By assuming that both DVD's cost $25 or less, we will reach an absurd. In that way we conclude that at least one of the two DVD's costs over $25.
How to use the indirect reasoning?
We know that Isaac bought two DVD's and spent over $50.
Let's define the variables:
x = cost of the DVD 1y = cost of the DVD 2Because the cost is over $50 we can write the inequality:
x + y > $50
Here we want to prove that at least one of the two DVD's costed over $25, now let's find an absurd here, let's assume that neither of the DVD's costed over $25, then we can write:
x ≤ $25
y ≤ $25
So we have a set of 3 inequalities:
x + y > $50
x ≤ $25
y ≤ $25
Now, the maximum values that x and y can take are $25, if we use these values in the first inequality we will get:
$25 + $25 > $50
$50 > $50
So this is an absurd, this means that we can't assume that neither of the DVD's costs over $25, then we conclude that at least one of the DVD's costs over $25, which is what we wanted to prove.
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Find the Scale Factor Sep 08, 5:47:30 PM The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answer:
1.5 or 3/2
Step-by-step explanation:
The scale factor is the factor by which the side lengths of the original shape are multiplied by. In this case, the original shape had side lengths 17 and was multiplied by [tex]x[/tex] to get the scaled shape.
Now we get the equation [tex]17\cdot x=51/2[/tex]. Solving, we get x=1.5
I dont understand what i am supposed to do
Applying the alternate exterior angles theorem, the value of x = 10.
How to Apply the Alternate Exterior Angles Theorem?According to the alternate exterior angles theorem, the following alternate interior angles are congruent to each other:
m<JPM = m<NQK
Given the following:
m<JPM = 125°
m<NQK = (13x - 5)°
Substitute
125 = 13x - 5
125 + 5 = 13x
130 = 13x
Divide both sides by 13
130/13 = 13x/13
10 = x
x = 10
Therefore, applying the alternate exterior angles theorem, the value of x = 10.
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Mrs. Schott gets a biweekly paycheck of $1,230.90.
What is her annual salary?
Answer:
Step-by-step explanation:
Answer:
biweekly salary =
365/14=
23
then total salary
of her is =$1230.90
*23
=
Step-by-step explanation:
3 for a decimal expansion k.d1d2d3d4 ···, let (sn) be defined as in discussion 10.3. prove sn < k 1 for all n ∈ n. hint: 9 10 9 102 ··· 9 10n
The proof for the decimal expansion d₁d₂d₃d₄.... is evaluated.
What is decimal expansion?A number's decimal expansion is its base-10 representation (i.e., in the decimal system).
Now, as per the given question;
We focus on non negative decimal expansions as well as nonnegative real numbers. Every nonnegative decimal expansion, in our opinion, is short form for the limit of a constrained increasing sequential manner of real numbers.
Assume we're given a decimal expansion K. d₁d₂d₃d₄.... where K is a non-negative integer and each value of dj belongs to {0,1,2,3,4,5,6,7,8,9}.
Then Sn is defined as the increasing sequential of real numbers and Sn is also restrained by (sn < k + 1) .
Using Theorem; converges to a real number, which we usually write as K. d₁d₂d₃d₄....
Like. 3.33333 can be written as;
[tex]\lim _{n \rightarrow \infty}\left(3+\frac{3}{10}+\frac{3}{10^2}+\cdots+\frac{3}{10^n}\right)[/tex]
We use the following geometric series fact to calculate this limit:
[tex]\lim _{n \rightarrow \infty} a\left(1+r+r^2+\cdots+r^n\right)=\frac{a}{1-r} \quad \text { for } \quad|r| < 1 .[/tex]
Where a =3 and r = 1/10.
Similarly, for 0.9999.....it can also be written as
[tex]\lim _{n \rightarrow \infty}\left(\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}\right)=\frac{\frac{9}{10}}{1-\frac{1}{10}}=1 .[/tex]
Therefore, 0.9999... and 1.0000... are different decimal expansions for the same number.
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The correct question is-
For a decimal expansion K. d₁d₂d₃d₄....let (sn) be defined. Prove (sn < k + 1) for all n ∈ N. Hint:' [tex]\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}=1-\frac{1}{10^n}[/tex]
i need help with this problem it says
one less than triple a number is the same as six times a number reduced by 7
15 points
Answer:
3x - 1 = 6x - 7
x = 2
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1. To solve it, first get the variable on same side.
