Given:
a1 = 4
a3 = 1
r = ½
Let's find the S3 of the sum of the geometric series.
Apply the sum of geometric series formula below:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]Let's solve for S3.
Substitute the values into the equation.
Where: n = 3
Thus, we have:
[tex]S_3=\frac{4(1-(\frac{1}{2})^3)^{}^{}}{1-\frac{1}{2}}[/tex]Solving further:
[tex]\begin{gathered} S_3=\frac{4(1-(\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}))}{\frac{1}{2}} \\ \\ S_3=\frac{4(1-\frac{1}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4(\frac{7}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4\ast\frac{7}{8}}{\frac{1}{2}} \\ \\ S_3=\frac{\frac{7}{2}}{\frac{1}{2}} \\ \\ S_3=\frac{7}{2}\ast\frac{2}{1} \\ \\ S_3=7 \end{gathered}[/tex]Therefore, the S3 of the sum of the given geometric series is 7
ANSWER:
7
answer step by step pleaseSteve determines that sides DK and BC are congruent. He also measures angle K and angle C and determines that they are congruent. He concludes that the triangles are congruent by SAS theorem. Is Steve correct?
Data Input
DK and BC are congruent.
Angle K and angle C are congruent.
Procedure.
To determine if the triangles are congruent median SAS, we need to know the size of one of the remaining sides
For them, we will measure the ED and AB sides using the Euclidean distance
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]For ED
E = (-6, 4)
D = (0, 8)
[tex]\begin{gathered} ED=\sqrt[]{(-6-0)^2+(8-4)^2} \\ ED=\sqrt[]{6^2+4^2} \\ \\ ED=\sqrt[]{(36+16)} \\ ED=\sqrt[]{52} \end{gathered}[/tex]For AB
A = (3, 6)
B = (9, 10)
[tex]\begin{gathered} AB=\sqrt[]{(9-3)^2+(10-6)^2} \\ AB=\sqrt[]{6^2+4^2} \\ AB=\sqrt[]{36+16} \\ AB=\sqrt[]{52} \end{gathered}[/tex]Now, AB is equaled to ED
Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
D1 ptsQuestion 3The bill of a white pelican can hold about 550 cubic inches of water,Nigel, the pelican from Finding Nemo, scoops up 160 cubic inches ofwater. Write an inequality that represents how much more waterNigel cal add to his bill.
let the additional water that is needed to add in the bill is x
[tex]\begin{gathered} 160+x\leq550 \\ x\leq550-160 \\ x\leq390 \end{gathered}[/tex]so, Nigel can add 390 cubic inches of water to the bill of a white pelican.
It turns out that as ice cream consumption increases, drowning deaths increase. In other words, there is a positive association between ice cream consumption and drowning deaths. However, ice cream consumption does not cause drowning deaths. So why is there a positive association? Explain.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ice cream consumption ====> increases
drowning deaths ====> increase
Step 02:
We must analyze the question to find the solution.
positive association:
There is an association because both values increase, that is, a positive association suggests that when one variable increases, the value of the other variable also increases.
That is the solution.
Please find arc JK and angle 1. Ignore the entered answers.
The Solution:
Given the figure below:
Solving for arc JK:
By angle subtends at the center of a circle is twice that subtends on the circumference, we have that:
[tex]2\times118=236^o[/tex]Subtracting 236 from 360, we get
[tex]arcJK=360-236=124^o\text{ (angle at a point)}[/tex]So, the correct answer for question 7 is [option 4]
To answer Question 8:
[tex]\begin{gathered} \angle JKM=\frac{70}{2}=35^o\text{ } \\ \\ \text{ Reason: Angle subtends at the center is twice that subtends} \\ \text{ at the circumference of the circle.} \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} \angle KJL=\frac{60}{2}=30^o \\ \\ \text{Reason: Angle subtends at the center is twice that subtends} \\ \text{ at the circumference of the circle.} \end{gathered}[/tex][tex]\text{ To get }\angle1[/tex][tex]\begin{gathered} \angle1=180-(\angle JLM+\angle KML) \\ \text{ Reason: sum of angles in a triangle.} \end{gathered}[/tex][tex]\begin{gathered} \angle JLM=\angle JKM=35^o \\ \text{ Reason: angles on the same segments.} \\ \text{ Similarly,} \\ \angle KML=\angle KJL=30^o \\ \text{ Reason: angles on the same segments.} \end{gathered}[/tex][tex]\begin{gathered} \angle1=180-(35+30) \\ \text{ Sum of angles in a triangle.} \\ \angle1=180-65=115^o \end{gathered}[/tex]Therefore, the correct answer to Question 8 is 115 degrees.
