Answer:
B
Step-by-step explanation:
take square on both sides
7x-4 = 4x
x = 4/3
If $4,500 is invested at an interest rate of 5.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a) 4 years
(b) 8 years
(c) 12 years
a) The value of the investment after 4 years is $5,544.90.
b) The value of the investment after 8 years is $6,849.42.
c) The value of the investment after 12 years is $8,453.35.
The formula for calculating the value of an investment that is compounded continuously is given by:
A = [tex]Pe^{(rt)[/tex]
where A is the final value of the investment, P is the initial investment amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time period in years.
(a) To find the value of the investment after 4 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05254)[/tex]
A = 4500[tex]e^{0.21[/tex]
A = 45001.2322
A = $5,544.90
(b) To find the value of the investment after 8 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05258)[/tex]
A = 4500[tex]e^{0.42[/tex]
A = 45001.5221
A = $6,849.42
(c) To find the value of the investment after 12 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.052512)[/tex]
A = 4500[tex]e^{0.63[/tex]
A = 45001.8785
A = $8,453.35
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Please reply me as soon as possible with step by step answer for this
The length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
What is the length of the curve?To use the arc length formula, we need to find the derivative of the curve y = 5 - 4x:
y' = -4
Then, we can use the arc length formula:
L = ∫[a,b] √(1 + (y')^2) dx
where a and b are the limits of integration. In this case, a = -2 and b = 2.
L = ∫[-2,2] √(1 + (-4)^2) dx
= ∫[-2,2] √(17) dx
= √(17) * [x]_(-2)^(2)
= 4√(17)
So the length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
To check this answer, we can note that the curve is a line segment with endpoints (-2, 13) and (0.75, 1), and we can calculate its length using the distance formula:
L = √((0.75 - (-2))^2 + (1 - 13)^2)
L = √(18.25 + 144)
L = √(162.25)
L = 4√(17)
This matches our previous answer, so we can be confident that the length of the curve is 4√(17).
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A map shows the vertices of a campsite are (25,10), (25,-5), (-5,-5), and (-5,10). The vertices of your tent are (0,-3), (0,6), (10,6), and (10,-3). The coordinates are measured in feet. What percent of the campsite is not covered by your tent?
The percent of the area that is not covered is 80 percent
How to calculate the area that is not coveredIn mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².
area of tent
= (10 - 0) * (6 - (-3))
= 90
The area of the campsite would be:
(25 - (-5) x (10 - (-5))
= 450
Then the area would be 450 - 90
= 360
the percentage that is not covered by tent = 360 / 450 x 100
= 80 percent
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A side of an equilateral triangle is 20 cm long. What is the area of the triangle
Lines and Angles
10) In the figure below BD is the perpendicular bisector of AC. Find the value of x.
3(2x-8)
4425
Enter your answer in the box.
x=
Since BD is the perpendicular bisector of AC, then AB = BC, which implies 2x - 8 = 5x - 17.
Solving for x, we have:
3(2x - 8) = 4425
6x - 24 = 4425
6x = 4451
x = 741.83
Rounding to the nearest whole number, we have x = 742.
Therefore, x = 742.
2010 2008
$971 $812
$977 $943
$900 $873
$1071 $1023
$501 $486
3. Identify whether the mean or median is a more accurate reflection of the data.
Explain why.
The median is the accurate reflection of the data
How to solve for the mean501, 900, 971, 977, 1071
The mean would be
summation of the values
mean = 884
The median is the value that occurs in the middle = 971
The median would be more accurate reflection of the data. 501 is an outler. This is what caused us to have a mean that is c loser to 884. Hence we have 971 the median to be more accurate reflection of the data
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The lodge has 420 skis. Predict the number of skis that are likely to be defective.
A ski lodge inspects 80 skis and discovers four that are faulty. The skis that are likely to be defective are 21.
It is assumed that there are 80 skis, four of which are faulty.
As a result, the total number of outcomes is 80.
Positive outcomes = 4
Let [tex]E_{1}[/tex] represent the event of selecting a faulty. As a result, the likelihood of selecting a defective ski is expressed mathematically as follows.
[tex]E_{1}[/tex] = Favorable case of defective / Total number of skis
= 4 / 80
= 1 / 20
=0.05
Skis will be discovered in 5% of cases.
So, the event of choosing a defective is 4 / 80.
