The most appropriate choice for slope of a line will be given by-
Slope of the line = [tex]\frac{-19}{12}[/tex]
What is slope of a line?
At first it is important to know about line.
Line is a geometrical object that has only length but no breadth and no height.
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta\\[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
m = [tex]tan\theta[/tex]
If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex]) , then
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]x_1 = -3, y_1 = 9. x_2 = 9, y_2 = -10[/tex]
Slope = [tex]\frac{-10 - 9}{9 - (-3))}[/tex]
= [tex]\frac{-19}{12}[/tex]
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A vehicle can cover 80 kilometers in 2 ½ hours. How many kilometers can it cover in 6 hours?
1) The probability of getting exactly three girls in a family of five children.
2)The probability of getting at least two boys in a family of seven children.
3) The probability of getting a total of 15 when four dice are thrown.
4) Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.
5) The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years).
Using the binomial distribution, the probabilities are given as follows:
1) Three girls in a family of five children: 0.3125 = 31.25%.
2) At least two boys in a family of seven children: 0.9375 = 93.75%.
3) Total of 15 when four dice are thrown: 0.1080 = 10.80%.
4) At least two left-handed people in a group of 7: 0.1497 = 14.97%.
5) At least five of them have the same birth date: 0%.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C(n,x).p^{x}.(1-p)^{n-x}[/tex]
[tex]C(n,x) = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Item 1A children is equally as likely to be a boy or a girl, hence the parameters are given as follows:
n = 5, p = 0.5.
The probability is P(X = 3), hence:
P(X = 3) = C(5, 3) x (0.5)³ x (0.5)² = 0.3125 = 31.25%.
Item 2The parameters are:
n = 7, p = 0.5.
The probability of at least two boys is:
P(X >= 2) = 1 - P(X < 2).
In which:
P(X < 2) = P(X = 0) + P(X = 1).
Then:
P(X = 0) = (0.5)^7 = 0.0078.P(X = 1) = C(7,1) x (0.5)^7 = 0.0547.P(X < 2) = P(X = 0) + P(X = 1) = 0.0078 + 0.0547 = 0.0625.P(X >= 2) = 1 - P(X < 2) = 1 - 0.0625 = 0.9375 = 93.75%.Item 3This one is simple probability, number of desired outcomes divided by the number of total outcomes.
When 4 dice are thrown, we have that:
There are 140 outcomes with a sum of 15.There are 6^4 total outcomes.Hence the probability is:
p = 140/(6^4) = 0.1080 = 10.80%.
Item 4The parameters are:
n = 7, p = 0.1.
Hence, similarly to item 2:
P(X = 0) = (0.9)^7 = 0.4783.P(X = 1) = C(7,1) x (0.1) x (0.9)^6 = 0.3720.P(X < 2) = P(X = 0) + P(X = 1) = 0.4783 + 0.3720 = 0.8503.P(X >= 2) = 1 - P(X < 2) = 1 - 0.8503 = 0.1497 = 14.97%.Item 5The parameters are:
n = 75, p = 1/365 = 0.0027.
Then the probability is:
P(X >=5) = 1 - P(X < 5).
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Using a calculator, it is found that P(X < 5) = 1, hence the probability is of 0%, as P(X >=5) = 1 - 1 = 0.
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find the length of arc JM. use 3.14 for pi. round to nearest tenth
hello
to solve this problem, we need the formula of length of an arc
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]t find the value of angle JM, we should take into cognizance that the sum of angles in a circle is equal to 360 degree and angle on a straight line is equal to 180 degree
[tex]\begin{gathered} jk+jm+mk=360 \\ 180+jm+90=360 \\ 270+jm=360 \\ jm=360-270 \\ jm=90 \end{gathered}[/tex]now we know the value of angle jm, let's find the length of the radius
[tex]\begin{gathered} \text{radius}=\frac{\text{diameter}}{2} \\ \text{diameter}=16.4 \\ \text{radius(r)}=\frac{16.4}{2}=8.2\text{miles} \end{gathered}[/tex]with all the necessary informations or data required, we can now proceed to solve for the length of arc jm
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ L_{\text{arc}}=\frac{90}{360}\times2\times3.14\times8.2 \\ L=12.87\text{miles} \end{gathered}[/tex]from the calculations above, the length of the arc is equals to 12.87 miles
Answer:
12.9
Step-by-step explanation:
Select the 3 options below that are equal in value. For example, if one of the terms
equals 0.85, so do the other two.
