The required final amount and interest are 3311.05 and 311.05
What is Compound interest?When you make interest on both the money you've saved and the interest you've earned, this is known as compound interest.
According to question:A. To find the amount of money in the account after 5 years, we can use the formula for compound interest:
[tex]$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$[/tex]
where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $3000, r = 0.02 (2%), n = 4 (compounded quarterly), and t = 5. Plugging in these values, we get:
[tex]$$A = 3000\left(1 + \frac{0.02}{4}\right)^{4\cdot5} \approx $3311.05$$[/tex]
Therefore, there will be approximately 3311.05 in the account after 5 years.
B. To find the interest earned, we can subtract the principal from the final amount:
[tex]$$I = A - P = $3311.05 - $3000 = $311.05$$[/tex]
Therefore, the interest earned is 311.05.
To know more about Interest visit:
brainly.com/question/28792777
#SPJ1
What is the solution of
3+
x <3
O x≤3
O x > 3
O x≥3
X-2
x-3542
Answer:25
Step-by-step explanation: easy
what is 2x32+5x20,ωωωωωω,,,,,,,,,,
Answer:
164
Step-by-step explanation:
Find the area of this semi-circle with radius, r = 90cm. Give your answer rounded to 1 DP. rcm The diagram is not drawn to scale. + Mu
Answer:
12723.5(cm^2)
Step-by-step explanation:
the area of the circle
S=Tur^2
The sems-circle is s.=1/2 s =1/2Tur^2
Please help asap!!
Thank you
The requried it cannot conclude whether the variable is normally distributed or skewed based on the given data. None of the options are correct.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
It is not possible to determine if the variable "footprint" is normally distributed or skewed based on the given data.
The data represents the measurements of shoe prints for 5 males, but it is not enough to determine the distribution of the variable without additional information such as a larger sample size, the mean and standard deviation of the variable, or a histogram or frequency plot of the data.
Therefore, we cannot conclude whether the variable is normally distributed or skewed based on the given data.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ1
Erik spends $680 for cable television service. The cable company offers a deal that promises Erik 3 free months of cable if he signs a contract with them for $40 per month.
Complete the equation below to find the number of months that Erik will have cable television service with this deal. Use m to represent the number of months.
Answer:
Step-by-step explanation:
The cable company offers Erik 3 free months of cable if he signs a contract with them for $40 per month. This means that Erik will pay for (m - 3) months of cable service, since he will get 3 months for free. So the cost of the cable service for (m - 3) months is:
Cost = $40 per month x (m - 3) months
Cost = $40m - $120
We know that Erik spent $680 for the cable television service. So we can set up an equation to relate the cost to the number of months:
$40m - $120 = $680
To solve for m, we can isolate the variable on one side of the equation:
$40m = $800
m = 20
Therefore, Erik will have cable television service for 20 months with this deal.
15. [-/6.67 Points] DETAILS
AUFINTERALG9 4.4.019.
MY NOTES
A carpenter purchased 50 ft of redwood and 90 ft of pine for a total cost of $292. A second purchase, at the same prices, included 90 ft of redwood and 70 ft of pine for a total cost of
$406. Find the cost per foot of redwood and of pine.
redwood
dollars per foot
pine
dollars per foot
The cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Let's use the variables r and p to represent the cost per foot of redwood and pine, respectively.
From the first purchase, we can set up the following system of equations:
50r + 90p = 292 (equation 1)
90r + 70p = 406 (equation 2)
To solve for r and p, we can use the method of substitution. Solving equation 1 for r, we get:
r = (292 - 90p) / 50
Substituting this expression for r into equation 2, we get:
90[(292 - 90p) / 50] + 70p = 406
Multiplying both sides by 50 to clear the fraction, we get:
162 - 27p + 70p = 4060
Combining like terms, we get:
43p = 3898
Dividing both sides by 43, we get:
p = 90.65
So the cost per foot of pine is $90.65.
To find the cost per foot of redwood, we can substitute this value of p into equation 1 and solve for r:
50r + 90(90.65) = 292
50r = 2118.5
r = 42.37
So the cost per foot of redwood is $42.37.
Therefore, the cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.
To know more about an expression follow
https://brainly.com/question/26397343
#SPJ1
1. Find the average of 16, 50, 14, 20 and 40.
Answer:
28
Step-by-step explanation:
you add up all the numbers and divide by the number of numbers there is
16+50+14+20+40=140
140/5=28
Given the probability histogram pictured for a discrete random variable X, what is μx?
