For the given exponential function there will be an exponential growth of 7%.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
we have
[tex]f(x) = 4200(1.07)^x[/tex]
This is an exponential function of the form
[tex]f(x)=ab^x[/tex]
where
a - is the initial value
b - is the base
If b > 1 ----> is a exponential growth
0 < b < 1 ----> is a exponential decay
r is the per cent rate
b = 1 + r
In this problem we have
a = 4200
b = 1.07
We can see that 1.07 > 1 -----> is a exponential growth
Find out the per cent rate
b = 1 + r
r = 1.07 - 1
r = 0.07
r = 7 x 100 = 7%
Therefore the given exponential function there will be an exponential growth of 7%.
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Mrs. Rykus does a survey of her 85 students.
20 say math is awesome
35 say math is the best
30 say math is fun
Based on these results, if Mrs. Rykus asks the whole student population 900 students what they think of math, what is the best approximation for how many students will say math is awesome?
A 400
B 212
C 200
D 315
Answer:
212
Step-by-step explanation:
85 here is 100%
And 900 is also 100%
That's for the different comparisons. So now, what we do is, we should divide 85 by 900, and then, whatever is our answer, multiply that by 20.
That is surely going to equal how many students are going to say that Math is Awesome for 900 student survey.
Step 1
85/900=10.5882352941
Let's round that to make it
10.5
Step 2
10.5x20=210
That means, if we go exactly, like multiplying all of those numbers, then our answer should be 212 or 200.
Just to be sure that our answer is correct, we will do it with 10.58 now.
Step 3
10.58x20=211.6
So now it looks like it's most probably going to be 212
But still, let's do 10.588 now.
Step 4
10.588x20=211.76
Okay, let's do it again, with 10.5882
Step 5
10.5882x20=211.764
Okay, so I just multiplied the whole number this time, and I still got a decimal, so that means that your answer is 212 basically.
Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?
The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
x² – 4x + 4 = 2x + 1 + x²
After solving:
-4x + 4 = 2x + 1
6x = 3
x = 1/2 = 0.5
Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
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This line plot shows the estimated amount of glue needed for summer projects at a camp. eric chose to complete a project with the greatest estimated amount of glue needed. the actual amount of glue he used was 3/4 of the estimated amount. how much glue did eric use for his project? enter your answer in the box as a mixed number in simplest form.
The amount of glue that eric used for his project is [tex]\mathbf{ 1\dfrac{11}{16}}[/tex]
How to interpret the line plot?The interpretation of the line plot involves a careful approach to how a series of data points are connected on coordinate planes.
From the Glue for summer project line plot:
The greatest estimated amount of glue needed can be seen at = 2 (1/4)The actual amount of glue needed = 3/4 of 2 (1/4)The amount of glue Eric used for the project is;
[tex]\mathbf{=\dfrac{3}{4}\times 2\dfrac{1}{4}}[/tex]
[tex]\mathbf{=\dfrac{3}{4}\times \dfrac{9}{4}}[/tex]
[tex]\mathbf{=\dfrac{27}{16}}[/tex]
[tex]\mathbf{= 1\dfrac{11}{16}}[/tex]
Therefore, we can conclude that the amount of glue used by Eric for this project is: [tex]\mathbf{ 1\dfrac{11}{16}}[/tex]
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what is the midpoint of (-2, -1) and (0, 9)
Answer:
(-1,4)
Step-by-step explanation:
For x the midpoint between -2 and 0 is -1
for y the midpoint between -1 and 9 is 4
Answer:
(-1,4)
Step-by-step explanation:
Midpoint can be found by:
(x1+x2)/2 ; (y1+y2)/2
So, if we substitute, we can find:
(-2+0)/2 ; (-1+9)/2
This gives us -2/2 and 8/2, which is:
(-1, 4)
Hope this helps!
a tractor driver plowed 1/5 of a field on the first day, and 1/4 on the second day. How much did he plow in the first two days? How much does he still need to plaw?
