55º
vertical angles are congruent
In 2000 the population of a small village was 2,400. With an annual growth rate of approximately 1.68%, compounded continuously, what will the population be in 2020 according to the exponential growth function?
Answer:
[tex]3,358\ people[/tex]
Step-by-step explanation:
The formula to calculate the exponential growth function is equal to
[tex]f(x)=P(e)^{rx}[/tex]
where
f(x) is the population
P is the population in the year 2000
r is the rate in decimal
x is number of years since 2000
e is the mathematical constant number
we have
[tex]x=2020-2000=20\ years\\ P=2,400\\ r=0.0168[/tex]
substitute in the formula above
[tex]f(x)=2,400(e)^{0.0168*20}[/tex]
[tex]f(x)=3,358\ people[/tex]
The scatterplot shows the number of home runs Mario hits during his first four seasons on the company softball team. If his output continues to follow the linear model, approximately how many home runs will Mario hit during his ninth season?
A. 30 home runs
B. 35 home runs
C. 45 home runs
D. 50 home runs
Answer:
i think its B on edge
Danielle bought a dress that was on sale at the clothing store. After taking 40% off the original price of the dress, Danielle paid $39.15, not including tax. What was the original price of the dress, to the nearest cent?
Answer:
Original price of the dress was $97.88
Step-by-step explanation:
40/100=39.15/d
0.4d=39.15
0.4d=39.15
d=39.15/0.4
d=97.88
The original price of the dress is $97.875.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Danielle paid $39.15.
But Danielle paid after 40% off.
So, the price before discount
40% of x = 39.15
x= 3915/40
x= $97.875
Hence, the original price is $97.875.
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Determine whether the given set s is a subspace of the vector space v.
a. v=mn(r), and s is the subset of all upper triangular matrices.
b. v is the vector space of all real-valued functions defined on the interval (−∞,∞), and s is the subset of v consisting of those functions satisfying f(0)=0.
c. v=c2(i), and s is the subset of v consisting of those functions satisfying the differential equation y′′−4y′+3y=0.
d. v=c1(r), and s is the subset of v consisting of those functions satisfying f′(0)≥0.
e. v=r2, and s is the set of all vectors (x1,x2) in v satisfying 5x1+6x2=0. f. v=p5, and s is the subset of p5 consisting of those polynomials satisfying p(1)>p(0). g. v=mn(r), and s is the subset of all nonsingular matrices.
a) Yes, s is a subspace of v because the three conditions for a subspace are satisfied. b) Yes, s is a subspace of v because the three conditions for a subspace are satisfied. c) Yes, s is a subspace of v because the three conditions for a subspace are satisfied.
Explanation:a. v=mn(r) is the vector space of all m x n matrices with entries in the real numbers. In this case, s is a subspace of v if it satisfies the three conditions: (1) the zero vector is in s, (2) s is closed under vector addition, and (3) s is closed under scalar multiplication. Since the zero matrix is an upper triangular matrix, it satisfies the first condition. If two upper triangular matrices are added, the result will also be an upper triangular matrix, satisfying the second condition. And if an upper triangular matrix is multiplied by a scalar, the result is still an upper triangular matrix, satisfying the third condition. Therefore, s is a subspace of v.
b. In this case, v is the vector space of all real-valued functions defined on the interval (-∞, ∞). The subset s consists of functions satisfying f(0) = 0. Similar to part a, we need to check if s satisfies the three conditions to be considered a subspace. The zero function satisfies f(0) = 0, so it satisfies the first condition. If two functions in s are added, the sum will also have f(0) = 0, satisfying the second condition. And if a function in s is multiplied by a scalar, the result will still have f(0) = 0, satisfying the third condition. Therefore, s is a subspace of v.
c. In this case, v is the vector space of all second-order linear homogeneous differential equations. The subset s consists of functions satisfying y'' - 4y' + 3y = 0. To be considered a subspace, s would need to satisfy the three conditions: (1) the zero element is in s, (2) s is closed under addition, and (3) s is closed under scalar multiplication. The zero function satisfies the differential equation, so it satisfies the first condition. If two functions in s are added, the sum will also satisfy the differential equation, satisfying the second condition. And if a function in s is multiplied by a scalar, the result will still satisfy the differential equation, satisfying the third condition. Therefore, s is a subspace of v.
