Answer:
x = 2
Step-by-step explanation:
3(2x+1) = 15
6x +3 = 15
6x = 12
x - 2
Which problem can we solve with 27 : 3?
Choose 1 answer:
A
Gino had 27 walnut trees in his yard. He cut 3 down
to use for firewood. How many walnut trees does
Gino have left?
Lindsey picked 3 bags of apples. There are 27 apples
in each bag. How many apples does she have in
total?
La Tasha has 27 rabbit stickers. She splits the stickers
evenly among 3 pieces of paper. How many stickers
did La Tasha put on each piece of paper?
Answer:
La Tasha has 27 rabbit stickers. She splits the stickers
evenly among 3 pieces of paper. How many stickers
did La Tasha put on each piece of paper?
Step-by-step explanation:
Find the missing side. Round your answer to the nearest tenth.
Answer:
76.9
Step-by-step explanation:
tan(α) = opposite leg/adjacent leg
tan(70°) = x/28
x = 28* tan(70°) = 76.9
Answer:
76.9 or 77
Step-by-step explanation:
tan(α) = opposite leg/adjacent leg
tan(70°) = x/28
x = 28* tan(70°) = 76.9
Find the value of this expression if x=-9 x^2 +3/ x+6
Answer:
-28.
Step-by-step explanation:
(x^2 + 3) / (x + 6)
x = -9
[(-9)^2 + 3] / (-9 + 6)
= (81 + 3) / (-3)
= 84 / (-3)
= -28
Hope this helps!
Answer: the value of the expression is 80
Step-by-step explanation:
[tex]x^2 +3/ x+6[/tex]
(-9)² + 3 / (-9 + 6) . PEMDAS: figure parentheses and exponents first
81 + 3/-3 division 3/-3 = –1
81 + (–1) .adding a negative is the same as subtracting
81 –1
80
ASAP! I really need help with this question! No nonsense answers, and please attach the solution.
Answer:
[tex]\boxed{\sf Option \ 4}[/tex]
Step-by-step explanation:
[tex]\sqrt{2x-3} +x=3[/tex]
Subtract x from both sides.
[tex]\sqrt{2x-3} +x-x=-x+3[/tex]
[tex]\sqrt{2x-3}=-x+3[/tex]
Square both sides.
[tex]( \sqrt{2x-3})^2 =(-x+3)^2[/tex]
[tex]2x-3=x^2-6x+9[/tex]
Subtract x²-6x+9 from both sides.
[tex]2x-3-(x^2-6x+9 )=x^2-6x+9-(x^2-6x+9)[/tex]
[tex]-x^2 +8x-12=0[/tex]
Factor left side of the equation.
[tex](-x+2)(x-6)=0[/tex]
Set factors equal to 0.
[tex]-x+2=0\\-x=-2\\x=2[/tex]
[tex]x-6=0\\x=6[/tex]
Check if the solutions are extraneous or not.
Plug x as 2.
[tex]\sqrt{2(2)-3} +2=3\\ \sqrt{4-3} +2=3\\\sqrt{1} +2=3\\3=3[/tex]
x = 2 works in the equation.
Plug x as 6.
[tex]\sqrt{2(6)-3} +6=3\\ \sqrt{12-3} +6=3\\\sqrt{9} +6=3\\3+6=3\\9=3[/tex]
x = 6 does not work in the equation.
Answer:
option d
Step-by-step explanation:
[tex]\sqrt{2x-3}+x = 3\\\\\sqrt{2x-3} = 3 -x\\[/tex]
Square both sides
[tex](\sqrt{2x-3})^{2}=(3-x)^{2}\\\\\\2x-3=9-6x+x^{2}\\\\0=x^{2}-6x + 9 - 2x + 3\\[/tex] {Add like terms}
[tex]x^{2} - 8x + 12 = 0[/tex]
Sum = -8
Product = 12
Factors = -2 , - 6
x² - 2x - 6x + (-2) * (-6) = 0
x(x -2) - 6(x -2) = 0
(x -2) (x - 6) = 0
x - 2 =0 ; x - 6 = 0
x = 2 ; x = 6
roots of the equation : 2 , 6
But when we put x = 6, it doesn't satisfies the equation.
When x = 6,
[tex]\sqrt{2x-3} + x = 3\\\\\sqrt{2*6-3}+6 = 3\\\\\sqrt{12-3}+6=3\\\\\sqrt{9}+6=3\\\\[/tex]
3 + 6≠ 3
Therefore, x = 2 but x = 6 is extraneous
A small airplane can fly 12 miles in 3 minutes. At this rate, how far can the airplane fly in 1 hour?
