The exponential function is illustrated below.
How to illustrate the example?An exponential function has a growth factor or 3.76. What is the percentage growth rate?
The growth factor (b) is given as:
b = 3.76
So, the percentage growth rate (r) is calculated as:
r = b - 1
Substitute known values
r = 3.76 - 1
Evaluate the difference
r = 276%
The way to solve Financial Problems using Sequences & Series will be:
The first salary that Mr James earn is 10000 and there is a yearly increase of 2000. Find his salary in the 5th year. This will be:
= a + (n - 1)d
= 1000 + (5 - 1)2000
= 10000 + (4 × 2000)
= 10000 + 8000.
= 18000
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In conducting a goodness-of-fit test, a requirement is that ________. Question content area bottom Part 1 A. the expected frequency must be at least five for each category B. the expected frequency must be at least ten for each category C. the observed frequency must be at least ten for each category D. the observed frequency must be at least five for each category
In conducting a goodness of fit test, a requirement is that the expected frequency must be at least ten for each category.
What is a goodness of fit test?In relation to the statistical model, the test tells how well it fits a set of observations.
The measures of the goodness of fit summarize the discrepancy between observed values and the values expected under the model in question.
Also, when conducting a goodness of fit test, a requirement is that the expected frequency must be at least ten for each category.
Therefore, the Option B is correct,
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7. stano. (2pt) Find the centers, foci, vertices and asymptotes of the hyperbola with equation given by: 16y²-x² - 6x - 32y = 57 And also sketch the hyperbola. (2pts)
The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.
According to the statement
we have to find the centers, foci, vertices and asymptotes of the hyperbola from the given equations.
So, For this purpose,
Hyperbola is a a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.
So, The given equation is:
16y²-x² - 6x - 32y = 57
So, rearrange it then
-x² - 6x - 32y + 16y² = 57
-(x² + 6x) + (16y² - 32y ) = 57
-(x² + 6x) + 16(y² - 2y ) = 57
-(x² + 6x + 9) + 16(y² - 2y +1 ) = 57 +1(16) + 9(-1)
-(x+ 3)² + 16 (y-1)² = 64
-(x+ 3)² + 16 (y-1)² = 64
divide whole equation by 64 then
[tex]\frac{-(x+ 3)^{2}}{64} + \frac{16 (y-1)^{2}}{64} =\frac{64}{64}[/tex]
then equation become
[tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex]
This become the equation of hyperbola.
So,
here coordinates of center is (0,0)
And asymptote is become 16.
So, The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.
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Anu is a photographer and was recently hired to photograph a wedding in Hawaii. While there, Anu had some time to
explore the island and capture other beautiful pictures.
During the trip, Anu took a total of 1,200 photographs. Of these, 25% were wedding photos, 35% were pictures of Lanikai
Beach, and the rest of the pictures were taken at the Honolulu Zoo. How many of Anu's pictures were taken at the Honolulu
Zoo?
ANSWER: 480 out of 1200 were taken at the Honolulu Zoo.
In a flower garden of rose and sunflower, 40% of flowers are rose. if there are 120 sunflower in the garden, total of how many flowers are there in the garden?
Answer:
200
Step-by-step explanation:
If 40% are roses than 60% must be sunflowers (40% + 60% = 100%)
We are trying to find 60% of some number is 120.
Let n = the total number of flowers
.6n = 120 Divide both sides by .6
n = 200
Find center,foci and vertices of ellipse for 4x2+y2+2x-10y=6
Answer:
center:
(-0.25, 5)
foci :
(-0.25, 0.158771) | (-0.25, 9.84123)
vertices :
(-0.25, -0.59017) | (-0.25, 10.5902)
wolframramalpha
a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times. How long is the vine?
The length of the vine is 21 ft
what is the circumference of a circle?
the circumference is the perimeter of a circle
the perimeter of the circle = 2πr = 3 ft
the vine is 7 times the perimeter
length of vine = 7×3= 21 ft
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If the tree is 20 feet tall with circumference 3 feet then the length of vince is around 21 feet.
Given the height of tree is 20 feet and the circumference of tree is 3 feet.
We have to find the length of vine.
Circumference is the perimeter of a circular object. Because the trunk of a tree is in shape of circle so the perimeter of the trunk is 2πr.
