The equation of the line that is parallel to given line is y = 4x + 12
What is slope of Parallel lines:Parallel lines have an equal slope. The slope of parallel lines is identical because they are all equally inclined with respect to the positive x-axis.
If m₁ and m₂ are slopes of parallel lines then => m₁ = m₂
Here we have
A line is parallel to y = 4x + 11 ---- (1)
The given line is in form of y = mx + c [ where slope of line = m ]
On comparing both lines, Slope given line = 4
Let the required line with slope m₁ is y = m₁x + c --- (2)
As we know slope of parallel lines are equal or same
=> Slope of line (2), m₁ 4
Line (2) => y = 4x + c
Given that the line passes through (-2, 4)
=> 4 = 4(-2) + c
=> 4 = -8 + c
=> c = 12
Therefore,
The equation of the line that is parallel to given line is y = 4x + 12
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Which of the following equations has a solution different from the rest? (1 point)
¾ x+5=− ¼
½ x−3= ½
−1/7 x−34=¼
−0.35x−0.52=1.93
Answer: (-1/7)x - 34 = 1/4
Step-by-step explanation: The solution for all other equations is 7 and for the 3rd equation, the solution is 239.75 or 959/4
1) 3/4 X +5=-1/4
x=-7
2) 1/2X - 3 = 1/2
x=7
3) x = -137×7 /4
4) x= -7
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THIS IS URGENT!
In orde to keep a specific bacteria alive,the temperature in a science lab cannot exceed -20 degrees farenheit. The electricity went out when the temperature was -72 degrees farenheit,but it increasing at a rate of 6.5 degrees per hour. How many hours do scientists have until the bacteria is not safe?
Rewrite one eighteenthx3y + seven eighteenthsxy2 using a common factor.
one thirdxy(6x2 + 7y)
one thirdx2y(6x2 + 9y)
one eighteenthxy(x2 + 7y)
one eighteenthx3y2(y + 7)
Answer:
C
Step-by-step explanation:
1/18 x³y + 7/18 xy²
1/18 xy (x² + 7y)
yu want to determine the percentage of fortune 500 ceos who think indiana university (iu) deserves its current business week rating. you mail a questionnaire to all 500 ceos and 160 respond. exactly half of the respondents believe iu does deserve its ranking. calculate a 95% confidence interval for the fraction of fortune 500 ceos who believe iu deserves its ranking. round your answers to three decimal places, if necessary.
A 95% confidence interval for the fraction of fortune 500 ceos who believe Indiana university(IU) deserves its ranking is ( 0.279, 0.361)
According to the question,
Total number of sample taken for questionnaire = 500
Number of people responded = 160
Sample Proportion : p = 160/500
=> p = 0.32
Proportion of people who has not responded : q = 1 - p
=> q = 0.68
We have to create a 95% confidence interval for the fraction of fortune 500 ceos who believe Indiana university(IU) deserves its ranking.
Formula of C.I = p ± z√pq/n
Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size
C.I at 95% = 0.32 ± 1.96√0.32×0.68/500
=> 0.32 ± 1.96 √0.0004352
=> 0.32 ± 1.96 × 0.0208
=> 0.32 ± 0.0408
C.I = ( 0.32 - 0.0408, 0.32 + 0.0408)
=> C.I = ( 0.279, 0.361)
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3, 1.6, 2.8, 2.5, 1.7, 2.8
What is the mean absolute deviation of these numbers?
The mean absolute deviation of the given numbers is 0.5.
What is a mean?The mean is the sum of all values divided by the total number of values.
The mean of the given number is obtained by dividing the sum of the values by its total number of value.
i.e. (1.6+1.7+2.5+2.8+2.8+3)/6 = 2.4
Then taking the difference of each number from the mean.
i.e. (1.6-2.4), (1.7-2.4),(2.5-2.4),(2.8-2.4),(2.8-2.4),(3-2.4)
i.e. -0.8,-0.7,0.1,0.4,0.4,0.6
Take the sum of the absolute value of the above numbers
i.e. |-0.8+-0.7+0.1+0.4+0.4+0.6| = 3
Divide 3 by 6 to obtain mean absolute deviation.
i.e 3/6 = 1/2 =0.5
Hence, 0.5 is the mean absolute deviation of the given numbers.
