[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(6,5)\qquad B(6,15)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(6,5)=3(6,15)[/tex]
[tex](\stackrel{x}{12}~~,~~ \stackrel{y}{10})=(\stackrel{x}{18}~~,~~ \stackrel{y}{45})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{12 +18}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{10 +45}}{3+2} \right)} \\\\\\ P=\left( \cfrac{30}{5}~~,~~\cfrac{55}{5} \right)\implies P=(6~~,~~11)[/tex]
Which one is the right conversion?
Answer:
1, 4, 5, 6
Step-by-step explanation:
to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).
you can also double check by plugging both into a calculator and see if they equal the same number.
Can someone pls help quickly?
From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.
What is a ratio?A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.
What is the explanation for the solution above?Step 1 - Indicate your assumptionsLet X be the width of one of the rectangles and let its height be Y.
It is clear from the image that:
4X = 3Y
Hence
(4/3)X = Y
Therefore,
Lenght (L) = 3Y
= 3 (4/3)X
= 4X
Width (W) = Y + 2X
= (4/3)X + 2X
= (10/3)X
Therefore,
L : W = 4X: 10/3X
= 4:10/3
To remove the fraction, multiply both sides of the ratio by 3
= 12 : 10, furhter simplify by halving each value, and we have
= 6:5
Hence, the ratio L: W in simplified form is 6 : 5.
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9x10^2 which sentence matches the question assigned
The computation of the index shows that the value of 9 × 10² will be 900.
How to calculate the indices?From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:
= 9 × 10²
Note that 10² simply means that you've to multiply 10 twice. This will be:
= 10 × 10 = 100
Therefore, 9 × 10² will be:
= 9 × 100
= 900
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Mike leaves the house traveling 2 miles per hour. Kim leaves 6 hours later to catch up traveling 8 miles per hour. It will take Kim Blank 1 hours to catch Mike.
any answers ?
Answer:
2 hours
Step-by-step explanation:
Mike has a six hour head start so he is 6 x 2 = 12 miles ahead
their 'closing speed' is 8-2 = 6 m/hr
it will take Kim 12 / 6 = two hours to catch Mike
Help me please I been trying to figure out how to do this problem
sin 30 = x/4
sin 30 = 0.5
0.5 = x/4
x = 2
a camp charges $40 per student for a full-day camp and the camp only runs if 5 students enroll but the enrollment limit is 16 students. the amount of revenue that the camp collects is a function of the number of students that enrolled defined by this equation: [tex]R(n)=40n[/tex]
please describe the set of all possible outputs of this function
please describe the set of all possible inputs of this function
The set of input of the function are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }
The set of output of the function is a multiple of 40 from 200 to 640
How to find the output and input of a function?The input of the function can be found as follows:
The camp can only run if we have at least 5 students.
The limits of student is 16.
Therefore, the input are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }
The output are the dependent variables or the range. They are gotten when we input the values of the input in the function.
Therefore,
R(n) = 40n
R(5) = 40(5) = 200
R(16) = 40(16) = 640
The output are multiple of 40 from 200 to 640
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If the probability that a person over 40-year-old is diabetic, is 0.55
and the probability that a person has hypertension is 0.62. If a person
is selected randomly, find the probability that he is diabetic and and has hypertension
Answer:
0.341
Step-by-step explanation:
Multiply the probabilities: 0.55 * 0.62 = 0.341
8 3/8 + 3 3/8 + 2 3/8 + 3/8
what is the answer of this ?
The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have an expression:
[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]
After simplification:
[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]
[tex]= \dfrac{67+27+19+3}{8}[/tex]
= 116/8
= 29/2
[tex]= 14\dfrac{1}{2}[/tex]
Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
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Answer:
i dont understand your question
Step-by-step explanation:
!!
Mum spent 3/5 of her money and put 1/8 of the remainder in the bank. If she had $750 left, how much did she start with?
Answer:
$2142.86
Step-by-step explanation:
The remaining part of her money, after spending 3/5 of it and depositing 1/8 of it is equal to $750.
===============================================================
Retracing the steps :
⇒ She put 1/8 of the remainder in the bank, which gives $750
⇒ R - R/8 = 750
⇒ 7R/8 = 750
⇒ R = 750/7 × 8
⇒ R = 107.142857 × 8
⇒ R = 857.142856
* Don't worry, we'll simplify at the end of the answer *
=============================================================
Now, this remainder is what was left after spending 3/5 of it.
