Answer:
18 minutes
Step-by-step explanation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is the time,
and T is the half life.
A = 140 when t = 10. Solve for the half life:
140 = 700 (½)^(10 / T)
0.2 = ½^(10 / T)
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31
When A = 40, t is:
40 = 700 (½)^(t / 4.31)
0.057 = ½^(t / 4.31)
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8
Rounded to the nearest whole number, it takes 18 minutes.
The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
The half-life decay formula is given as,
N(t) = N₀ [tex](1/2)^{(t / T)}[/tex]
Where T is half-life while t is the time taken.
N₀ is the initial amount,
As per the given,
N(t) = 140 when t = 10.
140 = 700 [tex](1/2)^{(t / T)}[/tex]
Take log both sides,
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31 minutes
Put N(t) = 40
40 = 700[tex](1/2)^{(t / 4.31)}[/tex]
Take log both sides,
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8 ≈ 18 minutes
Hence "The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes".
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What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - x
B.
y = -2x
C.
y = 2x
D.
y = x
E.
y = -4x
F.
y = - x
Answer:
The answer is option FStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To calculate the equation of the line first find the slope
Slope of the line using points
(0 , 0) and (4 , -2) is
[tex]m = \frac{ - 2 - 0}{4 - 0} = \frac{ - 2}{4} = - \frac{1}{2} [/tex]
Now use the formula
y - y1 = m(x - x1) to find the equation of the line using any of the points
Using point (0,0)
That's
[tex]y - 0 = - \frac{ 1}{2} (x - 0)[/tex]
The final answer is
[tex]y = - \frac{1}{2} x[/tex]
Hope this helps you
Answer:
F
Step-by-step explanation:
The average daily volume of a computer stock in 2011 was ų=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 30 trading days in 2014, he finds the sample mean to be 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.
Answer:
a
The null hypothesis is [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]
The alternative hypothesis [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]
b
The 95% confidence interval is [tex]27.475 < \mu < 37.925[/tex]
Step-by-step explanation:
From the question the we are told that
The population mean is [tex]\mu = 35.1 \ million \ shares[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = 32.7 \ million\ shares[/tex]
The standard deviation is [tex]\sigma = 14.6 \ million\ shares[/tex]
Given that the confidence level is [tex]95\%[/tex] then the level of significance is mathematically represented as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]
[tex]E = 5.225[/tex]
The 95% confidence interval confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]
[tex]27.475 < \mu < 37.925[/tex]
f(x )=x square +6x + 5 what is the x intercept to graph f(x)
Answer:
(-5, 0)
(-1, 0)
Step-by-step explanation:
x-intercepts are points where the graph intersects the x-axis (or when y = 0)
Step 1: Write out function
f(x) = x² + 6x + 5
Step 2: Factor
f(x) = (x + 5)(x + 1)
Step 3: Find binomial roots
x + 5 = 0
x = -5
x + 1 = 0
x = -1
Alternatively, you can graph the function and analyze the graph for x-intercepts:
Mary states, "If the diagonals of a parallelogramare congruent, then the
parallelogram is a rectangle." Decide if her statement is wue or false.
A. True
B. False
Answer:
True
Step-by-step explanation:
A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,
AD ≅ BC (opposite side property)
AB ≅ CD (opposite side property)
<ABC = <BCD = <CDA = <DAC = [tex]90^{0}[/tex] (right angle property)
Thus,
<ABC + <BCD + <CDA + <DAC = [tex]360^{0}[/tex]
AC ⊥ BD (diagonals are perpendicular to each other)
AC ≅ BD (congruent property of diagonals)
Therefore, the parallelogram is a rectangle.
According to the website www.costofwedding, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U. S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.
Choose the statement that is the best interpretation of the confidence interval.
I. That probability that the flowers at a wedding will cost more than $698is greater than 5%.
II. In about 95%of all samples of size 40,the resulting confidence interval will contain the mean cost of flowers at weddings.
III. We are extremely confident that the mean cost of flowers at a wedding is between $701and $767
A) II only
B) I only
C) III only
D) II and III are both correct
Answer:
D) II and III are both correct.
Step-by-step explanation:
The Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The cost of flowers for a wedding is $698. The 95% of all samples of size is 40 and the confidence interval will be mean cost of flowers at wedding. There is confidence that mean cost of wedding flowers is between $701 to $767.