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Sydney is going to the amusement park. where she has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money
Sydney will spend is given by the equation y = 18 + 4r. where y represents the
total amount of money, in dollars and cents, and a represents the number of rides Sydney goes on. What could the number 4 represent in the equation?
The number 4 could represent the cost of each ride Sydney goes on in the equation
How to determine what the number 4 could represent in the equation?From the question, we have the following parameters that can be used in our computation:
y = 18 + 4r
Where
y = total amount of money, in dollars and cents, r = the number of rides Sydney goes onThe equation y = 18 + 4r is a linear equation
A linear equation in its slope-intercept form can be represented as
y = c + mx
Where x and y are the variables
So, we have
Slope = m
By comparing the equations, we have
m = 4
This means that
Slope = 4
In this case, the slope is 4
So, the interpretation is that 4 is the cost of each ride
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Davina charges $15 an hour to weed gardens. What does she charge to weed a garden for 1, 2, 3, and 4 hours?
Answer:
1 - $15
2- $30
3 - $45
4 - $60
Step-by-step explanation:
$15/hour
1 - $15 =1*15
2- $30 =2*15
3 - $45 =3*15
4 - $60=4*15
55 is 40% of what number?
Answer:
55 is 40% of 137.5.
Step-by-step explanation:
To find the number that 55 is 40% of, you can divide 55 by 40% to get 137.5. This means that 55 is 40% of 137.5.
22. Is the following ordered pair (-2, 9) a solution of the linear inequality y ≥ 7x+3
Answer:
x=-3/7
Step-by-step explanation:
20 newspapers in 4 piles = newspapers per pile
Answer: 5
Step-by-step explanation:
20/4 = 5
Which shows the expression below in simplified form?
(6.3 × 1011) ÷ (7 × 105)
A.
9 × 105
B.
-0.7 × 105
C.
9 × 104
D.
9 × 107
Answer: It's D.
Step-by-step explanation: When you simplify you get the answer D.
Answer:
0.9 x 10^6
Step-by-step explanation:
6.3 divided by 7 is 0.9
10^11 ÷ by 10^5 is 10^6
What is the simplest form of (x^2+5x-6) / (x^2+9x+18)?
a) (x+2) / (x+6)
b) 1/3
c) (x-1) / (x+3)
d) -1/3
Answer:
a. [tex]\frac{x+2}{x+6}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]
Apples cost $1.47 per pound. Danielle buys an apple that weighs 0.62 pound. To the nearest cent, how much does Danielle's apple cost?
Answer:
x = 0.91
Step-by-step explanation:
x = 1.47 x 0.62
x = 0.9114
round x = 0.9114 to the required place
x = 0.91
In a group of 500 people determine how many are suspects in the following scenario.
A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.
30 people total in the office
22 wearing a white button down shirts
16 wearing black pants
7 wearing a multicolored tie
Using the data, how many suspects are there?
Using the given data, the number of suspects is; 7
How to find the intersection of mathematical sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.
However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
Now, we are told that;
Total number of people in the office = 30 people
Number of people wearing a white button down shirts = 22
Number of people wearing black pants = 16
Number of people wearing a multicolored tie = 7
Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;
The number of suspects = A ∩ B ∩ C = 7 people
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Mayerlin has two summer jobs. During the week she works in the grocery store, and on the weekend she works at a nursery. She gets paid $20 per hour to work at the grocery store and $19 per hour to work at the nursery. How many total hours does she work if she does 11 hours at the grocery store and 10 hours at the nursery? How many total hours does she work if she does g hours at the grocery store and n hours at the nursery?
The total number of hours Mayerlin worked is 21 and (g + n) respectively.
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. When two whole numbers are added, the sum or total of those values is obtained.
Given that, Mayerlin gets paid $20 per hour to work at the grocery store and $19 per hour to work at the nursery.
