Answer:
ΔBGC is right because Line E G is perpendicular-to CC'
Step-by-step explanation:
The midpoints of the segments joining a triangle vertex with its reflected image will lie on the line of reflection. The segment will be perpendicular to the line of reflection.
In this scenario, a triangle will be right if it has a leg that is part of the segment joining reflected points, and a leg on the line of reflection. ΔBGC is such a triangle.
ΔBGC is right
_____
Comment on the problem statement
Point D came out of nowhere. A diagram would be most helpful.
Answer:
D On Edg 2020
Step-by-step explanation:
Give the other dude credit ;D, he tried harder
The mean student loan debt for college graduates in Illinois is $30000 with a standard deviation of $9000. Suppose a random sample of 100 college grads in Illinois is collected. What is the probability that the mean student loan debt for these people is between $31000 and $33000?
Answer:
the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
Step-by-step explanation:
Given that:
Mean = 30000
Standard deviation = 9000
sample size = 100
The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:
[tex]P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)[/tex]
[tex]P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})[/tex]
From Z tables:
[tex]P(31000 < X <33000) = 0.9996 -0.8665[/tex]
[tex]P(31000 < X <33000) = 0.1331[/tex]
Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ticket prices were set at $12, the average attendance was 30,000. When the ticket prices were on sale for $10, the average attendance was 35,000.
(a) Let D(x) represent the number of people that will buy tickets when they are priced at x dollars per ticket. If D(x) is a linear function, use the information above to find a formula for D(x). Show your work!
(b) The revenue generated by selling tickets for a baseball game at x dollars per ticket is given by R(x) = x-D(x). Write down a formula for R(x).
(c) Next, locate any critical values for R(x). Show your work!
(d) If the possible range of ticket prices (in dollars) is given by the interval [1,24], use the Closed Interval Method from Section 4.1 to determine the ticket price that will maximize revenue. Show your work!
Optimal ticket price:__________ Maximum Revenue:___________
Answer:
(a)[tex]D(x)=-2,500x+60,000[/tex]
(b)[tex]R(x)=60,000x-2500x^2[/tex]
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]
Therefore, we have:
[tex]y=-2500x+b[/tex]
At point (12,30000)
[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]
Therefore:
[tex]D(x)=-2,500x+60,000[/tex]
(b)Revenue
[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]
Therefore:
Optimal ticket price:$12Maximum Revenue:$360,000Solve by completing the square. x2−12x=−27 Select each correct answer. −9 −3 3 9 15
Answer:
x=9,3
Step-by-step explanation:
x²-12x=-27
x²-12x+(12/2)²=-27+(12/2)²
x²-12x+6²=-27+36
(x-6)²=9
x-6=[tex] \frac{ + }{ - } \sqrt{9} [/tex]
x-6=+3 and x-6=-3
x=9 and 3
a silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by
Question:
A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by
s(t) = -16t² + v₀t + s₀
Determine the position and velocity functions for the coin.
Answer:
position function: s(t) = (-16t² + 64) ft
velocity function: v(t) = (-32t) ft/s
Step-by-step explanation:
Given position equation;
s(t) = -16t² + v₀t + s₀ ---------(i)
v₀ and s₀ are the initial values of the velocity and position of the coin respectively.
(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e
v₀ = 0.
Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e
s₀ = 64ft
Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;
s(t) = -16t² + (0)t + 64
s(t) = -16t² + 64
Therefore, the position function of the coin is;
s(t) = (-16t² + 64) ft
(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;
v(t) = [tex]\frac{ds(t)}{dt}[/tex]
v(t) = [tex]\frac{d(-16t^2 + 64)}{dt}[/tex]
v(t) = -32t + 0
v(t) = -32t
Therefore, the velocity function of the coin is;
v(t) = (-32t) ft/s
Use the table to identify values of p and g that can be used to factor X2 - x - 12
as (x + 2)(x + 9).
e
р
2
-2
ptq
-4
9
-6
6
-4
4
4
6
3
-3
-1
1
O A. -3 and 4
unctions
ving
O B-2 and 6
O C. 2 and -6
deling
O D. 3 and 4
Answer:
D. 3 and -4
Step-by-step explanation:
Given the expression, x² - x - 12, let's factorise to find the value of p and q using the table, for which we would have the expression simplified as (x + p)(x + q)
From the table, let's find the values of p and q that would give us -12 when multiplied together, and would also give us -1 when summed together.
Thus, from the table given, the row containing the values of p(3) and q(-4) gives us = -1 (p+q) . p = 3, q = -4 would be our values to use to factor x² - x - 12, as multiplying both will also give us "-12".