sample size
area under the curve
proportion
probability
One of the terms equals 0.85, so do the other two:
sample size
proportion
probability
How can sample size be determined?
to calculate the sample size in five easy steps
Define population size or total population.Indicate your error margin.You should assess your level of confidence.Calculate the anticipated variance.finalize the size of your sampleCalculating sample size requires knowledge of or estimation of three or four factors:
the effect size (often the difference between two groups); the population standard deviation (for continuous data); the required power of the experiment to detect the supposed effect; the significance threshold.To learn more about sample size refer to:
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Find the exact area of thetriangle below.
I am going to draw a picture to ilustrate the solution
Now, we are going to use the trigonometric functions for the right triangle on the left to calculate h
[tex]\sin (30)\text{ = }\frac{h}{10\sqrt[]{3}}\Rightarrow\text{ h= sin(30)}\cdot\text{ 10}\sqrt[]{3\text{ }}=\frac{1}{2}\cdot10\sqrt[]{3}=5\sqrt[]{3}[/tex]Now we use the formula for the area of a triangle
[tex]A=\frac{b\cdot h}{2}=\text{ }\frac{20\cdot5\sqrt[]{3}}{2}=50\sqrt[]{3}[/tex]A bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months. Find the interest rate.
If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%
The initial amount = $1100
The final amount = $1265
So simple interest = 1265-1100
= $165
Time period = 6 months = 6/12 years
We know
Simple interest I = P×r×t
Where P is the initial amount
r is the interest rate
t is the time period
Substitute the values in the equation
165 = 1100×r×(6/12)
165 = 550×r
r = 165/550
r = 0.3
r = 30%
Hence, If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%
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Fred, Max, and Ken went trick or treating. Fred had 2 bags of candy with 45 pieces each. Max had 3 bags with 20 pieces each and Ken had 4 bags of candy with 15 pieces each. The boys combined the candy and shared it among 12 people. How much candy is leftover?
Answer:
6 pieces of candy will be left.
Step-by-step explanation:
45×2 = 90
20×3 = 60 +
15×4 = 60
Ttl. of candies= 210
Candies ÷ people
210 ÷ 12 = 17.5
17-12= 5.5 (round to the tenth) 5.5-> 6
210-6= 204
you'll get 6 as the difference which is your answer.
The pie chart below representsEliana's monthly budget. Whatpercentage of her budget isallocated to savings?
Answer:
percentage = 528/ 3,300*100= 16%
Step-by-step explanation:From the pie chart we can see that saving are 528 dollars, so
now we need to calculate total from the given pie chart, which is
3,300 dollars. So percentage is savings( 528 dollars) divided by total( 3,300 dollars) and then finally multiply by 100
x+12% of x= 3.36 help
Answer:
x = 3
Step-by-step explanation:
x + .12x = 3.36 Combine like terms
1.12x = 3.36 Divide both sides of the equation by 1.12
x = 3
=======================================
Work Shown:
12% = 12/100 = 0.12
x + 12% of x = x + 0.12x = 1.12x = 3.36
1.12x = 3.36
x = 3.36/1.12
x = 3
---------------
Check:
12% of 3 = 0.12*3 = 0.36
x + 12% of x = 3 + 12% of 3 = 3 + 0.36 = 3.36
Or you could say 1.12x = 1.12*3 = 3.36
The answer is confirmed.
Choose the fraction that is equal to 0.81:
A.9/11
B.81/100
C.8/9
D.80/99
Answer: B
Step-by-step explanation:
Answer:
B. 81 / 100
Step-by-step explanation:
9 / 11 = 0.82
81 / 100 = 0.81
8 / 9 = 0.89
80 / 99 = 0.80
Hope this helps! :)
I can’t find the answer for the application
Value of x is 16/91
How to Find value of x ?
