Answer:
Step-by-step explanation:
125 I think
Six is called a perfect number because its factors (not including 6) add up to itself, i.e. 1 + 2 + 3 = 6. find all the perfect numbers between 20 and 30
A taxi company charges a $2.00 base fare plus an additional fare based on a per-mile rate and a per-minute rate. Ryan's first taxi ride was 3.0 miles, took 7 minutes, and cost $8.50. His second taxi ride was 7.0 miles, took 14 minutes, and cost $16.00. If his third taxi ride took 10 minutes and cost $13.50, approximately how many miles was the third taxi ride
A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles
How can the length of the third ride be calculated?The base fare = $2.00
Let x represent the per-mile rate, and let y represent the per-minute rate, we have;
The cost of Ryan's first taxi ride = $8.50
Distance traveled in the first ride = 3.0 miles
Time taken during the first ride = 7 minutes
Therefore;
2 + 3•x + 7•y = 8.5
Which gives;
3•x + 7•y = 8.5 - 2 = 6.5
3•x + 7•y = 6.5...(1)Distance traveled in the second ride = 7.0 miles
Duration of the second ride = 14 minutes
The second ride cost = $16.00
Therefore;
2 + 7•x + 14•y = 16
Which gives;
7•x + 14•y = 16 - 2 = 14
7•x + 14•y = 14...(2)Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;
(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1
x = 1
The per-mile rate, x = $13•x + 7•y = 6.5
7•y = 6.5 - 3•x
7•y = 6.5 - 3×1 = 3.5
y = 3.5/7 = 1/2 = 0.5
The per-minute rate, y = $0.5Duration of the third taxi ride = 10 minutes
Cost of the third ride = $13.50
Therefore;
2 + 1×a + 10×y = $13.50
Where a is the distance traveled during the third ride, we have;
2 + 1×a + 10×0.5 = $13.50
2 + a + 5 = 13.5
a = 13.5 - 2 - 7 = 4.5
The third ride was, a = 4.5 milesLearn more about simultaneous linear equations here:
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Plot graph of
5x+7y= 50
7x + 5y = 46
Answer:
It's attached you may see it!!
Answer:
see attachments
Step-by-step explanation:
Given equations:
[tex]\begin{cases}5x + 7y = 50\\7x + 5y = 46\end{cases}[/tex]
To plot the graphs of the given equations:
Rearrange each equation to make y the subject.Input at least two values of x into the equations to find two points on each line.Plots the points.Draw a straight line through the points.Equation 1
[tex]\implies 5x + 7y = 50[/tex]
[tex]\implies 7y = -5x + 50[/tex]
[tex]\implies y = -\dfrac{5}{7}x+\dfrac{50}{7}[/tex]
[tex]x=-4 \implies y = -\dfrac{5}{7}(-4)+\dfrac{50}{7}=10 \implies (-4,10)[/tex]
[tex]x=3 \implies y = -\dfrac{5}{7}(3)+\dfrac{50}{7}=5 \implies (3,5)[/tex]
Plot the points (-4, 10) and (3, 5) then draw a straight line through them (see attachment 1).
Equation 2
[tex]\implies 7x+5y=46[/tex]
[tex]\implies 5y=-7x+46[/tex]
[tex]\implies y=-\dfrac{7}{5}x+\dfrac{46}{5}[/tex]
[tex]x=3 \implies y=-\dfrac{7}{5}(3)+\dfrac{46}{5}=5 \implies (3,5)[/tex]
[tex]x=8 \implies y=-\dfrac{7}{5}(8)+\dfrac{46}{5}=-2 \implies (8,-2)[/tex]
Plot the points (3, 5) and (8, -2) then draw a straight line through them (see attachment 2).
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Can someone help me with this pls
Answer:
x = 1/3 or x = -2/3
Step-by-step explanation:
Let's solve your equation step-by-step.
9x2+3x−2=0
For this equation: a=9, b=3, c=-2
9x2+3x+−2=0
Step 1: Use quadratic formula with a=9, b=3, c=-2.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(3)\pm\sqrt{(3)^2-4(9)(-2)} }{2(9)}[/tex]
[tex]x=\frac{-3\pm\sqrt{81} }{18}[/tex]
x = 1/3 or x = -2/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the quadratic formula?}[/tex]
[tex]\rm{x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
[tex]\textsf{Or even}[/tex]
[tex]\rm{ax^2 + bx + c = 0}[/tex]
[tex]\huge\textbf{What are we looking for?}[/tex]
[tex]\rm{9x^2 + 3x - 2 = 0}[/tex]
[tex]\huge\textbf{What are the labels in the equation?}[/tex]
[tex]\mathsf{a \rightarrow 9}\\\\\mathsf{b\rightarrow 3}\\\\\mathsf{c \rightarrow -2}[/tex]
[tex]\huge\textbf{Solving for your equation:}[/tex]
[tex]\rm{x = \dfrac{-(3)\pm \sqrt{3^2 - 4(9)(-2)}}{2a}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x = \dfrac{-3\pm \sqrt{81}}{18}}[/tex]
[tex]\rm{x = \dfrac{1}{3}\ or\ x = - \dfrac{2}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\mathsf{x} = \dfrac{1}{3}\ or\ \mathsf{x} = - \dfrac{2}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The area of the base of the cone is 8 pi mm^2. what is the volume of the cone in terms of pi?