What is the volume of a sphere, to the nearest cubic inch, if the radius is 16 inches? Use π = 3.14.
Answer:
vol = 17,148 cu. in.
Step-by-step explanation:
vol = 4 / 3 * pi * r³
vol = 4 / 3 *3.14 * 16³
vol = 17,148 cu. in.
Answer:
The answer is
17149 cubic inchesStep-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]
where r is the radius of the sphere
π = 3.14
From the question
r = 16 inches
Volume of the sphere is
[tex]V = \frac{4}{3} (3.14) {16}^{3} [/tex]
V = 17148.586
We have the final answer as
V = 17149 cubic inches to the nearest cubic inch
Hope this helps you
You are ordering two pizzas. A pizza can be small, medium, large, or extra large, with any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8). How many possibilities are there for your two pizzas
Answer:
1048576
Step-by-step explanation:
Given the following :
Pizza order :
Size = small, medium, large, or extra large = 4 possible sizes
Toppings = any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8).
Combination of Toppings = 2^8
Four different sizes of pizza = 4
Number of possibilities in ordering for a single pizza :
(4 * 2^8) = 4 * 256 = 1024
Number of possibilities in ordering two pizzas :
(4 * 2^8)^2
(2^2 * 2^8)^2
From indices :
[2^(2+8)]^2
[2^(10)]^2
2^(10*2)
2^20
= 1048576
A charity organization is holding a food drive with a goal to collect at least 1,000 cans of
food by the end of the month. It currently has 565 cans from donations and is having an
event where 87 guests will attend and bring cans. Which solution set represents the
number of cans each guest must bring to meet the goal?
+
OA
++
0
1
2
3
4
5
6
7
8
9
10
---
+
OB. 4
+
0
1
2
3
4
5
6
7
8
9
10
OC.
+
1
2
3
5
6
7
8
9
10
OD. +
+
++
-
6
+
7.
+
0
1
2
3
4
5
8
9
10
Answer:
Each guest must bring 5 cans.
Step-by-step explanation:
1000-565=435
435/87=5
Suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. If 83 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams?
Answer: 0.129
Step-by-step explanation:
Let [tex]\overline{X}[/tex] denotes a random variable that represents the mean weight of babies born.
Population mean : [tex]\mu= \text{3316 grams,}[/tex]
Standard deviation: [tex]\text{324 grams}[/tex]
Sample size = 83
Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :
[tex]P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}<\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{-54}{\dfrac{324}{\sqrt{83}}})\\\\=1-[P(-1.518<Z<1.518)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-[P(Z<1.518)-P(z<-1.518)]\\\\=1-[P(Z<1.518)-(1-P(z<1.518))]\\\\=1-[2P(Z<1.518)-1]=2-2P(Z<1.518)\\\\=2-2(0.9355)\ [\text{By z-table}]\\\\=0.129[/tex]
hence, the required probability = 0.129
State the correct polar coordinate for the graph shown:
clearly, r=3 units
and 8 segments (sectors actually) in anti-clockwise direction , with each sector having 30° angle so angle is 240°
so option C
Answer:
Solution : ( 3, 240° )
Step-by-step explanation:
In polar coordinates the point is expression as the ordered pair ( r, θ ) where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. When r > 0, we can tell it = 3 as the point lies on the third circle starting from the center. Now let's start listing coordinates for when r is positive ( r > 0 ). There are two cases to consider here.
( 3, θ ) here theta is 60 degrees more than 180, or 180 + 60 = 240 degrees. Right away you can tell that your solution is ( 3, 240° ), you don't have to consider the second case.
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
In 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
You have 9kg of oats and cup scales that gears of 50g and 200g.
Total oats need to measure = 9kg
As we know in 1 kg there are 1000 grams.
1 kg = 1000 grams
9kg = 9000 grams
2kg = 2000 grams
Cup scales that gears: 50g and 200g
The number of cups if consider one cup is of 250 grams( = 200 + 50)
Number of cups = 2000/250
Number of cups = 8
In three weighs it is not possible to measure the 2kg or 2000 grams.
Thus, in 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.
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1) At AJ Welding Company they employ 253 people, 108 employees receive 2 weeks of paid 1) _______ vacation each year. Find the ratio of those who receive 2 weeks of paid vacation to those whose paid vacation is not 2 weeks.
