Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
Which statement about class ll is true
A?
B?
C?
D?
Answer:
D
Step-by-step explanation:
Let's first find the mean and median of each class.
Class 1:
The mean is simply all the numbers added up and then divided by the number of elements. There are 9 students in Class 1. Thus, we add all the ages up and then divide by 9. Thus:
[tex]\text{Class 1 Mean }= \frac{14+15+15+16+16+16+17+17+18}{9} \\=144/9=16[/tex]
The median is simply the middle number when the data sets are placed in order. The median of Class 1 is 16, the number in the middle.
Class 2:
Again, Class 2 has 9 students. Add up all the ages and then divide:
[tex]\text{Class 2 Mean }= \frac{13+14+15+16+16+17+18+18+19}{9}\\ =146/9\approx16.2222[/tex]
The median is the middle number of the data set. The median of Class 2 is 16.
Therefore, the mean of Class 2 is larger than the mean of Class 1. The medians of the two classes are equivalent.
Of the answer choices given, only D is correct.
Answer:
The mean of class II is larger and the median is the same
Step-by-step explanation:
Class I
14,15,15,16,16,16,17,17,18
The mean is
(14+15+15+16+16+16+17+17+18)/9
144/9 = 16
The median is the middle number
14,15,15,16, 16, 16,17,17,18
median = 16
Class II
13,14,15,16,16,17,18,18,19
The mean is
(13+14+15+16+16+17+18+18+19)/9
146/9 = 16.2repeating
The median is the middle number
13,14,15,16 ,16, 17,18,18,19
median = 16
1001112 = [ ? ]10
?
what number belongs where the question mark is
I suppose you're supposed to convert 100111 from base 2 to base 10. We have
[tex]100111_2=2^5+2^2+2^1+2^0=32+4+2+1=39_{10}[/tex]
so the missing number is 39.
Diabetic patients have normally distributed cholesterol with mean 200 and standard deviation=10.
Find the percentage of patients whose cholesterol is between 198 mg/dL and
207 mg/dL ?
Answer:
The percentage of patients whose cholesterol is between 198 mg/dL and 207 mg/dL is 33.73%
Step-by-step explanation:
To calculate this proportion, we follow the probability route, using the z-score statistics
Mathematically;
z-score = (x-mean)/SD
from the question, mean = 200 and SD = 10
So for 198
z-score = (198-200)/10 = -2/10 = -0.2
For 207
z-score = (207-200)/10 = 7/10 = 0.7
So the probability we want to calculate is;
P(-0.2<z<0.7)
Mathematically this can be calculated as;
P(z<0.7) - P(z<-0.2)
We can calculate the required probability using the standard normal distribution table
P(-0.2<x<0.7) = 0.3373 from the standard distribution table
So it is this 0.3373 that we now convert to percentage and that is 33.73%
Please answer this correctly without making mistakes
Answer:
3 1/4
Step-by-step explanation:
Hey there!
Well if Cedarburg to Westford is 8 3/4 miles and Oxford to Westford is 5 1/2 miles, we can make the following,
CO = CW - OW
CO = 8 3/4 - 5 1/2
Make the denominators the same,
5 1/2
improper
11/2
*2
22/4
Proper
5 2/4
8 3/4 - 5 2/4
3 1/4 miles
Hope this helps :)
What is the length of the arc on a circle with radius 16 inches intercepted by a 45° angle?
Find the circumference:
Circumference = 2 x PI x radius:
Circumference = 2 x 3.14 x 16 = 100.48 inches.
A full circle is 360 degrees, a 45 degree angle is 1/8 of a full circle.
Arc length = 100.48 / 8 = 12.56 inches.
Which of the following expressions are equivalent to (x+y) - (-z)? A. (x+y) - z B. x+ (y+z) C. None of the above
=========================================
Explanation:
Subtracting a negative is the same as adding. Example: 2-(-3) = 2+3 = 5.
So (x+y)-(-z) is the same as x+y+z. We can group up terms inside parenthesis and it won't change the result. Meaning that x+y+z is the same as any of the following below
(x+y)+zx+(y+z)We could also swap the order of either x, y or z, and still have the same result.
What is the product of 2p + q and -39 - 6p + 1?
0 -12p2 - 6pq – 4p - 32 + 1
O-12p2- 12pq + 2p – 392 +9
- gp² q² + 12pq - 2p + 9
12p2 + 12pq +2p + 302 + 9
Answer:
Option (2)
Step-by-step explanation:
In this question we have to find the multiplication of the two expressions.
(2p + q)(-3q - 6p + 1)
= 2p(-3q - 6p + 1) + q(-3q - 6p + 1) [By distributive property]
= -6pq - 12p²+ 2p - 3q² - 6pq + q
= -12p² - (6pq + 6pq) - 3q² + 2p + q
= -12p² - 12pq + 2p - 3q² + q
Therefore, Option (2) will be the correct option.