Letℎ()h(x)be the inverse of()f(x). Ifℎ()=−4+1h(x)=−4x+1, which of the following represents()f(x)?
In order to find f(x), we need to calculate the inverse of h(x)
[tex]h(x)=-4x+1[/tex]y=h(x)
[tex]y=-4x+1[/tex]We substitute x with y and y with x
[tex]x=-4y+1[/tex]Then we isolate the y
[tex]4y=-x+1[/tex][tex]y=-\frac{1}{4}x+\frac{1}{4}[/tex]ANSWER
f(x) is
[tex]f(x)=-\frac{1}{4}x+\frac{1}{4}[/tex]The correct choice is the first one
Hi, can you help me answer this question, please, thank you!
Answer
Standard deviation = 1.2083
Step-by-step explanation
[tex]\begin{gathered} \text{Mean = }\sum ^{}_{}xi\cdot\text{ p(xi)} \\ \text{Mean = }0\cdot\text{ 0.2 + 1 }\cdot\text{ }0.05\text{ + 2}\cdot\text{ }0.1\text{ + 3 }\cdot\text{ 0.65} \\ \text{Mean = 0 + 0.05 + 0.2 + 1.95} \\ \text{Mean = 2.2} \\ \text{Standard deviation = }\sqrt[]{\sum^{}_{}}(\text{ x - }\mu)^2\cdot\text{ p(xi)} \\ \text{let }\mu\text{ = 2.2} \\ \text{Standard deviation = }\sqrt[]{(0-2.2)^2\cdot0.2+(1-2.2)^2\cdot0.05+(2-2.2)^2\cdot0.1+(3-2.2)^2\cdot\text{ 0.65}} \\ \text{standard deviation = }\sqrt[]{0.968\text{ + 0.072 + 0.004 + 0.416}} \\ \text{Standard deviation = }\sqrt[]{1.46} \\ \text{Standard deviation = }1.2083 \\ \text{Hence, standard deviation is 1.2083} \end{gathered}[/tex]Find the simple interest earned, to the nearest cent, for the principal, interest rate, and time.
$650, 5%, 1 year
The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
The simple interest exists 32.5.
What is meant by simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay additional interest on the interest that has already accrued.
Let the equation be I = Prt
where, P be the principal amount = $650
r be the interest rate = 5%
t be the time = 1 year
substitute the values in the above equation, we get
I = 650 × 0.05 × 1
I = 32.5
Therefore, the simple interest rate exists 32.5.
To learn more about Simple Interest refer to:
https://brainly.com/question/20690803
#SPJ1
Amber rolls a 6-sided die. On her first roll, she gets a "6". She rolls again.(a) What is the probability that the second roll is also a "6".P(6 | 6) =(b) What is the probability that the second roll is a "4".P(46) =
Answer
Explanation
Given the word problem, we can deduce the following information:
1. Amber rolls a 6-sided die.
2. Amber gets a "6" on her first roll.
a)
To determine the probability that the second roll is also a "6", we note first that a 6-sided die has these values: 1,2,3,4,5,6
As we can see, there's only one 6 value on a 6-sided die while the total .So, the probability would be:
P(6 | 6) =1/6
b)
To determine that the second roll is a "4", we use the same reasoning above. Therefore, the probability is:
P(4 | 6) =1/6
Rusell runs 9/10 mile in 5 minutes. at this rate, how many miles can he run in one minute?
Answer:
in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]Explanation:
Given that;
Rusell runs 9/10 mile in 5 minutes.
[tex]\begin{gathered} \frac{9}{10}\text{mile }\rightarrow\text{ 5 minutes} \\ \text{dividing both sides by 5;} \\ \frac{9}{10\times5}\text{mile }\rightarrow\text{ }\frac{5}{5}\text{ minutes} \\ \frac{9}{50}\text{mile }\rightarrow\text{ 1 minutes} \end{gathered}[/tex]Therefore, in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]Write an equation in slope-intercept form for the line perpendicular to the given line that passes through the origin. y = 11/5 x + 7
y = 11/5 x + 7
Slope intercept form:
y=mx+b
Where:
m= slope
b= y-intercept
So, for the line given:
m= 11/5
b= 7
Perpendicular lines have negative reciprocal slopes.
negative reciprocal of 11/5 = -5/11
Slope = -5/11
So far we have:
y= -5/11 + b
Since it passes through the origin (0,0) replace and solve for b:
0= -5/11(0) +b
b=0
Final expression:
y= -5/11x
The GMAT scores of all examinees who took that test this year produced a distribution that is approximately normal with a mean of 430 and a standard deviation of 34.The probability that the score of a randomly selected examinee is between 400 and 480, rounded to three decimal places, is:
SOLUTION:
Case: Probability from a normal distribution
Given: Mean = 430, Standard deviation: 34
Required: To find the probability that the score of a randomly selected examinee is between 400 and 480
Method:
Steps
Step 1: Get the z-score with the lesser value:
[tex]undefined[/tex]Final answer:
I just need help with part b can you help me please
b) Recall that to evaluate a function at a given value, we substitute the variable by the given value.