⇒ T - 3/5T = 857.142856
⇒ 2/5T = 857.142856
⇒ T = 857.142856/2 × 5
⇒ T = 428.571428 × 5
⇒ T = $2142.86 (nearest cent)
Solve for x
x/8 = 3/5 give your answer as an improper fraction in its simplest form
Answer:
24/5
Step-by-step explanation:
x is 4.8, improper simplified is 24/5
Points ABC forms a right triangle.
A: (-2,4) B: (5,0) C: (2,6)
The sum of the squares of the lengths of the legs of the triangle is?
The square of the length of the hypotenuse of the triangle is?
The sum of squares of the lengths of the triangle is 130 and the square of the length of the hypotenuse is 65
What is a right-angled triangle?This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°
Analysis:
distance between two points = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
distance AB with coordinates A(-2,4) B(5,0) = [tex]\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }[/tex] = [tex]\sqrt{65}[/tex]
distance AC with coordinates A ( -2,4) C(2,6) = [tex]\sqrt{(2--2)^{2} + (6-4)^{2} }[/tex] = [tex]\sqrt{20}[/tex]
distance BC with coordinates B(5,0) C(2,6) = [tex]\sqrt{(2-5)^{2} + (6-0)^{2} }[/tex] = [tex]\sqrt{45}[/tex]
sum of squares of the lengths = [tex](\sqrt{45} )^{2}[/tex] + [tex](\sqrt{65}) ^{2}[/tex] + [tex](\sqrt{20}) ^{2}[/tex] = 65 + 45 + 20 = 130
the square of the length of the hypotenuse = 65
In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65
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Question 6(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = -5x² + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values.
O The value of f(1) cannot be compared to the value of f(2).
O The value of f(2) is larger than the value of f(1).
O The value of f(2) is smaller than the value of f(1).
O The value of f(1) is the same as the value of f(2). help
Answer:
O The value of f(2) is smaller than the value of f(1).
Step-by-step explanation:
First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)
What is the median of 3,4,5,5,7,8
Simplify the quotient 3-¹ ÷34
Answer:
[tex]\frac{1}{102}[/tex]
Step-by-step explanation:
1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].
[tex]\frac{1}{3}\div 34[/tex]
2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].
[tex]\frac{1}{3}\times \frac{1}{34}[/tex]
3) Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].
[tex]\frac{1\times 1}{3\times 34}[/tex]
4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].
[tex]\frac{1}{3\times 34}[/tex]
5) Simplify [tex]3\times 34[/tex] to [tex]102[/tex] .
[tex]\frac{1}{102}[/tex]
Solve for x to the nearest tenth of centimetre
Answer:
Step-by-step explanation:
Select the correct answer.
Over which interval of the domain is function h decreasing?
25?
Answer:
the function is only increasing.
Step-by-step explanation:
Identify the remainder when -2x2 + 15x is divided by x - 7.
Answer:
The remainder is 9
Step-by-step explanation:
x-7=0
x=7
Plug x=7 into the given fxn
-2(7)²+15(7)
-2(49)+105
-96+105
9
Convert the degree measure to radian measure. Round to three decimal places.
75°
radians
The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.
What is conversion?Conversion means to convert the same thing into different units.
Convert the degree measure to the radian measure.
⇒ 75°
We know the conversion is given as
180° = π radian
1° = π/180°
Then we have
75° = 75° x π/180° radian
75° = 1.30899 radian
75° ≅ 1.31 radian
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2x + 4y = 15
6x +12y = 45
What would the solution to the system of equations be?
Answer:
They both have an infinite number of solutions.
Step-by-step explanation:
Given system of equations:
a) 2x + 4y = 15
b) 6x + 12y = 45
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Rewrite both equations into slope-intercept form:
a) 2x + 4y = 15
⇒ 2x + 4y = 15 [subtract 2x from both sides]
⇒ 2x - 2x + 4y = 15 - 2x
⇒ 4y = - 2x + 15 [divide both sides by 4]
⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
b) 6x + 12y = 45
⇒ 6x + 12y = 45 [subtract 6x from both sides]
⇒ 6x - 6x + 12y = 45 - 6x
⇒ 12y = - 6x + 45 [divide both sides by 12]
⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
New equations:
[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.
System of equations can have the following:
No Solution: the same slope (both lines will be parallel)
One Solution: different slopes and different y-intercepts
Infinitely Many Solutions: the same slope and y-intercept
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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.
