Answer:
[tex]\large \boxed{\text{5.29 s}}[/tex]
Step-by-step explanation:
The appropriate free fall equation is
y = v₀t + ½gt²
Data:
v₀ = 0
g = 32.17 ft·s⁻²
Calculation:
[tex]\begin{array}{rcl}450 &=& v_{0}t + \dfrac{1}{2}gt^{2}\\\\& = & 0 \times t + \dfrac{1}{2}\times 32.17t^{2}\\\\& = & 16.08t^2\\t^{2}& = & \dfrac{450}{16.08}\\\\& = & 27.97\\t & = & \textbf{5.29 s}\\\end{array}\\\text{It took $\large \boxed{\textbf{5.29 s}}$ for the phone to reach the ground.}[/tex]
PLLZZZZ help me find x you are AWSOME!! I need this ASAP
Answer:
27°
Step-by-step explanation:
D is 72° because it alternates with B, alternate angles are equal.
2x+72°+2x= 180° because it is a straight line.
4x+72°=180°
4x=108°
x=27°
Good answer fast Find the value of y
Answer: y = 90°
Step-by-step explanation:
55.30786941 = sin-1 (148/180) round to 55.3° angle x
34.69213059 = cos-1 (148/180) . round to 34.7° "angle z" at right
34.7 +55.3 = 90
Sum of All angles of the triangle = 180° 180 -90 = 90
If angle x is 55.7 and angle z is 34.7° Angle y must be 90°
Ratio of inscribed arcs = ratio of chord to diameter
what percentage of 40 is 8?
(A) 5%
(B) 20%
(C) 32%
(D) 150%
Answer:
20%
Step-by-step explanation:
When you divide 40 by 8, you get 0.2. To convert a decimal into a percent, you multiply by 100 to get 20.
Hence,
8 is 20% of 40.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
The answer is option B.
Step-by-step explanation:
Let the percentage be x
We have
[tex] \frac{x}{100} \times 40 = 8 \\ \\ \frac{4}{10} x = 8 \\ \\ 4x = 80 \\ \\ x = \frac{80}{4} \\ \\ x = 20[/tex]
Hope this helps you
Translate into a variable expression the product of p and the sum of p and 12
They're making me write something here so I can post the answer:
p(p + 12)
The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time. When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year. By how much does the machine depreciate during the fifth year
Answer: The machine depreciates during the fifth year by $4000.
Step-by-step explanation:
Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.
When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.
Then, the machine depreciates A(x) during the fifth year as
[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]
Hence, the machine depreciates during the fifth year by $4000.
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation
Answer:
15
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
30 hcchxfifififififfud7dd7d
Hi Folks, l have this Rearranging difficult formulae exercise, l have the answer but l dont understand at all the procedure, the method applied, if someone can explain it to me please will be appreciatted thanks 1/a = 1/b+1/c the procedure is: 1= a/b + a/c (x a) b= a+ ab/c (x b) bc= ac +ab ( x c) b (c-a) = ac b= ac/c-a OR b= - ac /a - c Def l dont understand the method thanks for your help
Step-by-step explanation:
1/a = 1/b + 1/c
Multiply both sides by a.
1 = a/b + a/c
Multiply both sides by b.
b = a + ab/c
Multiply both sides by c.
bc = ac + ab
Subtract ab from both sides.
bc − ab = ac
Factor b.
b (c − a) = ac
Divide both sides by c − a.
b = ac / (c − a)
Answer:
see below
Step-by-step explanation:
1/a = 1/b+1/c
Multiply each side of the equation by a
a( 1/a) =a( 1/b+1/c)
1 = a/b + a/c
Then multiply each side of the equation by b
b*1 =b( a/b + a/c)
b = a + ab/c
Then multiply each side of the equation by c
cb = c( a+ ab/c)
bc = ac + ab
We have gotten rid of the fractions
Now we can solve for a
Factor out a on the right side
bc = a( c+b)
Then divide by c+b on each side
bc / ( c+b) = a ( c+b) / ( c+b)
bc / ( c+b) = a
Now we can solve for b
bc = ac + ab
Subtract ab from each side
bc -ab = ac + ab-ab
bc -ab = ac
Factor out b on the left side side
b( c-a) = ac
Then divide by c-a on each side
b( c-a) / ( c-a) = ac / ( c-a)
b = ac/ ( c-a)
We can factor out -1
b = -ac/( a-c)
How many different lists containing the numbers 1, 4, 5, 8, 17, 21, and nothing else are there in which each odd integer appears before any even integer?
