Answer:
Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138
S'ₙ =2.52
Step-by-step explanation:
sum of this sequence: Sₙ = A₁ x (1 - pⁿ) / (1 - p)
Sₙ: sum of n terms
A₁: initial value 6
p: common ratio 2
n: terms 10
Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138
Is there any mistake in the 2nd question - about the common ratio (-1/2)?
S'ₙ =1 + (-1/2) + 1 x (1 - (1/2)¹⁸)) / (1 - (1/2)) = 1/2 + 2 x (1 - (1/2)¹⁸)
S'ₙ = 1/2 + 2 x (1 - 1/262144) = 1/2 + 262143/130072= 0.5 +2.02 = 2.52
The Saxena family plans to install a light to illuminate part of their rectangular yard. Nikki and Dylan each proposed a
different spot to place the light. The proposed placements and the lit area that each produces are shown below.
Nikki's Proposed Placement
Light
27.5 ft
Dylan's Proposed Placement
Light
16.5 ft
38
38 ft
Lit area
Lit Area
60
60 ft
How do Nikki's and Dylan's proposals compare? Check all that apply.
Nikki's proposed placement will light a greater area than Dylan's placement
Dylan's proposed placement will light a greater area than Nikki's placement.
Both proposed placements will light the same sized area.
Answer
THE REAL ANSWER IS c and f
Step-by-step explanation:
I just finished and they are the only 2 and I got it right
Nikki's and Dylan's Both proposed placements will light the same sized area.
Area of triangleThe area of a triangle is defined as the total space that is enclosed by the three sides of the triangle.The area of a triangle can be determined using the formula below,A = 1/2 × b × h.
How to solve this problem?The steps are as follow:
From the question, of the base and height of Nikki's and Dylan's proposed placements are the same which is 60 and 38ft respectively.The area that would be covered by both of them would be,A= 1/2×60×38
A= 30×38
A = 1,140ft.
So, Nikki's and Dylan's Both proposed placements will light the same sized area.
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The equation 5x - 7(x-1) = ax+b has exactly one solution.
Answer:
a = -2 and b = 7
Step-by-step explanation:
We need to solve for the value of "a" and "b".
We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.
We will use the distributive property shown below to expand the left side and simplify.
Distributive Property: a(b-c) = ab - ac
Now, simplifying left hand side:
5x - 7(x - 1)
= 5x -7(x) -7(-1)
= 5x -7x +7
= -2x + 7
The right hand side is "ax + b".
If we match left-hand side and right-hand side, we see that:
a = -2
and
b = 7
THese are the only solution.
What is the probability of spinning these two spinners and having each one land
on a 3? Write the probability as a decimal.
Answer:
The probabilities are 0.4 and 0.6 respectively.
Step-by-step explanation:
We are given two spinning wheels with numbers on it and we have to find the probability of getting 3.
In the first wheel, there are 5 slots and the numbers are 3, 3, 2, 5 and 4.
So the probability of getting 3 =[tex]\frac{number of 3's}{total number of slots}[/tex]
= [tex]\frac{2}{5}[/tex]
= 0.4
In the second spinner there are three 3's and total of 5 slots.
So probability of getting 3 = [tex]\frac{number of 3's}{total number of slots}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
Hence the probabilities are 0.4 and 0.6 respectively.
CAN SOMEONE HELP ME FIND THE DISTANCE..
The angle of elevation from point C to point A is [tex]32^{\circ}[/tex]
Solution:
Given that we have to find the angle of elevation from point C to Point A
Given in figure that, angle A = [tex]58^{\circ}[/tex]
Given is a right angled triangle ABC where angle B = [tex]90^{\circ}[/tex]
We have to find angle C
The angle sum property of a triangle states that the angles of a triangle always add up to 180°
Therefore, in given triangle ABC
angle A + angle B + angle C = 180
[tex]58^{\circ} + 90^{\circ} + C = 180^{\circ}[/tex]
[tex]148^{\circ} + C = 180^{\circ}\\\\C = 180^{\circ} - 148^{\circ}\\\\C = 32^{\circ}[/tex]
Therefore angle C = [tex]32^{\circ}[/tex]
How to solve -7-8(6x+5)
Answer: -47 - 48x
Step-by-step explanation: When you first take a look at this problem, it's tempting to want to subtract -7 - 8 to get -15 and then distribute the -15 through the parentheses.
You wouldn't want to subtract however before you distribute because the distributive property is a form of multiplication and remember from your order of operations that multiplication comes before subtraction.
