[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
[tex]8ab^{2}:6a^{2}b\\\\=\dfrac{8ab^{2}}{6a^2b}\\\\=\dfrac{2×4×a×b×b}{2×3×a×a×b}\\\\=\dfrac{4b}{3a}\\\\=4b:3a[/tex]
(a). Find the value of log 216.
Answer:
2.334453751
Step-by-step explanation:
Press log on your Casio calculator (if you have one) and plug in 216, then close the parentheses!
PLEASE ANSWER I WILL GIVE BRAINLIEST FAST
Answer:
E &F
Step-by-step explanation:
The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).
Find the perimeter and area of a square with sides 6 inches in length.
Which of the following is NOT equivalent to 22/7?
a) 2 + 8/7
b) 1 + 15/7
c) 3 (7/1) + 1/7
d) 3 (7/7) + 1/7
Answer:
the option c is the answer for this question
Ron deposits $2,000 into an account that receives 3.1% interest compounded continuously. How much money is in the account after 9 years?
A.) $2,623.70
B.) $2,632.44
C.) $2,643.61
D.) $2,605.83
Answer
i think it's C. $2,643.61
What is the squad root of 81
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Find the square root of 81
[tex]\sqrt{81}[/tex]
[tex]\sqrt{9*9}[/tex]
[tex]\sqrt{9^{2}}[/tex]
[tex]9[/tex]
Answer: [tex]9[/tex]
Answer:
the square root of 81 is 9
Ann's first option is a plot of land adjacent to a current park.
The current park is a square, and the addition will increase the width by 200 meters to give the expanded park a total area of 166,400 square meters, This equation represents the area of the first option, where x is the side length of the current square park:
X2 + 200x = 166,400.
Use the most direct method to solve this equation and find the side length of the current square park.
Explain your reasoning for both the solving process and the solution.
Given:
The equation for the area of the first option is:
[tex]x^2+200x=166400[/tex]
Where x is the side length of the current square park.
To find:
The side length of the current square park.
Solution:
We have,
[tex]x^2+200x=166400[/tex]
It can be written as:
[tex]x^2+200x-166400=0[/tex]
Splitting the middle term, we get
[tex]x^2+520x-320x-166400=0[/tex]
[tex]x(x+520)-320(x+520)=0[/tex]
[tex](x-320)(x+520)=0[/tex]
[tex]x=320,-520[/tex]
We know that the side length of a park cannot be negative. So, the only possible value of x is 320.
Therefore, the most direct method to solve the given equation is splitting the middle term and the side length of the current square park is 320 meters.
The angles in a triangle are 89, 1, and 90 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answer: B. Right Scalene
Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.
Answer:
b
Step-by-step explanation:
A pyramid art installation has a surface area of 24 m2. An artist creates replicas with scale factors of 1/8, 1/10, and 1/12. What is the surface area of each replica?
Answer:
The replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.
Step-by-step explanation:
Given that a pyramid art installation has a surface area of 24 m2, and an artist creates replicas with scale factors of 1/8, 1/10, and 1/12, to determine what is the surface area of each replica, the following calculation has to be done:
24 x 1/8 = 3
24 x 1/10 = 2.4
24 x 1/12 = 2
Therefore, the replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.
Answer:
1/8 = 0.38 m^2
1/10= 0.24 m^2
1/12= 0.17 m^2
Step-by-step explanation:
A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?
a. One out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
Answer:
a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.
b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.
Step-by-step explanation:
For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One out of four cars needs to have oil added.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a. One out of the next four cars needs oil.
This is P(X = 1) when n = 4. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]
0.4219 = 42.19% probability that one out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
This is P(X = 2) when n = 8. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]
0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
This is P(X = 3) when n = 12. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]
0.2581 = 25.81% probability that three out of the next 12 cars need oil.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 135 minutes, her sample has decayed to 3.75 grams. Find an exponential formula for G ( t ) G(t) , the amount of goo remaining at time t t .
Answer:
[tex]G(t) = 120e^{-0.0257t}[/tex]
Step-by-step explanation:
Amount of substance:
The amount of the substance after t minutes is given by:
[tex]G(t) = G(0)e^{-kt}[/tex]
In which G(0) is the initial amount and k is the decay rate.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo.
This means that [tex]G(0) = 120[/tex], so:
[tex]G(t) = G(0)e^{-kt}[/tex]
[tex]G(t) = 120e^{-kt}[/tex]
After 135 minutes, her sample has decayed to 3.75 grams.
This means that [tex]G(135) = 3.75[/tex].
We use this to find k. So
[tex]G(t) = 120e^{-kt}[/tex]
[tex]3.75 = 120e^{-135k}[/tex]
[tex]e^{-135k} = \frac{3.75}{120}[/tex]
[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]
[tex]-135k = \ln{\frac{3.75}{120}}[/tex]
[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]
[tex]k = 0.0257[/tex]
So
[tex]G(t) = 120e^{-0.0257t}[/tex]
If four items are chosen at random without replacement from seven items, in how many ways can the four items be arranged, treating each arrangement as a different event (i.e., if order is important)?
Answer:
840 ways.
Step-by-step explanation:
The order is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
4 items from a set of 7, so:
[tex]P_{(7,4)} = \frac{7!}{(7-4)!} = 7*6*5*4 = 840[/tex]
840 ways.
Which choice is equivalent to the expression below?
V25x - V4x + 2 VX
Answer:
The correct answer is C)
Someone help me?????
