The amount of Rita deposit is $2556.
What is Simple Interest ?The interest calculated on the principal amount or the initial investment.
It is given in the question
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.
P = ?
S.I. = $63.90
Interest = 6%
T = 150days
S.I. = (P *R*T)/100
63.90 = P * 6 * 150*100 /360
63.90 * 360*100 /( 150 *6) = P
P = $2556
Therefore the amount of Rita deposit is $2556.
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S 2. Let f(x) = x - k√x
a. Find a value of k such that the function has a critical point at x = 25.
b. Is the above critical point a local maximum, local minimum or neither? Show calculus to support your answer.
a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative
[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]
so that
[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]
b. Taking the second derivative, we get
[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]
At x = 25, the second derivative has a positive sign,
[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]
which means f(x) is concave upward around x = 25, so this critical point is a local minimum.
Evaluate the expression.
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,128 was collected on the sale of 1,336 tickets. How many of each type of ticket were sold?
Answer:
Adults = 448
Students = 888
Step-by-step explanation:
Write equations with info given
A = Adult tickets
S = Student tickets
5A+1S=3,128
A+S=1336
Subtract equations from each other
4A=1792
Solve for A
A=448
Plug A into second equitation
448+S=1336
Solve for S
S=888
For a monthly family cookout, David
buys 3 packages of hot dogs and 4
packages of hamburger patties.
Hot dog packages each contain a hot
dogs. Hamburger packages each
contain y hamburger patties.
Complete the expressions for the total number of hot dogs and hamburger
patties David buys for 6 cookouts.
Use the number pad to enter your answers in the boxes.
6(
x+
Answer:
help me to find Xian pleaseee:( i miss him so much:(
sorry for answering Non sense po i hope u understand me ty po!
The average profit on each car sold was $2430, correct to the nearest $10. Calculate the lower bound for the total profit. Write down the exact answer.
The lower bound for the profit is $2425.
What is the lower bound?When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0
The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434
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Solve the following radical equation.
√2x-3 =2
Answer:
First, we have to add 3 to both sides.
[tex]\sqrt{2x} - 3 + 3 = 2 + 3[/tex]
Then we simplify the equation,
[tex]\sqrt{2x} = 5[/tex]
Divide both sides of the equation by [tex]\sqrt{2}[/tex]
[tex]\frac{\sqrt{2x} }{\sqrt{2}} = \frac{5}{\sqrt{2}}[/tex]
Finally, simplify.
[tex]x = \frac{5\sqrt{2}}{2}[/tex]
Therefore, our answer is [tex]x = \frac{5\sqrt{2}}{2}[/tex]
3.5
Step-by-step explanation:
square means 1/2.so,1/2(2x-3)=(2)^2
then square cancel by square. 2x-3=4
2x=4+3, 2x=7then divided by 2.
x=3,5
Explain a time in your life you underwent metamorphosis
Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time
Step-by-step explanation:
I Hope This Helps!
Carlos invests $4540 at a rate of r% per year compound interest.
At the end of 10 years he has earned $1328.54 in interest.
Calculate the value of r.
Answer:
Initial balance$1000
interest rate 8%
Term 20yrs
Step-by-step explanation:
The final balance is $4,926.8.The total compound interest is $3,926.8.
The value of r is 2 %.
What is simple & compound interest?Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. Formula. S.I. = (P × T × R) ⁄ 100.
Given:
Principal(P)= $4540
Rate = ?
Time=10 years
CI=$1328.54
We have to find the value of r.
According to given question we have
By the use of compound interest we have
[tex]CI=p((1+\frac{r}{100} )^{10} -1)\\\\1328.54 =4540 ((1+\frac{r}{100} )^{10} -1)\\\\\0.292= ((1+\frac{r}{100} )^{10} -1)\\[/tex]
After simplifying we get,
r=2 %
Therefore, the value of r is 2 %.
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I need help ASAP PLEASE > How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3? (Please explain with your on words)
Answer:
The graph has been moved 7 units to the left and 8 units down.
Step-by-step explanation:
When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.
When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.
A bowl contains 28 black, 21 red, 23 blue, and 10 green balls
A ball is drawn at random. P (blue).
Answer:
P (blue) = 23 / 82
Step-by-step explanation:
There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls
or,
23 / 82
So, the probability of a blue ball being chosen is 23/82
(or a 28% chance [rounded])
Suppose a nuclear power plant disaster occurs. How could GDP be a "false beacon" in this case?
If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.
Why would GDP be a false beacon?Two of the components of GDP are government spending and private investment.
If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.
GDP would therefore increase.
This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.
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1. Solve the quadratic function by graphing. x²-3x - 18 - 0
Answer:
that's easy all you have to do is find out what is the value of x then divided by 2 once you divide by 2 subtract 3x 18 and 0
vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months and vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 months
how do I solve this and do I have enough information to answer the question and what step would take to solve the problem and how do I calculate the results
The calculation of the interest based on the price given shows that vehicle B has a lower interest.
How to calculate the price?From the information given, vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months. The interest will be:
= (25000 × 5 × 5)/100
= $6250
Vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 months. The interest will be:
= (29000 × 4 × 5)/100
= $5800
Therefore, the calculation of the interest based on the price given shows that vehicle B has a lower interest.
