Answer:
(3x+4)(x-4) is your answer
Step-by-step explanation:
3x²-11x-4
=3x²-12x+x-4
=3x(x-4)+1(x-4)
=(x-4)(3x+4)
n
2. (a) If ^nP2= 20, find the value of n.
2
Answer:
[tex]n = 5[/tex]
Step-by-step explanation:
Given
[tex]^nP_2 = 20[/tex]
Required
Find n
To do this, we apply permutation formula.
[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]
So, we have:
[tex]\frac{n!}{(n-2)!} = 20[/tex]
Expand the numerator
[tex]\frac{n(n-1)(n-2)!}{(n-2)!} = 20[/tex]
Divide by (n-2)!
[tex]n(n-1)= 20[/tex]
Expand
[tex]n^2 - n = 20[/tex]
[tex]n^2 - n - 20 = 0[/tex]
Expand
[tex]n^2 +4n -5n - 20 = 0[/tex]
Factorize
[tex]n(n+4)-5(n+4)= 0[/tex]
[tex](n-5)(n+4) = 0[/tex]
[tex]n - 5 = 0[/tex] or [tex]n + 4 = 0[/tex]
[tex]n = 5[/tex] or [tex]n = -4[/tex]
Since n cannot be negative, then:
[tex]n = 5[/tex]
Reggie Jackson, one of the great baseball batters of modern times, was called Mr. October by his fans because he seemed to excel in the World Series. During the regular season, Reggie had 2584 hits in 9864 official at bats for a batting average (proportion of hits) of 0.262. During League Championship Series, he had 37 hits in 163 official at bats for a 0.227 batting average. During World Series play, he had 35 hits in 98 official at bats for a batting average of 0.357. Do you think the nickname is justified, based on the data
Answer:
Since 2.1387 is Greater Than 1.645;
we reject null hypothesis; we conclude that, the nickname is justified based on the data.
Step-by-step explanation:
Given the data in the question;
Null hypothesis H₀ : p = 0.262
Alternative Hypothesis H₁ : p > 0.262.
p" = 0.357
q = 1 - p = 1 - 0.262 = 0.738
n = 98
so;
z = (p" - p) / √(pq/n)
we substitute
z = (0.357 - 0.262) / √((0.262×0.738) / 98)
z = 0.095 / 0.04441869
z = 2.1387
at 5% CONFIDENCE INTERVAL
z-critical = 1.645
Since 2.1387 is Greater Than 1.645;
we reject null hypothesis; we conclude that, the nickname is justified based on the data.
multiply or divde as indicated. simplify your answer, if possible.
x⁻⁸/x⁵
Answer:
Step-by-step explanation:
[tex]\frac{x^{-8}}{x^5}\\ \\ x^{-13}[/tex]
With the information given, can you prove
that this quadrilateral is a parallelogram?
Yes
No
Answer:
no
Step-by-step explanation:
The provided quadrilateral is a parallelogram because diagonals are bisecting each other option Yes is correct.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
It is given that:
A quadrilateral is given in the picture.
As we know, in the parallelogram the diagonals of the parallelogram bisect each other.
In the figure, it is given that the diagonals are bisecting each other.
From the figure, the two opposite sides are parallel.
In the parallelogram the pair of opposite sides are parallel.
Thus, the provided quadrilateral is a parallelogram because diagonals are bisecting each other option Yes is correct.
Learn more about the parallelogram here:
brainly.com/question/1563728
#SPJ2
Simplify the expression given below.
A.
B.
C.
D.
An integrated circuit factory has three machines X, Y, and Z. Test one integrated circuit produced by each machine. Either a circuit is acceptable (a) or it fails (f). An observation is a sequence of three test results corresponding to the circuits for machines X, Y, and Z, respectively. For example, aaf is the observation that the circuits from X and Y pass the test and the circuit from Z fails the test.
a. What are the elements of the sample space of this experiment?
b. What are the elements of the sets:
ZF={circuit from Z fails},
XA ={circuit from X is acceptable}.
c. Are ZF and XA mutually exclusive?
d. Are ZF and XA collectively exhaustive?
e. What are the elements of the sets C={more than one circuit acceptable}, D={at least two circuits fail}.
f. Are C and D mutually exclusive?
g. Are C and D collectively exhaustive?