Step-by-step explanation:
4. b 612 (72/100) x 850)
5. c. 275 (33/100) x 835
6. b. 39% (3.24 - 2.85) x100%)
What is the slope formula?
Answer:
D is your answer
Step-by-step explanation:
Answer:
Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx
Step-by-step explanation:
Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction? On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
9514 1404 393
Answer:
2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3
Step-by-step explanation:
Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².
The function can be simplified to ...
f(x) = 5/x² -5
which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.
Avi uses 11 toothpicks to form a row of 5 attached triangles, as shown. Suppose he continues this pattern, using 89 toothpicks in all. What is the total number of triangles formed? (sorry the picture wasn't uplodaing)
Answer:
44
Step-by-step explanation:
Given that Avi used 11 toothpicks to form a row of 5 attached triangles.
Total number of toothpicks used = 89
Let the total number of triangles formed be represented by x, so that:
11 toothpicks = 5 triangles
It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;
the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]
= 2.2
The number of toothpicks per triangle = 2.0
Thus,
x = [tex]\frac{89}{2.0}[/tex]
= 44.5
x = 44
The total number of triangles formed is 44.
HELP!!!!!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not?
f(x) = ex
A) The base is x.
B) The base is e.
C) This is a polynomial.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
assuming that the equation was [tex]f(x) = e^{x}[/tex]
then the base is "e"
Step-by-step explanation:
first to answer gets brainiest
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
cm³
Answer:
V = 67 1/2 cm^3
Step-by-step explanation:
The volume is given by
V = l*w*h
V = 4 1/2 * 6 * 2 1/2
Changing to improper fractions
V = 9/2 *6*5/2
V =270/4
V = 135/2
Changing to a mixed number
V = 67 1/2 cm^3
Didi invested a total of $16125 in two accounts paying 8.5% and 4% simple interest. If her total return at the end of 2 years was 1740 , how much did she invest in each account?
Answer:
5000 ;
11125
Step-by-step explanation:
Given :
Total principal = 16125
Rates = 8.5% and 4%
Period, t = 2 years
Total interest = 1740
Let :
Principal amount invested at 8.5% = x
Principal amount invested at 4% = 16125 - x
Interest formula :
Interest = principal * rate * time
Hence, mathematically ;
(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740
(0.17x + 1290 - 0.08x ) = 1740
0.09x + 1290 = 1740
0.09x = 1740 - 1290
0.09x = 450
x = 450 / 0.09
x = 5000
Amount invested at 4% :
16125 - 5000 = 11125
Using the net below, find the surface area of the pyramid. (in the image) 2in 3in 3in
Answer:
Surface area = 21 in.²
Step-by-step explanation:
Surface area of the pyramid = sum of all areas of the faces or parts of the net = 4(area of triangle) + area of square base
✔️Area of the four triangles:
A = 4(½*b*h)
Where,
b = 3 in.
h = 2 in.
A = 4(½*3*2)
A = 2*3*2
A = 12 in.²
✔️Area of the square base = s²
s = 3 in.
Area = 3² = 9 in.²
✅Surface area of the pyramid = 12 + 9 = 21 in.²
Researchers study the relationship between interpersonal violence and health in college age women. The researchers report an OR for somatic symptoms among abused versus non abused women (OR 1.03 95% CI 0.79-1.71). Based on this information, you know:_________-
a. Abused women are significantly more likely to have somatic symptoms.
b. There is no significant difference in somatic symptoms for abused and non-abused women.
c. This is a clinically significant result.
d. In this study women who were abused were less likely to report somatic symptoms.
Answer:
There is no significant difference in somatic symptoms for abused and non-abused women. ( B )
Step-by-step explanation:
Given that OR = 1 simply shows that there is no difference in data for both groups
and 95% of Cl for the variable OR = ( 0.79 - 1.71 )
given the relationship between Cl and OR we can conclude that Cl is inclusive in the value OR = 1
Finally : we can conclude that There is no significant difference in somatic symptoms for abused and non-abused women
Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92
people to interview.
Answer:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 41, standard deviation of 28:
This means that [tex]\mu = 41, \sigma = 28[/tex]
Sample of 92:
This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]
Distribution of the sample means:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
For this exercise assume that the matrices are all nn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer.
If there is an n x n matrix D such that Ax =0, then there is also an nxn matrix C such that CAI.
a. True
b. False
Answer:
A) True
Hope this helps!
What is the domain of the relation described by the set of ordered pairs (-2,8), (-1,1) (0,0) (3,5), (4,-2)?
Step-by-step explanation:
(-2,-1,0,3,4) are the domain
(x,y)=(domain,range)
simply x components are the domain whereas y components are the range
Evaluate f (5)
f(5) =
Answer:
100
Step-by-step explanation:
f(5) means find the output value when x=5
When x =5 f(x) = 100
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
100Explanation:-
we have to find the value of f(5)
But in the questions attachment it tells that
f(5)=100
The longest leg is Select one:
a. 5√3
b. 10√3
c. 5
d. 20
Answer:
D:20
sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20
Step-by-step explanation:
ms.+sanchez+bought+3+pounds+of+turkey+to+make+sandwiches+for+her+family+.+She+uses+.25+of+a+pound+for+each+sandwich+.+How+many+sandwiches+can+she+make+?
Answer:
she can make 12 sandwiches
Step-by-step explanation:
3/.25 is the solution
find the exact value of tan -75
How do you know if a radical can be simplified? Explain.
Answer:
An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.
