Given:
A baseball player get a hit in 31% of his at-bats.
To find:
The probability that he will get a hit 5 at-bats in a row.
Solution:
Since, a baseball player get a hit in 31% of his at-bats, therefore
Probability that he get a hit = [tex]\dfrac{31}{100}[/tex]
= [tex]0.31[/tex]
Now, the probability that he will get a hit 5 at-bats in a row is
[tex]P=0.31\times 0.31\times 0.31\times 0.31\times 0.31[/tex]
[tex]P=(0.31)^5[/tex]
[tex]P=0.0028629151 [/tex]
Therefore, the required probability is [tex](0.31)^5[/tex] and it can be written as 0.0028629151 .
A donor gives $100,000 to a university, and specifies that it is to be used to give annual scholarships for the next 20 years. If the university can earn 4% interest, how much can they give in scholarships each year?
9514 1404 393
Answer:
$7,358
Step-by-step explanation:
Assuming the interest is compounded annually, the amortization formula is useful here.
A = Pr/(1 -(1+r)^-t)
A is the annual scholarship, P is the principal invested at rate r for t years.
A = $100,000(0.04)/(1 -1.04^-20) = $7,358.18
The university could give $7,358 in scholarships each year.
Aicha has 36 dress. She completes 1/2 of the dresses in 3/4 of an hour.If she continues at this rate what fraction of the dresses will she complete in one hour?
Answer:
2/3
Step-by-step explanation:
1/2 dresses = 36x1/2 = 18
18 dresses in 3/4 hr. ==> 1/4hr ==> 18/3 = 6
1hr ==> 6x4 = 24
fraction = 24/36 = 2/3
22. Find the slope and Y intercept of the line 3x+4y-9=0
hi there! here's my answer for you...
Answer:
slope:
m = -3/4
y-intercept:
y = −3x/4 + 9/4
hope this helped. have a good one!
a leaky faucet is losing water and it is filling a 5 gallon bucket every 12 hours. At the rate, how many gallons of water will the faucet leak 48 hours
Answer:
20 gallons
Step-by-step explanation:
First start off by dividing 48 by 12 to see how many times 12 goes into 48.
48 / 12 = 4
now that you know that 12 goes into 48 4 times, multiply 4 by 5 to see how many gallons the leaky faucet will fill in 48 hours.
4 x 5 = 20
therefore the answer is 20 gallons
I hope this helps ^^
A XYZ is translated left 4 units to form the image A X'Y'Z'.
What are the coordinates of the vertices of A X'Y'Z' ?
Enter your answer by filling in the boxes.
Plz Help
Answer:
y(1,6) x(-4,6) z(1,1)
Step-by-step explanation:
Answer:
X(-8,6)Y(-3,6)Z(-3,1)
Step-by-step explanation:
just moving the coordinate over to the left 4 times
Solve the inequality 8y - 3(y - 2)< 2y + 4(2y + 4) write solution in interval notation
Answer: y>-2
Step-by-step explanation:
8y-3(y-2) < 2y+4(2y+4)
8y-3y+6 < 2y+8y+16
6-16<2y+8y-8y+3y
-10<5y
y>-2
Answer:
(−∞,−2)
Step-by-step explanation:
Start by simplifying each side as much as possible by distributing and combining like terms to get
8y−3(y−2)8y−3y+65y+6>2y+4(2y+4)>2y+8y+16>10y+16
Subtract 10y from both sides to collect the variables on the left, then subtract 6 from both sides to collect all the constants on the right.
5y+65y+6−10y−5y+6−5y+6−6−5y>10y+16>10y+16−10y>16>16−6>10
Divide each side by −5 to solve for y. Since −5<0, the inequality changes direction.
−5y−5y−5y>10<10−5<−2
In interval notation, we write this as (−∞,−2).
Apples cost $0.75 per pound and bananas cost $1.05 per pound.
A baker bought a total of 12 pounds of apples and bananas for $10.20.
The system of equations {a+b=120.75a+1.05b=10.20 models this situation, where a is the number of pounds of apples, and b is the number of pounds of bananas.
