Answer:
The new price of this thing you're buying is about $35.58.
Step-by-step explanation:
To find the new price you could find 8.5% of 32.80 then add it to 32.80. That would give you the new price, or you could simply find 108.5% of 32.80. That one has less steps, so Im going to go with that.
What is 108.5% of 32.80?
Let's set up an equation then solve.
108.5% · 32.80 = X
1.085 · 32.80 = 35.588
The new price of this thing you're buying is about $35.58.
An installation technician for a specialized communication system is dispatched to a city only when 3 or more orders have been placed. Suppose the orders follow a Poisson distribution with a mean of 0.25 per week for a city with a population of 100,000 and suppose your city contains 800,000.
a. What is the probability that a technician is required after a one-week period?
b. If you are the first one in the city to place an order, what is the probability that you have to wait more than two weeks from the time you place your order until a technician is dispatched?
Answer:
0.3233
0.09
Step-by-step explanation:
Given that :
Mean, λ = 0.25 for a 100,000 per week
For a population of 800,000 :
λ = 800,000 / 100,000 * 0.25 = 8 * 0.25 = 2 orders per week
Probability that technician is required after one week ;
After one week, order is beyond 2 ; hence, order, x ≥ 3
P(x ≥ 3) = 1 - [p(x=0) + p(x= 1) + p(x =2)]
P(x ≥ 3) = 1 - e^-λ(1 + 2¹/1! + 2²/2!)
P(x ≥ 3) = 1 - e^-2(1+2+2) = 1 - e^-2*5 = 1 - e^-10
P(x ≥ 3) = 1 - e^-2 * 10
P(x ≥ 3) = 1 - 0.6766764
P(x ≥ 3) = 0.3233
B.)
Mean, λ for more than 2 weeks = 2 * 2 = 4
P(x < 2) = p(x = 0) + p(x = 1)
P(x < 2) = e^-4(0 + 4^1/1!)
P(x < 2) = e^-4(0 + 4) = e^-4(5)
P(x < 2) = e^-4(5) = 0.0183156 * 5 = 0.0915
P(x < 2) = 0.09
In a school there are totally 108 students in the third, fourth, and fifth grades. The third grade has 11 fewer students than the fourth grade, and the fourth grade has 16 more students than the fifth grade. How many students are there in each grade?
Answer:
there are about 36 students in each grade.
Step-by-step explanation:
divide the total amount of students by the amount of grades. 108/3 = 36
An isosceles triangle has legs of length 12 and base angles that measure 28°. What is the measure of its base to the nearest tenth? Be careful on this one.
Answer:
base = 21.2
Step-by-step explanation:
Let the base be 2x
Drawing a perpendicular bisector divides the bases into 2 equal parts.
Then using trigonometric ratio :
[tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex] , [tex][ \ where \ \theta = 28^{ \circ} , \ adjacent = x,\ hypotenuse = 12 \ ][/tex]
The trigonometric function gives the ratio of different sides of a right-angle triangle. The length of the base of the isosceles triangle is 21.19 units.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
In order to solve the problem, we will draw a line between the triangle such that it will bisect the angle at the top(∠A) and the base(BC). As shown in the image below.
Now, as we know that the line(AD) is perpendicular to the base(BC) of the isosceles triangle, therefore, using the function of trigonometry in the Δ ABD we can write,
[tex]Cos \theta=\dfrac{BD}{AB}\\\\\\Cos (\angle B)=\dfrac{BD}{12}\\\\\\Cos 28^o \times 12={BD}\\\\BD = 10.5953[/tex]
Now, we know that the line BD divides the base BC into two equal parts, therefore, BD=BC.
BC = BD + DC
BC = 10.5953 +10.5953
BC = 21.19 units
Hence, the length of the base of the isosceles triangle is21.19 units.
Learn more about Trigonometric functions:
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What is the area of the grey matting in this 8” by 10” picture frame if the picture to be framed is 4” x 6”? picture frame 64 square inches 56 square inches 24 square inches 80 square inches
Answer:
so if 8x10 is 80 and 4x6 is 24 then take 24 of 80 you get 56
Given a line passes through point (5,8) and the origin, find the equation of the line.
y=
Answer:
y = 8/5x
Step-by-step explanation:
I'm assuming that they're asking for the equation in point-slope form.
