Answer:
9 years
Step-by-step explanation:
Formula for continuous compounding is;
Total amount after the compounding period = P + P[(e^(rt)) - 1]
Where;
P = principal
r is interest rate
t is time period of compounding
We are given;
P = $12,000
Interest rate; r = 7.5% = 0.075
Time; t =?
Amount after investment; $23,568.40
Thus;
23568.40 = 12000(1 + [(e^(0.075t)) - 1])
(1 + [(e^(0.075t)) - 1]) = 23568.40/12000
[(e^(0.075t)) - 1] = (23568.40/12000) - 1
[(e^(0.075t)) - 1] = 0.964
(e^(0.075t)) = 1 + 0.964
(e^(0.075t)) = 1.964
0.075t = In 1.964
0.075t = 0.67498
t = 0.67498/0.075
t = 9 years
The sum of Randy’s age and Mike’s age is 41. The difference of their ages is 7. Mike is older than Randy.
Let r represent Randy’s age and let m represent Mike’s age. Write two equations that represent the sum and difference of their ages. Part B. Find Mike’s age
Answer: 41-7=m
Mike is 34 yrs
Step-by-step explanation:
What is 25.5 x 1.8 helppppp
Answer:
the answer is 45.9
Step-by-step explanation:
Answer:
45.9
Step-by-step explanation:
Approximately how much interest will accrue before next month's bill if Jill owes $4,500
on her credit card and it charges 21 percent annually?
Answer:78.75
Step-by-step explanation:21 percent of 4500 945 divided my 12 which is 78.75
Select the correct answer. What is the value of x?
log2(x+7)=2
a. -3
b. 11
c. 250
d. 22
Which shows the result of a correct substitution for the system y=2x+3 and 3x+2y=9?
o
A. y= 2y + 3
B. 3(2x + 3) + 2y = 9
C. 3x + 2(2x + 3) = 9
o
D. 2x + 2y = 3
Answer:
C. 3x + 2(2x + 3) = 9
Step-by-step explanation:
We are given the following relation:
y = 2x + 3
And we want to substitute into:
3x + 2y = 9.
So
[tex]3x + 2(2x + 3) = 9[/tex]
Which is given by option C.
y = 3x - 7
Is it linear or exponential
Answer:
Linear
Step-by-step explanation:
The equation y = 3x - 7 is a linear.
A linear equation represents a straight line on a graph, where the variables (in this case, x and y) have a linear relationship.
The equation has a constant coefficient (3) multiplying the variable (x), and a constant term (-7) added or subtracted.
An exponential equation involves variables in the exponent, such as
y = abˣ, where a and b are constants.
The variable x is in the exponent, indicating exponential growth or decay.
Since the equation y = 3x - 7 has a linear relationship and represents a straight line, it is classified as a linear equation.
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The cable company takes an SRS of 250 of the approximately 15,000 households who subscribe to them. They found that 75, percent of the sampled households watch sports on television at least once a month. The company is considering taking more samples like this. Suppose that it is actually 70, percent of their total subscribed households who watch those sports.
Let p represent the proportion of a sample of 250 households that watch sports on television at least once a month.
What are the mean and standard deviation of the sampling distribution of p?
Answer:
The mean of the sampling distribution of p is of 0.7 and the standard deviation 0.029
Step-by-step explanation:
We use the Central Limit Theorem to solve this question. So
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Percentage of 70%, sample of 250.
This means that [tex]p = 0.7, n = 250[/tex]
Mean:
[tex]\mu = p = 0.7[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.7*0.3}{250}} = 0.0290[/tex]
The mean of the sampling distribution of p is of 0.7 and the standard deviation 0.029
Answer:
μp^ = 0.7
σp^ = √0.7(0.3)/250
Step-by-step explanation:
I had this question on khans
The sum of two integers is +15 and one of them is - 7. Which is the next integer?
(a)
| Math Links Book 7
Earlohydrata Giuse
Sodium / Sodium 50 mg
Answer:
22
Step-by-step explanation:
Sum of two integers is 15. One integer is -7 and suppose other integer is x. Then
x+(-7)=15
x=22
Consider points A(2,3) and B(6,9). Find point C on the x-axis so AC + BC is a minimum. The point that minimizes AC + BC is C ( , ).
