Answer:
You mean that if we have two pairs of points, (x1, y1) and (x2, y2)
we can find the slope of the line that conects those two points as:
a = (y2 - y1)/(x2 - x1)
remember that a linear equation has the shape:
y(x) = a*x + b
Now let's prove it:
for our case we have that
y1 = a*x1 + b
y2 = a*x2 + b
we can isolate be in both equtaions and get:
b = y1 - a*x1
b = y2 - a*x2
this means that:
y1 - a*x1 = y2 - a*x2
then:
a*x2 - a*x1 = y2 - y1
a*(x2 - x1) = y2 - y1
a = (y2 - y1)/(x2 - x1)
Which is the thing we wanted to get.
The subtraction of y-values and x-values to find the slope of a line is based on measuring the rate of change of y (rise) per unit change in x (run). This concept is fundamental in determining and understanding the steepness of a line on a graph.
Explanation:To understand why we subtract y-values and x-values to find the slope, let's look at the formula for the slope of a line, m = (y2 - y1) / (x2 - x1). Here, 'm' represents the slope of the line, the y values (y2 and y1) represent points on the vertical axis, and the x values (x2 and x1) represent points on the horizontal axis.
When we say 'slope', we mean how steep a line is. That steepness is determined by how much y changes (the rise) for a certain amount of change in x (the run). By subtracting y-values and x-values from each other, we are able to accurately measure this change, and therefore calculate the slope of the line.
Graphically, if we consider two points on a straight line, the slope of the line (m) can be seen as how much the line rises (the difference in y-values) for each unit it runs horizontally (the difference in x-values).
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A survey of 480 high school students found that 37% had a pet. Find the margin of error. Round to the nearest percent. Use the margin of error to find an interval that is likely to contain the true population proportion.
Answer:
[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
And replacing we got:
[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]
And replacing into the confidence interval formula we got:
[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]
[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]
And the 95% confidence interval would be given (0.327;0.413).
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Assuming a 95% of confidence. For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.96[/tex]
The margin of error would be:
[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
And replacing we got:
[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]
And replacing into the confidence interval formula we got:
[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]
[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]
And the 95% confidence interval would be given (0.327;0.413).
For a game show, Jared has to choose 1 of 8 boxes to win a prize. One of the boxes has a big prize, 3 boxes have a medium prize, 3 boxes have smaller prizes, and 1 box is empty. How confident should Jared be that whatever box he chooses, he will win a prize?
Answer:
He should be very confident
Step-by-step explanation:
He should be very confident because he has a 7 out of 8 chance of getting a small medium or large prize and he has a 1 out of 8chance of getting nothing
The probability that the box selected will win the prize is A = 7/8 = 87.5 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the box selected will win the prize be A
Now , the total number of boxes = 8
The box which has a big prize = 1
The number of boxes which have medium prize = 3
The number of boxes which have small prizes = 3
So , the total number of boxes with prize = 7 boxes
And , probability that the box selected will win the prize A = total number of boxes with prize / total number of boxes
On simplifying , we get
The probability that the box selected will win the prize A = 7 / 8
The probability that the box selected will win the prize A = 0.875
Hence , the probability is 7/8
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The radius of a circle is 9 millimeters. What is the circle's circumference?
The circumference of a circle with a radius of 9 millimeters is approximately 56.54867 mm, or 57 mm when rounded to two significant figures.
Explanation:The circumference of a circle can be calculated using the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle. Given that the radius of the circle is 9 millimeters, we can plug this value into the formula to find the circumference.
C = 2 × 3.14159 × 9 mm
After calculating, the circumference (C) is 56.54867 mm. However, if we keep the significant figures consistent with the given radius, the circumference is approximately 57 mm.
The circumference of the circle with a radius of 9 millimeters is approximately 56.55 millimeters, calculated using the formula [tex]\(C = 2 \pi r\)[/tex].
The circumference (C) of a circle is calculated using the formula [tex]\(C = 2 \pi r\)[/tex], where r is the radius of the circle. Given that the radius (r) is 9 millimeters, substitute this value into the formula:
[tex]\[ C = 2 \pi \times 9 \][/tex]
Using an approximate value for [tex]\(\pi\)[/tex], which is 3.14159, the calculation is:
[tex]\[ C \approx 2 \times 3.14159 \times 9 \][/tex]
[tex]\[ C \approx 56.54867 \][/tex]
Therefore, the circumference of the circle with a radius of 9 millimeters is approximately 56.55 millimeters.
In the diagram, point C represents the center of the sphere. Diego says that the part of the sphere labeled D is the radius. Gregoire says that the part of the sphere labeled D is the diameter of the sphere.
