Answer: B. (5,2)
Step-by-step explanation:
Help bestiess
7x=5x÷67
Answer:
7x=5x/67
Step-by-step explanation:
PLEASE HELP
Which function is equivalent to f(x) = 10x2 – 17x + 3? A f(x) = (5x – 1) (2x + 3) B f(x) = (5x – 3)(2x – 1) cf(x) = (5x – 1) (2x – 3) D f(x) = (5x – 3)(2x + 1)
Answer:
f(x) = 10x2 – 17x + 3
f(x) = 10x2 – 15x -2x + 3
f(x) = 5x(2x – 3) -1(2x - 3)
f(x) = (2x – 3)(5x -1)
Step-by-step explanation:
Consider
In square ABCD, the diagonals intersect at G.
If mLAGD = a + 2b and mzABC = 2a - b, find the values of
a and b.
C
Answer:
a = 54
b = 18
Step-by-step explanation:
ABCD is a square. It's diagonals AC and BD intersects at G.
Since, diagonals of a square bisects at right angles.
[tex] \therefore m\angle AGD = 90\degree [/tex]
[tex] \implies a + 2b = 90\degree [/tex]
[tex] \therefore a = 90\degree - 2b.....(1)[/tex]
Since, measure of each angle of a square is right angle.
[tex] \therefore m\angle ABC = 90\degree [/tex]
[tex] \implies 2a-b = 90\degree.......(2) [/tex]
From equations (1) & (2)
2(90° - 2b) - b = 90°
180° - 4b - b = 90°
-5b = 90° - 180°
-5b = - 90°
b = - 90°/(-5)
b = 18
Plug b = 18 in equation (1)
a = 90° - 2*18
a = 90° - 36°
a = 54
3. Which pair is a solution to the equation?
2a – 4b = 12
(1,-3)
(0, -1)
(6,0)
I
(2,3)
Answer:
(6,0)
Step-by-step explanation:
The Chartered Financial Analyst (CFA) Institute reported that 63% of its U.S. members indicate that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry. (Data extracted from Global Market Sentiment Survey 2014, cfa.is/1dzvdF8.) Suppose that you select a sample of 100 CFA members.
a. What is the probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between 62% and 67
b. The probability is 90% that the sample percentage will be contained within what symmetrical limits of the population percentage?
c. The probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage?
d. Suppose you selected a sample of 400 CFA members. How does this change your answers in (a) through (c)7
Answer:
a. The probability that the percentage will be between 62% and 67% is 0.378348
b. For the central 90% the lack of trust in the financial industry is between 55.282% and 70.92%
c. For the probability within the central 95%, the lack of trust in the financial industry is between 56.77% and 56.77%%
d. Increasing the sample size increases the sensitivity and narrows the ranges and values
Step-by-step explanation:
a. The percentage of the CFA members that indicated that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry, p = 63%
The test statistic is given as follows;
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}[/tex]
p = 63% = 0.63
q = 1 - p = 0.37
a. When [tex]\hat p[/tex] = 62%, we get;
[tex]z=\dfrac{0.62-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} \approx -0.2071[/tex]
From the z-table the p-value p(z <-0.2071) = 0.42074, from the calculator, we get the more accurate value as p = 0.4179563
When [tex]\hat p[/tex] = 67%, we get;
(0.67 - 0.63)/((0.63*0.37)/100)^(0.5)
[tex]z=\dfrac{0.67-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} \approx 0.82849302133[/tex]
From the z-table the p-value p(z < 0.8) = 0.79673, from the calculator, we get the more accurate value as p(z < 0.828493) = 0.7963043
Therefore, using the calculator values, the probability that the percentage will be between 62% and 67% = 0.7963043 - 0.4179563 = 0.378348
The probability that the percentage will be between 62% and 67% = 0.378348
b. For the central 90% symmetrical limit, we get;
[tex]P\left(Z \le \dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}}\right) = 0.05[/tex]
Therefore;
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} = \phi^{-1}(0.05)[/tex]
z = -1.64
Therefore;
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} \approx -1.64[/tex]
x = -1.64×√(0.63*0.37/100) + 0.63 ≈ 0.55282, which is 55.282%
Similarly, we get;
[tex]P\left(Z \geq \dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}}\right) = 0.95[/tex]
Therefore;
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} = \phi^{-1}(0.95)[/tex]
z = 1.64
Therefore;