Histogram with x-axis labeled X with scale from 0 to 5, y-axis labeled P(X) with scale from 0 to 0.5 with five bars. Bar 1 height is 0.3, bar 2 height is 0.45, bar 3 height is 0.05, bar 4 height is 0.1, bar 5 height is 0.1.
1.5
1.85
2.1
2.25
2.5
Answer:
2.25
Step-by-step explanation:
A doctor orders a prescription that has a recommended dosage of 5 mg/lb every 12 hours. Our supply of the drug is a 0.9 g/mL solution. The patient is 72.7 kg. How many mL of the solution should we use for each dose?
The doctor should order a prescription of 0.8906 mL of the 0.9 g/mL solution for each dose.
What is the density?
Density is a physical property of matter that measures the amount of mass per unit volume. It is calculated by dividing the mass of an object or substance by its volume. The resulting number represents the amount of matter, or mass, that is present in a given volume.
The formula for density is:
Density = Mass / Volume
First, we need to convert the weight of the patient from kilograms to pounds, as the recommended dosage is in mg/lb:
72.7 kg x 2.205 lbs/kg = 160.305 lbs
The recommended dosage is 5 mg/lb, so for a 160.305 lbs patient, the total dosage per dose would be:
160.305 lbs x 5 mg/lb = 801.525 mg
Now we need to convert this dosage from mg to mL, using the concentration of the solution, which is 0.9 g/mL:
1 g = 1000 mg, so 0.9 g = 0.9 x 1000 = 900 mg
To convert mg to mL, we can use the density formula:
Density = Mass / Volume
Rearranging the formula to solve for volume, we get:
Volume = Mass / Density
So, the volume of solution needed for each dose would be:
Volume = 801.525 mg / 900 mg/mL
Volume = 0.8906 mL
Hence, the doctor should order a prescription of 0.8906 mL of the 0.9 g/mL solution for each dose.
To learn more about the density, visit:
https://brainly.com/question/1354972
#SPJ1
The model represents the quotient of two decimals.
Please look at pic to understand problem.
Which expression does this model represent?
A. 0.375 divided by 1.5
B. 0.375 divided 4.0
C. 1.5 divided by 0.375
D. 4.0 divided by 0.375
4/5 is greater, less than, or equal to 8/10?
Answer: 4/5 is equal to 8/10
Step-by-step explanation:
Find the slope of the line shown below?
3/8 or .375
You can find slope by doing rise/run (in fraction form) Rise is counting up or down spaces from one point until you hit the line of the next point. And then the run is counting over to the next point on the line. the number of spaces you counted up or down is the numerator and the run is the denominator.
6 cm
10) A water sample shows 0.37 grams of some trace element for every cubic centimeter of water.
Terrence uses a container in the shape of a right cylinder to collect a second sample, filling the
container all the way. The container has a radius of 7.9 centimeters and a height of 11.6 centimeters.
Assuming the sample contains the same proportion of the trace element, approximately how much of
pier[4 points]
the trace element has Terrence collected?oe bris ex
If a water sample shows 0.37 grams of some trace element for every cubic centimeter of water. Terrence has collected 841.51 grams of the trace element.
How to find how much of the trace element has Terrence collected?First, we need to find the volume of the cylinder container:
Volume of cylinder = π(radius)² height)
= π(7.9cm)²(11.6cm)
= 2,274.37 cm³
Amount of trace element = concentration x volume
= 0.37 grams/cm³ x 2,274.37 cm²
= 841. 51 grams
Therefore, Terrence has collected 841.51 grams of the trace element.
Learn more about cubic centimeter of water here:https://brainly.com/question/4594635
#SPJ1
Dividing integers. Question: A football team was penalized 30 points in 3 plays. Suppose the team was penalized an equal number of yards on each play. Write an integer that gives the yards for each penalty.
Answer:
The team was penalized 10 yards on each play.
Evaluate the expression 1/3x2 For x=6
The value of the expression 1 / 3x² when x equals 6 is 1/108.
What is the value of the expression when x equals 6?Given the expression in the question;
1 / 3x²
When x = 6, value of expression = ?
The expression 1 / 3x² is a mathematical formula that involves the variable "x".
When we substitute x = 6 into the expression, we are asked to calculate the value of the expression when x is equal to 6.