In question
(8/7)/(13/9) = x / (2/9)
Divide the numbers 72/91 =x/(2/9)
Multiply all terms by the same value to eliminate fraction denominators182* (72/91) = 182* (x/(2/9))
Cancel multiplied terms that are in the denominator2 *72 = 819 * x
Multiply the numbers144 = 819 * x
Divide both sides by the same factor(144/819) = 819 *x / 819
SimplifyX = 16/91
The value of x is 16/91
Definition of Fraction :
A fraction represents a part of a whole or, more generally, any number of equal parts.In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.There are in total six types of fractions such as:
Proper fractionImproper fractionMixed fractionLike fractionsUnlike fractionsEquivalent fractionsTo learn more about fractions refer :
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is y=3x+y=4 y=-1/3x-2 parallel, perpendicular or neither
The equations of the lines that are perpendicular are y = 3x and y = - 1 / 3 x - 2
How to know if an equation of a line is parallel or perpendicular?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptParallel line have the same slopes.
The products of the slopes of an equation of lines must be equals to negative one for it to be perpendicular.
Therefore,
m₁ m₂ = -1
The equation are as follows:
y = 3x
y = 4
y = - 1 / 3 x - 2
Hence, using m₁ m₂ = -1
3 × - 1 / 3 = -1
Therefore, y = 3x and y = - 1 / 3 x - 2 are perpendicular.
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A large cooler contains 16 lemonade 5 sprite 10 cans of coke and 9 cans of root beers you randomly pick two cans one at a time (without replacement) what is the probability you don’t get two cans of
The most appropriate choice for probability will be given by-
Probability of not getting two cans of coke is [tex]\frac{49}{52}[/tex]
What is probability?
Probability of an event is the chance of occurance of that event.
Probability is calculated by Number of favourable outcomes divided by total number of outcomes
Here,
Number of lemonades in a cooler = 16
Number of sprite in a cooler = 5
Number of cans coke in a cooler = 10
Number of cans of root beers in a cooler = 9
Total number of refreshments = 16 + 5 + 10 + 9
= 40
Probability of getting a can of coke in the first draw = [tex]\frac{10}{40}[/tex]
= [tex]\frac{1}{4}[/tex]
Probability of getting a can of coke in the second draw = [tex]\frac{9}{39}[/tex]
= [tex]\frac{3}{13}[/tex]
Probability of getting two cans of coke in the two draws = [tex]\frac{1}{4} \times \frac{3}{13}[/tex]
= [tex]\frac{3}{52}[/tex]
Probabilty of not getting two cans of coke in the two draws = [tex]1-\frac{3}{52}[/tex]
= [tex]\frac{52-3}{52}[/tex]
= [tex]\frac{49}{52}[/tex]
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Name the figure below in two different ways.
Answer:
VD; DV
Step-by-step explanation:
you can name the line in two ways
VD or DV
they are the two endpoints of the line
they are the same line
What is the value of 7!
Parallelogram
How divide the figure?
Determine the value of x. Use the Pythagorean Theorem. Show your work.
The value of x (hypotenuse) using the Pythagorean Theorem is 5 units.
What is Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in familiar algebraic notation, a² + b², are equal to the c² which is the hypotenuse.So, the formula of the Pythagorean Theorem:
c² = a² + b²Where a (AC) = 4 and b (CB) = 3 as the given figure is symmetric and so line CB will be equal to 3.
Now,
c² = a² + b²c² = 4² + 3²c² = 16 + 9c² = 25c = √25c = 5Therefore, the value of x using the Pythagorean Theorem is 5 units.
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HELP FOR 100pts
ONLY FOR TWACK
Answer:
3:2
Step-by-step explanation:
Find the distance between the points (−1,0) and (7,6).
The distance between the point (-1,0) and (7,6) is 10.
Distance between the points:
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by
d=√((x2 – x1)² + (y2 – y1)²).
Given,
(−1,0) and (7,6).
Here we need to find the distance between these points.
Apply the values on the formula , in order to solve it,
d = √(7 - (-1))² + (6 - 0)²
When we simplify it, then we get,
d = √(7 + 1)² + (6)²
d = √(8)² + 36
d = √64 + 36
d = √100
d = 10
Therefore, the distance is 10.
