Answers
Answer:
parallel lines both have slope 1/3; non-parallel lines both have length 5
Step-by-step explanation:
It generally works well to follow instructions.
A graph of the points shows you that the parallel sides are RA and PT. The difference between the end points of these segments are ...
A - R = (6, 8) -(-3, 5) = (9, 3) = (Δx, Δy)
So, the slope of RA is Δy/Δx = 3/9 = 1/3
And the other difference and slope are ...
P -T = (9, 4) -(-3, 0) = (12, 4) ⇒ Δy/Δx = 4/12 = 1/3
The slope of RA is the same as the slope of PT, so those segments are parallel.
__
The length of segment TR can be found from the differences of the end point coordinates:
R - T = (-3, 5) -(-3, 0) = (0, 5)
Since these points are on the same vertical line, this tells us the segment length is 5.
The other difference of coordinates is ...
A - P = (6, 8) -(9, 4) = (-3, 4)
The distance formula tells us the length of AP is then ...
AP = √((-3)² +4²) = √25 = 5
Non-parallel sides TR and AP have the same lengths, so the trapezoid is isosceles.
Related Questions
The Hartnett Corporation manufactures baseball bats with Pudge Rodriguez's autograph stamped on them. Each bat for $35 and has a variable cost of $22. there are $97,500 in fixed costs involved in the production process.
Find the sales (in units) needed to earn a profit of $300,000.
Answers
Answer:
Find the sales (in units) needed to earn a profit of $262,500
Step-by-step explanation:
hope this is helpful to you bro
a 680g patient comes in with diarrhea. the doctor orders anti-diarrhea medication at a dosage of 15 mcg/kg TID x 3 days. rhye medication concentration 50mcg/ml. What is the patients dose in MCG? What is the total volume of medication you will send home?
Answers
Answer:
dose in MCG = 10.2 mcg
Total volume to be sent home = 1.836 ml (1836μl)
Step-by-step explanation:
weight of patient = 680g
dosage in mcg of medication = 15mcg/kg
This means that
for every 1kg weight, 15mcg is given,
since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.
1000g = 15mcg
1g = 15/1000 mcg = 0.015 mcg
∴ 680g = 0.015 × 680 = 10.2 mcg
Dosage in MCG = 10.2 mcg
Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:
50mcg = 1 ml
1 mcg = 1/50 ml = 0.02 ml
∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml
since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.
therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)
Find five consecutive integers such that the sum of the first and 5 times the third is equal to 41 less than 3 times the sum of the second fourth and fifth
Answers
Answer:
see below
Step-by-step explanation:
We'll cal the first integer x and then the rest of them will be x + 1, x + 2, x + 3 and x + 4. We can write x + 5(x + 2) = 3(x + 1 + x + 3 + x + 4) - 41.
x + 5x + 10 = 3(3x + 8) - 41
6x + 10 = 9x + 24 - 41
6x + 10 = 9x - 17
3x = 27
x = 9
The numbers are 9, 10, 11, 12, 13.
ASAP
What is the sum of 16.87 + (–98.35)?
–115.22
–81.48
81.48
115.22
Answers
Solution,
16.87+(-98.35)
=16.87-98.35
= -81.48
Hope it helps
Good luck on your assignment
Answer:-81.48
Step-by-step explanation:
16.87 + (–98.35)
-81.48
If you stumble in other questions like there you can use a calculator or ask me. :D hope that helps
How many pound are in 28 ounces
Answers
Answer:
1.75
Step-by-step explanation:
Divide the ounces by 16 to get the value.
Jack buys a bag of 5 apples, each
equal in size. He eats of 1/2 of one apple.
What fraction of the bag of
apples did he eat?
Answers
Answer:
4 1/2
Step-by-step explanation:
5 apples - 1/2 apple =
4 1/2 apple
or
9/2
Which formula can be used to describe the sequence? - 2/3, -4, -24, -144
Answers
Answer:
They are all multiplied by 6
Answer:
Geometric sequence.