Your friend Stacy has given you the following algebraic expression: "Subtract 20
times a number n from twice the cube of the number. What is the expression that your
friend is saying?
Answer:
Expression = 2n³ - 20n
Step-by-step explanation:
Find:
Expression
Computation:
Assume given number is 'n'
Cube of number = n³
Twice of cube = 2n³
Subtract number = 20n
Expression = 2n³ - 20n
Suppose a jar contains 18 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer: 0.0993
Step-by-step explanation:
Since the jar contains 18 red marbles and 38 blue marbles, the total marbles will be:
= 18 marbles + 38 marbles
= 56 marbles
When 2 marbles are pull out at random at the same time, the probability that both are red will be:
= (18/56) × (17/55)
= 0.3214 × 0.3091
= 0.0993
A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?
Answer:
b = - 3.7
Step-by-step explanation:
here are the data values:
x y XY X²
14 46 644 196
15 49 735 225
16 37 592 256
17 42 714 289
18 37 666 324
19 31 589 361
20 25 500 400
21 23 483 441
22 20 440 484
23 15 345 529
24 12 288 576
now we are required to find the summation (total) of all values of X, Y, XY and X².
∑X = 209
∑Y = 337
∑XY = 5996
∑X² = 4081
The formular for finding b is given as:
b = n∑XY - (X)(Y) / n∑X² - (∑X)²
= 11(5996) - (209)(337) / 11(4081) - (209)²
= 65956 - 70433 / 44891 - 43681
= -4477/ 1210
= -3.7
The question asked us to find the value of b but we can go further to find the equation of the regression line:
a = ∑Y - b∑X / n
= 337 - (-3.7)(209)/ 11
=1110.3/11
= 100.94
the equation is:
Y = 100.94 - 3.7X
I hope you find my solution useful!
=
The radius of a circle measures 5 inches A central angle of the circle measuring 12 radians cuts off a sector
What is the area of the sector?
Enter your answer as a simplified fraction in the box
area =
inches squared
Answer:
25/4 square inches
Step-by-step explanation:
The area of a sector of a circle is given by the formula ...
A = (1/2)r²θ
where r is the radius and θ is the central angle in radians.
For your sector, the area is ...
A = (1/2)(5 in)²(1/2) = 25/4 in²
I need help on this question ASAP please?
Answer:
B.
Step-by-step explanation:
10c + 5 ≤ 45
10c ≤ 40
c ≤ 4
Since the inequality uses the less than or equal to sign, we use a shaded circle on the number line. Since c is less than or equal to 4, your answer will be B, since the line extends infinitely to the left of 4.
Hope this helps!
Answer:
B
Step-by-step explanation:
To get the answer, you need to simplify or re-write the equation given:
10c + 5 ≤ 45 = 10 × c + 5 - (45) ≤ 0Next, group the like terms together:
10c - 40Now, we can apply algebra to simplify the equation further:
(10c ÷ 10) ≤ (40 ÷ 10)c ≤ 4Now, look at your options. Only option B matches our equations. Therefore, B is the correct answer.
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H = 210 + 33t How fast does the tree grow? ANSWER centimeters per year.
Answer:
The tree grows 33cm per year
Step-by-step explanation:
Here in this question, we are interested in knowing how fast the growth of the tree is.
This is easily obtainable from the equation for the height of the tree.
Mathematically, the equation is given as;
H = 210 + 33t
Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.
So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree
Use the drawing tools to form the correct answers on the grid.
Mark the vertex and graph the axis of symmetry of the function.
fix) = (x - 2)2 - 25
Answer:
Step-by-step explanation:
Hello, this is pretty straight forward. Let me remind you the following.
The standard equation of a parabola is
[tex]y=ax^2+bx+c[/tex]
But the equation for a parabola can also be written in "vertex form":
[tex]y=a(x-h)^2+k[/tex]
In this equation, the vertex of the parabola is the point (h,k) .
So, here the vertex is the point (2, -25) and the axis of symmetry is x = 2
Thank you
Answer:
if anyone still needs the answer I added a pic
Step-by-step explanation:
Stephen Curry's record during the 2017 - 2018 NBA final game is made up of 2-point shots and 3-points.
His total points scored for the final game was 45 points with 19 shots made. How many 2-point shots did
he make? How many 3-point shots did he make?
2-Pointers:
3-Pointers:
Answer:
x = 12 ( two points shots )
y = 7 ( three points shots )
Step-by-step explanation:
Let´s call "x" two points shots, and "y" three points shots, then
x + y = 19
2*x + 3*y = 45
We have to solve a two-equation system for x and y
y = 19 - x
2*x + 3 * ( 19 - x ) = 45
2*x + 57 - 3*x = 45
- x = 45 - 57
-x = - 12
x = 12
And y = 19 - 12
y = 7
About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.