The volume of cone whose area of base is 8π[tex]mm^{2}[/tex] is 32π/3 [tex]mm^{3}[/tex].
Given area of base of the cone 8π[tex]mm^{2}[/tex].
We are required to find the volume of the cone.
We know that base of a cone used to be in circle so the area of base of cone is equal to π[tex]r^{2}[/tex].
Area=8π (given)
π[tex]r^{2}[/tex]=8π
[tex]r^{2}[/tex]=8
r=[tex]\sqrt{8}[/tex]
r=2[tex]\sqrt{2}[/tex]
Volume of cone=1/3*π[tex]r^{2} h[/tex]
=1/3*π[tex](2\sqrt{2} )^{2}[/tex]*4
=1/3*8*4π
=32π/3
(We are not required to put value of π so our answer will be 32π/3.)
Hence the volume of cone whose area of base is 8π is 32π/3.
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Question is incomplete as it should also include height of cone be 4 mm.
The radius of circle A is 4.4 units.Which element of circle A has a measure of 27.65 units
Answer:
The circumference
Step-by-step explanation:
[tex]circumference \: = 2\pi \times radius \\ c = 2\pi(4.4) \\ c = 8.8\pi = 27.65[/tex]
Three more than twice a number is five less than the square of the number.What is the number?
A linear function contains the following points. x 0 2 4 6 y 3 -1 -5 -9
What are the slope and y-intercept of this function?
A. The slope is -2. The y-intercept is (3,0).
B. The slope is -1/2 The y-intercept is (0,3)
C. The slope is 2. The y-intercept is (0,3)
D. The slope is -2. The y-intercept is (0,3)
Answer:
D. The slope is -2. The y-intercept is (0,3)
Step-by-step explanation:
You can use any two points.
Let's use the first two points: (0, 3), (2, -1)
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-1 - 3)/(2 - 0)
slope = -4/2
slope = -2
The y-intercept occurs when x = 0. For x = 0, y = 3, so the y-intercept is 3 which means the point (0, 3).
Answer: D. The slope is -2. The y-intercept is (0,3)
pls help asap............
See below for the solution to each question
Is the graph a function?Yes, the graph is a function.
This is because all x values have different y values
The domainThis is the set of input values of the graph.
From the graph, we have
x = 0 to x = 17
Hence, the domain is [0, 17]
The rangeThis is the set of output values of the graph.
From the graph, we have
y = 0 to y = 10
Hence, the range is [0, 10]
The maximumThis is the maximum point on the graph.
From the graph, we have
Maximum = (12, 10)
The minimumThis is the minimum point on the graph.
From the graph, we have
Minimum = (0, 0)
The increasing intervalsThese are the intervals where the y values increase as x increase.
From the graph, we have
Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)
The decreasing intervalsThese are the intervals where the y values decrease as x increase.
From the graph, we have
Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)
The constant intervalsThese are the intervals where the y values remain unchanged as x changes.
From the graph, we have
Constant intervals = (5, 7)
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A circular table has a radius of 5cm. decorative trim is placed along the outside edge. how long is the trim?single line text.
If the radius of the circular table is 5 cm then the length of the trim required is 31.4 cm.
Given that the radius of the circular table is 5 cm.
What is the length of trim needed to decorate along the outside trim?
Circumference is the length of arc of the circle.It is also known as the perimeter of the circle.
Circumference of the circle=2πr in which r is the radius of the circle.
It is given that the trim is placed and decorated along the outside edge, so the perimeter of the circle must equal to the length of trim needed.
Length of trim needed to decorate the circular table=2πr
=2*π*5
=10π
=10*3.14
=31.4 cm.
Hence the length of the trim needed to decorate along the table is 31.4 cm.
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The denominator of a fraction exceeds numerator by 3. If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction.
Answer:
The original fraction is 4/7Step-by-step explanation:
Let the fraction be x/y.
According to question we have the following equations.