If the total number of skis is 420, then the number of defective skis will be:
4 / 80 × 420
= 1/20 × 420
= 21
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Correct question:
A ski lodge inspects 80 skis and finds 4 to be defective. The lodge has 420 skis. Predict the number of skis that are likely to be defective.
I really need hep please
The valid row-operation which needs to be performed on the given matrix to get "1" in position of row1 and column1 are "R₁ → 2R₁ + R₂" and then "R₁ → R₁/2".
The "row-operation" is a type of matrix operation that involves swapping, scaling, or adding rows in a matrix. These operations are used to transform a matrix into a more reduced form.
The Augmented matrix on which we have to perform the "row-operation" is
⇒ [tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex],
To get "1" in first row and first column,
The first row-operation is R₁ → 2R₁ + R₂
We get,
⇒ [tex]\left[\begin{array}{ccc}7\times 2-12&-4\times 2+7&8\times 2-13\\-12&7&-13\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}14-12&-8+7&16-13\\-12&7&-13\end{array}\right][/tex]
⇒ [tex]\left[\begin{array}{ccc}2&-1&3\\-12&7&-13\end{array}\right][/tex],
The second , row-operation to get a "1", is R₁ → R₁/2,
We get,
⇒ [tex]\left[\begin{array}{ccc}2/2&-1/2&3/2\\-12&7&-13\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}1&-0.5&1.5\\-12&7&-13\end{array}\right][/tex].
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Complete the following using compound future value. (Use the Table provided.)
Note: Do not round intermediate calculations. Round your final answers to the nearest cent.
Time
6 years
Principal
$ 15,300
Rate
8 %
Compounded
Quarterly
What is amount &
Interest?
Answer:
We can use the formula for compound interest to calculate the amount and interest:
A = P * (1 + r/n)^(n*t)
I = A - P
Where:
P = Principal = $15,300
r = Rate = 8% = 0.08
n = Compounding frequency per year = 4 (since it is compounded quarterly)
t = Time period = 6 years
Plugging in the values, we get:
A = 15,300 * (1 + 0.08/4)^(4*6) = $23,659.28
I = 23,659.28 - 15,300 = $8,359.28
Therefore, the amount after 6 years is $23,659.28 and the interest earned is $8,359.28.
I hope this helps.
2. If 15% of the first digit equals 21% of the second digit, then what percentage of the second digit equals 25% of the first digit?
Answer:
35%
(I replaced the 1st digit by a and the second digit by b)
tamara plays video games for the same amount of time each day. in 4 days she played video games for 48 minutes in 9 days how many minutes did she play video games
Answer:
Step-by-step explanation:
Its simple, you need to find x
4 days the same amount of time (x) gives 48 min
4x = 48
x = 48/4
x = 12
then to get the amount of minutes in 9 days it would be:
9x=days
9(12)=108
the answer would be 108 min
Answer:
108 mins
Step-by-step explanation:
48 mins/4 days = x mins/9 days
4x= 432
x=108 mins
Complete the worksheet below please
Answer:
x= 3 cm
Explanation:
I am bad at it
P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
What is P(J)?
O 0.1105
O 0.8143
O 0.8895
O 0.1857
The conditional value probability is solved and P ( J ) = 0.1105
Given data ,
P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
We can use Bayes' theorem to find P(J):
P(J | K) = P(K | J) * P(J) / P(K)
0.35 = 0.95 * P(J) / 0.3
0.35 * 0.3 = 0.95 * P(J)
0.105 = 0.95 * P(J)
P(J) = 0.105 / 0.95
P(J) = 0.1105
Hence , the probability is P ( J ) = 0.1105
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You’re planning to buy a house and you want to have $35,000 to put as a down payment. If you have $20,000 today and you’re able to receive 12% interest rate for investing the money, how long will it take you to have enough money for the down payment saved?
It will take approximately 6.24 years to have enough money for the down payment saved.
How to calculate how long will it take you to have enough money for the down payment savedWe can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the amount of money we want to have (in this case, $35,000)
P = the initial amount we have (in this case, $20,000)
r = the annual interest rate (in this case, 12%)
n = the number of times interest is compounded per year (let's assume it's compounded monthly, so n = 12)
t = the number of years we're investing for (this is what we want to find)
Substituting the values we know:
$35,000 = $20,000(1 + 0.12/12)^(12t)
Simplifying:
1.75 = (1 + 0.01)^(12t)
Taking the natural logarithm of both sides:
ln(1.75) = 12t ln(1.01)
Dividing both sides by 12 ln(1.01):
t = ln(1.75) / (12 ln(1.01))
Using a calculator:
t ≈ 6.24 years
Therefore, it will take approximately 6.24 years to have enough money for the down payment saved.