Answer:
4! * 2! = 48
Step-by-step explanation:
In general you have 6 elements so there are 6! = 6*5*4*3*2*1 lists in total, now, you have to think about the second condition, an odd integer has to appear before any even integer. Therefore odd integers go first, and since there are 4 odd integers, there are 4! possible lists, and since there are two even integers there are 2! lists, so in total you have 4! * 2! lists
Determine the margin of error in estimating the population mean, μ . A sample of 74 college students yields a mean annual income of Assuming that , find the margin of error in estimating μ at the 99% level of confidence.
Answer:
$253
Step-by-step explanation:
Margin of error is the critical value times the standard error.
MoE = z × σ/√n
At 99% confidence, z = 2.576.
MoE = 2.576 × 844/√74
MoE = 253
Create a circle such that its center is point a and b is a point on the circle
Step-by-step explanation:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
Answer:
i think that this question is wrong
Step-by-step explanation:
need some help thxx ;)
Answer:
DEA
Step-by-step explanation:
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced?
Answer:
The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.
The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common
difference between them
Answer:
(a)11
(b)12
Step-by-step explanation:
The first term, a = 1
The last term, l=121
Sum of the series, [tex]S_n=671[/tex]
Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:
[tex]S_n=\dfrac{n}{2}(a+l)[/tex]
Substituting the given values, we have:
[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]
(a)There are 11 terms in the arithmetic progression.
(b)We know that the 11th term is 121
The nth term of an arithmetic progression is derived using the formula:
[tex]a_n=a+(n-1)d[/tex]
[tex]a_{11}=121\\a=1\\n=11[/tex]
Therefore:
121=1+(11-1)d
121-1=10d
120=10d
d=12
The common difference between them is 12.
Which table represents the inverse of the function defined above?
Hello!
Answer:
Table B.
Step-by-step explanation:
An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:
We can use points on the table:
[tex]f(x)[/tex] = (7, 21)
The inverse of this function would 7 as its y value, and 21 as its x value:
[tex]f^{-1} (x)[/tex] = (21, 7)
The only table shown that correctly shows this relationship is table B.
Use the line of best fit to determine the x-value when the y- value is 190
Answer:
A. 9
Step-by-step explanation:
Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.
Thus,
A.9 is the correct answer.
Hope this helps :)
Answer:
A. 9
Step-by-step explanation:
A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.
Use Bayes' theorem to find the indicated probability 5.8% of a population is infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
a. 0.905
b. 0.585
c. 0.038
d. 0.475
Answer:
b. 0.585
Step-by-step explanation:
According to Bayes' theorem:
[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]
Let A = Person is infected, and B = Person tested positive. Then:
P(B|A) = 93.9%
P(A) = 5.8%
P(B) = P(infected and positive) + P(not infected and positive)
[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]
Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:
[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]
The probability is 0.585.
A set of raw paired sample data is given below. Convert this raw data into paired ranks, and calculate the value of the rs test statistic for this data. a. 0.647 b. 0.652 c. 0.955 d. 0.921
here is the data set for the complete question
x: 18 21 19 21 20 21
y; 2 14 5 6 18 18
Answer:
B. 0.652
Step-by-step explanation:
x y rank of x rank of y d d²
18 2 1 1 0 0
21 14 4 4 0 0
19 5 2 2 0 0
21 6 4 3 1 1
20 18 3 5.5 -2.5 6.25
21 18 4 5.5 -1.5 2.25
∑d² = 8.5
rs = 1 - 6[∑di² + ∑m(m²-1)]/n(n²-1)
= 1 - 6[8.5 +{3(3²-10/12 + 2(2² - 1)/12}]/6(6²-1)
= 1 - 0.348
= 0.652
therefore option b is the right answer.
At noon a passenger train leaves the Dupont Railway station and travels due east for 2 hours. At 12:45 pm the same day a second passenger train leaves the same railway station and travels due west for 1 hour and 15 minutes at a speed 10 kilometers per hour slower than the first passenger train. At 2pm the two trains were 215 kilometers apart. How fast had each train been traveling
Answer:
The speed of the first train is 70 km/hr
The speed of the second train is 60 km/hr
Step-by-step explanation:
For the first train:
Travel time = 2 hours
The speed = ?
we designate the speed as V
For the second train:
The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)
speed = 10 km/hr slower than that of the first train, we can then say
the speed = V - 10
The total distance traveled by both trains in the opposite direction of one another is 215 km
we can put this problem into an equation involving the distance covered by the trains.
we know that distance = speed x time
the distance traveled by the first train will be
==> 2 hrs x V = 2V
the distance traveled by the second train will be
==> 1.25 hrs x (V - 10) = 1.25(V - 10)
Equating the above distances to the total distance between the trains, we'll have
2V + 1.25(V - 10) = 215
2V + 1.25V - 12.5 = 215
3.25V = 215 + 12.5
3.25V = 227.5
V = 227.5/3.25 = 70 km/hr this is the speed of the first train
Recall that the speed of the second train is 10 km/hr slower, therefore
speed of the second train = 70 - 10 = 60 km/hr
The speed of the trains are 70km/hr and 60km/hr respectively.