The speed limit on a higway is 70 miles per hour/ About how fast is this in miles per minute?
Answer:
1 mile a minute.
Step-by-step explanation:
A pile of 10 000 sheets of paper is 85 cm thick what is the thickness of 1 sheet of paper
Answer:
0.0085 centimeters.
Step-by-step explanation:
85/10000 is equal to 0.0085 centimeters, which is absurdly thin for anything, really.
Solve for x
(3/4)x-(7/3)=-2x+(5/3)
Answer:
your answer is x=16/11
explanation:
solve for x by simplifying both sides of the equation then isolation the variable.
exact form: 16/11
decimal form: 1.45
mixed number form: 1 5/11
hope this helps
~~bangtanboys7
Answer: [tex]x=\frac{16}{11}[/tex]
Step-by-step explanation:
To solve the equation shown in the problem you must:
- Add the like terms, as following:
[tex]\frac{3}{4}x+2x=\frac{5}{3}+\frac{7}{3}\\ \frac{11}{4}x=4[/tex]
- Multiply both sides by 4.
- Divide both sides of the equation by 11.
Therefore, the result is:
[tex](4)\frac{11}{4}x=4(4)\\11x=16\\x=\frac{16}{11}[/tex]
The ABC Book club charges a $40 monthly fee, plus $2 per book read in that month. The Easy Book Club charges a $35 monthly fee, plus $3 per book read in that month. For each club, how many books must be read in 1 month for the total charges from each club to be equal?
Answer:
5 books must be read in 1 month for the total charges from each club to be equal.
Step-by-step explanation:
Monthly Charges of ABC club = 40$
Per book read charges of ABC club = 2$
amount of book read = x
Total charges of ABC club = 40 + 2x
Monthly Charges of Easy book club = 40$
Per book read charges of Easy Book club = 3$
Total charges of Easy book club = 35 + 3x
To calculate how many books must be read in 1 month for the total charges from each club to be equal,
Total charges of ABC club = Total charges of Easy book club
40 + 2x = 35 + 3x
40 - 35 = 3x -2x
5 = x
x = 5
Therefore, 5 books must be read in 1 month for the total charges from each club to be equal.
If aₙ = 3(3)ⁿ⁻1 , what is S₃?
Answer:
S3 = 39
Step-by-step explanation:
* an = 3(3)^(n-1) is a geometric sequence
* The general rule of the geometric sequence is:
an = a(r)^(n-1)
Where:
a is the first term
r is the common difference between each consecutive terms
n is the position of the term in the sequence
The rules means:
- a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , ........................
∵ an = 3(3)^(n-1)
∴ a = 3 and r = 3
∴ a1 = 3
∴ a2 = 3(3) = 9
∴ a3 = 3(3)² = 27
* S3 = a1 + a2 + a3
∴ S3 = 3 + 9 + 27 = 39
Note:
We can use the rule of the sum:
Sn = a(1 - r^n)/(1 - r)
S3 = 3(1 - 3³)/1 - 3 = 3(1 - 27)/-2 = 3(-26)/-2 =3(13) = 39
Answer:
The correct answer is S₃ = 39
Step-by-step explanation:
It is given that,
aₙ = 3(3)ⁿ⁻¹
To find a₁
a₁ = 3(3)¹⁻¹ = 3(3)°
= 3 * 1 = 3
To find a₂
a₂ = 3(3)²⁻¹ = 3(3)¹
= 3 * 3 = 9
To find a₃
a₃ = 3(3)³⁻¹ = 3(3)²
= 3 * 9 = 27
To find the value of S₃
S₃ = a₁ + a₂ + a₃
= 3 + 9 + 27 = 39
Therefore the correct answer is S₃ = 39
Simplify the equation √3^15
Answer:
the answer is D. 3^7√3
Step-by-step explanation:
For this case we have to define properties of powers and roots:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
We also have to:
[tex]3 ^ {15} = 3 ^ {14} * 3[/tex]
So:
[tex]\sqrt {3 ^ {15}} = \sqrt {3 ^ {14} * 3} = 3 ^ {\frac {14} {2}} * \sqrt {3} = 3 ^ 7 * \sqrt {3}[/tex]
Answer:
[tex]3 ^ 7 * \sqrt {3}[/tex]
Option D
Let p(x)=909+50e−x .