We have been given the circumference of tree be 3 feet.
Circumference=2πr
Because vine is 7 times the circumference so the length of vine being:
Length of vine=7*3
=21 feet.
Hence if the tree is 20 feet tall with circumference 3 feet then the vince is around 21 feet long.
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-20, 10, -5,
I need the next sequence
Answer:
The next term in the sequence is 5/2 or 2.5.
========================
Given series:
-20, 10, - 5, ...We notice that this is a geometric progression.
The common ratio is:
r = -5/10 = 10/ -20 r = - 1/2To find the next term multiply the last term by the common ratio:
[tex]t_n=rt_{n-1}[/tex]The 4th term is:
[tex]t_4=(-1/2)*(-5)=5/2=2.5[/tex]Geometry: Explaining Volume Formulas
Step-by-step explanation:
volume = area of circle × hight of cylinder ....
V = πr² × h
so V = πr²h
Answer:
10831 mm³
Step-by-step explanation:
The volume of any solid figure with a uniform cross section parallel to the base can be found using the volume formula ...
V = Bh
where B is the area of the base, and h is the height perpendicular to the base.
Base areaThe base of this cylindrical stack of pennies is a circle of diameter 19.05 mm. The area formula for a circle in terms of diameter is ...
A = (π/4)d²
The stack of pennies has a base area of ...
A = (π/4)(19.05 mm)² ≈ 285.023 mm²
VolumeThe volume formula tells us the stack of pennies has a volume of ...
V = Bh
V = (285.023 mm²)(38 mm) ≈ 10830.9 mm³
The volume of the stack of pennies is approximately 10831 mm³.
What is the mean absolute deviation of this? 1 is 2 sundaes.
Using it's concept, the mean absolute deviation of the data-set is of 2 sundaes.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.The mean for this problem is:
(4 + 6 + 2 + 4)/4 = 4
Hence the MAD is:
(|4-4| + |6-4| + |2-4| + |4-4|)/4 = 1
Since each unit represents 2 sundaes, the mean absolute deviation is of 2 sundaes.
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Sam drove from his house to college. When he stopped at college, he saw on the instrument panel of his car that he covered 26.5km. What is the displacement?
Answer:
instruments are very important to the direction of the personal information and concerns about the direction
BECKY KUBIAK WISHES TO PURCHASE NEW APPLICANCES FOR HER HOME. THE
TOTAL COST FOR THE APPLICANCES IS $2900. TO FINANCE THE PURCHASE, BECKY
MUST PAY 20% DOWN, WITH THE BALANCE BEING FINANCED WITH A 24-MONTH
INSTALLMENT LOAN WITH AN APR OF 8.5%. DETERMINE BECKY’S TOTAL FINANCE
CHARGE AND HER MONTHLY PAYMENT.?
Using the monthly payment formula, it is found that:
Her monthly payments are of $105.46.The total finance charge is of $3,111.04.What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.Considering that she must pay 20% down, the parameters are given by:
P = 0.8 x 2900 = 2320, r/12 = 0.085/12 = 0.007083, n = 24.
Hence the monthly payments are found as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 2320\frac{0.007083(1.007083)^{24}}{(1.007083)^{24} - 1}[/tex]
A = $105.46.
The total finance charge is composed by the down payment plus the 24 monthly payments, hence:
F = 0.2 x 2900 + 24 x 105.46 = $3,111.04.
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Karin has 13 coins (2 quarters, 6 dimes, 4 nickels, and 1 penny) in a piggy bank. She turns the bank
upside down and shakes the bank until a coin falls out, puts it aside, and the shakes until another coin
falls out.
What is the probability that the first coin is a nickel and the second coin is a quarter?
Select one:
a. 2/30
b. 6/13
c. 2/13
d. 1/8
Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is:
2/39.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
For the first coin, 4 out of 13 will be nickels.For the second coin, considering a nickel was taken with the first coin, 2 out of 12 will be quarters.Hence the probability will be given as follows:
p = 4/13 x 2/12 = 4/13 x 1/6 = 2/13 x 1/3 = 2/39.
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A $8,000 principal is invested in two accounts, one earning 1% interest and another earning 6% interest. If the total interest for the year is $405, then how much is invested in each account?
The amount invested in the first account is $1,500 and $6,500 was invested in the second account.