Answer:
108 : 145
Step-by-step explanation:
253 - 108 = 145
Ratio of those who receive 2 weeks of paid vacation is 108
Ratio of those paid vacation is not 2 weeks is 145
108 : 145
What is the solution to the system of equations?
5x – 4y = 6
-5x + 4y = -10
O (4,4)
0 (-2,-5)
O infinitely many solutions
O no solution
Hey there! I'm happy to help!
We have a 5x is one equation and a -5x in another equation. We can combine the two equations to cancel out the x and then solve! This is called solving by elimination.
5x-4y=6
+
-5x+4y=-10
0= -4
Since we lost our x and y while solving, there cannot be any solution.
Therefore, the answer is no solution.
Have a wonderful day!
If the normality requirement is not satisfied (that is, np(1p) is not at least 10), then a 95% confidence interval about the population proportion will include the population proportion in ________ 95% of the intervals. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Answer:
less than
Step-by-step explanation:
If the normality requirement is not satisfied (that is, np(1 - p) is not at least 10), then a 95% confidence interval about the population proportion will include the population proportion in _less than__ 95% of the intervals.
The confidence interval consist of all reasonable values of a population mean. These are value for which the null hypothesis will not be rejected.
So, let assume that If the 95% confidence interval contains the value for the hypothesized mean, then the sample mean is reasonably close to the hypothesized mean. The effect of this is that the p- value is going to be greater than 0.05, so we fail to reject the null hypothesis.
On the other hand,
If the 95% confidence interval do not contains the value for the hypothesized mean, then the sample mean is far away from the hypothesized mean. The effect of this is that the p- value is going to be lesser than 0.05, so we reject the null hypothesis.
If the random variable X is normally distributed with mean of 50 and standard deviation of 7, find the 9th percentile.
Answer:
The 9th percentile is 40.52.
Step-by-step explanation:
We are given that the random variable X is normally distributed with a mean of 50 and a standard deviation of 7.
Let X = the random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 50
[tex]\sigma[/tex] = standard deviation = 7
So, X ~ Normal([tex]\mu=50, \sigma^{2} = 7^{2}[/tex])
Now, the 9th percentile is calculated as;
P(X < x) = 0.09 {where x is the required value}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-50}{7}[/tex] ) = 0.09
P(Z < [tex]\frac{x-50}{7}[/tex] ) = 0.09
Now, in the z table the critical value of x that represents the below 9% of the area is given as -1.3543, i.e;
[tex]\frac{x-50}{7}=-1.3543[/tex]
[tex]x-50=-1.3543 \times 7[/tex]
[tex]x=50 -9.48[/tex]
x = 40.52
Hence, the 9th percentile is 40.52.
Help me please thank y’all
Answer: x=60°
Step-by-step explanation:
The sum of the angles of a triangle is 180°. With this, we can find x°.
33+87+x=180 [combine like terms]
120+x=180 [subtact both sides by 120]
x=60°
Answer:
60 degrees
Step-by-step explanation:
All the angles in a triangle add up to 180 degrees.
We know two angles, 33 degrees and 87 degrees.
Now we have to find the last one.
So we make an equation to solve this.
33 + 87 + x = 180
120 + x = 180
Subtracting 120 fr0m both sides get us,
120 - 120 + x = 180 -120
x = 60
60 degrees
We can check by adding all three angles by substituting 60 for x,
33 + 87 + 60 = 120 + 60 = 180 degrees
For what value of x does (x + 3)^2-5=0
Answer:
x = -3±sqrt( 5)
Step-by-step explanation:
(x + 3)^2-5=0
Add 5 to each side
(x + 3)^2-5+5=0+5
(x + 3)^2 = 5
Take the square root of each side
sqrt((x + 3)^2 )=±sqrt( 5)
x+3 = ±sqrt( 5)
Subtract 3 from each side
x+3-3 = -3±sqrt( 5)
x = -3±sqrt( 5)
The time between consecutive uses of a vending machine is exponential with an average of 15 minutes. a)Given that the machine has not been used in the previous 5 minutes, what is the probability that the machine will not be used during the next 10 minutes
Answer5
Step-by-step explanation:
write 768,676 in words
Answer:
seven hundred sixty-eight thousand six hundred seventy-six
hope this answer correct :)
☆ =
MODULE
The length of a rectangle is eight centimeter less than
twice the width. The area of the rectangle is 24
centimeters squared. Determine the dimensions of the
rectangle in centimeters.
