Answer:
$ 12.16
Step-by-step explanation:
Spent = $ 37.84
Paid = $ 50
Change = $50 - $37.84
Change = $ 12.16
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!Answer:
$12.16
Step-by-step explanation:
You must subtract his total from his payment. $50-$37.84=$12.16
1. Transform the polar equation to a Cartesian (rectangular) equation: 2. Transform the Cartesian (rectangular) equation to a polar equation: y^2 = 4x
Answer:
Attachment 1 : 5x + 6y = 5, Attachment 2 : 4cotθcscθ
Step-by-step explanation:
Remember that we have three key points in solving these types of problems,
• x = r cos(θ)
• y = r sin(θ)
• x² + y² = r²
a ) For this first problem we need not apply the third equation.
( Multiply either side by 5 cos(θ) + 6 sin(θ) )
r [tex]*[/tex] ( 5 cos(θ) + 6 sin(θ) ) = 5,
( Distribute r )
5r cos(θ) + 6r sin(θ) = 5
( Substitute )
5x + 6y = 5 - the correct solution is option c
b ) We know that y² = 4x ⇒
r²sin²(θ) = 4r cos(θ),
r = 4cos(θ) / sin²(θ) = 4 cot(θ) csc(θ) = 4cotθcscθ - again the correct solution is option c
The points (0,3) and (1,12) are solutions of an exponential function. What is the equation of the exponential function?
Answer:
[tex]f(x) =3\,*\,\,4^x[/tex]
Step-by-step explanation:
to find the equation of an exponential function, just points on the function's graph are needed.
Recall that the exponential function has a general expression given by:
[tex]f(x) = a \,e^{b\,x}[/tex]
so we impose the condition for the function going through the first point (0,3) as:
[tex]f(0) = a \,e^{b\,(0)}= 3\\a\,e^0=3\\a\,(1)=3\\a = 3[/tex]
Now,knowing the parameter a, we can find the parameter b using the other point:
[tex]f(1) = 3 \,e^{b\,x}= 12\\3\,e^{b\,(1)}=12\\e^b=12/3\\e^b=4\\b=ln(4)[/tex]
Therefore, the function can be written as:
[tex]f(x) = 3 \,e^{ln(4)\,x}=3\,\,\,4^x[/tex]
Answer:
C)
h(x) = 3(4)x
HURRY WILL GIVE BRANLIEST
I believe that the answers in order are: Rational, Irrational, Irrational, Irrational. I think these answers are correct, but if not, please let me know. Thanks.
Answer:
I think 0.5 and 0/100 are rational
the others are irrational
11) Five must be the solution to 2x + 3 = 13 because 2(5) + 3 = 13.
Answer:
Yes, your right!
Order the following from least to greatest.
1/16
.0173
1/7
2.2
-0.25
Answer:
1.-0.25 2..0173 3. .1/16 4. 1/7 5.2.2
Step-by-step explanation:
You want to put all numbers in fractions to see which numbers are smallest
find the sum 7+7(2)+7(2^2)+...+7(2^9)
Answer:
7161
Step-by-step explanation:
7 + 7(2) + 7(2)² + ... + 7(2)⁹
= ∑₁¹⁰ 7(2)ⁿ⁻¹
= 7 (1 − 2¹⁰) / (1 − 2)
= 7161
Mia walks her dog twice a day. Her evening walk is two and a half times as far as her morning walk. At the end of the week she says she walked her dog 30 miles. How long is her morning walk?
9514 1404 393
Answer:
1 11/49 ≈ 1.224 miles
Step-by-step explanation:
Let m represent the length of the morning walk. Then the length of the evening walk is 2.5m, and the total each day is m+2.5m = 3.5m.
The total for 7 days is ...
7(3.5m) = 30
m = 30/24.5 = 60/49 ≈ 1.224 . . . . miles
Mia's morning walks are 1 11/49 miles, about 1.224 miles.
