Answers
______________________________________________________
→ " x = 47 " .
______________________________________________________
Explanation:
______________________________________________________
Note: The "vertex" is "floating around" inside the circle.
Answer:
47
Step-by-step explanation:
Related Questions
how do you do 27?????
Answers
To start, the equation needed to represent this problem would be an equation:
y= ab^x
a represents the initial amount. In this case, the initial amount would be 4 billion. It would be represented as 4 since each 1= one billion.
b represents the rate. Because the problem discusses a growth, convert the rate, 1.9% to a decimal and add 1 to it (add one if it is a growth, subtract one if it is a decay). b would be 1.019.
x represents the time in which the population grows or t.
When you piece this together, your equation should look like:
y=4(1.019)^t
or
Choice A.
Hope this helps and have a nice day! Feel free to ask any questions about my work. :)
_______________________________________________________
Explanation:
______________________________________________________
Use the formula for "exponential growth" :
______________________________________________________
→ " y = A * (1 + r)^t " ;
______________________________________________________
in which:
______________________________________________________
A = the "beginning population" ;
→ (in number representing "billions of people") ;
→ given the "beginning population" is "4 billion" ;
→ " A = 4 " ;
______________________________________________________
r = rate (of change) = 1.9% ; expressed as a decimal:
→ "r = rate = 1.9% = { 1.9 ÷ 100 } ;
→ {Take the "1.9" ; & move the decimal point 2 (two) spaces backward }:
→ 1.9% = 1.9 ÷ 100 = 0.019 ;
→ " r = 0.019 " ;
→ " t = time" ; (usually in "years" ; however, all the answer choices provided leave the "t" as it is; so we shall do so, too.
________________________________________________________
→ Replace "y" with: " P(t) " ;
→ And rewrite the equation of the function with our known values:
→ " y = A * (1 + r)^t " ;
____________________________________________________
→ becomes:
→ " P(t) = 4* (1 + 0.019)^t " ;
→ " P(t) = 4 * (1 .019)^t " ;
____________________________________________________
→ which is: Answer choice: [A]: " P(t) = 4 * (1 .019)^t " .
____________________________________________________
A number is chosen at random from 1 to 10. find the probabilty of not selecting a multiple of 3
Answers
So the probability is 7/10 = .7 = 70%
Find the Mean Median Mode and range of each data set that is obtained after adding the given constant. 12,10,15,17,15,9,10,15,12,14,+9. Please show work.
Answers
9, 9, 10, 10, 12, 12, 14, 15, 15, 15, 17
1. To find the mean, add all the number together and divide the summation by 11[ which is the total number of the figures given]
Mean = [9 + 9 + 10 + 10 + 12 + 12 + 14+ 15 + 15 + 15 + 17] / 11 = 138 / 11
Mean = 12.5
Therefore, the mean is approximately equal to 13.
2. The median of a number refers to the number in the middle of a sorted set of number.
To find the median of a set of numbers, the numbers have to be arranged first in the correct increasing order and the number that falls in the middle will be the median. If two numbers fall in the middle, add the two together and find the average. For the set of number given above, the number that falls in the middle is 12.
Therefore, the median = 12.
3. The mode of a set of number refers to the number in the set, which has the highest frequency of occurrence, that is, it is the number that occur most. Looking at the set of number given above, 15 occurred three different times. Therefore, the mode of the set of number given above is 15.
Mode = 15.
4. The range of a set of number refers to the difference between the highest and the lowest numbers in the set of a given number. It represents the spread of the data. In the set of numbers given above the range is determined thus:
Range = 17 - 9 = 8.
Therefore, Range = 8.
Mean: 12.545454545455
Median: 12
Range: 8
Mode: 15, appeared 3 times
Largest: 17
Smallest: 9
Sum: 138
Count: 11
Mary is walking 3 miles per hour jerry starts jogging at a rate of 4 miles per hour after marry has been walking for 15 minuets jerry jogs 2 miles as Mary continues walking and they both stop at the same time
Answers
Solution:
Mary: 3 mph
Jerry: 4 mph
Jerry starts jogging after Mary had been walking for 15 minutes.