What is p(5) ?
Answer:
The answer is 9.6
hope this helps!
The area of a right triangle is 30 ft2. The base of the triangle is 12 ft. What is the length of the hypotenuse?
Please show your work, and don't forget to label your answer!! Thank you!
➷ The formula for a right triangle is:
(b x h) / 2
We know this:
(12 x n) / 2 = 30
Multiply both sides by 2:
12 x n = 60
Divide both sides by 12:
n = 5
Now we know the height is 5
We can now use Pythagoras' theorem to calculate the hypotenuse:
c^2 = 5^2 + 12^2
c^2 = 169
Square root it:
c = 13
The hypotenuse is 13 ft
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
The formula for working out the area of a triangle:
(b x h) / 2
[tex](12*h)/2=30\\(*2)\\12*h=60h\\h=5[/tex]
Pythagoras' theorem to calculate the hypotenuse:
c² = 5² + 12²
c² = 169
c = 13
The hypotenuse is 13 ft
Step-by-step explanation:
Please answer this question, will give brainliest!
ANSWER
[tex] \angle \: KGI =50 \degree[/tex]
[tex]\angle \: KJI = 130 \degree[/tex]
EXPLANATION
Angles in the same segment are equal.
This implies that;
[tex] \angle \: KGI = \angle \:H[/tex]
Hence,
[tex] \angle \: KGI =50 \degree[/tex]
Also GJKI is a cyclic quadrilateral.
The opposite angles of a cyclic quadrilateral sums up to 180°.
This means that,
[tex] \angle \: KJI + \angle \: KGI = 180 \degree[/tex]
[tex] \angle \: KJI +50 \degree = 180 \degree[/tex]
[tex]\angle \: KJI = 180 \degree - 50 \degree[/tex]
[tex]\angle \: KJI = 130 \degree[/tex]
Solve the quadratic equation by square roots:
1. 4x²= 81
2. (4x-3)²+7=39
Answer:
see explanation
Step-by-step explanation:
(1)
given
4x² = 81 ( divide both sides by 4 )
x² = [tex]\frac{81}{4}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{81}{4} }[/tex] = ± [tex]\frac{9}{2}[/tex]
---------------------------------------------------------------------
(2)
subtract 7 from both sides
(4x - 3)² = 32 ( take the square root of both sides )
4x - 3 = ± [tex]\sqrt{32}[/tex] = ± 4[tex]\sqrt{2}[/tex]
Add 3 to both sides
4x = 3 ± 4[tex]\sqrt{2}[/tex] ( divide both sides by 4 )
x = [tex]\frac{3}{4}[/tex] ± [tex]\sqrt{2}[/tex]
Suppose you are a casino owner, and your casino runs a very simple game of chance. The dealer flips a coin. The customer wins $9 from the casino if it comes up heads and loses $10 if it comes up tails. Question 1. Assuming no one is cheating and the coin is fair, if a customer plays twice, what is the chance they make money?
Answer:
Step-by-step explanation:
The outcome of the game is
Toss 1 Toss 2 Result
H H 18
H T -1
T H -1
T T -20
His only winning position is H ---- H
That means he has only a 1/4 chance in winning. He shouldn't play at all. It might be a fair coin, but it is not a fair game.