How many pounds of each did the baker buy?
Suppose that $2000 is placed in a savings account at an annual rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the account to grow to $3000? Do not round any intermediate computations, and round your answer to the nearest hundredth.
If necessary, refer to the list of financial formulas.
Answer:
It will take 35.46 quarters for the account to grow to $3000.
Step-by-step explanation:
Since the annual rate is compounded quarterly, this can be calculated using the formula for calculating the future value as follows:
FV = PV * (1 + r)^n ............................ (1)
Where;
FV = future value or the amount the deposit expected to grow to = $3,000
PV = Present value or the amount place in the savings = $2,000
r = Quarterly rate = Annual rate / 4 = 4.6% / 4 = 0.046 / 4 = 0.0115
n = number of quarters it will take for the loan to grow to $3000 = ?
Substituting the values into equation (1) and solve for n, we have:
$3,000 = $2,000 * (1 + 0.0115)^n
$3,000 / $2,000 = (1.0115)^n
1.50 = (1.0115)^n
Loglinearise both sides, we have:
log(1.50) = n log(1.0115)
0.176091259055681 = n * 0.00496588710682352
n = 0.176091259055681 / 0.00496588710682352
n = 35.4601816891322
Rounding to the nearest hundredth, which also implies to rounding to 2 decimal places, we have:
n = 35.46
Since the the annual rate is compounded quarterly, it will therefore take 35.46 quarters for the account to grow to $3000.
Suppose that $2000 is placed in a savings account at an annual rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, it will take him 8.86 years for the account to grow to $3000
From the information given:
The principal amount placed in the savings account (P) = 2000The annual interest rate = 4.6%number of times interest is compounded n = 4By using the compound interest formula:
[tex]\mathbf{A = P( 1+\dfrac{r}{n})^{nt}}[/tex]
replacing the values from above, we have:
[tex]\mathbf{3000= 2000( 1+\dfrac{0.046}{4})^{4t}}[/tex]
[tex]\mathbf{\dfrac{3000}{2000}= ( 1+\dfrac{0.046}{4})^{4t}}[/tex]
[tex]\mathbf{\dfrac{3000}{2000}= ( 1+0.0115)^{4t}}[/tex]
[tex]\mathbf{\dfrac{3000}{2000}= ( 1.0115)^{4t}}[/tex]
[tex]\mathbf{log(\dfrac{3000}{2000})= 4t \times log ( 1.0115)}[/tex]
[tex]\mathbf{0.17609= 4t \times0.004966}[/tex]
[tex]\mathbf{t = \dfrac{0.17609}{4 \times 0.004966 }}[/tex]
t = 8.86 years to the nearest hundredth.
Learn more about compound interest here:
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A copy machine can print 48 copies every 4 minutes. A teacher printed 72 copies how long did it take to print
Answer:
6 minutes
Step-by-step explanation:
72-48 = 24
so 24 + 48 = 72
and 48 / 4=12
which means 12 copies per minute and 24 copies is 2 minutes
15 POINTS
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same shade of green paint?
A. 10 : 45
B. 30 : 54
C. 6 : 10
D. 27 : 15
explanation if you know how to explain
Answer:
The answer is B
Step-by-step explanation:
The problem is asking for the same ratio as 5:9
Multiply both sides by 6 to get 30:54
Can someone please answer this, I need help?
The price of a technology stock was $9.66 yesterday. Today, the price fell to $9.55. Find the percentage decrease.
Not quite sure about the answer but it seems simple. Please answer!
Answer:
Its A
Step-by-step explanation:
The local gym is charging a flat fee of $10 per month to be a member. Each time you go to the gym you are charged $3. What equation would represent
how much you paying total for the month if x is equal to the number of times you go to the gym?
These reverse processes are both part of
Answer:
you forgot the picture
Step-by-step explanation:
Please put a picture
Katie played 5 consecutive games of soccer without being taken off the field. Then, after a single game on the sidelines, she played another 7 consecutive games. What is the percent of increase in the number of consecutive games she played?
What is the decimal expansion for 14 over 33?
