Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Please help 20 points. I will give Brainly to who ever get it right.
Answer:
Step-by-step explanation:
(-∞,2)
6. Circle all the expressions that are equivalent to this expression: 6p+ 7.
You will lose a point for every wrong expression that you circle.
1.p+2+52 +5
2. 42p
3. 7p +6
4. 3p + 2p + P +7
5. 13P
6. p+p+p+p+p+p+5+1+1
Answer:
6
Step-by-step explanation:
because the equation above says p+p+p+p+p+p+5+1+1
so if we add up the p's it will give us 6p and if we add up the nos it will give us 6p+7
Find the length of AB
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we know the opposite side and want to know the hypotenuse. Therefore, we should use the sine function.
sin(54) = 16/AB
AB = 16/sin(54)
AB = 19.78 units
Hope this helps!
A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 101 feet and the radius of the hemisphere is r feet. Express the volume of the silo as a function of r.
Answer:
[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Step-by-step explanation:
Given
Shapes: cylinder and hemisphere
[tex]h = 101[/tex] --- height of cylinder
Required
The volume of the silo
The volume is calculated as:
Volume (V) = Volume of cylinder (V1) + Volume of hemisphere (V2)
So, we have:
[tex]V_1 = \pi r^2h[/tex]
[tex]V_1 = \pi r^2 * 101[/tex]
[tex]V_1 = 101\pi r^2[/tex] --- cylinder
[tex]V_2 = \frac{2}{3}\pi r^3[/tex] ---- hemisphere
So, the volume of the silo is:
[tex]V =V_1 + V_2[/tex]
[tex]V =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Write as a function
[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Where: [tex]\pi = \frac{22}{7}[/tex]
Which best describes the relationship between the line that passes through the points (6, -1) and (11, 2) and the line that passes through the
points (5-7) and (8-2)?
Answer:
D. Neither perpendicular nor parallel
Step-by-step explanation:
Let's find the slope (m) of both lines:
✔️Slope (m) of the line that passes through (6, -1) and (11, 2):
Slope (m) = change in y/change in x
Slope (m) = (2 -(-1))/(11 - 6) = 3/5
✔️Slope (m) of the line that passes through (5, -7) and (8, -2)
Slope (m) = change in y/change in x
Slope (m) = (-2 -(-7))/(8 - 5) = 5/3
✅The slope of both lines are not the same, therefore they are not parallel nor same line.
Also, the slope of one is not the negative reciprocal of the other, therefore they are not perpendicular.
List the sides of the triangle in order from largest to smallest.
Find the length of the arc round your answer to the nearest 10th
Answer:
12.6
Step-by-step explanation:
Length of arc=(2*pi*r)*(theta/360)
Length of arc=(2*12*pi)*(1/6)=12.6
A certain drug is used to treat asthma. In a clinical trial of theâ drug, 17 of 258 treated subjects experienced headachesâ (based on data from theâ manufacturer). The accompanying calculator display shows results from a test of the claim that less than 11â% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete partsâ (a) throughâ (e) below. â
1-PropZTest
prop<0.11
z=â2.264337000
p=0.0117766978
p=0.0658914729
n=258
a. Is the testâ two-tailed, left-tailed, orâ right-tailed?
b. What is the best statistics?
c. What is the P-value?
d. What is the nut hypothesis and what do you conclude who det hypothesis?
Identify the null hypothesis.
A. H0: pâ 0.11.
B. H0: p=0.11.
C. H0: p<0.11.
D. H0: p>0.11.
Decide whether to reject the null hypothesis.
A. Reject the null hypothesis because theâ P-value is greater than α.
B. Fail to reject the null hypothesis because theâ P-value is less than or equal to α.
C. Reject the null hypothesis because theâ P-value is less than or equal to α.
D. Fail to reject the null hypothesis because theâ P-value is greater than α
e. What is the finalâ conclusion?