3x - 1 = 6x - 7
- 3x - 3x
- 1 = 3x - 7
2. Isolate the variable by doing the inverse operation which is in this case addition (adding 7).
- 1 = 3x - 7
+ 7 + 7
6 = 3x
3. Isolate variable by doing the inverse operation which is in this case division (dividing by 3).
6 = 3x
3 3
2 = x
OR
x = 2
Check:
1. Substitute x with 2 and solve.
3(2) - 1 = 6(2) - 7
6 - 1 = 12 - 7
5 = 5
True statement.
Which is more affected by extreme observations, the mean or median? and how about the standard deviation or iqr?.
Extreme values have little impact on the median and quantiles because they all come inside the middle half of the data.
Calculation:
Let’s assume the 24 students in the room range in age from 185, 185, 186, 186,.... 195, 195, 196, 196 months.
The total of x2 is 871252.
The sum of x is 4572.
The mean is 190.5 (4572/24).
The median, which lies between positions 12 and 13, is 190.5.
Standard deviation is (871252/24 -190.52)^0.5 = 3.45
Halfway between the( 18th and 19th)- (6th and 7th)interquartile range
= 6 (193.5 - 187.5).
Include his age of 716 months in the calculations as the teacher now.
Total x2 = 1383908
Total x = 5288
Mean (5288/25) = 211.52
Median (13th) = 191
Standard Deviation is (1383908/25 - 211.522)^0.5 = 103.03
Interquartile range (7th minus 19th) is 194 - 188 = 6
Therefore the mean has changed by 21.02 after the addition of a piece of data that is vastly different from the rest, yet the median has changed by only 0.5.
The interquartile range has remained constant, whereas the standard deviation has increased by over 100 and by a factor of approximately 30.
Define arithmetic mean?The result of adding together and dividing the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.
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can someone help me with the problem?
where is the problem, how can I help you?
Point P is located 2/5 of the distance from W to Z. Point W is located at (-5, -2) and point P is located at (1, 4). What are the coordinates of point Z?
The coordinates of point Z is (-5/7, 16/7)
Calculating the midpoint of a line using a ratioThe formula for calculating a coordinate points using the points (-5, -2) and point P is located at (1, 4) in the ratio 2:5 is expressed as:
Z (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}
Substitute the coordinates and ratios to have;
Z (x, y) = {(2(-5)+5(1))/2+5, (2(-2)+5(4))/2+5}
Z(x, y) = {-10+5/7, -4+20/7}
Z(x, y) = (-5/7, 16/7)
Hence the coordinates of point Z is (-5/7, 16/7)
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When finding multiples of a number, you _________ the original number by 1, then 2, then 3 and so on.
Answer:
Step-by-step explanation:
jlfhwfhwfh
The length of the rectangular shed is 2x^2 + 3x - 1 feet, and the width is x + 4 feet. Write polynomials that represent the perimeter and area. Calculate the perimeter and area if x = 10 feet. Include correct units of measure
Answer:
Step-by-step explanation:
gnhbn
1/1+p+q^-1+1/1+q+r^-1+1/1+r+p^-1
The proof of the expression 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated for pqr = 1.
What is defined as the indices?The small floating number which shows up after a number or letter is known as an index or power. Indices represent the number of times a number or word has indeed been multiplied by itself.For the given expression;
pqr = 1. Then pq = 1/r; qr = 1/p; pr = 1/q.
OR, pq = r⁻¹ ; qr = p⁻¹ ; pr = q⁻¹ .
The given expression is;
1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1
Consider LHS part;
= 1/(1+p+pr) + 1/(1+q+pq) + 1/(1+r+qr)
Multiply and divide q in the first part;
= q/(q+qp+qpr) + 1/(1+q+pq) + 1/(1+r+qr)
Put prq = 1 (given)
= q/(q+qp+1) + 1/(1+q+pq) + 1/(1+r+qr)
Add 1st and 2nd part;
= (q+1)/(q+qp+1) + 1/(1+r+qr)
Multiply and divide r in the first part;
= (q+1)r/(rq+rqp+r) + 1/(1+r+qr)
Put prq = 1 (given)
= (qr+r)/(rq+1+r) + 1/(1+r+qr)
Add both
= (qr+r+1)/(rq+1+r)
Both will be cancelled;
= 1 = RHS
Therefore, proof for 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated.
