Answer:
The population of moose after 12 years will be 7,692
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
y ----> population of moose
x ----> the time in years
a is the y-intercept or initial value
b is the base of the exponential function
we have
[tex]a=40[/tex] ----> the y-intercept is given in the table (value of y when the value of x is equal to zero)
substitute
[tex]y=40(b^x)[/tex]
Find the value of b
For x=1, y=62
substitute in the equation
[tex]62=40(b^1)\\b=62/40\\b=1.55[/tex]
therefore
[tex]y=40(1.55^x)[/tex]
What will be the population of moose after 12 years?
For x=12 years
substitute in the exponential equation
[tex]y=40(1.55^{12})[/tex]
[tex]y=7,692[/tex]
what are the domain and range and asympote of h(x)=6^x -4?
Answer:
Domain: (-oo, oo)
Range: (-4,oo)
Horizontal asymptote: y=-4
Answer:
The domain is all Real numbers.
The range is all real values > -4.
Step-by-step explanation:
The asymptote is y = -4.
$5000 at 4% interest for 3 years?
Answer:
Simple Interest =$5600 (Principal and Interest)
Compound Interest = $5624.32 (Principal and Interest)
Step-by-step explanation:
Using Simple interest, use the formulae, Principal X Rate X Time
= 5000*4%*3
= $600 Interest
Principal plus Interest = $5600
Using compound Interest, use the formulae P(1+r)^n
P means Principal
R means rate
N means number of years
= 500(1+4%)^3
= $5624.32 (Principal with Interest)
Read the following scenarios. Who is better positioned to invest in bonds and why?
Jim is 24 and earns $62,000 a year. He wishes to invest for his newborn daughter's college education, which is 18 years away. Inflation is currently running at 4.1%, while real interest rates are rising.
Elizabeth is 63 years old and earns $137,000 a year. She wishes to invest for retirement, which is four years away. Inflation is currently running at 1.1%, while real interest rates are falling.
Select the best answer from the choices provided.
A.
Jim is better positioned to invest in bonds because he makes less and has longer before his investment matures.
B.
Jim is better positioned to invest in bonds because inflation is high.
C.
Elizabeth is better positioned to invest in bonds because she has less time before her investment matures.
D.
Elizabeth is better positioned to invest in bonds because real interest
rates are falling.
Answer:
The correct answer is A. Jim is better positioned to invest in bonds because he makes less and has longer before his investment matures.
Step-by-step explanation:
Jim is better positioned to invest in bonds for two reasons:
1. He can invest and take advantage of long-term bonds, between 12 and 20 years of term of maturity, that are those that usually have the highest interest rate. His goal is to invest and save for his daughter's college education, that is a newborn.
2. The real interest rates are rising. It means the bonds interest rates are clearly above the inflation rate in the country where Jim and his family live, having a better return for his investment.
Emelina wrote the equation of a line in point-slope form as shown below.
(y + 4) = 3 (x + 2)
What is Emelina’s equation in slope-intercept form?
y = 3x + 2
y = 3x +10
y = 3x – 4
y = 3x – 10
Answer:
y = 3x +2
Step-by-step explanation:
The first answer
Solve -3(2x-3)+10x=3q
Answer:
4x+9=3q
Step-by-step explanation:
-3(2x-3)+10x=3q
-6x+9+10x=3q
4x+9=3q
Answer:
q = 4/3x + 3
Step-by-step explanation:
-3(2x-3)+10x=3q
Multiply the -3 at the beginning by (2x - 3), the parenthesis
-6x + 9 + 10x = 3q
Now combine the like terms (add x's and variables separately)
(-6x + 10x) + 9 = 3q
4x + 9 = 3q
Divide both sides of the equation by 3
(4x + 9) ÷ 3 = q
4x/3 + 9/3 = q
Simplify
q = 4/3x + 3
Hope this helps :)
Find the cosine of ∠U. A) 15 17 B) 17 15 C) 8 15 D) 8 17
The calculated cosine of the angle U is 8/17
How to determine the cosine of the angle U
From the question, we have the following parameters that can be used in our computation:
The triangle
By definition:
The cosine of the angle is calculated using
cos(U) = VW/UW
Where
VW = 8 and UW = 17
Substitute the known values into the equation
cos(U) = 8/17
Hence, the cosine of the angle U is 8/17
evaluate x+6 when x=7
Answer:
13
Step-by-step explanation:
x + 6 = ?