For a certain casino slot machine, the odds in favor of a win are given as 17 to 83. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Step-by-step explanation:
83P (E)=17-17P (E),
P (E)=17/100=0.17
When x=5 what would the value of expression
Answer:
46
Step-by-step explanation:
6 more than the product of 8 and a number x
6 more means 6+
product of 8 and a number x means 8x
6+8x
when x=5
6+8(5)=6+40=46
Solve x/5 - 1/2 = x/6 (make sure to type the number only)
X/5 -1/2 = x/6
Find the least common denominator of the 3 denominators:5,2,6
The limited is 30
Multiply all 3 fractions by 30:
6x -15 = 5x
Subtract 6x from both sides:
-15 = -x
Multiply both sides by -1:
X = 15
Derivatives concept:
Exercise "position and instantaneous velocity"
(Full development)
(A) The blue line has a slope of 5/2, red has slope 4/4 = 1, and purple has slope 3/9 = 1/3.
To find the slope, take any two points (a, b) and (c, d) on the line, then
slope = (d - b)/(c - a)
i.e. the ratio between the changes in the y and x coordinates.
(B) Each line has equation
• blue: y = 5/2 x
• red: y = x
• purple: y = 1/3 x
This follows from the general equation for a line with slope m and y-intercept b,
y = mx + b
or from the more general equation for a line with slope m passing through a point (a, b),
y - b = m (x - a)
(C) Consider the blue line. If you take units into account, its slope is
(5 units of distance)/(2 units of time) = 5/2 (units of distance/time)
which means, per unit time, some object travels a 5/2 units of distance, and this is the definition of speed.
(D) The competitor with the blue line, Mary, would win the race because their speed is the highest (5/2 > 1 > 1/3).
(E) Average velocity is defined as
v (ave) = ∆d/∆t = (change in distance)/(change in time)
At time 0, no one has moved yet. At time 4,
• Mary has covered a distance of 5/2 × 4 = 10, giving her an average velocity of (10 - 0)/(4 - 0) = 5/2
• Mike has covered a distance of 4, so his average velocity is (4 - 0)/(4 - 0) = 1
• Sam has covered a distance of 1/3 × 4 = 4/3, so his average velocity is (4/3 - 0)/(4 - 0) = 1/3
It's not a coincidence that the average velocities are the same as the slopes, because each racer travels at a constant speed.
(F) The racers' instantaneous velocities are the same as their respective average velocities, again because they are each moving at a constant speed.
IF ANYONE IS READING THIS AND IS TIRED OF BOTS, MAY I PLEASE GET SOME HELP?
You deposit $400 in an account earning 5% interest compounded annually. How much will you have in the account in 15 years?
I'm a little bit stuck.
A(t)=P(1+r)t
A = accrued amount = what you are solving for
P = principle investment = $400
r = rate of growth = 5% = 0.05
t = time = 10 years
A(10) = 400(1.05)10 (use calculator to solve)
A(10) ≈ 4,200
a number t is less than 7
Answer:
6 or 5 or 4...........
Step-by-step explanation:
Answer:
x=N :x<7
Step-by-step explanation:
123456
hope it's helpful
About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.
Answer:
a. True
b. true
c. false
d. false
e. false
Step-by-step explanation:
a. true
polutation = 25% = 0.25
sample = n= 12
n x p
= 12 x o. 25 = 3 and 3 is less than 10
12(1 - p)
= 12 x 0.75
= 9 and is less than 10
b. True
the sample distribution of the population is normal when
sample size x population > or equal to 10
40 x 0.75
= 30 and 30 is greater than 10
c. false
50 x 0.25 = 12.5
50 x 0.20 = 10
z = 10 - 12.5/sqrt(12.5)
= -2.5/3.54
= -0.70
H0: Young american family who delayed
H1: young american family who did not delay
p(z = -0.70)
0.2420>0.005
therefore we accept the null hypothesis
d. false
150 x 0.20 = 30
150 x 0.75 = 37.5
z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22
p(z = -1.22) = 0.1112 > 0.05
therefore we do not reject the null hypothesis
e. false
se1 = sqrt(p(1-p)/n
se2 = sqrt(p(1-p)/3n
se2 = 1/sqrt(3)se2
Prove that the statement (ab)^n=a^n * b^n is true using mathematical induction.