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The complete question is-
If pqr = 1, then prove that 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1
Answer:
pqr = 1
Step-by-step explanation:
Please help for my homework
Answer:
260 m2
Step-by-step explanation:
Simplify the expression 11c+3(−5c+4d)
step by step explanation:
-4c+12d
1. Distribute:
11c+3(-5c+4d)
11c-15c+12d
2. Combine like terms:
11c-15c+12d
-4c+12d
(-3x^3+5x^2-6x-7) / (x+4)
The solution to the division of the polynomial equation is [tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]
The division of the polynomial equation:Polynomial long division is an extended form of the well-known arithmetic method of long division used in algebra to divide one polynomial with another polynomial of the same or lower degree. Addressing a difficult division issue and breaking it into manageable pieces makes it feasible to solve by using this method.
From the given information, we Divide:
[tex]=\dfrac{(-3x^3+5x^2-6x-7)}{(x+4)}[/tex]
[tex]=-3x^2+\dfrac{17x^2-6x-7}{x+4}[/tex]
Divide: [tex]\dfrac{17x^2-6x-7}{x+4}[/tex]
[tex]=-3x^2+17x + \dfrac{-74x-7}{x+4}[/tex]
Divide: [tex]=\dfrac{-74x-7}{x+4}[/tex]
[tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]
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in a large population, 63 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated? give your answer as a decimal (to at least 3 places) or fraction.
The probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical summaries of how likely an event is to occur or how likely a proposition is to be true. The likelihood of an event occurring is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.To find the probability that at least one of them has been vaccinated:
In a huge number, 63% of people are vaccinated, leaving 37% unvaccinated. The point of concern for the probability that at least one of the four randomly selected people has been vaccinated. As a result, we must account for the possibility that one, two, three, or four randomly selected people were vaccinated.We use P(1) for only one person; the same reasoning should apply to other subscripts.
P(1) = (63/100)(37/100)(37/100)(37/100) = 0.03089833P(2) = (63/100)(63/100)(37/100)(37/100) = 0.05094049P(3) = (63/100)(63/100)(63/100)(37/100) = 0.08398297P(4) = (63/100)(63/100)(63/100)(63/100) = 0.13845841Adding all these probabilities given 0.3042802.
As a result, the probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.
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A survey showed that 8 out of 20 homeowners in a neighborhood had cable television. if there were 320 homeowners in the neighborhood, how many could be expected to have cable television?
The number of homeowners in the neighborhood could be expected to have cable television is 128.
Given that, a survey showed that 8 out of 20 homeowners in a neighborhood had cable television.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Now, 8/20 × 320
= 8 × 16
= 128
Hence, the number of homeowners in the neighborhood could be expected to have cable television is 128.
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What does x equals to
The value of x is 20°
According to the question we have been given two parallel lines which is cut by a transversal line. There are total 8 angles and given is the measure of
∠4 = 5x + 35° and ∠7 = 45°.
We need to find the value of x.
Note that when two parallel lines are cut by a transversal then
i) corresponding angles are equal that is
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8
ii) alternate interior angles are equal that is
∠3 = ∠6, and ∠4 = ∠5
iii) alternate exterior angles are equal that is
∠1 = ∠8, and ∠2 = ∠7
iv) Consecutive interior angle sum is 180°
∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.
Now using these rules we will solve this problem
Because of corresponding angles , ∠3 = ∠7 = 45°
Also ∠3 and ∠8 make a linear pair and sum of linear pair is 180°.
Therefore , ∠3 + ∠8 = 180°
45° + 5x + 35° = 180°
5x = 180° - 80°
x = 20°
Hence the value of x is 20°
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find the lines slope and point on the line
picture below
The slope is 4 and point on the line is origin (0,0).
