The two linear equations are perpendicular.
What are the lines?
Here we have the two linear equations:
12y - 4x = 84
y = -3x + 8
If we write both of them in the slope-intercept form (as the second one) we will get:
12y - 4x = 84
12y = 4x + 84
y = (4x + 84)/12
y = (1/3)*x + 7
Now, if we take the product of the slopes of the two lines, we get:
p = -3*(1/3) = -1
when this product is -1, the lines are perpendicular, so that is the relation between our lines.
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Find the equation of a line, in slope intercept form, that has a slope of 3 and passes through the point of (-4, 2).
Answer:
y=3x+14
Step-by-step explanation:
First find the point using slope point form.
y-y₁=m(x-x₁)
Put y value in for y₁, x value in for x₁ and slope in for m.
y-2=3(x+4)
Simplify
y-2=3x+12
Solve for y to get slope intercept form Y=mx+b
y=3x+14
a survey of over 7{,}0007,0007, comma, 000 randomly selected employees in 151515 nations recently showed that employees who work in a digital workplace tended to be happier than those who don't work in a digital workplace. can we conclude that working in a digital workplace caused employees to be happier? why?
We cannot conclude that working in a digital workplace caused employees to be happier from the survey.
How is the conclusion from the survey explained?
A survey is a technique for acquiring data which could be considered as an information and not be considered as a conclusion.Surveys are statistical tools which are insufficient to generalize the entire population.A formal questionnaire is developed, and the questions are then asked in a specific order, according to the structured method of data gathering used in surveys , which doesn't include any scientific research or proof.Experimental research is not conducted in surveys which include only descriptive research.Scientific evidences from experiments are required to conclude that working in a digital workplace caused employees to be happier.To learn more about surveys, refer:
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X=
//////////////////////////
Answer:
x = 15
Step-by-step explanation:
150+3x-15=180 because of same-side interior angles therorem.
Then, we solve the problem to get 15.
Hope this helped! :)
helppppp!!!!!!! 16 points if solveddd!!!!!!!!
Answer:
£94
Step-by-step explanation:
24+ (14×5) = £94
p.s pls give brainliest answer :)
Your bus is traveling 60 km/hr on a class trip to a museum that is 90
kilometers from your school. How long will it take to get there?
OA. 1.5 hours
O
B. 2.0 hours
O
O
C. 0.5 hour
D. 1.0 hour
Answer:
nothing but B2. 0 hours
The bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.
Speed can be thought of as the rate at which an object covers distance.
i.e.
Speed = distance traveled/time taken
After arranging the equation we get,
Time taken = Distance traveled/Average speed
Here distance traveled by bus = 90 km
The average speed of the bus = 60 km/hr
So total time taken = 90/60 = 1.5 hours
So the bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.
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Please HELPPP!!!
Givin the figure below,find the values of x and z
Answer:
First, find x.
(12x + 20) + (6x + 70) = 180 (sum of angles on straight line = 180°)
18x + 90 = 180
18x = 90
x = 5
Next, find z.
z = 12x + 20 (vertically opposite angles)
Substitute x = 5 into equation.
z = 12(5) + 20
= 80
Using the distributive property, rewrite this equation and put the correct numbers in place of the blanks.
8 • 52 = (
•
) + (
•
The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)
Given,
The equation: 8 ( 5 + 2) = (__×___) + (___×__)
Distributive property:
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
Here,
8 (5 + 2)
Using distributive property open the brackets:
8 (5 + 2) = (8 × 5) + (8 × 2)
Now,
8 (5 + 2) = 40 + 16
That is,
8 (5 + 2) = 56
So,
The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)
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The first equation should be multiplied by 7 and the second equation by -6.
Answer:
Step-by-step explanation:
Us the given info to evaluate all six trig functions. If theta is a special angle so state.
I need help with question six
The angle in the fourth quadrant associated with trigonometric function is 314.415°. The exact values of the six trigonometric functions are listed below:
sin θ = - 5 / 7 cos θ = 2√6 / 7 tan θ = - 5 / 2√6 cot θ = - 2√6 / 5 sec θ = 7 / 2√6 csc θ = - 7 / 5What is the angle associated with a given trigonometric function?In this problem we find the exact form of a trigonometric function and the related quadrant on a Cartesian plane. By definition of the sine function and the features of the sine, the exact value has the following form and conditions:
y / √(x² + y²) = - 5 / 7, x > 0, y < 0
Then,
y = - 5, √(x² + y²) = 7
√[x² + (- 5)²] = 7
x² + 25 = 49
x² = 24
x = √24
x = 2√6
Then, the angle associated to the trigonometric function is:
θ = tan⁻¹ (y / x)
θ = tan⁻¹ (- 5 / 2√6)
θ ≈ 314.415°
And the five other trigonometric functions are:
cos θ = 2√6 / 7
tan θ = - 5 / 2√6
cot θ = - 2√6 / 5
sec θ = 7 / 2√6
csc θ = - 7 / 5
The angle associated with trigonometric function is 314.415°.