Since Mayerlin works 11 hours at the grocery store and 10 hours at the nursery, the total number of hours she worked is:
11 + 10
= 21
Now, if, Mayerline works g hours at the grocery store and n hours at the nursery, the total number of hours she worked is:
g + n
Hence, the total number of hours Mayerlin worked is 21 and (g + n) respectively.
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Which ordered pair is a solution to the equation y = –23x + 9?
A (−32,10)
B (0,10)
C (−1,1023)
D (23,10)
Answer: None of these
Step-by-step explanation:
A. If [tex]x=-32[/tex], then [tex]y=745[/tex], not [tex]10[/tex].
B. If [tex]x=0[/tex], then [tex]y=9[/tex], not [tex]10[/tex].
C. If [tex]x=-1[/tex], then [tex]y=32[/tex], not [tex]1023[/tex].
D. If [tex]x=23[/tex], then [tex]y=-520[/tex], not [tex]10[/tex].
A hockey goaltender has a save percentage of 0.920. This
means that the probability of any single shot taken on the
goaltender being a goal is 0.08. What would be the
expected number of goals scored on this goaltender in a
game where she faced 35 shots?
2.8 goals
2.0 goals
3.4 goals
1.5 goals
Answer:
2.8 goals
Step-by-step explanation:
35 * 0.08 = 0.35*8
0.35*8=2.8
The expected number of goals scored on the goaltender would be 2.8.
Explanation:The expected number of goals scored by the goaltender can be calculated using the formula:
Expected goals = Total shots * Probability of a goal
Therefore, for a goaltender with a save percentage of 0.920 (which means the probability of a goal is 0.08), and facing 35 shots:
Expected goals = 35 * 0.08Expected goals = 2.8The expected number of goals scored on this goaltender in a game where she faced 35 shots would be 2.8 goals.
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Here is the graph for one equation in a system of equations:
a) Write a second equation for the system so it has infinitely many solutions.
b) Write a second equation whose graph goes through (0, 1) so the system so it has no
solutions.
The answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.What is the general form of a straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line equation is given byy = mx + c
where -
[m] : slope of line
[c] : y - intercept
Given is the graph of a straight line as shown.
[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -
(0, 4) and (4, 1)
Let the line be -
y = mx + c
m = (1 - 4)/(4 - 0) = -3/4
m = -3/4
So, the equation will be -
y = (-3/4)x + 4
[B] -
For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.
Therefore, the answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.To solve more questions on functions, expressions and polynomials, visit the link below -
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-5 - y = -3x find the slope and y-intercept
Answer:
slope = 3 , y- intercept = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
- 5 - y = - 3x ( add 5 to both sides )
- y = - 3x + 5 ( multiply through by - 1 )
y = 3x - 5 ← in slope- intercept form
with slope m = 3 and y- intercept c = - 5
How many leave were longer then 7 centimeters
Answer:
You could pick as many as you like. Ideally you would use all the leaves on the tree, but that would be rather a large number to measure, and your parents might not be very happy if you stripped the tree bare!So let's try 100 leaves.How to get a random sample?Here is one way you could get a random sample:Try taking all the leaves on one branch of the tree. After you've discarded any that are broken, then see how many there are. If there are less than 100, then get the leaves from another branch until you have more than 100. Then write a different number (starting with 1) on each leaf with a marking pen.Write the same numbers on small pieces of paper.Fold the pieces of paper.Put them into a hat and mix them up.Draw 100 pieces of paper (without looking) from the hat. The first 100 pieces of paper you draw would give you the numbers of the leaves to use in the experiment.The next thing you need to decide is how to measure the leaves, andhow accurate your measurements should be:How to measure?Keeping your leaves flat, use a ruler to measure the length of each leaf from the pointy part at one end of the leaf to the point where the leaf joins the stalk at the other end. Maybe your leaves bend a bit, but don't follow the main rib of the leaf as this would make measurement too difficult.Just measure in a straight line as shown in the following diagram:leafHow accurate?You should measure the length of each leaf to the nearest millimeter.Now you're ready to begin.Measure the length of each leaf to the nearest millimeter and record you results in a table, as follows:
Step-by-step explanation:
Rewrite:4/6 : 1/3
as a unit rate.