[Replace x with 7]
7 + 6 = 13
13. Charles runs at a rate of 12 kilometers per hour.
What is Charles' speed in meters per minute?
A. 12 meters per minute
B. 20 meters per minute
C. 120 meters per minute
D. 200 meters per minute
Answer:
B.
Step-by-step explanation:
1000 meters in a kilometer and 60 minutes in a hour. 1000/60= 16.6666
(rounds to 20)
Final answer:
Charles' running speed of 12 kilometers per hour is equivalent to 200 meters per minute when converted, which corresponds to option D.
Explanation:
Charles runs at a rate of 12 kilometers per hour, and the question asks us to convert this speed to meters per minute. First, we need to convert kilometers to meters. One kilometer is equivalent to 1,000 meters.
So, Charles' speed in meters per hour is:
12 km/hr × 1,000 m/km = 12,000 m/hr
To convert this speed from meters per hour to meters per minute, we divide by 60 minutes, since there are 60 minutes in one hour:
12,000 m/hr ÷ 60 min/hr = 200 m/min
Therefore, Charles' speed is 200 meters per minute, which corresponds to option D.
The track team needs new uniforms. The students plan to sell plush toy hawks (the school mascot) for $5 each. The students find three companies on line that sell stuffed mascots. Company A sells 18 hawks for $49.14. Company B sells 12 hawks for $33.12. Company C charges $40.65 for 15 hawks. Which company has the Best Buy?
After calculating the cost per hawk for each company, Company C offers the best buy at $2.71 per hawk.
The goal is to find out which company offers the best buy for the plush toy hawks. To do so, we'll calculate the cost per hawk from each company and compare them.
Company A: 18 hawks for $49.14 so $49.14 ÷ 18 = $2.73 per hawkCompany B: 12 hawks for $33.12 so $33.12 ÷ 12 = $2.76 per hawkCompany C: 15 hawks for $40.65 so $40.65 ÷ 15 = $2.71 per hawkCompany C offers the lowest cost per hawk at $2.71, thus they have the best buy.
Dominic collected data on the favorite sports of the
grades. The table shows the relative frequencies of rows for the data collected:
Favorite Sport
Swimming Running Volleyb
Grade 8 0.24 0.17
Grade 9 0.18
Column totals 0.42
ON
Based on the data, which statement is most
O in Grade 8, 14 students liked swimmin
O In Grade 8, 17% of students liked running
O in Grade 9, 31% of students liked volleyball
O in Grade 9, 22 students liked volleyball
Answer:
In Grade 8, 17% of students liked running
Step-by-step explanation:
Although this table is incomplete, there are still enough information to answer.
First, we need to be aware that the data here is written in decimal numbers, which is another way to write percentages.
In other words, 100% equals to 1, which is to say that if we multiply decimal number with 100 we'll get the percentage:
0.39 = 39%
0.04 = 4%
Another important thing to establish is that the value of decimal number DOES NOT mean the number of people, it only suggests the ratio:
0.26 does not mean 26 people etc.
Knowing this, from this incomplete table, we see that 0.17 students from grade 8 liked running. And now we know that 0.17 equals to 17%, which makes B the correct answer.
Answer:
B. In Grade 8, 17% of students liked running
Step-by-step explanation:
The width of a rectangle is 4 1/6 feet, and its area is 35 square feet. What is the perimeter of this rectangle?
The perimeter of rectangle is 25.13 feet
Solution:
Given that,
width of a rectangle = [tex]4\frac{1}{6} \text{ feet }[/tex]
Convert the mixed fraction to improper fraction
[tex]\rightarrow 4\frac{1}{6} = \frac{6 \times 4 + 1}{6} = \frac{25}{6}[/tex]
Therefore,
[tex]\text{width of rectangle } = \frac{25}{6} \text{ feet }[/tex]
Area of rectangle = 35 feet
The area of rectangle is given by formula:
[tex]area = length \times width[/tex]
Substituting the given values, we get
[tex]35 = length \times \frac{25}{6}\\\\length = 35 \times \frac{6}{25} = \frac{42}{5}[/tex]
Thus we get,
[tex]\text{length of rectangle } = \frac{42}{5} \text{ feet }[/tex]
The perimeter of rectangle is given as:
perimeter = 2(length + width)
[tex]perimeter = 2(\frac{42}{5} + \frac{25}{6})\\\\perimeter =2(8.4+4.167)\\\\perimeter = 2(12.567)\\\\perimeter = 25.13[/tex]
Thus perimeter of rectangle is 25.13 feet
I need help please and thank you
Answer:
75
Step-by-step explanation:
6 and 4 are alternate interior angles meaning they have the same value
Brainliest if you are right
Answer:
e
Step-by-step explanation:
because the lines are less scattered and they all are going straight up. they are also higher then all of the other ones.
