Probability = \frac{Number \, of \, required\, outcomes}{Number \, of \, possible\ outcomes} = \frac{Dimension \, of \, the \, line}{Size \, of \, the \ needle} = \frac{l \times D}{\pi \times D \times l } = \frac{1}{\pi }[/tex]
Therefore, the probability that the needle will cut the line = 1/π.
Solve the equation.
-9x + 1 = -x + 17
X=-8
O X=-2
X = 2
X = 8
Answer:
-9x + x = 17 – 1
8x = 16
X = 16/8
X=2
Suppose that the mean time that visitors stay at a museum is 94.2 minutes with a standard deviation of 15.5 minutes. The standard error of the mean,ox, is 3.1. A random sample of 25 of the times chosen. What interval captures 68% of the means for random samples of 25 scores?
Answer:
[tex] 94.2 -0.994*3.1 = 91.1186[/tex]
[tex] 94.2 +0.994*3.1 = 97.2814[/tex]
And the 68% confidence interval is given by (91.1186, 97.2814)
Step-by-step explanation:
For this case we know that mean time that visitors stay at a museum is given by:
[tex] \bar X = 94.2 [/tex]
The standard deviation is given by:
[tex] s= 15.5[/tex]
And the standard error is given by:
[tex] SE = \frac{s}{\sqrt{n}} =3.1 [/tex]
And we want to interval captures 68% of the means for random samples of 25 scores and for this case the critical value can be founded like this using the normal standard distribution or excel:
[tex] z_{\alpha/2}= \pm 0.994[/tex]
We can find the interval like this:
[tex] \bar X \pm ME[/tex]
And replacing we got:
[tex] 94.2 -0.994*3.1 = 91.1186[/tex]
[tex] 94.2 +0.994*3.1 = 97.2814[/tex]
And the 68% confidence interval is given by (91.1186, 97.2814)
Which of the following are geometric series? 2 + 5 + 8 + 11 + 14 + 17 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 –256 + 64 – 16 + 4 – 1
Answer:
-102
Step-by-step explanation:
Answer:
1 and 4
Step-by-step explanation:
Dale can type 32 words in 8 minutes.
What is his rate in words per minute?
Answer:4 words per minute.
Step-by-step explanation:32 divided by 8 is 4.
Terry has 3 pairs of pants: black, khaki, and brown, and 4 shirts: yellow, red, blue, and white. He does not care which colors he wears together. If Terry chooses one pair of pants and one shirt at random, what is the probability that his outfit will be the black pants with the yellow shirt?
Answer:
1/12 my guy
Step-by-step explanation:
There really isn't one
Answer:
Would be 0.08333 or 1/12
Step-by-step explanation:
Trapezoid EFGH is inscribed in a circle, with [tex]EF \parallel GH[/tex]. If arc GH is 70 degrees, arc EH is x^2 - 2x degrees, and arc FG is 56 - 3x degrees, where x > 0, find arc EPF, in degrees.
Answer:
Arc EPF is 240°
Step-by-step explanation:
Since the quadrilateral, EFGH is a trapezoid and EF is parallel to GH, we have;
∠HGF + ∠GFE = 180°
∠GHE + ∠GFE = 180°
∠HGF + ∠HEF = 180°
∴∠HEF = ∠GFE
In ΔHEF and ΔGFE
∠EHF = ∠EGF (Angles subtending the same segment)
With side EF common to both triangles and ∠HEF = ∠GFE , we have;
ΔHEF ≅ ΔGFE (Angle Angle Side rule)
Hence, side FG = EH
For cyclic trapezoid side FG = EH
The base angles subtended by GH = 70
Arc EH = x² - 2·x
Arc FG = 56 - 3·x
Therefore;
70 + x² - 2·x + 56 - 3·x + arc EPF = 360 .............(1)
Also since the equation of a circle is (x-h)² + (y-k)² = r², where the center of the circle is (h, k), then as EF is a displacement of say z from GH, then arc EH = FG which gives;
x² - 2·x = 56 - 3·x
x² - 2·x - 56 + 3·x = 0
x² + x - 56 = 0
(x - 7)(x + 8) = 0
Therefore, since x > 0 we have x = 7
Plugging in the value of x into the equation (1), we have
70 + 7² - 2·7 + 56 - 3·7 + arc EPF = 360 .............(1)
70 + 70 + arc EPF = 360
arc EPF = 360 - 140 = 240°.