Step-by-step explanation:
Here are the terms :
-2/3, -4, -24, -144
Now the first term T1 = -2/3
The second Term T2 = -4
But T2/T1 = -4÷ -2/3 = -4 x -3/2 = 6
Similarly Term 3, T3 = -24
T3/T2 = -24/-4= 6
Hence the expression is a geometric sequence.
a×r^(n-1); a is the first term
r is the common ratio 6
n is the number of terms.
In order to understand reasons why consumers visit their store, a local business conducts a survey by asking the next 100 people who visit their store to fill out a short survey. The business finds that 40 of the 100 people state that the main reason they visited the store was because the store is running a sale on coats that week. A confidence interval is constructed for the population proportion of consumers who would visit the store because of the coat sale. Which confidence interval would be the narrowest?
a. 90%
b. 99%
c. 95%
d. 85%
Answers
Answer:
d. 85%
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The higher the confidence level, the higher the value of z, which means that the margin of error will be higher and the interval will be wider,
Which confidence interval would be the narrowest?
The one with the lowest confidence level. So the answer is d.
What is the answer to this question?
Answers
Answer:it is b
Step-by-step explanation:
3a^4b/7
A line intersects the point (-11, 4) and has
a slope of -2. What are the inputs to the
point-slope formula?
y - [?] = [ ](x-[])
Answers
Answer: Point slope form is y-y1=m(x-x1)
Step-by-step explanation:
Here y1=4
x1=-11
m i.e slope=-2
And there you go.
Merely needs to add enough water to 11 gallons of an 18% detergent solution to make 12% detergent solution which equation can she used to find g the number of gallon of water she should add?
Answers
1 × 18/100 = 12/100(g+11), is the equation. The answer is 12/100 gallons
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
Answers
Answer:
–2(5 – 4x) < 6x – 4
<=>
-10 + 8x < 6x - 4
<=>
2x < 6
<=>
x < 3
Hope this helps!
:)
Answer:
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
A. x < –3
B. x > –3
C. x < 3
D. x > 3
Step-by-step explanation:
The correct answer here is C. x < 3
find the slope of a line parallel to y=(2/5)x + (4/5)
Answers
Answer:
So if a line was parallel it would have same slope. You can search up what slope-intercept form means. But if you have an equation like this:
y = mx+b
The slope will be m. Your question is written in the form. 2/5 = m.
The slope is 2/5
The y-intercept is 4/5
Answer:
m=2/5
Step-by-step explanation:
Lines that are parallel have the exact same slope.
We have an equation in point slope form.
y=mx+b
where m is the slope and b is the y-intercept.
The slope is the number being multiplied by x. In the equation
y=2/5x+4/5
2/5 and x are being multiplied. Therefore, 2/5 is the slope. A line that is parallel will have the same slope of 2/5.
Write the point slope form of an equation of the line through the points (-2,6) and (3,-3)
Answers
Answer:
A.
Step-by-step explanation:
So first you need to find the slope:
[tex]\frac{-2-6}{3+2} =-\frac{8}{5}[/tex]
Since it's point slope, you have to use a point:
It's either:
[tex](y - 6)=-\frac{8}{5}(x+2)[/tex]
or
[tex](y+2)=-\frac{8}{5}(x-3)[/tex]
Check which answer has those:
A.
The solution is Option A.
The equation of line is y - 6 = ( -8/5 ) ( x + 2 ) where the slope is -8/5
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -2 , 6 )
Let the second point be Q ( 3 , -2 )
The slope of the line between the point is given by m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - ( - 2 ) ) / ( -2 - 3 )
On simplifying the equation , we get
Slope m = ( 8 / -5 ) = -8/5
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 6 = ( -8/5 ) ( x - ( -2 ) )
On simplifying the equation , we get
y - 6 = ( -8/5 ) ( x + 2 )
Hence , the equation of line is y - 6 = ( -8/5 ) ( x + 2 )
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ2
The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
Answers
Answer:
Option (2). 14 m
Step-by-step explanation:
Formula to get the area of a circle 'A' = [tex]\pi r^{2}[/tex]
where r = radius of the circle
Given in the question,
Area of the circle = 153.86 square meters
By putting the values in the formula,
153.86 = πr²
r = [tex]\sqrt{\frac{153.86}{\pi } }[/tex]
r = [tex]\sqrt{49}[/tex]
r = 7 meters
Diameter of circle = 2 × (radius of the circle)
= 2 × 7
= 14 meters
Therefore, diameter of the circle is 14 meters.