The formula is y=mx+b where:
m = slope
b = y intercept
However, the y intercept is just (0,0) so b = 0
To find the slope we already have 2 given points: (0,0) and (5,8)
To find slope you do rise/run and you get 8/5
Substitute the slope & y intercept in the formula:
y = 8/5x
Let me know if I'm wrong!!
Answer:
y=8/5x
Step-by-step explanation:
Hi there!
We need to find the equation of the line that passes through (5,8) and the origin (the point (0,0)).
There are 3 ways to write the equation of the line, although the most common way is slope-intercept form, or y=mx+b where m is the slope and b is the y intercept
first, let's find m (slope)
The formula for the slope calculated from two points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points
we have two points, but let's label their values to avoid any confusion
[tex]x_{1}[/tex]=5
[tex]y_{1}[/tex]=8
[tex]x_{2}[/tex]=0
[tex]y_{2}[/tex]=0
now substitute into the formula
m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m=[tex]\frac{0-8}{0-5}[/tex]
multiply
m=[tex]\frac{-8}{-5}[/tex]
divide
m=8/5
The slope of the line is 8/5
here's the equation so far
y=8/5x+b
now we need to find b
as the point will pass through both (5,8) and (0,0) we can use either one of them to solve for b
let's take (0,0) as an example
substitute 0 as x and 0 as y
0=8/5(0)+b
multiply
0=0+b
add
0=b
substitute 0 as b into the equation
Therefore the equation of the line is:
y=8/5x (the 0 is not necessary)
Hope this helps! :)
Question 5(Multiple Choice Worth 1 points)
(02.04 LC)
What is the equation of a line that contains the points (2,-2) and (0, -2)?
O y = 0
Ox= -2
O y = -2
Ox=0
The survey of a group of students showed that 50 like tea,40 liked coffee,35 liked milk,20 liked coffee as well as tea,18 liked tea as well as milk,12 liked coffee as well as milk and 7 liked all three. If every students liked at least one drink, how many students were asked this question ? Solve it by drawing a Venn- diagram.
Answer:
82
Step-by-step explanation:
whats the probabily of drawing one blue marbel from a bag that contains 4 red marbels 6 green marbles and 1 white marbel and 3 blue marble
Answer: 3/14
Step-by-step explanation:
Number of red marbles = 4
Number of green marbles = 6
Number of white marbles = 1
Number of blue marbles = 3
Total number of marbles = 14
Therefore, the probability of drawing one blue marble will be:
= Number of blue marbles / Total number of marbles
= 3/14
A bag contains 10 red marbles, 8
blue marbles and 2 yellow
marbles. What is the probability of
getting a blue marble?
The storage center sells rectangular storage spaces that are each 200 cubic feet. Each space is 5 feet long and 5 feet wide. What is the height of each storage space?
Answer:
h=8ft
Step-by-step explanation:
[tex]v = l \times w \times h[/tex]
[tex]h = \frac{v}{l \times v} = \frac{200}{5 \times 5} = 8[/tex]
please answer the question first then explain
Answer:
Option A.
Step-by-step explanation:
If I have two variables b and c and a constant of 10. I can write that problem like this:
10b = c
For example, my factory today will make 20 books:
10×20 = c
$ 200 = c
HELP MEEEEEEEEEEEE please
Answer:
X = 5
Step-by-step explanation:
Hope it's help you !!!!!!!!!
Answer:
X=5
Step-by-step explanation:
X=5
The other side is the same as X so it is 5. Also it the same as the bottom that = 5.
Q.1 You are Nu.9 in debt. You borrowed Nu. 15 more. What is the total amount of your debt?
Answer:
total of it is Nu.24
Step-by-step explanation:
just add all up into
9 + 15 = 24
Adele is 5 years older than Timothy. In three years, Timothy will be of Adele’s age. What is Adele’s current age?
