I WILL FIND THE GRADIENT FIRST
[tex]m = \frac{y2 - y1}{x2 - x1} \\ = \frac{5 - ( - 8)}{8 - 4} \\ m = \frac{5 + 8}{4} \\ m = \frac{13}{4} [/tex]
THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c
I will use the point (8,5)
to find the value of c
[tex]5 = \frac{13}{4} (8) + c \\ 5 = \frac{104}{4} + c \\ c = 5 - \frac{104}{4} \\ c = - \frac{84}{4} \\ c = -21[/tex]
THE EQUATION IS
[tex]y = \frac{13}{4} x - 21[/tex]
At a conference 1 car was provided for every 4 people if there were 17 cars how many people were there
Answer:
just multiply 17×4=?
and it will give u an anserew..
Answer:68 people
Step-by-step explanation:
You take the 17 cars multiplied by four people and you get 68
A hotel housekeeper earns an hourly wage of $15 per hour. What is this wage in dollars per year? (Assume a 40-hour work week.)
Answer: $31,200 per year
Step-by-step explanation:
The question tells us that they are working 40 hours a week and making 15 dollars an hour. We can find out how much they make a week and then multiply by 52 (number of weeks in a year) to find the amount they make in a year.
Per week:
15 * 40 = $600
Per Year:
600 * 52 = $31,200
Answer:
$31,285.74 per year
Step-by-step explanation:
What we know:
- $15 per hour
- 40 hour weeks
- 52.1429 weeks per year
What we need to find out:
- How much money per year
Step 1: Multiply for how much made per week
We know that we need $15 dollars for 40 hours so we start with multiplying them together to see how much we make a year.
40 x 15 = $600 per week
Step 2: Now multiply the amount of weeks a year by the amount made per week
So now we know that we make $600 per week now we have to multiply the amount of weeks in a year by the money made per week so.
52.1429 x 600 = $31,285.74 per year. So the house keeper makes $31,285.74 per year.
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Given diagram is a solid prism of a triangular base. if the base of the prism is 480 cm cube. find its height .
Answer:
20 cm
Step-by-step explanation:
Given a prism with a right triangle base and a volume of 480 cm³, you want the height of the prism. The base has one side 8 cm, and hypotenuse 10 cm.
Base edgeThe missing edge of the right triangle base can be found using the Pythagorean theorem. It tells us the square of the hypotenuse is the sum of the squares of the other two sides:
b² = c² +a²
10² = 8² +a² . . . . . . . use given lengths
a² = 100 -64 = 36 . . . . subtract 8², simplify
a = 6 . . . . . . . . . . . . . length of side BC
Base areaThe area of the right triangle base is ...
A = 1/2bh . . . . . . . . b is the triangle base; h is its height
A = 1/2(6 cm)(8 cm) = 24 cm²
VolumeThe volume of the prism is ...
V = Bh . . . . . . . . . . . . . . . where B is the base area, and h is the height
480 cm³ = (24 cm²)h . . . use known values
h = 20 cm . . . . . . . divide by the coefficient of h
The height of the prism is 20 cm.
Perform the indicated operation.55.557 + 121.4474 + 6.3
55.557 + 121.4474 + 6.3
we have that
55.557=55.5570
121.4474
6.3=6.3000
so
55.5570
121. 4474
6. 3000
------------------
183,3044What is the maximum volume of a rectangular prism (or box) if the prism has a square base and a total surface area of 100 cm^2?
A) First, let x = the side length of the base and h = the height of the prism. Write and solve the equation for h.
B) Write a function for the volume of the box, V, in terms of x.
a. The equation for h is h = 100/x²
b. The function for the volume of the box V, in terms of x is:
v(x) = x²×h
Given, the prism has a square base and a total surface area of 100 cm².
A) let x = the side length of the base and
h = the height of the prism.
equation for h = ?
Volume = b × h
100 cm² = x² × h
h = 100/x²
B) a function for the volume of the box, V, in terms of x.
we know that x is the base and h is the height.
So, volume in terms of x :
v = b×h
v = x² × h
Hence we get the required answers.
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Bella's mother is 5 less than 4 times her
daughter's age. If her mom is 39 years old, how
old Is Bella?
Which graph does not represent a function?