Answer:
The airplane can fly up to 240 miles in a hour
Step-by-step explanation:
Cross multiply
(12)(60)=3x
720=3x
Divide 3 on both sides
x=240
There are 60 minutes in 1 hour.
60 ÷ 3 = 20
12 × 20 = 240
In one hour, the airplane could fly at 240 miles.
0: A certain type of combination lock has 3 dials. The first 2 dials each have settings for all the digits 0 through 9, and the third has settings for all the 26 capital letters of the alphabet. A combination consists of one setting from each of the dials. How many different combinations are possible
Answer:
combinations = 10 * 10 * 26
combinations = 2,600
Step-by-step explanation:
i need help plzzzzz
Answer:
A
Step-by-step explanation:
Given
f(x) = [tex]\frac{3+x}{x-3}[/tex]
To evaluate f(a + 2), substitute x = a + 2 into f(x)
f(a + 2) = [tex]\frac{3+a+2}{a+2-3}[/tex] = [tex]\frac{5+a}{a-1}[/tex] → A
what is −67b+6≤9b+43 solve for b
Answer:
−67b + 6 ≤ 9b + 43
Group like terms
That's
- 67b - 9b ≤ 43 - 6
Simplify
- 76b ≤ 37
Divide both sides by - 76
b ≥ - 37/76Hope this helps you
what expressions are equal to the problem?
Answer:
A
Step-by-step explanation:
[tex] \frac{ {6}^{3}. {2}^{6} }{ {2}^{3 } } = \frac{ {2}^{3}. {3}^{3}. {2}^{6} } { {2}^{3} } = {2}^{6} . {3}^{3} [/tex]
Point A is located at (2, 3) on the coordinate plane. Point A is reflected over the x-axis to form point B and over the y-axis to form point C. Then, point A is reflected over both axes to form point D. The four points become vertices of a quadrilateral. What is the most precise name for the quadrilateral formed, and how do you know?
Answer:
Rectangle
Step-by-step explanation:
Well if point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).
Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)
Points
__________
A. (2,3)
B. (2,-3)
C. (-2,-3)
D. (-2,3)
__________
So graphing all these points we get a rectangle.
Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.
The most precise name of the quadrilateral will be rectangle .
Given,
Point A : (2,3) .
Here,
If point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).
Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)
Points
A. (2,3)
B. (2,-3)
C. (-2,-3)
D. (-2,3)
So, graphing all these points we get a rectangle.
Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.
Know more about rectangle,
https://brainly.com/question/15019502
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Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two decimal places.) X is the number of red marbles that Suzan has in her hand after she selects four marbles from a bag containing four red marbles and two green ones.
Answer:
The answer is below
Step-by-step explanation:
Since they are two green balls, x cannot assume value of 0 and 1. The minimum number of red balls must be two since there are only two green balls and we need to select 4 balls
For x = 2 (select two red balls from 4 red balls and 2 green balls from 2 green balls):
P(x = 2) = [tex]\frac{C(4,2)*C(2,2)}{C(6,2)} =\frac{6}{15}[/tex]
For x = 3 (select 3 red balls from 4 red balls and 1 green balls from 2 green balls):
P(x = 3) = [tex]\frac{C(4,3)*C(2,1)}{C(6,2)} =\frac{8}{15}[/tex]
For x = 4 (select 4 red balls from 4 red balls and 0 green balls from 2 green balls):
P(x = 4) = [tex]\frac{C(4,4)*C(2,0)}{C(6,2)} =\frac{1}{15}[/tex]
Expected value = E(x) = ΣxP(x) = (2×6/15) + (3×8/15) + (4×1/15) = 40/15 = 2.67
Variance = Σx²P(x) - [E(x)]² = (2²×6/15) + (3²×8/15) + (4²×1/15) - (40/15)² = 80/225 = 0.36
Standard deviation = √variance = √0.36 = 0.6
Using the hypergeometric distribution, it is found that:
The expected value is of 2.67.The variance is of 0.356.The standard deviation is of 0.596.The marbles are chosen without replacement, hence, the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this problem:
6 marbles, hence [tex]N = 6[/tex]4 red marbles, hence [tex]k = 4[/tex]She selects 4 marbles, hence [tex]n = 4[/tex].The expected value is:
[tex]E(X) = \frac{nk}{N}[/tex]
Hence:
[tex]E(X) = \frac{4(4)}{6} = 2.67[/tex]
The expected value is of 2.67.