Answer:
1) (9/20)x 2) (11/20)x
Step-by-step explanation:
x = total area of the field.
In the first two days he plowed (1/5)x + (1/4)x = (9/20)x
He still needs to plow x - (9/20)x = (11/20)x
00B0J0DD:
TIME REMAINING
57:39
The head of the math department compared the scores of students in two classes on the Chapter 2 test. He found that
the mean score of both classes was the same. He also found that there was greater variability in the scores of Ms.
Biren's students than in the scores of Mr. Hayes's students. Which quality of the data sets would lead the department*
head to that conclusion?
The median score i Ms. Biren's class is greater than the median score in Mr. Hayes's class.
The
median score in Ms. Biren's class is less than the median score in Mr. Hayes's class.
The range of scores in Ms. Biren's class is greater than the range of scores in Mr. Hayes's class.
The range of scores in Ms. Biren's class is
less than the range of scores in Mr. Hayes's class. The median score
Answer: B.
Explanation and reasoning:
The probability of sandy flipping a coin twice and getting heads both times is 0.25 the probability of john's spinner stopping on the color red is
The true statement is (c) Neither. Both events are equally likely.
Complete questionThe probability of Sandy flipping a coin twice and getting heads both times is 0.25. The probability of John's spinner stopping on the color red is 1/4.
Which of these events is more likely?
-Sandy flips a coin twice and gets heads both times.
-John's spinner stops on the color red.
-Neither. Both events are equally likely.
How to determine the likely event?The given parameters are:
P(Head twice) = 0.25
P(Red) = 1/4
Rewrite P(Red) as:
P(Red) = 0.25
By comparison, we have:
P(Red) = P(Head twice) = 0.25
This means that both events are equally likely
Hence, the true statement is (c)
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Helppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
what is 100+24/4*12?????????????? due is 5 minutes plsssssssssssssss
Answer:
172
Step-by-step explanation:
100 + 24 ÷ 4 × 12
Remember PEMDAS
100 + 6 × 12
100 + 72
172
Hope this helps!
Write the equation of the trigonometric graph.
Answer:
[tex]f(x)= \sin(6x)+3[/tex]
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
[tex]f(x) = \sf A \sin (B(x + C)) + D[/tex]
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftThe parent function y = sin(x) has the following:
Amplitude (A) = 1Period = 2πPhase shift (C) = 0Vertical shift (D) = 0Mid-line: y = 0From inspection of the given graph:
Amplitude (A) = 1[tex]\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}[/tex]Phase shift (C) = 0Vertical shift (D) = +3 (as mid-line is y = 3)[tex]\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6[/tex]
Substituting the values into the standard form:
[tex]\implies f(x) =1 \sin (6(x + 0)) + 3[/tex]
[tex]\implies f(x) = \sin (6x) + 3[/tex]
Therefore, the equation of the given trigonometric graph is:
[tex]f(x)= \sin(6x)+3[/tex]
Answer(s):
[tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3 \\ y = -sin\:(6x \pm \pi) + 3 \\ y = sin\:6x + 3[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{12}} \hookrightarrow \frac{\frac{\pi}{2}}{6} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cos\:6x + 3,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{12}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{12}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{12}} = \frac{\frac{\pi}{2}}{6}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-\frac{5}{12}\pi, 2],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{12}, 2],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{3}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{3}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
0. on a saturday evening in chicago, 34% of the people go out to dinner, 18% go out to
see a movie, 13% go out to a party, and 35% stay home. if five people are randomly
selected on monday morning, what is the probability that all but one went out saturday
night?
a) 0.048
b) 0.116
c) 0.181
d) 0.312
Hi, so I was wondering if anyone knows the surface area of a cylinder if the diameter is 7.5? Thank you so much! :)
Answer:
206.17
Key(s):
[tex]A = 2\pi \frac{d}{2} h + 2\pi \left(\frac{d}{2}\right)^2[/tex]
Substitute d for the actual diameter, 7.5, and h for the height, which is 5.
