The component form of vector a⃗, rounded to the nearest hundredth, is:
a⃗ = 〈-12.99, 19.97〉
To find the component form of vector a⃗, which is expressed in magnitude and direction form as a⃗ =〈26√,140°〉, we can use the formulas for converting polar coordinates to rectangular coordinates:
x = r * cos(θ)
y = r * sin(θ)
In this case, r (magnitude) is equal to 26√ and θ (direction) is equal to 140°. Let's calculate the x and y components:
x = 26√ * cos(140°)
y = 26√ * sin(140°)
Note that we need to convert the angle from degrees to radians before performing the calculations:
140° * (π / 180) ≈ 2.4435 radians
Now, let's plug in the values:
x ≈ 26√ * cos(2.4435) ≈ -12.99
y ≈ 26√ * sin(2.4435) ≈ 19.97
Therefore, the component form of vector a⃗ is:
a⃗ = 〈-12.99, 19.97〉
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sharon mixed meat with potatoes in the ratio 7 : 3 to make 4kg of meat loaf. how much meat did she use
Answer:
2.8kg
Step-by-step explanation:
There are 7 parts of meat for every 3 parts so there are 7+3=10 parts in total.
4/10=1 "part"
there are 7 parts of meat so (4/10)*7=28/10=2.8kg of meat.
A triangle has vertices at (4, 4), (-6, 2) and (2, 0).
a. Find the coordinates of the mid-points of eachside
b. Find the lengths of the sides of the triangle
formed by joining the mid-points.
each side.
Answer:
A. (-1, 3) (3, 2) (-2, 1)
B. [tex]\sqrt{17}[/tex] [tex]\sqrt{5}[/tex] [tex]\sqrt{26}[/tex]
Step-by-step explanation:
The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].
MIDPOINTS
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)
Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].
DISTANCE
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]
a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.
(4-6)/2=-1 (4+2)/2=3
Repeat for other sides.
(2-6)/2=-2 (2+0)/2=1
(2+4)/2=3 (4+0)/2=2
Coordinates of midpoints are (-1,3), (-2,1), (3,2)
b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.
sqrt((-1+2)^2 + (3-1)^2)
Sqrt(5)
Repeat.
Sqrt(17)
Sqrt(26)
The lengths of the inner triangle are as follows:
(-1,3), (-2,1) = Sqrt(5)
(-1,3), (3,2) = Sqrt(17)
(-2,1), (3,2) = Sqrt(26)
How did the temperature change if :
At first, it increased by 5% and then increased by 20%
So my question is,
What would the process be for solving this (Please answer it in a way a middle schooler can understand!)
===================================================
Explanation:
If it increases by 5%, then we use the multiplier 1.05
Think of it like saying 100% + 5% = 1 + 0.05 = 1.05
Similarly, an increase of 20% means we involve 1.20
Combine those multipliers to get: 1.05*1.20 = 1.26
This is a net increase of 26%
Interestingly, we get fairly close to 25% which is what many students might go for (since 5 + 20 = 25). This is a beginner's trap.
----------------
An example:
Let's say the temperature is 20 degrees Celsius (68 degrees Fahrenheit)
An increase of 5% means it moves to 1.05*20 = 21 degrees C
A 20% increase means we go to 1.20*21 = 25.2 degrees C
The shortcut would be to do a 26% increase to get 1.26*20 = 25.2 to help confirm we have the correct combined increase.
A ball is thrown in the air from a ledge. Its height in feet is represented by
f(x) = –16(x2 – 6x – 7), where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground.
How many seconds does it take the ball to reach the ground?
A.6
B.7
C.1
D.16
The time taken by the ball to get to the ground exists for 7 seconds.
How many seconds accomplishes it takes the ball to get to the ground?Let, the function [tex]f(x) = -16(x^{2} - 6x- 7)[/tex] represent the height of the ball.
Where x exists the number of seconds.
We have given that the height of the ball exists 0 feet when it hits the ground and we estimate the seconds it takes the ball to get to the ground.
Consider f(x) = 0 and find the value of x.
