Integers are 3, 4 and 5.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.
Given Data
Let the three consecutive integers are :
x, x+1 and x+2
According to question
3(x+1) = 4 - 2(x+x+2)
3x + 3 = 4 - 2(2x + 2)
3x + 3 = 4 - 4x - 4
3 = 4x-3x
x= 3
Integers are 3, 4 and 5.
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Earning Money: Marcus works at an ice cream shop. He eamns $14.50 each
hour. Use Marcus's timesheet for the week to answer the questions
Date. Time in. Time out
April 11 8:45 am 12.00pm
April 12 9:00am 12.00pm
April 13 7:30am 12:00pm
April 14 8:00am 1:15pm
April 15 8:30am 11:15am
A. How many hours did Marcus work for the week?
B. How much money did Marucs earn for the week?
Answer:
A. Marcus worked 27 hours and 45 minutes in the week.
B. He earned $391.5 for the week.
Step-by-step explanation:
First you calculate the hours he worked daily and you add them together, when you have the weekly hours you multiply the hours times what he earns each hour.
It's 27 • 14.50= $391.5
Answer:
A 88hours and 5 minutesB $70.250
What amount of pure acid must be added to 400 mL of a 30% acid solution to produce a 75% acid solution?
Step-by-step explanation:
pure acid is a 100% acid solution.
x = ml of 100% solution
1×x + 0.3×400 = 0.75×(400 + x)
x + 120 = 300 + 0.75x
0.25x = 180
x = 720 ml
we must add 720 ml of pure acid to the 400 ml of 30% solution to create a 75% solution (1,120 ml in total).
Find the slope of the graph
Answer:
-1
Step-by-step explanation:
You just have to divide the change in the x axis by change in the y axis on any arbitrary interval.
Answer:
-1
Step-by-step explanation:
Do rise-over-run for linear equations. Its the vertical change over the horizontal change between two points. Ex. between (-2,0) and (-1,-1) the line drops 1 unit horizontally (-1) and moves to the right one unit (1) so the slope would be -1/1 = -1
PLEASE HELP WITH THIS QUESTION!!!!!!!!!!
Answer:
Hope I helped you with this. Everything is explained in the photo
Find the x-coordinates of the x-intercepts of the parabola
y = 2x^2 + 13x - 7. If you find more than one, then list the values separated by commas.
The x-coordinates of the x-intercepts of the parabola are 1/2 and -7
What are parabola equations?Parabola equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the x-coordinates of the x-intercepts?The parabola is given as
y = 2x^2 + 13x - 7
It should be noted that the x-intercept of the function is the point or points where the graph of the function crosses the x-axis
i.e. the point where the function equals 0
So, we have
y = 2x^2 + 13x - 7
Expand
y = 2x^2 + 14x - x - 7
Factorize the equation
So, we have
y = 2x(x + 7) - 1(x + 7)
Set the equation to 0
So, we have
2x(x + 7) - 1(x + 7) = 0
Factor out x + 7
So, we have
(2x - 1)(x + 7) = 0
Expand
2x - 1 and x + 7 = 0
Solve for x
x = 1/2 and x = -7
Hence, the x-coordinates of the x-intercepts are 1/2 and -7
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What math is being used here? (Subject names)# 3
Select the correct answer. A soccer team wins 65% of its matches, and 15% of its matches end in a draw. If the team is scheduled to play 20 matches, about how many matches is it expected to lose? A. 13 B. 4 C. 8 D. 1 Reset
its B.4
Using percentage we can calculate that the team is expected to lose 4 matches.
A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. Although the abbreviations "pct," and occasionally "pc" is also used, the percent symbol "%" is most frequently used to denote it. A percentage is a number without any dimensions or established units of measurement.
By dividing the value by the entire value and multiplying the result by 100, the percentage may be computed. Calculating percentages using the formula (Value/Total Value)×100%.
Given in percentages the team will win 65% , team will draw =15%
Therefore in percentage the team will lose = 100 - ( 65 + 1 5 )% = 20 %
Now calculating the total number of matches the team will lose :
20% of 20 matches = 4 matches
Hence the team is expected to lose 4 matches out of 20.
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solve for X on each of them and find the measurements of the angles
The unknown angles are as follows:
∠1 = 67.9°, ∠2 = 22.08°∠1 = 129°, ∠2 = 51°∠1 = 13.5°, ∠2 = 13.5°How to solve angles?complementary angles are angles that sum up to 90 degrees.
in other words, When two angles add to 90°, we say they "Complement" each other.
Therefore,
9x + 2x + 7 = 90
11x = 90 - 7
11x = 83
x = 83 / 11
x = 7.54
Therefore,
∠1 = 9(7.54) = 67.9°
∠2 = 2(7.54) + 7 = 22.08°
Supplementary angles are angles that sum up to 180 degrees.
