Answer:
[tex]9p^2-16q^2[/tex]
[tex](3p)^{2} -(4p)^{2}[/tex]
[tex]\underline{x^2-y^2=\left(x+y\right)\left(x-y\right)}[/tex]
[tex]\left(3p\right)^2-\left(4q\right)^2=\left(3p+4q\right)\left(3p-4q\right)[/tex]
[tex]=\left(3p+4q\right)\left(3p-4q\right)[/tex]
------------------------
hope it helps....
have a great day!!
Given f(x)= 2^x and g(x)=x^2 answer the questions that follow
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
PLEASE HELP
Answer:
a. Yes it's correct, reasons;
I) let x=1, f(1)=2^1=2, g(x)=1^2=1 this proves that when a higher number is used the value of f(x) will be higher than g(x).
ii) As x approaches zero f(x) approaches 1, but g(x) approaches 0. Which will make the rate at which the graph of f(x) increase be faster than g(x)
b. f(x) has an infinite degree but g(x) has a finite degree of 2.
. It is known that the glucose level in blood of diabetic persons follows a normal distribution model with mean 106 mg/100 ml and standard deviation 8 mg/100 ml. a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml. b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?
Answer:
a. 0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.
b. 0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 106 mg/100 ml and standard deviation 8 mg/100 ml
This means that [tex]\mu = 106, \sigma = 8[/tex]
a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml.
This is the p-value of Z when X = 120. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 106}{8}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.
b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?
The proportion is the p-value of Z when X = 120 subtracted by the p-value of Z when X = 90. So
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 106}{8}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
X = 90
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 106}{8}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228
0.9599 - 0.0228 = 0.9371
0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.
For which equations below is x = -3 a possible solution? Select three options.
|x|=3
|x|=-3
|-x|=3
|-x|=-3
-|x|=-3
Answer:
-|x|=-3
|x|=-3
|-x|=-3
Step-by-step explanation:
Answer:
Only -lxl = -3 works
Step-by-step explanation:
The other options don't work because they all have numbers inside of the absolute value brackets. You would always get a positive end value when the absolute value equation is applied.
The last one is the only one that works because the negative is outside of the absolute value bracket. Therefore, if you plug in 3 for x, it will give you -3.
Which method is used in elimination to find the solutions of a - b = 9 and a + b = 5?
The substitution method is used in elimination to find the solution to the equation.
What is the system of two equations?A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.
The given equation in the problem is;
Equation P: a - b = 9
Equation Q: a+b=5
The value obtained from the equation P is;
a - b = 9
a=b+9
Substitute the value in the equation Q;
a+b=5
b+9+b=5
2b=9-5
b=2
The value of a is;
a-b=9
a-2=9
a=9+2
a=11
Hence the value of a and b will be 11 and 2.
To learn more about the system of two equations, refer to the link;
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Which length is equivalent to 12 yards?
4 feet
9 feet
15 feet
36 feet
Answer:
4 feet
Step-by-step explanation:
1 yard is 3 feet
then 12 yards is 4 feet
Answer:
It is 36.
Step-by-step explanation:
It's simple math
foiuhgfdknsmlaeszxcyfvugbihnoj
Answer:
Given : A=(1,2)≡(x
1 ,y
1
) and B=(3,−2)≡(x
2
,y
2
)
Let M=(x,y) be the midpoint of AB
x=(
2
x
1
+x
2
) and y=(
2
y
1
+y
2
)
Then, x=
2
1+3
and y=
2
2−2
⟹x=2 and y=0
∴M=(2,0)
∴ Coordinates of the midpoint of AB is (2,0)
Step-by-step explanation:
A circle has a diameter with endpoints (-8,2) and (-2,6). What is the equation of the circle?
Answer:
the equation would be (x+5)2+(y−4)2=r2
Step-by-step explanation:
The equation would be
(x+5)2+(y-4)2=r2
Which one of the following groups would be unbiased when asked, “What is your favorite kind of pizza?”
Group of answer choices
health & fitness fanatics leaving the gym
guests leaving a gourmet pizza restaurant
kids at the playground
families attending a sporting event
Answer:
kids at playground
children are too young to know calorie count and the health benefits of certain foods. So they would simply choose the one they think tastes best
What is the value of (3/10)^3?
♡ 3/1000
♡27/1000
♡9/10
♡27/10
Answer:
27/10 is the value of (3/10)^3.
Step-by-step explanation:
It is also written as 0.027
PLS PLS PLS PLS PLS PLS PLS HELP I DON'T GET IT!!! Write missing monomials to make an identity:
A) (.....+2a)^2=.....+12ab+4*....