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Drag tiles to fill in the blanks for o complete the experience that could be used to predict the number of possible outcomes
The first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners
How to explain the probabilitySuppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
= n(E) / n+S)
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Thus, the first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners
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Drag tiles to fill in the blanks to complete the expression that could be used to predict the number of winners of a game. Tiles may be used once or not at all. A)Total Number of Possible Outcomes B)Number of Winners C)Number of Unfavorable Outcomes D)Number of Games P(event) = Number of Favorable Outcomes _________________________ ????????????????????????????? = ????????????????????????????? _________________________ 11 Total Number of Contestants
Make x the subject of the formula where x is positive:
2(x-2y) = 6xz+5u
Answer:
x = [tex]\frac{5u+4y}{2-6z}[/tex]
Step-by-step explanation:
2(x - 2y) = 6xz + 5u ← distribute parenthesis on left side
2x - 4y = 6xz + 5u ( add 4y to both sides )
2x = 6xz + 5u + 4y ( subtract 6xz from both sides )
2x - 6xz = 5u + 4y ← factor out x from each term on the left side
x(2 - 6z) = 5u + 4y ← divide both sides by (2 - 6z)
x = [tex]\frac{5u+4y}{2-6z}[/tex]
Write a slope-intercept equation for a line passing(3,-2) through the point that is parallel to the line 3X+4Y= 9. Then write a second equation for a line passing through the point (3,-2) that is perpendicular to the line 3X+4Y= 9.
Solve the quadratic equation by completing the square.
2
x² - 4x-10=0
First, choose the appropriate form and fill in the blanks with the correct num
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Which is equivalent to 234 2/5
234 2/5 is equivalent to 1172/5.
234 2/5 is a mixed number, which means it is a combination of a whole number and a fraction.
To convert it to an improper fraction, we need to multiply the whole number by the denominator of the fraction and add the numerator.
The result becomes the new numerator, and the denominator stays the same.
In this case, we have:
234 2/5 = (234 x 5 + 2) / 5
= 1172/5
Therefore, 234 2/5 is equivalent to 1172/5 as an improper fraction.
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The data set shown below represents the distribution of daily high temperatures in a city for 8 days.
79
,
73
,
72
,
70
,
72
,
66
,
81
,
75
79, 73, 72, 70, 72, 66, 81, 75
What is the median high daily temperature, in degrees Fahrenheit, in the city?
For the given data set of temperatures, the median temperature is 72.5 degree Fahrenheit.
In order to find the median temperature, we first need to arrange the temperatures in order from lowest to highest:
The temperatures arranged in order is : {66, 70, 72, 72, 73, 75, 79, 81}
There are 8 temperatures in total, which is an even-number, so the median will be the average of fourth and fifth day temperature.
In this case, the temperature of the fourth day is 72, and fifth day is 73,
The average will be = (72+73)/2 = 72.5,
Therefore, the median high daily temperature in the city is 72.5 degrees Fahrenheit.
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The given question is incomplete, the complete question is
The data set shown below represents the distribution of daily high temperatures in a city for 8 days.
79,73,72,70,72,66,81,75.
What is the median high daily temperature, in degrees Fahrenheit, in the city?
Tyler is simplifying the expression: 6-2x+5+4x Here is his work
6-2x+5+4x
(6-2)x+(5+4)x
4x+x
13x
a. Explain the error he made
b. Simplify the expression: 6-2x+5+4x
Answer:
11-2x not 13x
Step-by-step explanation:
\(6-2)x + (5-4)x does = 13x
If there were parentheses as in the 2nd line, everything else is correct
the mistake is going from
6-2x + 5-4x to
(6-2x) + (5-4)x
PEMDAS is the order of operations. P for parentheses 1st, Multiplication 3rd, addition 4th, subtraction 5th
(there are no exponents or division or parentheses, so it's just M, A and S that apply)
combine like terms, 2x-4x =-2x
combine the constant terms 6+5 = 11
6-2x +5-4x = 11-2x
The mistake was assuming parentheses when they aren't there.
correct answer is 11-2x not 13x
Jaswat set out to walk a distance of 12 Km. After walking for 1 1/2 hours at a speed of
6 Km/h, he had to slow down to steady pace of 4 Km/h , which he maintained till the
end of the journey. How long did he take to complete the journey?