To evaluate the expression, we simply substitute x = 6 into the expression and simplify:
1 / 3x²
Plug in x = 6
1 / 3(6)²
Raise 6 to the power of 2 and get 36
= 1/(3 × 36)
= 1/108
Therefore, the value of the expression is is 1/108.
Learn more about algebraic expressions here: https://brainly.com/question/28959918
#SPJ1
MY NOTES
Electric current measures (in amperes or amps) the flow of electrons through wires. Like traffic flow, the current entering an intersection of wires must equal the current leaving it. Here is an
electrical circuit known as a Wheatstone bridge.
By measuring z, we can determine x, y, and w.
By measuring w, we can determine x, y, and z.
X
ASK YOUR TEACHER
(a) If the currents in two of the wires are a 18 amps and b-9 amps as shown, determine the currents in the other wires in terms of suitable parameters. (If there is no solution, enter NO
SOLUTION. If the system is dependent, express your answer using the parameters x, y, z, and/or w.)
(x, y, z, w) -
(b) Using the information obtained in part (a), in which wire should you measure the current in order to know all of the currents exactly? (Select all that apply.)
By measuring x, we can determine y, z, and w.
By measuring y, we can determine x, z, and w.
Need Help?
Read t
PRACTICE ANOTHER
Answer:
Step-by-step explanation:
(a) Since the current entering and leaving the intersection of wires must be equal, we have:
x + y = 18 (current entering the top intersection)
z + w = 18 (current leaving the top intersection)
x + z = 9 (current entering the bottom intersection)
y + w = 9 (current leaving the bottom intersection)
We can solve this system of equations using substitution or elimination. For example, we can eliminate w by adding the first two equations and subtracting the last two equations:
2x + 2y + 2z = 36
2y + 2z - 2x = 0
2z - 2x = 9
Solving for z in terms of x, we get:
z = (x + 9/2)
Substituting this into the first equation, we get:
x + y = 18
Substituting z in terms of x into the second equation, we get:
w = (18 - z) = (18 - x - 9/2) = (27/2 - x)
Therefore, the solution in terms of x, y, z, and w is:
(x, y, z, w) = (x, 18 - x, x + 9/2, 27/2 - x)
(b) To know all of the currents exactly, we need to measure the current in any one wire that is not already determined by the system of equations. From part (a), we see that w is determined in terms of x, y, and z. Therefore, we should measure the current in wire x or y to know all of the currents exactly.
Determine the domain and range
Step-by-step explanation:
To determine the domain and range of (g f) (x), we first need to find the composition of the functions f(x) and g(x):
(g f) (x) = g(f(x)) = g(2/(x^2-1)) = 2/(x^2-1) + 1
The domain of f(x) is all real numbers except x = -1 and x = 1, since these values would make the denominator equal to zero. Therefore, the domain of (g f) (x) is also all real numbers except x = -1 and x = 1.
To find the range of (g f) (x), we can start by finding the range of f(x). Since the denominator of f(x) is always positive (except at x = -1 and x = 1), the range of f(x) is all real numbers except 0.
When we add 1 to f(x), we shift the range of f(x) up by 1 unit. So, the range of (g f) (x) is all real numbers except 1.
Therefore, the domain of (g f) (x) is all real numbers except x = -1 and x = 1, and the range of (g f) (x) is all real numbers except 1.
Option B
Write the fraction as a sum of fractions three ways 7/10
First three sum 1/10 + 2/10 + 4/10 Proof: When the numbers in the denominator have the same value, fractions can be compute only with the sum of numerator values and the denominator doesn’t change. 1/10 + 2/10 + 4/10 = 1+2+4 / 10 = 7/10 Second three sum 1/10+1/5 + 2/5, Proof: such kind of fractions can be computed as follows: 1/10 + (1+2 )/5 (same denominators). 1/10 + (1+2 )/5= 1/10 + 3/5= 5x1 +10x3 / 5x10 = 5+30 /50 =35/50, by simplifying by 5, 35/50=7/10 The third three sum is 5/10+ 3/15+8/20,it can be computed by using the same method as given above
Hope it helps
1. Simplify √4x2y4
2. Simplify 4√x8y12
3. Simplify 5√32x5y15
4. Simplify 3√125p^6q³
5. Simplify √25a6b¹⁰c³
6. Simplify 3√64x¹²y5z⁹
7. Simplify √49a^6b³
8. Simplify 4√x^8y^12y^5z^9
9. Simplify 3√-64a³
10. Simplify √9x^2y^10z^13
The simplified forms are;
1) 2x[tex]y^2[/tex]
2) [tex]x^2y^3[/tex]
3) [tex]2xy^3z^5[/tex]
4)[tex]5p^2q[/tex]
5) [tex]5a^3b^5c^3/2[/tex]
6)[tex]4x^4y^5/3z^3[/tex]
7)[tex]7a^3b^3/2[/tex]
8) [tex]x^2y^3z^6[/tex]
9)-4a
10) [tex]3xy^5z^13/2[/tex]
How do you simplify a surd?To simplify a surd, you need to find the largest perfect square factor that divides the number under the square root symbol.
