Answer:
D. P(5+ 6's) = 0.4063
Step-by-step explanation:
Binomial distribution.
For the distribution to be applicable, the experiment must
1. Have a know and constant number of trials
2. Probability of success of each trial remains constant (and known if available)
3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.
4. Independence between trials.
Let
n = number of trials = 25
p = probability of success of each trial = 1 / 6
x = number of successes (0 ≤ x ≤ n) = 5
C(n,x) = number of combinations of picking x identical objects out of n
Applying binomial distribution
P(x,n) = probability of x successes in an experiment of n trials.
= C(n,x) * p^x * (1-p)^(n-x)
For n = 25 trials with probability of success (roll a 6) = 1/6
and x = 5,6,7,8,...25
It is easier to calculate the complement by
P(5+ 6's) = 1 - P(<5 6's)
= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )
1- (
P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961
P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051
P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532
P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883
P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171
)
= 1 - 0.59373
= 0.40626
= 0.4063 (to 4th decimal place)
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hour is desired. Past studies suggest that a population standard deviation of hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
What is the image point of (-5,9) after a translation left 1 unit and down 1 unit?
Answer: (-6,8)
Step-by-step explanation:
Translation is a rigid motion inn which every point of the figure moved in the same direction and for the same distanceTranslation rules are
Left c units : [tex](x,y)\to(x-c,y)[/tex]
Down c units : [tex](x,y)\to(x,y-c)[/tex]
The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:
[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]
Hence, the image point is (-6,8).
How do you graph y=2/3x-4
━━━━━━━☆☆━━━━━━━
▹ Answer
You can use a graphing calculator.
▹ Step-by-Step Explanation
Attached is a screenshot.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
See explanation and picture attached
Step-by-step explanation:
We can break down this expression into it's core components:
Since the constant here is -4, the y intercept is -4.
Since the value we are multiplying x by is [tex]\frac{2}{3}[/tex], the slope is [tex]\frac{2}{3}[/tex]. This means for every time we go horizontal 3 units, the line increases by 2.
The graph is attached.
Hope this helped!
Answer ASAP, Will give brainliest!!
Answer:
First. 115°
Second. 65°
Third. 65°
Fourth. 7
Fifth. 425.25
First
angle DAB = angle ADC (since this is an isosceles trapezoid)
Second
In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)
180-115 is 65°
Third
(Same reason as second)
Fourth
The side 3x+4 is same as the opposite side
So 3x + 4 = 25
on solving you get x = 7 in
Fifth
[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]
area = 1/2 × 13.5 (20+43)
area = 1/2 × 13.5 × 63
Thus area is 425.25
Answer:
Step-by-step explanation:
1)As ABCD is isosceles trapezium,
∠ADC= ∠DAB
∠ADC = 115°
2) AD //BC
∠ADC + ∠DCB = 180° {co interior angles}
115 + ∠DCB = 180
∠DCB = 180 - 115
∠DCB = 65°
3) As ABCD is isosceles trapezium,
∠CBA = ∠DCB
∠CBA = 65°
4) As ABCD is isosceles trapezium, non parallel sides are congruent.
AB = DC
3x + 4 = 25 in
3x = 25 - 4
3x = 21
x = 21/3
x = 7 in
5) height = 13.5 in
a= 43 in
b= 20 in
Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]
[tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]
A debt of $12,000 with interest at 5% compounded monthly is to be repaid by equal payments at the end of each year for three years and nine months. What is the term of repayment? None 12 months 3.9 years 3.75 years
Answer:
3.75 years
Step-by-step explanation:
If the debt is to be paid in 3 years, 9 months, then the term of the loan is ...
3 9/12 = 3 3/4 = 3.75 . . . years
1. At the end of one school day a teacher had 17 crayons left. The teacher remembered
giving out 14 crayons in the morning, getting 12 crayons back at recess, and giving out
11 crayons after lunch. How many crayons did the teacher have at the start of the
day?
Answer:
30 crayons
Step-by-step explanation:
Let x be the number of crayons he started with
gave out 14 crayons
x-14
Got 12 back
x-14+12
Gave out 11 after lunch
x-14+12 -11
This equals 17
x-14+12 -11 =17
Combine like terms
x-13 = 17
Add 13 to each side
x -13+13 =17+13
x = 30
Answer: 30
Step-by-step explanation:
For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!