What is simple interest?
Simple interest is determined as the principal multiplied by the interest rate ,then multiplied by the duration of the investment.
The formula for simple interest on an investment is as shown below:
I=PRT
P=principal=$8,000
R=interest rates= 1% and 6%
T=duration of investment=1 year
Let assume that X was invested at 1% and that the remaining of $8000-X is invested at 6%.
Interest on the first account=X*1%*1
Interest on the first account=0.01X
Interest on second account=($8000-X)*6%*1
Interest on second account=480-0.06X
Total interest=0.01X+480-0.06X
Total interest=480-0.05X
Total interest=$405
405=480-0.05X
0.05X=480-405
0.05X=75
X=75/0.05
X=amount invested in the first account=$1,500
Amount invested in the second account=$8000-X
Amount invested in the second account=$8,000-$1,500
Amount invested in the second account=$6,500
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QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Central angle in the circle is: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. measure of arc BEC is: 260°
e. m(BC) = 100°
What is a Central Angle?A central angle has two of its sides as radii of the circle, forming an angle at the center of the circle, where the vertex is at the center of the circle.
What is a Major Arc?A major arc has a measure that is greater than 180 degrees. That is, it is more than half a circle (semicircle). Thus, measure of major arc > 180 degrees.
What is a Minor Arc?A minor arc has a measure that is less than 180 degrees. That is, it is not more than half a circle (semicircle). Thus, measure of minor arc < 180 degrees.
a. Central angle in the circle is: Angle BAC
b. A major arc in circle A is: Arc BEC
c. A major arc in circle A is: Arc BC.
d. Measure of arc BEC = 360 - 100 [according to the central angle theorem]
Measure of arc BEC = 260°.
e. Measure of angle BAC = 100° [given]
Measure of arc BC = angle BAC [according to the central angle theorem]
Measure of arc BC = 100°
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One integer is 4 times another. If the product of the two integers is 144, then find the integers.
One possible set of answers is;
Another possible set of answers is:
Which of the following would be an acceptable first step in simplifying the expression
sinx/1- cosx?
A. sinx - sinx/1- cos x
B. 1/cscx - cosx
C. Cannot be simplified further
D. sin x(1+cosx)/(1-cosx)(1+cosx)
Answer: A
Step-by-step explanation: Because it can be simplified twice.
Create a two-column proof: Given: EAB and DCB are two right triangles. The figure has BED≅ BDE. Point B is the midpoint of segment AC. Prove: EAB≅ DCB
The two-column proof that shows that ΔEAB ≅ ΔDCB by SAS congruence theorem is explained below.
What is the the SAS Congruence Theorem?The Side-angle-side congruence theorem (SAS) that states that two triangles that are have two pairs of corresponding congruent sides and a pair of included corresponding congruent angles are congruent to each other.
What is an Isosceles Triangle?Any triangle with two equal base angles is referred to as an isosceles triangle, The sides opposite these base angles are also congruent to each other.
Given the diagram below, the proof is expressed as follows:
Statement 1: ΔEAB and ΔDCB are two right triangles
Reason 1: Given
Statement 2: ∠EAB ≅ DCB
Reason 2: Right angles
Statement 3: ∠BED ≅ BDE
Reason 3: Given
Statement 4: ΔBED is an isosceles triangle
Reason 4: Definition of isosceles triangle
Statement 5: BE ≅ BD
Reason 5: Definition of isosceles triangle
Statement 6: ΔEAB ≅ ΔDCB
Reason 6: SAS
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What is the divisor the dividend is 5/9
Answer
5/9 is the dividend
Step-by-step explanation:
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality. The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that to ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥. Be sure to use decimal numbers in your answer (such as using 0.40 for 40%). __________
Answer:
yes yes yes yes yes Yes Yes you are cute
Question is on the paper
Note: Spam/Irrelevant answers will be blocked and reported
The dimensions based on the area given are 15cm by 20cm.
How to calculate the sides?From the information given about the rectangle, the area is given as 300cm² and the margins are given as 1.5 and 2.
Therefore, the dimensions will be:
(1.5 × x) × (2 × x) = 300
1.5x × 2x = 300
3x² = 300
x² = 300/3
x² = 100
x = 10
Therefore the dimensions will be:
= 1.5x = 1.5 × 10 = 15
= 2x = 2 × 10 = 20
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We minimize the total area of the sheet
[tex]S = xy[/tex]
constrained by
[tex](x-4)(y-3) = 300[/tex]
Solve the constraint equation for [tex]y[/tex].