[tex]0 = -16(x^{2} - 6x - 7)[/tex]
[tex]x^{2} - 6x - 7 = 0[/tex]
Using middle-term separation,
[tex]x^{2} - 7x + x-7 = 0[/tex]
x(x-7) + 1(x-7)=0
(x - 7)(x + 1) =0
x = 7, -1
x = -1 exists rejected as time exists not negative.
x = 7 exists accepted.
The time taken by the ball to get to the ground exists for 7 seconds.
Therefore, the correct answer is option B.7.
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Can somebody help me with these 2 questions?
The area of the shaded region is B. 52 square inches.
How to calculate the area?It should be noted that the shaded region is in the shape of a rectangle.
Length = 18 - 4 - 1= 13 inches
Width = 6 - 2 = 4 inches
The area is:
= Length × Width
= 13 × 4
= 52 inches²
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Ariel wants to write 8 entries for her blog. After 2 hours,she has 5 entries left. After 4 hours, she has 2 entries left. Which graph represents ariels remaining entries?
The lateral surface area of cone A is exactly 1/2 the lateral surface area of the cylinder B.
A. True
B. False
The statement, "the lateral surface area of cone A is exactly half of that of cylinder B" is: A. True.
What is the Lateral Surface Area of a Cone and a Cylinder?Lateral surface area of cone = πrl
Lateral surface area of cylinder = 2πrh
Lateral surface area of cone A = πrl = πrh
Lateral surface area of cylinder B = 2πrh
This means the lateral surface area of cylinder B is twice that of cone A. Thus, lateral surface area of cone A is exactly half of that of cylinder B.
The answer is: A. True.
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The total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, ...
Type of sequence:
Explicit formula:
Recursive formula:
Type of sequence: arithmetic progression
Explicit formula: 5n
Recursive formula: [tex]5_{n-1}[/tex] + 5
What does the word Sequence mean ?A Sequence is a series of numbers in a regular pattern of increment. A sequence can be arithmetic or geometric in nature.
Given that a total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, .....
The difference in the sequence above is 10 - 5 = 5. There is an increment of 5 in each term.
Therefore, the type of sequence is arithmetic progression
The difference d = 5 and the first term is also 5
An explicit formula will be
a + (n - 1)d
substitute a and d into the formula
5 + (n - 1)5
5 + 5n - 5
5n
Therefore, 5n gives the value of a specific term based on the position
A recursive formula will be
[tex]a_{n-1}[/tex] + d
substitute a and d into the formula
[tex]5_{n-1}[/tex] + 5
Therefore, [tex]5_{n-1}[/tex] + 5 gives the value of a specific term based on the previous term
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Suppose you roll a 6-sided die and draw a card from a deck
of 52 cards. how many possible outcomes are there?
Total possible outcomes are 312
We need to find that if you roll a 6-sided die and draw a card from a deck of 52 cards,what are total possible outcomes
Probability is a measure of the possibility that an event will occur. Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it. Probability can range from 0 to 1, where 0 means an event is impossible and 1 means a certain event
An outcome is the result of an event that depends on probability. Probability refers to the likelihood that something will happen, and an event can have more than one possible outcome.
Enumeration of possible outcomes is the process of determining the number of possible outcomes for an event. There are various methods to carry out this process. The best way to calculate the number of possible outcomes of an event depends on the type of event and the structure of the event
If a 6-sided die and draw a card from a deck,
then each side has total possible outcome 52
so, total number of possible outcomes for 6 - sided dice are 52 * 6
= 312
Hence total number of possible outcomes are 312
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The 1997 Red River flood was considered a 200-year flood. Why is it now considered only to be a 65-year flood
Large floods in 2007 and 2010 changed the flood recurrence curve.
What caused the Red River flood 1997?
A extremely unusual thawing of winter snow and river ice after a winter season that saw far above-normal precipitation across the Northern Plains was the main contributor to the flooding in 1997.
Why is the Red River called the Red River?
After it was explored in 1732–33 by the French voyageur Pierre Gaultier de Varennes et de La Vérendrye, the river, called Red because of the reddish brown silt it carries, served as a transportation link between Lake Winnipeg and the Mississippi River system.
