Janet wants to calculate the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest. What equation can she use?
Answer:
T = 100I/PRStep-by-step explanation:
Given the amount invested for a particular period of time at an interest rate, the equation that can model the Interest achieved on investment is expressed using the simple interest formula as shown;
Simple Interest = PRT/100 where;
P is the principal (amount invested)
R is the rate (in %)
T is the time (in years)
From the equation I = PRT/100, we need to express tht time T as a function of the rest of the variable as shown;
I = PRT/100
cross multiply
100I = PRT
Divide both sides by PR
100I/PR = PRT/PR
100I/PR = T
Hence the the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest is expressed as
T = 100I/PR
What is the value of 2 over 5×5ovet4÷2over3
Answer:
3/4
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by its reciprocal.
[tex]\dfrac{2}{5}\times\dfrac{5}{4}\div\dfrac{2}{3}=\dfrac{2}{5}\times\dfrac{5}{4}\times\dfrac{3}{2}\\\\=\dfrac{(2)(5)(3)}{(2)(5)(4)}=\boxed{\dfrac{3}{4}}[/tex]
What is the solution for x in the equation? 16x − 4 + 5x = -67
Answer:
x = -3
Step-by-step explanation:
16x − 4 + 5x = -67
Combine like terms
21x -4 = -67
Add 4 to each side
21x-4+4 = -67+4
21x = -63
Divide each side by 21
21x/21 = -63/21
x = -3
Answer:
[tex]\huge \boxed{x = -3}[/tex]
Step-by-step explanation:
[tex]16x - 4 + 5x = -67[/tex]
Combine like terms.
[tex]21x - 4 = -67[/tex]
Add 4 to both sides.
[tex]21x = -63[/tex]
Divide both sides by 21.
[tex]x = -3[/tex]
Use Theorem to find ℒ{f(t)}.
f(t) = (et − e−t)2
Answer:
[tex]\frac{3s^2-4}{s(s^2-4)}[/tex]
Step-by-step explanation:
Here, the question is to find the Laplace transformation of [tex]f(t)[/tex]
where, [tex]f(t)=(e^t-e^{-t})^2[/tex]
We know that for [tex]t>0[/tex], [tex]\mathcal{L}\{f(t)\} =\int_0^{\infty} e^{-st}f(t)dt[/tex]
[tex]\mathcal{L}\{e^{at}\}=\int_0^{\infty} e^{-st}e^{at}dt[/tex]
[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\int_0^{\infty} e^{(a-s)t}dt[/tex]
[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\left[\frac { e^{(a-s)}}{a-s}\right]_0^{\infty}[/tex]
[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\frac { 1}{s-a}\cdots(i)[/tex]
Here, we have [tex]f(t)=(e^t-e^{-t})^2[/tex]
[tex]\Rightarrow f(t)=(e^t)^2+(e^{-t})^2-2(e^t)(e^{-t})[/tex]
[tex]\Rightarrow f(t)=e^{2t}+e^{-2t}-2e^{0t}[/tex]
So, the laplace transformation of [tex]f(t)[/tex] is
[tex]\mathcal{L}\{f(t)\}=\mathcal{L}\{e^{2t}+e^{-2t}-2e^{0t}\}[/tex]
[tex]\Rightarrow \mathcal{L}\{f(t)\}=\mathcal{L}\{e^{2t}\}+\mathcal{L}\{e^{-2t}\}+\mathcal{L}\{e^{0}\}[/tex]
Now, using equation[tex](i)[/tex]
[tex]\mathcal{L}\{f(t)\}=\frac{1}{s-2}+\frac{1}{s-(-2)}+\frac{1}{s-0}[/tex]
[tex]\Rightarrow \mathcal{L}\{f(t)\}=\frac{1}{s-2}+\frac{1}{s+2}+\frac{1}{s}[/tex]
[tex]\Rightarrow \mathcal{L}\{f(t)\}=\frac{3s^2-4}{s(s^2-4)}[/tex]
Hence, the Lapelace transformation of [tex]f(t)=(e^t-e^{-t})^2[/tex] is
[tex]\frac{3s^2-4}{s(s^2-4)}[/tex].
The area of a rectangular wall of a barn is 48 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.
l = 16 feet
w = 3 feet
Step-by-step explanation:A = l×w
l = 10+2w
48 = (10 + 2w)w
48 = 10w + 2w² | : 2
24 = 5w + w²
w² + 5w - 24 = 0
w² + 8w - 3w - 24 = 0
w(w + 8) - 3(w + 8) = 0
(w - 3)(w + 8) = 0
w - 3 = 0 => w = 3 feet
w + 8 = 0 => w = - 8 ∉ N
l = 10 + 2w
l = 10 + 6
l = 16 feet
A = l×w = 16ft×3ft = 48ft²
How can you use a rectangle to calculate the slope of a line ?
