Answer:
The answer is 405cm³Step-by-step explanation:
Volume of a pyramid is given by
[tex]V = \frac{1}{3} \times area \: of \: base \: \: \times height[/tex]
height = 15cm
From the question the pyramid is a square pyramid which means it's base is a square
Area of a square = l²
where l is the length of one side
l = 9cm
Area of square = 9² = 81cm²
So the volume of the pyramid is
[tex]V = \frac{1}{3} \times 81 \times 15[/tex]
[tex]V = 27 \times 15[/tex]
We have the final answer as
V = 405 cm³
Therefore the volume of the pyramid is
405cm³Hope this helps you
(05.06A LC)
Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B'. What is the length
of A'B'?
1 unit
4 units
5 units
6 units
Answer:
4 units
Step-by-step explanation:
A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.
If a shape is transformed, the length of its sides and shape remains the same, only the position changes.
If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:
Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:
[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:
[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
AB = A'B' = 4 units
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?
Answer:
federal loans = $29,000
private loans = $14,000
Step-by-step explanation:
x + y = 43000
.045x + .02y = 1585
x = 29,000
y = 14,000
Answer:
Amount of loan from federal : $ 29,000
Amount of loan from private bank : $ 14,000
Step-by-step explanation:
We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.
If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -
x + y = 43,000
At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -
0.045x + 0.02y = 1585
Let's solve the following system for x and y, the amount of each loan,
[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )
[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )
[tex]1935-0.025y=1585[/tex],
[tex]1935000-25y=1585000[/tex],
[tex]-25y=-350000[/tex],
[tex]y=14000[/tex],
[tex]x=29000[/tex]
Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.
8 sin2 x + cos x - 5 = 0
[tex]8 {sin}^{2} x + cos \: x - 5 = 0[/tex]
[tex]recall \: that \: {sin}^{2} x + {cos}^{2} x = 1[/tex]
[tex]then \: {sin}^{2} x = 1 - {cos}^{2} x[/tex]
then substitute,
[tex]8( 1 - {cos}^{2} x) + cos \: x - 5 = 0[/tex]
After Further Simplication,
[tex]8 {cos}^{2} x - cos \: x - 3 = 0[/tex]
[tex]let \: y = \cos(x) [/tex]
[tex]8 {y}^{2} - y - 3 = 0[/tex]
use quadratic formulae
[tex]y = 0.375 \: or \: - 0.25[/tex]
therefore
[tex] \cos(x) = 0.375 \: or \: - 0.25[/tex]
[tex] x = 70degrees \: or \: 104.5degrees[/tex]
What is 5 feet and 11 inches in inches
Answer:
60
Step-by-step explanation:
5 is 60 inch
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0). Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
A. they are parallel because their slopes are equal.
Step-by-step explanation:
edge 2020
Answer:
its A in egde
Step-by-step explanation:
According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?
Answer:
The probability is [tex]P(X > x ) = 0.19215[/tex]
Step-by-step explanation:
From the question we are told that
Th The population mean [tex]\mu = \$ 1,999[/tex]
The standard deviation is [tex]\sigma = \$ 574[/tex]
The values considered is [tex]x = \$ 2,500[/tex]
Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as
[tex]P(X > x ) = P(\frac{ X - \mu}{\sigma } > \frac{ x - \mu}{\sigma } )[/tex]
Generally
[tex]X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X > x ) = P(Z > \frac{ x - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X > 2500 ) = P(Z > \frac{ 2500 - 1999}{574 } )[/tex]
[tex]P(X > 2500 ) = P(Z >0.87 )[/tex]
From the normal distribution table the value of [tex]P(Z >0.87 )[/tex] is
[tex]P(Z >0.87 ) = 0.19215[/tex]
Thus
[tex]P(X > x ) = 0.19215[/tex]
Find the reciprocal of the equation in standard form. The selected answer is incorrect.
Answer:
C
Step-by-step explanation:
reciprocal of z=1/z
[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with mean 100 lb and 5 lb and standard deviation 1 lb and 0.5 lb, respectively. What percent of filled boxes weighing between 104 lb and 106 lb are to be expected?
a. 67%
b. None
c. 37%
d. 57%
Answer:
Option b. None is the correct option.