PLEASE HELP MEHHH
Which of the following represents a function?
Answer: The top one
Step-by-step explanation:
Because there can only be one input for one output. (X’s can’t repeat)
Lesson 8-5
Using the Distributive Property
b (b + 12) = 0
The value of b is -12
Solution:
The given equation, b (b + 12) = 0
On distributing the b inside the parentheses we get,
[tex]\Rightarrow\bold{ b\times b+b\times12=0}[/tex]
[tex]\bold{\Rightarrow b^{2}+12b=0}[/tex]
[tex]\bold{\Rightarrow b^{2}=-12b}[/tex]
[tex]\bold{\Rightarrow 1=\frac{-12b}{b^2}}[/tex]
[tex]\bold{\Rightarrow 1=\frac{-12}{b}}[/tex]
[tex]\bold{\Rightarrow b=-12}[/tex]
Steps to use distributive property to solve an equation:
Multiply the term outside of the parentheses by each term in the parentheses.Distribute a negative number together with its negative sign.Combine like termsSolve the equation.For fractions:
Identify any fractional coefficients or constants.Find the lowest common multiple (LCM) for all denominators.Multiply all terms of the equation by the LCM.Combine like terms and solve the equation.-3(x+5) = -9
Please answer asap
Steps to solve:
-3(x + 5) = -9
~Distributive Property
-3x - 15 = -9
~Add 15 to both sides
-3x - 15 + 15 = -9 + 15
~Simplify
-3x = 6
~Divide -3 to both sides
-3x/-3 = 6/-3
~Simplify
x = -2
Best of Luck!
Answer:
x= -2
Step-by-step explanation:
First, distribute the 3 into the parenthesis.
(-3)x+ (-3)5= -9
Then, multiply.
-3x-15= -9 *The negative makes it into becoming subtraction.
Now, add 15 to both sides since that's the opposite of subtraction.
-3x-15= -9
+15 +15
Then, divide by 3 to both sides to isolate the variable.
-3x= 6
-3 -3
x= -2
equation in slope intercept form for a line that passes through (1,5) and (1,1)
Answer:
x = 1
Step-by-step explanation:
If you graph this, you will see that you will get a line that is straight up and down (or perpendicular to the x axis). No matter what y is, x will always be 1.
(I will give brainliest, a thanks, 30 points, and 5 stars if you can answer these 2 questions)
1.C=6π yd, find area, answer in terms of π
2. C=22π in^2, find area, answer in terms of π
Answer:
1. 9 pi, 2. 121 pi
Step-by-step explanation:
The formula for circumference is pi d. So for the first question the radius would be three. The you do pi r ^2 for area so 3 times pi squared. Which is 9 pi. For the second you will do the same thing you will do 22 pi divided by 2 which is 11 pi then you will square 11pi and get 121 pi
Which point is the y-intercept of the graph of 5x - 3y = 15 ?
(-5, 0)
(3, 0)
0, -5)
(0,3)
Answer:
c
Step-by-step explanation:
Given that the points (-7, 6), (3, 6), (3, -6), and (-7, -6) are vertices of a rectangle, how much longer is the length than the width?
Answer:
Therefore,
The Length is longer than Width by 2 units.
[tex]Length=Width+2[/tex]
Step-by-step explanation:
Given:
Let the vertices of a Rectangle be
A ( -7 , 6)
B ( 3 , 6)
C ( 3 , -6)
D ( -7 ,-6)
To Find:
Relation between Length and Width = ?