A sphere. C is the center and D is the diameter.
Who is correct and why?
Gregoire is correct; the diameter is a chord that passes through the center of the sphere.
Gregoire is correct; the diameter is a chord that is from the center to the surface of the sphere.
Diego is correct; the radius is a chord that passes through the center of the sphere.
Diego is correct; the radius is a chord that is from the center to the surface of the sphere.
HELPPPP ASAPPP PLEASEEEEEE!!!!!!
Answer:
Gregoire is correct; the diameter is a chord that passes through the center of the sphere.
Step-by-step explanation:
A sphere is a geometrical shape formed from a circle. Some of its parts are: diameter, center, radius circumference, etc.
The center of a sphere is a point at its middle. The diameter is a straight line, e.g a chord, that is drawn from one point on the circumference of a sphere to another point and passes through its center. While radius is a line that is from the center of the sphere to a point on its circumference.
A diameter is twice of a radius, so that:
Radius = [tex]\frac{Diameter}{2}[/tex]
⇒ Diameter = 2 × Radius
Therefore with respect to the question, Gregoire is correct because a diameter is a chord that passes through the center of the sphere.
Answer:
a
Step-by-step explanation:
The area of a playground is 168 yd2. The width of the playground is 2 yd longer than its length. Find the length and width of the playground. Then, enter the sum of the length and width in the provided grid.
[ ] [ ] [2] [6]
/ ОО
. ООООO
0 ОООО
1 ОООО
2 ОООО
3 OOOO
4 ОООО
5 ОООО
6 OOOO
7 OOOO
8 OOOO
9 OOOO
Answer:
Length = 12yards
Width = 14yards
Sum = 26yards
Step-by-step explanation:
Let assume the play ground is rectangular in form.
Area of a rectangle = length × width
Given area of the playground = 168yd²
If the width of the playground is 2yd longer than its length, then:
W = L+2
Substituting W = L+2 into the formula above we have:
A = L × (L+2)
A = L²+2L
168 = L²+2L
L²+2L-168 = 0
L²+14L-12L-168 = 0
L(L+14)-12(L+14) = 0
(L-12)(L+14) = 0
L-12 = 0 and L+14 =0
L = 12 and -14
Taking the positive length, L = 12yards
If Length = 12yards
W = L+2
W = 12+2
Width = 14yards
Sum of the length and width will be:
L+W= 12+14
= 26yards
Answer:
The length of playground is 12 yd
The width of playground is 14 yd
The sum of the length and width of playground is 26 yd
Step-by-step explanation:
The area, A of the playground is given as 168 yd²
The formula for the area of the playground is given as follows;
Area, A of playground = Length, L × Width, W
The Width = length + 2 yd or W = L + 2
Therefore, A = L × (L + 2)
A = L² + 2·L
Where we have A = 168 yd², we have the area equation presented as follows
168 = L² + 2·L or
L² + 2·L - 168 = 0
Factorizing the above equation gives
L = 12 or L = -14 we note that the appropriate solution is L = 12 yd
Therefore W = L + 2 = 12 + 2 = 14 yd
The length of playground = 12 yd
The width of playground = 14 yd
The sum of the length and width of playground = 12 + 14 = 26 yd.
Jim has to choose between two gym membership plans. Plan A has a $50 initial fee and then it costs $10 per visit. Plan b has a initial $25 membership fee and then it will cost her $15 per visit
If we are looking for when they would be the same at a given time:
First, we need to set them to each other:
50 + 10x = 25 + 15x
Move them around and then get this:
25 = 5x
Divide by 5 from both sides
5 = x
Lincoln wants to mix 3/8 of a liter of red paint with 7/8 of a liter of blue paint to make purple paint. How many liters of purple paint will Lincoln make by mixing the two colors?
Answer: 1 1/4
Step-by-step explanation:
Solving the fraction parts
3/8 + 7/8 = 10/8
Reducing the fraction part, 10/8
10/8= 5/4
Simplifying the fraction part, 5/4
5/4= 1 1/4
Answer:
10/8
Step-by-step explanation:
You add 7/8 + 3/8 and that equals 10/8
I hope that's helpful
A cylindrical tank has a diameter of 10 and a height of 7 feet. If each cubic foot holds 7.48 gallons of water, how many gallons of water does the tank hold?
Answer:
The tank can hold 4110.26 gallons of water.
