Answer:
Step-by-step explanation:
Since you have this categorized under college math, I'm going to go out on a limb here and assume you're in calculus. We will solve using the position function and its first derivative (velocity) to solve. Remember that at an object's max height, the velocity is 0.
If the position function is
[tex]s(t)=-16t^2+24t+7[/tex] the first derivative, velocity, is
v(t) = -32t + 24. Set this equal to 0 to find the time when the object is at its max height:
0 = -32t + 24 and
-24 = -32t so
t = .75 seconds. Now we can plug that time into the position function to find where it is at that time. This "where" will be the max height:
s(.75) = [tex]-16(.75)^2+24(.75)+7[/tex] so
s(.75) = 16 feet
a bag contain 3 black balls and 2 white balls.
1. A ball is taken from the black and then replaced, a second is taken. what is the probabilities that.
(a) there are both black,
(b)one is black one is white,
(c) at lease one is black,
(d) at most one is one is black.
2. find out if all the balls are chosen without replacement.
please kindly solve with explanation. thank you.
Answer:
Step-by-step explanation:
Total number of balls = 3 + 2 = 5
1)
a)
[tex]Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\[/tex]
b)
[tex]Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]
c)
Probability of at least one black( means BB or BW or WB)
[tex]=\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}[/tex]
d)
Probability of at most one black ( means WW or WB or BW)
[tex]=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}[/tex]
2)
a) Probability both black without replacement
[tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]
b) Probability of one black and one white
[tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]
c) Probability of at least one black ( BB or BW or WB)
[tex]=\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}[/tex]
d) Probability of at most one black ( BW or WW or WB)
[tex]=\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}[/tex]
need help with algebra problem
Answer:
[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]
Step-by-step explanation:
Multiplication,
[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]
The polynomial 3x² + mx? - nx - 10 has a factor of (x - 1). When divided by x + 2, the remainder is 36. What are
the values of m and n?
Answer:
[tex]m = 12[/tex]
[tex]n =3[/tex]
Step-by-step explanation:
Given
[tex]P(x) = x^3 + mx^2 - nx - 10[/tex]
Required
The values of m and n
For x - 1;
we have:
[tex]x - 1 = 0[/tex]
[tex]x=1[/tex]
So:
[tex]P(1) = (1)^3 + m*(1)^2 - n*(1) - 10[/tex]
[tex]P(1) = 1 + m*1 - n*1 - 10[/tex]
[tex]P(1) = 1 + m - n - 10[/tex]
Collect like terms
[tex]P(1) = m - n + 1 - 10[/tex]
[tex]P(1) = m - n -9[/tex]
Because x - 1 divides the polynomial, then P(1) = 0;
So, we have:
[tex]m - n -9 = 0[/tex]
Add 9 to both sides
[tex]m - n = 9[/tex] --- (1)
For x + 2;
we have:
[tex]x + 2 = 0[/tex]
[tex]x = -2[/tex]
So:
[tex]P(-2) = (-2)^3 + m*(-2)^2 - n*(-2) - 10[/tex]
[tex]P(-2) = -8 + 4m + 2n - 10[/tex]
Collect like terms
[tex]P(-2) = 4m + 2n - 10 - 8[/tex]
[tex]P(-2) = 4m + 2n - 18[/tex]
x + 2 leaves a remainder of 36, means that P(-2) = 36;
So, we have:
[tex]4m + 2n - 18 = 36[/tex]
Collect like terms
[tex]4m + 2n = 36+18[/tex]
[tex]4m + 2n = 54[/tex]
Divide through by 2
[tex]2m + n=27[/tex] --- (2)
Add (1) and (2)
[tex]m + 2m - n + n = 9 +27[/tex]
[tex]3m =36[/tex]
Divide by 3
[tex]m = 12[/tex]
Substitute [tex]m = 12[/tex] in (1)
[tex]m - n =9[/tex]
Make n the subject
[tex]n = m - 9[/tex]
[tex]n = 12 - 9[/tex]
[tex]n =3[/tex]
²/₃ + ¹/₃ please answer
FINAL ANSWER:
1
Step-by-step explanation:
[tex]\frac{2}{3} +\frac{1}{3}[/tex]
the denominators are the same so all we need to do is add.
[tex]\frac{2}{3} + \frac{1}{3} =\frac{3}{3}[/tex]
[tex]\frac{3}{3} =[/tex] 1 whole
final answer: 1
hope this answer helps you :)
have a great day and may God Bless You!
Given right angle ABC, what the value of tan(A)?
5/13
12/13
12/5
13/12
need answer asap
Hi there!
