Answers
E to F is 6 F to G is x
and overall distance from e to g is 1.6x
so:
6+x = 1.6x
subtract x from each side
6 = 0.6x
now divide both sides by .6
x = 6/0.6 = 10
x = 10
Related Questions
) the length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3cm/s. when the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
Answers
It’s a little surprising that this question didn’t come up earlier. Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2). A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.
Determine the angular velocity in radians per second of 4.9 revolutions in 5 seconds. Use 3.14 for pi.
a) 89 miles per hour
b) 117 miles per hour
c) 149 miles per hour
d) 129 miles per hour
Answers
frequency = 4.9 / 5 seconds = 0.98 / second
Angular velocity = 2π radian * 0.98/sec = 6.1544 radian / sec
To pass it to radian per hour multiply by the factor 3600 sec / hour
=> 6.1544 rad / sec * 3600 sec / hour = 22,155.84 rad/hour.
Now, you have to realize that the answer choices are not angular velocities. They have units of miles per hour, which means that they are linear velocities
To calculate linear velocities you need the radius of the circular path described by the object.
With the radius, then you use the formula V = angular velocity * radius =>
For example if the radius is 0.0402 miles, the linear velocity is 0.00402 miles * 22,155.84/hour = 89 miles per hour
If the radius is 0.00528 miles, V = 0.00528 miles * 22,155.84 / hour = 117 mph
If the radius is 0.00673 miles, V = 0.00673 miles * 22,155.84 / hour = 149 mph
If the radius is 0.00582 miles, V = 0.00582 miles * 22,155.84 / hour = 129 mph.
Now you know how to calculate the angular and linear velocities.
In some countries congress, the number of representatives is 80 less than 5 times the number of senators. there are a total of 520 members. find the number of senators and the number representatives
Answers
r = 5s - 80
s + (5s - 80) = 520
6s - 80 = 520
6s = 520 + 80
6s = 600
s = 600/6
s = 100 <=== senators
r = 5s - 80
r = 5(100) - 80
r = 500 - 80
5 = 420 <=== representatives
If x varies inversely with y and x = 2 when y = 48, find x when y = 24.
Answers
X=k/y
X=2, y=48
2=k/48
K=2*48 = 96
X= 96/24
X=4
What is the range of the function g(x) = |x – 12| – 2?
{y | y > –2}
{y | y > –2}
{y | y > 12}
{y | y > 12}
Answers
what is the solution to this linear equation? 2/3x-1/2=1/3+5/6x
Answers
Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
Answers
Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
The polar coordinate of any point can be written as:
(r, θ) = (r, θ + 2nπ) --> when positive
(r, θ) = [ - r, θ + (2n + 1)π ] --> when negative
where n is any integer.
The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).
When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)
where n is any integer.
When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.
Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].
The polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
The coordinates of point p are given as:
p = (5, [tex]\pi[/tex]/3)
A point represented as (r, θ) has the following polar coordinates
(r, θ + 2n[tex]\pi[/tex]) for positive r, and (- r, θ + [2n + 1][tex]\pi[/tex]) for negative r
By comparing (r, θ) and (5, [tex]\pi[/tex]/3), we have:
r = 5
[tex]\theta = \pi/3[/tex]
So, we have:
(r,[tex]\theta[/tex]) = (r, [tex]\theta[/tex] + 2n[tex]\pi[/tex])
The equation becomes
(5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
Also, we have:
(-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
Hence, the polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
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AP calculus HW Need help on #61
Answers
Crossing the 1s , the 2xs, and the x^2s out, we get
(2x∆x+∆x^2-2∆x)/∆x
Dividing the ∆x, we get
2x+∆x-2.
Making the limit of ∆x=0, we get 2x-2.
bag has 2 green marbles, 3 red marbles, and 3 yellow marbles. What is the probability that you pick a red marble, do not replace it, and pick yellow marble?
Answers
(3/8)*(3/7) = is about 16% chance
3/8 * 3/7 = 9/56
What is the midpoint of (-3,-7) and (9,8)
Answers
Without plotting any points other than intercepts, draw a possible graph of the following polynomial:
f(x) = (x + 8)3(x + 6)2(x + 2)(x − 1)3(x − 3)4(x − 6).
Answers
0 = (x + 8)3(x + 6)2(x + 2)(x − 1)3(x − 3)4(x − 6)
There are 6 intercepts:
x+8=0 ---> x= -8
x+6=0 ---> x=-6
x+2=0 ---> x=-2
x-1=0 ---> x=1
x-3=0 ---> x=3
x-6=0 ---> x=6
The 6 intercepts are plotted as shown in the picture. The tool I used was Microsoft Excel. This is one possible sketch of the graph. The trend could move in any ways as long as it passes these 6 intercepts.
Final answer:
To sketch the polynomial graph without plotting points beyond intercepts, identify the x-intercepts from the factors, note the behavior at these points due to the powers, and connect them considering the end behavior akin to y = x^13.
Explanation:
To sketch a possible graph of the given polynomial f(x) = (x + 8)^3(x + 6)^2(x + 2)(x - 1)^3(x - 3)^4(x - 6), we can use its intercepts and the behavior near these intercepts. The intercepts are the x-values for which f(x) = 0. These are at x = -8, x = -6, x = -2, x = 1, x = 3, and x = 6.
Since these factors are raised to different powers, the graph will behave differently at each intercept. Also, since the highest power in the polynomial is 13 (3+2+1+3+4+1), the end behavior of f(x) as x approaches positive or negative infinity will resemble that of y = x^13.
Here's a step-by-step guide for sketching the graph:
Plot the x-intercepts on the x-axis: (-8, 0), (-6, 0), (-2, 0), (1, 0), (3, 0), (6, 0).