Distance Mary had walked before Jerry starts jogging = Speed * Time = 3*15/60 = 0.75 miles.
Time taken by Jerry to jog for 2 miles = Distance/Speed = 2/4 =1/2 = 0.5 hrs.
Since they stopped at the same time,
Distance Mary walked while Jerry jogged = Speed* Time = 3*0.5 = 1.5 miles
Therefore,
Total distance Mary walked = 0.75+1.5 = 2.25 miles.
Which graph would help solve the equation 5log(x+3)=5
Answers
The value of x is 7 for the given equation.
What is logarithm?Logarithm, a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.
For the given situation,
The equation is 5log(x+3)=5.
On solving this equation, we can get value of x.
⇒ [tex]5log(x+3)=5[/tex]
⇒ [tex]log(x+3)=1[/tex]
We know that, log 10 = 1
Then,
⇒ [tex]log(x+3)=log10[/tex]
⇒ [tex]x+3=10[/tex]
⇒ [tex]x=7[/tex]
Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.
Learn more about the logarithm here
https://brainly.com/question/20785664
#SPJ2
Will give brainliest! Which are simplified forms of the expression sec^2theta sin2theta
Which is the second answer? I already got the first one
Answers
Answer:
C) 2 tan θ
E) [tex]\frac{sin2[theta]}{cos^2[theta]}[/tex] (it wouldn't let me do the actual θ symbol)
Step-by-step explanation:
This is essentially what the other person said, but in a better format.
fatima wants to find the value of sin theta, given cot theta equals 4/7. which identity would be best for fatima to use?
Answers
1+cot ²∅=csc² ∅
cot ∅=4/7
so
1+(4/7)²=csc² ∅
csc² ∅=1+(16/49)
csc² ∅=(65/49)
csc ∅=(√65)/7
remember that
csc ∅=1/sin ∅
sin ∅=1/csc ∅------> sin ∅=7/√65-----> sin ∅=(7√65)/65
the answer is
the best identity to find sin ∅ is
1+cot ²∅=csc² ∅
Answer:
D edge
Step-by-step explanation:
A cube has a side length of 120 cm, what is its volume in cubic meters? (100 cm = 1 m)
Answers
a=120 cm and a=1.2m
V=120^3=1,728,000 cm^3
V=1,728 m^3
The value of volume of cube is,
⇒ V = 1.728 meter³
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
A cube has a side length of 120 cm.
Since, We know that;
1 m = 100 cm
Hence,
120 cm = 120 / 100 m
= 1.2 m
So, Volume of cube is,
⇒ V = side³
⇒ V = 1.2³
⇒ V = 1.728 meter³
Thus, volume of cube is,
⇒ V = 1.728 meter³
Learn more about the cuboid visit:
https://brainly.com/question/26403859
#SPJ3
On average, Carson spends $2 of his $20 monthly allowance on library fines. What percent of his allowance is spent on library fines?
Answers
2 x 5 = 10
10/100 = .1
he spends 10%
simplify the problem sqrt 245c^5
Answers
√[245c^5]-------> √245*√c^5
we know that
245-----> 5*7²
c^5---- c²*c²*c
so
√245-----> √[5*7²]----> 7√5
√c^5----> √[c²*c²*c]---> c²√c
√245*√c^5-----> [7√5]*[c²√c]----> 7c²√(5c)
the answer is
7c²√(5c)
Answer: the answer above is pretty much right, the answe is B
Karen is considering taking out a 20-year loan with monthly payments of $260 at an APR of 5.5%, compounded monthly, and this equates to a loan of $37,796.89. Assuming that the APR and the length of the loan remain fixed, which of these is a correct statement?
Answers
The correct statement is A;If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
How to calculate EMI?The EMI formula is :
[tex]\dfrac{pr(1 + r)^n}{(1 + r)^n - 1}[/tex]
Where r = 5.5/12/100 = 0.00425
p = 37,796.89
and n = 20 x 12 = 240
Putting the values in formula we get'
= (37,796.89x 0.00425 x 2.767)/1.767
= $350
Hence,
The correct statement is A; If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
Learn more about the compounded here;
brainly.com/question/11814596
#SPJ5
Answer:If Karen's monthly payment were $240, the amount of the loan that she is considering taking out would be less than $37,796.89.