The Answer is 63%
Step-by-step explanation:
To solve for this question, we would be using the z score formula
The formula for calculating a z-score is given as:
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
We have boxes X and Y. So we will be combining both boxes
Mean of X = 100 lb
Mean of Y = 5 lb
Total mean = 100 + 5 = 105lb
Standard deviation for X = 1 lb
Standard deviation for Y = 0.5 lb
Remember Variance = Standard deviation ²
Variance for X = 1lb² = 1
Variance for Y = 0.5² = 0.25
Total variance = 1 + 0.25 = 1.25
Total standard deviation = √Total variance
= √1.25
Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,
For 104lb
z = (x-μ)/σ,
z = 104 - 105 / √25
z = -0.89443
Using z score table ,
P( x = z)
P ( x = 104) = P( z = -0.89443) = 0.18555
For 1061b
z = (x-μ)/σ,
z = 106 - 105 / √25
z = 0.89443
Using z score table ,
P( x = z)
P ( x = 106) = P( z = 0.89443) = 0.81445
P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555
= 0.6289
Converting to percentage, we have :
0.6289 × 100 = 62.89%
Approximately = 63 %
Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%
Since there is no 63% in the option, the correct answer is Option b. None.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be
Then the Variance will be
[tex]Var = \sigma ^2[/tex]
Then for X, we have
[tex]Var (X) = 1^2 = 1[/tex]
Then for Y, we have
[tex]Var (Y) = 0.5^2 = 0.25[/tex]
Then the total variance will be
[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]
The total standard deviation will be
[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]
For 104 lb, then
[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]
For 106 lb, then
[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]
Then
[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]
Approximately, 63%.
More about the normal distribution link is given below.
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If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?
Answer:
[tex]\huge\boxed{a=9 ; b = -8}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{ax+b}{x}[/tex]
Putting x = 1
=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]
Given that f(1) = 1
=> [tex]1 = a + b[/tex]
=> [tex]a+b = 1[/tex] -------------------(1)
Now,
Putting x = 2
=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]
Given that f(2) = 5
=> [tex]5 = \frac{2a+b}{2}[/tex]
=> [tex]2a+b = 5*2[/tex]
=> [tex]2a+b = 10[/tex] ----------------(2)
Subtracting (2) from (1)
[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]
For b , Put a = 9 in equation (1)
[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]
what is the distance between the first and third quartiles of a data set called?
Answer:
Interquartile range is the distance between the first and third of a data.
Step-by-step explanation:
Hope it will help you :)
An experimental probability is ______ likely to approach the theoretical probability if the number of trials simulated is larger. A. as B. more C. less D. not
Answer:
B. More
Step-by-step explanation:
This is according to the law of large numbers
An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.
What is an experimental probability and theoretical probability?Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.
An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed
Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.
Learn more about probability here:
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A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t
The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.
Answer:
s = 17 units
Step-by-step explanation:
Given f(t) = t³ - 8t² + 27t
Differentiating f(t), we have
f'(t) = 3t² - 16 t + 27
At t = 0
f'(t) = 27
This is the required obtainaible distance, s.
a company should stop making a part internally and buy externally when
Answer:
Make-or-Buy Decision
Step-by-step explanation:
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
A study collects samples of water from the tap in Vacaville and from bottled water available from the Nugget stores and samples their pH levels. The results are in the table below. I find a bottle marked #13 but cannot read the label for the type of water. He measures the pH and gets 6.32. What type of water do you think it is?