Answer:
The slope is the inclination of a surface or a line with respect to the horizontal. It can be measured at an angle in degrees, radians or grades or even in percentage, that is to say according to the height to length ratio multiplied by 100.
Step-by-step explanation:
what value of c makes the equation true?
3/6=4/c
Answer:
c = 8
Step-by-step explanation:
3/6=4/c
Cross products
3c = 6*4
3c = 24
Divide each side by 3
3c/3 =24/3
c = 8
(5 points) The probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%. What is the probability that a randomly selected day in April will be rainy or windy?
Answer:
The probability that a randomly selected day in April will be rainy or windy is 0.62 or 62%.
Step-by-step explanation:
We are given that the probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%.
And we have to find the probability that a randomly selected day in April will be rainy or windy.
Let the probability of rain on any day in the month of April = P(A) = 0.34
The probability of windy on any day in the month of April = P(W) = 0.38
The probability of both windy and rainy on any day in the month of April = P(R [tex]\bigcap[/tex] W) = 0.10
Now, the probability that a randomly selected day in April will be rainy or windy is given by = P(R [tex]\bigcup[/tex] W)
P(R [tex]\bigcup[/tex] W) = P(R) + P(W) - P(R [tex]\bigcap[/tex] W)
= 0.34 + 0.38 - 0.10
= 0.62 or 62%
So, the probability that a randomly selected day in April will be rainy or windy is 62%.
What is the probability of choosing a card from a deck of cards that is a club or a ten? Is this event mutually
exclusive or inclusive?
A. Inclusive
B. Exclusive
A. 5/16
B. 4/13
C. 1/4
D. 7/16
Answer:
Hey there!
There are 13 clubs in a deck of cards.
There are 4 tens.
However, the tens overlap with the clubs, so there are 16 cards to choose.
16/52=4/13
Let me know if this helps :)
The events are mutually inclusive. Option B is correct because the required probability is [tex]\dfrac{4}{13}[/tex].
Important information:
A card is selected randomly from a deck of cards.We need to find the probability that the card is a club or a ten.Probability:A deck of cards has total 52 cards, which includes 4 suits and each suit has 13 cards. If S be the sample space, then n(S) = 52.
Let A be the event that the card is a club card and B be the event that it is a ten card.
The number of club cards is 13. So, n(A) = 13.
There are 4 cards of 10. So, n(B) = 4.
One ten card is of club. So, [tex]n(A\cap B)=1[/tex].
Since [tex]n(A\cap B)=1\neq 0[/tex], therefore the events are mutually inclusive.
The number of club or a ten card is:
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
[tex]n(A\cup B)=13+4-1[/tex]
[tex]n(A\cup B)=16[/tex]
Now,
[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]
[tex]P(A\cup B)=\dfrac{16}{52}[/tex]
[tex]P(A\cup B)=\dfrac{4}{13}[/tex]
Therefore, the probability of choosing a card from a deck of cards that is a club or a ten is [tex]\dfrac{4}{13}[/tex]. Hence, option B is correct.
Find out more about 'Probability' here:
https://brainly.com/question/15944614
The solution to an inequality is represented by the number line. A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5. How can this same solution be written using set-builder notation?
Answer:
3
Step-by-step explanation:
The number line is showing x>3.
If the circle were closed it would be x≥3.
Answer:
3.
Step-by-step explanation:
9.7292; thousandths *round to nearest thousandth*
Answer:
I am almost positive it is 9.729
Step-by-step explanation:
my teacher used to say 4 or less let it rest, 5 or more raise the score. In this situation it is 2 so leave it be and that’s your answer. Also, 9.7 is tenths, 9.72 is hundredth, which means 9.729 is thousanths.
Answer: 9.729
Step-by-step explanation:
my teacher used to say 4 or less let it rest, 5 or more raise the score. In this situation it is 2 so leave it be and that’s your answer. Also, 9.7 is tenths, 9.72 is hundredth, which means 9.729 is thousanths.
I NEED HELP PLEASE Francisco ran 8 miles. Being a football fan, Francisco wondered how many times he had run the equivalent of a full football field that’s a hundred yards. How many times had run?
Answer:
140.8 football fields.