Hi! I believe your answer is 0.42, (simplified form of 0.42424242424) which is 14/33 (or [tex]\frac{14}{33}[/tex] ) as a decimal. I hope this helps you! Good luck and have a great day. ❤️✨
S= √3+2√3+3√3+...10√3
write S as a√3
Answer:
S = 55√3Step-by-step explanation:
S=
√3+2√3+3√3+...10√3 =√3( 1 + 2 + 3+...+ 10) =√3(1/2)(10)(10 + 1) =√3(55) =55√3S = 55√3
Answer:
s=✓3(1+2+3+...10)
s=✓3[10/2×(10+1)]
here, applying sum of 1st n natural number is n/2×(n+1)
so, s=✓3×5×11
hence, s=55✓3.
25 percent of ____ is 6
Answer:
24
Step-by-step explanation:
1/4 of x is 6 so you multiply 6 by 4
How do you do this question?
Answer:
∑ₙ₌₀°° (-3x)ⁿ / n!
R = ∞
Step-by-step explanation:
Maclaurin series is:
∑ₙ₌₀°° f⁽ⁿ⁾(0) xⁿ / n!
Find the nth derivative and evaluate at x=0:
f(x) = e⁻³ˣ
f⁽ⁿ⁾(x) = (-3)ⁿ e⁻³ˣ
f⁽ⁿ⁾(0) = (-3)ⁿ
The Maclaurin series is therefore:
∑ₙ₌₀°° (-3)ⁿ xⁿ / n!
∑ₙ₌₀°° (-3x)ⁿ / n!
Use ratio test to find the radius of convergence.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-3x)ⁿ⁺¹ / (n+1)!] / [(-3x)ⁿ / n!]│< 1
lim(n→∞)│(-3x) n! / (n+1)!│< 1
lim(n→∞)│3x / (n+1)│< 1
0 < 1
The radius of convergence is infinite.
Determine the solution set of (3x - 5)2 = 36.
{-1/3, 11/3}
{11/3}
{-6, 6}
Answer:
[tex]the \: solution \: set \:is \to \{{-6, 6} \}[/tex]
Use the distance formula to show that the two triangles on the coordinate plane are congruent
Answer:
Step-by-step explanation:
d = [tex]\sqrt{(x_{2} -x_{1} )^2 + (y_{2} - y_{1} )^2}[/tex]
A(- 5, - 2) , B( - 1, - 6) , C ( - 9, - 6)
AB = √[(- 5 + 1)² + (- 2 + 6)²] = 4√2
BC = √[(- 1 + 9)² + (- 6 + 6)²] = 8
AC = √[(- 5 + 9)² + (- 2 + 6)²] = 4√2
D(2, 2) , E(6, - 2) , F( 10, 2)
DE = √[(2 - 6)² + (2 + 2)²] = 4√2
EF = √[(6 - 10)² + (- 2 - 2)²] = 4√2
DF = √[(2 - 10)² + (2 - 2)²] = 8
ΔABC ≅ ΔEDF
The two triangles ABC and DEF are not congruent by SSS.
What is the distance formula between two points?The distance formula between two points is,
[tex]D = \sqrt{(x_2 - x_1_)^2 + (y_2 - y_1)^2[/tex].
Two triangles will be congruent by SSS is the distance of their corresponding sides are equal.
In ΔABC coordinates of A and B are (-5, - 2) and (-1, - 6).
[tex]D_{AB} = \sqrt{(- 1 + 5)^2 + (- 6 + 2)^2}[/tex].
[tex]D_{AB} = \sqrt{(4)^2 + (-4)^2[/tex].
[tex]D_{AB} = \sqrt{(16) + (16)[/tex].
[tex]D_{AB} = \sqrt{32}[/tex].
Similarly, the distance of DF in ΔDEF is [tex]\sqrt{64}[/tex].
hence AB ≠ DF so the triangles are not congruent.
learn more about the distance formula here :
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A right triangle is shown below.
What is the value of x rounded to the nearest ten, if necessary?