The variance is:
[tex]V(X) = \frac{nk(N-k)(N-n)}{N^2(N-1)}[/tex]
Hence:
[tex]V(X) = \frac{4(4)(2)(2)}{6^2(6-1)} = 0.356[/tex]
The standard deviation is the square root of the variance, hence:
[tex]\sqrt{V(X)} = \sqrt{0.356} = 0.596[/tex]
The variance is of 0.356.The standard deviation is of 0.596.A similar problem is given at https://brainly.com/question/19426305
Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?
==================================================
Explanation:
Jane does the job alone and she can finish it in 5 hours. Her rate is 1/5 of a job per hour. By "job", I mean painting the entire fence. Notice that multiplying 1/5 by the number of hours she works will yield the value 1 to indicate one full job is done.
Through similar reasoning, Paul's rate is 1/6 of a job per hour.
Let x be the time, in hours, it takes Peter to get the job done if he worked alone. His rate is 1/x of a job per hour.
Combining the three individual rates gives
1/5 + 1/6 + 1/x = (6x)/(30x) + (5x)/(30x) + (30)/(30x)
1/5 + 1/6 + 1/x = (6x+5x+30)/(30x)
1/5 + 1/6 + 1/x = (11x+30)/(30x)
The expression (11x+30)/(30x) is the total rate if the three people worked together. This is assuming neither worker slows another person down.
Set this equal to 1/2 as this is the combined rate (based on the fact everyone teaming up gets the job done in 2 hours). Then solve for x
(11x+30)/(30x) = 1/2
2(11x+30) = 30x*1 .... cross multiply
22x+60 = 30x
60 = 30x-22x
60 = 8x
8x = 60
x = 60/8
x = 7.5
It takes Peter 7.5 hours, or 7 hours 30 minutes, to get the job done if he worked alone.
--------------
Here's another equation to solve though its fairly the same idea as above
1/5 + 1/6 + 1/x = 1/2
30x*(1/5 + 1/6 + 1/x) = 30x*(1/2) ... multiply both sides by LCD
30x(1/5) + 30x(1/6) + 30x(1/x) = 30x(1/2)
6x + 5x + 30 = 15x
11x + 30 = 15x
30 = 15x-11x
30 = 4x
4x = 30
x = 30/4
x = 7.5
We get the same answer
Answer: 7 . 5 hrs
Step-by-step explanation:
It takes Jane 5 hours to finish the fence so she can get [tex]\dfrac{1}{5}[/tex] of the job done in 1 hour.
It takes Paul 6 hours to finish the fence so he can get [tex]\dfrac{1}{6}[/tex] of the job done in 1 hour.
It takes Peter x hours to finish the fence so he can get [tex]\dfrac{1}{x}[/tex] of the job done in 1 hour.
Together, it takes them 2 hours to finish the fence so they can get [tex]\dfrac{1}{2}[/tex] of the job done in 1 hour.
Jane + Paul + Peter = Together
[tex]\dfrac{1}{5}\quad +\quad \dfrac{1}{6}\quad +\quad \dfrac{1}{x}\quad =\quad \dfrac{1}{2}[/tex]
Multiply everything by 30x to eliminate the denominator:
[tex]\dfrac{1}{5}(30x) + \dfrac{1}{6}(30x) +\dfrac{1}{x}(30x) =\dfrac{1}{2}(30x)[/tex]
Simplify and solve for x:
6x + 5x + 30 = 15x
11x + 30 = 15x
30 = 4x
[tex]\dfrac{30}{4}=x[/tex]
7.5 = x
Around which line would the following cross-section need to be revolved to create a sphere? circle on a coordinate plane with center at 1 on the y-axis and a radius of 1
Answer:
y= 1
Step-by-step explanation:
A circle forms a sphere only when it goes around a straight line throughout the center so y= 1 because it's (1,0).
The y = 1 is the axis around which the circle cross-section needs to be revolve to create a sphere.
It is given that the circle is on a coordinate plane with the centre at 1 on the y-axis.
It is required to find around which line would the following cross-section need to be revolved to create a sphere.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the centre of a circle).
We have a circle on the coordinate plane the centre of the circle lies on the y-axis at 1.