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The equation of the line is
y+4=4(x-2)
We have to find the slope and point on the line.
y+4=4(x-2)
y+4=4x-8
Substract 4 from both sides we get,
y=4x-12
Since the equation now is in y = mx + b form, we can identify the slope m=4 and the y-intercept b=-12 and point on the line origin (0,0).
Therefore, the slope is 4 and point on the line is origin (0,0).
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Thomas bought 12 glass and plastic cups from the store glass cups cost $3.25 and plastic cups cost $2.75 thomas spent a total of $36 how many cups and how many plastic cups did you buy
Thomas bought 6 plastic cups and 6 glass cups.
For given question,
Let a be the number of glass cups and b be the number of plastic cups.
Thomas bought 12 glass cups and plastic cups.
So, we get an equation
a + b = 12 .................(1)
The glass cups cost $3.25 and plastic cups cost $2.75
Thomas spent a total of $36
From this information we get equation,
3.25 a + 2.75 b = 36 ............(2)
We have a system of equations.
From equation (1),
a = 12 - b .............(3)
Substitute above value of a in equation (2)
3.25 (12 - b) + 2.75 b = 36
39 - 3.25 b + 2.75 b = 36
39 - 0.5 b = 36
-0.5 b = -3
b = 6
This means, Thomas bought 6 plastic cups.
Substitute above value of b in equation (3)
So, a = 12 - 6
a = 6
Thomas bought 6 glass cups.
Therefore, Thomas bought 6 plastic cups and 6 glass cups.
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6,3.1,9 can it make a triangle
Yes
Step-by-step explanation:We can tell if a triangle can exist based on the relationship between the side lengths.
Side Length Relationships
For a triangle to really exist, the sum of the smaller legs must be greater than the length of the longest leg. This can be expressed with the inequality a + b > c, where a and b are the shorter legs.
Now, we can plug the values we are given into this inequality.
6 + 3.1 > 99.1 > 9Since the inequality is true, this triangle does exist.
Other Examples
One of the most important things to remember is that the sum of the shorter legs must be greater than, not equal to, the longest leg. So take the sides 4, 6, and 10.
4 + 6 > 1010 > 10This statement is not true. 10 is not greater than 10; they are equal. Thus, these sides cannot make a triangle.
Additionally, if the 3 numbers are Pythagorean triples, then it will be a right triangle. For example, the sides 5, 12, and 13 will create a right triangle.
r=14m Use \mathrm{\pi } = 3 . 14π=3.14 and round your answer to the nearest hundredth.
We get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².
We are given the radius of the circle as:
Radius = r = 14 m
We are also given the value of π as:
π = 3.14
We need to find the perimeter and area of the circle.
Perimeter of the circle is given by:
Perimeter = 2 π r
Substituting the values in the formula, we get that:
P = 2 × (3.14) × (14) m
P = 87.92 m.
Area of the circle is given by:
Area = π r²
Substituting the values in the formula, we get that:
Area = (3.14) × (14)²
A = 615.44 m²
Therefore, we get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².
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BRAINLIES AND 30 POINTS PLS HELP
. Why is using iodine helpful when looking at cells?
Answer:
As a biological stain, iodine is useful for studying plant cells because it stains starch blue-black and in animal tissue, it can help in the demonstration of nuclei and cell membranes
Answer: Iodine is also a useful stain. When studying plant cells, iodine is used. Because it is a starch indicator, it reacts with starch and turns blue-black. Iodine can also be used as a stain on animal cells, making the cell membrane and nucleus appear more visible
Step-by-step explanation:
How are one variable absolute equations created ?
Answer: Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. The challenge is that the absolute value of a number depends on the number's sign: if it's positive, it's equal to the number: |9|=9. If the number is negative, then the absolute value is its opposite: |-9|=9.
Step-by-step explanation:
Please awnser this problem and please show work!!
Answer:
111/22 or 5 and 1/22
Step-by-step explanation:
9 and 7/22 equals 205/22
4 and 3/11 equals 47/11
multiply 47/11 times 2/2 to get common denominator
47/11 times 2/2 is 94/22
205/22 minus 94/22 is 111/22 which is also 5 and 1/22
Brooke is buying a tent that is in the shape of a rectangular pyramid. The base is 6 feet by 8 feet. If the tent holds 88 cubic feet of air, how tall is the tent's center pole?