Which of the following is a disadvantage to purchasing points
A.they lower monthly payments
B.closing costs are increased
C.An immediate tax break is received
D.the interest rate is lowered for the life of the loan
Apex Answers
Answer:
B - closing costs are increased
Step-by-step explanation:
All of the other options are advantages to purchasing points. You want lower monthly payments (a), a tax break (c), and lower interest rate (d)
Answer:
The correct answer is option B.closing costs are increased.
Step-by-step explanation:
Mortgage points or discount points refers to the fees paid directly to the lender during closing in exchange for a reduced interest rate.
In this way the buyer buys down the rate, that helps in reducing his monthly mortgage payments.
So, option A, C and D are the advantages of purchasing discount points.
What is the probability that you draw a diamond or a spade from a standard deck of cards? A) 1 16 B) 1 4 C) 1 2 D) 3 4
Answer:
The answer is 1/2 which i think that's what you meant from C.
Step-by-step explanation:
A standard deck of cards has 52 cards. 13 of these cards are spades and 13 are diamonds.
the answer to your question is c :]
(9CQ) Find the distance from the balloon to the soccer fields.
Answer:
The distance from the balloon to the soccer fields = 3.6 miles ⇒ answer (b)
Step-by-step explanation:
* Let the hot air balloon at point A , the soccer fields
at point B and the football field at point C
∵ The measure of the angle of depression to the
soccer fields is 20° 15'
∴ The measure of angle B = 20° 15'
∵ The measure of the angle of depression to the
football field is 62° 30'
∴ The measure of angle C = 62° 30'
∵ The sum of measures of the interior angles of any triangle = 180°
∴ The measure of angle A = 180 - (20° 15' + 62° 30') = 97° 15'
* The distance between the balloon and the soccer field
is represented by the side AB of triangle ABC
- Use the sin Rule to find the length of side AB
∵ a/sin(A) = b/sin(B) = c/sin(C)
- a is the side opposite to angle A, b is the side opposite
to angle B and c is the side opposite to angle C
∵ AB = c ⇒ opposite to angle C
∵ The distance between the two fields = 4 miles
∴ BC = 4 miles
∵ BC = a ⇒ opposite to angle A
∴ 4/sin(97° 15') = c/sin(62° 30')
∴ c = (4 × sin(62° 30')) ÷ sin(97° 15')
∴ c = 3.6 miles
∴ The distance from the balloon to the soccer fields = 3.6 miles
answer (b)
Remi invests ?600 for 5 years in a saving account. By the end of the 5 years he has received a total of ?75 simple interest. Work out the annual rate of simple interest
Answer:
2.5 %
Step-by-step explanation:
The simple interest formula is
I = Prt
Data:
I = $75
P = $600
t = 5 yr
Calculation:
75 = 600 × r × 5
75 = 3000 r
Divide each side by 3000
r = 75/3000 = 0.025 = 2.5 % APR
The annual percentage rate is 2.5 %.
Final answer:
The annual rate of simple interest that Remi received from his savings account is 2.5%. This was calculated using the simple interest formula I = PRT, rearranged to solve for R, the annual interest rate.
Explanation:
To work out the annual rate of simple interest that Remi received from his savings account, we can use the formula for simple interest:
I = PRT
where I is the total interest earned, P is the principal amount invested, R is the annual interest rate, and T is the time the money is invested in years.
From the question, we know that Remi invested £600 (P=600), received £75 in interest (I=75), and the investment was for 5 years (T=5). We need to find the annual rate (R).
Rearranging the formula to get value of R, we get:
R = I / (PT)
Substituting the given values:
R = 75 / (600 × 5) (× is the multiplication symbol)
R = 75 / 3000
R = 0.025
To Convert decimal to a percentage, we multiply by 100:
R = 0.025 × 100
R = 2.5%
So, the annual rate of simple interest that Remi received is 2.5%.
A window is in the shape of a rectangle with a base of 4 ft and a height of 5 ft. The window has a colored glass in the shape of a kite. Use the grid to identify the area of the colored glass.