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} \approx 1.64[/tex]
x = 1.64×√(0.63*0.37/100) + 0.63 ≈ 0.7092, which is 70.92%
Therefore, the central 90% is between 70.92% and 55.282%
Therefore, the lack of trust in the financial industry is between 55.282% and 70.92%
c. Given that the probability is 95%, we get
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} = \phi^{-1}(0.025)[/tex]
Therefore;
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} \approx -0.67[/tex]
x = -0.67×√(0.63*0.37/100) + 0.63 ≈ 0.5977 = 56.77%
Similarly, we have;
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} = \phi^{-1}(0.975)[/tex]
Therefore;
[tex]\dfrac{x-0.63}{\sqrt{\dfrac{0.63 \times 0.37}{100}}} = 1.96[/tex]
x = 1.96×√(0.63*0.37/100) + 0.63 ≈ 0.72463 =%
Therefore, at a probability of 95%, the lack of trust in the financial industry is between 56.77% and 56.77%%
d. Increasing the sample size increases the sensitivity and narrows the ranges and values such that we get;
For a) z = 0.62-0.63×√(0.63*0.37/400) ≈ 0.605
P ≈ 0.72907
0.67-0.63×√(0.63*0.37/400) ≈ 0.655
P ≈ 0.74527 - 0.72907 = 0.0162 = 1.62%
For b)
The p-value = 0.74527 -
-1.64×√(0.63*0.37/400) + 0.63 ≈ 0.5904 ≈ 59.04%
1.64×√(0.63*0.37/400) + 0.63 ≈ 0.7 = 70%
For c)
x = -0.67×√(0.63*0.37/400) + 0.63 ≈ 0.61383= 61.83%
x = 1.96×√(0.63*0.37/400) + 0.63 ≈ 67.73=%
If AC is the perpendicular bisector of BD and BD is the perpendicular bisector of AC, then how is triangle APB congruent to triangle CPB?
Answer:
AB=BC
4X-1=1+2x so x=1 and both sides are 3
Step-by-step explanation:
since bd is a perpendicular bisector the two triangles formed are congruent so AB=BC
4X-1=1+2x so x=1 and both sides are 3
Someone help and plz make sure it’s right
Answer:
9.4km
Step-by-step explanation:
6.2^2 +7.1^2 = x^2
so 38.44+ 50.41= 88.85
x^2= 88.85 so x = 9.4
Sorry if it's really confusing lol, if you need help i could explain it further but your answer is 9.4
plEASE HELP ME plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
24 people were in the sample !
Help ASAP please
Which algebraic expressions are like terms with 16K. Choose all that apply .
I need help ASAP !!!!!!!!!!
Answer:
the first one
Step-by-step explanation:
-.8x + 4.8y + 16
hope this helps
A number is chosen at random from the first 7 integers. Find the probability that the number is a multiple of 3
pls help im doing my stats exam
Answer:
2/7 (29%)
Step-by-step explanation:
out of 7 there are only 2 multiples of 3, (3 & 6) therefore 2/7 integers are multiples of 3
what's the value of given expression
[tex] \sqrt{ {20 + 5}^{2} } [/tex]
Step-by-step explanation:
√(20+5²)=√{20+25}=√45=3√5
a square was altered so that one side is increased by 9 inches and the other side is decreased by 2 inches. the area of the resulting rectangle is 60 square inches. What was the are f the original square.
Answer:
36 square inches.
Step-by-step explanation:
Since the original figure was a square, all four side lengths are equivalent. The area for the square will be:
[tex]A=s^2[/tex]
Where s is the length of one side.
One side is increased by nine inches and the other side was decreased by two inches. The area of the resulting rectangle is 60 square inches.
So, one of the new sides is (s + 9).
And the other is (s - 2).
The area with these dimensions is 60. Thus:
[tex]60=(s-2)(s+9)[/tex]
Solve for s. Distribute:
[tex]60=s^2+7s-18[/tex]
Isolate the variables:
[tex]s^2+7s-78=0[/tex]
Factor:
[tex](s+13)(s-6)=0[/tex]
Zero Product Property:
[tex]s+13=0\text{ or } s-6=0[/tex]
Solve for each case:
[tex]s=-13\text{ or } s=6[/tex]
A side length cannot be negative. So, our only solution is:
[tex]s=6\text{ inches}[/tex]
Since each side of the square measures six inches, the area of the original square will be 36 square inches.
Please help me !! Find the missing length indicated.
Answer:
Step-by-step explanation:
use the law of Cosines so that you can solve a SSS triangle
Cos(C) = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - [tex]c^{2}[/tex] / 2ab
c is the side of 24 for our triangle and angle C is the top one in the picture.