B) (3x+.....)^2=....*x^2+.....+49y^2
Answer:
I only have the answer for B
Step-by-step explanation:
This is the answer: 1st blank: 7y
2nd blank: 9
3rd blank: 42xy
(a+1)(b+2)
please help me!!!
Answer:
(a + 1) (b + 2 ) = 2a + b + ab + 2
Step-by-step explanation:
[tex](a +1 )(b + 2) \\\\= a( b+ 2) + 1 (b +2) \\\\= ab + 2a + b + 2\\\\=2a + b + ab + 2[/tex]
[tex](a + 1)(b + 2) \\ = a(b + 2) + 1(b + 2) \\ = ab + 2a + b + 2[/tex]
Answer ↦ [tex]\boxed{\tt{ab + 2a + b + 2}}[/tex]
Method Used:↦ Distributive Property.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
If “the notation arcsin x represents the inverse function to sine” is true or false.
If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].
What is the sin function?The sine function is one of the three primary functions in trigonometry, the others being cosine, and tan functions.
The confusion is compounded by the fact that we use the notation sin⁻¹(x) interchangeably with arcsin(x), and we call it the inverse sine.
Here is a counterexample disproving your given statement:
Let x = π.
The value π is in the domain of sin(x).
arcsin[sin(π)] = arcsin(0) = 0
arcsin[sin(π)] ≠ π
Therefore arcsin(x) is not the inverse of sin(x).
If you restrict the sine function to the interval [ -pi/2, pi/2 ]. Otherwise, arcsin will not be a function.
Hence, If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].
Learn more about sin function here;
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The daily listening audience of an AM radio station is five times as large as that of its FM sister station. If 144,000 people listen to these two radio stations, how many listeners does the FM station have?
Answer:
The number of FM listereners are 24000.
Step-by-step explanation:
Let the listeners of FM are p and thus the istereners of AM are 5p.
According to the question,
p + 5 p = 144000
6 p = 144000
p = 24000
The number of FM listereners are 24000.
work out the number of ham sandwiches Tina had
Answer:
Number of ham sandwiches Tina made = 60
Step-by-step explanation:
Total number of sandwiches = 480
Fraction of total sandwiches which are Tuna = [tex]\frac{3}{8}[/tex]
Therefore, number of Tuna sandwiches = [tex]480\times \frac{3}{8}[/tex]
= 180
Percentage of beef sandwiches = 35%
Therefore, beef sandwiches = [tex]480\times \frac{35}{100}[/tex]
= 168
Ratio of ham sandwiches (h) and cheese sandwiches (c) = 5 : 6
[tex]\frac{h}{c}=\frac{5}{6}[/tex]
[tex]c=\frac{6}{5}h[/tex] ------(1)
Total number of Tuna sandwiches + Total number of beef sandwiches + Total number of ham sandwiches + Total number of cheese sandwiches = 480
180 + 168 + h + c = 480
h + c = 480 - 348
h + c = 132
Substitute the value of c from equation (1),
[tex]h+\frac{6}{5}h=132[/tex]
[tex]\frac{11}{5}h=132[/tex]
[tex]h=\frac{132\times 5}{11}[/tex]
[tex]h=60[/tex]
Therefore, number of ham sandwiches Tina made = 60
Graph: Y - 3 = 1/2 (x+2)
Answer:
see graph
Step-by-step explanation:
Personally I put into slope intercept form before graphing
y - 3 = 1/2 (x+2)
y -3 = 1/2x + 1
y = 1/2x + 4
4 is y-intercept
1/2 is slope. [tex]\frac{Rise= 1}{Run= 2}[/tex]
x+3=5 . Find x in the given equation
Answer:
2
Step-by-step explanation:
x + 3 = 5
x = 5 - 3
x = 2
Therefore, x=2 in the given equation
Answer:
2
Step-by-step explanation:
x+3=5
x=5-3
x=2
Hope it helps
probability, please help i will give brainliest
Answer:
Step-by-step explanation:
2 colours were taken
Ashvin want to replace the carpet in your living room and hallway with laminate flooring.
Find the total area of the hallway and living room.
Answer:
I’m sorry but you need to edit this question, it is incomplete.
Step-by-step explanation:
I see nothing, if there is supposed to be an image attached, please i attach it again, tnx!
I could help you though
A trader bought some oranges at 5c each She finds that 6 of them are rotten. She sells the rest at 8c each and makes a profit of $4,50. How many oranges did she buy? (Hint: let the number of oranges be x. Work in cents.)
can someone please help me
s part of a science experiment, Natasha drops a bouncy ball from various heights, h, and observes the height to which the ball rebounds, r. The table shows the results of Natasha's experiment.