A. There is not sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
B. There is not sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
C. There is sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
Solution :
a). The test is a left tailed test.
b). The sample proportion is :
[tex]$\hat p = \frac{x}{n}$[/tex]
[tex]$\hat p = \frac{17}{258}$[/tex]
= 0.065
Determining the Z statistics using the formula :
[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]
[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]
= -2.31
∴ Z statistics value is -2.31
c). Using the excel function, the P-value is :
P-value = Normsdist(-2.31)
= 0.0104441
d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]
The level of significance is 0.01
We fail to reject the null hypothesis as the P value is less than or equal to the significant level.
Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.
The area bounded by a chord and arc it intercepts is known as a segment of a circle segment of a circle
The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units
The reason the above value is correct is as follows:
The given parameters in the question are;
The radius of the circle, r = 11
The length of the chord PL = 16
The measure of angle ∠PAL = 93°
Required:
The area of part of the circle enclosed by chord PL and arc PL
Solution:
The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL
The area of a segment of a circle is given by the following formula;
Area of segment = Area of the sector - Area of the triangle
Area of segment = Area of minor sector APL - Area of triangle APL
Area of minor sector APL:
Area of a sector = (θ/360)×π·r²
Where;
r = The radius of the circle
θ = The angle of the sector of the circle
Plugging in the the values of r and θ, we get;
Area of the minor sector APL = (93°/360°) × π × 11² ≈ 98.2 square units
Area of Triangle APL:
Area of a triangle = (1/2) × Base length × Height
Therefore;
The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units
Required shaded area enclosed by line PL and arc PL:
Therefore, the area of shaded segment enclosed by line PL and arc PL is found as follows;
Area of the required segment PL ≈ (98.2 - 60.58) square units = 37.62 square units
The area of the circle enclosed by line PL and arc PL ≈ 37.62 square units
Learn more about the finding the area of a segment can be found here:
https://brainly.com/question/22599425
The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
The calculation of the area between line segment PL and circle arc PL is described below:
1) Calculation of the area of the circle arc.
2) Calculation of the area of the triangle.
3) Subtracting the area found in 2) from the area found in 1).
Step 1:
The area of a circle arc is determined by the following formula:
[tex]A_{ca} = \frac{\alpha\cdot \pi\cdot r^{2}}{360}[/tex] (1)
Where:
[tex]A_{ca}[/tex] - Area of the circle arc.
[tex]\alpha[/tex] - Arc angle, in sexagesimal degrees.
[tex]r[/tex] - Radius.
If we know that [tex]\alpha = 93^{\circ}[/tex] and [tex]r = 11[/tex], then the area of the circle arc is:
[tex]A_{ca} = \frac{93\cdot \pi\cdot 11^{2}}{360}[/tex]
[tex]A_{ca} \approx 98.201[/tex]
Step 2:
The area of the triangle is determined by Heron's formula:
[tex]A_{t} = \sqrt{s\cdot (s-l)\cdot (s-r)^{2}}[/tex] (2)
[tex]s = \frac{l + 2\cdot r}{2}[/tex]
Where:
[tex]A_{t}[/tex] - Area of the triangle.
[tex]r[/tex] - Radius.
[tex]l[/tex] - Length of the line segment PL.
If we know that [tex]l = 16[/tex] and [tex]r = 11[/tex], then the area of the triangle is:
[tex]s = \frac{16+2\cdot (11)}{2}[/tex]
[tex]s = 19[/tex]
[tex]A_{t} = \sqrt{19\cdot (19-16)\cdot (19-11)^{2}}[/tex]
[tex]A_{t} \approx 60.399[/tex]
Step 3:
And the area between the line segment PL and the circle arc PL is:
[tex]A_{s} = A_{ca}-A_{t}[/tex]
[tex]A_{s} = 98.201 - 60.399[/tex]
[tex]A_{s} = 37.802[/tex]
The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -1x + 2
Step-by-step explanation:
HELP ME OUT ASAPPP PLSSS
Answer:
https://linksharing.samsungcloud.com/ul5cX9oOmhzt
n rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=3 and BC=11, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your answer.