C = arcCos ( [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - [tex]c^{2}[/tex] / 2ab )
C = arcCos ( -32 / 480 )
C = 93.82255373 °
the angles at the top are each half of that or 46.91127 °
let's solve another angle for the big triangle now let's go for the one on the left and call it A
Cos(A) = [tex]c^{2}[/tex] + [tex]b^{2}[/tex] - [tex]a^{2}[/tex] / 2bc where a = 20
A = arcCos( [tex]c^{2}[/tex] + [tex]b^{2}[/tex] - [tex]a^{2}[/tex] / 2bc)
A = arcCos( [tex]24^{2}[/tex] + [tex]12^{2}[/tex] - [tex]20^{2}[/tex] / 2*12*24
A = arcCos(320 / 576)
A = 56.2510 °
then angle B is 180 =93.823 + 56.251 + B
29.926 ° = B
so now we know all 3 angles.. seems like a lot of work , huh :D
for the triangle with the question mark we now know two angles and the Hyp, so let's use Law of Sines to find that last side :)
Sin(A)/a = Sin(B) /b where A can be the angle at the top and B can be the angle at the base. which we have to find still :/
it's 180 = 46.9112 + 29.926 + B
103.162 = B
Sin(46.91127 ) / a = Sin(103.162) /20
Sin(46.91127 ) * 20 / Sin(103.162) = a
14.99998 = a I feel confident this is supposed to be 15 and I have a tiny bit of rounding error..
? = 15 there you go
your answer is 15
based on the graph which period of history could best described as "the beginnings of the slave trade in North America
A . 1701 - 1721
B . 1761 - 1770
C . 1721 - 1750
D . 1750 - 1761
HELP ME PLEASE ASAP!
Using the given segment lengths, find the value of the missing length x.
In a lottery there are 37 balls.
What is the probability of a particular ball being drawn first?
Answer:
1/37
Step-by-step explanation:
Its only talking about 1 ball so its a 1 and 37 chance of a particular ball being drawn.
Solve for the measure of each angle. Trigonometry.
Answer:
∠A=26º
∠B=137º
∠C=17º
Step-by-step explanation:
We can use the Law of Cosines because we have all 3 side lengths.
cosA = [tex]b^2+c^2-a^2/2bc[/tex]
cosA=28^2+12^2-18^2 / 2(28)(12)
cosA=604/672
cos-1(604/672
angle A ≈ 26º
cosB = [tex]c^2+a^2-b^2/2ca[/tex]
cosB=-316/432
cos-1(-316/432
angle B ≈ 137º
26+137=163
180-163=17
angle C ≈ 17º
pls will heart and give 5 stars if you answer within 2-3 min
Answer:
v=Bh
12*8= 96. <---B
2 <----h
v=192
Step-by-step explanation:
I hope that helps
I need help on this plz thx
Answer:q=3
Step-by-step explanation:
14 multiplied by 3 equals 42
Answer: q = 3
Step-by-step explanation:
14q/14 = 1q
42/14 = 3
1q = 3
q = 3
Find LM
a. 4.5
b.2
c.5.5
d.48
PLEASE ANSWER WILL MARK BRAINLIEST
Answer:
c. 5.5
Step-by-step explanation:
A scale on a blue print drawing of a house shows that 10 centimetres represents 22 meters.
What number of actual meters are represented by 18 centimetres on the blue print?
Answer:
39.6
Step-by-step explanation:
if
10=22
18=x
18x22=396/10= 39.6
find the value of given expression
[tex] \sqrt{22\times 22} [/tex]
Answer:
hello!!
your answer is 22
Step-by-step explanation:
what is the next term for 1/2 1/4 1/81/16
Answer:
1/32
Step-by-step explanation:
Because each denominator is multiplied by 2
Solve the inequality -8 - 1/3n < -25
A scale drawing of Juanita‘s back porch is shown.
Using the scale, how long is Juanita‘s 8 foot long swing in the scale drawing?
Scale: 1/2 inch=4 feet
Select one:
2 inches
8 inches
4 inches
1 inch
PLEASE HELP I GOT 5 MINUTES
Answer:
1 inch
Step-by-step explanation:
IT ONE INCH NOW HURRY!!!
If 5 fidgets cost $35, then how much would 2 fidgets cost?
what is number 9 if you leave a step by step ill mark you as best question
A: 82 dollors per month
B. 50 per month
i need help this is dude tomorrow
Answer:
Answer is D hope this helps
Step-by-step explanation:
You are flying a kite and have left out 50M of string. The kites angle of elevation with the ground is 25°. If the strings stretch straight how high is the kite above the ground.
Round your answer to the nearest 10th of a metre.
Answer:
21.13 m
Step-by-step explanation:
Height of the string, (Hyoptenuse) = 50 m
The kite makes an angle of elevation with the ground of 25°.
We need to find how high is the kite above the ground. Let it is h. We can find it using trigonometry as follows :
[tex]\sin\theta=\dfrac{P}{H}\\\\h=H\sin\theta\\\\h=50\times \sin(25)\\\\H=21.13\ m[/tex]
So, the required height is 21.13 m.