Answer:
A = 10 ft²Step-by-step explanation:
Look at the picture.
A₁ = 2 · 2 = 4
A₂ = 2 · 3 = 6
The area of a rhombus:
A = A₁ + A₂ ⇒ A = 4 + 6 = 10
You can use the formula of an area of a rhombus:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁ = 4, d₂ = 5
Substitute:
[tex]A=\dfrac{(4)(5)}{2}=(2)(5)=10[/tex]
Answer:
10 ft²
Step-by-step explanation:
A = 1/2 (d1) (d2)
A = 1/2 (4) (5)
1/2 x 20
=10 ft²
Easy question!
Are the two hexagonal prisms similar? if so, what is the scale factor of the first figure to the second figure?
Answer:
yes5 : 2 or 2.5 : 1Step-by-step explanation:
The ratios of corresponding linear dimensions are identical:
5/2 = 15/6 = 2.5
so we can conclude the figures are similar. The scale factor is the ratio of corresponding dimensions:
first : second = 5 : 2 . . . or . . . 2.5 : 1
Answer:
Yes.
Scale factor = 2.5.
Step-by-step explanation:
They are similar because corresponding dimensions are in the same ratio:
2/5 = 6/15.
The scale factor = 5/2 = 2.5.
The cost of fabric (y) is directly proportional to he length is yards (x). If 5 yards of fabric cost $14, which equation models this situation?
Answer:
5x = 14
Step-by-step explanation:
If 5 yards of fabric is $14 you need an equation that would solve how much 1 yard of fabric costs. You can say 5x = 14 or x = 2.8 which means that one yard of fabric (1x or just x) is $2.80.
Answer: [tex]y==\frac{14}{5}x[/tex]
Step-by-step explanation:
By definition, we know that Direct proportion equation has the following form:
[tex]y=kx[/tex]
Where k is the constant of proportionality.
Then, If 5 yards of fabric cost $14, you can calculate k as following:
[tex]14=k(5)\\k=\frac{14}{5}[/tex]
Therefore substituting the value of k into the first equation, you obtain the following equation:
[tex]y==\frac{14}{5}x[/tex]
Susan has $800 in a savings account that earns 6% annually. If the interest is not compounded, how much interest will she earn in 5 years?
$240
800x.06= 48
48x5=240
The division algorithm states that if p(x) and d(x) are polynomial functions with d left parenthesis x right parenthesis not equals 0 comma and the degree of d(x) is less than or equal to the degree of p(x), then there exist unique polynomial functions q(x) and r(x) such that
Final answer:
The division algorithm for polynomials establishes that a polynomial p(x) can be divided by a non-zero polynomial d(x) (with degree less or equal to p(x)), to yield unique quotient q(x) and remainder r(x), with r(x) having a lower degree than d(x).
Explanation:
The division algorithm in the context of polynomials is a fundamental concept in algebra that stipulates for any two polynomials p(x) and d(x), with d(x) ≠ 0 and the degree of d(x) less than or equal to the degree of p(x), there exist unique polynomials q(x) and r(x) such that p(x) = d(x) × q(x) + r(x).
In this scenario, q(x) is referred to as the quotient and r(x) is the remainder. The degree of the remainder r(x) will always be less than the degree of d(x), following the division algorithm.
When applying this algorithm to special sets of polynomials like Legendre polynomials, additional properties can be observed, such as the roots of the polynomials or specific transformations like the Poisson bracket that could arise in mathematical physics. Moreover, the concept extends to rational functions, which are the quotients of polynomials.
Line AD is a tangent to circle B at point C and m
What is the measure of
(The answer is 90 but how do you get this answer?)
BCA is 90 degrees, because a tangent line is perpendicular to the raduis line BC.
Final answer:
The measure of angle M is 90 degrees.
Explanation:
The measure of angle M is 90 degrees. To understand why, we can use the fact that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. In this case, line AD is tangent to circle B at point C, so we can draw line AC, which is the radius of the circle, and find the measure of angle M by finding the complement of the angle formed by lines AD and AC. Since the complement of a 90-degree angle is 90 degrees, the measure of angle M is 90 degrees.