The denominator of a fraction exceeds numerator by 3:
y = x + 3If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:
2x/(y + 14) = (2/3)*(x/y)Change the fraction as below and solve for y:
2x /(y + 14) = 2x/(3y) Nominators are samey + 14 = 3y Compare denominators2y = 14y = 7Find the value of x using the first equation:
7 = x + 3x = 7 - 3x = 4The fraction is:
x/y = 4/7Answer:
Original fraction = ⁴/₇
Step-by-step explanation:
Numerator: top of the fraction
Denominator: bottom of a fraction
Let x be the original numerator.
If the denominator of a fraction exceeds the numerator by 3:
[tex]\implies \dfrac{x}{x+3}[/tex]
If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:
[tex]\implies \dfrac{2x}{x+3+14}=\dfrac{2}{3}\left(\dfrac{x}{x+3}\right)[/tex]
[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3(x+3)}[/tex]
[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3x+9}[/tex]
Cross multiply:
[tex]\implies 2x(3x+9)=2x(x+17)[/tex]
Divide both sides by 2x:
[tex]\implies 3x+9=x+17[/tex]
Subtract x from both sides:
[tex]\implies 2x+9=17[/tex]
Subtract 9 from both sides:
[tex]\implies 2x=8[/tex]
Divide both sides by 2:
[tex]\implies x=4[/tex]
Substitute the found value of x into the original fraction:
[tex]\implies \dfrac{4}{4+3}=\dfrac{4}{7}[/tex]
Therefore, the original fraction is ⁴/₇.
Solving inequalities( need help checking my answer)
Step 1. You need x isolated.
[tex]x < 13+7[/tex]
When you move a number from the left to right (and its addition or subtraction, the sign stays (< ≤ > and ≥ is signs).
x<20 or in words, x is less than 20, and cannot be 20.
Answer:
x < 20
Any number less than 20 is a solution
Step-by-step explanation:
x-7 < 13
The first step to solve this inequality is to add 7 to each side
x-7+7 < 13+7
x < 20
Any number less than 20 is a solution
A regular pair of gloves are $35. If its sale price is $24.50, what is the percent of disount?
Answer:
30% discount
Step-by-step explanation:
(35 - 24.50) / 35 * 100% = 30%
0.04 less than 1.38
First, you need to understand the vocabulary.
Saying x less than y means that you are subtracting from y. Your x here is 0.04, and your y is 1.38
y-x = 1.38-0.04 = 1.34
Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle of elevation of 61°. Dan is standing on the ground at a point directly west of the base of the tower and must look up at an angle of elevation of 72° in order to see the top. If the CN Tower is 553.3 m tall,how far apart are Vic and Dan to the nearest meter? Include a well-labeled diagram as part of your solution.
Vic and Dan are 2, 897m apart.
How to determine the distance
It is important to note that the distance between Vic and Dan is the base of CN
Let's say the distance to Dan is x
The distance to Vic is y
Using cosine ratio, we have
cos α = opposite / adjacent
α = 72°
opposite = 553. 3cm
Adjacent = x
cos 72° = [tex]\frac{553. 3}{x}[/tex]
Cross multiply
[tex]cos 72[/tex] × [tex]x[/tex] = [tex]553. 3[/tex]
[tex]0. 3090x= 553. 3[/tex]
[tex]x = \frac{553. 3}{0. 3090}[/tex]
[tex]x = 1, 790. 61[/tex] m
The distance to Vic is y
Using the cosine ratio, we have
[tex]cos 60 = \frac{553. 3}{y}[/tex]
Cross multiply
[tex]0. 5y = 553. 3[/tex]
[tex]y = \frac{553. 3}{0. 5}[/tex]
[tex]y = 1,106. 6[/tex]m
To determine how far apart Vic and Dan, we use = x + y
= 1790. 61 + 1106. 6
= 2, 897. 21m
= 2, 897m
Thus, Vic and Dan are 2, 897m apart.
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Please help! It is due right now!!!
The total bill for dinner was $33.03 (including tax and a tip). If they paid a 20.2% tip, what was their bill before adding the tip?
Using proportions, it is found that their bill before adding the tip was of $27.48.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
They paid a 20.2% tip, hence 120.2% = 1.202 of the price x is equals to $33.03, hence the bill before the tip is found as follows:
1.202x = 33.03
x = 33.03/1.202
x = $27.48.
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A student missed 45 problems on a mathematics test and received a grade of 39%. If all the problems were of equal value, how many problems were on the test
There were 74 problems in the test.
Rounding-off percentageLet the student got total number of problems in the test to be X.