*see attachment for clearer diagram
Answer:
16.5
Step-by-step explanation:
BC = 11
AB = 3
Area of the shaded region = area of ∆AEB + area of ∆CED
Area of a triangle is given as,
A = ½*base*height
Find the area of each triangle and add together
✔️Area of ∆AEB = ½*bh
Where,
base (b) = 3
height (h) = ½(BC) = ½(11) = 5.5
Area of ∆AEB = ½*3*5.5 = 8.25
✔️Area of ∆CED = ½*bh
Where,
b = 3
h = ½(BC) = ½(11) = 5.5
Area of ∆CED = ½*3*5.5 = 8.25
✅Area of the shaded region = area of ∆AEB + area of ∆CED
= 8.25 + 8.25
= 16.5
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and three Chevrolets cost $107 per day, whereas four Nissans, three Fords, and two Chevrolets cost $102 per day. Find the rental rate for the Fords.
Answer:
The rental rate for the Fords is of $12 per day.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the cost of a Nissan.
y is the cost of a Ford.
z is the cost of a Chevrolet.
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.
This means that:
[tex]3x + 2y + 4z = 106[/tex]
Two Nissans, four Fords, and three Chevrolets cost $107 per day
This means that:
[tex]2x + 4y + 3z = 107[/tex]
Four Nissans, three Fords, and two Chevrolets cost $102 per day.
This means that:
[tex]4x + 3y + 2z = 102[/tex]
From the first equation:
[tex]4z = 106 - 3x - 2y[/tex]
[tex]2z = 53 - 1.5x - y[/tex]
[tex]z = 26.5 - 0.75x - 0.5y[/tex]
Replacing into the third equation:
[tex]4x + 3y + 53 - 1.5x - y = 102[/tex]
[tex]2.5x + 2y = 49[/tex]
From the second equation:
[tex]2x + 4y + 3z = 107[/tex]
[tex]2x = 107 - 4y - 3z[/tex]
[tex]x = 53.5 - 2y - 1.5z[/tex]
[tex]x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)[/tex]
[tex]x - 1.125x = 53.5 - 2y - 39.75 + 0.75y[/tex]
[tex]-0.125x = 13.75 - 1.25y[/tex]
[tex]0.125x = 1.25y - 13.75[/tex]
[tex]x = \frac{1.25y - 13.75}{0.125}[/tex]
[tex]x = 10y - 110[/tex]
Find the rental rate for the Fords.
We have to find y, so:
[tex]2.5x + 2y = 49[/tex]
[tex]2.5(10y - 110) + 2y = 49[/tex]
[tex]25y - 275 + 2y = 49[/tex]
[tex]27y = 324[/tex]
[tex]y = \frac{324}{27}[/tex]
[tex]y = 12[/tex]
The rental rate for the Fords is of $12 per day.
Please help no links.Mr. Longley is buying a $15 box of trail mix at Whole Foods, where tax is 6%. If Mr. Longley has
a coupon for 10% off the price of any item, how much does he end up paying?
I
Answer:
$14.40
Step-by-step explanation:
my way of doing things:
15/100=0.15=1%of total amount
0.15 x 6=0.9= the 6% which is the tax
0.15 x 10 = 1.5=the coupon
Take the coupon amount $1.50 minus the tax amount $0.90 =$0.60. Because the coupon amount is greater than the tax the 60 cents gets taken away from the original 15 dollars leaving Mr. Longely only having to pay $14.40.
1/10
9/10
Q
Find the perimeter of the rectangle pictured above. Give your answer as a reduced mixed number.
Answer:2
Step-by-step explanation:
Current
How many years will it take for an initial investment of $60,000 to grow to $90,000? Assume a rate of interest of
4% compounded continuously.
>It will take about _years for the investment to grow to $90,000.
(Round to two decimal places as needed.)
