Final answer:
The compound interest inequality for the investment account is 3500(1 + 0.08)^t < 6000. Solving this, we find that the account will have less than $6,000 for approximately 6 years.
Explanation:
To solve this problem, we will use the formula for compound interest which is [tex]A = P(1 + r)^t,[/tex] where:
A is the future value of the investment/loan, including interestP is the principal investment amount ($3,500 in this case)r is the annual interest rate (decimal)t is the number of years the money is invested or borrowed forWe are trying to find the number of years, t, when the account will have less than $6,000, at an annual interest rate of 8%, i.e., r = 0.08.
The inequality will be:
[tex]3500(1 + 0.08)^t < 6000[/tex]
To solve for t, we first divide both sides by 3,500:
[tex](1 + 0.08)^t[/tex]< ≈ 1.7143
Now, take the natural logarithm of both sides:
[tex]ln((1 + 0.08)^t) < ln( 1.7143)[/tex]
t · ln(1.08) < ln(≈ 1.7143)
Divide both sides by ln(1.08) to isolate t and calculate:
t < ≈ ln(≈ 1.7143) / ln(1.08) < ≈ 6.6
Therefore, the investment account will have less than $6,000 for approximately 6 years.
What is the percent increase modeled in the function f(x)=30(1.25)*
A. 30%
B. 1.25%
C. 25%
D. 75%
the increase would be 1.25-1 = 0.25 = 25%
Answer is C
A wildlife biologist catches and releases 20 fish from two different lakes at random locations. he catches 10 fish at lake palmer and 10 fish at lake dalton. he measures the length of each fish to the nearest quarter of an inch. palmer dalton first quartile 6.75 5.5 second quartile (median) 10.25 6.75 third quartile 13 7.5 based on the samples, what generalization can be made? at least 25 percent of the fish in both lakes are no longer than 6 inches. the interquartile range for lake dalton is 2 inches greater than the interquartile range for lake palmer. the first quartile value at lake palmer is 1.25 inches longer than the first quartile value at lake dalton. not enough information is provided to draw any of these conclusions.
Answer:
The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.
Step-by-step explanation:
For f(x)=4x squared -3 and g(x)=x +1 find (f - g)(x) PLEASE HELPP
1) AB¯≅AD¯ Given
2)∠ACD is a right angle.- Given
3) m∠ACD=90° -Definition of right angle
4) m∠ACB=90° -Given
5) m∠ACB=m∠ACD -Transitive Property of Equality
6) ∠ACB≅∠ACD Definition of congruent angles
7) C is the midpoint of BD¯ Given
8)C bisects BD¯ ?
9) BC¯≅CD¯ Definition of bisect
10) AC¯≅AC¯ Reflexive Property of Congruence
11) △ABC≅△ADC -SAS Congruence Postulate
What is the correct reason for Statement 8?
Given
Definition of bisect
Definition of congruent segments
Definition of midpoint
Answer:
By definition of midpoint.
Step-by-step explanation:
proof:
1.Statement: [tex]\overline{AB}\cong \overline{AD}[/tex].
Reason: Given.
2.Statement: [tex]\angleACD[/tex] is a right angle.
Reason:Given.
3.Statement:[tex]m\angle ACD=90^{\circ}[/tex].
Reason: By definition of right angle.
4.Statement: [tex]m\angle ACB=90^{\circ}[/tex].
Reason: Given.
5.Statement: [tex]m\angle ACB=m\angle ACD[/tex]
Reason: Transitive property of equality.
6. Statement:[tex] m\angle ACB\cong m\angle ACD[/tex].
Reason: By definition of congruent triangles.
7.C is the midpoint of [tex]\overline {BD}[/tex].
Reason: Given.
8.Statement: C bisect [tex]\overline{BD}[/tex]
Reason: By definition of midpoint.
9.Statement:[tex]\overline{BC}\cong \overline{CD}[/tex]
Reason: By definition of bisect.
10.Statement:[tex]\overline{AC}\cong\overline{AC}[/tex]
Reason: By reflexive property of congruence.
11.Statement:[tex]\triangle ABC\cong \triangle ADC[/tex].
Reason: SAS congruence postulate.
The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes?