Answer:
3
Step-by-step explanation:
+2
The following data represent the weights in pounds of a sample of 25 police officers:
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
Required:
a. Determine the location and value of the lower quartile of the weights
b. Determine the location and value of the upper quartile of the weights.
c. Find the interquartile range of the weights.
Given:
The data values are:
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
To find;
a. Lower quartile.
b. Upper quartile.
c. Interquartile range.
Solution:
We have,
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, 171.
Arrange the data values in ascending order.
134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157, 162, 163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177.
Divide the data values in two equal parts.
(134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177)
Divide each parentheses in two equal parts.
(134, 137, 140, 145, 146, 148), (151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169), (171, 172, 173, 174, 174, 177)
a. Location of lower quartile is:
[tex]Q_1=\dfrac{1}{4}(n+1)\text{th term}[/tex]
[tex]Q_1=\dfrac{1}{4}(25+1)\text{th term}[/tex]
[tex]Q_1=\dfrac{26}{4}\text{th term}[/tex]
[tex]Q_1=6.5\text{th term}[/tex]
The lower quartile of the weights is:
[tex]Q_1=\dfrac{148+151}{2}[/tex]
[tex]Q_1=\dfrac{299}{2}[/tex]
[tex]Q_1=149.5[/tex]
Therefore, the location of the lower quartile of the weights is between 6th term and the 7th term. The value of the lower quartile is 149.5.
b. Location of upper quartile is:
[tex]Q_3=\dfrac{3}{4}(n+1)\text{th term}[/tex]
[tex]Q_3=\dfrac{3}{4}(25+1)\text{th term}[/tex]
[tex]Q_3=\dfrac{3\cdot 26}{4}\text{th term}[/tex]
[tex]Q_3=19.5\text{th term}[/tex]
The upper quartile of the weights is:
[tex]Q_3=\dfrac{169+171}{2}[/tex]
[tex]Q_3=\dfrac{340}{2}[/tex]
[tex]Q_3=170[/tex]
Therefore, the location of the upper quartile of the weights is between 19th term and the 20th term. The value of the upper quartile is 170.
c. The interquartile range of the given data set is:
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=170-149.5[/tex]
[tex]IQR=20.5[/tex]
Therefore, the interquartile range of the weights is 20.5.
đường cầu về tiền có hướng nghiêng dốc xuống thể hiện?
13. The pair of figures are congruent. Find the value of e.
37°
10 ft
8 ft
53°
6 ft
Answer:
No solution is possible from the provided information
Step-by-step explanation:
312/132 (fraction simplified as a mixed number)
Answer:
2.3636363636 or 2 4/11
For the following right triangle find the side length x
Answer:
the answer should be 120 as the hypotenuse is obtained by √(a²+b²=c² )
Answer:
x = 17
Step-by-step explanation:
We're given a right triangle with the measures of two legs . We're also given as measures of hypotenuse as x .We need to find x.
Using Pythagorean theorem
a ² + b ² = c²
Where, a and b is the length of measures of legs and c is the measures of hypotenuse.Lebels the values , we get
( 15 ) ² + ( 8 )² = ( x ) ²
Expand the exponent
225 + 64 = x²
Add the numbers
289 = x²
Taking square root of both side
√289 = √x²
17 = x.
Hence, the length of side x is 17.
Write .125 as a fraction reduced to lowest terms.
Answer:
125 as a fraction is 1/8.
0.125 = 125/1000. We can reduce this to lowest terms by dividing the numerator and denominator by 125 to get the equivalent fraction 1/8.
Step-by-step explanation:
hey mate hope it cleared your problem!!
Mckenna kept track of the number of miles she rode her horse each day for 2 weeks 3.2.8, 8, 2,8, 8, 10, 4, 0, 0, 0, 0, 0, 0, 0 Part A Find the measures of center and variability that best summarize Mckenna's data. Use the dropdown menus to explain your reasoning, Choose The Choose is the best measure hours, is the best measure of center, so the Chooso... of variability LIVE Part 1 Mckenna says that she typically rides her horse for about 6 hours because the mode is 6. Is Mokenna's conclusion appropriate? Use the dropdown menus to explain your reasoning, Mckenna's conclusion Choose... accurate. The mode of her data Choose... 6 hours. However, Choose... than half of the time, she spends Choose.... than 6 hours riding her horse.