So the first thing you want to do here is distribute and change the minus sign in front of the -8 to plus a negative 8 so that you know you are distributing a -8 through your parentheses.
So we have -7 + -8 times 6x which is -42x + -8 times 5 which is -40.
Now we have -7 + -48x + -40.
Now just combine your like terms. -7 + -40 is -47 and plus a negative 48x can be written as -48x so we have -47 - 48x.
So your answer is just -47 - 48x.
Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 8 cm/min. How fast is the area of the pool increasing when the radius is 13 cm?
Answer:
The area of the pool increasing at the rate of 653.12[tex]cm^2/min[/tex] when the radius is 13 cm
Step-by-step explanation:
Given:
radius of the pool increases at a rate of 8 cm/min
To Find:
How fast is the area of the pool increasing when the radius is 13 cm ?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A =[tex]\pi r^2[/tex]-----------------------------(1)
The area of the pool os increasing at the rate of 8 cm/min, meaning that the arae of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
[tex]\frac{d A}{d t}=\pi \cdot 2 r \cdot \frac{d r}{d t}[/tex]
we have to find [tex]\frac{d A}{d t}[/tex] with [tex]\frac{d r}{d t}[/tex] = 8 cm/min and r = 13cm
substituting the values
[tex]\frac{d A}{d t}=\pi \cdot 2 (13) \cdot 8[/tex]
[tex]\frac{d A}{d t}=\pi \cdot 26 \cdot 8[/tex]
[tex]\frac{d A}{d t}=\pi \cdot 208[/tex]
[tex]\frac{d A}{d t}= 208 \pi[/tex]
[tex]\frac{d A}{d t}=653.12[/tex]
Answer:
208pi cm^2/min
Step-by-step explanation:Take the derivative of the formula for Area and substitute the values
14. © MP.1 Make Sense and Persevere
Hodi is building a birdhouse. Each of the
four walls of the birdhouse needs to be
5.5 inches long. Hodi has a piece of
board that is 24.5 inches long. Is the
board long enough to be cut into the four
walls of the birdhouse? Estimate using
compatible numbers.
Answer:
This board of 24.5 inches long is not enough to be cut into the four walls of the bird house.
Step-by-step explanation:
Hodi is building a birdhouse. Each of the four walls of the birdhouse needs to be 5.5 inches long.
So, to get four 5.5 inches long walls we need to have (5.5 × 4) = 22 inches ling board from which four equal 5.5 inches board can be made.
Now, Hodi has a piece of a board that is 24.5 inches long.
Therefore, this board is not enough to be cut into the four walls of the birdhouse. (Answer)
you want to save $5,000 for future family vacation. if the bank pays 4.3% compounded monthly for 3 years, then how much will you need to invest to reach your vacation goal?
Answer:
The principal amount invested is $4395.93 .
Step-by-step explanation:
Given as :
The Amount that saved for future = A = $5,000
The bank applied rate of interest = r = 4.3% compounded monthly
The time period of loan = t = 3 years
Let the principal amount invested = $p
Now, From monthly Compound Interest method
Amount = principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{12\times 100})^{12\times t}[/tex]
Or, $5000 = p × [tex](1+\dfrac{\textrm 4.3}{12\times 100})^{12\times 3}[/tex]
Or, $5000 = p × [tex](1.003583)^{36}[/tex]
Or, $5000 = p × 1.137414
∴ p = [tex]\dfrac{5000}{1.137414}[/tex]
i.e p = $4395.93
So, The principal amount invested = p = $4395.93
Hence, The principal amount invested is $4395.93 . Answer
Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. How many total kilograms of candy did he buy?
Answer:
1.26 kg.
Step-by-step explanation:
We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.
First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:
[tex]\text{Amount of candy bought in grams}=14\times 90[/tex]
[tex]\text{Amount of candy bought in grams}=1260[/tex]
We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:
[tex]\text{Amount of candy bought in kilograms}=\frac{1260}{1000}[/tex]
[tex]\text{Amount of candy bought in kilograms}=1.26[/tex]
Therefore, Mr. Snow bought 1.26 kilograms of candy.
the sum of 6c- 5c and the opposite of 6c
Answer:
[tex]-5c[/tex]
Step-by-step explanation:
To find: The sum of [tex]6c-5c[/tex] and opposite of [tex]6c[/tex]
Opposite of [tex]6c[/tex] means taking the opposite sign.