Thus, x² - x - 12 would be factorised or simplified as (x + 3)(x - 4)
Therefore, the answer is: D. 3 and -4
Answer:
D a p e x
Step-by-step explanation:
Brainliest for correct awnser! Hannah thinks of a number. She multiplies the number by 2, adds 4, and then divides the result by 3. The number she ends up with is 6. What number did Anna start with? If you work backward to solve this problem, what do you do first?A.Multiply 6 by 2B.Multiply 6 by 3C.Divide 6 by 2D.Subtract 4 from 6
Answer:
B. Multiply 6 by 3
Step-by-step explanation:
Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:
B. Multiply 6 by 3
Your step by step for getting the number Hannah started with:
First, multiply 6 with 3:
6 x 3 = 18
Next, subtract 4:
18 - 4 = 14
Next, divide by 2:
14/2 = 7
Hannah started with the number 7.
~
Answer: Hannah started with 7.
B. Multiply 6 by 3
Explanation:
Let the number be y
2 × y = 2y
(2y + 4)/3 = 6
2y + 4 = 6×3 = 18
2y + 4 = 18
2y = 18 - 4 = 14
y = 14/2 = 7
To solve the problem backward, the first step is to multiply 6 by 3.
Applying the Segment Addition Postulate
Point D is on segment BC. Segment BC measures 8x
units in length.
С
D
B
What is the length of segment BC?
units
3x + 8
4x + 10
Answer:
144
Step-by-step explanation:
Find: Length of segment BC
CD+DB=BC
3x+8+4x+10=BC
7x+18=BC
BC also equals 8x (given on the screen shot)
7x+18= 8x
x=18
18 times 8 = 144
Check:
3( 18) + 8 + 4(18) + 10
54+8 + 72+10
64+ 80= 144 TRUE
Apply the distributive property to factor out the greatest common factor of all three terms. {10a - 25 + 5b} =10a−25+5b =
Answer:
5(2a -5 + b)
Step-by-step explanation:
(10a - 25 + 5b) = 5( 2a - 5 + b)
5(b + 2a - 5) = 5(2a - 5 + b)
Answer:
5(2a -5 + b)
Step-by-step explanation:
Can you help me please solve
Answer:
(-0.5, 0)
Step-by-step explanation:
Coordinates of endpoints of segment are:
A= (-2, 1)
B= (1, - 1)
By mid-point formula:
The midpoint of [tex] \overline{AB} [/tex]
[tex] = \bigg(\frac{ - 2 + 1}{2}, \: \: \frac{1 + ( - 1)}{2} \bigg) \\ \\ = \bigg(\frac{ - 1}{2}, \: \: \frac{0}{2} \bigg)\\ \\ = \bigg(\frac{ - 1}{2}, \: \: 0 \bigg)\\ \\ = ( - 0.5, \: \: 0 )[/tex]
The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in increasing order)].
68.6 71.9 72.6 73.1 73.3 73.5 75.5 75.7 75.8 76.1 76.2
76.2 77.0 77.9 78.1 79.6 79.8 79.9 80.1 82.2 83.7 93.4
Calculate a 90% CI for the standard deviation of the fracture toughness distribution. (Give answer accurate to 2 decimal places.)
Answer:
A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].
Step-by-step explanation:
We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;
68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.
Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;
P.Q. = [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2} __n_-_1[/tex]
where, s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }[/tex] = 5.063
[tex]\sigma[/tex] = population standard deviation
n = sample of observations = 22
Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.
So, 90% confidence interval for the population standard deviation, [tex]\sigma[/tex] is ;
P(11.59 < [tex]\chi^{2}__2_1[/tex] < 32.67) = 0.90 {As the critical value of chi at 21 degrees
of freedom are 11.59 & 32.67}
P(11.59 < [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] < 32.67) = 0.90
P( [tex]\frac{ 11.59}{(n-1) \times s^{2}}[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{ 32.67}{(n-1) \times s^{2}}[/tex] ) = 0.90
P( [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ) = 0.90
90% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] , [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ]
= [ [tex]\frac{21 \times 5.063^{2} }{32.67 }[/tex] , [tex]\frac{21 \times 5.063^{2} }{11.59 }[/tex] ]
= [16.48 , 46.45]
90% confidence interval for [tex]\sigma[/tex] = [[tex]\sqrt{16.48}[/tex] , [tex]\sqrt{46.45}[/tex] ]
= [4.06 , 6.82]
Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].
the diagram shows a circle drawn inside a square the circle touches the edges of the square
Answer:
69.5309950592 cm²
Step-by-step explanation:
Area of Square:
Area = [tex]Length * Length[/tex]
Area = 18*18
Area = 324 square cm
Area of circle:
Diameter = 18 cm
Radius = 9 cm
Area = [tex]\pi r^2[/tex]
Area = (3.14)(9)²
Area = (3.14)(81)
Area = 254.469004941 square cm
Area of Shaded area:
=> Area of square - Area of circle
=> 324 - 254.469004941
=> 69.5309950592 cm²
if my medical expenses are $40,000 per year for 35 years with an increase of 6% a year what is the total amount?