Option (2) is the answer.
Answer:
14m
Step-by-step explanation:
If 25% of a number is 100, what is the number?
OA.
50
B.
100
O C.
150
D.
200
o E.
400
Answers
Answer:
E. 400
Step-by-step explanation:
So this is how we set this up, and how we solve
[tex]0.25x=100\\x=100/0.25\\x=400[/tex]
Hope this helps!
So you are solving for circumference of a quarter circle: [tex]\frac{1}{4}2 \pi r[/tex]
r= 28
[tex]\pi=3.14[/tex]
[tex]\frac{1}{4}2(87.92)=\\43.96[/tex]
A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will not be sold if there are actually three dead batteries in the package
Answers
Answer:
There is a probability of 76% of not selling the package if there are actually three dead batteries in the package.
Step-by-step explanation:
With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:
n=4 (the amount of batteries picked for the sample).p=3/10=0.3 (the proportion of dead batteries).k≥1 (the amount of dead batteries in the sample needed to not sell the package).The probability of having k dead batteries in the sample is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]
Then, the probability of having one or more dead batteries in the sample (k≥1) is:
[tex]P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{4}{0} p^{0}q^{4}=1*1*0.7^4=0.2401\\\\\\P(x\geq1)=1-0.2401=0.7599\approx0.76[/tex]
What is the distance from point N to line LM in the figure below?
Answers
Answer:
The correct answer would be F. 7.8
Step-by-step explanation:
the line is more or less a reflection of segment ON
so they are more or less the same.
I hope this helped you!
Select and place the symbol that will make the statement true |-a| |a|
Answers
Answer:
|-a|=|a|
Step-by-step explanation:
The lines beside the a's mean that you are trying to find the absolute value of what's inside. The absolute value of something is the distance it is from 0. You can't have a negative distance so anything inside of absolute value line are positive.
Therefor this is how we can solve this.
|-a| __ |a|
a __ a
a=a
we choose a sample of size 100 from a population of monthly cable bills having standard deviation $20 If we assume the population mean bill is $65, what is the probability mean of our sample is greater than $70.
Answers
Answer:
0.0062
Step-by-step explanation:
Find the standard error.
σ = 20 / √100
σ = 2
Find the z-score.
z = (x − μ) / σ
z = (70 − 65) / 2
z = 2.5
Find the probability.
P(Z > 2.5) = 1 − 0.9938
P(Z > 2.5) = 0.0062
g A cannonball is shot with an initial speed of 62 meters per second at a launch angle of 25 degrees toward a castle wall that is 260 meters away. If the wall is 20 meters tall, how high off the ground will the cannonball hit
Answers
Answer:
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Step-by-step explanation:
Given;
Initial speed v = 62m/s
Angle ∅ = 25°
Horizontal distance d = 260 m
Height of wall y = 20
Resolving the initial speed to vertical and horizontal components;
Horizontal vx = vcos∅ = 62cos25°
Vertical vy = vsin∅ = 62cos25°
The time taken for the cannon ball to reach the wall is;
Time t = horizontal distance/horizontal speed
t = d/vx (since horizontal speed is constant)
t = 260/(62cos25°)
t = 4.627 seconds.
Applying the equation of motion;
The height of the cannonball at time t is;
h = (vy)t - 0.5gt^2
Acceleration due to gravity g = 9.81 m/s
Substituting the given values;
h = 62sin25×4.627 - 0.5×9.81×4.627^2
h = 16.2264134736
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Please answer this correctly
Answers
Answer:
pic wont load
Step-by-step explanation:
Answer:
The quarter circle's area is 38.47 yard²
Step-by-step explanation:
The area of a full circle is pi * r ²
The area of a quarter circle is 1/4 * pi * r ²
Given:
Use 3.14 for pi
Round to the nearest hundredths.
Perimeter of quarter circle is 24.99 yards
For r you must leave it as 'r' because we do not know it for now...
1. Circumference of a full circle = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * r )
1/2 * 3.14 * r
1.57 * r
3 Since r = 'r'
We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.