Answer:
a. True
b. true
c. false
d. false
e. false
Step-by-step explanation:
a. true
polutation = 25% = 0.25
sample = n= 12
n x p
= 12 x o. 25 = 3 and 3 is less than 10
12(1 - p)
= 12 x 0.75
= 9 and is less than 10
b. True
the sample distribution of the population is normal when
sample size x population > or equal to 10
40 x 0.75
= 30 and 30 is greater than 10
c. false
50 x 0.25 = 12.5
50 x 0.20 = 10
z = 10 - 12.5/sqrt(12.5)
= -2.5/3.54
= -0.70
H0: Young american family who delayed
H1: young american family who did not delay
p(z = -0.70)
0.2420>0.005
therefore we accept the null hypothesis
d. false
150 x 0.20 = 30
150 x 0.75 = 37.5
z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22
p(z = -1.22) = 0.1112 > 0.05
therefore we do not reject the null hypothesis
e. false
se1 = sqrt(p(1-p)/n
se2 = sqrt(p(1-p)/3n
se2 = 1/sqrt(3)se2
At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?
Answer:
£32 in total for the top and two trousers
Step-by-step explanation:
The price for a top In the "cloth for you" shop= £10
The price for a bermuda trouser In the "cloth for you" shop= £12
There is a 20% discount on tops
The price If I bought one top and would trouser will be
(10-(0.2*10)) for the top
2(12) for the trouser
Total= (10-(0.2*10))+ 2(12)
Total = 10-2+24
Total = £32
So I spent £32 in total for the top and two trousers
if a salesman has a base salary of 35,000 per year makes 5% commission on each sales ,how much must he do in sales to make a total of 75,000 for the year
He must do a 8,00,000 sales to make total of 75000 for the year.
For salesman base salary = 35000, Salary to be atained is 75000. Having commission of 5% on every sales. Sales to be determine so the salesman attained 75000 for year.
In mathematics it deals with numbers of operations according to the statements.
Here, according to the statement.
Let x be sales,
35,000 + 5%x = 75,000
0.05x = 75000-35000
x = 40000/0.05
x = 8,00,000
Thus, he must do a 8,00,000 sales to make total of 75000 for the year
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
After a 75% reduction, you purchase a new clothes dryer for $200. What was the original price of the clothes dryer?
Answer:
$800
Step-by-step explanation:
Let the original price be $x.
75% reduction ----- 100% -75%= 25%
25%x= 200
[tex] \frac{25}{100} x = 200 \\ x = 200 \div \frac{25}{100} \\ x = 200 \times \frac{100}{25} \\ x = 800[/tex]
Thus, the original price of the clothes dryer is $800.
Answer:
$800
Step-by-step explanation:
Let the original price be x.
Final price=100%-75%
=25%
x-75%=200
x=200 x 100/75
x=8 x 100
x=800
Thank you!
How many variables terms are in the expression 3xcube y+5xsquare+y+9
Answer: Please Give Me Brainliest, Thank You!
2
Step-by-step explanation:
There are two variables here, X and Y
Which polynomial represents the sum below?
Answer:
The sum is represented by the polynomial:
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
Step-by-step explanation:
Recall that polynomials are added by combining like terms. The only like terms in this addition are: 5 x and 8 x which added render: 13 x. therefore, the addition of these polynomials renders;
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
5 STARS IF CORRECT! Can you find the value of an expression when values for x and y are given? Explain.
If the expression has only two variables [tex] x[/tex] and $y$, or if there's just one variable out of these two, then the answer is yes.
If the expression has more variables (other than X and y), then the answer is no.
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7exyz, (0, 0, 7)
Answer:
Full question is:
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7[tex]e^{xyz}[/tex] at a specified point (0, 0, 7)
Step-by-step explanation:
If we have a level surface, then it will give us
f(x,y,z) = x+y+z = 7[tex]e^{xyz}[/tex]. where f is the function of the x, y, and z coordinates.
Now let us calculate the ∇ gradient of f at point (0,0,7):
∇[tex]f|_{(0,0,7)}[/tex] = (fx,fy,fz) = (1−7yz[tex]e^{xyz}[/tex],1−7xz[tex]e^{xyz}[/tex],1−7xy[tex]e^{xyz}[/tex])[tex]|_{(0,0,7)}[/tex]
= (1, 1, 1)
We get the equation for the tangent plane A:
A: 1(x−0) + 1(y−0) + 1(z−7)=0
This can also be written as:
x+y+z = 7 ------------------------------------------------------------------(a)
The equation for the normal line B gives us :
L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)
Barry’s pet turtle, Turtlelini, escaped from his backyard. Barry found Turtlelini by the creek and wanted to determine how far Turtlelini had walked. On the map, Barry’s house is 0.6 inch from the creek. If the scale on the map shows that 1.5 inches are equivalent to 0.8 mile, how far did Turtlelini walk, to the nearest tenth of a mile?