Answer:
the point C(x,0) = C(3,0) is the point where AC + BC is minimum.
Step-by-step explanation:
Solution:
This question is very simple to solve.
We need to find the x and y elements of point C, which is on the x-axis such that AC + BC = minimum.
So,
As, we have said that, point C is on the x-axis then, it means its y co ordinate will be equals to zero.
Now, we just need to find x co ordinate of the point C.
C (x, 0) as it is on the y -axis.
So, for that, we need to take the mirror image of point B. It means, its x co-ordinate will remain same but y co-ordinate will be negative.
So, our mirror image of B(6,9) = B'(6,-9)
Now, we have to join the points A and B'. Point C, which we are trying to find is the point where this line AB' intersects with x - axis.
So,
Slope of the line AB'
m = [tex]\frac{y1-y2}{x1-x2}[/tex]
m = [tex]\frac{3- - 9}{2 - 6}[/tex] = [tex]\frac{3+9}{2-6}[/tex]
m = [tex]\frac{12}{-4}[/tex] = -3
m = slope = -3
We also know that the equation of line:
y = mx + b
where b = y-intercept.
Now, we need to find the y - intercept of this line.
y = (-3) x + b
where y = -9 and x = 6
so,
-9 = (-3) (6) + b
b = -9 + 18
b = 9 = y - intercept.
SO,
y = mx + b
and For point C(x, 0) y = 0
0 = -3x + 9
Solve for x:
3x = 9
x = 3
Hence, the point C(x,0) = C(3,0) is the point where AC + BC is minimum.
A system of equations that consist of parallel lines has
all the answers that apply)
.. (select
2
no solutions
an infinite number
of solutions
one solution
Answer:
no solutions or infinite solutions
Step-by-step explanation:
Addison prepared 30 kilograms of dough after working 3 hours. How many hours did Addison work if she prepared 50 kilograms of dough? Assume the relationship is directly proportional.
Answer:
Addison worked 5 hours
Step-by-step explanation:
Proportions
A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:
y = kx
Where k is the constant of proportionality.
The relationship between the number of kilograms of dough Addison prepares (y) is proportional to the number of hours he works on it (x).
Knowing he prepared y=30 kilograms of dough after t=3 hours, we substitute in the function:
30 = 3k
Solving for k:
k = 30/3 = 10
The relationship is:
y = 10x
If he prepared y=50 kg of dough, then:
50 = 10x
Solving for x
x = 50/10 = 5
Addison worked 5 hours
Simplify the expression 1/6(12x-30)+18x
find two solutions for the equation 2x + y = 3
Answer:
x=(3-y)/2
y=3-2x)
Step-by-step explanation:
2x+y = 3
x=(3-y)/2
y=3-2x)
Answer: [tex]X =\frac{3-y}{2}[/tex] OR [tex]y = 3 - 2x[/tex]
Step-by-step explanation:
Jada walks at a speed pf 3 miles per hour. Elena walks at a speed of 2.8 per hour. If they both begin walking along a walking trail at the same time how much farther will Jada walk after 3 hours? Explain your reasoning
A bracelet that regulaurly sells for $44 is on sale for 25% off. Find the sale price of the bracelet.
help me please:( please
Answer: In that equation, the -30 represents the rate of change.
Step-by-step explanation
Find the signs of the six trigonometric function values for the given angle.
48°
Answer:
The sign of all will be positive because 48 lie in 1st quadrant
Step-by-step explanation:
sin(48)= 0.743
cos(48)=0.669
tan(48)=1.11
cosec(48)=1.345
sec(48)=1.495
cot(48)=0.90
The sign of all will be positive because 48 lie in 1st quadrant.
What is trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
here, we have,
sin(48)= 0.743
cos(48)=0.669
tan(48)=1.11
cosec(48)=1.345
sec(48)=1.495
cot(48)=0.90
Hence, The sign of all will be positive because 48 lie in 1st quadrant.
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Lily sorted these solid figures into two groups. What is true about the groups
Answer:
One group is completely made of cones whilst the other has cylinders
Step-by-step explanation:
7x+3y=-21 in slope intercept form
Answer:
[tex]y= -\frac{7}{3}x -7[/tex]
Step-by-step explanation:
Answer:
y
=
−
7
3
x
−
7
Step-by-step explanation:
Brainliest?
