Hence option (B) is a correct choice and rest all other options are incorrect
1/b^2 ∑ (-1)^k(t^2/b^2)^k
Step-by-step explanation:
Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r
S=a/1 - r
Wherever the common ratio r falls within the interval (-1,1)
When the given series is compared to the infinite sum:
First term=a
Common ratio=r
S= a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:
Hence option (B) is a correct choice.
What are real numbers simple definition?
Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.
INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k
To learn more about real numbers:
https://brainly.com/question/551408
#SPJ4
EASY POINTS!! EASY POINTS!!
A factory ships sunglasses in boxes that each have the same number of sunglasses. The table shows the data for 4 shipments.
Which rate represents the relationship in the table?
A. 100 sunglasses per 4 boxes
B. 5 sunglasses per 125 boxes
C. 4 sunglasses per 100 boxes
D. 225 sunglasses per 8 boxes
NO LINKS OR FILES!!!
Answer:
A
Step-by-step explanation:
2 boxes has 50 glasses
times by 2 and its equal to A
Answer: A or B
Step-by-step explanation:
Which form of payment can Courtney lose and not get back?
Answer:
Probably cash
Step-by-step explanation:
Because the other one would have your name and information on it and cash doesn't have any information or anything.
Answer:
credit
Step-by-step explanation:
because someone could take it hack into your account and steal your money with the information
A marketing research company desires to know the mean consumption of meat per week among males over age 50. They believe that the meat consumption has a
mean of 3.5 pounds, and want to construct a 95 % confidence interval with a maximum error of 0.08 pounds. Assuming a standard deviation of 0.6 pounds, what is
the minimum number of males over age 50 they must include in their sample? Round your answer up to the next integer.
Answer:
we get a required sample size of 122.
Step-by-step explanation:
We can use the following formula to calculate the required sample size:
n = (Z * sigma / e)^2
where:
n is the required sample size
Z is the z-score corresponding to the desired confidence level (e.g. for a 95% confidence level, Z = 1.96)
sigma is the standard deviation of the population
e is the maximum error allowed
Plugging in the given values, we get:
n = (1.96 * 0.6 / 0.08)^2 = 121.6
Rounding up to the next integer, we get a required sample size of 122.
Over the closed interval [3,8] for which function can the extreme value theorem be applied?
Answer:
A
Step-by-step explanation:
The extreme value theorem can be applied on an interval if the function is continuous in the entire interval. Testing the continuity for each function, we get that the correct option is the third option.
Continuity:
A function f is continuous at an interval if all points in the interval are in the domain of the function, and, for each point of [tex]x^{\ast}[/tex], the limit exists and:
[tex]\lim_{x \rightarrow x^{\ast}} = f(x^{\ast})[/tex]
First function:
At [tex]x = 4[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.
Second function:
At [tex]x = 5[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.
Third function:
The only point there can be a discontinuity is at [tex]x = 4[/tex], where the definition of the function changes. First we have to find the lateral limits, and if they are equal, the limits exist:
To the left(-), it is less than 4, so we take the definition for x < 4.
To the right(+), it is more than 4, so we take the definition for x >= 4.
[tex]\lim_{x \rightarrow 4^{-}} h(x) = \lim_{x \rightarrow 4} \frac{9x}{10-x} = \frac{9*4}{10-4} = \frac{36}{6} = 6[/tex]
[tex]\lim_{x \rightarrow 4^{+}} h(x) = \lim_{x \rightarrow 4} x + 2 = 4 + 2 = 6[/tex]
The lateral limits are equal, so the limit exists, and it's value is 6.
The definition at [tex]x = 4[/tex] is [tex]h(x) = x + 2[/tex], so [tex]h(4) = 4 + 2 = 6[/tex].
Since [tex]\lim_{x \rightarrow 4} = h(4)[/tex], the function is continuous over the entire interval, and this is the correct answer.
Fourth function:
There can be a discontinuity at [tex]x = 5[/tex], so we test the limits:
[tex]\lim_{x \rightarrow 5^{-}} h(x) = \lim_{x \rightarrow 5} -x = -5[/tex]
[tex]\lim_{x \rightarrow 5^{+}} h(x) = \lim_{x \rightarrow 5} x^2 - 20 = 5^2 - 20 = 25 - 20 = 5[/tex]
Different limits, so the limit does not exist and the function is not continuous at [tex]x = 5[/tex], and the extreme value theorem cannot be applied.
For more on the extreme value theorem, you can check https://brainly.com/question/15585098
A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available, how many ways can the knobs be painted
If six different colors of paint are available, 360 ways can the knobs be painted.
how many ways can the knobs be painted?A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available,
When examining permutations and combinations, we use factorials. Permutations tell us how many different ways we can arrange things if their order matters. Combinations tells us how many ways we can choose k item from n items if their order does not matter.
coat hanger has four knobs
6! / 4! ( 4!)
6 * 5 * 4* 3 / 4 * 3 * 2* 1 (4 * 3 * 2 * 1)
= 30 * 1 2
=360
360 ways can the knobs be painted.