Answer: The length is 4 centimeters and the width is 6 centimeters.
Step-by-step explanation:
If the length of the rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 . And we know that to find the area of a rectangle we multiply the length by the width and they've already given the area so we will represent the width by w since it is unknown.
Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.
w(2w-8) = 24
2[tex]w^{2}[/tex] - 8w = 24 subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.
2[tex]w^{2}[/tex] - 8w -24 = 0 divide each term by 2.
[tex]w^{2}[/tex] - 4w - 12 = 0 Five two numbers that multiply to get -12 and to -4
[tex]w^{2}[/tex] +2w - 6w - 12 = 0 Group the left hand side and factor.
w(w+2) -6( w + 2) = 0 factor out w+2
(w+2)(w-6) = 0 Set them both equal zero.
w + 2 =0 or w - 6 = 0
-2 -2 + 6 +6
w= -2 or w=6
Since we are dealing with distance -2 can't represent a distance so the wide has to 6.
Now it says that the length is 8 less that twice the width.
So 2(6) - 8 = 12 -8 = 4 So the length in this care is 4.
Check.
6 * 4 = 24
24 = 24
Life rating in Greece. Greece has faced a severe economic crisis since the end of 2009. A Gallup poll surveyed 1,000 randomly sampled Greeks in 2011 and found that 25% of them said they would rate their lives poorly enough to be considered "suffering".
a. Describe the population parameter of interest. What is the value of the point estimate of this parameter?
b. Check if the conditions required for constructing a confidence interval based on these data are met.
c. Construct a 95% confidence interval for the proportion of Greeks who are "suffering".
d. Without doing any calculations, describe what would happen to the confidence interval if we decided to use a higher confidence level.
e. Without doing any calculations, describe what would happen to the confidence interval if we used a larger sample.
Answer:
a
The population parameter of interest is the true proportion of Greek who are suffering
While the point estimate of this parameter is proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%
b
The condition is met
c
The 95% confidence interval is [tex]0.223 < p < 0.277[/tex]
d
If the confidence level is increased which will in turn reduce the level of significance but increase the critical value([tex]Z_{\frac{\alpha }{2} }[/tex]) and this will increase the margin of error( deduced from the formula for margin of error i.e [tex]E \ \alpha \ Z_{\frac{\alpha }{2} }[/tex] ) which will make the confidence interval wider
e
Looking at the formula for margin of error if the we see that if the sample size is increased the margin of error will reduce making the confidence level narrower
Step-by-step explanation:
From the question we are told that
The sample size is n = 1000
The population proportion is [tex]\r p = 0.25[/tex]
Considering question a
The population parameter of interest is the true proportion of Greek who are suffering
While the point estimate of this parameter is proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%
Considering question b
The condition for constructing a confidence interval is
[tex]n * \r p > 5\ and \ n(1 - \r p ) >5[/tex]
So
[tex]1000 * 0.25 > 5 \ and \ 1000 * (1-0.25 ) > 5[/tex]
[tex]250 > 5 \ and \ 750> 5[/tex]
Hence the condition is met
Considering question c
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_\frac{ \alpha }{2} * \sqrt{ \frac{\r p (1 - \r p ) }{n} }[/tex]
substituting values
[tex]E = 1.96 * \sqrt{ \frac{ 0.25 (1 - 0.25 ) }{ 1000} }[/tex]
[tex]E = 0.027[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
substituting values
[tex]0.25 - 0.027 < p < 0.25 + 0.027[/tex]
substituting values
[tex]0.223 < p < 0.277[/tex]
considering d
If the confidence level is increased which will in turn reduce the level of significance but increase the critical value([tex]Z_{\frac{\alpha }{2} }[/tex]) and this will increase the margin of error( deduced from the formula for margin of error i.e [tex]E \ \alpha \ Z_{\frac{\alpha }{2} }[/tex] ) which will make the confidence interval wider
considering e
Looking at the formula for margin of error if the we see that if the sample size is increased the margin of error will reduce making the confidence level narrower
determine if the following side lengths create an acute,obtuse,or right triangle. a) 20, 21, 28 b) 3, 6, 4 c) 8, 12, 15
Answer:
a) 20, 21, 28 : acute
b) 3, 6, 4 : obtuse
c) 8, 12, 15 : obtuse
Step-by-step explanation:
You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:
If [tex]a^2+b^2=c^2[/tex] , then the triangle is right.