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Evaluate the function for the following values:
f(1) =
f(2)=
f(3) =
Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]
Step-by-step explanation:
[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]
What is the value of x?
Answer:
x=62
Step-by-step explanation:
X=62 because all angles of a triangle should add up to 180 degrees no matter what. All you have to do is subtract the already known angles in the triangles from 180 to receive your x value. 180-65-53=x 180-65-53=62.
-Hope this helps
Ms. Fern is stocking up on school supplies
for the start of the school year. She finds a
four pack of colored pencils on sale for
$4.50 proportional or non proportional?
Answer:
proportional!!!!!!
Step-by-step explanation:
imagine that a long stretch of single-strand dna has 30% adenine, 25% thiamine, 15th% cytosine, and 30% guanine. what is the probability of randomly drawing 10 adenine in a row in a sample of 10 randomly chosen nucleotides? explaination
In a sample of 10 nucleotides, the likelihood of drawing 10 consecutive adenines at random is 0.000006.
Probability: The probability of an occurrence is defined as the ratio between the number of favorable outcomes to a certain event and the entire number of potential outcomes.
The following calculation shows the likelihood of picking 10 consecutive adenines at random from a sample of 10 nucleotides:
According to the information provided, there are 10 adenines and a likelihood of 0.30 that DNA contains them. n = 10 and p = 0.30
Therefore, Probability = (0.30)10 = 0.000006
The likelihood of randomly selecting 10 consecutive adenines from a sample of 10 nucleotides is calculated by multiplying the likelihood that DNA contains adenines by 10 times.
Therefore, The probability of picking 10 consecutive adenines at random from a sample of 10 nucleotides is 0.000006.
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The value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.
Find the rate at which the value of the car is depreciating
And
write an equation that models the depreciation of the value of the car
And
How much will the car be worth when it is 8 years old?
The equation of the car can be given as and the price of the car after 8 years is $4445.
What is an exponential function?
A function of the form [tex]a^{x}[/tex] is known as exponential function. In short the function which has an exponent is known as exponential function.
We are given that the value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.
Let the original price of the car be [tex]P_{0}[/tex]
After two years the price of the car is $11200
Mathematically it can be given as
[tex]11200= P_{0}e^{2x}[/tex]
After 6 years the price of the car is $6100
Mathematically it can be given as
[tex]6100=P_{0}e^{6x}[/tex]
Dividing both equations we get,
[tex]1.83=e^{-4x}[/tex]
Which can also be written as
[tex]e^{4x}=0.54[/tex]
on solving we get,
x=-0.154
Hence the rate at which price of the car is dropping is
[tex]P=P_{0}e^{-0.154t}[/tex]
No we have to find the original price of the car
To do so we substitute t=2 in the equation
we get
11200=[tex]P_0e^{-0.308}[/tex]
On solving we get,
15240=[tex]P_0[/tex]
Now we find the price of the car after 8 years
P=15240·[tex]e^{-1.232}[/tex]
On simplifying we get
P=$4445
Hence the price of the car after 8 years will be $4445
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Write a linear function in witch f(3)=-4 and f(1)=2
The linear function is y = -3x -5 with f(3)=-4 and f(1)=2.
Define linear function.The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields. The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. Any function with the formula f(x) = mx + b—where m and b are constants—is said to be linear. Because the graphs of these functions are lines in the plane, we refer to them as linear.
Given Data
f(3) = -4
f(1) = 2
The ordered pairs are (3,-4) and (1,2)
The equation of the line :
y - y₁ = [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex](x - x₁)
y + 4 = [tex]\frac{2+4}{1-3}[/tex] (x-3)
y + 4 = -3(x -3)
y + 4 = -3x + 9
3x + y = -5
y = -3x -5
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An investor purchased 50 shares ofstock in a company for $40 pershare. One year later, the investorsold all the shares for $2,200. Whatis the investor's rate of return?A. 9.1%B. -9.1%C. -10.0%D. 10.0%
Investor purchased 50 shares of stock in a company for $40.
So, the total initial amount he invested is
[tex]50\cdot40=2000[/tex]Then the rate of return is:
[tex]\begin{gathered} \text{rate of return=}\frac{shares\text{ sold price-initial amount invested}}{\text{ initial amount invested}}\cdot100 \\ =\frac{2200-2000}{2000}\cdot100 \\ =\frac{200}{2000}\cdot100 \\ =10 \end{gathered}[/tex]So, the requied rate of return is 10.0%.