Solution:
First we will find the Length and Width of Rectangle by Distance Formula ,
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting the values we get
[tex]l(AB) = \sqrt{((3-(-7))^{2}+(6-6)^{2} )}[/tex]
[tex]l(AB) = \sqrt{((10)^{2}+(0)^{2} )}\\l(AB)=\sqrt{100}=10\ unit[/tex]
Similarly for BC we will have,
[tex]l(BC) = \sqrt{((3-3)^{2}+(-6-6)^{2} )}\\l(BC)=\sqrt{144}=12\ unit[/tex]
Now
Length = 12 units.
Width = 10 units.
Therefore,
Let Length be denoted by "L" and Width by "W" then
[tex]Length=Width+2=10+2=12\\\\\therefore L=W+2[/tex]
Therefore,
The Length is longer than Width by 2 units.
[tex]Length=Width+2[/tex]
Evaluate a Composit
Given f(x) = x - 7 and g(x) = x2
Find g(4)).
G(f(4)) =
g(x) = x²
g(4) = 4² = 16
g(f(4)) = (f(4))² = (4-7)² = (-3)² = 9
The number 57 is more than the number of situps Lyle can do. Which of the following inequalities represents the number of situps Lyle can do?
A.
x = 57
B.
x > 57
C.
x = 49
D.
x < 57
Final answer:
The correct inequality to represent the number of situps Lyle can do, if 57 is more than he can do, is D. x < 57, indicating that Lyle can do fewer than 57 situps.
Explanation:
The inequality that represents the number of situps Lyle can do, given that the number 57 is more than the number of situps Lyle can do, is x < 57. This is because if 57 is more than what Lyle can do, then Lyle can do any number of situps that is less than 57.
To represent this relationship mathematically, we use the inequality sign '<'. Thus, the correct option from the provided choices is D. x < 57. This means Lyle can do 56, 55, 54, etc., situps, but not 57 or any number greater than 57.
27/9+8ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
Answer:
3+8g
Step-by-step explanation:
27/9+8g=3+8g
A 41-foot ladder is placed against a vertical wall of an apartment building. The base of the ladder is 9 feet from the base of the apartment building
The ladder reaches 40 feet up the wall.
41 squared (1681) minus 9 squared (81) is 1600. 40 is the square root of 1600.
The required distance between the top of the ladder and the ground is 40 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. Let's call the distance from the base of the ladder to the wall "x", and let's call the length of the ladder "y".
According to the problem statement, we know that the ladder is 41 feet long and that the base of the ladder is 9 feet from the base of the apartment building.
y = 41 feet
x = 9 feet
We can use the Pythagorean theorem to solve for the distance between the top of the ladder and the ground. The Pythagorean theorem tells us that:
y² = x² + z²
where "z" is the distance between the top of the ladder and the ground. Plugging in the values we know,
(41 feet)² = (9 feet)² + z²
1681 = 81 + z²
1600 = z²
z = 40 feet
Therefore, the distance between the top of the ladder and the ground is 40 feet.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
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2 3/4 convert this number into an Improper fraction
Answer:
11/4
Step-by-step explanation:
is 0.325 a rational or irrational
Answer:
rational number
Step-by-step explanation:
Answer:
It's a rational. You can convert this to a simplified fraction
An irrational number is a number which cannot be expressed in a ratio of two integers. In rational numbers, both numerator and denominator are whole numbers, where the denominator is not equal to zero. While an irrational number cannot be written in a fraction.
6 times a number plus 21 is greater than 6
A. 6 x plus 21 greater than 6
B. 6 x plus 21 less than or equals 6
C. 6 x plus 21 greater than or equals 6
D. 6 x plus 21 less than 6
How do you workout 28 divided by 812
Answer:
29
Step-by-step explanation:
Look at image
Angela puts $520 in an account that earns 6% per year. What interest will she get at the end of 1 year?
Answer:
$31.20
Step-by-step explanation:
Angela will get an amount of $31.2 as the interest at the end of 1 year.
What is Simple Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Given that Angela puts $520 in an account that earns 6% per year.
Principal or initial amount = $520
Rate of interest = 6% = 6 / 100 = 0.06
We have to calculate the amount of interest.
Interest amount = $520 × 0.06
= $31.2
Hence the amount of interest that Angela get at the end of the year is $31.2.
To learn more about Simple Interest, click on the link given below :
https://brainly.com/question/22621039
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Find the inverse of f(x)=5x+11
Answer:
f^-1 (x)=1/5x-11/5
Step-by-step explanation:
y=5x+11
x=5y+11
5y=x-11
y=1/5x-11/5