To learn more about factorials refer to:
https://brainly.com/question/9214272
#SPJ4
The effect of wearing different types of running shoes on the time it takes to
complete a race is being studied in an experiment. Which of these is most
likely to be an extraneous factor that could also affect the time it takes to
complete the race?
A. Number of people the stadium can hold
OB. Color of the shoes
OC. Day of the week
OD. Type of treads on the shoes
Most likely one of these unrelated factors that could possibly have an impact on how long it takes to finish the race is the environment
What is meant by extraneous solution?An extraneous solution (also known as a spurious solution) is a solution that develops during the problem-solving process but is not a true solution to the issue at hand, such as the answer to an equation. Any variable that you are not researching but that might have an impact on the results of your research study is referred to as an extraneous variable in an experiment. Uncontrolled auxiliary variables can result in conclusions regarding the link between independent and dependent variables that are incorrect. The numbers we obtain when solving equations that aren't actually solutions to the equation are referred to as extraneous solutions. Extraneous variables are anything that could potentially influence the outcomes but is not the independent variable.Therefore the correct option is a) Number of people the stadium can hold
To learn more about extraneous solution, refer to:
https://brainly.com/question/4563555
#SPJ1
7+2x÷3=5 what is x Pls help
Answer:
x = 4
Step-by-step explanation:
Given
[tex]\frac{7+2x}{3}[/tex] = 5 ( multiply both sides by 3 to clear the fraction )
7 + 2x = 15 ( subtract 7 from both sides )
2x = 8 ( divide both sides by 2 )
x = 4
Need the answer for these
Answer:
Step-by-step explanation:
2A. 3x=6 ⇒ x=2
2B. 3n=2(n-3) ⇒ 3n=2n-6 ⇒ n= -6
1. cross multiplication method
How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16 cm, the iron being 2 cm thick throughout? If 1 cubic cm of iron weighs 15 g. find the weight of the open box in kg
A triangle has an angle that measures 115°. The other two angles are in a ratio of 6:7. What are the measures of those two angles?
Answer:
30° ; 35°
Step-by-step explanation:
Recall:
Sum of angles in a triangle = 180°
One of the 3 angles = 115
The sum of the other 2 Angles will be :
(180 - 115) = 65°
The other two angles are in the ratio 6:7
Hence,
Each of the two angles can be calculated thus :
Angle 2 :
Sum of ratio = 6 + 7 = 13
(6 / 13) * 65 = 30°
Second angle :
(7 / 13) * 65 = 35°
What’s the area of a square is all sides are 6 feet long?
Answer:
36 sq ft
Step-by-step explanation:
The area of a square is equal to the length of one side squared. Therefore, if all sides of a square are 6 feet long, the area of the square is 6 feet * 6 feet = 36 square feet.
Answer:
36
Step-by-step explanation:
you multiply just two of the sides hxw and you get your answer
Given
A
B
‾
∥
D
C
‾
AB
∥
DC
and
B
C
‾
∥
A
D
‾
BC
∥
AD
, prove
△
A
B
C
≅
△
C
D
A
△ABC≅△CDA by filling out the flowchart below.
The second row's third box AC = AC ( common side ) ( common side ) box last. Therefore, by applying the ABCD ASA congruence axiom.
What is triangle ?Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is depicted in the above figure. Triangular polygons in geometry are those with three sides and three vertices. There are three straight sides to this two-dimensional figure. Three-sided polygons include triangles. A triangle's three angles add up to a full 180 degrees. A single plane contains the triangle. Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."
given
AB||DC , BC||AD
To show that
ΔABC≅ ΔCDA
First box
AB || DC (given )
below box to the first box
∠BAC = ∠DCA ( parallel lies cut by the transverse form congruent alternate interior angles )
Second box
BC||AD ( given )
Below box to the second box
∠DAC = ∠BCA ( parallel lies cut by the transversal form congruent alternate interior angles )
Third box in the second row
AC = AC ( common side )
Last box
So by using ASA congruence axiom
ΔABC ≅ΔCDA
To know more about triangle visit :-
https://brainly.com/question/2773823
#SPJ1
WILL GIVE BRAINLIEST + 5 STAR
x=
Length=
Width=
Answer:
16
14
8
Step-by-step explanation:
Ms Steward is training for an IronMan Competition. She is determined to shatter every record ever known. She bikes, runs and swims. In two weeks she bikes 75.4 miles 8 times. She runs 22.4 miles three days and 27.5 miles 5 days. She swam 15 miles for 7 days consecutively. How many miles did Ms. Steward train in all?
Answer:
912.9 miles total
Step-by-step explanation:
75.4 miles biking x 8 times = 603.2 miles in biking
22.4 miles running x 3 days = 67.2 miles in running
27.5 miles running x 5 days = 137.5 miles running (2nd)
15 miles swimming x 7 days = 105 miles swimming
603.2+67.2+137.5+105 =
912.9 miles total
In the figure below ∠B=63∘. What is the measure of arc DB in degrees? (4 points) 27 126 54 63
Answer:
54
Step-by-step explanation:
63 x 2 = 126
180 - 126 = 54
Bought a board game for $30. The board game is now worth $55. Calculate the percent change in the game's value.