We can see that the surds here can be reduced to the simplest forms when we apply the basics of the rules of exponent which have been used to show the simplified forms as shown here.
Learn more about surd:https://brainly.com/question/30069850
#SPJ1
15. Blaine works for a battery manufacturing company. He wants to develop a method to test the batteries made each day to determine if they work.
Which method would provide the most valid results?
A. sampling the first 25 batteries made each day and testing to see if they work
B. sampling the last 25 batteries made each day and testing to see if they work
C. sampling the first 50 batteries made each day and testing to see if they work
D. randomly sampling 50 batteries throughout the day and testing to see if they work
Correct option is D. randomly sampling 50 batteries throughout the day and testing to see if they work would provide the most valid results.
What is a sample?A sample is described as a smaller, more manageable representation of a larger group. a smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.
The sample may be biased if it is taken from the first 25 batteries made each day (option A) or the last 25 batteries made each day (option B).
The first and final batteries made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent throughout the day.
Although battery quality can change during the day, sampling the first 50 batteries produced each day (option C) may also add bias into the sample.
The ideal course of action is to randomly select 50 batteries throughout the day (option D), since this helps to ensure that the sample is reflective of the general caliber of batteries manufactured that day.
Random sampling reduces the possibility of bias into the sample.
A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.
Therefore, option D would provide the most valid results.
To learn more about sample from the given link
https://brainly.com/question/28583871
#SPJ1
A cube has a length of 12 cm , what is its surface area?
72 sq. cm
864 sq. cm
1500 cubic cm
1728 sq cm
HELP!!
Therefore , the solution of the given problem of area comes out to be
option B 864 sq. centimetres is the correct response.
Describe surface regionThe amount of area it takes to cover the outside is a good indicator of its overall size. When calculating a trapezoidal shape surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capacity of a cuboid is the sum of the limits for each of its six rectangular edges. Utilize the following technique to determine the box's dimensions: The area is the same in 2lh, 2lw, but also 2hw (SA). The area is represented by the adaptable shape's face.
Here,
The following algorithm determines a cube's surface area:
=> SA = 6s²
where s represents the cube's edge lengths.
=> S =12 cm in this instance.
The result of substituting into the algorithm is:
=> SA = 6 (12)²
=> 6 (144 )²
=> 864 square centimetres.
The cube's surface size is 864 sq. cm as a result.
B) 864 sq. centimetres is the correct response.
To know more about surface area visit:
https://brainly.com/question/2835293
#SPJ1
A right square pyramid has the dimensions shown below.
l = 5 cm
h = 3 cm
s = 8 cm
What is the volume of the pyramid? Include correct units.
Show all your work.
The vοlume οf the pyramid is 64 cubic centimeters (cm^3).
What is the vοlume οf the pyramid?The vοlume οf a pyramid is given by the fοrmula V = (1/3) Bh, where B is the area οf the base and h is the height.
In this case, the base οf the pyramid is a square with side length s = 8 cm, sο its area is [tex]B = s^2 = 8^2 = 64 cm^2[/tex].
The height οf the pyramid is h = 3 cm.
Therefοre, the vοlume οf the pyramid is:
[tex]V = (1/3) Bh = (1/3) (64 cm^2) (3 cm) = 64 cm^3[/tex]
Hence, the vοlume οf the pyramid is 64 cubic centimetres (cm^3).
To learn more about the volume of the pyramid, visit:
https://brainly.com/question/218706
#SPJ1
hercules counted some animals at the farm. He saw that 2 of them were sheep and 6 were other animals. If this trend continues, how many of the next 12 animals will be sheep?
Assuming the trend continues, the next 12 animals will include 4 sheep.
