Answer:
Step-by-step explanation:
A + B = 750
A = 1.5 B
~~~~~~~~~~~~~~
750-B = 1.5 B
750 = 1.5 B + B
750 = B(1.5 +1)
750 = B (2.5)
B = 300
A = 450
prove that 1 + sin a + cos 2A upon 1 + Sin A minus Cos 2A = 2 cot a prudent
Answer:
LHS×0=RHS×0
0=0
hence,proved
When we expand (2x + 1/2)^6, what is the coefficient on the x^4 term?
Answer: The coefficient before x^4 is 60
Step-by-step explanation:
Hey! So I am not an expert at this, but you have to use the binomial theorem
I have attached of the Pascals Triangle (one shows the row numbering as well)
Basically in a pascal triangle, you add the two numbers above it to get the next number below
As you can see, the rows start from 0 instead of 1
The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms
NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)
Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)
It would be 15 × 2^4 × (1/2)^2 = 60
The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power
Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)
a basketball team playd 64 games they won 28 more than they lost
Which is the graph of f(x) = 2 (4)?
5
40.4)
404)
4
(4,4)
3
3
3 2
2
2
2
(2.1)
6,2)
1
5 -4 -3 -2 -14
1
3
4
-5 4 -3 -2 -14
234
-5 6 -3 -2 -14
2
3
4
5
X
-2
-2
نا دیا
-3
-3
4
W4
-5
5
Tu
5
4
(
24)
Answer:
The Third one
Step-by-step explanation:
Your Welcome :)
Graph of the function is attached below.
Correct option is D.
What is exponential function?As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:
Definition of exponential function
In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.
Given, exponential function
f(x) = (1/4)4ˣ
exponential function is defined for x∈R
Putting x = 0
f(0) = (1/4)4⁰
f(0) = 1/4
Point on curve is (0,1/4)
Putting x = 1
f(1) = (1/4)4¹
f(1) = (1/4)4
f(1) = 1
Point on curve is (1,1)
Putting x = 2
f(2) = (1/4)4²
f(2) = (1/4)16
f(2) = 4
Point on curve is (2,4)
Putting x = 3
f(3) = (1/4)4³
f(3) = (1/4)64
f(3) = 16
Point on curve is (3,16)
Point (0, 1/4), (1, 1), (2, 4), (3, 16) can be used to draw graph of the function.
Hence, graph of the function is drawn as follows.
Learn more about exponential function here:
https://brainly.com/question/14355665
#SPJ7
please help! (listing BRAINLIST and giving points) :)
Answer:
Tan B = 12/5
Sin B = 12/13
Cos B = 5/13
Step-by-step explanation:
sine B = opposite (12)/hypotenuse (13)
= 12/13
Cosine B = adjacent/hypotenuse
= 5/13
Tangent B = opposite/adjacent
= 12/5
Here is a picture that can always help you with the three trig ratios.
which of the following statements is true
Answer: B ACE is similar to DCB
Step-by-step explanation:
course
Look at the following number line:
- 10
-5
0
5
10
What are two ways to write the inequality graphed?
x>-1 and -1
XS-1 and -12X
x < -1 and -1 > X
x2-1 and -1 5x
first and last one i think
(08.07 MC)
A polynomial function is shown below:
f(x) = x3 − 3x2 − 4x + 12
Which graph best represents the function? (5 points)
Answer:
Graph A (first graph from top to bottom)
Step-by-step explanation:
Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.
Factoring the polynomial:
[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]
Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).
The graph that corresponds with this is graph A.
is the sum of two rational numbers sometimes zero ture or false?
Answer:
True.
Step-by-step explana
-4/5 + 4/5 is 0
Find the difference of (4.2x10^3)-(2.7x10^3)
Show work!
Step-by-step explanation:
Is it helpful ?
plz let me know
!PLS HELP I WILL GIVE BRAINLEST!
The net of a rectangular prism is shown
What is the surface area of this prism?
The answer would be 18 square units
Step-by-step explanation:
When talking about surface area, just add up all the units that is listed in the question. - just a tip ;)
Anyways, Hope this helps!! If it's wrong, feel free to curse me out.. haha...
Razon trigonometría que se requiere para calcular la altura de la torre si desde una distancia de 50 m se observa su punto mas alto con un ángulo de 48
Answer:
se supone que debes usar el SINE RATIO ya que se trata del lado opuesto y la hipotenusa.