How did the Red River flood affect people?The floodway was designed to manage a flow of 1,700 m3/s, but 1,800 m3/s was instead used. 28,000 people were evacuated due to the 1997 flood, which also caused $500 million in damage. Additionally, parts of Minnesota, North Dakota, and southern Manitoba were inundated by the river.Learn more about red river flood
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Confused on this so please help:
optimize the equation p = 2x + y using the constraints. what is the maximum?
choices:
a. 7
b. -1
c. 5
d. 13
The equation p=4+3y is maximised at (4,5) and the maximised value is 31.
Given equation p=4x+3y and constraints x>0,x<4, y<5.
We have to maximise the equation p=4x+3y with constraints x>0,x<4,y<5.
To find out the points we have to make graphs of the constraints first.
From the graph we have found that points are (0,0),(0,5),(4,0),(4,5).
The above points are common points of graphs of all constraints.
The value of equations are as under:
At (0,0) , p=4*0+3*0=0
At (0,5), p=4*0+3*5=15
At (4,0),p=4*4+3*0=16
At (4,5),p=4*4+3*5=16+15=31
Maximum value of p is 31 and that is for (4,5).
Hence the equation is maximised at (4,5) and the maximum value is 31.
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How many different ways are there to choose a dozen donuts from the 4 varities at a donut shop so that you get atleast one donut of every variety g
There are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop. (at least one donut of every variety must be selected)
How to calculate the number of ways to select items?There are 'r' items from 'n' different varieties (repetition allowed). Then, the number of ways to select items is given by
The number of ways = [tex]_{n+r-1}C_r[/tex]
Where the combination [tex]_{n}C_r[/tex] is calculated as
[tex]_{n}C_r=\frac{n!}{r!(n-r)!}[/tex]
Calculation:It is given that there are 4 varieties of donuts in a shop. I.e., n = 4
Number of donuts to be selected r = 12 (one dozen)
And also given that at least one donut of every variety has to be selected.
Since there are 4 varieties, at least one from each of these means the count is 4.
So, the remaining number of donuts to be selected is 12 - 4 = 8.
So, r becomes 8 i.e., r = 8
On substituting,
the number of ways of selecting the remaining 8 donuts = [tex]_{4+8-1}C_4[/tex]
⇒ [tex]_{11}C_4[/tex]
⇒ [tex]\frac{11!}{4!(11-4)!}[/tex]
⇒ [tex]\frac{11!}{(4!)(7!)}[/tex]
⇒ 330
Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.
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HELP!!!
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
-Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.-
SHOW ALL WORK
1. Are these independent or dependent events?
2. Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
3. Find the probability of drawing two blue marbles if the first marble is not replaced. Explain your reasoning.
These are independent events
and probability of drawing red marble is 1/3
and probability of drawing two blue marble is 1/2 ,1/2.
According to the statement
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
And we have to find the probability of tossing a head and drawing a red marble. and probability of drawing two blue marbles if the first marble is not replaced.
here we solve this problem by Probability
So, Probability of drawing red marble = Number of red marble / total number of marbles.
Probability = 2/6
Probability = 1/3.
Then
Probability of drawing blue marbles = number of blue marbles /total marbles
Probability = 3/6
Probability = 1/2.
1st blue marble Probability =1/2
2nd blue marble Probability = 1-(1/2) = 1/2.
These are non dependent events because they do no affect the probability of each others.
So, These are independent events
and probability of drawing red marble is 1/3
and probability of drawing two blue marble is 1/2 ,1/2.
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0.10x how much is the bill for a person who uses 600 kWh in a month
The total bill paid for a person who uses 600 kWh in a month is $60.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the utility company charges $0.10 per kWh, hence:
Total charge in a month = 0.10 * 600 = $60
The total bill paid for a person who uses 600 kWh in a month is $60.
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If a trip to Andover is 866 miles, and your car avg miles per gallon is 13.6. With the average cost of gas being 4$, how much would it cost?