The distance of the first train will be represented by: = 2 × D = 2D
The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).
Based on the information given in the question, the equation to solve the question will be:
2D + 1.25(D - 10) = 215
Collect like terms
2D + 1.25D - 12.5 = 215
3.25D = 215 + 12.5
3.25D = 227.5
D = 227.5/3.25
D = 70km/hour
The speed of the second train will be:
= 70 - 10 = 60km per hour.
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There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are there in the bookstore.
Answer:
there are 620 comic books
Step-by-step explanation:
let number of comic books be x
total books=3x+x
2480=4x
2480/4=x
620=x
Answer:
620Step-by-step explanation:
Let comic books be ' X '
Let Novels be ' 3x '
Now, finding the value of X
According to Question,
[tex]3x + x = 2480[/tex]
Collect like terms
[tex]4x = 2480[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{2480}{4} [/tex]
Calculate
[tex]x = 620[/tex]
Thus, There are 620 comic books in the book store.
Hope this helps...
Best regards!!
Someone help me please
Answer:
3
Step-by-step explanation:
If the cube has 54 stickers across its six faces, and each face has the same number of stickers, first we can find the number of stickers in each face by dividing the number of stickers by the number of faces:
[tex]stickers\ per\ face = number\ of\ stickers / number\ of\ faces[/tex]
[tex]stickers\ per\ face = 54/6 = 9[/tex]
Each face has 9 stickers.
If each row and column has the same number of stickers, we can find the numbers of rows and columns by finding the square root of the number of stickers in the face:
[tex]\ number\ of\ rows = \sqrt{9} = 3[/tex]
If we have 3 rows, and each roll has the same number of stickers, the number of stickers per row or column is:
[tex]stickers\ per\ row = stickers\ per\ face / number\ of\ rows[/tex]
[tex]stickers\ per\ row = 9/3 = 3[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the trigonometric ratios with their values based on the triangle shown in the diagram.
Answer:
A-2, B-DNE*, C-3, D-DNE, E-4, F-1
---------------------
The first attachment shows the solutions to A and C.
The second attachment shows the solutions to E and F.
There are no real number solutions to systems B and D.
_____
In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.
A.
(3-x) +12 = x^2 +x
15 = x^2 + 2x
16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root
±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A
__
B.
(x -1) -15 = x^2 +4x
-16 = x^2 +3x
-13.75 = x^2 +3x +2.25 = (x +1.5)^2
roots are complex: -1.5 ±i√13.75
__
C.
(1-2x) +5 = x^2 -3x
6 = x^2 -x
6.25 = x^2 -x + .25 = (x -.5)^2
±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C
__
remaining problems are done in a similar way.
_____
* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.
---------------------
Hope this helps!
Brainliest would be great!
---------------------
With all care,
07x12!
The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? PLEASE COMMENT, I Can't SEE ANSWERS CAUSE OF A GLITCH
Answer:
x + 1 - ( 4 / x³ + 3x² + 8 )
Step-by-step explanation:
If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.
Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is$31 . The total cost to rent 6 chairs and 5 tables is $59 . What is the cost to rent each chair and each table?
Answer:
The cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Step-by-step explanation:
Let the:
Cost to rent a chair = x
Cost to rent a table = y
We would form an algebraic equation.
The total cost to rent 2 chairs and 3 tables is $31
2x + 3y = 31 ...... Equation 1
The total cost to rent 6 chairs and 5 tables is $59
6x + 5y = 59 ......... Equation 2
We solve the above equation above using elimination method
Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2
Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1
Hence, we have:
2x + 3y = 31 ...... Equation 1 × 6
6x + 5y = 59 ......... Equation 2 × 2
12x + 18y = 186........ Equation 3
12x + 10y = 118 .…...... Equation 4
Subtracting Equation 4 from Equation 3
= 8y = 68
y = 68/8
y = 8.5
Therefore, the cost to rent a table = $8.50
Substituting 8.5 for y in Equation 1 to get the value of x
2x + 3y = 31 ...... Equation 1
2x + 3(8.5) = 31
2x = 31 - 3(8.5)
2x = 31 - 25.5
2x = 5.5
x = 5.5/2
x = 2.75
The cost to rent a chair = $2.75
Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. nequals=5353, pequals=0.30.3, and Xequals=20
Answer and Step-by-step explanation: P(X) calculated by the binomial probability formula is:
P(X) = [tex]\left[\begin{array}{ccc}n\\X\end{array}\right][/tex].[tex]p^{x}.(1-p)^{n-x}[/tex]
P(20) = [tex]\left[\begin{array}{ccc}53\\20\end{array}\right] .(0.3)^{20}.(1-0.3)^{33}[/tex]
P(20) = [tex]\frac{53!}{33!.20!}.3.5.10^{-11}.7.7.10^{-6}[/tex]
P(20) = 0.0552
To determine whether the normal distribution can be used to estimate this probability, both n.p and n.(1-p) must be greater than 5:
n . p = 53*0.3 = 15.9
n.(1-p) = 53(1-0.3) = 37.1
Since both ARE greater than 5, normal distribution can be used.