What are the solutions to this equation?
-7 + (x2 – 19) = 20
-10
5.6
There are no solutions.
10
-5.6
For each of the following properties write down a matrix that has this property or explain why there is no such matrix (Hint: Check first whether the dimensions add up)
(a) The column space contains (1,0,0)T, (0,0,1)T while the row space contains (1,1)T and (1, 2)T.
(b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
(c) The column space is R4 and the row space is R3.
Answer:
a) A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
b) attached below ( Matrix dose not exist )
c) attached below ( Matrix does not exist )
Step-by-step explanation:
a) Matrix
A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
From the matrix ; Column 1 and Column 2 Belong to COL(A)
while : (1,1)^T = ( 1,0 )^T + ( 0,1 )^T i.e. (1,1)^T ∈ Row( A )
and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T i.e. (1, 2)^T ∈ Row( A )
Hence ; all requirements are fulfilled in Matrix A
b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
Matrix is Non-existent because condition is not met
attached below
c) Rank | A |
dimension of column space= 4 , dimension of Row space = 3
Given that ; column space ≠ Row space
Hence Matrix does not exist
the probability that a customer of a network operator has a problem about you needing technical staff's help in a month is 0.01. This operator installs internet for 500 households in a residential area a, Calculate the average number of households in this residential area having internet problems in a certain month
b, Calculate the probability that in 6 consecutive months there is only one month that no customer in this area has a network problem that needs the help of technical staff
Answer:
(a) average calls = 5
(b) probability that there is exactly one call in 6 consecutive monts = 0.038
Step-by-step explanation:
Let event of a customer requiring help in a particular month = H
and event of a customer not requiring help in a particular month = ~H
Given
p= 0.01, therefore
Number of households, n = 500.
Binomial distribution:
x = number of households requiring help in a particular month
P(x,n,p) = C(x,n)*p^x*(1-p)^(n-x)
where
C(x,n) = n!/(x!(n-x)!) is the the number of combinations of x objects out of n
(a) Average number of households requiring help = np = 500*0.01 = 5
(b)
Probability that there are no calls requiring help in a particular month
P(0), q= C(0,n)*p^0(1-p)^(n-0)
= 1*1*0.99^500
= 0.006570483
Applying binomial probability over six months,
q = 0.006570483
n = 6
x = 1
P(x,n,q)
= C(x,n)*q^x*(1-q)^(n-x)
= 6!/(1!*5!) * 0.006570483^1 * (1-0.006570483)^5
= 0.038145
Therefore the probability that in 6 consecutive months there is exactly one month that no customer has called for help = 0.038
The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (Rockwell hardness is measured on a continuous scale.)a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?b. If the acceptable range of hardness is (70-c, 70+c) , for what value of c would 95% of all specimens have acceptable hardness?c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?d. What is the probability that at most eight of ten independently selected specimens have a hardness of less than73.84? [Hint: Y = the number among the ten specimens with hardness less than 73.84 is a binomial variable; what is p?]
Answer:
a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.
b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.
c) Expected number of acceptable specimens among the ten is 7.938.
d) Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Step-by-step explanation:
a )
[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]
b )
[tex]c = 1.96 * 3 = 5.88[/tex] { Since Z = 1.96 for 95% CI refer table.}
c )
Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]
d )
Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Express the following repeating decimal as a fraction in simplest form.
Answer:
[tex]0.\overline{369} = \frac{41}{111}[/tex]
Step-by-step explanation:
x = 0.369369369...
10x = 3.69369369...
100x = 36.9369369...
1000x = 369.369369...
1000x - x = 369
999x = 369
[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]
If the diameter of the Ferris wheel is 70 feet across, find the total distance traveled in one revolution.
Answer: Assuming pi is rounded off to 3.14, it is 219.8 feet; if not it is 70π feet
Circumference=one revoloution
Circumference=Diameter times pi
C=Dπ
C=3.14*70
=219.8
219.8 feet
A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.
9514 1404 393
Answer:
AC = 17
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
Substituting the given expressions, we have ...
(3x +4) +(4x -1) = (6x +5)
x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides
AC = 6x +5 = 6(2) +5
AC = 17
_____
AB = 10, BC = 7
at the present time, gerald is eight less than five times his nephews age. seven years ago gerald was 9 times his nephews age.