Help me get the right answer please
Answer:
3x + 5 + (8x - 3) = 180
11x + 2 = 180
11x = 178
x = 16.18
= 16.2
12x^2(y^8)/3xy^7 solve
The value of the expression given as 12x^2(y^8)/3xy^7 is 4xy
How to solve the expression?From the question, the expression is given as
12x^2(y^8)/3xy^7
Start by removing the bracket in the above expression
So, we have the following equation
12x^2(y^8)/3xy^7 = 12x^2y^8/3xy^7
Divide 12 by 3 in the above equation
So, we have the following equation
12x^2(y^8)/3xy^7 = 4x^2y^8/xy^7
Divide x^2 by x
So, we have the following equation
12x^2(y^8)/3xy^7 = 4xy^8/y^7
Divide y^8 by y^7
So, we have the following equation
12x^2(y^8)/3xy^7 = 4xy
Hence, the expression is 4xy
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this exercise refers to choosing two cards from a thoroughly shuffled deck. assume that the deck is shuffled after a card is returned to the deck. if you do not put the first card back in the deck before you draw the next, what is the probability that the first card is a 10 and the second card is a jack?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Solve the problem?
Given that a card is selected from a 52-card deck that has been thoroughly shuffled without being replaced, the following card is drawn.
A: The top card is a 4, and B: The next card is an ace.
Probability =A∩B
After this first card is pulled, if 10is drawn, we have 51 cards left with 4 aces in them. This is the probability we need to discover for
P(A). = 10/52
P(B) = number of aces in 51 cards divided by 51, thus = 4/51
Hence A∩B =10/52×10/51
= 100/2652
(From this, we can see that, after changing the card count, A and B are independent.
Additionally, we multiply the probability for both.)
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look at photo and solve quick pls
Answer:what photo
Step-by-step explanation:
where
suppose that 30% of the 10,000 signatures on a certain recall petition are invalid. would the number of invalid signatures in a sample of 3000 of these signatures have (approximately) a binomial distribution? explain. g
Approximately, all of the signatures in the sample of 3000 signatures are invalid . We get this outcome by using binomial distribution .
This problem it is said that 30% of 10000 signatures on certain recall petition are invalid . So, here is the two outcomes possible one is the signatures are invalid and other signature are valid .
Probability of Success (signature are valid ) = p = favourable outcomes / total outcomes
Favourable outcomes for Success = 70% of 10,000= 7000
Total number of possible outcomes = 10,000
P = 7000/10,000 = 7/10
Probability of failure (signature are invalid ) = q= 1- p = 1- 7/10 = 3/10
We have to find out probability of getting invalid signature from a sample of 3000 signatures..
Using the binomial distribution,
P(X = x ) = ⁿ C ₓ pˣ (1- p)⁽ⁿ⁻ˣ⁾
n = 3000 , x= 0 for none of signatures from 3000 are invalid.
P(X=0) = ³⁰⁰⁰C ₀ (3/10)⁰ ( 7/10) ³⁰⁰⁰
= 1 . 1 . (7/10)³⁰⁰⁰ = (7/10)³⁰⁰⁰ = 0
Probability of getting invalid signature out of sample 3000 is
1 – ( 7/1000)³⁰⁰⁰ = 1
This implies that all the signatures in sample of 3000 are invalid.
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(1 point) the shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 8 years and a standard deviation of 0.3 years. what value of shelf life do 16% of the battery shelf lives fall below? round your answer to one decimal place.
8.27 is the normally distributed value of the shelf life which falls under 16% of the battery shelf life.
Because the shelf life of a battery manufactured by one big business is known to be regularly distributed, we would use the normal distribution formula, which is stated as
z = (x - µ) ÷ σ
Where
x = shelf life of a battery in years.
µ = mean shell life
σ = standard deviation
Based on the facts provided,
µ = 8 years
σ = 0.3 years
The z score corresponds to a p-value of 16% in the normal distribution table,
(16 ÷ 100 = 0.16) is - 0.9.
Therefore,
- 0.9 = (x - 9) ÷ 0.3
0.3 × (- 0.9) = x - 8
0.27 = x - 8
x = 0.27 + 8
x = 8.27
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answer these quick please!
Answer: The daily cost of production in a factory is calculated using
c(x) = 200 +16 x, where x is the number of complete products manufactured.
Complete products manufactured will can not be a decimal or fraction number.
The domain of function c(x) will be the set of values x can take.x will be a set of whole numbers. Whole numbers are positive numbers, including zero, without any decimal or fractional parts.
Option D) whole numbers is the right answer.