[tex]6c[/tex] is positive. So, opposite sign is [tex]-6c[/tex].
Therefore, the addition is given as:
[tex]=6c-5c+(-6c)[/tex]
Opening the parenthesis, we get:
[tex]6c-5c-6c[/tex]
Now, as per PEDMAS rule, we subtract [tex]6c\ and\ 5c[/tex], we get
[tex]6c-5c=(6-5)c=1c[/tex]
Now, we are left with [tex]1c-6c[/tex]
Subtracting a bigger number from a smaller number will give a negative answer.
So, [tex]1c-6c=(1-6)c=-5c[/tex]
Therefore, the final answer is [tex]-5c[/tex]
An amusement park charges an admission fee of 40 dollars per person. The cost, C (In dollars), of admission for a group of p people is give by the following
C=40p
What is the cost of admission for a group of 3 people
Cost of admission for a group of 3 people is $ 120
Solution:
Given that amusement park charges an admission fee of 40 dollars per person
The cost, C (In dollars), of admission for a group of p people is give by the following expression:
C = 40p
Here "p" denotes the number of people
To find: cost of admission for a group of 3 people
For a group of 3 people, p = 3
Substituting p = 3 in given cost formula, we get the cost of admission for a group of 3 people
[tex]c = 40p\\\\c = 40(3) = 120[/tex]
Thus cost of admission for a group of 3 people is $ 120
if 10,000 bacteria are present initially and the number of bacteria doubles in 5 hours, how many bacteria will there be in 24 hours?
Answer:
20,000
Step-by-step explanation:
Study the graph below.
Coordinate plane with x-axis labeled as quantity A and the y-axis labeled as quantity B. Graph contains a line that passes through the following points: (0, 0), (3, 4) and (6, 8).
Describe the functional relationship between the two quantities in the graph.
Answer:
[tex]B=\frac{4}{3}A[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have a proportional relationship because the line passes through the origin (0,0)
Find the value of k
[tex]k=\frac{B}{A}[/tex]
take the point (3,4)
A=3,B=4
substitute
[tex]k=\frac{4}{3}[/tex]
The equation of the line is
[tex]B=\frac{4}{3}A[/tex]
10 POINTS!!
Point p is chosen at random on KN. Find the probability that p is on LM.
Answer:
[tex]\frac{4}{11}[/tex]
Step-by-step explanation:
The total length of KN is 11 units and the length of LM is 4 units. This means that the probability would be [tex]\frac{4}{11}[/tex]
Answer : The probability that p on LM is, [tex]\frac{4}{11}[/tex]
Step-by-step explanation :
Probability : It is defined as the extent to which an event is likely to occur. That means, it is measured by the ratio of the favorable outcomes to the total number of possible outcomes.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of favorable outcomes}}[/tex]
Favorable outcomes on line KN are, 2, 4, 5
Favorable outcomes on line LM is, 4
Number of favorable outcomes = 4
Total number of outcomes = 2 + 4 + 5 = 11
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}[/tex]
[tex]\text{Probability}=\frac{4}{11}[/tex]
Therefore, the probability that p on LM is, [tex]\frac{4}{11}[/tex]
Write the equation of the line that passes through the point (3, -5) and is perpendicular to the line x = 4.
Answer:
3r-5r
Step-by-step explanation:
How much less would a 23-year-old female pay for a $25,000 policy of 20 year life insurance (@ $2.90 per $1000) than straight life (@ $15.78 per $1000)?
Answer:
The female would pay $322.00 less for a policy of $25,000
Step-by-step explanation:
Since we have given that
Amount for policy = $25000
If she opt for 20 year life insurance at $2.90 per $1000.
so, her amount of premium becomes
[tex]25000\times \frac{2.9}{1000}[/tex]
=$72.50
If she opt for straight life insurance at $15.78 per $1000,
Then, her amount of premium becomes
[tex]25000 \times \frac{15.78}{1000}[/tex]
= $394.50
Difference between them is given by
$394.50-$72.5 = $322.00
Answer:
The answer to this question is $322.
Step-by-step explanation:
From the question, we recall the following
23-year-old female pay for a $25,000 policy less policy of 20 year life insurance.
The first step is to calculate the policy of 20 year life insurance
The number of thousands on 2500 is, 25000/1000=25
25*2.9 = 72.5
The next step is to get the straight life
Thus,
25×15.78 = 394.5
Now,
How much less would the 23 year old pay
394.5−72.5 = $322
Theatre are of a square park is 400sqm. Calcuate the length of side of park
Answer:
The Length of side of park is 20 meter.