74.3%
55.2%
44.8%
37.2%
Actually variation is simply equivalent to the square of the correlation coefficient r. So we can say that:
variation = r^2
So given an r value of 0.743, so the variation is:
variation = 0.743^2
variation = 0.552
Answer:
55.2%
A equation whose solutions form a straight line on a coordinate plane is a what
Evaluate the given expression if k=-84
5 |k+10| - |4k|
what is the value of x (I will give 20 points to best answer)
Answer options
61
37
85
122
The value of x is 61 after using the concept of vertically opposite angles option (A) 61 is correct.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that:
The angles are shown in the picture.
As we know, from the definition of vertically opposite angles, the angles when two lines intersect each other and at the intersecting point.
The first angle = 2x + 24
The second angle = 146
Equating both the angles:
2x + 24 = 146
2x = 146 - 24
2x = 122
x = 122/2
x = 61
Thus, the value of x is 61 after using the concept of vertically opposite angles option (A) 61 is correct.
Learn more about the vertically opposite angles here:
brainly.com/question/24287162
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You flip a coin and then roll a fair six sided die. Then the coin lands heads up and the die shows a one
A function is given. Determine the average rate of change of the function between the given values of the variable: f(x)= 4x^2; x=3, x=3+h
3/8(z+11)=y solve for z in the literal equation
When h has the value of 5 calculate 6h +9
Round 28,573 to the nearest thousand
Under which condition does a country with a small GDP have a large per capita income?
A jar contains n nickels and d dimes. There are 20 coins in the jar, and the total value of the coins is $1.40. How many nickels and how many dimes are in the jar?
twenty-four players divided into three teams?
If you shift the quadratic parent function, f(x) = x2, left 12 units, what is the equation of the new function?
A. g(x) = (x – 12)2
B. g(x) = (x + 12)2
C. g(x) = x2 – 12
D. g(x) = x2 + 12
solve the system by substitution. -4.5-2y=-12.5 , 3.35x-y=-0.75
If it starts out at -10 degrees, what will the temperature be if it rises 30 degrees?
A.10 degrees
B.20 degrees
C.30 degrees
D.40 degrees
add 30 to -10:
-10 + 30 = 20
Answer is B.
The students at Campbell High School have been planting trees as part of an ongoing service project. This month, they averaged 15 trees per participant. That is 150% more trees than their average the last time they did it. What was their average last time?
___ trees
Final answer:
The average number of trees planted by participants last time was 10 trees, calculated by understanding the percentage increase and using basic arithmetic.
Explanation:
The average number of trees planted by participants last time was 10 trees.
To solve this, we know that the current average is 15 trees per participant, which is 150% more than the last average. This means the current average is 250% of the last average. To find the last average, you divide the current average by 2.5 (250%), giving you 6. Then, you calculate 150% of 6, which equals 9. Adding 6 and 9 together gets you 15 trees, the current average, confirming the last average was 10 trees.
The lengths of the sides of a triangle are represented by 3 consecutive even integers. if the perimeter of the triangle is 72 feet, find the lengths of its sides
help me and show how you got it please
Dana was picking strawberries to sell and placing them in baskets on a table. the number of strawberries in the basket is 4 more than the number of baskets on a table. if b represents the number of baskets on each table, which expression can be used to represent the number of strawberries on 5 tables? 5b4 5(b + 4) 5b(b + 4) 5b + 4
karen says that 6 is a common factor of 2 and 3 ken says that 6 is a common multiple of 2 and 3 who is correct
One hundred percent of the fish in a pond are goldfish. i take 10$\%$ of the goldfish out of the pond. what percentage of goldfish does the pond now contain?
Help please!! Find domain and range for 20 points
suppose a research team takes a simple random sample of 100 parma wallabies. in this sample, the tails of the wallabies have a mean length of 46 centimeters and a standard deviation of 2.6 centimeters.
What percent of the time could a simple random of 100 parma wallabies have a sample mean that is not in the 95% confidence interval?
5%
0%
2.5%
20%
The volume of a can (right circular cylinder) is 10 cubic feet. the curved surface area is the area of the side. write the curved surface area s as a function of the radius r. s =
The volume formula of a cylinder is given as:
V = π r^2 h
So plugging in the value of the volume:
10 ft^3 = π r^2 h
h = 10 / (π r^2) ---> eqtn 1
The formula for the surface area of cylinder is:
s = 2 π r h + 2 π r^2
plugging in eqtn 1:
s = 2 π r [10 / (π r^2)] + 2 π r^2
s = (20 / r) + 2 π r^2 (ANSWER)
How many integers less than 1000 have no factors (other than 1) in common with 1000?
25% of what number is 9
can you explain how you got your answer and show your answer too.
Thank You