[tex]\large\boxed{12/5}}[/tex]
tan (angle) = Opposite side / Adjacent side, so:
Tan (A) = opposite side / adjacent side
= 24 / 10
Simplify:
= 12 / 5
What is the inverse of function f? f(x)=10/9+11
Answer:
Option D is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = 10/9 X + 11
Let f(X) be "y".
y = (10/9) X + 11
Interchange "X" and "y".
x = (10/9) y + 11
or, 9x = 10y + 99
or, y = (9x-99)/10
Therefore, f'(X) = (9x-99)/10.
Hope it helps!
After deduction of 4 paisa in a Rupee a sum of Rs 720 is left.What was it originally?
Given:
After deduction of 4 paisa in a Rupee a sum of Rs 720 is left.
To find:
The original amount.
Solution:
We know that,
1 Rs. = 100 paisa
After deduction of 4 paisa in a Rupee, we get
[tex]100-4=96[/tex]
It means Rs. 720 is the 96% of the original amount.
Let x be the original amount.
[tex]720=\dfrac{96}{100}x[/tex]
[tex]72000=96x[/tex]
[tex]\dfrac{72000}{96}=x[/tex]
[tex]750=x[/tex]
Therefore, the original amount is Rs. 750.
If 3 3/4m of cloth was used for one suit, how many suits can be made with 30m cloth
Answer:
8 suits
Step-by-step explanation:
Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then
30 ÷ 3.75 = 8
Then 8 suits can be made from 30 m of cloth
Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.
Answer:
The sum is 2275
Step-by-step explanation:
Given
[tex]75,76,77....99,100[/tex]
Required
The sum
Using arithmetic progression, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where:
[tex]T_1 = 75[/tex] --- first term
[tex]T_n = 100[/tex] --- last term
[tex]n = T_n - T_1 + 1[/tex]
[tex]n = 100 - 75 + 1 = 26[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]
[tex]S_n = 13*175[/tex]
[tex]S_n = 2275[/tex]
AB is a diameter of Circle O. Find the measure of BCA
Answer:
∠ BCA = 90°
Step-by-step explanation:
∠ BCA is an angle in the semicircle and equals 90°
write the equation of the line shown in the graph above in slope-intercept form
Find a power series representation for the function. (Assume a>0. Give your power series representation centered at x=0 .)
f(x)=x2a7−x7
Answer:
Step-by-step explanation:
Given that:
[tex]f_x = \dfrac{x^2}{a^7-x^7}[/tex]
[tex]= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}[/tex]
[tex]= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}[/tex]
since [tex]\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)[/tex]
Then, it implies that:
[tex]\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}[/tex]
[tex]\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}[/tex]
Hello!
i need help with question 67 & 68
Answer:
67. A
68. D
Step-by-step explanation:
I don't remember exactly the explanation, but I recommend you try to learn more about number lines sometime when you aren't under stress from schoolwork, because they're pretty simple questions to answer once you get a better understanding of them!
U have to work out the value of a by the way
Answer:
Step-by-step explanation:
180-90=2b+b
90=3b
90/3=b
30=b
2b=2*30
=60
180-90=a+a
90=2a
a=90/2
a=45
the answer is 45 degrees
hope it helps!!let me know if it does
Answer:
a= 15°
Step-by-step explanation:
> use the fact that the sum of angles in a triangle is 180°
> based on the picture in the small right triangle we have b° +2b° +90° =180°
b +2b +90 =180° , combine like terms
3b +90 = 180, subtract 90 from both sides of the equation
3b = 90, divide by 3 both sides of the equation
b = 30°
> angle b has a ray that continues as a line so it makes an 180° angle and we have the acute triangle so we can write that
a + a+ (180-b) =180, substitute b
2a + 180-30 =180, subtract 180 from both sides, and add 30 to both sides
2a=30, divide by 2 both sides
a= 15°
Find the equation of the lines in problem 1 (0,0) slope =2.
Answer:
y = 2x
Step-by-step explanation:
Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,
[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]
The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)
Answer:
Area swept by the blade = 448[tex]in^{2}[/tex]
Step-by-step explanation:
The arc the wiper wipes is for 135 degrees angle.
So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.
Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.
So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]
Simplify it,
=216[tex]\pi[/tex]
Now, let's find area of sector with radius 14 inches
Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]
Simplify it
=73.5[tex]\pi[/tex]
So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]
Simplify it and use pi as 3.14.....
Area of swept =678.584 - 230.907
=447.6769
Round to nearest whole number
So, area swept by the blade = 448[tex]in^{2}[/tex]
. A small home business is set up with an investment of Birr 1,000,000 for equipment. The business manufactures a product at a cost of Birr 60 per unit. If the product sells for Birr 140, how many units must be sold before the business breaks even?
Answer:
12,500
Step-by-step explanation:
P = R-E
b.e.p : P=0
R=E
140x = 1000000 + 60 x
80x = 1000000
x=12,500
the cost of 7 shirts is $63. find the cost of 5 shirts
1. $35
2. $45
3. $52
4. $70
can anyone help with this please !!!!