Answer:
Kindly check explanation
Step-by-step explanation:
Acceptable = a
Fails = f
For machines X, Y, Z ;
Sample space, S = {aaa, aaf, aff, fff, faa, afa, ffa, faf}
Total elements in sample space = 8
B.)
Elements of the set:
ZF={circuit from Z fails},
XA ={circuit from X is acceptable}.
ZF = {aaf, aff, fff, faf}
XA = {aaa, aaf, aff, afa}
C.)
c. Are ZF and XA mutually exclusive?
Check if ZF n XA = ∅
ZF n XA = {aaf, aff}
Hence, ZF and XA are not mutually exclusive
d. Are ZF and XA collectively exhaustive?
To be collectively exhaustive :
ZF u XA = Sample space
ZF u XA = {aaa, aaf, aff, afa, faf, fff}
{aaa, aaf, aff, afa, faf, fff} ≠ sample space
Hence, ZF and ZA are not collectively exhaustive.
e. What are the elements of the sets
C={more than one circuit acceptable},
C = {aaa, aaf, faa, afa}
D={at least two circuits fail}.
D = {ffa, faf, aff, fff}
f. Are C and D mutually exclusive?
Check if C n D = ∅
C n D = ∅
Hence, A and D are mutually exclusive
g. Are C and D collectively exhaustive?
To be collectively exhaustive :
C u D = Sample space
C u D = {aaa, aaf, aff, afa, faf, fff}
{aaa, aaf, faa, ffa, aff, afa, faf, fff} = sample space
Hence, C and D are collectively exhaustive.
Need help with the last part I know I need to do 55x+60 = ? But I don’t know what ? Is
Answer:
- Discount car rentals charges less daily
- After 3 days
Step-by-step explanation:
Required
Which charges less per day
When is the total cost the same
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
From the table, we have:
[tex](x_1,y_1) = (2,185)[/tex]
[tex](x_2,y_2) = (6,345)[/tex]
So, we have:
[tex]m = \frac{345 - 185}{6 - 2}[/tex]
[tex]m = \frac{160}{4}[/tex]
[tex]m = 40[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 40(x - 2) + 185[/tex]
[tex]y = 40x - 80 + 185[/tex]
[tex]y = 40x + 105[/tex]
So, the equation of the table (i.e. Discount Car rental) is: [tex]y = 40x + 105[/tex]
While the equation of Pay Less is: [tex]y = 55x + 60[/tex]
The company that charges less per day has the smaller slope and that is: Discount car rental because the slope (40) is less than the slope (55)
For the total cost to be the same, we simply equate both expressions:
i.e.
[tex]y = y[/tex]
[tex]55x + 60 = 40x + 105[/tex]
[tex]55x - 40x = - 60 + 105[/tex]
[tex]15x =45[/tex]
[tex]x = 3[/tex]
Based on historical data, your team knows what proportion of the company's number of orders come from Indiana residents. However, your team would like to expand its orders beyond the state of Indiana. By the end of this year, you think you would like your total proportion of orders from Indiana to be between 0.66 and 0.73. If you took a simple random sample of 99 current orders, what is the probability that the sample proportion of sales to Indiana residents is between 0.66 and 0.73
This question is incomplete, the complete question is;
Based on historical data, your team knows what proportion of the company's number of orders come from Indiana residents. However, your team would like to expand its orders beyond the state of Indiana. By the end of this year, you think you would like your total proportion of orders from Indiana to be between 0.66 and 0.73. If you took a simple random sample of 99 current orders, what is the probability that the sample proportion of sales to Indiana residents is between 0.66 and 0.73
Note: You should carefully round any intermediate calculations to 4 decimal places to match wamap's approach and calculations. After you round to 4 places, use THAT rounded value in later steps. You may need an appropriate population proportion (which you actually found in a previous problem).