Step-by-step explanation:
[tex]A = 2\cdot\pi \cdot\frac{7.5}{2} \cdot5 + 2\cdot\pi \cdot\left(\frac{7.5}{2}\right)^2[/tex] ≈ 206.17(2 DP)
Think about the function f(x) = 3 - 2x.
What does the notation f(0) mean?
Answer:
the answer is 3
what is 2x-45y=22 when y=21
answer:
483.5
step by step explanation:
2x-45y=22
2x-45(21)=22
2x-945=22
2x =22+945
2x=967
x=483.5
Using the cards 3,2,4,7 show a valua closest to 5000
4,7,3,2
Step-by-step explanation:
THESE ARE THE THE ARRANGEMENT OF NUMBERS IN ORDER TO GET THE CLOSEST TO 5000
(Refer to the attached image)
Explanation:
Provided 2 length sides and one angle also need to find one missing side.
So, use cosine rule:
a² = b² + c² - 2bc cos(A)
Part 1c² = 9² + 11² - 2(11)(9) cos(57)
c² = 94.16147
c = √94.16147 = 9.70 cm
Part 2d² = 5² + 7² - 2(5)(7) cos(48)
d² = 27.16
d = √27.16 = 5.21
Part 35² = 7² + 9² - 2(7)(9) cos(H)
-126cos(H) = 25 - 49 - 81
cos(H) = -105/-126
cos(H) = 5/6
H = cos⁻¹(5/6) = 33.56°
Part 48² = 4² + 7² - 2(4)(7) cos(J)
-56cos(J) = 64 - 16 - 49
cos(J) = -1/-56
J = cos⁻¹(1/56) = 88.98°
Passcode: 3142
Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 35% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
Answer:
Based on the data given on Northlake High School, we can infer that B. A greater percentage of second-lunch students (39%) eat outside.
What does the data on the First and Second lunches show?
The percentage of second-lunch students who eat outside is:
= Second lunch students who eat outside / Second lunch students
Solving gives:
= 0.18 / 0.46 x 100%
= 0.3913 x 100%
= 39%
This shows that the percentage of students eating their second lunch outside is 39%.
so the answer is B
Step-by-step explanation:
Solve this please-
Thanks!!!
Answer:
130 m²
Step-by-step explanation:
Area of a parallelogram is given by the formula :
A = bh (b is the base length and h is the perpendicular height)
Now we simply substitute values given in diagram to find our answer:
A = bh
A = (13)(10)
A = 130
Units will be m² as this is area
Hope this helped and have a good day
Volume of pyramids cones and spheres
Answer:
48 cm³Step-by-step explanation:
Volume = (1/3) * base_area * height
1/3 * 4 * 4 * 9 =
48 cm³
Complete the table for y=1/2x-3
Tables are created by substitute a set of input values into the function to create outputs. The required table is as shown below
x | y
0 -3
1 -2.5
2 -2
Tables and valuesTables are created by substitute a set of input values into the function to create outputs
Using x = 0, 1 and 2 as the input values
Given the function
y = 1/2x - 3
If x = 0
y = 1/2(0) - 3
y = -3
If x = 1
y = 1/2(1) - 3
y = -2.5
If x = 2
y = 1/2(2) - 3
y = -2
Hence the required table is as shown below
x | y
0 -3
1 -2.5
2 -2
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right triangles to find the exact length of:
T
30°
14 in
a) TI = in
60°
R
a) TI = 7√3 in
b) IR = 7 in
Explanation:Using cosine rule:
[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]
[tex]\hookrightarrow \sf cos(30) = \dfrac{TI}{14}[/tex]
[tex]\hookrightarrow \sf TI = 14cos(30)[/tex]
[tex]\hookrightarrow \sf TI = 7\sqrt{3}[/tex]
Using sine rule:
[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\hookrightarrow \sf sin(30) = \dfrac{IR}{14}[/tex]
[tex]\hookrightarrow \sf IR = 14sin(30)[/tex]
[tex]\hookrightarrow \sf IR = 7[/tex]
Based on the data in this two-way table, which statement is true?