Answer: c
Step-by-step explanation:
Elliptical graphs fail the vertical line test as they have same x and y values at some places. Thus elliptical graph is not a function
14#A corporation that maintains a large fleet of company cars for the use of its sales staff is interested in the mean distance driven monthly per salesperson. The following list gives the monthly distances in miles driven by a random sample of 11 salespeople.2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290Send data to calculatorBased on this sample, find a 95% confidence interval for the mean number of miles driven monthly by members of the sales staff, assuming that monthly driving distances are normally distributed. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
Solution
Given the data set 2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290
The confidence interval formula is
Calculate the standard deviation of the data
The standard deviation is
237.67
Calculate the sample mean
The mean is 2262.91
[tex]\begin{gathered} s=237.67 \\ n=11 \\ mean=2262.909 \\ z=1.96 \end{gathered}[/tex][tex]\begin{gathered} CI=2262.909\pm1.96(\frac{237.67}{\sqrt{11}}) \\ CI=2262.909\pm1.96(71.6602) \\ CI=2262.909\pm140.453992 \\ CI\text{ = 2122.455008 to 2403.362992 to} \end{gathered}[/tex]Thus, the lower limit is
2122.455 ( 3 decimal places)
The Higher limit is 2403.363 ( 3 decimal places)
if a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand? (round your answer to five decimal places.) two pairs
=========================================================
Explanation:
A hand of two pairs is when we have 2 cards of the same value, and another 2 of the same value, then the fifth card is something else entirely.
An example hand is:
king of hearts, king of clubs ...... 1st pairqueen of spades, queen of clubs ..... 2nd pair7 of diamonds-------------
We use the nCr formula since order doesn't matter.
C(n,r) = (n!)/(r!*(n-r)!)
For any suit, there are n = 13 cards. We make r = 2 selections for each of the two pair.
C(n,r) = (n!)/(r!(n-r)!)
C(13,2) = (13!)/(2!*(13-2)!)
C(13,2) = (13!)/(2!*11!)
C(13,2) = (13*12*11!)/(2!*11!)
C(13,2) = (13*12)/(2!)
C(13,2) = (13*12)/(2*1)
C(13,2) = (156)/(2)
C(13,2) = 78
There are 78 ways to select which two ranks will be chosen to represent each of the two pair.
Let's say one of the ranks of the two pair is a king. There are n = 4 kings and we select r = 2 of them. That gives C(4,2) = 6 ways to select those two kings. We'll also have 6 ways to select the other two cards in the other pair.
Therefore, we have 78*6*6 = 2808 ways to pick the first four cards that consist of the two pair (eg: 2 kings and 2 queens).
-----------------
So far we've considered just the two pairs. We have one card left to select. There are 13-2 = 11 cards of any particular suit that weren't part of the two pair. There are 4 suits to pick from, which means we have 11*4 = 44 cards to pick from for that fifth and final slot.
-----------------
Summary so far:
2808 ways to pick the two pair (eg: 2 kings and 2 queens)44 ways to pick the fifth card that differs from the first four cards (anything other than what was chosen for the two pair).That gives 2808*44 = 123,552 different two pair hands possible.
This is out of C(52,5) = 2,598,960 hands
Divide those two values to get the final answer
(123,552)/(2,598,960) = 0.04753901560624
This then rounds to 0.04754 as the final answer.
5.What is the area of the triangle?Include the unit of measurein your answer.:::::
Answer: Area = 126 square inches
Explanation:
The formula for calculating the area of a triangle is expressed as
Area = 1/2 x base x height
From the information in the diagram,
base = 18
height = 14
Thus,
Area = 1/2 x 18 x 14
Area = 1/2 x 252 = 252/2
Area = 126 square inches
Nick is splitting 4 quarts of ice cream with 9 members of the team. If the ice cream is split evenly, how many cups will each person get? Explain1 quart equals _ pints, which equals _ cups, so 4 quarts equals _ cups. Dividing the ice cream among _ people means each gets _ cup(s)
ANSWER
[tex]\text{1}\frac{7}{9}\text{ cups}[/tex]EXPLANATION
Nick has 4 quarts of ice and he wants to split it with 9 members of the team.