Therefore,
3x + 8 + 9x = 180
12x + 8 = 180
12x = 180 - 8
12x = 172
x = 172 / 12
x = 14.3
Hence,
∠1 = 9(14.3) = 129°
∠2 = 180 - 129 = 51°
Vertically opposite angles share the same vertex. Vertically opposite angles are equal.
Therefore,
9x = 3x + 9
9x - 3x = 9
6x = 9
x = 9 / 6
x = 3 / 2
x = 1.5
Therefore,
∠1 = 9(1.5) = 13.5°
∠2 = 13.5°
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1a)Determine whether the relation is a function. (3,-3) (-3,3) (2,-2) (-2,-3) and explain.
1b)If the relation in 1a is a one to one?explain.
I really need help on this question but if anyone wants to help it would be greatly appreciated! 20 points for this!
Part a
It is a function because each x-value matches with only one y-value.
Part b
No, because the x-values of 3 and -2 both correspond to a y-value of -3.
A machine fills boxes at a constant rate. At the end of 35 minutes, it has filled 5 boxes.
Which table represents the relationship between the number of minutes the machine fills boxes and the number of boxes it has filled?
The machine will take 7 minutes to fill one box. Hence, table A. represents the correct relationship between the number of minutes the machine fills boxes and the number of boxes it has filled.
Boxes filled by machine in 35 minutes = 5 boxes
So, the number of boxes the machine fills in each minute = Time taken to fill 5 boxes/ Number of boxes filled
= 35/5
= 7 minutes
Time taken by machine to fill one box = 7 minutes
Time taken to fill two boxes = 14 minutes
Time taken to fill three boxes = 21 minutes
Time taken to fill four boxes = 28 minutes
Hence, table A is the correct answer from the given options
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75 + 25x = 300
PLEASE EXPLAN WHY AND HOW YOU GOT THE ANSWER
the round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5 mm. round values to 4 decimal places when possible.
The following are the results for measuring the distance that a long jumper has jumped which is uniformly distributed between 0 and 5mm
a) Mean = 2.5
b) Standard deviation = 1.4434
c) P(X = 2.5) = 0
d) P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4
e) P(X > 1) =0.8
f) P(X > 4 | X > 2) = 0.33
g) 60th percentile = 3
h) Upper quartile = 3.75
Mean = (0 + 5)/2 = 2.5
Standard deviation =[tex]\sqrt{(5-0)^{2} }[/tex] / [tex]\sqrt{12}[/tex] = 1.4434
P(X = 2.5) = 0
P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4
P(X > 1) = (5 - 1)/(5 - 0) = 4/5 = 0.8
P(X > 4 | X > 2) = P(X > 4 and X > 2)/P(X > 2) = (5 - 4)/(5 - 2) = 1/3 = 0.33
60th percentile = 0.60*(5 - 0) = 3
Upper quartile = 75th percentile = 0.75*(5 - 0) = 3.75
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The perimeter of a rectangle is 198 feet. Find the length and width if the length is an integer and the width is 3 times the next consecutive integer.
Answer:l=p/2-w=198/2-3=96
Step-by-step explanation:yes
Please help I don't know how to do this and I was wondering if someone could help.
Applying the concept of the or operation, the solution to the given inequality is as follows:
r < -5/8 or r ≥ 3/8.
How to find the or operation between two data sets?Considering two data-sets, the or operation between them is the set composed by all the elements that belong to at least one of the data-sets.
In the case of an inequality, the data set is represented by the intervals.
The first inequality is:
0.5r + 3 < 7/4.
0.5r < 7/4 - 3
r/2 < -5/4 (as -3 = -12/4)
r < -5/8.
The second inequality is:
-r + 3/4 ≤ 3/8
-r ≤ 3/8 - 3/4
-r ≤ -3/8 (as 3/4 = 6/8)
r ≥ 3/8 (multiply by -1, hence the signal also changes).
As the intervals do not intersect, the solution to the inequality is given as follows:
r < -5/8 or r ≥ 3/8.
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Which of these is equal to 0.428571?
A. 42/99
B. 1/7
C. 4/9
D. 3 5/7
From the options provided in the question, we may conclude that Option A is equivalent to 0.428571.
In mathematics, what is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
What are the division steps?Step 1: Take the dividend's first digit from the left. Determine whether this digit is greater than or equal to the divisor.
Step 2: Next, divide it by the divisor and write the result as the quotient on top.
Step 3: Subtract the result from the digit and record the difference.
Step 4: Subtract the dividend's next digit (if present).
Step 5: Repeat the procedure.
We need to find the given option that is equal to 0.428571.