Answer:
see below
Step-by-step explanation:
(ab)^n=a^n * b^n
We need to show that it is true for n=1
assuming that it is true for n = k;
(ab)^n=a^n * b^n
( ab) ^1 = a^1 * b^1
ab = a * b
ab = ab
Then we need to show that it is true for n = ( k+1)
or (ab)^(k+1)=a^( k+1) * b^( k+1)
Starting with
(ab)^k=a^k * b^k given
Multiply each side by ab
ab * (ab)^k= ab *a^k * b^k
( ab) ^ ( k+1) = a^ ( k+1) b^ (k+1)
Therefore, the rule is true for every natural number n
Hello, n being an integer, we need to prove that one statement depending on n is true, let's note it S(n).
The mathematical induction involves two steps:
Step 1 - We need to prove S(1), meaning that the statement is true for n = 1
Step 2 - for k integer > 1, we assume S(k) and we need to prove that S(k+1) is true.
Imagine that you are a painter and you need to paint all the trees on one side of a road. You have several colours that you can use but you are asked to follow two rules:
Rule 1 - You need to paint the first tree in white.
Rule 2 - If one tree is white you have to paint the next one in white too.
What colour do you think all the trees will be painted?
Do you see why this is very important to prove the two steps as well ?
Let's do it in this example.
Step 1 - for n = 1, let's prove that S(1) is true, meaning [tex](ab)^1=a\cdot b =a^1\cdot b^1[/tex]
So the statement is true for n = 1
Step 2 - Let's assume that this is true for k, and we have to prove that this is true for k+1
So we assume S(k), meaning that [tex](ab)^k=a^k\cdot b^k[/tex]
and what about S(k+1), meaning [tex](ab)^{k+1}=a^{k+1}\cdot b^{k+1}[/tex] ?
We will use the fact that this is true for k,
[tex](ab)^{k+1}=(ab)\cdot (ab)^k =(ab) \cdot a^k \cdot b^k[/tex]
We can write it because the statement at k is true and then we can conclude.
[tex](ab)^{k+1}=(ab)\cdot (ab)^k =(ab) \cdot a^k \cdot b^k=a^{k+1}\cdot b^{k+1}[/tex]
In conclusion, we have just proved that S(n) is true for any n integer greater or equal to 1, meaning [tex](ab)^{n}=a^{n}\cdot b^{n}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Carolyn and Paul are playing a game starting with a list of the integers $1$ to $n.$ The rules of the game are: $\bullet$ Carolyn always has the first turn. $\bullet$ Carolyn and Paul alternate turns. $\bullet$ On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list. $\bullet$ On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed. $\bullet$ If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers. For example, if $n=6,$ a possible sequence of moves is shown in this chart: \begin{tabular}{|c|c|c|} \hline Player & Removed \# & \# remaining \\ \hline Carolyn & 4 & 1, 2, 3, 5, 6 \\ \hline Paul & 1, 2 & 3, 5, 6 \\ \hline Carolyn & 6 & 3, 5 \\ \hline Paul & 3 & 5 \\ \hline Carolyn & None & 5 \\ \hline Paul & 5 & None \\ \hline \end{tabular} Note that Carolyn can't remove $3$ or $5$ on her second turn, and can't remove any number on her third turn. In this example, the sum of the numbers removed by Carolyn is $4+6=10$ and the sum of the numbers removed by Paul is $1+2+3+5=11.$ Suppose that $n=6$ and Carolyn removes the integer $2$ on her first turn. Determine the sum of the numbers that Carolyn removes.