[tex](x-4)(y-3) = 300 \implies y-3 = \dfrac{300}{x-4} \implies y = 3 + \dfrac{300}{x-4} = \dfrac{3x+288}{x-4}[/tex]
Substitute this into [tex]S[/tex] and find the critical points.
[tex]S = \dfrac{3x^2+288x}{x-4} = 3x + 300 + \dfrac{1200}{x-4}[/tex]
[tex]\dfrac{dS}{dx} = 3 - \dfrac{1200}{(x-4)^2} = 0[/tex]
[tex]\implies \dfrac{1200}{(x-4)^2} = 3[/tex]
[tex]\implies (x-4)^2 = 400[/tex]
[tex]\implies x-4 = \pm20[/tex]
[tex]\implies x=-16 \text{ or } x = 24[/tex]
Of course [tex]x[/tex] can't be negative, so the page dimensions that minimize [tex]S[/tex] are [tex]x=24[/tex] and [tex]y=18[/tex].
Divide
8x⁴-6x³+2÷2x²+3
WhenWhen we divide 8x⁴ - 6x³ + 2 by 2x² + 3 The result obtained is 4x² - 3x - 6 remainder 9x + 20
What is quotient?Quotient is the result obtained when division operation is carried out.
For example when 6 is divided by 2, the result obtained is 3. Thus, the quotient is 3
How to divide 8x⁴ - 6x³ + 2 by 2x² + 3To divide 8x⁴ - 6x³ + 2 by 2x² + 3, we shall apply the long division method. This is illustrated below:
4x² - 3x - 6
2x² + 3 | 8x⁴ - 6x³ + 2
-(8x⁴ + 12x²)
-6x³ - 12x² + 2
-(-6x³ - 9x)
-12x² + 9x + 2
-(-12x² - 18)
9x + 20
Thus, the result obtained when we divide 8x⁴ - 6x³ + 2 by 2x² + 3 is 4x² - 3x - 6 remainder 9x + 20
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SOMEONE PLEASE HELLPPPP
Answer:
93.39
Step-by-step explanation:
So the sum of exterior angles of the convex octagon is: 360 degrees
This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x
[tex](x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)[/tex]
Group like terms
[tex](x+2x+3x+3x+2x+3x+3x+6x) + (14-3+8+16-17-4-12)[/tex]
Add like terms
[tex]23x+2[/tex]
Now let's set the sum of exterior angles to 360
[tex]23x+2 = 360[/tex]
Subtract 2 from both sides
[tex]23x=358[/tex]
Divide both sides by 23
[tex]x\approx 15.565[/tex]
So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one
Original equation
6x
Subsitute
6(15.565)
Simplify
[tex]93.39[/tex]
An envelope contains $1.20 in dimes and nickels. if the dimes were quarters and the nickels were dimes, there would be $1.35 more in the envelope. How many nickels are in the envelope?
The nickels in the envelope is $0. 12
How to determine the number
From the information given, we have that;
Dimes + nickels = $1. 20
1/4 dimes + dimes = $ 1. 35
Let dimes = d
Nickels = n
d + n = 1. 20 equation a
d/4 + d = 1. 35 equation b
Make 'd' subject from equation a
d = 1. 20 - n
Substitute into equation b
1. 20 - n/ 4 + 1. 20 - n = 1. 35
0. 3 - 0. 25n + 1. 20 - n = 1. 35
collect like terms
- 1. 25n = 1. 35 - 1. 5
- 1. 25 = - 0. 15
n = -0. 15/ -1. 25
n = 0. 12
Thus, the number of nickels in the envelope is $0. 12
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Which expression can be used to find the sum of the polynomials?
(9 - 3x2) + (-8x2 + 4x + 5)
The expression which can be used to determine the algebraic sum of the given polynomials as in the task content is; -11x² +4x +14.
Which expression can be used to find the sum of the given polynomials?It follows from the task content that the polynomials whose sum are to be determined are; (9 - 3x2) + (-8x2 + 4x + 5).