Answer:
$4,457,391.19
Step-by-step explanation:
The sum of n terms of a geometric sequence with common ratio r and initial value "a" is ...
S = a(r^n -1)/(r -1)
Here, your growth factor is r = 1 +6% = 1.06. So, the sum of expenses over 35 years will be ...
S = $40,000(1.06^35 -1)/(1.06 -1) = $4,457,391.19
What is the measure of angle z in this figure?
Enter your answer in the box.
z =
°
Two intersection lines. All four angles formed by the intersecting lines are labeled. Clockwise, the angles are labeled 124 degrees, x degrees, y degrees, and z degrees.
Answer:
z= 56°
hope u understood it...
Answer:
Z=56
Step-by-step explanation:
Because i said so
solve and find the value of (1.7)^2
Answer:
2.89
Step-by-step explanation:
just do 1.7×1.7=2.89
The average duration of labor from the first contraction to the birth of the baby in women over 35 who have not previously given birth and who did not use any pharmaceuticals is 16 hours. Suppose you have a sample of 29 women who exercise daily, and who have an average duration of labor of 17.8 hours and a sample variance of 77.4 hours. You want to test the hypothesis that women who exercise daily have a different duration of labor than all women. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is s M
Answer:
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.
Standard error sm = 1.634
Test statistic t = 1.102
P-value = 0.28
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that women who exercise daily have a significantly different duration of labor than all women.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=16\\\\H_a:\mu\neq 16[/tex]
The significance level is 0.05.
The sample has a size n=29.
The sample mean is M=17.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{8.8}{\sqrt{29}}=1.634[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.8-16}{1.634}=\dfrac{1.8}{1.634}=1.102[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=29-1=28[/tex]
This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>1.102)=0.28[/tex]
As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.
A pet store has 10 puppies, including 2 poodles, 3 terriers, and 5 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement find the probability that both select a poodle.
The probability is
Answer:
2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.
Step-by-step explanation:
do some math
Solve the system by the method of elimination.
Answer:
no solution
Step-by-step explanation:
4x+3y = 6
8x + 6y = 5
Multiply the first equation by -2
-2(4x+3y) = 6*-2
-8x -6y = -12
Add this to the second equation
-8x-6y = -12
8x + 6y = 5
---------------------
0x + 0y = -7
0 = -7
Since this is never true there is no solution
Answer:
X = 8/3, y= -14/9
Step-by-step explanation:
using elimination method:
subtract equation 1 from equation 2
8x-4x + 6y-3y = 5-6
4x+3y= -1
4x= -1-3y
divide both sides by 4
x = -1-3y÷4
substitute x = -1-3y/4 in equation 2
8(-1-3y)/4 +6y = 5
-8-24y/4+ 6y =5
-8-24y+6y/4 =5
-8-18y/4 = 5
Cross multy
-8-18y × 1 = 4×5
-8-18y = 20
collect like terms
-18y = 20+8
-18y = 28
divide both sides by-18
y = 28/-8
y = -14/9
put y = -14/9 in equation 1
4x+3(-14/9) = 6
4x-42/9 = 6
42/9 = 14/3
so, 4x=6+14/3
LCM =3
4x = 18+14/3
4x= 32/3
cross multiply
4x×3 = 32
12x = 32
divide both sides by 12
12x/12= 32/12
x = 8/3
so, x = 8/3, y = -14/9
check:
first equation:
4(8/3) + 3(-14/9)
32/3 - 14/3( 3 cancels 9 rem 3)
LCM= 3
32 - 14/3
= 18/3
= 6
Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas's fastest-moving inventory item has a demand of 6,100 units per year. The cost of each unit is $101, and the inventory carrying cost is $8 per unit per year. The average ordering cost is $31 per order. It take about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and the are 250 working days per year.)A) What is the EOQ?B) What is the average inventory if the EOQ is used?C) What is the optimal number of orders per year?D) What is the optimal number of days in between any two orders?E) What is the annual cost of ordering and holding inventory?F) What is the total annual inventory cost, including cost of the 6,100 units?