Answer: 110
Step-by-step explanation:
I did it it’s correct :)
Which mathematical operation changes 2amd 1/3 to 2
the addition sign thus 2+1÷3=2
These are two similar triangles. What is the measure of X?
Answer:
18
Step-by-step explanation:
just type the thing in the calculator
The measure of x for the given similar triangle will be 18 units.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
The triangle is a highly common shape that we deal with on a daily basis. For instance, the right-angle triangle is frequently used to estimate the height of towers.
By similar triangle rule ;
If two triangles are similar then the ratio of the corresponding side will be the same.
So,
x/12 = 24/(12+4)
x/12 = 1.5
x = 18 units.
Hence the measure of x will be 18 units.
For more information about triangle
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Determine whether the following event is mutually exclusive or not mutually exclusive.
Choosing a student who is a mathematics major or a business major from a nearby university to participate in a research study. (Assume that each student only has one major.)
Answer:
The event is mutually exclusive.
Step-by-step explanation:
Mutually exclusive events are events that cannot exist simultaneously.
Thus, events that are not mutually exclusive can exist simultaneously.
Since each student only has one major, a single student cannot be both a mathematics major and a business major.
So, the event is mutually exclusive.
Consider the function
f(x) = 327
=
As x + -00, then f(x) approaches what?
O A O
OB) 7
C) –00
C
D) 3
Ouestion 3 (1 point)
|-5| >3 true or false plssssss answer it’s important
Answer:
TRUE
Step-by-step explanation:
Those lines around the -5 mean the absolute value of the number, basically the value of the number without any negative signs. SO the absolute value of -5 is just 5.
5 IS GREATER than 3, so this is true
ur welcome :)
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 6 minutes and a population standard deviation of 2 minutes.
Find the probability that it took less than one minute to find a parking space. Round answer to four decimal places.
Answer:
56
Step-by-step explanation:
Answer: 0.0062
Step-by-step explanation:
((X + 2) + (y - 5) =1
Answer:
on like term
Step-by-step explanation:
x+2)=(y-5)=2+5=7
x-y{x-y]=7x-y
by Emmanuel okorie
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 14 cups of coffee, using 204 ounces of coffee, while collecting a total of $16.70. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Answer:
Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
Step-by-step explanation:
Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.
Since a total of 14 cups of coffee was served:
[tex]a+b+c=14[/tex]
A total of 204 ounces of coffee was served. Therefore:
[tex]10a+14b+20c=204[/tex]
A total of $16.70 was collected. Hence:
[tex]0.95a+1.15b+1.5c=16.7[/tex]
This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.
From the first equation, let's subtract a and b from both sides:
[tex]c=14-a-b[/tex]
Substitute this into both the second and third equations:
[tex]10a+14b+20(14-a-b)=204[/tex]
And:
[tex]0.95a+1.15b+1.5(14-a-b)=16.7[/tex]
In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:
For the Second Equation:
[tex]\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}[/tex]
And for the Third:
[tex]\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}[/tex]
We can solve this using substitution. From the second equation, isolate a:
[tex]\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b[/tex]
Substitute into the third:
[tex]-0.55(7.6-0.6b)-0.35b=-4.3[/tex]
Distribute and simplify:
[tex]-4.18+0.33b-0.35b=-4.3[/tex]
Therefore:
[tex]-0.02b=-0.12\Rightarrow b=6[/tex]
Using the equation for a:
[tex]a=7.6-0.6(6)=4[/tex]
And using the equation for c:
[tex]c=14-(4)-(6)=14-10=4[/tex]
Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
What is the slope of the line?
Answer:
3/1
Step-by-step explanation:
Answer:
[tex]-3[/tex]
Step-by-step explanation:
The slope of the line is -3 because to get to one point from another point, you would need to go down 3 and right 1 which is -3/1, and that is also just -3
Hope this helps