What is the value of g(0)?
O-2
O-1
O 3
O 6
Answer:
-1
Step-by-step explanation:
Well, at g(0), x = 0, and -2 ≤ 0 < 1, so according to the function definition, we'll need to use [tex]g(x)=-x-1[/tex] to evaluate g(0).
Plugging in 0 for x in this expression gives us [tex]g(0)=-0-1=-1[/tex].
A group of friends were working on a student film that had a budget of $1200. They used 63% of their budget on equipment. How much money did they spend on equipment?
Answer:
0.63
Step-by-step explanation:
Simplify (-56) = 7.
o
O A-8
O B. 9
O a -9
O
D. 8
Answer:
Step-by-step explanation:
o=-8
-56=7*(-8)=-56
In EFG e=2.6 cm f =7.2 cm and g=8.3 cm find the measure of
F(t) = 212 - 61
what the value of t when F(t)= 140 ?
Answer:
[tex]t = -7\ \ \ or\ \ t = 10[/tex]
Step-by-step explanation:
Given
[tex]f(t) = 2t^2 - 6t[/tex]
Required
Find t, when [tex]f(t) = 140[/tex]
Substitute 140 for f(t) in [tex]f(t) = 2t^2 - 6t[/tex]
[tex]140 = 2t^2 - 6t[/tex]
Divide through by 2
[tex]\frac{140}{2} = \frac{2t^2 - 6t}{2}[/tex]
[tex]70 = t^2 - 3t[/tex]
[tex]t^2 - 3t = 70[/tex]
Subtract 70 from both sides
[tex]t^2 - 3t - 70= 70 - 70[/tex]
[tex]t^2 - 3t - 70= 0[/tex]
Expand
[tex]t^2 -10t + 7t - 70 = 0[/tex]
Factorize:
[tex]t(t - 10) + 7(t - 10) = 0[/tex]
[tex](t + 7)(t - 10) = 0[/tex]
Split:
[tex]t + 7 = 0\ \ \ or\ \ t - 10 = 0[/tex]
[tex]t = -7\ \ \ or\ \ t = 10[/tex]
Hence, the values of t are -7 and 10
Pls be honest I’ll mark u
Answer:
C) 10
Step-by-step explanation:
IMMEDIATE HELP PLEASE, IT IS TIMED!!!!
True or False questions
3t + 7 = 3t + 6 Has NO Solution
5x - 6 = 3x - 6 + 2x Has NO solution
5+5b - 3 = 2 + 5b Has infinity many solutions
When an equation has one solution, the variable terms on both sides are the same.
Step-by-step explanation:
True
When an equation has one solution,The variable terms on both sides are the same
Answer:
true
hope it helps
thank you.....
2x + 1 =5
What does x=
Answer:
2
Step-by-step explanation:
2x + 1 =5
2x=4
x=2
First isolate the term containing x which is 2x.
Subtract 1 from both sides to get 2x = 4.
Since x is being multiplied by 2, divide both sides by 2 and we have x = 2.
5
Subtract. Write the expression below in simplest form.
(6x-2)-(-x+5)
===========================================
Work Shown:
(6x-2)-(-x+5)
6x-2+x-5
(6x+x)+(-2-5)
7x-7
When distributing the negative, don't forget to apply the negative to every term inside the parenthesis. So that means -x flips to x, while +5 flips to -5.
Alonzo deposited $4800 into a traditional IRA that grew to $9900 at his
retirement. If Alonzo is currently in the 25% tax bracket and is 75 years old,how much tax will he have to pay when he withdraws the entire $9900?
A. $1200
B. $3675
c. $0
D. $2475
Answer:
$2,475
Step-by-step explanation:
Given that :
Worth of IRA retirement = $9900
Alonzo's tax bracket = 25%
Amount to be paid as tax upon withdrawal :
25% * $9900
0.25 * $9900
= $2,475
A principal of S4800 is invested at 9% Interest, compounded annually. How much will the investment be worth after 7 years?
Use the calculator provided and round your answer to the nearest dollar.
sil
Х
$
?
Answer:
$8775 is the value of the investment after seven years