If [tex]a^2+b^2>c^2[/tex] , then the triangle is acute.
If [tex]a^2+b^2<c^2[/tex] , then the triangle is obtuse.
Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):
a) 20, 21, 28
Insert numbers, using 28 as c:
[tex]20^2+21^2[/tex]_[tex]28^2[/tex]
Simplify exponents ([tex]x^2=x*x[/tex]):
[tex]400+441[/tex]_[tex]784[/tex]
Simplify addition:
[tex]841[/tex]_[tex]784[/tex]
Identify relationship:
[tex]841>784[/tex]
The sum of the squares of a and b is greater than the square of c. This triangle is acute.
b) 3, 6, 4
Insert numbers, using 6 as c:
[tex]3^2+4^2[/tex]_[tex]6^2[/tex]
Simplify exponents:
[tex]9+16[/tex]_[tex]36[/tex]
Simplify addition:
[tex]25[/tex]_[tex]36[/tex]
Identify relationship:
[tex]25<36[/tex]
The sum of the squares of a and b is less than the square of c. This triangle is obtuse.
c) 8, 12, 15
Insert numbers, using 15 as c:
[tex]8^2+12^2[/tex]_[tex]15^2[/tex]
Simplify exponents:
[tex]64+144[/tex]_[tex]225[/tex]
Simplify addition:
[tex]208[/tex]_[tex]225[/tex]
Identify relationship:
[tex]208<225[/tex]
The sum of the squares of a and b is less than the square of c. This triangle is obtuse.
:Done.
The correct values are,
a) 20, 21, 28 = Acute
b) 3, 6, 4 = Obtuse
c) 8, 12, 15 = Obtuse
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sides are,
a) 20, 21, 28
b) 3, 6, 4
c) 8, 12, 15
Now,
We know that;
If three sides of a triangle are a, b and c.
Then, We get;
If a² + b² = c², then the triangle is right triangle.
If a² + b² > c², then the triangle is acute triangle.
If a² + b² < c², then the triangle is obtuse triangle.
Here, For option a;
⇒ 20, 21, 28
Clearly, a² + b² = 20² + 21²
= 400 + 441
= 841
And, c² = 28² = 784
Thus, a² + b² > c²
Hence, It shows the acute angle.
For option b;
⇒ 3, 6, 4
Clearly, a² + b² = 3² + 4²
= 9 + 16
= 25
And, c² = 6² = 36
Thus, a² + b² < c²
Hence, It shows the obtuse angle.
For option c;
⇒ 8, 12, 15
Clearly, a² + b² = 8² + 12²
= 64 + 144
= 208
And, c² = 15² = 225
Thus, a² + b² < c²
Hence, It shows the obtuse angle.
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If AD=2/3AB, the ratio of the length of BC to the length of DE is A. 1/6 B. 1/4 C. 3/2 D. 3/4
Answer:
The correct answer is c
Step-by-step explanation:
Answer:
C.) 3/2
Explanation:
PLATO
Is it ever possible that after an elastic collision (where a moving mass (1) strikes a stationary mass (2)) that the two objects will have exactly the same final speeds? If so, how must the two masses compare? (Hints, 1st : there are two possibilities as to how the speeds could be equal, 2nd : equations below should be helpful).V1f=V1o (m1-m2/m1+m2) V2f=V1o (2m1/m1+m2)
Answer:
Step-by-step explanation:
It is possible that after an elastic collision a moving mass (1) strikes a stationary mass (2) and the two objects will have exactly the same final speed.
During an elastic collision, the momentum and kinetic energy are both conserved. Since one of the object is a stationary object, its velocity will be zero hence the other moving object will collide with the stationary object and cause both of them to move with a common velocity. The expression for their common velocity can be derived using the law of conservation of energy.
Law of conservation of energy states that the sum of momentum of bodies before collision is equal to the sum of momentum of the bodies after collision.
Since momentum = mass*velocity
Before collision
Momentum of body of mass m1 and velocity u1 = m1u1
Momentum of body of mass m2 and velocity u2 = m2u2
Since the second body is stationary, u2 = 0m/s
Momentum of body of mass m2 and velocity u2 = m1(0) = 0kgm/s
Sum of their momentum before collision = m1u1+0 = m1u1 ... 1
After collision
Momentum of body of mass m1 and velocity vf = m1vf
Momentum of body of mass m2 and velocity vf = m2vf
vf is their common velocity.