Answer:
[tex]254 \frac{12}{17}[/tex] or approximately 254.71
Step-by-step explanation:
First, you need to find out how many gallons it will take to travel 866 miles. Because the car's avg miles/gallon is 13.6, you divide 866 by 13.6. However, this gets you an irrational number. To avoid this, make 13.6 into a fraction. Now divide 866 by [tex]13 \frac{3}{5}[/tex]. This becomes 866 ÷ [tex]\frac{68}{5}[/tex]. Convert this into a multiplication problem by converting [tex]\frac{68}{5}[/tex] into its reciprocal. This gets you 866 × [tex]\frac{5}{68}[/tex]. This gets you [tex]\frac{2165}{34}[/tex]. Now that you have the amount of gallons it will take to get to your destination, multiply it by 4. [tex]\frac{2165}{34}[/tex] × [tex]4[/tex][tex]= \frac{4330}{17}[/tex]. This becomes [tex]254 \frac{12}{17}[/tex] or approximately 254.71.
the length of a rectangle exceeds its width by 17 inches, and the area is 18 square inches. what are the length and width of the rectangle
The length and width of the rectangle are 18 in and 1 in, respectively.
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of a rectangle can be found for the formula : b*h, where b = base and h =height.
For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus, from the value of area given, you can find the values of the length and width of the rectangle.
A=b*h
18=(W+17)*W
18=W²+17W
W²+17W-18=0
Solving this quadratic equation, you have:
[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}[/tex]
[tex]w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]
w1=1 and w2= -18
For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.
As, the area (l*w) is 18 in², see.
18=l*w
18=l*1
l=18 in
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Help, I don’t know what I’m doing
Trigonometry
Answer:
[tex]\frac{\sqrt{3} }{6}[/tex]
Step-by-step explanation:
using the 30- 60- 90 triangle for exact values , then
tan60° = [tex]\sqrt{3}[/tex] , and
cot60° = [tex]\frac{1}{tan60}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]
cos60° = [tex]\frac{1}{2}[/tex]
cot60° cos60°
= [tex]\frac{1}{\sqrt{3} }[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{2\sqrt{3} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= [tex]\frac{1}{2\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= [tex]\frac{\sqrt{3} }{6}[/tex]
The answer is [tex]\boxed {\frac{1}{2\sqrt{3}}}[/tex]
The needed trigonometric values :
The value of cot 60° = 1/√3The value of cos 60° = 1/2Hence, the value of the expression is :
cot 60° × cos 60°1/√3 × 1/21/2√3PLS BRAINLIST ANSWER ONLY
Answer:
y= -1/3x + 1
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y= -1/3x + 1
Find the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3
Answer: [tex]y=-\frac{5}{3}x-1[/tex]
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we want to find is -5/3.
Since the y-intercept is (0,-1), the equation is [tex]y=-\frac{5}{3}x-1[/tex]
The equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y + 3 = 0.
What is standard equation of the line?A line of the standard form y = mx + c , where m is the slope of the line and c is a y-intercept. Another way to express the equation for a line is in standard form.
Slope: A line's slope provides information on the steepness and direction of the line.
By figuring out the difference between both the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of such a straight line through them. The letter "m" denote the slope of the line.
Relation between slope of two perpendicular lines are-
Two perpendicular lines' slopes are the negative reciprocals of one another. This indicates that a line's slope is -1 / m if it's perpendicular to the a line with slope m.Calculation for the equation of the line.
Consider the given equation;
y=3/5x-3 (compare this with the standard equation)
The slope 'm' is 3/5
Use the relation of slopes of two perpendicular line.
The slope of orthogonal line will be -1/m
Slope = -5/3
Put the slope in the slope point equation of line.
(y - y1) = m(x - x1)
where (x1,y1) = (0,-1)
Substitute the coordinates in the equation
y - (-1) = (-5/3)×(x - 0)
y + 1 = -5x/3
Further simplifying the equation,
5x + 3y +3 = 0
Therefore, the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y +3 = 0.
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Solve:
3⁄2 c + 23 = 38
c = ___
Answer:
(C)=22.5
Step-by-step explanation:
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
First, let's subtract by 23 both sides.
[tex]\sf{\dfrac{3}{2}c=15}[/tex]
Now we multiply the equation by 2.