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x(x+5)+2x(x-4)
can anyone awnser me this step by step :)
Answer: 3x^2−3x
Step-by-step explanation:
1.) Distribution
2.) Combine like Terms
3.) Combine like Terms.. again
4.) Common Factor
5.) GET UR SOLUTION!!
Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
_______________________________________________________
Food ÷ amount of food per dog
5 1/2 pounds of dog food ÷ 1/3
5 1/2 ÷ 1/3 = (10/2 +1/2) ÷ 1/3 = 11/2 ÷ 1/3 = 11/2 x 3/1 = 33/ 2
33/ 2 = 16 1/5 = 16.5
_______________________________________
Can you see the updates?
___________________________________
Answer
She can feed 16.5 (16) dogs with 5 1/2 pounds of dog food
_________________________________________
Do you have any questions regarding the solution?
Please answer please please
As part of your job you spend time each day contacting former customers. During one week, you contacted 15 people on Monday, 12 on Tuesday, 14 on Wednesday, 11 on Thursday, and 13 on Friday. What is the average number of customers contacted each day? Which averaging method did you use?
The average number of customers contacted each day is 13. We used the basic average method which is explained below.
The formula for calculating the average is:
Sum of all the observations ÷ Total number of observations
So, according to the formula
Sum of all the observations = People contacted on (Monday+ tuesday+wednesday+thursday+friday)
= 15+12+14+11+13
= 65
Number of observations = 5
So putting values in the formula, we get
65÷5
= 13
Hence, the average number of customers contacted is 13.
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A company produces brake pads for commercial airliners.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write out the given data for Team A
STEP 2: Find the mean
[tex]\begin{gathered} The\:arithemtic\:mean\:\left(average\right)\:is\:the\:sum\:of\:the\:values\:in\:the\:set\:divided\:by\:the\:number\:of\:elements\:in\:that\:set. \\ \mathrm{If\:our\:data\:set\:contains\:the\:values\:}a_1,\:\ldots \:,\:a_n\mathrm{\:\left(n\:elements\right)\:then\:the\:average}=\frac{1}{n}\sum _{i=1}^na_i\: \\ sum=224250 \\ n=6 \\ mean=\frac{224250}{6}=37375 \end{gathered}[/tex]Hence, the mean of the data for production team A is 37375
How many people would it be if I did 1.2% of French speakers and 5,053,004, representing the whole population? I needed help on calculating how many people it would be with those two numbers.
60,636.048 people are french speakers when the population is 5,053,004 and only 1.2% are the french speakers.
What is Percent?Percentages are basically fractions with a denominator of 100. We use the percent symbol (%) beside a number to indicate that it is a percentage. A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; thus, 100 percent represents the entire amount.
What is method to calculate the percent?To manually calculate percentages, follow these steps:
1. Determine the number's initial format to be converted to a percentage.
The decimal or fraction format of the number to be converted to a percentage can be used. The next mathematical process to be performed on the number will be determined by the initial format.
2. Perform a mathematical calculation on the number to be converted to a percentage.
If the number to be converted to a percentage is a decimal number, such as 0.57, you may not need to proceed to the next step.
3. Multiply the result by 100.
To convert a decimal number, such as 0.57, to a percentage, simply multiply it by 100.
here we need to calculate 1.2% of 5053004
(1.2*5053004)\100
=60636.048
60636.048 people speak french in the country with population of 5053004.
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Please help I need this answer immediately
Answer:
Step-by-step explanation:
−2x−y−2z−4x−2y+3z
Combine −2x and −4x to get −6x.
−6x−y−2z−2y+3z
Combine −y and −2y to get −3y.
−6x−3y−2z+3z
Combine −2z and 3z to get z.
−6x−3y+z
DIFFERENTIATE W.R.T. X
−6
HELP PLEASEEEEEEEEEEEEEE
Using equation;
The monthly payment is 67.5 dollars
The hours of labour that is required to replace the water pump is 4 hours
How to use equation to solve a problem?The purchase of the large TV including finance charges is 1615 dollars . A down payment of 400 dollars was paid. The remainder was paid in 18 monthly instalment payment.