Step-by-step explanation:
Given:
Shape of a Park is SQUARE
Area of a square park = 400 sqm
To Find:
The length of side of park = side = ?
Solution:
We know For a SQUARE
All the sides are equal
And Area of a square is given as
[tex]\textrm{Area of Square Park}= (Side)^{2} \\[/tex]
Substituting the given values we get
[tex]400=(side)^{2} \\\\\textrm{Square rooting we get}\\\\side=\sqrt{400} \\\\\therefore side = 20\ meter[/tex]
The Length of side of park is 20 meter.
dose y= -3 have a negative slope
Answer:
no because it is just a straight line. a dot is plotted at (0,-3) and a straight line is horizontal.
Is 4 and 4 perpendicular
Answer:
No.
Step-by-step explanation:
Because perpendicular means negative reciprocal of the slope. So 4 and -1/4 are perpendicular.
Given that AD and BC are parallel, find the value of x.
Answer:
Therefore the value of x is 15.
Step-by-step explanation:
Given:
AD || BC
m∠ B = (9x + 15)°
m∠ A = (3x - 15)°
To Find:
x = ?
Solution:
AD || BC ...............Given
If two lines are parallel and sum of the interior angles are supplementary.
i.e m∠ B and m∠ A are interior between Parallel lines.
∴ [tex]\angle B + \angle C =180\\[/tex]
Substituting the given values we get
∴ [tex](9x + 15)+( 3x - 15)=180\\12x=180\\\\x=\frac{180}{12} \\\\\therefore x =15[/tex]
Therefore the value of x is 15.
Which number(s) from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, if any, will solve this equation? I PROMISE TO MARK BARINLEST + EXTRA POINTS!!!!!!!!!!!!
2x + 3 = 5x - 3
Answer:
2
Step-by-step explanation:2x + 3 = 5x - 3
Move x to one side:
[tex]2x-2x+3=5x-2x-3\\3=3x-3[/tex]
Remove the -3:
[tex]3x-3(+3)=(3+3)[/tex]
[tex]3x=6[/tex]
Remove the 6 to get x by itself:
[tex]\frac{3x}{3} =\frac{6}{3} \\x=2[/tex]
The number 2 from the number set would solve the equation.
Checking the Answer:2(2) + 3 = 5(2) - 3
4 + 3 = 10 - 3
7 = 7
The statement is true.
An equation is formed of two equal expressions. The number(s) from the set that will satisfy the given equation is 2.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be simplified as shown below,
2x + 3 = 5x - 3
Subtract 2x from both sides of the equation,
2x + 3 - 2x = 5x - 3 - 2x
3 = 5x - 3 - 2x
Add 3 on both sides of the equation,
3 + 3 = 5x - 3 - 2x + 3
6 = 3x
3x = 6
Divide both the sides of the equation by 3,
3x/3 = 6/3
x = 2
Hence, the number(s) from the set that will satisfy the given equation is 2.
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-5(4m - 2) = -2/3 + 6m).
Answer:
m=16/39
Step-by-step explanation:
-5(4m-2)=-2/3+6m
-20m+10=-2/3+6m
-20m-6m=-2/3-10
-26m=-2/3-30/3
-26m=-32/3
26m=32/3
m=(32/3)/26
m=(32/3)(1/26)
m=32/78
m=16/39
Consider a circle that has a circumference of 28/3.14 centimeters. What is the area of this circle? Answer fast plz also can you show work???
Answer:
[tex]A=6.33\ cm^2[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=\frac{28}{3.14}\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute the values
[tex]\frac{28}{3.14}=2(3.14)r[/tex]
[tex]r=\frac{28}{19.7192}\ cm[/tex]
[tex]r=1.42\ cm[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
substitute the values
[tex]A=(3.14)(1.42)^{2}[/tex]
[tex]A=6.33\ cm^2[/tex]
please help 56 POINTS
m=7/4 (3,-4) point slope form
Answer:
y+4=7/4(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=7/4(x-3)
y+4=7/4(x-3)
Match the real-world problem to its constant of proportionality.
$4.16 for 4 pounds of bananas
$16.48 for 8 pounds of potatoes
$18.36 for 2 pizzas
2 cups of flour to make 36 cookies
9.18,1.04,18,2.06
Real word problem ⇒ constant of proportionality
$4.16 for 4 pounds of bananas ⇒ 1.04
$16.48 for 8 pounds of potatoes ⇒ 2.06
$18.36 for 2 pizzas ⇒ 9.18
2 cups of flour to make 36 cookies ⇒ 18
Solution:
A proportional relationship is one in which two quantities vary directly with each other.