Some data:
Total population: 2327
Indiana residents: 1845
Other: 482
Frequency table results for Total Sales:
Count = 2327
Total Sales Frequency
0 to 200 1960
200 to 400 303
400 to 600 53
600 to 800 9
800 to 1000 2
Answer:
The probability that the sample proportion of sales to Indiana residents is between 0.66 and 0.73 is 0.0612
Step-by-step explanation:
Given the data in the question;
p" = Indiana residents / Total population
p" = 1845 / 2327
p" = 0.7929
Now, the probability that the sample proportion of sales to Indiana residents is between 0.66 and 0.73 will be;
P( 0.66 < p < 0.73 ) = P{ [x1 - p" / √( p"(1-p")/n )] < p < [x2 - p" / √( p"(1-p")/n )] }
we substitute
= P{ [0.66 - 0.7929 / √( 0.7929(1-0.7929)/99 )] < p < [0.73 - 0.7929 / √( 0.7929(1-0.7929)/99 )] }
= P{ [-0.1329 / 0.0407] < p < [-0.0629 / 0.0407] }
= P{ -3.2654 < z < -1.5455 }
= ⊕( -1.5455) - ⊕(-3.2654)
from the standard normal table;
= 0.0618 - 0.0006
P( 0.66 < p < 0.73 ) = 0.0612
Therefore, the probability that the sample proportion of sales to Indiana residents is between 0.66 and 0.73 is 0.0612
(2,3), y = (3/2)x - 1
I'm just as confused as you are
Find the value of x and y
Answer:
x = 63°, y = 27°
Step-by-step explanation:
We know that x + y = 90°
Since ∠ x and 117° are on the same line, they are adjacent angles and add up to 180°.
x + 117 = 180
x = 180 - 117
x = 63°
Now back to the first equation:
x + y = 90°
63 + y = 90
y = 90 - 63
y = 27°
Answer:
x=63
y=27
Step-by-step explanation:
x y 117 son suplementarios x+117=180, entonces para obtener x debemos de restarle 117 a 180
el angul x y y son complementarios x+y=90 , en el anterior x nos dio igual a 63, entonces 90-63=y(que y es 27)
You have 5/8 of a large bottle of shampoo. You pour 3/10 of the shampoo into a smaller bottle. How much of the entire large bottle do you pour into the smaller bottle
Answer:
13/40
Step-by-step explanation:
Answer:
Step-by-step explanation:
if you have 5/8 of a large bottle of shampoo,
(5/8)*(3/10)=15/80=3/16
find a simplified expression to represent the area of the triangle. the area formula for a triangle is 1/2bh, where b is the base and h is the height . The expression that represents the area of this triangle is _x^2 +_ x +_ cm^2
Answer:-4x^2+22x+-12cm^2
Step-by-step explanation:
a table bought for $450 was sold for $975 what the profit?
Step-by-step explanation:
cost price = $450selling price = $975profit = selling price - cost price
= $975 - $450
= $525--------------------------FOLLOW MEWhat is the equation of the line
Answer:
y=-7
Step-by-step explanation:
5/9 times 3/7 WHOEVER ANSWERS IN UNDER 2 MINUTS I WILL MARK BRAINLIEST
Answer:
5/21
Step-by-step explanation:
Answer:
i dont know but the answer comes out as 0.238095
Step-by-step explanation:
Find the value of (1.7)²
2.89
Hope you got your answer.
water is placed in a cylinder bucket own a bench The bucket has a diameter of 12 in and a height of 12 in The bench is capable of holding 200 lb per cubic feet water weighs 64.2 cubic feet how much does the water in the bucket weigh
Answer:
bucket of water = 50.397 lbs
Step-by-step explanation:
Pi(r^2)(h) = volume
3.14(6^2)(12) = 1356.48 in^3 = volume of bucket
one ft^3 = 12 x 12 x 12 = 1728 in^3
1356.48/1728 = 0.785 ft^3 (volume of bucket)
0.785(64.2) = 50.397 lbs
Write the exponent for 3 x 3 x 3 x 3 x 3 (shift 6 to make the ^ sign). *
Answer:
3^5Step-by-step explanation:
The exponent is just the amount of times you multiply a number by itself. So if you're multiplying three five times, the power would be 5.
Identify the diameter of circle A
AB
AS
BT
TS
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Circles.