Answer:
On the map:
0.8 mile / 1.5 inches
= 0.533 mile / 1 inch
Total distance on the map:
0.6 inches
distance travelled in miles:
0.6 * 0.533 = 0.32 miles
please mark brainly if you want
Answer:
The answer is A = 0.3 mile
Step-by-step explanation:
I got it right in 2021.
The length of a rectangle is twice its width.
If the area of the rectangle is 200 yd?, find its perimeter.
Answer:
The answer is 60cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
Area of rectangle = l × w
where
l is the length
w is the width
From the question
The length is twice its width is written as
l = 2w
Substitute this into the formula for finding the area of the rectangle
Area = 200 yd²
200 = 2w²
Divide both sides by 2
w² = 100
Find the square root of both sides
width = 10cm
Substitute this value into l = 2w
That's
l = 2(10)
length = 20cm
Perimeter of the rectangle is
2(20) + 2(10)
= 40 + 20
= 60cmHope this helps you
If a square has an area of x, then, in terms of x, what is the circumference of the largest circle that can be inscribed in the square? Answer: pi square root x AKA π√ x This is an SAT Math question no CALCULATOR. Show all the work
Answer:
C = pi sqrt(x)
Step-by-step explanation:
The area of a square is x
A = s^2 where s is the side length
x = s^2
Take the square root of each side
sqrt(x) = s
This would be the diameter of the inscribed circle
The circumference of a circle is given by
C = pi d
C = pi sqrt(x)
Answer:
See below.
Step-by-step explanation:
Assign the variable n to be the sides of the square.
Since a square has four equal sides, the area of the square is n^2 or x.
Therefore:
[tex]n=\sqrt{x}[/tex]
The largest circle that can be inscribed in the square will have the largest possible diameter. The largest possible diameter will be straight across the center of the circle. So, the largest possible diameter will be the side length, n.
Therefore, the radius will be n/2.
The circumference of a circle is:
[tex]C=2\pi r[/tex]
Plug in n/2 for the radius:
[tex]C=2\pi (\frac{n}{2})\\ C=n\pi[/tex]
Now, substitute n for the square root of x:
[tex]C=\pi\sqrt{x}[/tex]
prove:
[tex] \frac{1}{secθ + \tanθ} - \frac{1}{cosθ} = \frac{1}{cosθ} - \frac{1}{secθ - tanθ} [/tex]
Answer:
I hope you are searching for this......
In a study of pain relievers, 50 people were given product A, and 35 experienced relief. In the same study, 25 people were given product B, and 19 experienced relief. Fill in the blanks of the statement below to make the statement the most reasonable possible. Product __ performed better in the study because __% got relief with this product, whereas only __% got relief from product __
Answer:
Product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A
Step-by-step explanation:
Product A
Total number of people tested = 50
Total number o who experienced relief using product A
= 35
% of people who got relief using product A
= 35/50 x 100%
= 70%
Product B
Total number of people tested = 25
Total number of people who experienced releif using product B
= 19
% of peope who got relief using product B
= 19/25 x 100%
= 76%
From the above:
76% of people got relieved whilst using product B
70% who got relieved using product A.
Therefore, product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A
Which equation is represented by the graph shown in the image? A. y + 2= x B. y + 1= x C. y - 1= x D. y - 2= x Please show ALL work! <3
Answer:
A. y + 2= x
Step-by-step explanation:
Which equation is represented by the graph shown in the image?
A. y + 2= x
B. y + 1= x
C. y - 1= x
D. y - 2= x
Please show ALL work! <3
The graph shown has a slope of +1 and a y intercept of -2.
All given answer choices have a slope of +1, so that's not the problem.
We need one that has a y-intercept of -2, or the equation should be
y = x-2, or equivalently y+2 = x
which corresponds to answer choice A.
Suppose you are standing such that a 32-foot tree is directly between you and the sun. If you are standing 140 feet away from the tree and the tree casts a 160-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 160 ft 140 ft 32 ft
Answer:
Height = 4 feet
Step-by-step explanation:
To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree
But the tree is 32 feet tall but on shadow it's 160
So lemme determine how long I'll be in my shadow first
Distance away from tree= 140 feet
Length of shadow cast by tree
= 160 feet
Length of shadow= 160-140
Length if shadow= 20 feet
My height= x
X/20= 32/160
X= 20*32/260
X = 4 feet
Height = 4 feet
