For each probability, transform the normal random variable X with mean 19 and s.d. 4.04 to a standard normal random variable Z with mean 0 and s.d. 1, using the rule
Z = (X - 19) / 4.04
(a) Pr[15 ≤ X ≤ 20] = Pr[(15 - 19)/4.04 ≤ (X - 19)/4.04 ≤ (20 - 19)/4.04]
… ≈ Pr[-0.9901 ≤ Z ≤ 0.2475]
… ≈ Pr[Z ≤ 0.2475] - Pr[Z ≤ -0.9901]
(since Z is a continuous random variable)
… ≈ 0.4367
(b) Pr[X > 20] = Pr[(X - 19)/4.04 > (20 - 19)/4.04]
… ≈ Pr[Z > 0.2475]
… ≈ 1 - P[Z ≤ 0.2475]
(taking the complement probability)
… ≈ 0.4023
(c) Pr[X < 15] = 1 - Pr[15 ≤ X ≤ 20] - Pr[X > 20]
(also taking the complement)
… ≈ 0.1611
Factorise fully 12x + 18y
Answer:
6(2x + 3y)
Step-by-step explanation:
6 is the largest greatest common factor you can take out. As all powers are 1, nothing else can be done.
The factorize form of the expression 12x + 18y is 6(2x+3y)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 12x + 18y
Twelve times of x plus eighteen times of y
x and y are the variables in the expression
Let us factorize the expression
The Gcd of 12 and 18 is 6
So take 6 as common from the expression
6(2x+3y)
Hence, the factorize form of the expression 12x + 18y is 6(2x+3y)
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Which phase change takes place when heat is removed from water?
A. Liquid to gas
B. Solid to liquid
C. liquid to solid
Answer:
I don't see an option Gas to liquid but the correct answer will be gas to liquid.
Explanation:
If u heat water will evaporate and form water vapour (gas form). Anytime heat is released from a gas, it will change forms to be a liquid. It is like reverse condensation.
The number of manatee deaths along the Florida coast was recorded each year from 1977 to 1990. Below is a regression printout for number of deaths versus number of boats for each of the 14 years. Which of the following would give a 95% confidence interval for the slope of the regression line?Regression AnalysisThe regression equation isDeaths = - 41.4 + 0.125 BoatsPredictorCoefStdevt-ratiopConstant-41.4307.412-5.590.000Boats0.124860.012909.680.000s = 4.276 n = 15 R-sq = 88.6% R-sq(adj) = 87.7%0.125± 2.160(.013)0.125± 2.145(.013)0.125± 2.179(.013)0.125± 2.179(4.276)0.125± 2.145(4.276)
the anser is 333399999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
which is equivalent to this equation
Answer:
The correct option is (b).
Step-by-step explanation:
We need to find the value of the given expression i.e.
3⁷ × 3⁻⁴
We know that, one of the property of exponent is:
[tex]x^{-a}=\dfrac{1}{a}[/tex]
So,
[tex]3^7\times 3^{-4}=3^7\times \dfrac{1}{3^4}\\\\=3^3\\\\=27[/tex]
Hence, the correct option is (b).
8;3;-2:-7:12 calculate the nth term
Answer:
45544554554554445455544
Step-by-step explanation:
31 more than a number is 12
Answer:
-19.
Step-by-step explanation:
-19+31 gets you 12.
Identify each triangle based on angles. (Acute, Obtuse or Right)please I don’t understand this
Answer:
45
Step-by-step explanation:
Answer:
2. right
3.obtuse
hope this helps
have a good day :)
Step-by-step explanation:
What is the differential means?
Answer:
Diffrence is the mean of differential
Write the Plural! Spanish, help!!
Please help me I need these ASAP. I'll mark as brilliant!
make c the subject: (a+c)^2=t
make x the subject: p=3(y+2x)^2
[tex](a + c) ^{2} = t \\ c = \sqrt{t } - a \\ c = - \sqrt{t} - a[/tex]
[tex]p = 3(y + 2x) ^{2} \\ x = \frac{ \sqrt{3p} }{6} - \frac{y}{2} \\ x = - \frac{ \sqrt{3p} }{6} - \frac{y}{2} [/tex]
PLEASE HELP ASAP/ SOON
THANK YOU
Find the sum, if it exists, of the infinite geometric series that is related to the infinite geometric sequence {1,521, ; 1,369 ; 1,232; ...}. Round the value of r to the nearest hundredth, if needed
S = 16,643
S = 15,210
The infinite geometric series diverges.
S = 12,560
9514 1404 393
Answer:
(b) S = 15,210
Step-by-step explanation:
The common ratio is ...
r = 1369/1521 ≈ 0.90
So, the sum is ...