Evaluating P(t) at t=2007-1992=15 we get:
[tex]P(15)=29000(1.06)^{15}.[/tex]Simplifying the above result we get:
[tex]P(15)\approx69500.[/tex]Answer: $69,500.
I need to know the answer to this like asap
In general, a vertically compression of a function f(x) is obtained by the transformation:
[tex]f(x)\rightarrow g(x)=\frac{1}{k}\cdot f(x).[/tex]Where k > 1 is the factor of compression.
In this case we have f(x) = |x| and k = 4. Applying the transformation above, we get:
[tex]g(x)=\frac{1}{4}\cdot|x|.[/tex]AnswerC.
[tex]g(x)=\frac{1}{4}|x|[/tex]if M angle ABD equals 7X - 31 n m a angles c d b equals 4x + 5 find M angle ABD
The quadrilateral is a rectangle, all of its corner angles are rigth angles.
5)
m∠DAC=2x+4
m∠BAC=3x+1
Both angles are complementary, which means that they add up to 90º
You can symbolize this as:
[tex]m\angle DAC+m\angle BAC=90º[/tex]Replace the expression with the given measures for both angles:
[tex](2x+4)+(3x+1)=90[/tex]Now you have established a one unknown equation.
Solve for x:
[tex]\begin{gathered} 2x+4+3x+1=90 \\ 2x+3x+4+1=90 \\ 5x+5=90 \\ 5x=90-5 \\ 5x=85 \\ \frac{5x}{5}=\frac{85}{5} \\ x=17 \end{gathered}[/tex]Next is to calculate the measure of m∠BAC, replace the given expression with x=17
m∠BAC=3x+1= 3*17+1=52º
6)
m∠BDC=7x+1
m∠ADB=9x-7
Angle m∠BDC is a corner angle of the rectangle, as mentioned before, all corner angles of a rectangle measure 90º, so there is no need to make any calculations.
Note: the diagonals of the rectangle bisect each corner angle, this means that it cuts the angle in half, so m∠BDC=2*(m∠ADB)
Find the angle between the vectors u = i – 9j and v = 8i + 5j.
Answer:
[tex]\theta\text{ = 115.67}\degree[/tex]Explanation:
Here, we want to find the angle between the two vectors
Mathematically, we have that as:
[tex]cos\text{ }\theta\text{ = }\frac{a.b}{|a||b|}[/tex]The denominator represents the magnitude of each of the given vectors as a product while the numerator represents the dot product of the two vectors
We have the calculation as follows:
[tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{(1\times8)+(-9\times5)}{\sqrt{1^2+(-9)\placeholder{⬚}^2}\text{ }\times\sqrt{8^2+5^2}} \\ \\ cos\text{ }\theta\text{ = }\frac{8-45}{\sqrt{82}\text{ }\times\sqrt{89}} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{-37}{\sqrt{82}\text{ }\times\sqrt{89}} \\ cos\text{ }\theta\text{ = -0.4331} \\ \theta\text{ = }\cos^{-1}(-0.4331) \\ \theta\text{ = 115.67}\degree \end{gathered}[/tex]I need help with graphing
to grpah a line, we need two points and join it
so, we give values for x and find the solution to find one point
[tex]y=-4+\frac{6}{5}x[/tex]x=0
[tex]\begin{gathered} y=-4+\frac{6}{5}(0) \\ \\ y=-4 \end{gathered}[/tex]First point (0,-4)
x=5
[tex]\begin{gathered} y=-4+\frac{6}{5}(5) \\ \\ y=-4+6 \\ y=2 \end{gathered}[/tex]second point (5,2)
now place on the graph and join
this is the line
how do I know where which choices below go into the correct blanks?
In a 30-60-90 special right triangle, we have the following.
If the short leg is 7 cm, then x = 7.