Therefore, using equation,
let
x = amount paid each month
The monthly payment can be found as follows:
1615 = 400 + 18x
1615 - 400 = 18x
1215 = 18x
divide both sides by 18
x = 1215 / 18
x = 67.5 dollars
Therefore,
monthly payment = 67.5 dollars
The cost of replacing a water pump was 465 dollars. This include 145 dollars for water pump plus 80 dollars per hour for labour .
The number of hours for labour that was used to replace the water pump can be calculated as follows:
Using equation,
465 = 145 + 80h
where
h = number of hours for labour
465 - 145 = 80h
320 = 80h
h = 320 / 80
h = 4 hours
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solve similar triangles (advanced) khan academy. solve for x
The length of the unknown side of the triangle using similar triangle ratio concept is; x = 24
How to Solve similar triangles?We want to find the length of the unknown side of the similar triangles.
Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. Thus, we can say that if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the given triangle ADE which is divide into a similar triangle ABC with an unknown side x, we can use the concept of similar triangle ratios to get the unknown value of x as;
6/x = 8/(x + 8)
Cross multiply to get;
6(x + 8) = 8x
6x + 48 = 8x
8x - 6x = 48
2x = 48
x = 48/2
x = 24
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The angle of elevation to the top of a building changes from 15° to 30° as an observer advances 140 feet toward the building. Find the height of the building, x, to the nearest foot.
pls explain
Answer:
70 ft
Step-by-step explanation:
To find the height of the building, we can use the trigonometric relationship between the angle of elevation, the distance from the object, and the height of the object.
In this case, we have a right triangle formed by the observer, the top of the building, and the base of the building. Therefore, we can use the tangent trigonometric ratio, since the height of the building is the opposite the angle of elevation, and the distance between the observer and the building is the side adjacent the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
Let "x" be the height of the building.
Let "d" be the initial distance from the observer to the building.
The angle of elevation changes from 15° to 30° as the observer advances 140 feet toward the building.
(See the attachment for a visual representation).
Based on this information, we can set up the following equations:
[tex]\tan 15^{\circ}=\dfrac{x}{d}[/tex]
[tex]\tan 30^{\circ}=\dfrac{x}{d-140}[/tex]
Rearrange both equations to isolate d:
[tex]d=\dfrac{x}{\tan 15^{\circ}}[/tex]
[tex]d=\dfrac{x}{\tan 30^{\circ}}+140[/tex]
Solve this system of equations by the method of substitution.
[tex]\dfrac{x}{\tan 15^{\circ}}=\dfrac{x}{\tan 30^{\circ}}+140[/tex]
[tex]\dfrac{x}{\tan 15^{\circ}}-\dfrac{x}{\tan 30^{\circ}}=140[/tex]
[tex]\dfrac{x\tan 30^{\circ}-x \tan 15^{\circ}}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]
[tex]\dfrac{x(\tan 30^{\circ}- \tan 15^{\circ})}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]
[tex]x=\dfrac{140\tan 30^{\circ}\tan 15^{\circ}}{\tan 30^{\circ}- \tan 15^{\circ}}[/tex]
[tex]x=\dfrac{140\cdot \frac{\sqrt{3}}{3}(2-\sqrt{3})}{\frac{\sqrt{3}}{3}- (2-\sqrt{3})}[/tex]
[tex]x=\dfrac{\dfrac{140(2\sqrt{3}-3)}{3}}{\dfrac{4\sqrt{3}-6}{3}}[/tex]
[tex]x=\dfrac{140(2\sqrt{3}-3)}{2(2\sqrt{3}-3)}[/tex]
[tex]x=\dfrac{140}{2}[/tex]
[tex]x=70[/tex]
Therefore, the height of the building is exactly 70 feet.
Number 12 I don’t get it y’all know ?
Answer:
Approximately $18 each month.
Step-by-step explanation:
This is quite simple. So, we know that there are 12 months in a year. And we know that in a year, the store has given out discounts totaling up to $216. All we have to do is divide the total number by how many months there are in a year.
[tex]216\div12=18[/tex]
This means that the store gives out $18 of discounts per month.
(Also, you don't seem college level)