Answer:
The sum of the numbers that Carolyn removes is 5.
Step-by-step explanation:
The provided instruction for the game are:
Carolyn always has the first turn. Carolyn and Paul alternate turns.On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list.On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed.If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers.The value of n is supposed as 6.
And it is also provided that Carolyn removes the integer 2 on her first turn.
The table displaying the outcomes of the game are as follows:
Player Removed Remaining
Carolyn 2 1, 3, 4, 5, 6
Paul 1 3, 4, 5, 6
Carolyn 3 4, 5, 6
Paul 6 4, 5
Carolyn None 4, 5
Paul 4, 5 None
The sum of the numbers that Carolyn removes is:
S = 2 + 3 = 5
Thus, the sum of the numbers that Carolyn removes is 5.
I believe the answer is 8, but I am not sure.
A homeowner needs two loads of gravel for the driveway to their new house. One loads weighs 8 tons and the second load
weighs 1,200 pounds. What is the total weight of the gravel, in tons, used for the driveway?
Total weight of the gravel, in tons used for the driveway is 8.6 tons
Weight of first load = 8 tons
Weight of second load = 1200 pounds
Convert pounds to tons:
1 pound = 0.0005 ton
1200 pounds = 0.6 ton
Then,
Weight of second load = 0.6 ton
Total weight of the gravel, in tons = Weight of first load + Weight of second load
= 8 tons + 0.6 tons
= 8.6 tons
https://brainly.com/question/24370065
The perimeter of a rectangular garden is 43.8 feet. It's length is 12.4t . What is it's width ?
Answer:5
Step-by-step explanation:
1 +32-10 divided by 2
Step-by-step explanation:
1+32-10 ÷21+32-533-528Hope it is helpful to youThe value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
The numerical expression is given below.
⇒ 1 + 32 – 10 ÷ 2
According to the PEMDAS rule, the computation wrapped in quotes or the parenthesis comes first in the sequence of operation.
This rule is used to solve the equation in a proper and correct manner.
PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.
⇒ 1 + 32 – (10 ÷ 2)
Simplify the numerical expression, then the expression will be
⇒ 1 + 32 – 5
⇒ 33 – 5
⇒ 28
Then the value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Assume that adults have IQ scores that are normally distributed with a mean of and a standard deviation . Find the probability that a randomly selected adult has an IQ between 81 and 119 .
Complete Question
Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 81 and 119.
Answer:
The probability is [tex]P( x_1 < X < x_2) = 0.79474[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is σ = 15.
The mean μ= 100
The range we are considering is [tex]x_1 = 81 , \ x_2 = 119[/tex]
Now given that IQ scores are normally distributed
Then the probability that a randomly selected adult has an IQ between 81 and 119 is mathematically represented as
[tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <\frac{X - \mu }{\sigma } < \frac{x_2- \mu }{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]
So
[tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <Z < \frac{x_2- \mu }{\sigma } )[/tex]
substituting values
[tex]P( x_1 < X < x_2) = P(\frac{81 - 100 }{15 } <Z < \frac{119- 100 }{15 } )[/tex]
[tex]P( x_1 < X < x_2) = P( -1.2667 <Z <1.2667 )[/tex]
[tex]P( x_1 < X < x_2) = P(Z <1.2667 )-P( Z < -1.2667 )[/tex]
From the standardized Z table
[tex]P(Z <-1.2667 ) = 0.10263[/tex]
And [tex]P(Z <1.2667 ) = 0.89737[/tex]
So
[tex]P( x_1 < X < x_2) = 0.89737 - 0.10263[/tex]
[tex]P( x_1 < X < x_2) = 0.79474[/tex]
6x47
Which multiple of 10 is closest to 47?
Answer:
50 is your answer:)Step-by-step explanation:
Answer:
50
Step-by-step explanation:
50 is the multiple of 10 that is closest to 47.