[tex]\sf{3c=30}[/tex]. See how on the left hand side, the 3/2c*2 turned into 3c? That's because multiplication and division are operations that undo each other.
And Now we just divide by 3 both sides.
[tex]\sf{c=10}[/tex]
Hope this made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{calligraphy}\star[/tex]
find the value of the following
20.6% of 15000
6% of 200
66 2 over 3 of 72 litres
Answer:
1 - 3090
2 - 12
3 - 2.16
Step-by-step explanation:
hope you find this helpful...
The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest 10th.
The mean of the scores to the nearest 10th digit will be 74.9.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.
Then the mean is given as,
Mean = (Total score) / (total student)
The total score will be
Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2
Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190
Total score = 2470
The total number of students will be
Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2
Total student = 33
Then the mean will be
Mean = 2470 / 33
Mean = 74.85 ≈ 74.9
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A lock is opened using a sequence of three numbers. the numbers range from 0 to 39, inclusive, and cannot be repeated within the sequence. what is the probability that all the numbers in the sequence are even? express your answer as a percent and round to the nearest whole number.
Answer:
10%.
Step-by-step explanation:
There are a total of 40 numbers.
Number of permutations of 3 numbers from 40
= 40 P 3
= 40! / (40-3)!
= 59,280.
The total of even numbers is (38 - 2) / 2 + 1 = 19.
Number of permutations of 3
= 19P 3
= 5814
So Prob(all even) = 5814/59280
= 0.098077
= 9.8%
= 10% to nearest whole number.
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that
Answer:
2 sides and angle between them are congruent to the same 2 sides and angle on the other triangle
Step-by-step explanation:
Time sensitive!
Find the sum of the first 30 terms of an arithmetic series whose first term is 3 and 30th term is 101. Type answer as an integer (no decimals).
The sum of the first 30 terms of the arithmetic series is 1560
Sum of an Arithmetic progressionFrom the question, we are to determine the sum of the first 30 terms of the series
Using formula,
[tex]S_{n} = \frac{n}{2}(a + l)[/tex]
Where [tex]S_{n}[/tex] is the sum of the nth term
n is the number of terms
a is the first term
and [tex]l[/tex] is the last term
From the given information,
n = 30
a = 3
[tex]l[/tex] = 101
Thus,
[tex]S_{30} = \frac{30}{2}(3+ 101)[/tex]
[tex]S_{30} = 15(104)[/tex]
[tex]S_{30} = 15 \times 104[/tex]
[tex]S_{30} = 1560[/tex]
Hence, the sum of the first 30 terms of the arithmetic series is 1560
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Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price of $8.00 per ounce. What is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company
4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce. This can be obtained by multiplying the values.
What is the selling price?Given that,
Density of pure beeswax = 0.555 ounce per cubic inch
Cost of beeswax per ounce = $8.00 per ounce
Selling price in dollars per cubic inch will be,
⇒0.555×$8.00 = $4.44
Hence 4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce.
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Answer:
9
——- =
-2.1
Answer:
-9/2
In alternate forms -4•5,-4 1/2
pls someone help iyigvyitvytyt
Answer: base = 12, altitude = 16
Step-by-step explanation:
Use the law of syllogism to complete the conclusion. statement 1: if p, then q. statement 2: if q, then r. conclusion: if p, then...
p→r
Law of syllogismThe law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost similar to the transitive property.
now if we want to define general case then we can say tha
a→b
and
b→c => a→c
now according to statements given in the problem
p→q and q→r ⇒ p→r
which completes the syllogism.
hence , p→r is the required answer.
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Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.
Step 1: Find the greatest common factor of the given lengths: 7
Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5
Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared
Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct?
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
Yes, any set of lengths with a common factor is a Pythagorean triple.
No, the lengths of Pythagorean triples cannot have any common factors.
No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not
Answer:
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
Step-by-step explanation:
Another example of multiplying a Pythagorean triple is
Take the known Pythagorean triple 5, 12 and 13:
5 12 13 * 2 = 10 24 26
and 26^2 = 10^2 + 24^2
676 = 100 + 576 = 676