To solve this, we have to convert quarts to cups. We have that:
1 quart = 2 pints
and
1 pint = 2 cups
This means that:
1 quart = 2 * 2 cups
1 quart = 4 cups
So, 4 quarts will be:
4 quarts = 4 * 4 cups
4 quarts = 16 cups
Therefore, dividing the ice cream among 9 people would mean that we have to divide 16 cups by 9 people.
That is:
[tex]\begin{gathered} \frac{16}{9} \\ =\text{ 1}\frac{7}{9}\text{ cups} \end{gathered}[/tex]The complete statement is:
1 quart equals 2 pints, which equals 4 cups, so 4 quarts equals 16 cups. Dividing the ice cream among 9 people means each gets 1 7/9 cup(s)
ive been struggling pls help
The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.
Given,
A random sample of n = 40
The mean time μ = 21.4
and, standard deviation is σ = 3.6 min
The z score (z) is given by the equation:
z = (x - μ) / σ / [tex]\sqrt{n}[/tex]
Substituting , the values we get
z = (20 - 21.4) / 3.6 /[tex]\sqrt{40}[/tex]
z = -2.45
Using the z table:
P(x < 20) = P(z < -2.45)= 0.00714
Hence, The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.
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a box contains 2828 red balls, 2020 green balls, 1919 yellow balls, 1313 blue balls, 1111 white balls, and 99 black balls. what is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 1515 balls of a single color will be drawn?
7069 are the minimum number of balls that must be drawn without replacement to complete the requirement that all balls of a single color be drawn.
First of all, we’ll look at the worst possible scenario and determine the minimum number of balls needed. We know that the color we are looking for is not blue, nor white, nor black (as there are less than 1515 of the same color when talking about those). In our worst possible scenario, we’ll first pull out all the blue, white, and black balls. Add them up. That means that we’ll definitely pull out 2523 balls( 1111 white + 1313 blue + 99 black). We are not done yet. From all the given balls, we are left with red, green, and yellow colored balls. In our worst scenario, we’ll pull out 1514 balls of every single color, and then we’ll finish it with one color (it doesn’t matter which). Since, we have 3 different colors left, that’s 3*1515+1 = 4545+1 = 4546 that is 4546 more balls.
To finish, we simply add the first 2523 balls with 4546, yielding 2523+4546 = 7069 balls.
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To prepare for a bake-Off, Sebastian used 830 grams of flour each day for 4 weeks. How many kilograms did Sebastian use in those 4 weeks?
1 q = 0.001 kg
If 830 grams = 1 day.
23.24 kilograms = 4 weeks.
23.24 kilograms were used by Sebastian in those 4 weeks.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 3x = 4 is an equation.
We have,
830 grams is used each day.
830 grams = 1 day ___(1)
1 week = 7 days
Multiply 4 on both sides.
4 weeks = 28 days ___(2)
From (1) and (2) we get,
4 weeks = 28 days
4 weeks = 28 x 1 day
4 weeks = 28 x 830 grams
4 weeks = 23240 grams ____(3)
1000 grams = 1 kg
Multiply both sides by 23240/1000.
23240 grams = 23.24 kilograms _____(4)
From (3) and 94) we get,
4 weeks = 23.24 kilograms
Thus,
23.24 kilograms were used by Sebastian in those 4 weeks.
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Answer the question below in the picture please and thank you
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
What is meant by isotope?Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.
If we start with 180 g of the isotope, after one half-life the quantity will diminish to 180 g/2 = 90 g which exists half the original quantity.
This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]
After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]
After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]
But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.
The original quantity can then be rapidly computed for six half-lives using the formula below:
[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
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James and Simon have a reading assignment to complete. James has read rrr pages, and Simon has read 757575 pages. Together they have read a total of 200200200 pages.
determine if two triangles are necessarily congruent. if so in a flowchart proof to prove the they are.
Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.
What is Congruency?Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
What are the rules of congruency?If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).
Here the ΔCED and ΔPOR,
∠CED=∠POR
Side PR=CD
Side ED=PO
by using SAS rule,
ΔCED≅ΔPOR
Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.
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4560=12 ÷ y
What is y equal to?