Answer and Step-by-step explanation:
The computation is shown below:
a. The economic order quantity is
[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]
[tex]= \sqrt{\frac{2\times \text{6,100}\times \text{\$31}}{\text{\$8}}}[/tex]
= 217 units
b. The average inventory used is
[tex]= \frac{economic\ order\ quantity}{2}[/tex]
[tex]= \frac{217}{2}[/tex]
= 108.5 units
c. The optimal order per year
[tex]= \frac{annual\ demand}{economic\ order\ quantity}[/tex]
[tex]= \frac{6,100}{217}[/tex]
= 28 orders
d. The optima number of days is
[tex]= \frac{working\ days}{optimal\ number\ of\ orders}[/tex]
[tex]= \frac{250}{28}[/tex]
= 8.9 days
e. The total annual inventory cost is
= Purchase cost + ordering cost + carrying cost
where,
Purchase cost is
[tex]= \$6,100 \times \$101[/tex]
= $616,100
Ordering cost = Number of orders × ordering cost per order
= 28 orders × $31
= $868
Carrying cost = average inventory × carrying cost per unit
= 108.50 units × $8
= $868
So, the total would be
= $616,100 + $868 + $868
= $617,836
What is m<3 ? M<6 is and m<8 is (x+5
Answer:
m∠3 = 115 degrees
Step-by-step explanation:
angle 6 and angle 8 are on a straight line
we know that sum of angles on straight line is 180
therefore
m∠8 = x+5
m∠6 + m∠8 = 180
2x - 5 + x+5 = 180
=> 3x = 180
=> x = 180/3 = 60
Thus,
m∠6 = 2x-5 = 2*60 - 5 = 115
we know that for two parallel lines cut by a transversal
alternate opposite angles are equal
m∠6 and m∠3 are alternate opposite angles
thus
m∠6 = m∠3 = 115 (answer)
The tread life of a particular brand of tire is normally distributed with mean 60,000 miles and standard deviation 3800 miles. Suppose 35 tires are randomly selected for a quality assurance test. Find the probability that the mean tread life from this sample of 35 tires is greater than 59,000 miles. You may use your calculator, but show what you entered to find your answer. Round decimals to the nearest ten-thousandth (four decimal places).
Answer:
P [ x > 59000} = 0,6057
Step-by-step explanation:
We assume Normal Distribution
P [ x > 59000} = (x - μ₀ ) /σ/√n
P [ x > 59000} = (59000 - 60000)/ 3800
P [ x > 59000} = - 1000/3800/√35
P [ x > 59000} = - 1000*5,916 /3800
P [ x > 59000} = - 5916/3800
P [ x > 59000} = - 1,55
We look for p value for that z score n z-table and find
P [ x > 59000} = 0,6057
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h
Answer:
C
Step-by-step explanation:
We know that A is not true because we know that h(8) is 19, not 21. B is also not true because the value of h(x) can't be -1. D can't be true because x can't be 13, therefore the answer is C.
Adelphi Company purchased a machine on January 1, 2017, for $60,000. The machine was estimated to have a service life of ten years with an estimated residual value of $5,000. Adelphi sold the machine on January 1, 2021 for $21,000. Adelphi uses the double declining method for depreciation. Using this information, how much is the gain or (loss) for the equipment sale entry made on January 1, 2021. Enter a loss as a negative number.
Answer:
-$3576
Step-by-step explanation:
Depreciation using double declining method=100%/useful life*2
Depreciation using double declining method=100%/10*2=20%
2017 depreciation=$60,000*20%=$12000
2018 depreciation=($60,000-$12000)*20%=$9600
2019 depreciation=($60,000-$12000-$9600 )*20%=$7680
2020 depreciation=($60,000-$12000-$9600-$7680 )*20%=$6144
carrying value in 2021=$60000-$12000-$9600 -$7680-$6144 =$24576
Loss on disposal of machine=$21,000-$24576 =-$3576
Which steps would be used to solve the equation? Check all that apply. 2 and two-thirds + r = 8 Subtract 2 and two-thirds from both sides of the equation. Add 2 and two-thirds to both sides of the equation. 8 minus 2 and two-thirds = 5 and one-third 8 + 2 and two-thirds = 10 and two-thirds Substitute the value for r to check the solution.
Answer:
Subtract 2 and two-thirds from both sides of the equation
8 minus 2 and two-thirds = 5 and one-third
Substitute the value for r to check the solution.