Step-by-step explanation:
In order to solve this question we need to compute the volume of this tank, the volume is given by:
V = (area of the base)*height
Since the base is circullar, it is given by:
area of the base = pi*r^2
So we have:
V = height*pi*r^2
The radius of circle is the diameter divided by 2, so in this case r = 10/2 = 5 ft. We can now use the values on the equations:
V = 7*3.14*(5)^2 = 549.5 ft^3
Since each cubic foot holds 7.48 gallons of water the volume in gallons is:
V = 549.5*7.48 = 4110.26 gallons
The tank can hold 4110.26 gallons of water.
To find the number of gallons a cylindrical tank can hold, calculate the volume in cubic feet using the formula V = πr^2h, where the diameter is 10 feet (radius is 5 feet) and the height is 7 feet, then multiply the volume by 7.48 gallons per cubic foot.
Explanation:To calculate the number of gallons a cylindrical tank can hold, we first need to find the volume of the cylinder in cubic feet and then convert that volume to gallons. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the diameter of the tank is given as 10 feet, the radius (r) would be half of that, which is 5 feet. The height (h) is given as 7 feet. Plugging these values into the formula, we get:
V = π(5)^2(7) = π(25)(7) = π(175) cubic feet.
Using the conversion factor 7.48 gallons per cubic foot, we can find the total gallons the tank holds:
Gallons = Cubic feet × 7.48 gallons/cubic foot
Gallons = π(175) × 7.48 gallons/cubic foot
We thus calculate the total volume in gallons.
Convert the decimal expansion of 0.152 into a rational number (fraction) in the simplest form
Answer:
The answer to your question is 77/500
Step-by-step explanation:
Data
decimal number = 0.154
fraction number = ?
Process
To convert a decimal number into a fraction, express the decimal number without the zero and the decimal point (this number will be the numerator) and write as a denominator a number one plus as many zeros after this number as numbers there are after the decimal point of the numerator.
Example
0.154 has three number after the decimal point then we write 1000
154/1000 =
Simplify
77/500
Use the spinner to identify the probability to the nearest hundredth of the pointer
landing on a shaded area.
Describe how to find the number of seats on the middle and lower levels of the stadium when solving for the variable only gives the number of seats on the upper level.
Answer:
Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level. Substitute the value for the variable into the expression for the number of seats on the lower level.
If tan A = 4/5; what does CSC A =?
Round to nearest tenth.
Answer:
1.6
Step-by-step explanation:
[tex] \tan \: A = \frac{4}{5} \\ \\ \cot \: A = \frac{1}{ \tan \: A } = \frac{1}{ \frac{4}{5} } = \frac{5}{4} \\ \\ csc\: A = \sqrt{1 + {cot}^{2}\: A} \\ = \sqrt{1 + { \bigg( \frac{5}{4} \bigg)}^{2} } \\ = \sqrt{1 + \frac{25}{16} } \\ = \sqrt{\frac{16 + 25}{16} } \\ = \sqrt{\frac{41}{16}} \\ = \frac{ \sqrt{41} }{4} \\ = \frac{6.40312424}{4} \\ = 1.60078106 \\ \therefore \: csc \: A =1.6[/tex]
Find the product.
(x + 9)(4x2 + 5x + 6)
Answer:
4x^3 + 41x^2 +51x + 54
Step-by-step explanation:
This is a polynomial distribution
(x + 9 )(4x^2 + 5x + 6) We start by multiplying every term with x
4x^3 + 5x^2 + 6x there is plus sign between (x+9) so we put plus and start multiplying every term by 9
4x^3 + 5x^2 + 6x + 36x^2 + 45x + 54
4x^3 + 41x^2 +51x + 54
How many children answered
any adults?
Answer:
Step-by-step explanation:
Santiago buys T-shirts for $6 each and marks up the price by 45%. How much profit does Santiago make from each T-shirt sold?
Answer:
Santiago earns 8.7 $ from each sold shirt
Step-by-step explanation:
1). 45 % of 6 is = 6 * 0.45 = 2.7 $
2). 6 $ + 45 % of 6 = 6 + 2.7 = 8.7 $ - Answer
Given ABC = EDC find m
Answer: m<D = 80º
Step-by-step explanation:
Since we know triangle ABC is congruent to triangle EDC, the angle 60º can be know for angle ACB. Triangles have a interior total of 180, so 40+60 is 100. Subtract 100 from 180 to get your angle of B. Since the triangles are similar we know that B=D so D=80º
Find the value of x
6
5
10
Answer:
10
Step-by-step explanation:
You can use process of elimination for this question
Since one of the chord is drawn in and part on the radius is connected to it, that "part" radius bisects the chord
Therefore, the chord is 16 units long
Then the diameter must be even longer
The only option that works for the radius is 10 as the diameter would be 20
If the radius was 5, the diameter would be 10 which is less than the chord
If the radius was 6, the diameter would be 12 which is less than the chord
what is the product of (x+9)(x-9)
Answer:
x^2 - 81
Step-by-step explanation:
There is a formula called the difference of squares, which is
(a+b)(a-b) = a^2 - b^2
Answer: 9x²-81x
Step-by-step explanation:
1. Reorder the terms like this: (9x)• (x-9)
2. Remove unnecessary Parentheses like this: 9x•(x-9)
3. Distribute 9x through the Parentheses like this:
9x would become 9x² (because I combined 9x and 9x which become 9x²)
(x-9) would become -81x (so if you need further explanation I took the (x-9) and made it -9x then multiplied it by the 9x because of distributive property.)