What is number?Number is a mathematical concept that represents a quantity or amount. It is usually used to identify a specific value or set of values that can be used for calculation and measurement. Numbers are used in many different fields, including mathematics, science, engineering, and economics. They help us to keep track of quantity and count objects, measure distances and time, and even help to solve problems. Numbers are an essential part of our everyday lives and are essential for understanding the world around us.
This is calculated by taking 2 sheep from the initial group of 8 animals and then multiplying that number by the additional 12 animals for a total of 4 sheep.
To know more about number click-
https://brainly.com/question/24644930
#SPJ1
in the poem hiawatha where did she grow up
Answer: Along the shores of Gitche Gumee
Solve this system of equations for x using the addition method. (Must show steps of addition method to get credit. Do not solve using the substitution method. )
hi
here is the answer
i hope it helps
good luck:))
8. (02.02 LC)
Which of the following rational numbers is equal to 3.1? (5 points)
22/9
24/9
26/9
28/9
Answer: 28/9 (choice D)
Explanation:
You don't need a calculator for this.
Each fraction involves 9 in the denominator. The numerators are the only thing that change. Let x be the numerator.
x/9 = 3.1 can be estimated to x/9 = 3 and that solves to x = 27
The numerator is around 27.
If x = 26, then 26/9 is slightly smaller than 3If x = 27, then 27/9 is exactly 3If x = 28, then 28/9 is slightly larger than 3Choices A,B,C are ruled out since the numerators are smaller than 28. The only thing left is choice D.
You can use a calculator or long division to confirm that 28/9 = 3.1111... where the '1's go on forever.
10. Let's simplify = 3³- 3²-3.
Answer:
15.
Step-by-step explanation:
Given: simplify 3³- 3²-3
First, write the equation:
3³- 3²-3
Then using BODMAS, complete the 'power of' numbers:
27 - 9 - 3
Then subtract 27 from 9:
18 - 3
Finally subtract 18 from 3:
= 15
[tex] \: [/tex]
Solution:-[tex] \sf \: 3³ - 3² - 3[/tex][tex] \: [/tex]
[tex] \sf \: 27 - 9 - 3[/tex][tex] \: [/tex]
[tex] \sf \: 18 - 3[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \sf{ \color{orange} \: 15 \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
ƒ(x) =x²-2x-8/x+2
k
if x = -2
if x = -2
The given piecewise function is not continuous.
What is a continuous function?Continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.
Given is the piecewise function as -
f(x) = {(x² - 2x - 8)/(x + 2)} x ≠ -2
f(x) = {k} x = - 2
At {x} = - 2, the function is not defined and we get -
k = {(-2)² - 2(-2) - 8)/(- 2 + 2)} = {(-2)² - 2(-2) - 8)/0} = ∞
So, the function is not continuous.
Therefore, the given piecewise function is not continuous.
To solve more questions on continuous function, visit the link-
https://brainly.com/question/12990870
#SPJ9
QUESTION 9
Consider the following argument: If Benji's parents buy him a puppy for Christmas, he learns important care-giving skills.
Benji learns important care-giving skills. So, Benji's parents buy him a puppy for Christmas. What is the logical form of
this argument?
O a. Modus Ponens
O b. Hypothetical Syllogism
O c. Disjunctive Syllogism
O d. Denying the antecedent
O e. Affirming the consequent
e. Affirming the Consequent. The argument takes the form of "If P then Q. Q, therefore P."
What is Consequent?Consequent is an outcome or result of an event, action, or decision. It is the result of a cause or premise. Consequents are usually expected and predictable, and can be measured or observed. Consequents are important in the study of cause and effect relationships and can be used to determine the success or failure of certain actions. Consequents can also be used to measure the degree of success or failure of certain objectives. Consequents are often used in decision-making, as well as in research and problem-solving, to help determine the best course of action and the best solution.
In other words, the conclusion (Benji's parents buy him a puppy for Christmas) is based on the premise that Benji learns important care-giving skills.
To learn more about Consequent
https://brainly.com/question/24911665
#SPJ1
Let h(x) = f(x) + g(x). If f(x)=x^3 and g(x)=4x^4, what is h’(1)
Answer:
h'(1) = 19
Step-by-step explanation:
if h(x) = f(x) + g(x), and f(x) = x³ and g(x) = 4x⁴,
then h(x) = (x³) + (4x⁴)
h(x) = x³ + 4x⁴
h'(x) is the derivative of h(x), which = 3x² + 16x³. Thus, h'(1) = 3(1)² + 16(1)³ = 19