Step-by-step explanation:
2 2/3 + r = 8
Subtract 2 2/3 from each side
2 2/3 + r - 2 2/3 = 8 - 2 2/3
r = 5 1/3
Check the solution
2 2/3 +5 1/3 =8
8 =8
Answer:
1, 3, 5
Step-by-step explanation:
edge
On the "Compiled Information" tab, a VLOOKUP formula has been pre-entered into cell E3. This formula was written correctly, and it uses references to the numbers in cells E1 through G1 to determine the correct index_number parameter. Fill in cells F1 and G1 with the correct index numbers, then copy the formula in cell E3 down to all the rows in columns E, F, and G. What number did you enter into cell G1?
Answer:
3
Step-by-step explanation:
Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:
=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.
where true is approximate match and false is exact match.
Find the square root of 8-2√5
Answer:
1.88
Step-by-step explanation:
8-2√5=3.527864045
square root of 3.527864045=1.87826090972
the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88
Answer:
The square root of 8 - 2√5 is
[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]
Step-by-step explanation:
To find the square root
8-2√5 must be in the form √a - √b where a > b
√ 8 - 2√5 = √a - √b
Square both sides
8 - 2√5 = (√a - √b)²
That's
8 - 2√5 = (a + b) - 2√ab
Since the two surd expressions are equal we can equate them
That's
8 = a + b ........ 1
a = 8 - b ........ 2
2√5 = 2√ab
Simplify
Divide both sides by 2
√5 = √ab
square both sides
We have
5 = ab ....... 3
Substitute a = 8 - b into equation 3
5 = ( 8 - b)b
5 = 8b - b²
b² - 8b + 5 = 0
After solving
b = 4 + √ 11 or 4 - √ 1
Since b is less than a
b = 4 - √11
a = 4 + √11
So the square root of 8 - 2√5 is
[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]
Hope this helps you.
a geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .
Answer: [tex]\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}[/tex]
Step-by-step explanation:
a₁, 375, a₃, a₄, 81
First, let's find the ratio (r). There are three multiple from 375 to 81.
[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]
Next, let's find a₁
[tex]a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625[/tex]
Lastly, Use the Infinite Geometric Sum Formula to find the sum:
[tex]S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}[/tex]
The table shows three unique functions. (TABLE IN PIC) Which statements comparing the functions are true? Select three options. Only f(x) and h(x) have y-intercepts. Only f(x) and h(x) have x-intercepts. The minimum of h(x) is less than the other minimums. The range of h(x) has more values than the other ranges. The maximum of g(x) is greater than the other maximums.
Answer:
(A)Only f(x) and h(x) have y-intercepts.
(C)The minimum of h(x) is less than the other minimums.
(E)The maximum of g(x) is greater than the other maximums.
Step-by-step explanation:
From the table
f(0)=0 and h(0)=0, therefore, Only f(x) and h(x) have y-intercepts. (Option A)
Minimum of f(x)=-14Minimum of g(x)=1/49Minimum of h(x)=-28Therefore, the minimum of h(x) is less than the other minimums. (Option C).
Maximum of f(x)=14
Maximum of g(x)=49
Maximum of h(x)=0
Therefore, the maximum of g(x) is greater than the other maximums. (Option E)
Answer: It's B,C, and E
Step-by-step explanation:
Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 86 and 125 miles in a day. Round your answer to four decimal places.
Answer:
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles
Step-by-step explanation:
Step(i):-
Given mean of the Population = 100 miles per day
Given standard deviation of the Population = 23 miles per day
Let 'X' be the normal distribution
Let x₁ = 86
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]
Let x₂= 86
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]
Step(ii):-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)
= P(Z≤ 1.08) - P(Z≤ -0.61)
= 0.5 +A(1.08) - ( 0.5 - A(-0.61))
= A(1.08) + A(0.61) ( A(-Z)= A(Z)
= 0.3599 + 0.2291
= 0.5890
Conclusion:-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles per day
PLEASEEE HELP ME ITS DUE ASAP PLS
Answer:
V ≈ 1436.03 cm³
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}[/tex]πr³. r represents the radius, which is 7 cm since the diameter is 14 cm, so plug 7 into the equation as r. Also remember that the question states to use 3.14 for pi/π.
V = [tex]\frac{4}{3}[/tex] (3.14)(7)³
V ≈ 1436.03 cm³
The graph shows a gasoline tank being filled at a rate of 2,500 gallons of gas per
hour. How will the graph change if the rate slows?
The correct answer is The line will be less steep because the rate will be slower
Explanation:
The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.
However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.