To approximate:
mean = n . p = 15.9
standard deviation = [tex]\sqrt{n.p.(1-p)}[/tex] = 3.34
Find the z-score:
z = [tex]\frac{x - mean}{sd}[/tex] = [tex]\frac{20-15.9}{3.34} = 1.23[/tex]
z-score = 0.8907
Comparing values:
0.8907 - 0.0552 = 0.8355
6. Find x. (2 pt)
48°
X
Answer:
x = 96
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
48 = 1/2 ( x)
Multiply by 2
96 = x
Answer:
[tex]\boxed{x=96}[/tex]
Step-by-step explanation:
Apply the inscribed angle theorem, where the measure of an inscribed angle is half the measure of the intercepted arc.
[tex]48=\frac{1}{2}x[/tex]
Multiply both sides by 2.
[tex]48(2)=\frac{1}{2}x(2)[/tex]
[tex]96=x[/tex]
i
dont
get
this
help
rn
Answer:
6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.
Step-by-step explanation:
Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.
There are five questions listed below. Each question includes the quantity 22. Match
the 22 in each question on the left to which part of the problem it represents on the right
-- the base, percent, or amount. Some answer options on the right will be used more
than once.
What percent of 22 is 3?
percent
22 is what percent of 164?
base
What is 4% of 22?
amount
8 is 22% of what number?
What is 5% of 22?
Using concepts of percentage,
3 is 16.63% of 22.
22 is 13.41% of 164.
0.88 is 4% of 22.
8 is 22% of 36.36.
1.1 is 5% of 22.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Let 3 be x% of 22.
[tex]=\frac{x}{100} *22 = 3\\\\=x = \frac{3*100}{22} = 13.63%[/tex]
3 is 13.63% of 22.
Let 22 be y % of 164.
[tex]=\frac{y}{100} *164 = 22\\\\=y = \frac{22*100}{164} = 13.41%[/tex]
13.41% of 164 is 22.
4% of 22 = 0.88
[tex]\frac{4}{100}*22 = 0.88[/tex]
Let 8 is 22% of z.
[tex]\frac{22}{100}*z = 8\\ \\z = \frac{8*100}{22} = 36.36[/tex]
5% of 22 = 1.1
[tex]\frac{5}{100}*22 = 1.1[/tex]
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Could anyone help me with this? T+S+U=130 T=3(U) S= T+10 U= ?? I need to decipher the value of T,S and U.
Answer:
U = 17 1/7
T = 51 3/7
S = 61 3/7
Step-by-step explanation:
Given
T+S+U=130\
T=3(U)
S= T+10 we have to find value of u
First step:
find S and T in terms of U
T is given
T = 3U
S = T +10 , using T = 3U
S = 3U+10
Using the above value in T+S+U=130
3U + 3U+10 + U = 130
=> 7U = 130-10 = 120
=> U = 120/7 = 17 1/7
T = 3U = 3*120/7 = 360/7 = 51 3/7
S = T+10 = 360/7 + 10 = (360+70)/7 = 430/7 = 61 3/7
Thus,
U = 17 1/7
T = 51 3/7
S = 61 3/7
you are given the following functions: g(x) = x^2 + 4x + 5 and h(x) = 3x - 4 What is (g+h)(x)
Answer:
g(x) = x² + 4x + 5
h(x) = 3x - 5
To find (g+h)(x) add h(x) to g(x)
That's
(g+h)(x) = x² + 4x + 5 + 3x - 4
Group like terms
(g+h)(x) = x² + 4x + 3x + 5 - 4
Simplify
We have the final answer as
(g+h)(x) = x² + 7x + 1Hope this helps you
In the diagram of RST, which term describes point U?
A.
Circumcenter
B.
Centroid
C.
Incenter
D.
Orthocenter
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.
Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.
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