S = 1521/(1 -r) = 1521/0.10 = 15,210 . . . . . sum of the series
9514 1404 393
Answer:
(b) S = 15,210
Step-by-step explanation:
The common ratio is ...
r = 1369/1521 ≈ 0.90
So, the sum is ...
S = 1521/(1 -r) = 1521/0.10 = 15,210 . . . . . sum of the series
a serving of crackers has 1.5 grams of fat. How many grams of fat are in 3.75 servings
Answer:
5.625
Step-by-step explanation:
You just have to multiply 1.5 by 3.75 which is 5.625.
So there are 5.625 grams of fat in 3.75 servings.
5.625 grams of fat are in 3.75 servings.
You just have to multiply 1.5 by 3.75 which is 5.625.
So there are 5.625 grams of fat in 3.75 servings.
What is a Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
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A and B are independent events. P(A) = 0.50 and P(B) = 0.30. What is
PA and B)?
Answer:
0.15
Step-by-step explanation:
Find the value for a,b,c,d
9514 1404 393
Answer:
B. a = 10√3, b = 5√3, c = 15, d = 5
Step-by-step explanation:
When you examine the angles of these triangles, you see that all of the triangles are 30°-60°-90° triangles, so ratios of corresponding sides are the same.
Examining the answer choices, you see that all of them agree that ...
a = 10√3, c = 15
Since b is the long leg of the smallest triangle, you know that b > d. This is only the case in answer choices B and D.
The leg marked 'a' is the long leg of the largest triangle, whose short leg is 10. That is the ratio of the longer to shorter legs is 10√3 : 10 = √3 : 1. The ratio of 'b' to 'd' needs to be the same, matching only answer choice B.
__
The ratios of the sides of a 30-60-90 triangle are 1 : √3 : 2. This tells you that ...
d = 10/2 = 5
c+d = 10×2 = 20 ⇒ c = 20 -5 = 15
b = 5√3
a = 10√3
As a check, c = b×√3 = (5√3)(√3) = 5·3 = 15. (matches above)
Can someone help me?
Answer:
Second one: (1,2) (2,4) (3,6)
Step-by-step explanation:
y = 2x
2 = 1(2)
4 = 2(2)
6 = 2(3)
Answer:
(1,2),(2,4),(3,6)
Step-by-step explanation:
y = 2x
y = 2(1)
y = 2
y = 2x
y = 2(3)
y = 6
y = 2x
y = 2(2)
y = 4
x axis and y axis of each coordinate match with equation
Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of the minor axis: (1, 7), (7, 7)
Answer:
The standard form of the ellipse is [tex]\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1[/tex].
Step-by-step explanation:
The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:
[tex](h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)[/tex] (1)
If we know that [tex]V_{1} (x,y) = (4,0)[/tex] and [tex]V_{2}(x,y) = (4, 14)[/tex], then the coordinates of the center are, respectively:
[tex](h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)[/tex]
[tex](h,k) = (2,0) + (2, 7)[/tex]
[tex](h, k) = (4, 7)[/tex]
The length of each semiaxis is, respectively:
[tex]a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}[/tex]
[tex]a = 3[/tex]
[tex]b = \sqrt{(4-4)^{2}+(0-7)^{2}}[/tex]
[tex]b = 7[/tex]
The standard equation of the ellipse is described by the following formula:
[tex]\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1[/tex]
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the ellipse.
[tex]a[/tex], [tex]b[/tex] - Length of the orthogonal semiaxes.
If we know that [tex]h = 4[/tex], [tex]k = 7[/tex], [tex]a = 3[/tex] and [tex]b = 7[/tex], then the standard form of the ellipse is:
[tex]\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1[/tex]
(Click on the picture to see question) please help me!
Hi there! Using one of the logarithmic property below:
[tex] \large \boxed{ log_{a}(b) = n \longrightarrow {a}^{n} = b}[/tex]
From the equation:
[tex] \large{ log_{2}(y) = x + 7}[/tex]
Therefore,
[tex] \large{ {2}^{x + 7} = y} \\ \large{y = {2}^{x + 7} }[/tex]
Answer
y = 2^(x+7) the second choice.2w+22=-6(w+7) what is the answer for w
Answer:
w=-8
Step-by-step explanation:
2w+22=-6(w+7)
2w+22=-6w-42
8w+22=-42
8w=-64
w=-8
Therefore, w=-8
Answer:
w = -8
Step-by-step explanation:
2w+22=-6(w+7)
2w+22 = -6w - 42
8w +22 = -42
8w = -64
w= -64/8
w = -8
An executive board consists of a president (P) and three vice-presidents ( V 1 , V 2 , V 3 ) . For a motion to pass it must have yes votes from three of the voting members, one of which must be the president's. A weighted system that could represent this situation is:_________
Answer:
[P, V1, V2]
[P, V1, V3]
[P, V2, V3]
Step-by-step explanation:
From the question, the executive board has 4 persons.