(A)if g represents geralds age now and n represents his nephews age today. use a system of equations that could be used to model this scenario?
(B)than use the equations to determine algebraically the ages of both Gerald and his nephew.
(C)than determine in how many years Gerald will be three times as old as his nephew?
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean, ayy
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean
Please help please guys how are you doing
Answer:
the answer of the the triangle is 6
Answer:
6
Step-by-step explanation:
First row:
8 ÷ 2 = 4. → Square: 4
Second row:
14 - 4 = 10.
[two circles] = 10. So, 10÷2 = 5.
Circle = 5
Third Row:
[triangle] + 5 = 11
11 - 5 = 6
Triangle = 6
Which ordered pair (x,y) satisfies the inequality?
Which is correct?????????????
Answer:
It discusses the role of the God in influencing our decisions
Answer:
I believe it is choice D
Step-by-step explanation:
in the excerpt it talks about how sight gives us the ability to observe and experience. it also states "we prefer sight to almost everything else." hope I'm right! ☺️
Kyle buys a bag of cookies that contains 4 chocolate chip cookies, 9 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies. What is the probability that Kyle randomly selects a sugar cookie from the bag, eats it, then randomly selects a peanut butter cookie
Which expression is equivalent to -6(-⅔+2x)?
O-4-12x
O-4+ 2x
O 4-12x
O 4+ 12x
Answer:
4-12x
Step-by-step explanation:
opening the brackets;
(-6×-2/3)- 12x
-2×-2 -12x
4-12x
Answer:
4 - 12x
Step-by-step explanation:
We can find an equivalent expression by distributing
-6(-⅔+2x)
Distribute by multiplying -6 times what's inside of the parenthesis ( -2/3 and 2x )
-6 * -⅔ = 4
-6 * 2x = -12x
We would be left with 4 - 12x
Given that yx is a diameter of V, find mZVX if mYVZ=(15r -1)", mWVX =(8x- 2).mUVW =(7x +15).
and mYVU = 3x + 5).
A 32
B 45°
C 70
D. 134
Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces.
(a)What is the standard deviation of the average fill volume of 22 bags?
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
Answer:
a) 0.0171 fluid ounces.
b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces
c) The mean should be of 6.153 fluid ounces.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
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.
Standard deviation of 0.08 fluid ounces.
This means that [tex]\sigma = 0.08[/tex]
(a)What is the standard deviation of the average fill volume of 22 bags?
This is s when n = 22. So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{0.08}{\sqrt{22}}[/tex]
[tex]s = 0.0171[/tex]
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]
[tex]Z = -12.3[/tex]
[tex]Z = -12.3[/tex] has a p-value of 0.
0% probability that the average fill volume of 22 bags is below 5.95 ounces.
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]
[tex]6.1 - \mu = -3.09*0.0171[/tex]
[tex]\mu = 6.153[/tex]
The mean should be of 6.153 fluid ounces.
What's the area of the trapezoid
Answer:
i dont know just study hard bro
Step-by-step explanation:
Answer:
A =36 ft^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2)h where b1 and b2 are the lengths of the bases
A = 1/2 ( 13+5) *4
A = 1/2 ( 18)*4
A =36 ft^2
What is the median of the following set of numbers?
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD.
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD. ????????????????
Median of the given data is 8.5.
What is median?In statistics, the median is the middle value of the given list of data in order. Data or observations can be sorted in ascending or descending order.
Given data,
1 , 5, 12, 1, 121, 1, 121, 13
Arranging in ascending order
1, 1, 1, 5, 12, 13, 121, 121
Number of elements N = 8
When number of elements is odd
Median = (N/2 th term + (N/2)+1 th term)/2
Median = (8/2 th term + (8/2)+1 th term)/2
Median = (4th term + 5th term)/2
Median = (5+12)/2
Median = 17/2
Median = 8.5
Hence, 8.5 is the median of the given data.
Learn more about median here:
https://brainly.com/question/28060453
#SPJ7
The volume of a rectangular prism is given by 24x3+78x2+49x+10. The height of the prism is given by 2x+5. Find an expression for the area of the base of the prism
Answer:
?
Step-by-step explanation:
i cant not explian that