Answer:
I think it's 2:1
Step-by-step explanation:
if I'm wrong in sorry
Answer:
Step-by-step explanation:To rewrite 4/6 : 1/3 as a unit rate, we need to first find a common denominator for the fractions. The least common multiple of 6 and 3 is 6, so we can use this as the common denominator.
We can then rewrite the fractions as follows:
4/6 : 1/3 = (4/6) * (3/3) : (1/3) * (2/2)
Simplifying, we get:
2/3 : 2/3
This is a unit rate, with a value of 2/3.
Factor each completely.
5) 250a³ +54
The required factorized form of the given expression is 2(125a³ + 27).
What is the greatest common factor?The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.
Here,
In the given expression,
Taking 2 common,
= 250a³ + 54
= 2(125a³ + 27)
Thus, the required factorized form of the given expression is 2(125a³ + 27).
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what is the probability of having x failures in the next 100 mowers tested for x from 0 to 20 mower test
The ratio of the number of mowers that fail to the overall number of mowers is known as the fraction of mowers that fail the functional performance test. Consequently, 9/500 lawnmowers fail, then the probability of having x failures in the next 100 mowers is = [tex]0.018x[/tex]
Probability of having x mower fail = 0.018x
Number of mowers that fail = 54
Total number of mowers = 3000
The probability of failure can be defined as,
= [tex]\frac{Number of mowers that fail}{Total number of mowers}[/tex]
Fraction that failed = [tex]\frac{54}{3000}[/tex]
Fraction that failed = [tex]\frac{9}{500}[/tex]
Fraction that failed = 0.018
Therefore,
The ratio of the number of mowers that fail to the overall number of mowers is known as the fraction of mowers that fail the functional performance test. Consequently, 9/500 lawnmowers fail, then the probability of having x failures in the next 100 mowers is = [tex]0.018x[/tex]
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write a logarithmic equation (using only real numbers) that has no real solutions. explain why there are no real solutions.
The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.
This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.
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according to a jhu study published in the american journal of public health, widows live longer than widowers. consider the following survival data collected on 100 widows and 100 widowers following the death of spouse: years lived widow widower less than 5 25 39 5 to 10 42 40 more than 10 33 21 can we conclude at 0.05 level of significance that the proportions of widows and widowers are equal with respect to the different time periods that a spouse survives after the death of his or her mate?
To determine whether the proportions of widows and widowers living different lengths of time after the death of their spouse are equal, you can conduct a chi-squared test of independence. This test compares the observed frequencies (the number of widows and widowers living different lengths of time) to the expected frequencies, which are the frequencies that you would expect to see if the two variables (widowhood and length of time survived) were independent.
To perform the chi-squared test, you will need to calculate the chi-squared statistic and the corresponding p-value. If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers.
To calculate the chi-squared statistic and p-value, you will need to follow these steps:
Calculate the expected frequencies for each group (widows and widowers) in each time period (less than 5 years, 5-10 years, more than 10 years). To do this, you will need to multiply the total number of widows (100) by the proportion of widows in each time period, and the total number of widowers (100) by the proportion of widowers in each time period.
Subtract the expected frequencies from the observed frequencies and square the result for each time period.
Divide each squared difference by the expected frequency and sum the results. This is the chi-squared statistic.
To calculate the p-value, you will need to consult a chi-squared table or use a statistical software program to determine the p-value corresponding to the chi-squared statistic and the degrees of freedom (which is equal to the number of time periods minus 1).
If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers
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4x² -16x+16=0
how to find the roots by factoring
4x^2 - 16x + 16 = 0
factor out the CGF which is 4
rewrite
x^2 - 4x + 4
factor
(x - 2)(x-2)
x = 2
1 point
Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the closest estimate of the sales
of soft drinks and hot dogs?