We say the variable y varies directly as x,
if for x ∝ y
then, x = y k
Where "k" is called constant of proportionality
[tex]k = \frac{x}{y}[/tex]
$4.16 for 4 pounds of bananas
x = 4.16 and y = 4
[tex]k = \frac{4.16}{4} = 1.04[/tex]
Thus constant of proportionality is 1.04
$16.48 for 8 pounds of potatoes
x = 16.48 and y = 8
[tex]k = \frac{16.48}{8} = 2.06[/tex]
Thus constant of proportionality is 2.06
$18.36 for 2 pizzas
x = 18.36 and y = 2
[tex]k = \frac{18.36}{2} = 9.18[/tex]
Thus constant of proportionality is 9.18
2 cups of flour to make 36 cookies
x = 36 and y = 2
[tex]k = \frac{36}{2} = 18[/tex]
Thus constant of proportionality is 18
Compare the line passing through the points (-2,-9) and (4, 6) with the line given by the equation
y = 2/5x -4.
A) they have the same slope
B) they have the same x-intercept
C) the two lines are perpendicular
D) they have the same Y-intercept
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
We have the following points:
[tex](x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): (- 2, -9)[/tex]
We can find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-9-6} {- 2-4} = \frac {-15} {- 6} = \frac {5} {2}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {5} {2} x + b[/tex]
We substitute one of the points and find "b":
[tex]6 = \frac {5} {2} (4) + b\\6 = 10 + b\\6-10 = b\\b = -4[/tex]
Finally, the equation is:
[tex]y = \frac {5} {2} x-4[/tex]
Thus, it is observed that the lines have the same y-intercept
Answer:
Option D
WILL GIVE BRAINLIST
Fill in the blank with a number to make the expression a perfect square.
w² - 6w + ___
Answer:
9 should be added to the expression to make it a perfect square
Step-by-step explanation:
Given expression:
[tex]w^2-6w+_-[/tex]
To fill in the missing term such that the expression becomes a perfect square.
Solution:
In order to make the expression a perfect square we will use completing the square method.
We have : [tex]w^2-6w[/tex]
By complete the square method we will add the square of the quotient of the co-efficient of the middle term which is [tex]-6w[/tex] and 2.
The co-efficient of middle term = -6
Thus the number to be added will be = [tex](\frac{-6}{2})^2=(-3)^2=9[/tex]
Thus, on adding 9 the expression will become:
[tex]w^2-6w+9[/tex] which is a perfect square of the binomial [tex](w-3)[/tex]
This can be shown as:
[tex](w-3)^2=w^2-6w+9[/tex]
Thus, we add 9 to the expression to make it a perfect square.
Answer:
9
Step-by-step explanation:
Given: [tex]w^{2} -6w+[/tex]
Finding the number to make expression a perfect square.
From the expression we can see that coefficient of variable is 1 and -6.
Now, lets take a= 1 and b= -6 and finding c .
∴ c= [tex]\frac{b^{2} }{4a}[/tex]
Subtituting the value of a and b.
⇒ c= [tex]\frac{-6^{2} }{4\times 1} = \frac{36}{4}[/tex] (∵ [tex]-6\times -6= 36[/tex])
∴ c= 9
Next putting the value in the expression.
[tex]w^{2} -6w+9[/tex]
= [tex](w-3)(w-3)[/tex]
= [tex](w-3)^{2}[/tex]
Hence, 9 is a number to make the expression a perfect square.
A student measures the temperature of boiling water a number of times. If the
boiling point of water is 212 degrees, which of his measurements is the most
accurate?
A: 205.46 degrees F
B: 212.1 degrees F
C: 210 degrees F
D: 213.15 degrees F
The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.
Explanation:The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.
When measuring the temperature of boiling water, it is important to consider the accuracy and precision of the measuring instrument. The given options range between 205.46 and 213.15 degrees F, but the boiling point of water is widely accepted to be 212 degrees F at standard atmospheric pressure.
Therefore, the measurement closest to this accepted value is the most accurate, which is option B: 212.1 degrees F.
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what is the solution set of -9x greater than 27
Answer:
x<-3
Step-by-step explanation:
-9x>27
x>27/-9
x>-3