Answer:
see below
Step-by-step explanation:
the observed ph is 6.32
the mean pH of Tap water is shown below
sum of observations
Mean (Tap) = -----------------------------------
number of observations
(7.24 +7.05 +7.07 +6.6 +7.28 +7.29 +7.05 +6.7 +7.16 +7.07 +7.12 +6.56
= ---------------------------------------------------------------------------------------------------------
12
= 7.016
then mean pH of bottle water is shown below
sum of observations
Mean (Bottles) = -----------------------------------
number of observations
(5.35 + 5.29 + 5.46 + 5.4 + 5.95 + 6.22 + 5.43 +5.48 +6.06 +5.33 +5.46 +5.41)
= --------------------------------------------------------------------------------------------------------------
12
= 5.57
theoretically.. the higher the pH values should be between 0 to 14.
based from the above results, the mean tap water has an average of 7.016 and by looking at the pH chart... its a neutral or pure water.
while the average pH Bottles has 5.57, this means its more acidic water, or by looking at the pH chart its an acid rain water.
a 6.32pH is below pure water, based on the chart looks like a urine/saliva.
Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
Answer:
(5x³+3x²-5x+4) + (8x³-5x²+8x+9)
= 5x³+3x²-5x+4 +8x³-5x²+8x+9
= 5x³+8x³+3x²-5x²-5x+8x+4+9
= 13x³-2x²+3x+13
Hope this helps
if u have question let me know in comments ^_^
(a^8)3/2 in simplest form
Answer:
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Step-by-step explanation:
([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]
Remove the parenthesis by multiplying
[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]
This expression cannot be simplified further
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Hope this helps :)
Jilk Inc.'s contribution margin ratio is 62% and its fixed monthly expenses are $45,000. Assuming that the fixed monthly expenses do not change, what is the best estimate of the company's net operating income in a month when sales are $132,000?
Answer: $ 36,840.
Step-by-step explanation:
contribution margin=62% =0.62
fixed monthly expenses = $45,000
Sales = $132,000
We assume that the fixed monthly expenses do not change.
Then, company's net operating income = (contribution margin×Sales )-fixed monthly expenses
=$( (0.62×132000)-45000 )
= $ (81840-45000)
= $ 36,840
Hence, the best estimate of the company's net operating income in a month when sales are $132,000 is $ 36,840.
what is the average rate of change from 1 to 3 of the function represented by the graph? the graph is attached.
Answer: -4
At 1, the parabola is at (1, 3). And at 3, it's at (3, -5). The rate of change is -4, since each time it moves right 1, it goes down 4.
Hope that helped,
-sirswagger21
14. Twice the sum of a number and eight
Answer: 2(x + 8) is the expression.
Use distributive property to simplify,
2x+16
I didn't know which answer you wanted so....
Answer:
2(x + 8)
Step-by-step explanation:
Hello!
Twice the sum means we multiply by 2
2
the sum of a number and eight is x + 8
2 * x + 8
Since we have to twice the sum we put x + 8 in parenthesis to show to do that first
2(x + 8)
Hope this Helps!
10/7p+13/8+15/2p=909/56 i NEED THiS solving multi step equations w fractions and #8 PLEASE
Answer:
P= 2
Step-by-step explanation:
10/7p+13/8+15/2p=-909/56
Combine like terms
10/7p+15/2p=-909/56-13/8
20p+105p/14=-909-13*7/56
125/14p=-909-91/56
125/14p= -1000/56
125/14p*14/125= -1000/56*14/125
simplify
P= 8/4=2
And for #8 n =1 I answered this question it
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The manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2. The manufacturer also has fixed costs each month of $8,000.
Answer:
C(x)=1.2x+8,000.
Step-by-step explanation:
C(x)=cost per unit⋅x+fixed costs.
The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by
In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.
Suppose that you have to sell [x] number of bars to make profits. So, we can write -
{2x} - {1.20x} > {8000}
0.8x > 8000
8x > 80000
x > 10000
Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
To solve more questions on functions, expressions and polynomials, visit the link below -
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How long will it take for a lump-sum investment to double in value at an interest rate of 1.5% per month, compounded continuously
Answer:
It will take 47 months ( 3 years and 11 months)
Step-by-step explanation:
We use the compound interest formula here.