Initial height, h (in meters) Rebound height, r (in meters)
0.30 0.24
0.50 0.4
0.80 0.64
1.00 0.8
1.20 0.96
Answer: r = 0.6h
your welcome :D
Answer:
The actual correct answer is r = 0.8h
Step-by-step explanation:
You divide 0.24 ÷ 0.30 and get 0.8
Do the same thing for all the rest of the numbers but,
you must put the numbers that are on the right FIRST then divide them by the numbers on the left, all of these are the same answer which means it's
r = 0.8h
Hope this helps!
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is
3/8
There are 56 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
red marbles
Step-by-step explanation:
Since the formula is;
Probability = number of required outcome
_______________________
number of possible outcome
3/8. = x/56
8x. = 168
x. 21 ( number of blue marbles)
Therefore if the total marbles = 56 and 21 of the marbles are blue then to get the red marbles
= 56 - 21
= 35
WILL PICK BRAINLIEST
A 2-column table with 7 rows. Column 1 is labeled x with entries 2.1, 2.5, 2.7, 3.1, 3.4, 3.9, 4.2. Column 2 is labeled y with entries 30, 36, 34, 38, 39, 42, 41.
Which best describes the data in the table?
There are no outliers, but there is a cluster.
There is a cluster and outliers.
There are no clusters or outliers.
There are no clusters, but there are outliers.
Answer:
A
Step-by-step explanation:
Just did it
Answer:
c
Step-by-step explanation:
m.c.m (35;50)
m.c.d (35;50)
m.c.m (116;92)
m.c.d (116;92)
Answer:
hxgdhsksuflskjtnsjfbdyfyjagdjxfhhfbejfbodwkkgodl
the green line below _____ check all that apply
Answer:
A, C, and D
Step-by-step explanation:
Answer:
the answer is A, C And D
Step-by-step explanation:
ADC
Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary.
Answer:
5.8
Step-by-step explanation:
Y e s .
Using the Distance formula and all.
Graph the function F(x)=2^x-4
Answer:
The plotting are correct .
HOPE IT HELPED!!
What is the perimeter of parallelogram WXYZ? StartRoot 5 EndRoot + StartRoot 17 EndRoot units 2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units 16 units 22 units
Answer:
2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units
Step-by-step explanation:
The perimeter of the parallelogram is expressed as
Perimeter = WX + XY + YZ + WZ
Using the distance formula;
WX = √(0-(-1))²+(4-0)²
WX = √1²+4²
WX = √17
For XY:
XY = √(-2-(0))²+(3-4)²
XY = √(-2)²+(-1)²
XY = √4+1
XY = √5
For YZ:
YZ = √(-2+3))²+(3+1)²
YZ = √(1)²+(4)²
YZ = √1+16
YZ = √17
For WZ;
WZ = √(-3+1)²+(-1-0)²
WZ = √(-2)²+(-1)²
WZ = √4+1
WZ = √5
Perimeter = √17+√5+√17+√5
Perimeter = 2√17 + 2√5 units
Answer:
B
Step-by-step explanation:
A store charges 7% sales tax. Which expression can be used to find the total cost of an item with a price of p?
0.07p
0.93
1.07
7.000
HELP PLS SMb!
Answer:
0.07.
Step-by-step explanation:
Below. Lets say 1 is 100 dollars sale tax. If 1 is 100 7 would be 7.00
3 of item A, 7 of item B and 1 of item C in a toy collection cost $31.50. 4 of item A, 10 item B and 1 C in the same collection cost $42. Find the price of item A+B+C.
bAnswer: the answers is most likely a because of the nomination
Step-by-step explanation:
use the order of operations -5 + 3(7.2 - 3.2)
Answer:
-5 + 3(7.2 - 3.2) equals 7.
Step-by-step explanation:
The order of operations states the order in which different mathematical operations should be done first, you can use the mnemonic PEMDAS to remember the order to complete each operation. PEMDAS states that the order must be followed as Parenthesis, Exponents, Multiplication/Division, and Addition/Subtraction. In the expression -5 + 3(7.2 - 3.2), the three mathematical operations being used are subtraction, multiplication, and parenthesis, so based on PEMDAS, the order to complete them is parenthesis, multiplication, and subtraction. -5 + 3(7.2 - 3.2) = -5 + 3(4) = -5 + 12 = 7, so that is your final answer.
[tex]\displaystyle\bf -5+3(7.2-3.2)=7\\\\1)\:7.2-3.2=4\\\\2)\:4\cdot3=12\\\\3)\:12-5=7[/tex]