Step-by-step explanation:
If you buy a computer directly from the manufacturer for $ 2,469 and agree to repay it in 48 equal installments at 2.1 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
Answers
Final answer:
The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.
Explanation:
To calculate the monthly payments, you can use the formula for the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^-n)
Where:
P is the monthly paymentr is the monthly interest ratePV is the present value or the loan amountn is the total number of paymentsUsing the given values, we can calculate:
P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)
P ≈ $61.02
Therefore, the monthly payments would be approximately $61.02.
To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:
Total Interest = (P * n) - PV
Total Interest ≈ ($61.02 * 48) - $2469
Total Interest ≈ $1704.96 - $2469
Total Interest ≈ -$764.04
Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.
Add (13a + 5b) + (a + 5b - 3)
Answers
= 13a + 5b + a + 5b - 3
= 14a + 10b - 3
Roman saves $500 each year in account earning interest at an account earning interest at an annual rate of 4% compounded annually.How much interest will the account earn at the end of each of the first 3 years?
Answers
562.432-500= 62.432
62.432 / 3= 20.8106
Parallel lines r and s are cut by two transversals, parallel lines t and u.
Which angles are alternate exterior angles with angle 11?
Answers
Answer:
The alternate exterior angles with angle 11 are angle 13 and angle 5.
Step-by-step explanation:
Two angles are called Alternate exterior angles if
1. They are on the exterior side of parallel lines and
2. Lie on the opposite sides of the transversal line.
It is given that
[tex]r\parallel s[/tex] and [tex]t\parallel u[/tex]
From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.
Therefore alternate exterior angles with angle 11 are angle 13 and angle 5.
Answer:
The alternate exterior angles with angle 11 are angle 13 and angle 5.
Step-by-step explanation:
Find the surface area 4cm 5cm 6cm 13cm
Answers
help! I will give thanks!
Answers
Reason: 60 appeared 4 times.
My coin collection had 27 coins. They are only quarters and half-dollars. If its worth $10.50. How many are there of each coin?
PLEASE SHOW WORK
Answers
what is 3√27x^9
3x^6
3x^3
9x^3
9x^6
Answers
[tex] \sqrt[3]{27} \sqrt[3]{ x^{9} } [/tex]
Write the number in the first square root in exponential form with a base of 3.
[tex] \sqrt[3]{ 3^{3} } \sqrt[3]{ x^{9} } [/tex]
Now reduce the index of the radical and exponent in the second square root with 3.
[tex] \sqrt[3]{ 3^{3} } [/tex] x³
Lastly,, reduce the index of the radical and exponent with 3 to get your final answer.
3x³
This means that the correct answer to your question will be option B.
Let me know if you have any further questions.
:)
The value of the expression ∛27x⁹ is 9x³.
The given expression is ∛27x⁹.
Cube root of twenty seven times of x power nine.
We can split the terms inside the cube root.
27=3×3×3
∛x⁹ = x³
Now let us plug in the above expression.
= 3√3³ × x⁹
= 3√3³ × √ x⁹
= 3 × 3 × x³
= 9x³.
Hence, the value of the expression ∛27x⁹ is 9x³.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ6
what is 3 ^9? how to solve?
Answers
3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
What I would do it is narrow it down piece by piece.
3 * 3 * 3 = 27. Do that 3 times, now you are left with:
27 * 27 * 27
27 * 27 or 27² = 729.
That leaves you with:
729 * 27
You can multiply by hand or use a calculator to get your answer of 19683.
To check your answer, plug 3⁹ into a calculator. Your answer should match this.
David, Egil and Frances share money in the ratio 2:7:9. David gets £25. Work out how much Egil and Frances get.
Please help. Needed for tomorrow.