On y=axis the value of x is zero ie. x= 0
The centre of the circle = (0,1)
If a half-circle revovle around the axis which is dividing the circle into two halves.
As we can see in the graph the y-axis and y=1 divide the circle into two halves.
Thus, the line y = 1 is the axis around which the circle cross-section needs to be revolve to create a sphere.
Learn more about circle here:
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This school has 800 students. Every Wednesday, 12% of the students stay after school for this club. how many students attend this club on Wednesdays?
Answer:
96
Step-by-step explanation:
800*0.12=96
Answer:
96
Step-by-step explanation:
12% of 800 is 96
Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. If they start at the same position, chosen at zero, and bike in straight, opposite directions, what will the distance between them be after 45 minutes?
Answer:
15 miles
Step-by-step explanation:
Speed is the ratio of distance traveled to the time taken to reach the distance. The formula for speed is given by:
Speed = distance / time
Distance = speed × time
Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. At time t = 45 minutes = 45/ 60 hour = 0.75 hour, the distance traveled by Claire and Han is given as:
For Claire:
Distance = speed × time = 12 miles / hour × 0.75 hour = 9 miles
For Han:
Distance = speed × time = 8 miles / hour × 0.75 hour = 6 miles
Since both Han and Claire are traveling in opposite directions, the distance between them after 45 minutes = 9 miles + 6 miles = 15 miles
Assume that an opinion poll conducted in a 1998 congressional race found that on election eve, 54% of the voters supported Congressman Stevens and 44% supported challenger Jones. Also assume that the poll had a +/- 3% margin of error. What would the pollster be able to safely predict?
Answer:
Congressman Stevens will win the race
Step-by-step explanation:
Considering the margin of error, the possible outcomes for each candidate would be:
Congressman Stevens: from (54 - 3)% to (54+3)%
Challenger Jones: from (44 - 3)% to (44+3)%
Congressman Stevens: from 51% to 57%
Challenger Jones: from 41% to 47%
Therefore, even considering the margin of error, the pollster would be able to safely predict that Congressman Stevens will win the race.
Third-degree, with zeros of −5, −4, and 1, and a y-intercept of −15
Answer:
y = 3/4( x+5)( x+4) ( x-1)
Step-by-step explanation:
The formula for the polynomial is
y = c( x- a1)( x- a2) ( x-a3) where c is a constant and a1,a2,a3 are the zeros
We have zeros -5,-4 and 1
y = c( x- -5)( x- -4) ( x-1)
y = c( x+5)( x+4) ( x-1)
We have a y intercept of -15
That means x=0 and y = -15
-15 = c ( 0+5)( 0+4) ( 0-1)
-15 = c( 5) ( 4) (-1)
-15 = c( -20)
Divide each side by -20
-15/-20 = c
3/4 =c
The equation is
y = 3/4( x+5)( x+4) ( x-1)
ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
We have f(x) and g(x). We are to evaluate each of these functions at the domain values given (1, 2, 3, 4, 5, and 6) and see where the output is the same.
[tex]f(1)=-(1)^2+4(1)+12[/tex] and f(1) = 15
[tex]f(2)=-(2)^2+4(2)+12[/tex] and f(2) = 16
[tex]f(3)=-(3)^2+4(3)+12[/tex] and f(3) = 15
[tex]f(4)=-(4)^2+4(4)+12[/tex] and f(4) = 12
[tex]f(5)=-(5)^2+4(5)+12[/tex] and f(5) = 7
[tex]f(6)=-(6)^2+4(6)+12[/tex] and f(6) = 0
Now for g(x) at each of these domain values:
g(1) = 1 + 2 and g(1) = 3
g(2) = 2 + 2 and g(2) = 4
g(3) = 3 + 2 and g(3) = 5
g(4) = 4 = 2 and g(4) = 6
g(5) = 5 + 2 and g(5) = 7
g(6) = 6 + 2 and g(6) = 8
It looks like the outputs are the same at f(5) and g(5). Actually, the domains are the same as well! f(5) = g(5)
Determine the equation of the line that is parallel to y=2/3x+4 and passes through the point (3,7)
Step-by-step explanation:
If the line is parallel to y=2/3x+4 then,
m=m
slope of eqn y=2/3x+4
m=2/3(On comparing with y= mx + c)
the passing point is (3,7) then,
y-y1 = m(x-x1)
y-7=2/3(x-3)
y-7=2/3x -2
y-7= -4x/3
3y-7= -4x
4x + 3y - 7=0
So, The reqd eqn is 4x + 3y - 7 = 0
Lines m and n are parallel, as shown in the diagram below. What are the measures of angles A and B? Hint: The sum of all interior angles of a triangle must equal 180 degrees.