4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch
1.57 * r + 2 * r = 24.99
( 1.57 + 2 ) * r = 24.99
3.57 * r = 24.99
Divide left and right of the = sign by 3.57
3.57 / 3.57 * r = 24.99 / 3.57
1 * r = 24.99 / 3.57
r = 7
The area of a quarter circle is 1/4 * pi * r ²
1/4 * pi * 7²
1/4 * 49 * pi
49/4 * pi
49/4 * 3.14
38.465
Round to the nearest hundredths gives 38.47 yard²
The quarter circle's area is 38.47 yard²
An aeroplane X whose average speed is 50°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then changes its course and flies on a bearing 1200 to an airstrip A. Another aeroplane Y leaves kano airport at 10.00am and flies on a straight course to the airstrip A. both planes arrives at the airstrip A at 11.30am. calculate the average speed of Y to three significant figures. the direction of flight Y to the nearest degree
Answers
Answer:
(a)123 km/hr
(b)39 degrees
Step-by-step explanation:
Plane X with an average speed of 50km/hr travels for 2 hours from T (Kano Airport) to point U in the diagram.
Distance = Speed X Time
Therefore: Distance from T to U =50km/hr X 2 hr =100 km
It moves from Point U at 9.00 am and arrives at the airstrip A by 11.30am.
Distance, UA=50km/hr X 2.5 hr =125 km
Using alternate angles in the diagram:
[tex]\angle U=110^\circ[/tex]
(a)First, we calculate the distance traveled, TA by plane Y.
Using Cosine rule
[tex]u^2=t^2+a^2-2ta\cos U\\u^2=100^2+125^2-2(100)(125)\cos 110^\circ\\u^2=34175.50\\u=184.87$ km[/tex]
Plane Y leaves kano airport at 10.00am and arrives at 11.30am
Time taken =1.5 hour
Therefore:
Average Speed of Y
[tex]=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)[/tex]
b)Flight Direction of Y
Using Law of Sines
[tex]\dfrac{t}{\sin T} =\dfrac{u}{\sin U}\\\dfrac{125}{\sin T} =\dfrac{184.87}{\sin 110}\\123 \times \sin T=125 \times \sin 110\\\sin T=(125 \times \sin 110) \div 184.87\\T=\arcsin [(125 \times \sin 110) \div 184.87]\\T=39^\circ $ (to the nearest degree)[/tex]
The direction of flight Y to the nearest degree is 39 degrees.
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5? A. 1 over 13 B.1 over 8 C.5 over 13 D.5 over 8 PLEASE HURRY!!!!!!!!!!!!!!!!!
Answers
Answer:
B. 1 over 8
Step-by-step explanation:
To determine the probability of the spinner landing on 5, we need to first know what probability is,
probability = required outcome/all possible outcome
since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner. This implies that all possible outcome = 64
In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.
This implies that the required outcome = 8
but
probability = required outcome/all possible outcome
probability (of the spinner landing on 5) = 8/64 =1/8
Answer:
b
Step-by-step explanation:
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply.
Answers
Answer:
see below
Step-by-step explanation:
In my opinion, Antoinette should make use of a graphing calculator to find the solution. (second attachment)
__
Slope-intercept form can be useful for graphing, so it often works well to start with equations in that form. If that is Antoinette's strategy, she should rewrite the first equation to that form. The second equation is already in slope-intercept form.
In doing that rewrite, she will want to get the y-term on one side of the equal sign by itself. She can do that by subtracting 2x from the first equation:
-7y = -2x +56
As a final step in her rewrite, she would divide by -7 to get ...
y = 2/7x +56
This 2nd equation has a positive slope of 2/7. The slope of the second equation is similarly the x-coefficient, -2.5. Neither is 4 and they have different signs.
The appropriate answer choices are shown checked below.
Answer:
B and D
Step-by-step explanation:
I got it right m8. Good day
WRITING BOOK
Personal Writing
AD 1
NUMBERS
Which of the following cannot be an integer?