Which are perfect squares? Check all that apply. 9 , 24 , 16 , 200 , 169 , 625
Answer:
A. 9
C. 16
E. 169
F. 625
Step-by-step explanation:
15 points PLEASE ANSWER
Answer:
D. (25π - 50) sq m
Step-by-step explanation:
Since ABCD is a square with the area of 100, we know that the dimensions are 10 by 10. With that, we can find that triangle ABC = 50 sq m because of (h*l)/2. Since A is the center of the circle that contains arc BD, we know that 10 is the radius of the quarter-circle ABC. Using (πr^2)/4 to get the area of the quarter-circle, we get that the quarter-circle ABC = 25π sq m. But the original triangle ABC in the quarter-circle is not shaded. Therefore, we subtract 50 from 25π, which leads to (25π - 50) sq m.
I hope this helped! :D
A baseball player has a batting average of 0.26. What is the probability that he has exactly 6 hits in his next 7 at bats
Answer:
0.0016
Step-by-step explanation:
Batting average, p = 0.26
n = 7
x = 6
With p = 0.26 as success rate
1-p is equal to failure rate which is = 0.74
We have to solve this by using the binomial distribution formula.
P(X= x)
= nCx * p^x * (1-p)^(n-x)
P(X = 6)
=7C6 × 0.26^6 ×(1-0.26)^(7-6)
= 7 × 0.0003089 × 0..74¹
= 0.0016
So probability that he has exactly 6 hits in his next 7 bats is equal to 0.0016.
How to calculate pvalue
Answer:
If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.
Answer:
The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test). The p-value for: a lower-tailed test is specified by: p-value = P(TS ts | H 0 is true) = cdf(ts)
Step-by-step explanation:
May this answer is helpful for you
PLEASE HELP !!! (5/5) -50 POINTS-
Answer:
at least one solution
Step-by-step explanation:
Consistent solutions have at least one solution, but may have more than one solution. Intersecting lines and Lines that are the same are consistent solutions
Answer:
[tex]\boxed{Atleast\ one \ Solution}[/tex]
Step-by-step explanation:
A consistent system of equations have at least one solution. It can be more than that. There are no compulsions.
Is 3.6 a integer or a whole number?
36 is a whole number.
Answer:
The number 3.6 is a rational number.
All numbers that can be represented as fractions made of two integers (whole numbers) are considered to be
there are 5 discs, 6 jump ropes, 3 balls, and 12 pieces of sidewalk chalk in a bin. If two items are drawn at random without replacement, what is the probability that both items removed are not jump ropes?
Answer: 0.584
Step-by-step explanation:
We have:
5 discs
6 jump ropes
3 balls
12 pieces of sidewalk.
5 + 6 + 3 + 12 = 26
If all of them have exactly the same probability of being removed, then:
in the first selection, we do not want to remove a jump rope, so we can remove one disc, one ball or one piece of sidewalk.
The total number of those objects is:
5 + 3 + 12 = 20.
Then the probability of removing one of those objects is:
P1 = 20/26 = 0.769
Now in the second selection, we have the same situation, but now we have 25 objects in total, and because in the previous selection we removed one ball, or one disc, or one piece of sidewalk, the total number of these things now is 19.
So the probability of removing another object of that set is:
P2 = 19/25 = 0.76
The joint probability is equal to the product of the individual probabilities, so we have:
P = P1*P2 = 0.769*0.76 = 0.584
if 25 liters of milk can make 8 tin of cheese how many liters of milk would b needed to make 11 tin of cheese?
Answer:
Step-by-step explanation:
34.375 Liters of milk make 11 tins of cheese. Assuming that milk is available in whole liters only, 35 Liters of milk are needed.
Suppose that y varies directly with x and y=20 when x=2 Find y when x=8
Answer:
80
Step-by-step explanation:
x y
2 = 20
8 = x
cross multiply( 8*20)/2
= 4 * 20
= 80