Step-by-step explanation:
8 miles = 8 * 1760 yard.
So the number of football fields that he ran
= (8 * 1760) / 100
= 8 * 17.6
= 140.8.
simplify the expression. -2 3/5 - (-1 2/5) - 4/5 = ?
I write each number in expanded form:
6.458 = _ + _+ _ + _
6.458 = 6 + 0.4 + 0.05 + 0.008
Each blank slot is filled with a digit from the original number. The zeros are placeholders to make sure we have the right alignment.
Answer:
6.458 = 6 + 0.4 + 0.05 + 0.008Step-by-step explanation:
6.458
---------------------
6.000
0.400
0.050
0.008
6.458 = 6.000 + 0.400 + 0.050 + 0.008
trailing zeros can be omitted
Hugh is struggling in his history class. His last five grades on tests were 67, 72, 63, 77, and 59. On the next test, he studies hard, but gets a 75. What is his average?
Answer:
Step-by-step explanation:
[tex]\frac{67+72+63+77+59+75}{6} \\\\\frac{413}{6} \\\\68.833333 or 68.8[/tex]
For the equation 17h+6=40, select the appropriate property of equality to move the constant term to the right side of the equation.(20pt) A. Division Property of Equality- B. Subtraction Property of Equality - C. Multiplication Property of Equality- D. Addition Property of Equality
Answer:
Option B.
Step-by-step explanation:
The given equation is
[tex]17h+6=40[/tex]
We need to find the property of equality to move the constant term to the right side of the equation.
In the given equation 6 is the constant term on the left side.
Using subtraction property of equality, subtract 6 from both sides.
[tex]17h+6-6=40-6[/tex]
[tex]17h=34[/tex]
So, the appropriate property of equality to move the constant term to the right side of the equation is Subtraction Property of Equality.
Therefore, the correct option is B.
PLEASE HELP *13 POINTS*! A) -4 B) -0.25 C) 4 D) 0.25
Answer: Choice C) 4
=========================================
Work Shown:
Set the denominator equal to zero and solve for x
4x-16 = 0
4x-16+16 = 0+16 ... add 16 to both sides
4x = 16
4x/4 = 16/4 ... divide both sides by 4
x = 4
--------
If x = 4, then the denominator is 0
4x-16 = 4(4)-16 = 16-16 = 0
So this x value is what we exclude from the domain to avoid a division by zero error.
If speed varies inversely as the time it takes to drive and Kris takes 5 hours driving at 55 mph, what speed will Martin need to
drive if he wants to take 5 hours?
O 50 mph
52.4 mph
O 60.5 mph
O 51.5 mph
Answer:
55mph . None of the options are correct
Step-by-step explanation:
If the speed varies inversely as the time it takes to drive, then v ∝ 1/t. where;
v is the speed
t is the time taken
Hence;
v = k/t with k being the constant of proportionality.
Since it takes Kris 5 hours when driving at 55 mph, we will substitute v = 55mph and t = 5 hours. into the equation above to get the value of k as shown:
55 = k/5
Cross multiply
k = 55*5
k = 275
Hence, to calculate the speed it will Martin to drive for 5 hours, we will substitute k = 275 and t = 5 into the original equation v = k/t as shownl
v = 275/5
v = 55 mph
Hence, we can conclude that Martin will also need to drive at a speed of 55mph if he wants to take 5hours.
What is the absolute value of -4
Answer:
4
Step-by-step explanation:
Easiest way to remember absolute value is the number always comes out positive.
l-4l=4
Answer:
the answer is 4
Step-by-step explanation:
the absolute value means it doesn't consists of any sign (neither positive nor negative)
Determine the value of x shown in the diagram
Answer:
x = 145
Step-by-step explanation:
If we look at the right triangle with sides of 24 and 30, we can find the missing leg using the Pythagorean Theorem. If we look carefully, we notice that 18:24:30 is basically the 3:4:5 Pythagorean Triple multiplied by 6, so the missing side is 18. If we look at the right triangle with sides of x and 24, we can find the missing side by calculating 161 - 18 = 143. Using the Pythagorean Theorem, we know that 143² + 24² = x² so x = 145.
Ashanti and Maria went to the store to buy snacks for their back-to-school party. They bought bags of chips, pretzels, and nachos. They bought three times as many bags of pretzels as bags of chips, and two fewer bags of nachos than bags of pretzels. If x represents the number of bags of chips they bought, express, in terms of x, how many bags of snacks they bought in all.