The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220 * 2
How to determine the calculation that will give the closest estimateFrom the question, we have the following parameters that can be used in our computation:
Time = one week
Number of cans = 362
Unit price of soft drink = $1.75
Number of hot dogs = 221
Unit price of hot dogs = $2.35
The calculation that will give the closest estimate is represented as
Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs
Substitute the known values in the above equation, so, we have the following representation
Estimate = 362 * 1.75 + 221 *2.35
Approximate
Estimate = 360 * 2 + 220 * 2
Hence, the expression is 360 * 2 + 220 * 2
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John can ride his bicycle at a rate of 14 miles per hour. Convert this rate to
feet per second.
O 20.53 feet per second
O 25.03 feet per second
O205.33 feet per second
O250.33 feet per second
correct answer is a) 20.53 feet per second
John can ride his bicycle at a rate of 20.53 feet per second.
How do I calculate feet per second?
Multiplying your foot-per-minute speed by 60. This is how many seconds there are in a minute. Your speed in feet per second is the outcome. For instance, 88 feet per second is equal to 5,280 feet per minute divided by the 60 seconds in a minute.
How long is a second in feet?
One-degree of longitude equals 288,200 feet (54.6 miles), one minute equals 4,800 feet (0.91 mile), and one second equals 80 feet.
Is feet per second velocity?
A unit of velocity and speed (scalar) is the foot per second (plural feet per second) (vector quantity, which includes direction). It represents the traveled or displaced distance in feet (ft) divided by the time (in seconds) (s).
[tex]\frac{14 miles}{1 h}[/tex] × [tex]\frac{5280 ft}{1 mile}[/tex]= [tex]\frac{73920 ft}{1 hr}[/tex]
[tex]\frac{73920 ft}{1 hr}[/tex] × [tex]\frac{1 hr}{60 min}[/tex]= [tex]\frac{1232 ft}{1 min}[/tex] ×[tex]\frac{1 min}{60s}[/tex]= [tex]\frac{20.53ft}{1s}[/tex]
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The area of the caribbean sea is 2.7182 × 106 km2. the area of the south atlantic ocean is 4.027 × 107 km2. find the total area. write the final answer in scientific notation with the correct number of significant digits. 4.29882 × 108 km2 4.299 × 107 km2 3.75518 × 1013 km2 3.755 × 1013 km2
The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²
Calculating total areaFrom the question, we are to determine the total area of the water bodies.
From the given information
"The area of the Caribbean sea is 2.7182 × 10⁶ km²"
and
"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"
To determine the total area, we will add up the two areas
Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²
Total area = 4.29882 × 10⁷ km²
Total area ≈ 4.299 × 10⁷ km²
Hence, the total area is 4.299 × 10⁷ km²
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Answer:
Hence, the total area is 4.299 × 10⁷ km²
Step-by-step explanation:
The surface area of a rectangular prism is A=2lw+2lh+2wh, where l, w, and h are the length, width, and height of the prism, respectively. Determine the width of a rectangular prism with a surface area of 930 square units if its length is 12 units and its height is 9 units. (1 point)
1. 108 units
2. 12,11/12units
3. 8,11/12
4.17 units
Complete the input-output table below for f(x)=2(x−1)2−4.(2 points)
The width of a rectangular prism with a surface area of 930 square units is 21.4 units.
What is the surface area of the rectangle?
The area of the rectangle can be calculated by multiplying l×w, The units associated with the surface area will always be units squared. The area is the result of multiplying two dimensions, length, and width, which can be represented as a power of 2.
The surface area of the rectangular prism is given by:
SA = 2lw + 2lh + 2wh
Where,
l: length
w: width
h: height
Therefore, by substituting values we have:
the surface area of 930 square units if its length is 12 units and its height is 9 units.
SA = 2lw + 2lh + 2wh
930 = 2(12)w + 2(12)(9) + 2w(9)
930 = 24w + 33 + 18w
930 - 33 = 24w + 18w
897 = 42w
w = 897/42
w = 21.4
Hence, the width of a rectangular prism with a surface area of 930 square units is 21.4 units.
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