The solution: 9x²-81x
Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. The second cylinder has a diameter of 3 inches.
If the second cylinder has the same ratio of diameter to height, what is its height?
Answer:
7 inches
Step-by-step explanation:
Height : Diameter
14 : 6
H : 3
H/14 = 3/6
H = 14 × 3/6
H = 7
Answer:
7 inches
Step-by-step explanation:
Find the indicated limit, if it exists.
Answer:
limit is 2.
Step-by-step explanation:
f(x) = 10x + 2 for x< 0 ,
f(x) = |2 - x| for x>=0
get x close to 0
lim 10x + 2 x-->0- = 2
lim |2 - x| x-->0+ = 2
PLEASE HELP
55 50 54 57 50 55 53 52 55
What is the median length of the data?
50 mm
54 mm
55 mm
57 mm
Answer:
54mm
Step-by-step explanation:
50, 50, 52,53, 54, 55, 55, 55, 57
3. Suppose m = 2 + 6i, and |m+n|=3√10, where n is a complex number.
a. What is the minimum value of the modulus of n?
b. Provide one example of the complex number, n.
Answer:
Answer:
Step-by-step explanation:
Suppose m = 2 + 6i, and |m+n|=3√10,
The modulus sign means m+n can either be positive or negative as shown.
If it is positive:.2+6i+n = 3√10
n = 3√10-(2+6i)
n = 3√10-2-18√10i
n = (-2+3√10)+√10i
b) Example of the complex number is given as (-2+3√10)+√10i. This is a complex number because it contains the real part and the imaginary part.
in a class of 30 students,13 of them are boys what parcentage of the class are girl give your aswer to 1 decimal place
Answer:
56.7% to one decimal place
Step-by-step explanation:
30 students
13 are boys
30-13=17
17 are girls
As a decimal 0.5667
As a percentage 56.67%
56.7% to one decimal place
A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots?
The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28
Explanation:
School students = 40
Total people = 130
Total contestant spot = 9
Probability of 3 contestant from school = ?
The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃
The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆
The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆
The total number of possible 9 contestants from the audience = ¹³⁰C₉
Probability of the group of contestants having 3 students = [tex]\frac{^4^0C_3 X ^9^0C_6}{^1^3^0C_9}[/tex]
Solving the equation further we get:
Probability of the group of contestants having 3 students = 0.28
(18,15) and (36,30) whats the slope?
Answer:
5/6
Step-by-step explanation:
Rise over run
y2-y1 / x2-x1
30-15 / 36-18
Hope this helps!
It cost ruby $4 to send 48 text messages what was her cost of texting in texts per dollar? Express your answer in simplest form
Answer:
Ruby pays a dollar every 12 messages.
Step-by-step explanation:
It costs Ruby $4 to send 48 text messages. To find the unit rate, you would divide 48 by 4. So the result would lead to 12 messages per dollar.
PLEASE HELP ME IF YOU CAN!
Answer:
y = 5[tex]e^{tan(x)}[/tex]
Step-by-step explanation:
work in picture below
Determine which of the following graphs does not represent a function
(Help me ASAP please)
Answer:
C
Step-by-step explanation:
In order to be a function, all of the graphs need to pass the vertical line test
Vertical line test- Only one point per vertical line, if there are more than one, it is not a function
C is the only one that has more than one point at a vertical line
The answer is c. If there are 2 points in a vertical line, it is not a function.
Which of the following statements are true of this rational function? Check all of the boxes that apply.
(x+ a) (x + b)
x² + ax
f(x)=-
Answer:
B.- There is no vertical asymptote at x=0
E.- There is a removable discontinuity at x= -a
Step-by-step explanation:
Answer:
The above answers are correct! The correct options are B and E!
Step-by-step explanation:
Hope this helped confirm :)
Have a great day!
what dimension or dimensions do you need to know to find the volume of a sphere?
Answer:
the radius
Step-by-step explanation:
4/3*pi*r squared