Percentage of correct answer = 39 %
⇒ 61% of X were incorrect
⇒61/100 x X = 45
⇒61X = 45x100
⇒X = 4500/61
⇒X=73.77
After rounding off 73.77, we get 74.
Hence, we can say that there were total of 74 problems in the test.
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7.
Ja
In the diagram below, M is the midpoint of KL.
Solve for the value of x.
Skip step
Enter your
here
K
4x + 1
M
8x - 15
Answer:
x = 4
Step-by-step explanation:
Since M is the midpoint of segment KL, then segments KM and LM are congruent. They have the same length.
4x + 1 = 8x - 15
4x = -16
x = 4
HELP PLEASE ASAP:<
Consider the expressions given below.
A. 2x³ - x² - 6x
B. 2x³ + 8x + 4
C. 3x^4+ x² + x - 7
D. 3x^4 - 3x^2 + 5x - 7
For each expression below, select the letter that corresponds to the equivalent expression from the given list.
(4x³ 4 + 7x) - (2x³ 8)is equivalent to expression
(-3x² + x¹ + x) + (2x¹ - 7+ 4x)is equivalent to expression
(²2x) (2x + 3)is equivalent to expression
3x² + 5x - 7
For how many positive integers $n$ less than or equal to $24$ is $n!$ evenly divisible by $1 2 \dots n$
The value of positive integers in the set are 16.
According to the statement
we have given that the there is a set of numbers from 1 to n and we have to find that the how many integers in this set. and there is one condition that the numbers in the set are less than or equal to 24.
So, For this purpose,
Since [tex]$1 + 2 + \cdots + n = \frac{n(n+1)}{2}$[/tex]
the condition is equivalent to having an integer value for [tex]$\frac{n!} {\frac{n(n+1)}{2}}$.[/tex]
This reduces, when [tex]$n\ge 1$[/tex], to having an integer value for [tex]$\frac{2(n-1)!}{n+1}$[/tex]
This fraction is an integer unless n+1 is an odd prime. There are 8 odd primes less than or equal to 24,
so there are 24-8 = 16.
So, The value of positive integers in the set are 16.
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Two numbers are independently selected from the set of positive integers less than or equal to 5. What is the probability that the sum of the two numbers is greater than their product
There is a 9/25 chance that two numbers will be added together such that their total exceeds their product.
How to find out the probabilityThe set of positive numbers are:
{1,2,3,4,5}
We have to independently select two numbers from these sets.
We are trying to determine the likelihood that the sum is larger than the product of the integers.
When one of the chosen numbers is 1, the total will always be greater than the product because:
1*1=1 & 1+1=2
1*2=2 & 1+2=3
1*3=3 & 1+3=4
1*4=4 & 1+4=5
1*5=5 & 1+5=6
and so on.
If we select 2 as both numbers then,
2*2=4 & 2+2=4
Here sum and the product are equal.
If not, the product will be bigger than the sum.
Now, the first stage is to evaluate the total number of two combinations that are feasible:
We have 5 alternatives for the first number and 5 alternatives for the second number.
The product of the number of possibilities in each scenario yields the total number of combinations:
C= 5*5=25
The following combinations have a sum that is greater than the product :
1 and 1
1 and 2
1 and 3
1 and 4
1 and 5
2 and 1
3 and 1
4 and 1
5 and 1
So, we get 9 combinations.
So, Probability,p=9/25
Therefore it is concluded that the probability is 9/25.
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Answer 1/4 + 3/5-3/10 =
Answer:
11/20
Step-by-step explanation:
1/4= 10/40
3/5=24/40
3/10=12/40
10/40+24/40= 34/40
34/40 - 12/40= 22/40
simplifies to 11/20
The average height of students at UH from an SRS of 14 students gave a standard deviation of 2.5 feet. Construct a 95% confidence interval for the standard deviation of the height of students at UH. Assume normality for the data.
The 95% confidence interval for the standard deviation of the height of students at UH is given by; CI = (1.81, 4.03)
How to find the confidence interval for standard deviation?
The formula for the confidence interval for the standard deviation is given by the formula;
CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]
We are given;
Sample size; n = 14
D F = n - 1 = 14 - 1 = 13
Standard Deviation; s = 2.5
Confidence Level; CL = 95% = 0.95
Significance level; α = 1 - 0.95 = 0.05
Thus, using Chi-square distribution table online we have;
χ²₁₃, ₀.₀₂₅ = 24.736
(χ²₁₃, ₀.₉₇₅) = 5.01
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
CI = √[(13 * 2.5²/(24.736)], √[(13 * 2.5²/(5.01)]
CI = (1.81, 4.03)
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Jaun rides the bus to school each day he always arrives at his bus stop on time but his bus is late 80% of the time
The correct probability that Juan's bus is going to be late every week next week is 20 percent.