Answers
Egil:
(ratio of Egil to David)×(Amount David gets)
7/2×25
=£87.5
Frances:
(ratio of Frances to David)×(Amount David gets)
9/2×25
=£112.5
Simplify the rational expression. state any excluded values. 4x - 4/ x - 1
Answers
[tex] \frac{4x-4}{x-1} [/tex]
So, we will call this expression as:
[tex] f(x) = \frac{4x-4}{x-1} [/tex]
We can write this equation like this:
[tex]f(x) = \frac{4(x-1)}{(x-1)} [/tex]
So, if we simplify it, this can be written like this:
f(x) = 4 but given that the denominator can't be zero, then:
[tex] x-1 \neq 0 [/tex] ∴ [tex]x \neq 1[/tex]
Therefore:
f(x) = 4 if and only if [tex]x \neq 1[/tex]
Answer:
1 and 4 i believe
Step-by-step explanation:
The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to find the measure of the vertex and base angles?
A)
v + 2b = 180; 2b - 20 = v
B)
v + 2b = 180; 2b + 20 = v
C)
v - 2b = 180; v + 2b = -20
D)
v - 2b = 180; -2b - 20 = v
Answers
The answer to the above question can be explained as under -
We know that, the sum of angles of triangle is 180°.
So, vertex angle plus base angles are equal are equal to 180°.
Let the vertex angle be represented by "v" and base angles be represented by "b".
Thus, v + b + b = 180°
So, v + 2b = 180°
Next, the question says, the vertex angle is 20° less than the sum of base angles.
Thus, 2b - 20° = v
Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v
The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.
The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:
The sum of the angles in a triangle is 180°, leading to the equation: v + 2b = 180.The vertex angle v is 20° less than the sum of the base angles, giving us the equation: 2b - 20 = v.To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.
A fair dice is rolled 5 times in sequence. what is the probability that you will get exactly the same number for all 5 rollings
Answers
What is grater 9km or 145cm
Answers
9km is greater than 145cm due to the conversion factor between kilometers and centimeters.
9km is greater than 145cm because when comparing the two, you need to ensure they are in the same unit. To compare, convert km to cm, 9km = 9,000,000cm. So, 9,000,000cm is greater than 145cm.
which of the points satisfy the linear inequality graphed here?
a) (0,0)
b) (10,0)
c) (-10,0)
d) (10,10)
Answers
c) (-10,0)
because that is the only point in the shaded region.
What is the volume of a pyramid with slant height 17 feet and square base with edges of 16 feet?
Answers
[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ ------\\ B=\stackrel{16\times 16}{256}\\ h=15 \end{cases}\implies V=\cfrac{1}{3}(256)(15)\implies V=1280[/tex]
The volume of the pyramid is 1280 cubic feet.
To find the volume of a pyramid, we can use the formula:
Volume = (1/3) * Base Area * Height
Given that the pyramid has a square base with edges of 16 feet, the base area (A) is calculated as:
[tex]Base Area (A) = side^2\\A = 16^2 = 256 square feet[/tex]
The height of the pyramid can be found using the Pythagorean theorem. The height, slant height, and half the length of a side form a right triangle. The half length of a side is 16/2 = 8 feet. The slant height is 17 feet. So, using the Pythagorean theorem:
[tex]Height^2 + (Half side length)^2 = Slant height^2\\Height^2 + 8^2 = 17^2\\Height^2 + 64 = 289\\Height^2 = 289 - 64\\Height^2 = 225\\Height = \sqrt{225}\\Height = 15 feet\\[/tex]
Now that we have the base area (A = 256 square feet) and the height (h = 15 feet), we can find the volume:
Volume = (1/3) * 256 * 15
Volume = (1/3) * 3840
Volume = 1280 cubic feet
Therefore, the volume of the pyramid is 1280 cubic feet.
To know more about volume:
https://brainly.com/question/15699665
#SPJ2
The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?
Answers
we know that
The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.
so
the answer is the option
A. the remote interior angles
The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.
so
the answer is the option
A. the remote interior angles
Find the variable of each pair
Answers
B. Y= 24, X= 6
For parametric equations x= a cos t and y= b sin t, describe how the values of a and b determine which conic section will be traced
Answers
In mathematics, a conic section is
a curve obtained as the intersection of the surface of
a cone with a plane. The four types of conic section are
the hyperbola, the parabola, the circumference and the ellipse.