Answer:y=1/380
Step-by-step explanation:
if you are trying to do y divided by 12 it would be 4560x12
In trIangle OPQ, p = 3.4 cm, q = 3.2 cm and angle 0=99º. Find the area of Triangle OPQ, to the nearest10th of a square centimeter.
we know that
The area of a triangle applying the law of sines is equal to
[tex]A=\frac{1}{2}\cdot p\cdot q\cdot\sin (O)[/tex]substitute the given values
[tex]\begin{gathered} A=\frac{1}{2}\cdot3.4\cdot3.2\cdot\sin (99^o) \\ A=5.37\text{ cm\textasciicircum{}2} \end{gathered}[/tex]the answer is
5.37 square centimeters3What is the inverse of the function h(x) = - 2 + 12?h-'(x) =(2
We have the next function
[tex]h(x)=\frac{3}{4}x+12[/tex]First we need to make h(x)=y
[tex]y=\frac{3}{4}x+12[/tex]Then we make x=y and y=x
[tex]x=\frac{3}{4}y+12[/tex]Then we isolate the y
[tex]x-12=\frac{3}{4}y[/tex][tex]4(x-12)=3y[/tex][tex]y=\frac{4(x-12)}{3}[/tex][tex]y=\frac{4x-48}{3}[/tex]Therefore the inverse function is
[tex]h^{-1}(x)=\frac{4x-48}{3}[/tex]Please help ASAP for 20 Points! and a brainliest!
You are running a fuel economy study. You want
to find out which car can travel a greater distance
on 1 gallon of gas.
a. What is the gas mileage, in miles per gallon,
for the blue car?
b. What is the gas mileage, in miles per gallon,
for the silver car?
c. Which car could travel the greater distance
on 1 gallon of gas?
Thank you!
Answer:
a) gas mileage of blue car: 23.667 miles/gallonb) gas mileage of silver car: 34 miles/gallonc) The silver car would travel a greater distance on 1 gallon than the blue car.Step-by-step explanation:
a) gas mileage of blue car:gas mileage = miles covered/gallons used
but:
miles covered = [tex]35\frac{1}{2}[/tex]
= 35.5
gallons used = 1[tex]\frac{1}{2}[/tex]
= 1.5
gas mileage = 35.5/1.5
gas mileage = 23.667 miles/gallon (to 3 decimal places)
b) gas mileage of silver car:gas mileage = miles covered/gallons used
but:
miles covered = [tex]27\frac{1}{5}[/tex]
= 27.2
gallons used = [tex]\frac{4}{5}[/tex]
= 0.8
gas mileage = 27.2/0.8
gas mileage = 34 miles/gallon
c)
gas mileage of blue: 23.667 miles/gallon implies the blue car will travel 23.667 miles on 1 gallon
gas mileage of silver: 34 miles/gallon implies the silver car will travel 34 miles on 1 gallon
Hence the silver car would travel a greater distance on 1 gallon than the blue car.
The cost of a computer in a computer store is reduced by 12.5% in a sale. İf the computer was priced 7800$ what is the price in the sale?
Answer:
$6825.
Step-by-step explanation:
Price in the sale
= 7800 - 12.5% of 7800
= 7800 - 1/8 * 7800
= 7800 - 975
= $6825.
Kylie has ten chocolate squares.
His friend Allison takes three of them.
What fraction of chocolate did Kylie give his friend?
3/10ths if im not wrong
a company wants to study the effectiveness of a new pain relief medicine. they recruit 100100100 volunteers who suffer chronic pain. they assign each subject a number from 111 to 100100100 and use a random number generator to assign the first 505050 subjects selected to the treatment group. the remaining 505050 subjects are assigned to the control group. what type of experiment design is this?
The experimental design which is used in the study is Completely randomized design.
Completely Randomized design may be defined as a technique in which all the solutions are assigned at random so that each questions receive all the possible solutions. According to the question we know that the sample size is 100 volunteers who are suffering from chronic pain. Now, out of the 100 volunteers, 50 males and 50 females are chosen. Further out of the 50 males, 25 males are randomly assigned to the treatment group while the other 25 males are assigned to a control group. Since, the treatments are randomly assigned completely, each of the volunteers have an equal chance of receiving the treatments.
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a random sample of 80 observations results in 50 successes. a. construct the 95% confidence interval for the population proportion of successes. b. construct the 95% confidence interval for the population proportion of failures
In 95% confidence interval for the population proportion of successes
exists CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80).