Answer:
A = 55
B = 60
Step-by-step explanation:
We know that 55+ b+ other angle = 180 since they make a straight line
The other angle = 65 since they are alternate interior angles
55+ B+ 65 = 180
Combine like terms
120 + B = 180
B = 60
A + B + 65 = 180 interior angles of a triangle must equal 180 degrees
A +60+ 65 =180
Combine like terms
A +125 = 180
A = 55
Answer:
[tex]\boxed{A = 55\°}[/tex]
[tex]\boxed{B = 60\°}[/tex]
Step-by-step explanation:
Exterior Angle with A = 180 - 55 = 125 degrees (Angles on a straight line)
The measure of exterior angle is equal to the sum of non-adjacent interior angles.
So,
125° = B + 65°
B = 125 - 65
B = 60°
Now,
A = 180 - 60 - 65 (Interior angles of a triangle add up to 180 degrees)
A = 55°
There are 30 names in a hat. If two names are picked without repalcement, which expression shows the probability that Jack and Jill will be picked?
Step-by-step explanation:
The probability that either Jack or Jill will be selected on the first draw is 2/30.
The probability that the other person will be selected on the second draw is 1/29.
The probability of both events is (2/30) (1/29), which simplifies to 1/435.
A veterinarian clinic, there are twice as many dogs as there cats. If the total number of dogs and cats is 57, how many are dogs and how many are cats?
Answer: There are 19 cats and 38 dogs.
Step-by-step explanation:
Given, A veterinarian clinic, there are twice as many dogs as there cats.
Let x = Number of cats
then, number of dogs = 2x
Since , total number of dogs and cats = 57
So, x+ 2x= 57
[tex]\Rightarrow\ 3x= 57[/tex]
Divide both sides by 3 , we get
[tex]x=\dfrac{57}{3}=19[/tex]
[tex]\Rightarrow\ x= 19[/tex]
Number of cats =19
then, number of dogs = 2(19) = 38
hence, there are 19 cats and 38 dogs.
Answer: 19 cats and 38 dogs
Step-by-step explanation:
hope this helps
Determine the solution to the following set of linear equations by using the graph below
a) 2x + y = 5
2x - 2y = 2
Answer:
(2,1)
Step-by-step explanation:
Well first we single out y or x in one of the equations,
we’ll use 2x + y = 5 and single out y.
2x + y = 5
-2x to both sides
y = -2x + 5
So we can plug in -2x + 5 into y in 2x - 2y = 2.
2x - 2(-2x + 5) = 2
2x + 4x - 10 = 2
combine like terms,
6x - 10 = 2
Communicarice property
+10 to both sides
6x = 12
divide 6 to both sides
x = 2
If x is 2 we can plug 2 in for x in 2x + y = 5.
2(2) + y = 5
4 + y = 5
-4 to both sides
y = 1
(2,1)
Thus,
the solution is (2,1).
Hope this helps :)
If two lines are parallel to each other. Does that mean they are equal to each other as well?
Answer:
No.
Step-by-Step Explanation:
When two lines are parallel, they might or might not be equal. It is not necessary that they should be equal.
See the triangle below in which two lines are parallel to each other.
What is the approximate circumference of a circle that has a diameter of 25 yards? (Use 3.14 for pi ). C = a0 yd
Answer:
78.5 yds
Step-by-step explanation:
The circumference is given by
C = pi *d
C = 3.14 * 25
C =78.5
Answer:
[tex]\huge\boxed{C=25\pi\ yd\approx78.5\ yd}[/tex]
Step-by-step explanation:
The formula of a circumference of a circle:
[tex]C=d\pi[/tex]
d - diameter
We have d = 25yd.
Substitute:
[tex]C=25\pi\ yd[/tex]
Use [tex]\pi\approx3.14[/tex]:
[tex]C\approx(25)(3.14)=78.5\ yd[/tex]
Solve the following: (1 point) x + 3y = 9 3x − 3y = −13
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
(
−
1
,
10
3
)
Equation Form:
x
=
−
1
,
y
=
10
3
Tap to view steps...
image of graph
Tap to hide graph...