How to solve for the probabilityWe have the total number in the stimulation on to be from 0 to 9
On the fact that it would be late, the number ranges from 2 to 9
Hence the fact that it would be late would be
2/10
= 0.2
0.2 is also the same as 20 percent.
Complete questionJuan rides the bus to school each day. He always arrives at his bus stop on time, but his bus is late 80% of the time. Juan runs a simulation to model this using a random number generator. He assigns these digits to the possible outcomes for each day of the week:
• Let 0 and 1 = bus is on time
• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is late
The table shows the results of the simulation.
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During a snowstorm, Madeline tracked the amount of snow on the ground. When the storm began, there were 3 inches of snow on the ground. Snow fell at a constant rate of 1 inch per hour until another 2 inches had fallen. The storm then stopped for 3 hours and then started again at a constant rate of 2 inches every 3 hours for the next 9 hours. When the storm stopped again, the sun came out and melted the snow for the next 2 hours at a constant rate of 3 inches per hour. Make a graph showing the inches of snow on the ground over time using the data that Madeline collected.
The graph depicts that at the end of the snowstorm, there was 5 inches of snow left. See the attached graph.
How many hours did the snow fall?It is not be noted that the total amount of hours which the snow fell is:
2 + 9 = 11 hours.
Although the graph depicts a peak of 14 hours, recall that there were three hours when the snow didn't fall.
While the maximum depth of the snow was 11 inches.
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PLEASE HELP IM STUCK
Answer:
#3
Step-by-step explanation:
To create a number line to represent x<= 0, draw a solid circle at 0 (because 0 is included), then draw an arrow extending to the left (because it's less than or equal to).
PLEASE HELPPPoirnginrigniniervifire
Answer:
555 m
Step-by-step explanation:
Because the model should have identical proportions to the real-life tower, the ratio between the height and shadow length of both diagrams should be the same.
Height (model) Height (real)
------------------------- = ------------------------
Shadow (model) Shadow (real)
Math:
0.9 meters x
-------------------- = ---------------------- <----- Ratio
0.2 meters 123.3 meters
4.5 = x / 123.3 meters <----- Divide 0.2 from 0.9
555 meters = x <----- Multiply both sides by 123.3
Suppose in a class of 60 students 5 have no siblings, 26 have one sibling, 14 have two siblings, and 15 have three siblings. Calculate the relative frequency of students who have three siblings. (please express as a percentage)
The relative frequency of students who have three siblings is 25% given that there are 60 students in a class in which 5 have no siblings, 26 have one sibling, 14 have two siblings and 15 have three siblings. This can be obtained by using the formula for relative frequency.
What is the relative frequency of students who have three siblings?Given that,
total number of students in the class = 60
number of students who have no sibling = 5
number of students who have 1 sibling = 26
number of students who have 2 sibling = 14
number of students who have 3 sibling = 15
Formula for relative frequency = f/n, where f is the number of times the data occurred, n is the total number of frequencies.
Therefore,
relative frequency of students who have three siblings = 15/60 = 0.25
In percentage ⇒ 0.25 × 100 = 25%
Hence the relative frequency of students who have three siblings is 25% given that there are 60 students in a class in which 5 have no siblings, 26 have one sibling, 14 have two siblings and 15 have three siblings.
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Use facts about tangents and sextants to find new angles and arcs. PLS HELP!! GEOMETRY!! WILL MATK BRAINLIST!!
Applying the angle of intersecting secants theorem, the measure of angle B is: 35°.
What is the Angle of Intersecting Secants Theorem?The measure of the angle formed outside a circle by two intersecting secants is equal to half the positive difference of the measures of the arcs they intercept based on the angle of intersecting secants theorem.
Applying the angle of intersecting secants theorem, we have the following:
Let the missing measure of the arc for angle A be x. Therefore:
6 = 1/2(x - 17)
2(6) = x - 17
12 = x - 17
12 + 17 = x
x = 29°
m∠B = 1/2(99 - x)
Plug in the value of x
m∠B = 1/2(99 - 29)
m∠B = 35°
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A model pirate ship uses the scale
5 inch: 20 meters. If the model is
50 inches long, how long is the
pirate ship?
Answer:
200 meters
Step-by-step explanation:
If the ratio is 5 inches to 20 meters that means for every 5 inches in the model there will be 20 meters on the real ship.
If the model is 50 inches long that means that there are 10 5 inch segments, multiply this 10 by the 20 meters in the ratio and you will get 200 meters as the final length for the ship.