P = president
V1 = vice president 1
V2 = vice president 2
V3 = vice president 3
The president must be part of three members formed from these 4 to vote yes for a motion to pass
The weighted system can be represented as
[P, V1, V2]
[P, V1, V3]
[P, V2, V3]
These are the 3 possibilities.
Name:
Date:
TRIGONOMETRIC IDENTITIES - DAY #1
ALGEBRA 2 WITH TRIGONOMETRY - HOMEWORK
Answer:
4567,4678..............
Help me PLEASEEEEEEEEEEEEE
Answer:
D. 144
Step-by-step explanation:
find the volume of the shipping container and divide it by the volume of a box.
[tex]2\frac{2}{3}[/tex] × [tex]1[/tex] × [tex]2[/tex] = [tex]\frac{16}{3}[/tex]
[tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{27}[/tex]
[tex]\frac{16}{3}[/tex] divided by [tex]\frac{1}{27}[/tex] is 144.
Find the median of the following numbers. 15, 28, 44, 42, 32, 48
Answer:37
Step-by-step explanation:
Answer:
37
Step-by-step explanation:
First, sort the data in increasing order.
15, 28, 32, 42, 44, 48
The number of data is even (there are 6 numbers), so there isn't one in the middle. In that situation, you average the middle 2 data (32 and 42).
(32 + 42)/2 = 74/2 = 37
If there IS a middle numbe, just use it.
Electrical power (P) is measured in watts using the formula P = V · I where V is the voltage in volts and I is the current in amperes. If there are 40 volts running to a light bulb of 60 watts, how much current is flowing through the light bulb?
Answer:
1.5 amps
Step-by-step explanation:
P = V.I
60 = 40.I
60/40 = 40.I/40
I = 1.5
Jeremy is randomly selecting an outfit to celebrate Probability Day at his school. He can choose from a green (G) or purple (P) shirt, denim (D) or khaki (K) pants, argyle (A) or crew (C) socks, and boots (B), sneakers (S). What is the probability that Jeremy will select an outfit that includes flip-flops (F) and argyle (A) socks?
Which table represents a function? Please respond within 5 minutes!
Answer:
The last one at right bottom
Answer:
Is bottom left
Step-by-step explanation:
A man buys a marker at Rs. 40 and sells it at Rs. 50. What is the profit percentage?
Answer:
may be 10%hope it helps uh
A certain television station has been providing live coverage of a particularly sensational criminal trial. The station's program director wishes to know whether more than half the potential viewers prefer a return to regular daytime programming. A survey of randomly selected viewers is conducted. Let p represent the proportion of all viewers who prefer regular daytime programming. What hypotheses should the program director test to answer the question of interest
Answer:
H0 : p = 0.5
H1 : p > 0.5
Step-by-step explanation:
The the claim to test and determine if a signifant evidence for is if more than half of viewers want a return to original day time program. Since, this is
Since, p is the proportion who prefer the regular day time program;
The hypothesis to test is :
If p > 0.5 `; this represents the alternative hypothesis which we want to check if it we have significant evidence to adopt the claim.
The Null value on the other hand will take the a proportion equal to the p: and it is the initial truth until the alternative has a strong evidence to reject the null.
The null ;
H0 : μ = 0.5
help needed with math
Answer:
angle y = 49°
Step-by-step explanation:
If AB = AD and BC = DC, then the two triangles are isosceles triangles. The altitude from the top to the base divides the top angle into two equal angles, with 90° angles at the base. If angle C is divided into two equal angles (41°) and at the base is a 90° angle, that makes angle CBD 49°. On an isosceles triangle, the two angles opposite to the equal sides are identical. So angle y is identical to angle CBD.
When 0.3(4x-8)-0.5(-2.4x+4) is simplified. What is the resulting expression?
Answer:
2.4x-4.4
Step-by-step explanation:
0.3(4x-8)-0.5(-2.4x+4)
DISTRIBUTE: 1.2x-2.4+1.2x-2
COMBINE LIKE TERMS: 2.4x-4.4
your answer is: 2.4x-4.4
I need help doing my homework
Answer:
A= πr^2
45=πr^2
45/1 =22/7×r^2
45/1=22r^2/7 cross multiply
22r^2 ×1=45×7
22r^2=315 divide both sides by 22
22r^2/22=315/22
r^2=14.318