Slope-Intercept Form ⇒ [tex]y = mx + b[/tex]m = slopeb = y-interceptEquation #1
Subtract 2x from both sides
[tex]2x + 4y = 15[/tex][tex]2x - 2x + 4y = 15 - 2x[/tex][tex]4y = -2x + 15[/tex]Divide both sides by 4
[tex]\frac{4y}{4} = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = -0.5x + 3.75[/tex]Equation #2
Subtract 6x from both sides
[tex]6x + 12y = 45[/tex][tex]6x - 6x + 12y = 45 - 6x[/tex][tex]12y = -6x + 45[/tex]Divide both sides by 12
[tex]\frac{12y}{12} = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = -0.5x + 3.75[/tex]Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other. Therefore, there are infinite solutions as they will always continue on top of each other.
Find the area of a circle with radius, r = 60cm. Give your answer rounded to 3 SF.
The area of the circle will be equal to 11309.733 square centimetres.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The area of the circle will be calculated by the following formula:-
Area = πr²
Area = π x ( 60 x 60 )
Area = 3.14 x 60 x 60
Area = 11309.733 square centimeters.
Therefore the area of the circle will be equal to 11309.733 square centimetres.
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The methods of solving quadratic equations
There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.
[1] using the quadratic formula
When the equation is in the form of ax² + bx + c = 0.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
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[2] factoring
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[3] completing the square
To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c
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Solve for (x): (14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
Answer:x ≤ 3
Step-by-step explanation:
(14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
14.5x - 5x-10 ≤ 4 + 16 - 1/2x Get rid of the parenthesis
9.5x-10 ≤ 20-1/2x Combine like terms
10x - 10 ≤ 20
10x/10 ≤ 30/10
x ≤ 3
Please help I am so confused
The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 480 minutes, the monthly cost will be $277. If the customer uses 990 minutes, the monthly cost will be $532.
A) Find an equation in the form
y=mx+b, where x is the number of monthly minutes used and
y is the total monthly cost of the Ringular plan.
Answer:
y=
B) Use your equation to find the total monthly cost if 881 minutes are used.
Answer: If 881 minutes are used, the total cost will be
The total cost when 881 minutes is used is $477.50.
What are the equation that model the question?a + 480b = 277 equation 1
a + 990b = 532 equation 2
Where:
a = flat fee b = variable fee What is the flat fee and the variable fee?Subtract equation 1 from equation 2
510b = 255
b = 255 / 510
b = $0.50
In order to determine the flat fee, substitute for b in equation 1
a + 480(0.5) = 277
a + 240 = 277
a = 277 - 240
a = $37
What is the total cost when 881 minutes is used?
Total cost = flat fee + (variable cost x number of minutes spoken)
$37 + (881 x 0.5) = $477.50
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The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. 6, 4, 6, 8, 7, 7, 6, 3, 3, 8, 10, 4, 8 7, 8, 7, 5, 9, 5, 8, 4, 3, 8, 5, 5, 4 4, 4, 8, 4, 5, 6, 2, 5, 9, 9, 8, 4, 8 9, 9, 5, 9, 7, 8, 3, 10, 8, 9, 6 Develop, a, 95%, confidence, interval, estimate, of, the, population, mean, rating, for, Miami.
Using the t-distribution, it is found that the 95% confidence interval for the population mean rating for Miami is (5.73, 6.95).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.
Considering the given sample, the other parameters are given as follows:
[tex]\overline{x} = 6.34, s = 2.16, n = 50[/tex]
Hence, the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6.34 - 2.0096\frac{2.16}{\sqrt{50}} = 5.73[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6.34 + 2.0096\frac{2.16}{\sqrt{50}} = 6.95[/tex]
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What is the volume, in cubic meters, if the prism below?
=================================================================
Explanation:
Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.
The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.
Multiply this floor area with the height of the room (22 m) to get the volume of the room.
volume = (floor area)*(height) = 84*22 = 1848 cubic meters
41 is a prime number found in the middle of a list of 7 consecutive numbers. find the 7 consecutive numbers
Answer: 29, 31, 37, 41, 43, 47, 53.
Step-by-step explanation:
Match each graph with the function it represents.
A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function f(x) and g(x) can be plotted as shown in the below image.
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Chandler wants to buy a bike
that costs $345. He has a job that
pays an hourly wage of $6. He
needs to pay back $35 that he
borrowed from his mom. How
many hours does Chandler need to
work to have enough money to
purchase the bike?
HELP!!! PLEASE HURRY!!!!
Answer:
B, I solved then used interval notion to convert it.
Answer:
the answer is b
Answer:
the answer is b
Write the converse of the statement
below.
If it is 9 a.m., then I am awake.
Answer:
if I am awake then it is 9 am.
Step-by-step explanation:
if p then q the converse is if q then p.