Answer: 2 hours 15 minutes
Step-by-step explanation:
To solve this problem, we need to use the formula:
distance = speed x time
First, let's calculate the distance Jaswat covered in the first 1 1/2 hours:
distance = speed x time
distance = 6 Km/h x 1.5 h
distance = 9 Km
So, Jaswat covered 9 Km in the first 1 1/2 hours. He still had to cover 12 Km - 9 Km = 3 Km.
Now, we need to calculate the time Jaswat took to cover the remaining 3 Km at a speed of 4 Km/h:
distance = speed x time
3 Km = 4 Km/h x time
time = 3 Km / 4 Km/h
time = 0.75 hours = 45 minutes
Therefore, Jaswat took 1 1/2 hours + 45 minutes = 2 hours 15 minutes to complete the journey.
Assignments...
Library Search
Khan Academy
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
fy=
=−x+2
Get Al Guide
y = 3x -4
Donate
The solution of the given system of equations is (1, 2.5)
How to explain the equationFrom the graph attached, it van be seen that two intersecting lines represent the system of equations.
And the solution of the system of equations is a common point where these lines intersect.
The graph shows both the line are intersecting each other at (1, 2.5).
Therefore, the solution of the given system of equations will be (1, 2.5).
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If angle 3=61, what should angle 1 and angle 2 be?
Answer:
Step-by-step explanation:
so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)
This is so hard. Can you help me with this?
Answer: 70, 6
Step-by-step explanation:
(a) For <F that is the same as <D. The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same
All of the angles are = 180 if you subtract <E, you are left with 140 to be split between <F and <D
<F= 70
(b) all of the sides are the same because all the angles are the same
so AB=6
QUESTION 1
Joe's Pizza Company faces a demand for its pizzas which obeys the "law of demand." This means if Joe lowers the price he charges
per pizza
His profit will rise.
He will sell more pizzas.
His profit will fall.
He will sell fewer pizzas.
If Joe lowers the price he charges per pizza, he will sell more pizzas. option B
Why would he sell more?To sell more pizza, Joe must decrease the price he charges per unit. The law of demand dictates that when a product's cost decreases, its quantity demanded rises resulting in an increased sales volume.
It follows then that if Joe reduces his pizza prices more people will be inclined to purchase it creating this increase in sales . Nonetheless, whether Joe’s profit will rise or diminish depends on the extent of the rise in sales compared to the lowering of the price.
Even if there is a reduction in the price of every pizza, if the resultant sales volume is significant enough, Joe’s profit margin could still experience a positive turn.
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100 Points!!! Algebra question. Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Please show as much work as possible. Photo attached. Thank you!
The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at;
-3, f(-3) = 390 and at 4, f(4) = 537
What is a functionA function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers
By substitution:
For x = -3;
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3
f(-3) = 243 + 108 + 27 + 15 - 3
f(-3) = 390
For x = 4;
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
f(4) = 3(256) - 4(64) + 3(16) - 20 - 3
f(4) = 768 - 256 + 48 - 20 - 3
f(4) = 537
Therefore, the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537 respectively.
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The mean pulse rate in beats per minute of a certain group of adult males is 76 bpm. The hypothesis test results in a p-value of 0.0075
State a conclusion about the null hypothesis
The conclusion on the null hypothesis is B. Reject H₀ because the P-value is less than or equal to a.
How to conclude on the null hypothesis ?It is posited that the mean pulse rate for a specific grouping of adult males equals 76 bpm as set forth by the null hypothesis. In its place, an alternative hypothesis suggests this figure does not reflect actuality.
At a given significance level identified by alpha = 0.05, rejection of the null hypothesis requires us to identify a P-value lesser than or equal to 0.05.
The P-value determined within the question happens to be below such a threshold at 0.0075, which results in the rejecting of the null hypothesis.
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ibrahim drew the graph below.
which of the following statements best describes the graph?
Answer:
B
Step-by-step explanation:
This is a linear function.
:D
You want to determine the number of students in your school who have visited a public library. You survey 30 students at random. Twenty-four have visited a public library, and six have not. So, you conclude that 80% of the students in your school have visited a public library.
Determine whether the conclusion is valid
Answer: e
Step-by-step explanation:
Answer:Valid
Step-by-step explanation: