The required linear function in slope intercept form is C = 5x + 20
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Let Chandler uses x gigabytes of data and let Chandler's monthly cell phone plan cost be C
Chandler's monthly cell phone plan costs $20 plus $5 per gigabyte of data that he uses
So,
C = 20 + 5x
C = 5x + 20
This is the required linear function in slope intercept form
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if the flow rate in an artery has been reduced to 12% of its normal value by a blood clot and the average pressure difference has increased by 22%, what percent of the original is the radius of the reduced artery?
The percentage by which the radius of the artery reduces is 1.44% of original radius.
According to Poiseuille’s law, we got that there is relation between radius, length, average pressure for blood which is flowing in our body and that relation is is given by
Q = ((P₂-P₁)πr⁴) /(8ηl)
where Q is flow rate
P is the pressure
r is the radius of the artery
η is the viscosity
Now,we have given that Flow rate is reduced by 12%,new flow rate is 88% of normal value.
Also, we have also given that pressure is increased by 22%,so new pressure is 122% of initial value,
therefore Q = ((P₂-P₁) × π × r⁴) /(8ηl)
=>(Q-12Q/100)=[((122 / 100) × P₁-P₁) × π × r₂⁴] / (8ηl)
=>(88 / 100)Q=(22 / 100)×(P₁ × π × r₂⁴)/(8ηl)
=>(88/22)Q=(P₁ × π × r₂⁴)/(8ηl)
=>[[4 × (8ηl)] × Q]/ (P₁ × π)=r₂⁴
=>4r₁ =r₂⁴
=>r₂=√2r₁
or r₂=1.44% of original radius.
Hence, by 1.44% radius of artery would reduce.
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One karaoke location, Singing Star, is charging $20 for 10 songs. Construct a graph to model the relationship between cost and number of songs.
A graph to model the proportional relationship between cost and number of songs is shown in the image attached below.
How to construct the required graph?Mathematically, a proportional relationship and the constant of proportionality can be represented or modeled with the following equation or mathematical expression:
y = kx
Where:
x represents the cost in dollars.y represents the number of songs.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for a song as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 10/20
Constant of proportionality (k) = 0.2
Therefore, an equation for any number of song for this karaoke is given by:
y = 0.2x.
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plsss don't pickk E
...................................
Answer:
answer is c!
because it's domain is -7!!
Help me please :) thank you
Answer:
a=90°
c=45°
b=45°
Step-by-step explanation:
this triangle is a right triangle. (shown by the box in angle a) this means a must equal 90°
and by extension means the other two angles have to equal 45° each because right angles always have two angles of the same degree and the angles of a triangle always Equal 180°
How would I prove that RTP is congruent to JKO by SAS?
When two pairs of corresponding sides and the corresponding angles between them are congruent, the triangles are congruent.
How do you prove that something is congruent in SAS?Side-Angle-Side (SAS) Rule
Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.Using words: If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent. Using labels: If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF.The proof by S A S congruence rule is given below.
Given from fig, JK || LM.
And JK = LM
Since JK is parallel to LM and JN is a transversal so the angle made on the same side of JN are corresponding angles which are equal to each other.
So, angle KJL = angle MLN........equation 1
Also given L is the midpoint of JN so, JL = NL.....equation 2
Now, in triangle JLK and triangle LNM
JK = LM (given)
angle KJL = angle MLN (from 1)
JL = NL (from 2)
So by S A S congruence rule, triangle JLK conguent triangle LNM proved.
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what is the smallest possible perimeter for a rectangle whose area is 16 in2?
Answer: 4in
Step-by-step explanation:
the typing speeds for the students in a typing class is normally distributed with mean 44 (μ) words per minute and standard deviation 6 (σ) words per minute. what is the probability that a randomly selected student has a typing speed of less than 38 words per minute? use the empirical rule provide the final answer as a percent. if necessary round the percent to the nearest whole number.
The probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
The formula for z-score is z = (x -μ)/σ
Where,
Z is standard score.
x is observed value.
μ is mean of the sample.
σ is standard deviation of the sample.
According to the given question.
The mean of the distribution is μ = 44
The standard deviation of the distribution is σ = 6
The observed value is x = 38
Therefore, z-score = (38 -44)/6 = -1
So, the are P(z > -1) = 15.87%
Hence, the probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.
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a grandfather, two fathers and two sons bought passage for a voyage together and everyone paid for one berth each. how many berths did they buy in total?
The total number of tickets they bought was 3.
What is a math riddle?
To solve a math riddle, children must translate a few sentences from a real-life scenario into the correct combination of mathematical equations. Children can decipher any code, including math riddles, using logic, creative problem-solving, and common sense.
Total 3 tickets-
Grandfather-Also Father of His son
Father-Also son of his father.
Son.
So Two fathers and two sons.
Hence, a total of 3 tickets were bought.
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what is the answer i need answers now
The graph below shows the number of hours Dario
worked and the amount he earned.
DARIO'S EARNINGS
Earnings (in dollars)
100
90
80
70
60
30
20
10
(2, 24).
Review / End Test
(5, 60)
0 1 2 3 4 5 6 7 8 9 10
Time (in hours)
Flag
(8, 96)
Options
V
What was Dario's hourly wage?
A $10
B
$12
(C) $24
D $54
Answer:
Step-by-step explanation:
B.
you need to buy some chicken for dinner tonight. you found an ad showing that the store across town has it on sale for $3.19 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.59 a pound. is it worth the extra drive? first, determine what information you need to answer this question, then click here to display that info (along with other info). how much chicken will you be buying? 3 pounds how much far are the two stores? my neighborhood store is 2.1 miles away, and takes about 7 minutes. the store across town is 8.5 miles away, and takes about 23 minutes. how kind of mileage does your car get? it averages about 19 miles per gallon in the city. how many gallons does your car hold? about 17 gallons how much is gas? about $3.83/gallon right now. going to the close store is cheaper going to the further store is cheaper the cheaper option saves you $
Yes, it is worth the extra drive, going to the further store is cheaper.
The cheaper option saves you $0.09.
Given:
Price or sale = $3.19 a pound
1.) Neighborhood store
Distance = 2.1 miles away
As, the car averages about 19 miles per gallon,
=2.1 miles / (19 miles/gallon)
= 0.1105 gallons of gas < 17 gallons
The gas is about $3.83/gallon, then the cost be
=0.1105 gallons x ($3.83/gallon)
= $0.42
The chicken is sold for $3.59 a pound, and you need 3 pounds, then you would pay:
= 3 pounds x ($3.59/pound)
= $10.77
So, the total is
= $0.42 (gas) + $10.77 (chiken)
= $11.19
2.) Store across town
Distance = 8.5 miles away
The car averages about 19 miles per gallon, then you would need:
=8.5 miles / (19 miles/gallon)
= 0.447 gallons of gas < 17 gallons
The gas is about $3.83/gallon, then the gas would cost:
=0.447 gallons x ($3.83/gallon)
= $1.71
The chicken is sold for $3.19 a pound, and you need 3 pounds, then you would pay:
= 3 pounds x ($3.19/pound)
= $9.57
The total cost
= $1.71 (gas) + $9.57
= $11.28
Thus, $11.19 < $11.28, then it is worth the extra drive.
Hence, cheaper option saves you= $11.28 - $11.19 = $0.09
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alex has $600 in her checking account. she wants to spend a part of this money on a computer. she wants to have at least $250 left in her checking account after buying the computer. write an inequality that can be used to find t, the amount of money in dollars that alex can spend on the computer, and solve for t.
An inequality that can be used to find t the amount of money in dollars is
c)t ≤ 350, t is less than or equal to 350. So, correct option is c.
In science, a disparity or an inequality is a connection which makes a non-equivalent examination between two numbers or other numerical expressions. It is utilized generally normal to look at two numbers on the number line by their size. There are a few unique documentations used to address various types of disparities:
The documentation a < b implies that an is not as much as b.
The documentation a > b implies that an is more noteworthy than b.
Regardless, an isn't equivalent to b. These relations are known as severe inequalities, implying that an is completely not exactly or rigorously more prominent than b. Identicalness is barred.
We have Alex total amount =$600 and amount which he want on his account after spending is $250.
So,t+250 ≤600
=>t≤ 600-250
=>t≤ 350.
Hence, option c is correct.
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(Complete question) is:
Alexandra has $600 in her checking account. She wants to spend part of this money on a computer. She wants to have at least $250 left in her checking account after buying the computer. The inequality shown can be used to find t, the amount of money in dollars that Alexandra can spend on the computer.
Which inequality represents all possible values of t?
a)t ≥ 350,
t is greater than or equal to 350
b)t ≤ 850,
t is less than or equal to 850
c)t ≤ 350,
t is less than or equal to 350
d)t ≥850,
t is greater than or equal to 850
Phone-Phriends charges $35 for a text-message plan with 250 text messages included. If the customer goes over the 250 messages, the cost is $0.14 per extra text message.
A customer sent and received 329 text messages last month. What are the total charges?
Answer:
Step-by-step explanation:
11.
a credit card company surveys its customers to determine the number of times they use the card each month. there are 5,500 customers and 2,756 indicate that they use the card at least twice each month. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The standard deviation of the sampling w would be 0.06.
What is a standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
Population proportion
[tex]p=\frac{2756}{5500} \\\\\\p=0.501091\\\\p=0.501[/tex]
The mean of the sampling distribution for samples of size n=70 customers = 0.501
The standard deviation of the sampling distribution for samples of size n=70 customers is
[tex]=\sqrt{\frac{p* (1-P)}{n}} \\\\=\sqrt{\frac{ 501091(1-0.501091) }{2}}\\\\ = 0.059761 \\\\=0.06[/tex]
Hence, the standard deviation of the sampling w would be 0.06.
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A person weighing 150 pounds burns about 320 calories per hour walking at a moderate rate. Suppose the same person burns about 1500 calories per day through basic activities. The total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking. What is the slope and y- intercept
The slope of the equation and y- intercept is 320 and 1500 respectively.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
Given that the total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking.
To find the slope and y- intercept.
y=320x+1500
Therefore, the slope of the line is;
m =320
Then the y- intercept is 1500
Hence, The slope of the equation and y- intercept is 320 and 1500 respectively.
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5. Find the measure of each angle in the figure below.
Lines are named with the capital letter; angles are named with the lower case letter.
B
A a
e d
C
The measure of each angle are mentioned below
What is angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The measure of each angle is
∠a = 90°
∠b = 45°
∠c = 45°
∠d = 90°
∠e = 45°
∠f = 45° {coordinate judgment angle }
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WILL GIVE BRAINLEST! AND 20 POINTS!
The relationship is not proportional because the number of used bottles increases more. Option B
What is a proportional relationship?A relationship is said to be proportional when the two variables that are in question are either increasing or decreasing at the same rate. It could also be that one one quantity is increasing and the other is decreasing.
If we look at the proportionality in the proper sense of it, there appears to be no relationship between the two variables as the number of used bottles is increasing at a much higher rate than the number of bottles that is recycled.
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Mya saved
$
640
for food for her family’s upcoming vacation. Breakfast is included with the hotel, but lunch and dinner are not. When Mya cooks lunch or dinner it costs, on average,
$
16
. When the family goes to a restaurant for lunch or dinner it costs, on average,
$
63
. Let
c
represent meals that Mya cooks and let
r
represent meals the family eats at a restaurant. Write an inequality to represent the situation.
The inequality to represent the situation is 16c + 63r ≤ 640.
What is simple inequality?
Mathematical expressions with simple inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given, total saving = $640
Mya cooks lunch or dinner = $16
restaurant for lunch or dinner = $63
For c meals that Mya cooks = 16c
For r meals, the family eats at a restaurant = 63r
Total cost = 16c + 63r
Based on conditions, 16c + 63r ≤ 640
Hence, the inequality representing the situation is 16c + 63r ≤ 640.
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Question
The points in the table lie on a line. Find the slope of the line.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{4 }{7 +3} \implies \cfrac{ 4 }{ 10 } \implies \cfrac{2 }{ 5 }[/tex]
480 people went to the Yellowstone National Park yesterday.
180 of them were children, and the remaining were adults.
What percent of the visitors at the park were adults?
%
Answer:
11
Step-by-step explanation:
Laptop computers are measured according to the diagonals of their screens.
8 in.
19 in.
A(n) 19-inch laptop has a screen that is 8 inches tall. How wide is the screen?
Round your approximation to 2 decimal places.
Check the picture below.
express 8 3/5 in simplest radical form
5 radical 8 to the power of 3
Step-by-step explanation:
4.) 2x + 3y = 12
x + y = 5
Answer:
x = 3
and
y = 2
Step-by-step explanation:
Which of the following lines have the greatest slope? EXAM DUE IN 20 MINUTES!!
Samuel prob please answer
The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.
What is meant by linear equation?A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.
Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.
Sodium contains in a can of soup is 300mg
Sodium contains in a can of frozen dinners is 450mg
Let the number of cans of soup purchased be x
Then, the number of frozen dinners purchased=x+5
Total sodium purchased=6000mg
So, 300x+450(x+5)=6000mg
Therefore, the system is 300x+450(x+5)=6000mg
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the unemployment rate does not reflect the true extent of the unemployment problem. which of the following groups is not counted as unemployed in the official unemployment statistics?
Groups not counted as unemployed in the official unemployment statistics are the underemployed and discouraged workers.
A discouraged worker is someone who can work and is qualified for employment but is not already working and has not looked for work in the past four weeks. Discouraged workers typically have given up looking for work because they have discovered no relevant employment possibilities or have not been successful in getting a job after applying.
Discouragement among employees has a wide range and complex root causes. Because they lack the skills to deal with technological change at work, workers occasionally leave the workforce. During the Great Recession, the manufacturing industry let go of senior workers who were unable to operate the modern computer numeric control (CNC) equipment, which was used to cut wood and other hard materials.
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describe how nonresponse might lead to bias in this survey. does the stated margin of error account for this possible bias?
The margin of error does not take into account the bias caused by nonresponse.
What is nonresponse bias?
The phenomenon known as participation bias, also known as non-response bias, occurs when a disproportionate number of participants have certain characteristics that have an impact on the results of surveys, polls, and other types of research.
Nonresponse bias happens when a portion of the sample's respondents fail to respond. The main distinction in this instance is that the error arises from a lack of respondents rather than the collection of false data.
Usually, the number of responses is used to calculate the margin of error. You can treat a sample from a finite population as infinite if the sampling fraction is small, but if the sampling fraction is high (say, more than 10% of the population size), you must make a finite population correction.
So, the non-response bias is not taken into account by the margin of error.
Longer commuters might take less time to complete a survey.
This would result in our estimate from the sample being lower than the actual mean travel time to work.
Hence, the margin of error does not take into account the bias caused by nonresponse.
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Consider the figure shown below. Find the value of each variable mentioned in the figure below
-------------------
The measure of an inscribed angle is half the measure of the intercepted arc:
a = 52/2 = 26,c = 84/2 = 42.Angles a and b sum to a right angle since inscribed between the tangent and diameter.
Then we have:
a + b = 9026 + b = 90b = 90 - 26b = 64In ACDE, M/C = (x-4)°, m/D = (9x + 4)°, and m/E = (2x + 12)°.
Find m/D.
Thus, in ΔCDE the m/∠D = 130⁰, which can be calculated using angle sum property of triangle.
What is triangle?Triangle is derived from the Latin word triangulus, which means "three-cornered" or "having three angles," and is composed of the roots tri-, "three," and angulus, "angle or corner." Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Given that: In ΔCDE
m/∠C = (x-4)°
m/∠D = (9x + 4)°
m/∠E = (2x + 12)°
Now, to find m/∠D
So, We know that sum of internal angles of a triangle is equal to 180⁰ .Here, we are given a ΔCDE and all its three internal angles.
Putting the sum of all three equal to 180⁰:
∠C + ∠D + ∠E = 180⁰(x-4)°+ (9x + 4)°+ (2x + 12)°
= 180⁰12x +12
= 180⁰x +1 = 15⁰
x = 14⁰
Thus, Putting value of x in m/∠D = (9x + 4)°.
m/∠D = (9 × 14 +4)⁰
m/∠D = 130⁰
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The complete question is as follows:
In ΔCDE, m ∠ C = ( x − 4 ) ∘ m∠C=(x−4) ∘ , m ∠ D = ( 9 x + 4 ) ∘ m∠D=(9x+4) ∘ , and m ∠ E = ( 2 x + 12 ) ∘ m∠E=(2x+12) ∘ . Find m ∠ D.
Planet A has a mass of 6 x 10^28 kilograms. Planet B has a mass of 8 x 10^25 kilograms. Choose which planet has the lager mass. Then fill in the blank with a number written in scientific notation.
Answer:
Step-by-step explanation:
Planet A has a mass of 8× 10²5 kilograms. Planet B has a mass of 6×10 kilograms. Choose which planet has the larger mass. Then fill in th blank with a number written in standard notation. Planet A has the larger mass. The mass of Planet A is times as large as the mass of Planet B. O Planet B has the larger mass. $0 times as large as the mass of Planet A.
Answer:
10
Step-by-step explanation:
im him trust