Do the ratios 2/3 and 12/18 form a proportion?
yes
no
Answer:
Yes
Step-by-step explanation:
Because 12/18 = 2/3..(cancel 12 and 18 by 6)
Answer:
yes
Step-by-step explanation:
2x6=12
3x6=18
6 is the multiplying number
( the 2 equations are the same amount )
The circle shown above has a radius of 5 units, and the central angle of the sector that is shaded is 25π radians. Determine the area of the shaded sector, in terms of π. Enter the area of the sector.
Answer:
The answer is below
Step-by-step explanation:
Given that:
The radius of the circle (r) = 5 units
The central angle (θ) = 25π
A sector of a circle is the portion of a circle made up of two of its radii and an arc. The area of a sector that subtends with a central angle (θ) and a radius (r) is given by the formula:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2[/tex]
Substituting the radius of the circle and the central angle:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2\\\\Area\ of\ sector=\frac{25\pi}{360} *\pi (5)^2\\\\Area\ of\ sector=\frac{125\pi^2}{72}[/tex]
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
Answer:
2,041 square centimeters
Step-by-step explanation:
surface area = (2 × π × r × h) + ((π × r) × (r+ (√(c² + r²))))+(π × r²)
where,
cylinder base radius (r) = 10 cm
height of cylinder (h) = 16 cm
total height = 28 cm
cone height (c) = total height - height of cylinder = 28 - 16 = 12cm
π = 3.14
surface area = (2 × 3.14 × 10 × 16) + ((3.14 × 10) × (10+ (√(12² + 10²))))+(3.14 × 10²)
surface area = 1004.8 + (31.4 * 25.6) + 314
surface area = 2122.64 cm²
therefore the approximate surface area given is 2,041 square centimeters
E
What is the value of x in the equation 3x.. by y 18, when y27
Answer:
x = 15
Step-by-step explanation:
We need to find the value of x in the equation 3x – y = 18 when y = 27.
To find the value of x, put y = 27 in the above equation.
So,
3x - 27 = 18
3x = 45
x = 15
So, the value of x is 15.
243 as a power of 3
Answer:
243 as a power of 3
= 3^5
=243
What's the correct answer to this..? Need help
Answer:
A.
Step-by-step explanation:
All of those graphs represent functions. You are able to tell because they all pass the vertical line test. The vertical line test is conducted by drawing a line that goes vertically and intercepts any point of the line in question. If the function crosses the vertical line twice, it is not a function. If it only intercepts once, it is a function. In this case, every graph is a function because they would intercept a vertical line once.
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 6 gallons.
Answer:
3.625 gpm
Step-by-step explanation:
The fraction subtracted from 5/3 to get 1 is_____
Answer:
2/3
Step-by-step explanation:
I am not sure
Answer:
2/3Step-by-step explanation:
[tex]Let \:the \: unknown \: fraction \: be \: x\\\\\frac{5}{3} -x = 1\\\\\frac{5}{3}-x=1\\\\\mathrm{Subtract\:}\frac{5}{3}\mathrm{\:from\:both\:sides}\\\\\frac{5}{3}-x-\frac{5}{3}=1-\frac{5}{3}\\\\\frac{5}{3}-x-\frac{5}{3}=-x\\\\1-\frac{5}{3}=-\frac{2}{3}\\-x=-\frac{2}{3}\\\\x=\frac{2}{3}\\[/tex]
Solve: 3a^2-4b a= -6 b= -5 If you could also leave an explanation that would be great! Thank you for your time!
Answer:
128
Step-by-step explanation:
3a² - 4b
plug in values
3(-6)² - 4(-5)
use PEMDAS and simplify (-6)² first
3(36) -4(-5)
multiply
108 + 20
add
128
hope this helps :)
Nina is training for a marathon. She can run 4 1/2 kilometers in 1/3 of an hour. At this pace, how many kilometers can Nina run in 1 hour?