Answer:
hmmmmm.... i'm only in 7th grade and to be honest i don't really know but i'll try on this. am i going to be doing this this year?
So from my logic in my empty brain: 4.2?
Step-by-step explanation:
Because i flipped the pic around and so ,
First i got "x" in my brain and turned it into 9 from 8.5
then 9 divided by 8.5
wait a sec i just realized i made the most dumb mistake by dividing welp i'll just put out what i just fixed in my head and yea here ya go.
B+ for effort ?
Z- for iq?! .-.?
You finance a $500 car repair completely on credit, you will just pay the minimum payment each month for the next three months. The APR is 18.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, carry-over balance, and minimum payment required for each of the next two months, and the starting balance for month 2 in the table below.
Answer:
Determination of the Finance Charge, Carry-over balance, Minimum Payment for each of the next two months:
Finance Charge:
First month = $7.91
Second month = $7.72
Carry-over balance:
First month = $487.59
Second month = $475.50
Minimum Payment:
First month = $20.32
Second month = $19.81
Starting balance (Carry-over balance + Finance charge):
First month = $507.91
Second month = $495.31
Step-by-step explanation:
a) Data and Calculations:
Credit Finance = $500
APR = 18.99%
Minimum monthly payment = 4% of the balance
Monthly rate of interest = 0.1899/12 = 0.015825
Finance Charge:
First month = $7.91 ($500 * 0.015825)
Second month = $7.72 ($487.59 * 0.015825)
Carry-over balance:
First month = $487.59($507.91 - $20.32)
Second month = $475.50 ($495.31 - $19.81)
Minimum Payment:
First month = $20.32 ($507.91 * 4%)
Second month = $19.81 ($495.31 * 4%)
Starting balance (Carry-over balance + Finance charge):
First month = $507.91 ($500 + $7.91)
Second month = $495.31 ($487.59 + $7.72)
help please : (
convert 10.0 cm into in
Answer:
3.93700787 Inch
Step-by-step explanation:
:)
Answer:
3.93701
Step-by-step explanation:
In order to convert cm into inches you divide the cm by 2.54.
Andre looks at a box of paper clips. He says: "I think the number of paper clips in the box is less than 1,000."
Lin also looks at the box. She says: "I think the number of paper clips in the box is more than 500."
Choose an inequality to show Andre's statement, using LaTeX: p
p
p
for the number of paper clips.
Group of answer choices
p > 1000
1000 > p
Answer:
Andre says: "I think the number of paper clips in the box is less than 1000.
The equality that shows Andre's statement, or information:
p p p (for the number of clips)
So,
p>1000
1000>p
Hope that helps...
Consider the limaçon with equation r = 3 + 4cos(θ). How does the quotient of a and b relate to the existence of an inner loop?
A polar graph that is a limacon has a formula similar to [tex]r=a+bcos\theta[/tex]
Option B is correct.
A limacon has a formula similar to [tex]r=a+bcos\theta[/tex]
Case 1 . If a < b or [tex]\frac{b}{a}>1[/tex]
Then the curve is limacon with an inner loop.
Case 2. If a>b or [tex]\frac{b}{a}<1[/tex]
Then the limacon does not have an inner loop.
Here, given that, [tex]r=3+4cos\theta[/tex]
It is observed that, a < b or [tex]\frac{b}{a}>1[/tex]
Therefore, the curve is limacon with an inner loop.
Hence, option B is correct.
Learn more:
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i need help with this ^
Answer:
23
Step-by-step explanation:
17 pluse 2 is 19
180 minus 19 is 161
add all the vs you get 7
so 161 divided by 7 is 23
Answer:
Select the correct answer.
Which path describes the movement of oxygenated blood leaving the heart? Use the standard image of the heart to guide you.
A.
left atrium → left ventricle → aorta
B.
left ventricle → left atrium → pulmonary artery
C.
right atrium → right ventricle → pulmonary artery
D.
right ventricle → right atrium → aorta
Step-by-step explanation:
Mrs.Rodriquez is purchasing trophies for each child that plays little league she wants to spend no more than $7.00 per thropy
Answer:
7 trophies for $49.00
5 trophies for $30.00
-----------------------------------
Explination:
It says that she wants to pay no more than 7 dollars for each trophy she buys, which means 7 and less. So we have to multiply 7 x the number of trophies, And if it gives you the excact number or less its correct.