Mr. Stewart used a gallon of vinegar to make 15 different color egg dipping containers. He used the same amount of vinegar in each container. How much vinegar in gallons was used in each egg dye container?
Answer:
0.067 gallons ( to 2 decimal places)
Step-by-step explanation:
First, note that since the same amount of vinegar was used in each container, it means that the 1 gallon of vinegar was divided equally to the 15 containers, hence the amount of vinegar used in each dye container is calculated as follows:
total volume of vinegar = 1
number of egg dye containers = 15
if equal volume of vinegar was used in each container:
volume of vinegar in each egg dye container = 1 ÷ 15 = 0.067 gallons ( to 2 decimal places)
I NEED HELP NOWwwwwwww
Answer:
523 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
V = 4/3 (3.14) (5)^3
V = 523.33333
Rounding to the nearest whole number
V = 523
A circle is shown. 4 radii are drawn. Chords are drawn to connect the radii points on the circle to form 2 triangles. The triangles have base lengths of 6 centimeters and the other 2 sides have lengths of 5 centimeters. The distance between the base of the triangle to the outline of the circle is 1 centimeter. Everything around the triangles is shaded. What is the area of the shaded region? (25π – 48) cm2 (25π – 30) cm2 (25π – 24) cm2 (25π – 12) cm2
Answer:
Area of Shaded Region = (25π - 24) cm²
Step-by-step explanation:
See attachment
From the attached, the following observations are made;
Radius, r = 5cm
Base of triangles = 6cm.
Required
Area of shaded region.
If the distance between the base of the triangle to the outline of the circle is 1cm then the height of the triangle is 1cm less than the radius
Height = 5cm - 1cm
Height = 4cm
To calculate the area of the shaded region, we first calculate the area of the circle.
Area = πr²
Substitute 5 for r
Area = π * 5²
Area = π * 25
Area = 25π cm²
Then we calculate the area of both triangles
Area of 1 triangle is calculated as follows.
Area = ½ * base * height
Substitute 4 for height and 6 for base.
Area = ½ * 4 * 6
Area = 2 * 6
Area = 12cm²
Since both triangles are equal.
Area of two triangles = 2 * Area of 1 triangle
Area = 2 * 12cm²
Area = 24cm²
Having calculated the area of the circle and that of both triangles.
Area of shaded region = Area of Circle - Area of Triangles
Area of Shaded Region = 25π cm² - 24 cm²
Area of Shaded Region = (25π - 24) cm²
Answer:
The third one
Step-by-step explanation:
The total time T (in hours) needed to fly from New York to Los Angeles and back can be
modeled by the equation below, where d is the distance (in miles) each way, a is the average
speed (in miles per hour), and j is the average speed (in miles per hour) of the jet stream.
Simplify the equation. Then find the total time to the nearest minute it takes to fly 2468 miles
when a = 512 miles per hour and j = 103 miles per hour.
Answer:
complicated process just think and do the math If I was helpful pls be thnked
Step-by-step explanation:
what is the length of a diagonal of a cube with a side length of 1 cm?
Answer:
sqrt3 or about 1.7
Step-by-step explanation:
length^2 + Width^2 + Height^2 = Diagonal^2
so 1 + 1 + 1 = 3, which when square rooted equals
sqrt3 or about 1.7
Answer:
b
Step-by-step explanation:
edg
Sue invested $1,000 at an interest rate of 4% compounded semiannually. How much money
would she have in 3 years?
Answer:
She would have $1,126.16 in 3 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question:
Invested 1000, which means that [tex]P = 1000[/tex].
Interest of 4%, so [tex]r = 0.04[/tex]
Semianually is twice a year, so [tex]n = 2[/tex]
How much money would she have in 3 years?
This is A(3).
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(3) = 1000(1 + \frac{0.04}{2})^{6} = 1,126.16[/tex]
She would have $1,126.16 in 3 years.
maya was asked whether the following equation is an identity (2x+3)(x+1) = 2(x+1)^2 + (x+1)
Answer:
Maya is correct.
Step-by-step explanation:
Khan Academy gave me the answer.
A road bike has a wheel diameter of 622 mm. What is the circumference of the wheel? Use 3.14 for Pi.