Mathematically;
A = P( 1 + r)^t
Where A is the amount which is 2 times the principal here, so we can call it 2P
P is the lump-sum invested
r is the monthly interest rate given as 1.5% = 1.5/100 = 0.015
t = time , which we want to calculate
Substituting these values, we have;
2P = P(1 + 0.015)^t
divide both sides by P
2 = 1.015^t
Take the log of both sides;
log 2 = log (1.015)^t
log 2 = t log 1.015
t = log2/log1.015
t = 46.55
which is approximately 47 months
Please answer! I am struggling with this question! Please show ALL work! <3 (the answer choices are provided on a separate image)
Answer:
The radius is 18 inches
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r
36 pi = 2 * pi *r
Divide each side by pi
36 = 2r
Divide each side by 2
18 =r
Answer:
The answer is option CStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius of the circle
From the question
Circumference = 36π inches
To find the radius substitute the value of the circumference into the above formula and solve for the radius
That's
[tex]36\pi = 2\pi r[/tex]Divide both sides by 2π
We have
[tex] \frac{36\pi}{2\pi} = \frac{2\pi \: r}{2\pi} [/tex]We have the final answer as
r = 18 inchesHope this helps you
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
h = –21.962x + 114.655
As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.
Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
Learn more about the line of best fit here:
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what are the steps required to determine the equation of a quadratic function given its zeros and a point?
Answer:
Below
Step-by-step explanation:
The quadratic equations form is:
● ax^2+bx+c
Using the zeroes, we can write a factored form.
● a (x-x') (x-x")
x and x' are the zeroes
■■■■■■■■■■■■■■■■■■■■■■■■■■
●y = a (x-x') (x-x")
x' and x" are khown but a is not.
We are given a point so replace x and y with its coordinates to find a.
So the steps are:
● 1) Write the factored form of the quadratic equation
● 2) replace x' and x" with their values.
● 3) replace x and y with the coordinates of a khwon point.
● 4) solve the equation for a.
The steps are write the factored form of the quadratic equation then, replace x' and x" with their values. To replace x and y with the coordinates of a known point. To solve the equation for a.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Using the zeroes, we can write a factored form;
a (x-x') (x-x")
x and x' are the zeroes
y = a (x-x') (x-x")
x' and x" are known but a is not.
We are given a point so replace x and y with their coordinates to find a.
So the steps are:
1) Write the factored form of the quadratic equation
2) To replace x' and x" with their values.
3) To replace x and y with the coordinates of a known point.
4) To solve the equation for a.
Learn more about quadratic equations;
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3.24 (4 being repeated) to a fraction
Answer:
146/45
Step-by-step explanation:
Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.
[tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]
__
Comment on procedure
The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.
Which expression is equivalent to (jk)l? A. (j + k) + l B. j(kl) C. (2jk)l D. (j + k)l
Answer:
B. j(kl)
Step-by-step explanation:
(jk)l
We can change the order we multiply and still get the same result
j(kl)
Answer:
Step-by-step explanation:
its B i did it
A signal light is green for 4 minutes, yellow for 10 seconds, and red for 3 minutes. If you drive up to this light, what is the probability that it will be green when you reach the intersection? Round your answer to two decimal places.
Answer:
0.56 is the required probability.
Step-by-step explanation:
Time for which signal shows green light = 4 minutes
Time for which signal shows yellow light = 10 seconds
Time for which signal shows red light = 3 minutes
To find:
Probability that the signal will show green light when you reach the destination = ?
Solution:
First of all, let us convert each time to same unit before doing any calculations.
Time for which signal shows green light = 4 minutes = 4 [tex]\times[/tex] 60 seconds = 240 seconds
Time for which signal shows yellow light = 10 seconds
Time for which signal shows red light = 3 minutes = 3 [tex]\times[/tex] 60 seconds = 180 seconds
Now, let us have a look at the formula for probability of an event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, E is the event that green light is shown by the signal.
Number of favorable cases mean the time for which green light is shown and Total number of cases is the total time (Time for which green light is shown + Time for which Yellow light is shown + Time for which red light is shown)
So, the required probability is:
[tex]P(E) = \dfrac{240}{240+10+180}\\\Rightarrow P(E) = \dfrac{240}{430}\\\Rightarrow \bold{P(E) \approx 0.56 }[/tex]