Type of Flower/Color Red Pink Yellow Total
Rose 40 20 45 105
Hibiscus 80 40 90 210
Total 120 60 135 315
A.
A flower being pink and a flower being a rose are independent of each other.
B.
A flower being pink is dependent on a flower being a rose.
C.
A flower being a rose is dependent on a flower being pink.
D.
A flower being pink and a flower being a rose are the same.
help me please :)
ytfrtrghjhgfdsfghjyutredfghjytredsfg
Answer:
what ya need man I can help but give me a question
What is the measure of angleq to the nearest whole degree? 43° 49° 53° 58°
Based on the calculations, the measure of angle Q to the nearest whole degree is equal to 53°. The correct answer is option C.
The complete question is attached with the answer below.
How to calculate the measure of angle Q?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Based on the triangle attached in the image above, we can deduce the following parameters:
Side QM = 18 units.
Side MN = 17 units.
Side QN = 20 units.
In this scenario, we would apply the cosine trigonometry function to determine the measure of angle Q:
MN² = QM² + QN² - 2(QM)(QN)cosθ
17² = 18² + 20² - 2(18)(20)cosθ
289 = 324 + 400 - 720cosθ
720cosθ = 724 - 289
720cosθ = 435
θ = cos⁻¹(435/720)
θ = cos⁻¹0.6042
θ = 52.8 ≈ 53°.
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Which intervals show f(x) decreasing?
An exponential function contains the points (1, 0.9) and
(2, 1.62). What is an exponential function that contains
these points?
Answer:
Hi,
Step-by-step explanation:
Let's say y=a*b^x the equation of the exponential function.
0.9=a*b^1 (1)
1.62=a*b² (2)
(2)/(1) ==> b=1.62/0.9=1.8
and
0.9=a*1.8 ==> a=0.5
y=0.5*1.8^x
I don’t know how to do this please help
Answer:
84 cm²
Step-by-step explanation:
The figure has a uniform horizontal cross section, so its area is the product of that cross section length and its vertical dimension.
__
A = bh
A = (6 cm)(14 cm) = 84 cm²
The area of the shape is 84 square centimeters.
_____
Additional comment
You could decompose the figure into a rectangle with base 6 and height 8, and a parallelogram with base 6 and height 14-8=6. The area formula is the same for each: A = bh, so the area of the composite figure is ...
A = 6×8 +6×(14 -8)
= 6×(8 +(14 -8))
= 6×14 . . . . same as above.
Please help me
Find the value of x
Answer:
x = 5 and y = 22
Step-by-step explanation:
See attached image.
which is the greatest 30000 millimeters 1 kilometer 5000 meters or 6000 centimeters?
Jessie invests $33 in the stock market. Over the 3 years she has this invested she gets an average return of 7,8%. How much will her investment be worth after the 3 years?
Answer:
it would end up being about $40.73
Step-by-step explanation:
multiply 0.078 by 3 then multiply that by 33
Answer:
hope you can understand
solve for K
7K-6
2K+14
Answer:
[tex]k=4[/tex]
Step-by-step explanation:
Using the diagram, we can conclude that the given angles are vertical angles. Vertical angles are opposite angles that are formed when two lines intersect. Vertical angles are always congruent.
Using this information we can set up an equation.
[tex]7k-6=2k+14[/tex]
Subtract 2k from both sides.
[tex]7k-2k-6=2k-2k+14\\5k-6=14[/tex]
Add 6 to both sides
[tex]5k-6+6=14+6\\5k=20[/tex]
Divide both sides by 5
[tex]\frac{5k}{5}=\frac{20}{5}\\k=4[/tex]
CHECK:
7(4) - 6 = 28 - 6 = 22
2(4) + 14 = 8 + 14 = 22
22 = 22