The graphed line shown below is y = negative 2 x minus 8. Which equation, when graphed with the given equation, will form a system that has infinitely many solutions? y = negative (2 x + 8) y = negative 2 (x minus 8) y = negative 2 (x minus 4) y = negative (negative 2 x + 8)
Answer: A y = -(2x+8)
Step-by-step explanation:
The first line is y=-2x-8
Thus, the answer that simplifies to y = -2x-8 is the answer.
a) y=-(2x+8)
Distribute
y=-2x-8
Because it works, no need to try the others.
Hope it helps <3
Answer:
[tex]\boxed{y = -(2x + 8)}[/tex]
Step-by-step explanation:
For the two lines to have infinite [tex]\infty[/tex] solutions, the two equations must be the same.
First equation : y = -2x - 8
A. y = -(2x + 8)
y = -2x - 8 correct
B. y = -2(x - 8)
y = -2x + 16 incorrect
C. y = -2(x - 4)
y = -2x + 8 incorrect
D. y = -(-2x+8)
y = 2x - 8 incorrect
y = -2x - 8 and y = -(2x + 8) when graphed are the same, they intersect at infinite points and there are infinite solutions.
The average age of 15 students is 16 years. If teacher’s age is included the average increases by 1. Find teacher’s age. (a) 30 years (b) 32 years (c) 58 years (d) 60 years
Answer:
Age of teacher = 32 years
Step-by-step explanation:
Average age of 15 students = 16 years
Sum of age of 15 students = 16 * 15 = 240 years
Average of age 15 students and a teacher = 17 years
Sum of age 15 students and a teacher = 17 * 16 = 272 years
Age of teacher = 272 - 240 = 32 years
Answer:
Age of teacher = 32 years
Therefore, the correct answer is (b)
Step-by-step explanation:
We know that average is given by
Average age = Sum of ages /no. of students
We are given that the average age of 15 students is 16 years.
16 = Sum of ages/15
Sum of ages = 16×15
Sum of ages = 240
We are given that If teacher’s age is included the average increases by 1.
16 + 1 = New sum of ages/15 + 1
17 = New sum of ages/16
New sum of ages = 17×16
New sum of ages = 272
So the age of the teacher is found by
Age of teacher = New sum of ages - Sum of ages
Age of teacher = 272 - 240
Age of teacher = 32 years
Therefore, the correct answer is (b)
When doctors prescribe medicine, they must consider how much the drug’s effectiveness will decrease as time passes. If each hour a drug is only 95% as effective as the previous hour, at some point the patient will not be receiving enough medicine and must be given another dose. If the initial dose was 250 mg, what will the level of the dose be after 3 hours?
Answer: The level of the dose be after 3 hours= 0.03125 mg.
Step-by-step explanation:
General exponential decay equation : [tex]y=A(1-r)^x[/tex] , where A = initial value , r= rate of decay , x =Time period.
Here, drug’s effectiveness is decreasing exponentially.
AS per given , we have
A= 250 mg
x=3
r= 95% = 0.95
Then, [tex]y=250(1-0.95)^3 = 250(0.05)^3=250*0.000125=0.03125[/tex]
Hence, the level of the dose be after 3 hours = 0.03125 mg.
Answer:
214.34 about (213.75 on calculator)
Step-by-step explanation:
95% of 250=237.5
95% of 237=225.15
95% of 225=213.75
A total of $10,000 is invested in two mutual funds. The first account yields 5% and the second account yields 6%. How much was invested in each account if the total interest earned in a year is $575?
Answer:
$2,500 was invested in the first account while $7,500 was invested in the second account
Step-by-step explanation:
Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments
Now, since we do not know the amount invested , we shall be representing them with variables.
Let the amount invested in the first account be $x and the amount invested in the second account be $y
Since the total amount invested is $10,000, this means that the summation of both gives $10,000
Mathematically;
x + y = 10,000 ••••••(i)
now for the $x, we have an interest rate of 5%
This mathematically translates to an interest value of 5/100 * x = 5x/100
For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100
The addition of both interests, gives 575
Thus mathematically;
5x/100 + 6y/100 = 575
Multiplying through by 100, we have
5x + 6y = 57500 •••••••••(ii)
From 1, we can have x = 10,000-y
let’s substitute this into equation ii
5(10,000-y) + 6y = 57500
50,000-5y + 6y = 57500
50,000 + y = 57500
y = 57500-50,000
y = 7,500
Recall;
x = 10,000-y
so we have;
x = 10,000-7500 = 2,500