Hence, the sum can be evaluated as follows;
= 9 - 3x² + -8x² + 4x + 5
= -11x² +4x +14.
Consequently, the required expression is; -11x² +4x +14.
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Answer:
Step-by-step explanation:
is 100 for the points
What whole numbers are factors of both 20 and 30?
Answer: 1, 2, 5, 10
Step-by-step explanation:
1 x 30 = 30
1 x 20 = 20
2 x 15 = 30
2 x 10 = 20
5 x 6 = 30
5 x 4 = 20
10 x 3 = 30
10 x 2 = 20
What are two ordered pairs that the midpoint is (4, -10)? Please show that your points work.
The two ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20).
Given the coordinates of mid point be (4,-10).
We are required to find the ordered pairs that the mid point is (4,-20).
Coordinates show positions of points or something else on a surface.
There are various combinations whose mid point is (4,-10).
First are (4,-20),(4,0).
Mid point =[(4+4)/2,(-20+0)/2]
=(4,-10)
Second are (4,0) , (4,-20)
Mid point=[(4+4)/2,(0-20)/2]
=(4,-10)
Third are (8,-20),(0,0)
Mid point=[(8+0)/2,(-20+0)/2]
=(4,-10)
Fourth are (0,-20),(8,0)
Mid point =[(0+8)/2,(-10+0)/2]
=(4,-10)
Hence the ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20)& (8,-20),(0,0)&(0,-20),(8,0)&(0,0),(8,-20).etc.
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3. In AABC, a = 35, c = 25, and m can be drawn given these measurements?
Only one triangle possible with angle 38.2° at C.
According to the given statement
we have to seek out that the measurement of m with the help of the a and c.
Then for this purpose, we all know that the
The ambiguous case occurs when one uses the law of sines to see missing measures of a triangle when given two sides and an angle opposite one in every of those angles (SSA).
According to the this law
The equation become
35/sin(60) = 25/sinC
sinC = 0.6185895741
C = 38.2, 141.8
Since 141.8+60 = 201.8 > 180
It will not form a triangle.
So, only 1 triangle possible with angle 38.2° at C
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Law of Sines and the Ambiguous Case.
In ∆ ABC, a =35, c = 25, and m < A = 60*
How many distinct triangles can be drawn given these measurements?
If the volume of the cone is 180 in³, what is its surface area?
Answer:
Hi, to find the surface area of a cone is πrl
if your radius and length is given.
hope this helps (•‿•)
Apply the rule (-x, y - 2) to the following point, what is the result?
(-3,5)
O (-5,-5)
O (3, 3)
O (-5,3)
O (-3,7)
Answer:
[tex] - 3 \times - 1 = 3 \\ \\ 5 - 2 = 3[/tex]
Step-by-step explanation:
3,3
Answer: Second Choice. (3, 3)
Step-by-step explanation:
Given point
(x, y) = (-3, 5)
Given the rule for application
(-x, y - 2)
Determine the new x-value
x = -3
-x = - (-3) = 3
Determine the new y-value
y = 5
y - 2 = (5) - 2 = 3
Therefore, the result is [tex]\Large\boxed{(3,~3)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The scatter plot shows the relationship between the test scores of a group of students and the number of hours they exercise in a week:
On a grid, Label Hours of Exercise on x axis and Test Scores on y axis. The title of the graph is Test Scores and Exercise. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 1.1, 12 and 1, 30 and 2.1, 21 and 2.5, 42 and 3.5, 30 and 3.5, 45 and 4, 55 and 5, 45 and 5.5, 60 and 5.5, 70 and 6.5, 40 and 7, 50 and 7.5, 80 and 8, 75, and 8.5, 60 and 9, 75. The ordered pair 9, 15 is circled and labeled as T. All the other points are put in an oval and labeled as P.
Part A: What is the group of points labeled P called? What is the point labeled T called? Give a possible reason for the presence of point T. (5 points)
Part B: Describe the association between students' test scores and the number of hours they exercise. (5 points)
It should be noted that Group A is a cluster of points with similar property or relationship and Point B is an outlier. This is the point outside of the common relationship in the scatterplot
What is a scatterplot?It should be noted that scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.
In this case, the independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.
The association between students' test scores and the number of hours they exercise is that there is a negative tendency. As number of hours spent on computer games increase, the test scores decrease.
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