Answer:
Nina can run:
13 1/2 km in 1 hour
Step-by-step explanation:
4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2
proportions:
9/2 hours ⇔ 1/3 hour
N hours ⇔ 1 hour
N = (9/2)*1 / (1/3)
N = (9/2) / (1/3)
N = (9*3) / (2*1)
N = 27/2
27/2 = 26/2 + 1/2 = 13 + 1/2 = 13 1/2
Nina can run:
13 1/2 km/h
13 1/2 km in 1 hour
Nina can run [tex]13\frac{1}{2}[/tex] km in an hour
The distance Nina can run in an hour can be determined by dividing the distance she can run in 1/3 of an hour by 1/3
Distance Nina can run in an hour = distance run ÷ [tex]\frac{1}{3}[/tex]
[tex]4\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]
Convert the mixed fraction to an improper fraction [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex]
Convert the improper fraction back to an mixed fraction = [tex]13\frac{1}{2}[/tex] km
To learn more about fractions, please check:
https://brainly.com/question/21449807?referrer=searchResults
Evaluate without actual multiplication 1) 95x96 2)103x107
Answer:
:
"(100 + 3) (100 + 7)
Now, by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = 3 , b = 7
= (100)² + (3+7)*100 + (3*7)
= 10000 + 1000 + 21
= 11021
.
(110 - 7) (110 - 3)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = (-7) , b = (-3)
= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}
= 12100 + (-10)*110 + 21
= 21200 - 1100 + 21
= 11021
.
➖➖➖➖➖➖➖➖➖➖
.
(90 + 5) (90 + 6)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 90 , a = 5 , b = 6
= (90)² + (5+6)*90 + (5*6)
= 8100 + 990 + 30
= 9120
.
(100 - 5) (100 - 4)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = (-5) , b = (-4)
= (100)² + { (-5) + (-4) }*100 + 20
= 10000 + (-9)*100 + 20
= 10000 - 9000 + 20
= 10020 - 900
= 9120
.
➖➖➖➖➖➖➖➖➖➖
.
(100 + 4) (100 - 4)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = 4 , b = (-4)
= (100)² + { 4 + (-4) }*100 + 4*(-4)
= 10000 + (4 - 4)*100 - 16
= 10000 + 0*100 - 16
= 10000 - 16
= 9984
.
(90 + 14) (90 + 6)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 90 , a = 14 , b = 6
= (90)² + (14 + 6)*90 + (14*6)
= 8100 + 20*90 + 84
= 8100 + 1800 + 84
= 9984"
This answer was in another question
This answer was given by BloomingBud
Step-by-step explanation:
Answer:
1) 9120 2) 11021
Step-by-step explanation:
95 * 96 = (100-5)(100-4) = 10000 - 500 - 400 + 20 = 9120
103 * 107 = (100+3)(100+7) = 10000 + 300 + 700 + 21 = 11021
a rectangle is 12 in wide and 18 in tall.if it is reduce to a height of 3 inches, then how wide will it be?
Answer:
2 in
Step-by-step explanation:
18/3=6 , 6 is the scale factor
12/6=2
Answer:
width= 2
Step-by-step explanation:
18 inches is the original height and we are now reducing that to 3 inches.
In order to do that, we have to divide 18 by 3 which equals 6.
Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which equals 2.
Your final answers should be: width= 2
Write the expression 12-2 in simplest form.
Answer:
convert into a whole number 6
what is the lcm of 7÷25 and 3÷25
Answer:
LCM of 7/25 and 3/25 is 25
Step-by-step explanation:
The full meaning of LCM is Lowest (Least) Common Multiple
Lowest (Least)Common Multiple can be defined as the lowest or least number that is the multiple of two or more number. Note that this least number is not zero
Lowest(Least) common Multiple when applied to fractions is the least number that is the multiple of the denominators of the fraction.
In the above question, we are asked stop find the LCM of 7÷25 and 3÷25
= LCM of 7/25 and 3/25
The two denominators are the same, hence, the LCM is 25.
which one is irrational?
Basically everything but choice C
==========================================
Explanation:
sqrt is shorthand for square root
sqrt(4) = 2 = 2/1 showing that sqrt(4) is rational. We can write it as a fraction of two whole numbers, where 0 is not in the denominator.
-------
In contrast, we cannot write sqrt(2), sqrt(3), or sqrt(5) as a fraction of two whole numbers. Using your calculator, note how
sqrt(2) = 1.4142135623731
sqrt(3) = 1.73205080756888
sqrt(5) = 2.23606797749979
all of those decimal expansions go on forever without any pattern, which is a sign that those numbers are irrational. If they were rational, then a pattern would repeat at some point or the decimals would terminate at some point.