976.24 mm
976.54 mm
1,852.08 mm
1,953.08 mm
Answer:
4th option: 1953.08 mm
Step-by-step explanation:
circumference of circle= [tex]\pi d[/tex]
Thus, circumference of wheel
[tex] = 3.14(622) \\ = 1953.08mm[/tex]
Answer:
D.
Step-by-step explanation:
can someone please help me ill give a brainliest
Answer:
C
Step-by-step explanation:
-
Answer:
yes
Step-by-step explanation:
Use the graph of the function y = (x + 3)(x - 2) to find the
solutions of the quadratic equation 0 = (x + 3)(x - 2).
The solutions of the quadratic equation 0 = (x + 3)(x - 2) are
-6 and 0.
4 and 3.
-3 and 2
-2 and 1.
Answer:
Third option (-3 and 2)
Step-by-step explanation:
You do not need graphs for this necessarily. you just have to build two equations:
0=x+3
0=x-2
if you solve them, the results are:
-3 = x
2 = x
Answer:
option 3 is correct that is (-3,2) is the solution.
Step-by-step explanation:
-2 x (-7) =
24 divided by (-3) =
Answer:
1) 14
2) -8
Step-by-step explanation:
-2 × (-7) = 14
24 ÷ (-3) = -8
What is the error in the flow chart
there is no flow chart
Answer:
WHAT FLOWCHART?
Step-by-step explanation:
I need help very urgent
Remember: volume=length x width x height
So i think its 15, 15, and neither of them have greater volume.
Find and interpret the mean absolute deviation of the data. round your answer to the nearest tenth if necessary.
_______________
| 60 | 105 | 80 | 125 |
| 140 | 95 | 65 | 170 |
----------------------------
please help i have asked this questions 3 times and people keep being like " sorry i need these." or " thx for the points!!!" so please help i don't understand this.
The mean absolute deviation of the data is 30.
Given data:
To find the mean absolute deviation (MAD) of the given data, we need to follow these steps:
Calculate the mean (average) of the data set.
Find the absolute difference between each data point and the mean.
Calculate the mean of these absolute differences.
Given data set: 60, 105, 80, 125, 140, 95, 65, 170
Step 1:
Calculate the mean
Mean = (60 + 105 + 80 + 125 + 140 + 95 + 65 + 170) / 8
Mean = 840 / 8
Mean = 105
Step 2:
Find the absolute difference between each data point and the mean
|60 - 105| = 45
|105 - 105| = 0
|80 - 105| = 25
|125 - 105| = 20
|140 - 105| = 35
|95 - 105| = 10
|65 - 105| = 40
|170 - 105| = 65
Step 3:
Calculate the mean of the absolute differences
MAD = (45 + 0 + 25 + 20 + 35 + 10 + 40 + 65) / 8
MAD = 240 / 8
MAD = 30
The mean absolute deviation of the given data set is 30.
Interpretation:
The mean absolute deviation represents the average amount by which each data point deviates from the mean. In this case, the MAD of 30 indicates that, on average, the data points in the set deviate from the mean by approximately 30 units.
To learn more about mean absolute deviation, refer:
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You start a chain email and send it to 3 friends. The process continues and each of your friends forward the email to 3 other people. What is an expression for the nth term an?
Answer:
[tex]a_{n}=3^{n}[/tex]
Step-by-step explanation:
We can start solving this problem by making a list of the number of chain emails that are sent on each round:
Round one:
[tex]a_{1}=3[/tex]
which represents the three friends you send the mail to.
Round two:
[tex]a_{2}=3*3=9[/tex]
since each of your friends sends the mail to another three friends, then we multiply the original 3 friends by 3 to get a total of 9.
Round three:
[tex]a_{3}=3*3*3=9*3=27[/tex]
on the next round we multiply the previous 9 persons by 3 mails each giving us a total of 27 persons receiving the mail. A patter starts showing here. Notice that for each round we need to take the previous round number an multiply it by 3. When we have a number being multiplied by itself n times, we rewrite it as a power, so the expression for the nth term will be:
[tex]a_{n}=3^{n}[/tex]
which is our final answer.
how do u do this pls help me understand
Answer:
10.8
Step-by-step explanation:
5 times what gives 6? 5 times 1.2
So now you just do 9 times 1.2 which is 10.8
Answer:
10.8
Step-by-step explanation:
5*x=6
5*1.2=6
9*1.2=r
r=10.8
when nathan was 2 1/2 years old, he was 34 inches tall. the doctor told his mother that he will be two times and 4 inches taller than that when he is an adult. which of the following equation will give h, nathans height, as an adult
Answer 5 ft 4 in
Step-by-step explanation:
2 1/2 + 2 1/2=5 + 4 inches
A savings account balance is compounded continuously.If the interest rate is 3.1% per year and the current balance is 1077.00 in how many years will the balance reach 1486.73?