Answer:
"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
Step-by-step explanation:
Let be the following system of linear equations:
[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)
[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)
[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)
1) We eliminate [tex]y[/tex] by adding (1) and (2):
[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]
[tex]6\cdot x +2\cdot z = 24[/tex] (4)
2) We eliminate [tex]y[/tex] by adding (1) and (3):
[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]
[tex]9\cdot x -4\cdot z = 36[/tex] (5)
Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
If interest is 8% and it is compounded semiannually, and after one year, the total value is $10,816, what was the original investment?
Golf Scores In a professional golf tournament the players participate in four rounds of golf and the player with the lowest score after all four rounds is the champion. How well does a player's performance in the first round of the tournament predict the final score
Answer:
Mean scores.
Step-by-step explanation:
The golf player will score in the first round, according to these scores the golf player scores can be predicted. The golf player can perform high in first round but he may score lesser in the second round due to stress or mental pressure. The scores can be predicted taking mean of the scores and adding standard deviation to it.
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
In the word PARADISE,how many pairs are there which have as many letters between them in the word as in the alphabet?
Answer:
three
P A R
A R A D
A D I S E
P Q R
A B C D
A B C D E
There are three such pairs of letters.
The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test them out. A number of the club's fastest swimmers performed a 50m freestyle swim in a regular spandex bodysuit and in a Speedo Fastskin suit. The table below summarizes their times in seconds.Swimmer Spandex Speedo Fastskin1 31.1 29.12 28.9 30.43 31.4 32.04 34.9 31.75 27.7 28.26 36.7 32.97 33.3 28.68 30.8 26.2Perform a t-test for dependent means to determine if there is a difference between the regular spandex suit and the Fastskin bodysuit in terms of performance.t = _____df = _____Critical value of t = _____ (use alpha = 0.05)Would you reject the null hypothesis?
Answer:
T = 2.215
df = 7
Critical value = 2.364
Fail to reject the null
Step-by-step explanation:
Swimmer __Spandex __Speedo Fastskin__ d
1 __________31.1 _______29.1 __ 2
2_________ 28.9 ______30.4 __ -1.5
3_________ 31.4 ______ 32.0 __ - 0.6
4_________ 34.9 ______31.7 __ 3.2
5 _________27.7 ______28.2 __ - 0.5
6_________ 36.7 _____ 32.9 ___ 3.8
7 _________ 33.3 _____28.6 ___ 4.7
8_________ 30.8 _____26.2 ___ 4.6
The mean difference = Σd / n
2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6
μd = Σd / n = 15.7 / 8 = 1.9625
Sd = standard deviation of difference = 2.5065 (using calculator)
H0 : μd = 0
H1 : μd ≠ 0
The test statistic:
T = μd / (Sd/√n)
T = 1.9625 / (2.5065/√8)
T = 2.2145574
The degree of freedom, df = n - 1 = 8 - 1 = 7
Using a Pvalue calculator :
α = 0.05
Critical value, Tcritical = 2.364 (T distribution table)
Since Test statistic < Critical value
we fail to reject H0 ;
which statements are true for the functions g(x)=x^2 and h(x)=-x^2? Check all that apply
Answer:
if x=0 then they have same value
1 and 2 options are out
for x=-1
g(-1)=1
h(-1)=-1
3 is true
4th
FALSE
for all values except 0, g(x)>h(x)
correct ones are
g(x) > h(x) for x = -1.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Step-by-step explanation:
Which one is a better deal?
paying $2.88 for a 12 roll package of toilet paper
paying $1.20 for a 6 roll package of toilet paper
Answer:
paying $1.20 for a 6 roll package of toilet paper
Step-by-step explanation:
to find the answer, double 6 to equal 12 and double the price as well. therefore, it is 2.40. since 2.40 is cheaper than 2.88, it is a better deal.
What are the domain and range of the function represented by the set of
ordered pairs?
{(-16, 0), (-8, -11), (0, 12), (12,4)}
Answer:
domain:-16,-8,0,12
range:0,-11,12,14
help please i don't know how to do this
ASAP!!!!!!!!! Please show process!!! Using law of sines!!!!!!!! Thank you so much
Answer:
the answers are on the picture but the numbers may be rounded
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on an even number and a number greater than 17? (A number is even if it is divisible by 2. 0 and 00 are considered even as well.)
Answer:
the wording (punctuation) of the question can lead to different interpretations....
I assume that the question was >17 & even which is "5/19",
BUT... it can also be read as two questions
first >17 which is "10/19"
and second an even number which is "9/19"
BUT !!! I think that the question answer is 5/19
Step-by-step explanation:
Even Number = 18/38 = 9/19
greater 17 = 20/38 = 10/19
Even & greater 17 = 10/38 = 5/19