A. 0.8
B. -3
C. 4
D. 25
Answers
Answer:
A
Step-by-step explanation:
Integers are negative and positive whole numbers
Answer: A. 0.8
Step-by-step explanation:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $18.5 for a random sample of 2253 people. Assume the population standard deviation is known to be $6.1. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Answers
Answer:
= ( $18.2, $18.8)
Therefore, the 98% confidence interval (a,b) = ( $18.2, $18.8)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $18.50
Standard deviation r = $6.10
Number of samples n = 2253
Confidence interval = 98%
z(at 98% confidence) = 2.33
Substituting the values we have;
$18.5+/-2.33($6.1/√2253 )
$18.5+/-2.33($0.128513644290)
$18.5+/-$0.299436791196
$18.5+/-$0.3
= ( $18.2, $18.8)
Therefore at 98% confidence interval (a,b) = ( $18.2, $18.8)
Given that y = 1.5 at x = -2. Find the function y = f(x) such that
dy/dx=√(4y+3)/x²
Answers
Answer:
[tex]y=\frac{(-\frac{4}{x}+1)^2-3 }{4}[/tex]
Step-by-step explanation:
We are given the following information. y have the point [tex](-2,\frac{3}{2} )[/tex] and [tex]\frac{dy}{dx} =\frac{\sqrt{4y+3} }{x^2}[/tex]
First, we need to separate the variables to their respective sides
[tex]\frac{1}{\sqrt{4y+3} } dy=\frac{1}{x^2} dx[/tex]
Now, we need to integrate each side
[tex]\int \frac{1}{\sqrt{4y+3} } dy=\int\frac{1}{x^2} dx[/tex]
But first, let us rewrite these functions
[tex]\int (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Before we can integrate, we need to have the hook for the first function. When we integrate [tex](4y+3)^{-\frac{1}{2} }[/tex], we must have a lone 4 within the integral as well.
[tex]\frac{1}{4} \int4 (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Now we can integrate each side to get
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + c[/tex]
Now is the best time to use the given point in order to find the value of c.
[tex]\frac{1}{4} \sqrt{4(\frac{3}{2}) +3} =-\frac{1}{-2} + c\\\\\frac{1}{4}\sqrt{6+3} =\frac{1}{2} +c \\\\\frac{3}{4}=\frac{1}{2} +c\\ \\c=\frac{1}{4}[/tex]
Now we can plug in our value for c and then solve for y
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + \frac{1}{4} \\\\\sqrt{4y+3}=-\frac{4}{x} +1\\ \\4y+3=(-\frac{4}{x} +1)^2\\\\4y=(-\frac{4}{x} +1)^2-3\\\\y=\frac{(-\frac{4}{x} +1)^2-3}{4}[/tex]
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of points scored during a basketball game b. The number of free dash throw attempts before the first shot is made c. The response to the survey question "Did you smoke in the last week question mark " d. The number of people in a restaurant that has a capacity of 150 e. The time it takes for a light bulb to burn out f. The height of a randomly selected giraffe a. Is the number of points scored during a basketball game a discrete random variable, a continuous random variable, or not a random variable?
Answers
Answer:
a. Discrete random variable
b. Discrete random variable
c. Discrete random variable
d. Discrete random variable
e. Continous random variable
f. Continous random variable
Step-by-step explanation:
a. The number of points scored during a basketball game.
This is a random variable, that only takes integer values, so it is a discrete random variable.
b. The number of free dash throw attempts before the first shot is made.
This is a count, so it is a discrete random variable.
c. The response to the survey question "Did you smoke in the last week question mark".
This is a boolean random variable (only two values), and can be considered discrete.
d. The number of people in a restaurant that has a capacity of 150.
This is a count of people, so it is a discrete random variable.
e. The time it takes for a light bulb to burn out.
Time is continous, so it is a continous random variable.
f. The height of a randomly selected giraffe.
Height, as it is a distance, is also a continous variable, so it is a continous random variable.
PLEASE HELP ME GUYS!!
Answers
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
csc(Ф) is equivalent to the inverse of sin(Ф)
[tex]csc = \frac{1}{sin}[/tex]Since sin(Ф) = 3/7, the inverse of this would be 7/3
So, [tex]csc = \frac{1}{\frac{3}{7} }=\frac{7}{3}[/tex]