Answer:
a, b, d are irrational
Step-by-step explanation:
root 2 = 0.414.....
root 3 = 0.732.....
root 5 = 2.236.....
Hope this helps.....
Pls mark my ans as brainliest
If u mark my ans as brainliest u will get 3 extra points
A line passes through point (4,-3) and has a slope of 5/4. Write an equation in Ax + By = C
Answer:
The answer is
5x - 4y = 32Step-by-step explanation:
To write an equation of a line using a point and slope use the formula
y - y1 = m(x - x1)where
m is the slope
(x1 , y1) is the point
So we have
Equation of the line using point (4 , -3) and slope 5/4 is
[tex]y + 3 = \frac{5}{4} (x - 4)[/tex]
Multiply through by 4
4y + 12 = 5(x - 4)
4y + 12 = 5x - 20
5x - 4y = 20 + 12
The final answer is
5x - 4y = 32Hope this helps you
i need help with this question
Answer:
1000ml
Step-by-step explanation:
4 days she drank ½ of the bottle
so she drank ⅛ l of juice everyday
so
1000ml is the answer
standard form of 6,32,94,000
Answer:
6.3294✖️10^7
Step-by-step explanation:
To find the statdard form, you place the decimal after the largest unit, int his case 6.
Then you write down all the numbers except for "0".
This becomes:
6.3294
Then, you add the multiplying sign, and count how many digits are there after 6, and in this case, there are 7, so you add the power "7" after 10.
6.3294✖️10^7
Hope this helped!
Have a nice day:)
Find the next three terms in the geometric sequence.
Answer: D
Step-by-step explanation:
The common difference is -2/3 so using the last term which is -8/27 multiply it by -2/3 to find the next terms.
[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]
[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]
[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]
is 1 whole 1 by 3 considered as an integer??
Answer:
No it's not.
Step-by-step explanation:
[tex]1 \frac{1}{3} = \frac{4}{3} = 1.333333[/tex]
Integers are set of numbers consisting
Whole numberNatural numberNegative numbersIt doesn't consist
Fractions &DecimalsHope this helps ;) ❤❤❤
Answer:
[tex]\boxed{\sf No}[/tex]
Step-by-step explanation:
[tex]\displaystyle 1 \frac{1}{3} =1.3333333...[/tex]
Integers are whole numbers that can be positive or negative. Integers do not include fractions and decimals.
if a man works 400km in 6 minutes.How long will he work in 9 minutes
Answer:
600 kmStep-by-step explanation:
400 km = x
6 min 9 min
cross multiply:
6x = 400 ( 9)
x = 3600 / 6
x = 600 km
Write an expression that can be used to find the price of a television that is on sale for 20% off the regular price of p dollars. Can you write a second expression equivalent to the one you wrote in the last questions.
Answer:
The expression that could help calculate the price of the TV is;
$P - 20% of $P
Step-by-step explanation:
Here, we want to write an expression that corresponds to the price of a television set that is on sale at a price which is 20% off the regular price.
From the question, we can see that the regular price is $P
So now we are having 20% off;
This corresponds to;
20/100 * p = p/5 = 0.2p
So in the expression form, we can have;
$P - 20% of $P
Given that ΔABC is a right triangle with the right angle at C, which of the following is true?
1. tan A = 1/(tan B)
2. tan A = sin B
3. cos A = 1/(cos B)
4. sin B = 1/(sin A)
Answer:
1. tan A = 1/(tan B)
Step-by-step explanation:
By definition,
tangent A = opposite / adjacent = a / b
and
tangent B = opposite / adjacent = b / a
Therefore tangent A = a/b = 1/tan(B)
Answer: Tan a=tan b
I belive
Step-by-step explanation:
Plz Help I Will Mark Brainliest If Right!!!!!!!!!!!!!!!!!!!!!!!
Determine the domain of the function.
f as a function of x is equal to the square root of one minus x.
A). All real numbers
B). x > 1
C). x ≤ 1
D). All real numbers except 1
Hey There!!~
Your best answer choice is B). x > 1.
Good Luck!!