What is a algebraic expression for 1,10,19
The algebraic expression for the given sequence 1, 10, 19 as required to be determined is; a (n) = 1 + ( n - 1 ) 9.
What is the algebraic expression for the given sequence?As evident in the task content; it follows that the common difference of the given sequence is constant since; 19 - 10 = 10 - 1 = 9.
On this note, since the nth term of arithmetic sequences take the form;
a (n) = a (1) + ( n - 1 )d
Since the first term is; 1 and the common difference is; 9; the resulting algebraic expression is;
a (n) = 1 + (n - 1)9.
Read more on arithmetic sequence;
https://brainly.com/question/28369191
#SPJ1
SOMEBODY PLEASE GIVE ME THE ANSWERS! I AM GIVING AWAY A LOT OF POINTS!
A quarter equals 0.25
You want to multipole the number of quarters you have by 0.25 to get the total value.
The equation would be V = 0.25n
The output would be V which is the dollar value of the number of quarters you have.
The independent value would be the input value (n) which is the number of quarters you have.
HELP
Ps; i am only writing like this becase i need people to see this
Thanks dude!
Step-by-step explanation:
Can i have brainly?
u get brainliest if you anser first and is right if i get this wrong i fail pls help me
for 50 points
In the figure, triangle ABC is a right triangle and m of angle A = 40 degrees. What is the measurement of angle ECD?
Answer:
Solution given:
<A=49°
<B=90°
angle ECD=?
we have
<A+<B+<C=180°[sum of interior angle of a triangle is 180°
<A+40+90=180°
<A=180°-130°
<A=50°
wehave
<A=<ECD[vertically opposite angle]
:.angle ECD=50°.
solve the following equations graphically
x + y=3 & x-3y= -5
Answer:
[tex](x,y)\rightarrow(1,2)[/tex]
Step-by-step explanation:
Multiply first equation by 3 to help cancel out the "y" variable:
[tex]\displaystyle \left \{ {{x+y=3} \atop {x-3y=-5}} \right.\\\\\rightarrow \left \{ {{3x+3y=9} \atop {x-3y=-5}} \right.[/tex]
Combine system of equations on both sides:
[tex](3x+3y)+(x-3y)=9+(-5)\\4x=9-5\\4x=4\\x=1[/tex]
Thus,
[tex]x+y=3\\1+y=3\\y=2[/tex]
A solution of 60 quarts of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar
On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
1200=300+5x
900 = 5x
x=180
To know more about equation visit:
https://brainly.com/question/649785
#SPJ4
What does a 30 60 90 triangle look like?
The 30-60-90 triangle is shaped like half of an equilateral triangle.
A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.
The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.
30°-60°-90° Triangle Rule:
In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.
To know more about 30°-60°-90° Triangle Rule:
https://brainly.com/question/30109611
#SPJ4
Annie and Bonnie are running laps around a 400-meter oval track. They started together, but Annie has pulled ahead, because she runs 25% faster than Bonnie. How many laps will Annie have run when she first passes Bonnie
Bonnie will complete four laps before being passed by Annie because she runs an additional quarter lap for every lap she completes. This indicates that Annie and Bonnie are on an equal footing, and Annie must complete an additional lap to pass Bonnie. Annie will have completed five laps after that.
What unitary method examples are there?We can use the unitary method to calculate 100% of an amount. For instance, if 10% of the marbles in a pot are 35, then the total number of marbles in the pot will be 35 x 10%, or 350.
What circumstances allow us to use the unitary method in our daily lives?The unitary method can be used to calculate how many kilometres a car will travel on one litre of gas if it travels 44 km on two litres of fuel. In other words, the unitary method is the process by which we determine the value of a single unit and then use that information to determine the values of multiple units.
To know more about unitary method visit:-
brainly.com/question/22056199
#SPJ4
look at the screenshot, please. (no links)
Answer: 14
Step-by-step explanation: 18 x 14 = 252
Answer:
14
Step-by-step explanation:
recall that area of figure, A= length x. breadth
and A=252
and b=18
therefore, 252= 18b
l= 252/18
l= 14
therefore p= 14
Sherane rolls a standard, six-sided number cube.
What is the probability of rolling a multiple of 3?
The length of an object in feet is equal to 3 times it's length in yards. The length of the boat is 36 feet. Write and solve a multiplication equation to find the length of the boat in yards
In linear equation ,The length of waterslide is 12 yards.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given that,
The length of an object object in feet is equal to 3 times it’s length in yards
The length of wall water side slide is 36 feet
Let "y" be the length of object in yards
From given,
Length in feet = 3 times length in yards
36 = 3 * y
3y = 36
y = 36/3
y = 12
Thus length of waterslide is 12 yards.
Learn more about linear equation
brainly.com/question/11897796
#SPJ4
I have a 1 in the ones place, a 4 in the tens place, and a 5 in the hundreds place.
Answer:
541
Step-by-step explanation:
if you have a 1 in the ones place and a 4 in the tens place and a 5 in the hundreds place this will be your number
How do you find out if a triangle is acute obtuse or right?