So we multiply
7 x 7 = 49 (The excact number, correct)
9 x 7 = 63 (The price they are selling it at is higher, incorrect)
12 x 7 = 84 (The price they are selling it at is higher, incorrect)
5 x 7 = 35 (Paying less, Correct)
3 x 7 (The price they are selling it at is higher, incorrect)
---------------------------------------------------------------------------------------
Its really easy if you put your mind into it! Goodluck <3
Consider the feasible region in the xy-plane defined by the following linear inequalities.
x≥0
y ≥0
x ≤ 10
x +y≥ 5
x + 2y ≤ 18
Part 2 Exercises:
1. Find the coordinates of the vertices of the feasible region. Clearly show how each vertex is determined and which lines form the vertex.
2. What is the maximum and the minimum value of the function Q = 60x+78y on the feasible region?
Answer:
1. (0,5), (0,9), (10,4), (10,0), (5,0)
2. [tex]Q_{max}=912[/tex]
[tex]Q_{min}=300[/tex]
Step-by-step explanation:
1.
In order to determine the coordinates of the vertices of the feasible region, we must first graph each of the inequalities. The feasible region is the region where all the inequalities cross each other. In this case it's the region shaded on the attached picture.
The first point is the intercept between the equations x=0 and x+y=5 so in order to find this first coordinate we need to substitute x=0 and solve for y.
0+y=5
y=5
(0,5)
The next point is the intercept between the equations x=0 and x+2y=18, so again, we substitute x for zero and solve for y:
0+2y=18
[tex]y=\frac{18}{2}[/tex]
y=9
(0,9)
The next coordinate is the intercept between the lines x=10 and x+2y=18, so we substitute x for 10 and solve for y:
10+2y=18
2y=18-10
2y=8
[tex]y=\frac{8}{2}[/tex]
y=4, so the oint is
(10,4)
The next point is the intercept between the lines x=10 and y=0, so the point is:
(10,0)
The final point is the intercept between the equations: y=0 and x+y=5. We substitute y for zero and solve for x:
x+0=5
x=5
so the point is:
(5,0).
2. In order to determine the maximum and minimum value of the function Q=60x+78y on the feasible region, we must evaluate it for each of the points found on part 1.
(0,5)
Q=60(0)+78(5)
Q=390
(0,9)
Q=60(0)+78(9)
Q=702
(10,4)
Q=60(10)+78(4)
Q=912
(10,0)
Q=60(10)+78(0)
Q=600
(5,0)
Q=60(5)+78(0)
Q=300
So now we compare the answers and pick the minimum and maximum results.
We get that:
[tex]Q_{max}=912[/tex]
when x=10 and y=4
and
[tex]Q_{min}=300[/tex]
When x=5 and y=0
The feasible region is the possible set of a constraint
The vertices are: [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]The maximum and the minimum values are 702 and 300, respectively.(a) The coordinates of the vertices at the feasible region
The constraints are given as:
[tex]\mathbf{x \ge 0}[/tex]
[tex]\mathbf{y \ge 0}[/tex]
[tex]\mathbf{x \le 0}[/tex]
[tex]\mathbf{x + y\ge 5}[/tex]
[tex]\mathbf{x + 2y\ge 18}[/tex]
See attachment for the graph of the constraints
From the graph, the vertices are:
[tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]
(b) The minimum and the maximum values of objective function Q
The objective function is:
[tex]\mathbf{Q=60x +78y}[/tex]
Substitute [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex] in Q
[tex]\mathbf{Q=60(0) +78(5) = 390}[/tex]
[tex]\mathbf{Q=60(0) +78(9) = 702}[/tex]
[tex]\mathbf{Q=60(5) +78(0) = 300}[/tex]
Hence, the maximum and the minimum values are 702 and 300, respectively.
Read more about feasible regions at:
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