So, the hypotenuse would be
[tex]h=2x=2(7)=14\operatorname{cm}[/tex]The length of the long leg is
[tex]x\sqrt[]{3}=7\sqrt[]{3}\approx12.12\operatorname{cm}[/tex]Therefore, the hypotenuse is 14 cm, and the long leg is 12.12 cm, approximately.i need help with this questionsfind the slope to the following graphs?
Answer:
b
Step-by-step explanation:
Can you please tell me
The area of kite when both diagonals are given is
[tex]A=\frac{d_{}\times D}{2}[/tex]where d=17 m and D=21 m. By substituting the given values, we get
[tex]\begin{gathered} A=\frac{17\times21}{2} \\ A=178.5 \end{gathered}[/tex]then, the answer is 178.5 square meters
What is the probability that the person has no high school diploma and earns more than $30,000?
Find the lateral surface area and volume please round up to nearest integer
For this problem we will use the following formula for the surface area of a truncated cone:
[tex]\begin{gathered} SA=\pi(r_1+r_2)\sqrt[]{(r_1-r_2)^2+h^2}+\pi(r^2_1+r^2_2), \\ \text{Where r}_1\text{ is the lower radius, r}_2\text{ is the upper radius, and h is the height.} \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} r_1=\frac{11in}{2}=5.5in, \\ r_2=\frac{14in}{2}=7in, \\ h=21in, \end{gathered}[/tex]we get:
[tex]\begin{gathered} SA=\pi(7in+5.5in)\sqrt[]{(7in-5.5in)^2+(21in)^2}+\pi((5.5in)^2+(7in)^2) \\ =\pi(12.5in)\sqrt[]{2.25in^2+441in^2}+\pi(30.25in^2+49in^2) \\ =\pi(12.5in)(21.05in)+\pi\cdot79.25in^2 \\ =\pi(263.125+79.25)in^2 \\ =\pi(342.375)in^2 \\ \approx1076in^2. \end{gathered}[/tex]Now, to compute the volume we will use the following formula:
[tex]V=\frac{1}{3}\pi(r^2_1+r_1r_2+r^2_2)h\text{.}[/tex]Substituting the given values we get:
[tex]\begin{gathered} V=\frac{1}{3}\pi((5.5in)^2+(5.5in)(7in)+(7in)^2)21in \\ =\frac{1}{3}\pi(30.25in^2+38.5in^2+49in^2)21in \\ =\frac{1}{3}\pi(117.75in^2)21in \\ =824.25\pi in^3 \\ =2589in^3\text{.} \end{gathered}[/tex]Answer: The total surface area is
[tex]1076in^2\text{.}[/tex]The volume is
[tex]2589in^3\text{.}[/tex]I would like to know the break down to solve for this problem.
Train A travels at a speed of 25 miles per hour south and train B travels at a speed of 20 mph east.
We can find the distance for each one of the trains by using the following formula:
[tex]X=Vt[/tex]Where X is distance, V is velocity and t is time
Let's find the dinstance that A and B will travel in 6 hours
[tex]\begin{gathered} Xa=Va\cdot t \\ Xa=25\cdot6=150 \end{gathered}[/tex]Train A travels 150 miles in 6 hours
[tex]\begin{gathered} Xb=Vb\cdot t \\ Xb=20\cdot6=120 \end{gathered}[/tex]Train B travels 120 miles in 6 hours
Now, in order to determine how far they are from each other, we need to take into account their direction. From the picture we can see that their route describes a right triangle, so the distance between them is the hypotenuse of this right triangle I will draw...
if D is the distance that separates the two trains, D is given by the following formula
[tex]D=\sqrt[]{150^2+120^2}[/tex]Solving the equation we obtain...
[tex]\begin{gathered} =\sqrt[]{22500+14400^{}} \\ =\sqrt{36900} \\ \end{gathered}[/tex]Solving this square root by using prime factorization and laws of exponents:
[tex]\begin{gathered} =\sqrt{2^2\cdot\:3^2\cdot\:5^2\cdot\:41} \\ =\sqrt{41}\sqrt{2^2}\sqrt{3^2}\sqrt{5^2} \\ =2\cdot\: 3\cdot\: 5\sqrt{41} \\ =30\sqrt{41} \end{gathered}[/tex]which is approximately the same as 192.09372...
How do you know if a sequence is a geometric sequence. A It has a common difference. B It has a common ratio.
A geometric sequence in which each next term is found by multiplying the previous term by a constant; therefore, every adjacent pair on entires in a geometric sequence have a common ratio. Hence, if any two consecutive entries in a sequence have a common ratio, it is a geometric series; therefore, choice B is the correct one to choose.