For option A,
42/99 =0.428571 = 0.42
Therefore, we can say that Option A is equal to 0.428571 from the options given in the question.
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Deb found 56 tulips for $8. Please help Deb by figuring out the ratio. (round to 2 decimal places)
A. $0.70 per tulip
B.$7.00 per tulip
C. 7 tulips per dollar
D. .7 tulips per dollar
Answer:
C should be the correct answer
Step-by-step explanation:
56 Tulips for $8
56÷8=7
7 Tulips for $1
prove me wrong
Answer:
C
Step-by-step explanation:
56 Tulips for $8
56÷8=7
7 Tulips for $1
Can someone tell me how I can reply to questions I didn't ask?
a refrigerator was originally priced at $250. it was then put on sale for 20% of. what is the number of dollars in the final price of the refrigerator if an additional 15% is taken off from the sale price?
The final price of the refrigerator after the additional 15% discount is $170
Given
The original sale price of the refrigerator = was $250
Given a 20 % discount on the original price, the new sale price would be as follows
Sale price = original price - Discount
= [tex]250-(\frac{20}{100} )250[/tex]
Sale price = $200
After this an additional 15% discount is given on new sale price.
So again deducting the discount from the sale price we get,
Sale price = 200 - discount(15%)
= [tex]200-(\frac{15}{100} )200[/tex]
Sale price = 170
Hence the final sale price after discount is $170
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Mahnoor owns and operates mahnoor's coffee shop. the city of laketown, australia, where mahnoor's coffee shop is located, recently enacted a ban on all foam cups to help protect the environment. instead of switching to paper cups, mahnoor has decided to risk being fined by the city and to continue to use foam cups. she estimates that this will save her 10{,}00010,00010, comma, 000 australian dollars. she also estimates that there is a 12\%12%12, percent chance that she will be fined. the fine would be for 100{,}000100,000100, comma, 000 australian dollars. find the expected value of mahnoor's decision to continue to use foam cups.
Answer: -2000
Step-by-step explanation:
how do you solve x^2-11x+18=0
Answer: x = 9, 2
Step-by-step explanation:
I'm going to give you two main ways to solve this type of problem.
First is doing it mentally:
When we're given the setting of ax^2 + bx + c
We want to find two numbers that multiply to c and add to b. (If a isn't 1, then we need to add that into our calculation, but in this case a = 1)
So, what two numbers multiply to 18 and add to -11?
-9 and -2, so we rewrite the equation as (x-9)(x-2)
We then solve for x, x - 9 = 0, so x = 9 and x - 2 = 0, so x = 2
Second is we use the quadratic formula:
It would be [tex](-b+\sqrt{b^{2} -4ac})/2a\\(-b-\sqrt{b^{2} -4ac})/2a\\\\Plugging in your numbers: \\\\(11+\sqrt{11^{2} -72})/2\\(11-\sqrt{11^{2} -72})/2[/tex]
The distribution ages for students at the state college is positively skewed with a mean of μ= 21.5 and a standard deviation of σ= 3.
a. What is the probability of selecting a random sample of n = 4 students with an average age greater than 23?
b. What is the probability of selecting a random sample of n = 36 students with an average age greater than 23?
c. For a sample of n = 36 students, what is the probability that the average age is between 21 and 22?
Probability of selecting a random sample of n = 4 students with an average age greater than 23 is 0.1587, the probability of selecting a random sample of n = 36 students with an average age greater than 23 is 0.00135 and for a sample of n = 36 students, the probability that the average age is between 21 and 22 is 0.6826
In the distribution ages for students at the state college is positively skewed with a mean value μ= 21.5 and a standard deviation of σ = 3.
a)P(z> (23-21.5)/(3/√4))
P(z>1) = 0.1587
b) P(z> (23-21.5)/(3/√36))
P(z>3) = 0.00135
c) P((23-21.5)/(3/√36) < z < (22-21.5)/(3/√36 ))
P(-1 < z < 1) = 1 - 0.1587 - 0.1587 = 0.6826
Therefore, probability of selecting a random sample of n = 4 students with an average age greater than 23 is 1587, the probability of selecting a random sample of n = 36 students with an average age greater than 23 is 0.00135 and for a sample of n = 36 students, the probability that the average age is between 21 and 22 is 0.6826
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Help pls!! will award brainiest
3(2x+4)=24 solve for x
Answer:
x = 2
Step-by-step explanation:
Use distributive property:
3(2x+4) = 24
3*2x + 3*4 = 24
6x+12 = 24
6x = 12
x = 2
A line passes through the point (-8,3) and has a slope of -5/4
Write an equation in slope intercept form for this line
Answer:
y=2x+13
that is the slope of the intercept
follow up to previous question
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y^{-5}}{x^{-3}}\implies \cfrac{y^{-5}}{1}\cdot \cfrac{1}{x^{-3}}\implies \cfrac{1}{y^5}\cdot \cfrac{x^3}{1}\implies {\Large \begin{array}{llll} \cfrac{x^3}{y^5} \end{array}}[/tex]
A student is running for president of student government. Her friend has designed a campaign poster that measures 27 feet by 14 feet. She duplicated the poster on a
rectangular button measuring 6 inches by 3 1/9 inches. What is the scale factor?