Answer:
I think i don't know the answer i am so sorry!!!
maybe someone else can Answer
If the function y=x^5 is transformed to y=x^5+3 what’s the statement
I dont know what you mean by the question but according to me.
If y=x^5
y=x^5+3
Then y+3=x^5+3
Answered by Gauthmath must click thanks and mark brainliest
50 times what equals 10 million
Find the missing side round your answer to the nearest tenth.
Answer: 20.5
Step-by-step explanation:
Cos 43 = X/28
O.73 = x/28
(0.73)(28)=20.5
Which equation can she use as statement 5? 60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)
An internet provider states that, on average, the daily amount of time an adult spends on the internet is 4.5 hours. A sociologist studying the behaviors of internet consumers believes the average daily amount an adult spends on the internet is different than the amount stated by the internet provider. After completing a study, the sociologist found that the average daily amount of time an adult spends on the internet is 5.9 hours, on average. As the sociologist sets up a hypothesis test to determine if their belief is correct, what is their claim?
a. The average daily amount of time an adult spends on the internet is different than 4.5 hours.
b. The average daily amount of time an adult spends on the internet is different than 5.9 hours.
c. Adults spend a majority of their time on the internet.
d. The average daily amount of time an adult spends on the internet is 4.5 hours.
Answer:
a. The average daily amount of time an adult spends on the internet is different than 4.5 hours.
Step-by-step explanation:
An internet provider states that, on average, the daily amount of time an adult spends on the internet is 4.5 hours.
At the null hypothesis, it is claimed that the mean is of 4.5 hours, that is:
[tex]H_0: \mu = 4.5[/tex]
A sociologist studying the behaviors of internet consumers believes the average daily amount an adult spends on the internet is different than the amount stated by the internet provider.
At the alternative hypothesis, the sociologist claim, is that the mean is different of 4.5, that is:
[tex]H_1: \mu \neq 4.5[/tex]
Thus, the correct answer is given by option a.
Triangle ABC has vertices of A(-6, 7), B(4, -1), and C(-2, -9). Find the length of the median from ZB in triangle ABC
A. 4
B. 18
C. 8
D. 768
Please select the best answer from the choices provided
Ο Α
D
9514 1404 393
Answer:
C. 8
Step-by-step explanation:
The median from vertex B is the line segment between there and the midpoint of side AC. That midpoint is ...
D = (A +C)/2 = ((-6, 7) +(-2, -9))/2 = (-8, -2)/2 = (-4, -1)
So, we want the length of the line between (-4, -1) and (4, -1). These points are on the same horizontal line (y=-1), so the length is the difference of the x=coordinates:
median AD = 4 -(-4) = 8 . . . . units in length
How many different arrangements of 5 letters can be formed if the first letter must be W or K (repeats of letters are allowed)?
There are ___ different 5-letter combinations that can be formed.
(Simplify your answer.)
Answer:
2.5
Step-by-step explanation:
i had it
A magazine conducted a survey among its readers in a certain state. They reported the following results:
Out of 1200 respondents, 312 are professionals, 470 are married, 524 are college graduates, 193 are professional college graduates, 178 are married college graduates, 136 are married professionals, and 35 are married professional college graduates.
What is the probability that a randomly selected reader in that state is:
a. Either married, or a college graduate, or a professional?
b. Neither married, nor a college graduate, nor a professional?
Answer:
The answer is "0.695 and 0.305".