The height of the rectangular pyramid tent's center pole = 5.5 feet.
What is the Volume of a Rectangular Pyramid?Volume of rectangular pyramid = 1/3(length)(width)(height).
Given the following:
Volume of the rectangular pyramid tent = 88 cubic feetLength = 8 feetWidth = 6 feetHeight = ?Substitute
88 = 1/3(8)(6)(height)
88 = 16(height)
88/16 = height
5.5 = height
Therefore, the height of the rectangular pyramid tent's center pole = 5.5 feet.
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Can someone help me with this question?
Answer:
Step-by-step explanation:
Compare both shapes
Find out the length of the red line through Pythagoras theorem
a² + b² = c²
9² + b² = 15²
15²- 9² = b²
144 = b²
√144 = b
b = 12
Red line is 12 and the other length of one side of the triangle is x - 9
The hypotenuse of the other triangle will be equal to:
a² + b² = c²
12² + (x-9)² = c²
144 + x² - 9x -9x + 81 = c²
x² - 18x + 225 = c²
THE HYPOTENUSE OF THE 2ND TRIANGLE = x² - 18x + 225
NOW COMPARE BOTH TRIANGLES
x² - 18x + 225 : 15
x - 9 : 9
Cross multiply
9(x² - 18x + 225) = 15(x - 9)
9x² - 162x + 2025 = 15x - 135
9x² - 162x - 15x + 2025 + 135 = 0
9x² - 177x + 2160 = 0
Now use the quadratic equation
x = (-b +- √b² - 4ac)/2a
a = 9
b = -177
c = 2160
x = (-(-177) +- √(-177)² - 4(9)(2160))/(2×9)
x = (177 +- √31329 - 77760)/(18)
x = (177 +- √-46431)/18
At this point I have lost hope in the question as i got a negative value under square root which means it can't be solved.
I don't know where I am wrong but I hope the starting parts of the answer help you reach the final answer.
Goran's annual salary is $63,000. a total of $15,438.12 will be deducted for taxes and health insurance. he will receive his paycheck monthly in 12 equal installments. how much will he get paid with each paycheck?
Goran's monthly salary would be $3963.49
In this problem, the Annual salary or his Gross Salary is $63,000 and annual deductions for his salary which includes taxes & health insurance is $15,438.12 annually. The formula to calculate the Net salary is :
=> Net Salary = Gross Salary - Deductions
By the formula mentioned above, we can calculate Goran's Net salary which he gets Annually. Here, Gross = $63,000, Deductions = $15,438.12 :
=> Net = 63,000 - 15438.12 => Net Salary = 47,561.88
Goran gets a Net Salary of $47,561.88, Now we have to calculate the equal amount of paychecks he will receive monthly for 12 months.
Monthly Paycheck = Net/12 => 47561.88/12 => $3963.49
Hence, Goran's monthly paycheck will be $3963.49
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what is square root 25/49
A. 25/49
B. 5/9
C. 5/7
D. 5/8
Answer: C. 5/7
CALCULATOR
What is the answer to the.
-2(x - 5) = 6(2- 1/5x) and show me how you solved it
Answer:
x = -2.5
Step-by-step explanation:
Which expression is equivalent to quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity? negative forty nine over 8 times d minus one tenth forty nine over eight times d minus one tenth negative three eighths times d minus one and three tenths negative three eighths times d minus one tenth
Answer: The Answer would be -49/8d -1/10
Step-by-step explanation: I got it right on the test
have a good day
The answer for the given expression is -49d/8 - 1/10. Thus, the correct option is option A.
The expression can be solved by simple arithmetic operation.
(-3 1d/4 + 3/5) - (2 7d/8 + 7/10)
In the next step simplify the terms and open brackets.
-13d/4 + 3/5 -23d/8 - 7/10
Taking the like terms together.
-13d/4 - 23d/8 + 3/5 - 7/10
Solving the terms by taking L.C.M.
(-104d-92d/32) + (30-35/50)
-196d/32 - 5/50
Simplifying the terms.
-49d/8 - 1/10.
Thus, the value of the expression is -49d/8 - 1/10.
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