Sum of their momentum before collision = m1vf+m2vf ... 2
Equating 1 and 2 according to the law;
m1u1 = m1vf+m2vf
m1u1 = (m1+m2)vf
vf = m1u1/m1+m2
vf s their common velocity after collision. This shows that there is possibility that they have the same velocity after collision.
Fill in the blanks and explain the pattern.
XA, XB, XC, __,__,__
Answer:
XD,XE,XF
Step-by-step explanation:
XA,XB,XC,XD,XE,XF
IT IS BECAUSE OF THE ALPHABETICAL ORDER AFTER X
Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?15x – 15 = 15x – 2415x – 5 = 15x – 2439x – 45 = 15x – 2439x – 15 = 15x – 24?
Answer:
3[x + 3(4x – 5)] = (39x-15)
Step-by-step explanation:
The given expression is : 3[x + 3(4x – 5)]
We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,
[tex]3[x + 3(4x -5)]=3[x+12x-15][/tex]
Again open the brackets,
[tex]3[x+12x-15]=3x+36x-45[/tex]
Now adding numbers having variables together. So,
[tex]3[x + 3(4x - 5)]=39x-15[/tex]
So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).
Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600
Answer:
A. 1,162.5
Step-by-step explanation:
Write the next two terms and add them up:
S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A
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Explanation:
{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5
Sn = a*(1-r^n)/(1-r)
S5 = 600*(1-0.5^5)/(1-0.5)
S5 = 1,162.5
-----------
Check:
first five terms = {600, 300, 150, 75, 37.5}
S5 = sum of the first five terms
S5 = 600+300+150+75+37.5
S5 = 1,162.5
Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.
The age of some lecturers are 42,54,50,54,50,42,46,46,48 and 48 calculate the mean age and standard deviation
Answer:
Mean age: 48
Standard deviation: 4
Step-by-step explanation:
a) Mean
The formula for Mean = Sum of terms/ Number of terms
Number of terms
= 42 + 54 + 50 + 54 + 50 + 42 + 46 + 46 + 48+ 48/ 10
= 480/10
= 48
The mean age is 48
b) Standard deviation
The formula for Standard deviation =
√(x - Mean)²/n
Where n = number of terms
Standard deviation =
√[(42 - 48)² + (54 - 48)² + (50 - 48)² +(54 - 48)² + (50 - 48)² +(42 - 48)² + (46 - 48)² + (46 - 48)² + (48 - 48)² + (48 - 48)² / 10]
= √-6² + 6² + 2² + 6² + 2² + -6² + -2² + -2² + 0² + 0²/10
=√36 + 36 + 4 + 36 + 4 + 36 + 4 + 4 + 0 + 0/ 10
=√160/10
= √16
= 4
The standard deviation of the ages is 4
Find the slope of a line perpendicular to the line defined by the equation 3x-5y=12
Answer:
-5/3
Step-by-step explanation:
Note the slope intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Isolate the variable, y. First, Subtract 3x from both sides:
3x (-3x) - 5y = 12 (-3x)
-5y = -3x + 12
Next, divide -5 from both sides. Remember to divide from all terms within the equation:
(-5y)/-5 = (-3x + 12)/-5
y = (-3x/-5) + (-12/5)
Simplify.
y = (3x/5) - 12/5
y = (3/5)x - 12/5
You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:
Original m = 3/5
Flipped m = -5/3
-5/3 is your perpendicular slope.
Answer:
5
m = - ---- perpendicular slope
3
Step-by-step explanation:
3x - 5y = 12 -------->> convert to y = mx + b
- 5y = - 3x + 12
- 5y = - (3x + 12) --- eliminate the negative
5y = 3x + 12
3x + 12
y = -------------
5
3 12
y = -----x + -----
5 5
the above equation is the form of y = mx + b
where m is the slope and b is the intercept
5
therefore, m = - ---- perpendicular slope
3
If y varies directly with x and y = 5 when x = 4, find the value of y when x = -8
Answer:
-10
Step-by-step explanation:
y : x
= 5 : 4
4z = -8
= -8 / 4 = -2 = z
y : x
= 5 * -2 : 4 * -2
= -10 : -8