The scale factor that is used for student is running for president of student government is 1:54.
What is the scale factor?From the information, her friend has designed a campaign poster that measures 27 feet by 14 feet and she duplicated the poster on a
rectangular button measuring 6 inches by 3 1/9 inches.
1 feet = 12 inches
27 feet = 27 × 12 = 324 inches.
The scale factor will be the division of the values and this will be:
= 6/324
= 1/54
The scale factor is 1:54.
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PLSSS HELP MEEE WILL GIVE 20 POINTS
Estimate the quotient of 42.4 ÷ 7.28.
9
8
7
6
Answer:
6
Step-by-step explanation:
angle A and angle B are vertical angles. If mA = (2x +29)° and m
B = (3x - 17)°, then find the measure of angle B.
The angle B has a measure of 121 degrees
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the measure of the angle?The angles are given as
A = 2x + 29
B = 3x - 17
Also, we have:
The angles are vertical angles
Vertical angles are congruent angles
This means that
A = B
So, we have
2x + 29 = 3x - 17
Evaluate the like terms
x = 46
Substitute x = 46 in B = 3x - 17
B = 3 x 46 - 17
Evaluate
B = 121
Hence, the measure of the angle B is 121 degrees
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Answer:
Step-by-step explanation:
b=(3x-17) degrees.
Question 9(Multiple Choice Worth 1 points) (04.05 MC) A company determines an employee's starting salary according to the number of years of experience, as detailed in the table. Years of experience Salary 0 $40,000 1 $42,150 $44,260 $46,785 $48,820 $51,126 2 3 4 5 Use the equation for the line of best fit to predict the salary for an employee with 7 years of experience? (Round your answer to the nearest dollar) O $52,900 O $53,340 O $53,914 O $55,573
By using the equation for the line of best fit, the salary for an employee who has seven (7) years of experience is: D. $55,573.
What is a line of best fit?A line of best fit is a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between a data.
In this scenario, the employee's salary would be plotted on the y-axis of the scatter plot while the years of experience would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the data in the given table, an equation for the line of best fit is given by:
y = 2233.3x + 39940
Next, we would use the above equation for the line of best fit to predict the salary for an employee with 7 years of experience:
y = 2233.3(7) + 39940
y = 15,633.1 + 39940
y = 55,573.1 ≈ $55,573.
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What are the domain and range of this relation? pt3 last one
The Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5}.
In the question
let us first write down the coordinates in the order from bottom to top .
The coordinates of the points are (4,-2) ,(2,1) ,(0,2) ,(0,5) ,(3,5) .
the x coordinates in the point (x,y) is called as Domain .
the y coordinates in the point (x,y) is called as Range .
Hence , the Domain of the given relation is {4,2,0,3}
writing in the order we get , Domain = {0,2,3,4}
and the range of the given relation is {-2,1,2,5}
writing in the order we get , Range = {-2,1,2,5}
Therefore , the Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5} .
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Find the coordinates of a point P that lies along the directed line segment from E (-5, 5) to F (-2,-2) and partitions the segment in the ratio of X2 12. 1 to 1.5.
the coordinates of a point P that lies along the directed line segment from E (-5, 5) to F (-2,-2) and partitions the segment in the ratio of 2 : 1.5 is (- 23 / 7 , 1).
We are given a line segment formed by joining the points:
E (- 5, 5)
F (- 2, - 2)
We need to find the coordinate of a point P which divides this line segment in the ratio 2 : 1.5
Now, we can also write this ratio as:
4 : 3
The formula for finding the coordinate of point P is:
x = (m x₂ + n x₁) / (m + n)
y = (m y₂ + n y₁) / (m + n)
Substituting the values in the formula, we get that:
x = 4(-2) + 3(-5) / 4 + 3
x = - 8 - 15 / 7
x = - 23 / 7
y = 4(- 2) + 3(5) / 4 + 3
y = - 8 + 15 / 7
y = 7 / 7 = 1
So, point P = (- 23 / 7 , 1)
Therefore, we get that, the coordinates of a point P that lies along the directed line segment from E (-5, 5) to F (-2,-2) and partitions the segment in the ratio of 2 : 1.5 is (- 23 / 7 , 1).
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