(Theres two more problems in a picture, you don’t have to answer all three tho but if you do it i will love you forever :( )
Answer:
Hey there!
For the first one:
Chips: x
Pretzels: 3x
Nachos: 3x-2
Total snacks: x+3x+3x-2=7x-2
For the second one:
In the equation, 150+5d, 150 represents the starting amount of money, in this case, 150 dollars. 5d means that for every day, five dollars get put into his account.
For the third one:
In this equation, 1.50 represents to initial fee, and 2.25m represents the cost per mile. Dividing by 2 gives us what each person in the cab pays.
Let me know if this helps :)
Let p: x = 4 Let q: y = -2 Which represents if x = 4, then y = -2. Please hurry
Answer:
p: x = 4
q: y = -2
If p happens then q will also happen
Step-by-step explanation:
Given two propositions, we want to rearrange them in a conditional statement.
The correct answer is:
p → q
First, a conditional statement is something of the form:
If [Hypothesis] then [Conclusion]
So, if the first part is true, then the second part must be true.
Now, here we have two propositions:
p: "x = 4"
q: "y = -2"
We want to write:
"if x = 4, then y = -2"
this is just written as: "p implies q" or:
p → q
Where "→" means "then", and the initial "if" is tacit.
If you want to learn more, you can read:
https://brainly.com/question/10714086
What is lim x → 9+ ( x - 9/| 9 - x | )
Answer:
The answer is nonexistent
Step-by-step explanation:
The period T(in seconds) of a pendulum is given by T=2 pi root L over 32 where the L stands for Length(in feet) of the pendulum. If `pi 3.14, and the period is 3.14 seconds, what is the length?
Answer:
8 feet = L
Step-by-step explanation:
The period T(in seconds) of a pendulum is given by T=2 pi root L over 32
T= 2π√(L/32)
where the L stands for Length(in feet) of the pendulum.
If π= 3.14, and the period is 3.14 seconds
Length will be
T= 2π√(L/32)
3.14= 2*(3.14)√(L/32)
(3.14/3.14)/2= √(L/32)
(1/2)²= L/32
1/4 = L/32
32/4= L
8 feet = L
When determining how well an observed set of frequencies fits an expected set of frequencies, what is the test statistic
Answer: [tex]\chi^2[/tex] test statistic.
Step-by-step explanation:
The chi-square ([tex]\chi^2[/tex] ) test is a non-parametric statistical test(also known as Goodness of fit test) which is used to determine if a distribution of observed frequencies differs from the expected frequencies.
Chi-square statistic uses either nominal (categorical) or ordinal level data.
Hence, When determining how well an observed set of frequencies fits an expected set of frequencies, the test statistic is [tex]\chi^2[/tex] test statistic.
A circuit shows that the impedance of a component is −56i−56i. Is the component a resistor, a capacitor, or an inductor? Select the correct component from the drop-down list to correctly complete the statement. It is a(n) A. inductor B. resistor C. capacitor
Answer:
c
Step-by-step explanation:
BRAINLIEST FOR RIGHT ANSWER!!! The graph shows two lines, A and B. (IMAGE BELOW) How many solutions are there for the pair of equations for lines A and B? Explain your answer.
Answer:
1 solution; (1,4)
Step-by-step explanation:
Whenever two lines intersect, their solution is the point that the two share in common. Here, it's (1,4), so that is the answer.
Simplify. 7x + 13 – 9x – 5 16x + 8 6x –2x + 18 –2x + 8
Bridge Ais 4780 feet long. Bridge B, in the same state, is 650 feet shorter than Bridge A. Find the length of Bridge B.
The length of Bridge Bis feet
Answer:
4,130
Step-by-step explanation:
4780-650=4130 ft
What are the intercepts of y = x + 5 (Remember that intercepts mean both x-intercept & y-intercept.) a) (5, 0) & ( 0, 5) b) ( -5, 0) & (0 , 5) c) (5, 0 ) & (0, -5) d) (-5, 0 ) & ( 0, -5)
Greetings from Brasil...
We have to remember 2 details:
→ When X = 0, the function intersects the Y axis
→ When Y = 0, the function intersects the X axis
So
1: X = 0
Y = X + 5
Y = 0 + 5
Y = 5
X = 0 and Y = 5 ⇔ (0; 5)
2: Y = 0
Y = X + 5
0 = X + 5
X = - 5
Y = 0 and X = - 5 ⇔ (- 5; 0)
Then the point at which the graph intersects the X and Y axis will be
(0; 5) and (- 5; 0)