Solve on the interval [0/2pi]
1-cos(theta) = (1/2)
Answer:
Final answer is [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex].
Step-by-step explanation:
Given equation is [tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex]
Now we need to find the solution of [tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex] in given interval [tex][0, 2\pi ][/tex].
[tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex]
[tex]-\cos\left(\theta\right)=\frac{1}{2}-1[/tex]
[tex]-\cos\left(\theta\right)=-\frac{1}{2}[/tex]
[tex]\cos\left(\theta\right)=\frac{1}{2}[/tex]
which gives [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex] in the given interval.
Hence final answer is [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex].
In the interval [0, 2π], the cosine function takes on the value 1/2 at two specific angles: π/3 and 5π/3.
What is the interval
To solve the equation 1 - cos(theta) = 1/2 on the interval [0, 2π], this is done by:
Subtract 1/2 from both sides of the equation to isolate the cosine term:
1 - cos(theta) - 1/2 = 0
-cos(theta) + 1/2 = 0
So multiply both sides by -1 to get rid of the negative sign: cos(theta) - 1/2 = 0
1/2 can be written as 2/4: cos(theta) - 2/4 = 0
So look for common denominator for the fraction on the left side, and is 4:
(4*cos(theta) - 2)/4 = 0
Then Multiply both sides by 4 to remove the fraction: 4*cos(theta) - 2 = 0
So, add 2 to both sides: 4*cos(theta) = 2
Lastly divide both sides by 4: cos(theta) = 1/2
Therefore, the solutions to the equation are: theta = π/3 and theta = 5π/3.
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Find the x-intercept of the function: f(x) = 6^x - 2. Round answer to the nearest hundredth, if necessary.
Answer:
x = log base 4 of 2
Step-by-step explanation:
I'm assuming this is truly an exponential function as you state and not a mistype.
6^x = 2
Take the log of each side:
x · log(6) = log(2)
Divide each side by log(6):
x = log(2) / log(6)
x = 0.30103 / 0.77815
x = 0.3869... (rounded)
Factor. 49x^2−36y^2
Enter your answer in the boxes.
[tex]\\Rewrite \ in \ form.\\\\(7x)^2 - (6y)^2\\\\\\\\Use \ difference \ of \ squares \ rule.\\\\(7x + 6y) (7x - 6y)\\\\\\Therefore, \ you \ get \fbox{(7x+6y)&(7x-6y)}.[/tex]
Solve with proper methods.
There are 50 habits on a farm. They are increasing at the rate of 12% every month, How many months will it be until there are 1000 rabbits? Show your work.
Answer:
17.85 months
Step-by-step explanation:
original number of rabbits=50
% increase per month=12%
number of months=x
form equation for 1000 rabbits
(112/100) ×50× x = 1000
56x=1000
x=1000/56
x=17.857 months
Rewrite this sum of two logarithms as a single logarithm.
Answer:
log9(11x)
Step-by-step explanation:
log9(11) + log9(x)
We know that loga(b) + loga(c) = loga(b*c)
log9(11*x)
log9(11x)
Final answer:
To rewrite a sum of two logarithms as a single logarithm, combine them using the property that the log of a product equals the sum of the logs. For example, log a + log b becomes log (ab).
Explanation:
To rewrite the sum of two logarithms as a single logarithm, we use the relevant log properties. One of the most important properties of exponents is that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, which is log xy = log x + log y. Conversely, the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So, if you have two logarithms of the same base you're adding, like log a + log b, you can combine them into a single log by multiplying the two arguments to get log (a*b).
An example using numbers could look like this:
log₂(3) + log₂(5) = log₂(3*5) = log₂(15)
Therefore, the sum of two logarithms, log a + log b, can be rewritten as log (ab), which expresses the multiplication of a and b within a single logarithm.