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If you help me you get a lot of points
Answer:
Step-by-step explanation:
#a
pattern 0 will include 4 reds in square
Because it's independent of pattern no
#b
Figure 1 has 4+4=8
Figure 2=4+8+2=14
Figure 3=4+12+3=19
The pattern n rule is
n²+3n+4So for 13th n
13²+3(13)+4169+39+4212squares#c
attached
y=x²+3x+4#d
Already given in c
What is the median of the data set?
16, 21, 28, 30, 40, 45, 54, 58
A. 58
Β. 35
C. 10
D. 19
Answer:
I think 10 is the answer it's not sure.
Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
The solution to the given system of equation is (4, 4)
Factorizing quadratic functionsFrom the solved steps, the final quadratic functions is given as;
x^2 - 8x + 16 = 0
Factorize to have;
x^2 - 4x - 4x + 16 = 0
x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0
x = 4 and 4
Hence the solution to the given system of equation is (4, 4)
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Julian calculates the volume of a rectangular prism with the dimensions 3/4ft by 4 feet by 1/2 ft. His work is shown here.
What error did Julian make?
He multiplied the numerators incorrectly.
He multiplied the denominators incorrectly.
He simplified 12/6 incorrectly.
He wrote 4 as a fraction incorrectly.
Answer:
He multiplied the denominators incorrectly
Step-by-step explanation:
we know that
The volume of a rectangular prism is given by the formula
V=LWH
we have
L=3/4 ft
W=5/1 ft
H=1/2
substitute
V=(3/4)(5/1)(1/2)= 3x5x1= 15
₋₋₋₋₋₋₋₋ ₋₋₋₋ ft³
4x1x2= 8
therefore
He multiplied the denominators incorrectly
Calculate the discriminant to determine the number of real roots of the equation.
y = x2 + 3x + 9
one real root
no real roots
three real roots
two real roots
find D which is the discriminant and with D < 0.
therefore the equation has an imaginary root and not a real root.
Find the area of a regular polygon with 5 sides that has a side length of 6 inches and an apothem of 9 inches.
Area = [?]in2
Answer:
see the attachment photo!
Answer: The correct answer is 135 in².
Step-by-step explanation: An area of a polygon is this:
Area = (number of sides × length of one side × apothem)/2
(5 x 6 x 9) / 2 = 135
How many liters each of a 24% iodine solution in a 40% iodine solution must be used to produce a total make sure of 100 L of 28% iodine solution
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
How to determine the volume associated with a given concentrationPhysically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:
x · 24 + (1 - x) · 40 = 28
40 - 16 · x = 28
16 · x = 40 - 28
16 · x = 12
x = 3/4
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
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A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.
Answer:
33,75 clients(huh?)
Step-by-step explanation:
75 / 100 = 0,75(1% of all clients)
0,75 * 45 = 33,75(number of business clients)
A group of kids just finished trick-or-treating. The number of pieces of candy collected by each of the 5 kids is listed below.
31,33,36,41,34
Find the standard deviation of the data set. Round your answer to the nearest hundredth.
find the slope of the lined graph
Answer:
1
Step-by-step explanation:
The points go rise:1 up:1 so the slope is 1.
Answer:
hey!! we can taIk here
Step-by-step explanation:
WHAT IS THIS HELP
if u put a bad answer i'll report
Answer:
C
Step-by-step explanation:
Two negatives cancel out and turn into a positive.
In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8
So the answer is C
12. Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
A)(-7,-1)
B)(4,5
C)(7,-1)
D)(-3,7)
x² + 10x + 3 = -21?!?!!?!?!!!?
Answer:
-6,-4
Step-by-step explanation:
if you have to evaluate its 4
and there is 2 solutions
A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets. There were more student tickets sold than adult tickets. How many adult tickets were sold?
A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets is mathematically given as
How many adult tickets were sold?Generally, the equation for a sold tickets is mathematically given as
S=x+72
Therefore
x+x+72=772
2x+72=772
2x=772-72
x=350
In conclusion, tickets sold was
x=350
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Find the measure of the remote exterior angle. m/x (198-5n)
m2y = (5n+37)
m²z = (n+7)
The measure of the remote exterior angle is 128°.
How to calculate the angle?From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)
198 - 5n = 6n + 44
Collect like terms
154 = 6n + 5n
154 = 11n
n = 154/11
n = 14
The value of angle x will be:
= 198 - 5n
= 198 - 5(14)
= 198 - 70
= 128
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A box has candies in it: are taffy, are peppermint, and are caramel. (Each candy falls into only one of these categories.) Brian wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the first candy selected is taffy and the second candy is caramel?
Do not round your intermediate computations. Round your final answer to three decimal places.
Probability that the first candy selected is taffy and the second candy is caramel is 0.144.
The data missing in the question is
A box has 18 candies in it: 3 are peppermint, 4 are caramel, and 11 are taffy.
What is Probability ?Probability can be defined as the study of likelihood of an event to happen.
It has a range of 0 to 1.
Probability is the ratio of the expected outcomes / total coutcome.
Total outcomes = 18
The probability that the first candy is taffy is 11/18
Now as there is no replacement , the total outcomes can be 17
The probability that the second candy is caramel is 4/17
Probability that the first candy selected is taffy and the second candy is caramel = (11/18)(4/17)
= 0.144
Therefore the Probability is 0.144
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AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC
Answer:
60°
Step-by-step explanation:
Arc BC and Angle BWC are the same number of degrees.
When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.
Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.
180° - 120° is 60°
Angle BWC is 60° so Arc BC is 60°