Step-by-step explanation:
Please find the attached file of the given question:
From question a:
[tex]\text{P(Either married, or a college graduate, or a professional)} \\\\=\frac{(312+143+188+191)}{1200}\\ \\ =\frac{834}{1200}\\\\=0.695[/tex]
From question b:
[tex]\text{P( Neither married, nor a college graduate, nor a professional )}\\\\=\frac{366}{1200} \\\\=0.305[/tex]
The sum of two numbers is -17. Their difference is 41. Find the numbers
Answer:
x = 12
y = -29
Step-by-step explanation:
Our given equations: x + y = -17 and x - y = 41
Solve for x and substitute.
x = -17 - y
(-17 - y) - y = 41
-17 - 2y = 41
2y = -58
y = -29
Solve for x using y
x + (-29) = -17
x = 12
Five subtracted from seven times a number is 9. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is _____________
B) Solve your equation in part [A] for
Answer:
x=
Answer:
18
Step-by-step explanation:
7-5=2
2x9=18
Plz help me find x and y on these triangles
Answer:
x=15, y=2
Step-by-step explanation:
By AA similarity, the triangles are similar. Therefore, we can find the ratios of the side lengths.
9/3=3=ratio of the side length of a larger triangle to a smaller one.
3=6/y, y=2
3=x/5, x=15
Hope this helped,
~cloud
Write an equation for the following: y varies directly with x. Find K
when x=4 and y=5.
Answer:
4/5
Step-by-step explanation:
y varies as x
y=kx
k=x/y
URGENT 100 POINTS AND BRAINIEST!!!!!!
Question 4 (Essay Worth 10 points)
(02.05 HC)
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Using the points stated in the original problem, I have determined the lines for the graph.
f(x)=3x-1
g(x)= 3x+17
Using the basic descriptions of transformations, we can determine the movement of the lines as being either horizontal or vertical shifts. (to put a visual to this problem, I the diagram in Desmos and then marked the stated points on the graph.)
Horizontal shifts move the line either to the left or to the right. Vertical shifts move the line either up or down.
If you look at the graphs as being the same x-value for the functions, the change in the y- value is +18, which is a vertical shift.
If you look at the graphs as being the same y-values, the change in x is -6 which is a horizontal shift.
So, the value of k is the amount of change each equation has to have to match the points given. (from f(x) to g(x))
The vertical shift is g(x)=f(x) +18
The horizontal shift is g(x)=f(x-6)
Answer:
The vertical shift is g(x)=f(x) +18
The horizontal shift is g(x)=f(x-6)
Step-by-step explanation:
The length of a rectangle is 4 meters longer than the width. If the area is 22 square meters. find the rectangles dimensions. The width is what? The length is what?
Answer:
The width is:
[tex]-2+\sqrt{26}\text{ meters}\text{ }(\text{or approximately 3.0990 meters})[/tex]
And the length is:
[tex]2+\sqrt{26}\text{ meters}\text{ } (\text{or approximately 7.0990 meters})[/tex]
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length of a rectangle is four meters longer than the width. Thus:
[tex]\ell = w + 4[/tex]
And we also know that the area of the rectangle is 22 square meteres.
Substitute:
[tex](22)=w(w+4)[/tex]
Distribute and isolate the equation:
[tex]w^2+4w-22=0[/tex]
The equation isn't factorable, so we can instead use the quadratic formula:
[tex]\displaystyle w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 4, and c = -22. Substitute:
[tex]\displaystyle w = \frac{-(4)\pm\sqrt{(4)^2-4(1)(-22)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle\begin{aligned} w &= \frac{-4\pm\sqrt{104}}{2}\\ \\ &=\frac{-4\pm\sqrt{4\cdot 26}}{2} \\ \\ &=\frac{-4\pm2\sqrt{26}}{2} \\ \\ & = -2\pm \sqrt{26} \end{aligned}[/tex]
Thus, our two solutions are:
[tex]w_1=-2+\sqrt{26}\approx 3.0990\text{ or } w_2=-2-\sqrt{26}\approx-7.0990[/tex]
Since the width cannot be negative, we can ignore the second solution.
Since the length is four meters longer than the width:
[tex]\ell = (-2+\sqrt{26})+4=2+\sqrt{26}\text{ meters}[/tex]
Thus, the dimensions of the rectangle are:
[tex]\displaystyle (2+\sqrt{26}) \text{ meters by } (-2+\sqrt{26})\text{ meters}[/tex]
Or, approximately 3.0990 by 7.0990.