For the problem we have this parametric
equation:
(1) [tex]\left\{{{x=acost}\atop{y=bsint}}\right[/tex]
From geometry, we know that we can express a
circumference in terms of parameters like this:
(2) [tex]\left \{ {{x=rcost} \atop {y=rsint}}\right[/tex]
being r the radius of the circumference.
On the other hands, we know that a ellipse can
be expressed in terms of parameters like this:
(3) [tex]\left \{ {{x=acost} \atop {y=bsint}}\right[/tex]
Therefore, we will have three answers that are
the cases for the values a and b, namely.
Case 1:
Circumference
To the case of a circumference, the more simple
ordinary equation is given by:
(4) [tex]x^{2} + y^{2} = r^{2}[/tex]
Substituting (1) into (4):
[tex]a^{2}cos^{2}t+b^{2}cos^{2}t=r^{2}[/tex]
But because of the equation (2), necessarily:
[tex]a = b = r[/tex]
Case 2: Ellipse
(focal axis matches the x-axis)
In this case, the simple ordinary equation is
given by:
(5) [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]
being a and b semi-major axis and semi-minor
axis respectively.
Given that a an b are variables of the
parametrization, and a and b are variables of the ellipse as well, to avoid
confusion we will modify the equation (5) like this:
(6) [tex]\frac{x^{2}}{a'^{2}}+\frac{y^{2}}{b'^{2}}=1[/tex]
So, substituting (2) into (6):
[tex]\frac{a^{2}cos^{2}t}{a'^{2}}+\frac{b^{2}cos^{2}t}{b'^{2}}=1[/tex]
Necessarily:
[tex]a=a'[/tex] and [tex]b=b'[/tex]
and given that the focal axis matches the
x-axis, then:
[tex]a>b[/tex]
Case 3: Ellipse
(focal axis matches the y-axis)
In this case, applying the same previous
reasoning, the simple ordinary equation is given by:
(7) [tex]\frac{x^{2} }{b'^{2}}+\frac{y^{2}}{a'^{2}}=1[/tex]
being a' and b' semi-major axis and semi-minor
axis respectively.
So, substituting (2) into (7):
[tex]\frac{a^{2}cos^{2}t}{b'^{2}}+\frac{b^{2}cos^{2}t}{a'^{2}}=1[/tex]
Necessarily:
[tex]a = b'[/tex] and [tex]b = a'[/tex]
and given that the focal axis matches the y-axis, then:
[tex]a<b[/tex]
Finally, the conclusions are:
1. If [tex]a = b[/tex] then a circumference will be traced. (See Figure 1)
2. If [tex]a>b[/tex] then a ellipse will be traced with focal axis matching the x-axis. (See Figure 2)
3. If [tex]a<b[/tex] then a ellipse will be traced with focal axis matching the y-axis. (See Figure 3)
How the values of a and b determine which conic section will be traced was discussed thoroughly.
What is a conic section?A conic section is a curve obtained as the intersection of the surface of a cone with a plane.
The given parametric equations are:
[tex]x=acos t[/tex]
[tex]\frac{x}{a} =cost[/tex]....(1)
[tex]y=bsint[/tex]
[tex]\frac{y}{b} =sint[/tex]....(2)
Adding the squares of (1) and (2)
[tex](\frac{x}{a} )^2+(\frac{y}{b} )^2=cos^{2} t + sin^{2} t[/tex]
We know [tex]cos^{2} t + sin^{2} t=1[/tex]
So, [tex]\frac{x^{2} }{a^{2} } +\frac{y^2}{b^2} =1[/tex]........(3)
If [tex]a=b[/tex], (3) will be reduced into:
[tex]x^{2} +y^{2} =a^{2}[/tex] representing a circle.
If [tex]a > b[/tex], (3) will represent an ellipse with the length of the major axis > length of the minor axis.
if [tex]a < b,[/tex] (3) will represent an ellipse with the length of the major axis < length of the minor axis.
Thus, How the values of a and b determine which conic section will be traced was discussed thoroughly.
To get more about conics visit:
https://brainly.com/question/4017703