Answer:13.8 is the best answer i could get
Step-by-step explanation:1,077 multiply that × 13.8 =14,862
Since the area of the circle is StartFraction pi Over 4 EndFraction the area of the square, the volume of the cylinder equals
StartFraction pi Over 2 EndFraction the volume of the prism or StartFraction pi Over 2 EndFraction(2r)(h) or πrh.
StartFraction pi Over 2 EndFraction the volume of the prism or StartFraction pi Over 2 EndFraction(4r2)(h) or 2πrh.
StartFraction pi Over 4 EndFraction the volume of the prism or StartFraction pi Over 4 EndFraction(2r)(h) or StartFraction pi Over 4 EndFractionr2h.
StartFraction pi Over 4 EndFraction the volume of the prism or StartFraction pi Over 4 EndFraction(4r2)(h) or Pir2h.
Answer:
StartFraction 2 Over h EndFraction = StartFraction 3 Over m EndFraction
StartFraction 2 Over n EndFraction = StartFraction 3 Over h EndFraction
StartFraction 2 Over h EndFraction = StartFraction h Over n EndFraction
Startfraction 2 Over h EndFraction = StartFraction h Over 3 EndFraction
Step-by-step explanation:
Answer:
It's D
Step-by-step explanation:
Sumara Kato's savings account has a balance of $1663. After 19 years, how much interest
will she have earned if her rate is 5.5% compounded annually?
(1) $3159.70 (2) $2936.27 (3) $2942.27
(4) $2925.27
Answer: $2936.27
Step-by-step explanation:
Present value = $1663
Rate = 5.5%
Time(n) = 19years
Future value= PV(1+r)^n
= 1663(1+5.5%)^19
= 1663(1.055)^19
=1663 × 2.766
=4599.86
Interest = Future value - Present value
= $4599 - $1663
= 2936
Factor the expression 2x4y – 18x2y3 completely.
A. 2x2y(x2 – 9y2)
B. 2x2y(x – 3y)(x + 3y)
C. 2x2y(x – 3y)2
D. 2x2y(x – 9y)(x + 2y)
Answer:
B
Step-by-step explanation:
[tex]2x^{4}y - 18x^{2}y^{3}[/tex]
Both sides have [tex]x^{2}[/tex]
[tex]x^{2} (2x^{2}y - 18y^{3})[/tex]
Both sides have y
[tex]yx^{2} (2x^{2} - 18y^{2})[/tex]
Both sides have 2
[tex]2yx^{2} (x^{2} - 9y^{2})[/tex]
Rule : [tex]x^{2} - y^{2} = (x+y)(x -y)[/tex][tex]x^{2} = x.x\\9y^{2} = 3y. 3y[/tex]
[tex](x^{2} - 9y^{2}) = (x +3y) (x-3y)[/tex]
Final:
[tex]\red{ 2 {x}^{2} y(x - 3y)(x + 3y)}[/tex]
Hope this helps ^-^
The factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.
What is Factorization?The act of expressing a number or other mathematical object as the sum of numerous factors is known as factorization.
The given expression is 2x⁴y-18x²y³.
Factor the expression as follows:
2x⁴y-18x²y³
= 2x²y(x² - 9y²)
= 2x²y(x² - (3y)²)
= 2x²y(x + 3y)(x- 3y)
Hence, the factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.
Learn more about factorization:
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solve system of linear equations by substitution -2x+9y=15
x+7=4
Answer:
1
Step-by-step explanation:
-2x+9y=15
x+7=4
Solve for X.
x +7=4
-7. -7
x = -3
Plug in X into the first equation
-2(-3) + 9y = 15
6 + 9y = 15
-6. -6
9y = 9
Divide by 9 on both sides
9/9=1
Answer:
x = -3. | y = 1. | (-3,1)
Step-by-step explanation:
-2x+9y=15
x+7=4
-7. -7
x= -3
-2(-3) + 9y =15
6 + 9y= 15
-6. -6
9y = 9
÷9. ÷9
y = 1