Since we know that, diameter is always twice of radius, and also one important point that,
A diameter is the longest chord of the circle passing from the centre of the circle, hence here,
BT is the diameter of the circle,
option c.) BT
Answer:
BT
Step-by-step explanation:
This is because a line which passes through the centre of a circle and falls on the circumference is called the diameter.
how to figure the surface area 4yd 4yd 1yd they say the answer is 48yd2. how do they get this answer
Answer:
area of top and bottom (total of 2) = 4x4x2 = 32 yd^2
area of 4 sides = 4x1x4 =16 yd^2
32+16 = 48 yd^2
A box is 5 inches high, 10
inches wide, and 8 inches
deep. What is the volume
of the box?
800 cubic inches
189 cubic inches
80 cubic inches
400 cubic inches
Answer: D
Step-by-step explanation:
The volume of the box is equivalent to 400 cubic inches.
What is the volume of a cuboid? What is a mathematical function, equation and expression? The volume of a cuboid is equivalent - V{C} = L x B x Hfunction : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a a box is 5 inches high, 10 inches wide, and 8 inches deep.
The volume of a cuboid is equivalent to -
V{C} = L x B x H
V{C} = 8 x 10 x 5
V{C} = 80 x 5
V{C} = 400 cubic inches
Therefore, the volume of the box is equivalent to 400 cubic inches.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
PLEASE HELP!!!
Everyone at Greg's school wore either blue or orange for school spirit day. Of the 100 students at the school, 80% wore blue. How many students wore blue?
Answer:80 students
Step-by-step explanation:
80% of 100 is 80. :)
Find the measure of S
Answer:
151°
Step-by-step explanation:
Pentagons interior angles are always 540°. So to solve, you must put
540= (5x+2)+(10x-3)+(8x-19)+(7x-11)+(13x-31). After solving this you will get x=14 and you can now substitute x in for measure s.
13(14) -31
182 - 31
measure of s = 151°
Answer: 151
Step-by-step explanation:
Step-by-step explanation:Pentagons interior angles are always 540°.
So to solve, you must put 540= (5x+2)+(10x-3)+(8x-19)+(7x-11)+(13x-31).
After solving this you will get x=14 and you can now substitute x in for measure s.
13(14) -31182 - 31
measure of s = 151°
A car is advertised for £3000.
The car will be in a sale next month.
Tom can afford to pay £2500.
By what percentage will the price have to be reduced so that he can afford the car?
Answer:
Hello, Guys..
The Answer for this would be this..
percentage of this will be 5% ..
Step-by-step explanation:
Hope you have received your answer..
Happy Learning!..
1. There are 4 quarts in 1 gallon. How many quarts are in 4 ½ gallons?
Answer:
18 quarts
Step-by-step explanation:
tom and ben ordered a pizza for lunch. they each ate 1/3 of the pizza. how much pizza was eaten and how much pizza was left?
Answer:
they ate 1/3 and thrte is 2/3 left
Step-by-step explanation:
subtraction
One-third of the pizza will be left
Proportions and RatiosLet the total amount of pizza eaten be "x
Amount of pizza ate by Tom is 1/3 xAmount of pizza ate by Ben is 1/3 xTotal pizza ate = x/3 + x/3
Total pizza eaten = 2x/3
Amount of pizza left = x - 2x/3
Amount of pizza left = (3x-2x)/3
Amount of pizza left = x/3
Hence one-third of the pizza will be left
Learn more on ratio and proportion here: https://brainly.com/question/21602143
Can someone help me pls I need help realllll bad right now someone pls
Answer:
A,C,and E!
Step-by-step explanation:
Obtuse=>90
Equilateral triangles do not have right angles, because then the angles wouldn't be equal!
Both acute and Equilateral have angles smaller than 90!
Hope this helps, and don't forget to follow!
Each side of a square sticky note is 9 centimeters long. What is the sticky note's area?
Answer:
Have not done this in a while but I believe it is 81
Step-by-step explanation:
Please excuse me if I am wrong but hope this helps
Help please I’ll give u brainliest but pls explain how as well
Answer:
Its 9!
Step-by-step explanation:
6×3=18
18/2=9
Hope this helps and don't forget to follow!
diagram this statement.Then answer the questions that follow.
Joseph gave three fourths of his 288 sports cards to his brother.
A) what percent of his sports cards did his Joseph give to his brother?
B)How manny sports cards did Joseph have left?