A local newspaper delivers 364 papers split evenly among n delivery people. Q is the number of papers delivered by each delivery person. Write a formula for Q as a function of n, including finding the value of any unknown constants. Q =
The formula for Q is:
[tex]Q(n)=\frac{364}{n}[/tex]where n = the number of delivery people.
We just have to divide the 364 papers to the number of delivery people to determine how many papers each person delivered.
2) The shape of a playground is a parallelogram. The city is going to treat the asphalt with sealant this spring with cans that will cover 4 square yards each. The figure below is a drawing of the playground, For how many cans of sealant does the city need to budget for the treatment, if the playground has a perimeter of 34 yards and the height is 1.4 yards less than the diagonal side of the parallelogram? 10.6 yd 6.4 yd a. Write the equation in words. b. Find the unknown height. c. Calculate the area of playground. d. Choose a variable for the unknown quantity and write the equation with the substituted values. e. Solve the equation. Include appropriate units in your answer. f. How many cans of sealant are needed?
In this situation, you have a parallelogram with lateral sides of L length and top and bottom sides of length D. The letter h represents the height of the parallelogram.
L=6.4 yd and D=10.6 yd. The perimeter is the sum of all 4 edges, so perimeter=2*L+2*D
a) If one can cover 4 square yards and you need to find how many cans you will need for the whole playground area, then you need to find the total area which is calculated by its height times its base (D), so it would be h*D=area. This area divided by 4 square yards will give you the number of cans you need.
b) If the height is 1.4 yards less than the diagonal side, then
[tex]h=L-1.4=6.4-1.4=5\text{ yards}[/tex]c)Then the area is given by:
[tex]h\cdot D=5\cdot10.6=53\text{ square yards}[/tex]d)The number of cans can be represented by a variable called n (n as in number), so:
[tex]n=\frac{area}{4}=\frac{53}{4}[/tex]e) Then, by calculating:
[tex]\frac{53}{4}=13.25\text{ cans}[/tex]f) You will need 14 cans of sealant, you will only use some of it from the last can
Divide 22 stars to represent the ratio 4:7.
Answer
Dividing 22 stars into the ratio 4:7 will give
8 stars : 14 stars
Explanation
We need to divide 22 stars into the ratio 4:7
Divide the ratio through by 11 (the sum of the two numbers in the ratio)
4:7 = (4/11) : (7/11)
Multiplying through by 22
(4/11) : (7/11)
= (4 × 22/11) : (7 × 22/11)
= 8 : 14
Hope this Helps!!!
Bernies cafe has regular coffee and decaffeinated coffee this morning the cafe served 80 coffees in all 48 of which were regular what percentage of the coffees were regular
We have to divide the number of regular ones by the total. Then multiply the result by 100.
48/80*100 = 60
Our answer is 60 % of the coffees were regular.
You can only use cross multiplication in solving rational equation if and only if you have one fraction equal to one fraction, that is, if the fractions are _______
Answer:
Proportional
Explanation:
Gym membership is $45.75 a month. How much will the gym membership be for one year? If Sherrie budcets $550 for gym costs, will she have enough?
Since a year has 12 months, we have to multiply the monthly membership cost by 12 to get the cost of a year's memberhsip:
[tex]45.75\times12=549[/tex]This way, the gym membership be for one year would be $549
Therefore, Sherrie would be able to pay for it with the $550 budget
how can you use number patterns to find the greatest common factor of 120 and 360
Greatest common factor (GCF)
• 120
Finding the factors:
[tex]\begin{gathered} \frac{120}{2}=60\text{ (2 is a factor)} \\ \frac{60}{2}=30\text{ (again 2 is a factor)} \\ \frac{30}{2}=15\text{ (again 2 is a factor)} \\ 15\text{ is not divisible over 2, we search for 3:} \\ \frac{15}{3}=5\text{ (3 is another factor as 15 is divisible over 3)} \\ 5\text{ is not divisible over 2, 3, or 4, we search for 5:} \\ \frac{5}{5}=1\text{ (5 is another factor, and the last one)} \end{gathered}[/tex]Placing the factors as a multiplication:
[tex]120=2\cdot2\cdot2\cdot3\cdot5[/tex]• 360
[tex]360=2\cdot2\cdot2\cdot3\cdot3\cdot5[/tex]The factors that repeat in each integer are: 2, 2, 2, 3, 5
Therefore, the GFC is:
[tex]\text{GFC}=2\cdot2\cdot2\cdot3\cdot5=120[/tex]Answer: 120