In 95% confidence interval for the population proportion of failures
exists CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80).
What is meant by confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
a) Sample proportion of successes (phat) = 50/80 = 0.625
z-critical for 95% CI is 1.96
CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80)
b) sample proportion of failures (phat) = 30/80 = 0.375
CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80)
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When Luke left his house in the morning, his cell phone battery was partia
charged. Let B represent the charge remaining in Luke's battery, as a perc
hours since Luke left his house. The table below has select values showing t
relationship between t and B. Determine the number of hours until Luke's
dies.
Step-by-step explanation:
Solution:
From the graph, the coordinates of the points A, B and C are (- 1, 0) (0, - 2) and (2, 0) respectively.
Let the equation representing the graph be y = a * x ^ 2 + bx + c
(1)
The curve represented by (i) passes through A(- 1, 0) B(0, - 2) and C(0, 2) So,
- 2 = 0 + 0 + c
c = - 2
Also 0 = a - b - 2
and 0 = a * (0.4 + 2b - 2)
⇒a a - b = 2 2a + b = 1 (ii) ..(iii)
Adding (ii) and (iii)
3a = 3
a = 1
Substituting the value of a in (ii), we have
1 - b = 2
b = - 1
The equation of the curve is y = a * x ^ 2 + bx + c i.e. y = x ^ 2 - x - 2
A soccer ball is kicked on a field and follows the path of a parabola. It reaches a maximum height of 80 feet above the ground after traveling 160 feet from where it was kicited.a) Draw a diagram to represent this situation.b) Write an exact equation in vertex form to model this situation.c) Suppose there is a 30 feet tree 280 feet from where the ball was kicked. Will the ball sail over the tree? If yes, by how much? If not, by how much?
a) We will draw the situation.
b) Considering the theory, the vertex of a parabola is represented in (h,k) where h is the x-coordinate, in this case, if our parabola has an amplitude of x=320feet then h=320/2=160feet, and k is the highest y-coordinate 80 feet. So the equation is:
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=a(x-160)^2+80 \end{gathered}[/tex]We have to know the value for a, so we will use a point to replace it in the equation and with that, we will know the value, so in x=0 the y-value is 0 too so:
[tex]\begin{gathered} 0=a(0-160)^2+80 \\ a(-160)^2=-80 \\ a=-\frac{80}{25600}=-\frac{1}{320} \end{gathered}[/tex]So the equation is:
[tex]y=-\frac{1}{320}(x-160)^2+80[/tex]c. To know the answer to this question we will have to replace x=280feet with the y value we will know if at the moment the ball can go over the tree or if it would crash into it.
[tex]\begin{gathered} y=-\frac{1}{320}(280-160)^2+80 \\ y=35feet \end{gathered}[/tex]At that point, the ball would be 35 feet up so if it could pass over the tree 5 feet higher.
Which equation does not represent a linear function?
a. y = 8x
by = ½x+2
c. y=0.5x - 1
d. y = 2x³
Answer:
d. y= 2x³
Step-by-step explanation:
All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.
PLSSSSSSSSS HELP DUE SOON!!!
The problem can be modeled with the linear equation:
2c - 1.5 = 6
Where c is the old amount of chips.
So the correct option is the last one.
Which is the correct expression?First, let's define the old amount as the variable "c".
1.5 less than twice the old amount is then written as:
2c - 1.5
And the total text says:
"1.5 less than twice the old amount is equal to 6"
So we have an equation, that equates the above expression and the number y, so we can write the linear equation:
2c - 1.5 = 6
This is the last option
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A furniture store is having a 20% sale.
(a) A sofa usually costs £1200. Work out the sale price of the sofa.
(b) The sale price of a table is £480. Work out the original price of the table.
Answer:
a) £960
b) £576
Step-by-step explanation:
Hi!
Ok so since the store has a 20% sale we multiply 0.2 to the original amount it would have costed without the sale:
a) [tex]1200*0.2 = 240[/tex]
Then we subtract the number we got from the price:
1200 - 240 = 960
Now we do the same thing but this time add since we are trying to find the price of the table before the sale:
b) [tex]480*0.2 = 96[/tex]
480 + 96 = 576
Please ask me if you have any more questions!
and Have a great day! :)