(4) f(1) = 3, f(n+1)=3f(n) - 2
Step-by-step explanation: I hope this helps.
Answer:
See attached worksheet
Step-by-step explanation:
Hi can you please help on the q
Answer: 55
Step-by-step explanation: 180-78 to get the complementary angle. 180-157 to get complementary angle. 180-102+23 to get the last angle inside the triangle. 180-125 and get 55
a binomial experiment with probability of success and trials is conducted. what is the probability that the experiment results in fewer than successes? do not round your intermediate computations, and round your answer to three decimal places. (if necessary, consult a list of formulas.)
One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials.
How to find the number of success in a binomial distribution?The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.
One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials. In other words, the results of one trial do not influence those of the others.
An experiment with a fixed number of independent trials and just two results is referred to as a binomial experiment.
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please help thanks please give explanation
The price of the car after 15% markup will be $8,280
How to calculate price after 15% of markup ?
The cost price of car for Hanks = $7200
Marking up of price is done by 15%
To find Markup price = Cost price + 15% of cost price
= 7,200 + 7,200 * 15/100
= 7,200 + 1,080 = $8,280
The 15% of car price is $1,080
The price of the car after 15% markup will be $8,280
What is percentage ?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.The formula used to calculate percentage is: (value/total value)×100%.To find 50 apples as a percentage of 1250 apples, one first computes the ratio 50/1250 = 0.04, and then multiplies by 100 to obtain 4%.To learn more about percentage refer :
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The snail travels 10 cm in 4 min. How far does a snail travel in 6 min?
Given.
The distance covered by the snail in 4 minutes is 10 cm.
The speed of snail is,
[tex]\begin{gathered} Spe\text{ed=}\frac{dis\tan ce}{time} \\ =\frac{10}{4}\frac{cm}{\min } \\ =2.5\text{ cm/min} \end{gathered}[/tex]The distance covered by snail in 6 minute is,
[tex]\begin{gathered} \text{Distance}=\text{speed }\times time \\ =2.5\times6 \\ =15\text{ cm} \end{gathered}[/tex]Hence, the distance covered by the snail is 15 cm.
Speed :
Speed is defined as the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling.
Hence , speed can be calculated by using the formula,
Speed = [tex]\frac{Distance-travelled}{Time-taken}[/tex]
Given data :
Distance travelled by the snail = 10 cm = 0.1 m
Time taken by the snail to travel a distance of 10 cm = 4 min = 240 s
Then , speed of the snail = [tex]\frac{10}{4}[/tex] = 2.5 cm/min = 0.0004 m/s
If the time taken by the snail is 6 min = 360 s
Then, the distance travelled by the snail in 6 min
= speed x time taken
= 2.5 cm/min x 6 min
= 15 cm = 0.15 m.
Therefore, the snail travels a distance of 15 cm in 6 min.
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A landscaper mows lawns for at least 3 hours but not more than 6 hours. the landscaper can mow 44,000 ft2 per hour. the function f(t)=44,000t represents the number of square feet the landscaper can mow in t hours. what is the practical range of the function?
Answer: [tex]132000 \le f(t) \le 264000[/tex]
Explanation:
The domain is [tex]3 \le t \le 6[/tex] to represent the time values between 3 and 6 hours, including the endpoints. This represents the set of possible inputs to the function.
The function f(t) = 44000t is an increasing function. This means the smallest range value corresponds to the smallest domain value.
Plug in t = 3 to find that:
f(t) = 44000t
f(3) = 44000*3
f(3) = 132000
This says he mows 132,000 sq ft of lawn in 3 hours.
Now plug in the largest domain value to find the largest range value
f(t) = 44000t
f(6) = 44000*6
f(6) = 264000
He mows 264,000 sq ft of lawn in 6 hours.
The range is the set of f(t) values between 132,000 and 264,000
We can write that as [tex]132000 \le f(t) \le 264000[/tex]
Tom’s car has 1119 gallons of gas. If he uses 38 of the gas, how much gas does the car have left?
Answer:
1,081 gallons
Step-by-step explanation:
1,119 - 38 = 1,081
Wich is closest to the volume of the cone in cubic feet?
Therefore let us input the values to find the volume of the cone
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\pi r^2h \\ r=\frac{8}{2}=4\text{ ft} \\ h=9ft \\ \text{volume}=\frac{1}{3}\pi r^2h \\ \text{volume}=\frac{1}{3}\times3.14\times4^2\times^{}9 \\ \text{volume}=\frac{1}{3}\times3.14\times16\times9 \\ \text{volume}=\frac{452.16}{3} \\ \text{volume}=\text{ }150.72ft^2 \end{gathered}[/tex]The answer should be A.