For each intercept, note that if the factor has an odd power, the graph crosses the x-axis, and if it has an even power, the graph touches the x-axis and turns back.
At x = -8, since the power is 3 (odd), the graph crosses the axis and behaves similarly to y = x^3, starting from the bottom.
At x = -6 and x = -2, the powers are 2 (even), so the graph will just touch the axis and turn back.
At x = 1, the power is 3 (odd), so the graph will cross the axis with the behavior of y = x^3.
At x = 3, the power is 4 (even), hence the graph touches the axis and turns back.
At x = 6, as the factor is raised to the first power (odd), the graph crosses the x-axis.
Finally, connect these points with smooth curves, keeping in mind the end behavior of the graph will rise on both ends because the degree is 13, an odd number.
Remember that the final graph should show the pattern of rising and falling appropriately between these intercepts based on the powers of each factor.
A bag contains 25 marbles: 10 black, 13 red, and 2 blue. a marble is drawn from the bag at random. what is the probability of getting a red or a blue marble? 3/5 2/3 1/2 1/6
Answers
Final answer:
The probability of drawing a red or blue marble from a bag containing 25 marbles (10 black, 13 red, 2 blue) is 3/5. This is calculated by dividing the total number of red and blue marbles (15) by the total number of marbles (25).
Explanation:
The question involves calculating the probability of drawing a red or a blue marble from a bag containing 25 marbles: 10 black, 13 red, and 2 blue. To find the probability of an event happening, we divide the number of ways that event can happen by the total number of outcomes. Here, the total number of marbles is 25.
The total ways to get a red or a blue marble is the sum of red and blue marbles, which is 13 (red) + 2 (blue) = 15. Therefore, the probability of drawing a red or blue marble is 15/25. Simplifying that fraction gives us 3/5.
The correct answer is 3/5. This calculation shows how to approach problems involving the probability of one event or another happening, especially when dealing with specific quantities.
What is the probability that the student will have score between 71 and 80
Answers
Larry's dining room table measures five feet in diameter. what scale diameter will he use if the scale he is using is 1 inch = 2 feet?
Answers
1/2 = x/5
2x = 5
X = 5/2
2.5 inches would measure 5 feet according to the scale
Answer: 2.5 inches.
Step-by-step explanation:
The given statement : Larry's dining room table measures five feet in diameter.
i.e. We are given that the diameter of Larry's dining room table = 5 feet
The scale used by him 1 inch =2 feet
i.e. [tex]\text{1 feet =}\dfrac{1}{2}\text{ inch}[/tex]
Now, [tex]\text{5 feet =}5\times\dfrac{1}{2}\text{ inches}=2.5\text{ inches}[/tex]
Therefore, the scale diameter he will use = 2.5 inches.
The art club spent $45 on supplies for Valentines to sell during lunches. they made 60 valentines. what's selling price for a valentine would result in a profit of zero if all valentines are sold?
Answers
Answer:
0.75
Step-by-step explanation:
As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commision on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $388. If she sells $1,000, she is paid $520. Find Alysse's salary when she sells $3,300 worth of merchandise.
Answers
[tex]388=x+(y%*400)[/tex] where 388 is what she earns after her base salary, x, is paid and her commission of 400. y is the percent of the commission that she earns. As you can see, we have 2 unknowns, which COULD be a problem. But let's move on first before we freak out.
The next equation involves the other bit of info: that she earns 520 after her base salary of x and her commission of 1000 based on whatever the percentage of her sales is, which is y. That equation looks like this:
[tex]520=x+(y%*1000)[/tex]
Because her base salary is constant, the x's are the same number in both equations. So we can solve each for x:
[tex]x=-388+400y[/tex]
[tex]x=-520+1000y[/tex]
Now that these are both solved for x, and x is the exact same number, we can set those 2 equations equal to each other by the transitive property of equality:
=388+400y= -520+1000y
Solving for y gives you:
132=600y and
[tex] \frac{132}{600} =y[/tex]
Because this is a percentage, we will multiply the decimal we get by 100 to find that the percentage she earns on a sale is 22%. Now that we have that percentage, we can find her base salary. Do that like this:
Use one of your equations to solve for x:
388=x+[(.22)(400)]
388=x+88 and x = 300. That's her base salary. Now use that base salary in an equation to find out her monthly pay after she sells $3,300 worth of merchandise in a month:
x = 300 + [(.22)(3300)]
x = 300 + 726
x = $1,026
That's how much she makes after her base salary of $300 plus her earning off selling $3,300 worth of merchandise at 22% commission.
Answer:
Step-by-step explanation:
In order to solve this we just have to create a system of equations, because we have to unknown values, for the base salary we are going to use X and for the comission we will use Y, now we know that when she sold $400 in merchandise she earned $388 and and when she sold $100 se got paid $520 both equations would look like this:
[tex]x+400y=388\\x+1000y=520][/tex]
Now we can solve them by elimination, multiplying one function by -1.
[tex](-1)(x+400y=388)= -x-400y=-388\\x+1000y=388\\1000y-400y=132\\600y=388\\y=\frac{132}{600} \\y=0.22=22%[/tex]
Now we know that the percentage that she earns is 22% of the merchandise she sells.
Now to know how much does she makes on her base pay we just put the value into one of the functions:
[tex]x+1000y=520\\x+1000(.22)=520\\x+220=520\\x=300[/tex]
So her base pay is $300.
To calculate how much she will earn when she sells $3,300 in merchandise we just put that value into the formula:
[tex]x+3300y=\\300+3300(.22)\\300+726=1026[/tex]
So when she sells 3300 she will make 1026 total.
To isolate the variable in the equation -3x - 9 = -27, the first step is to add 9 to both sides. This gives you -3x = -18. What is the next step to isolate the variable?
A.+ 18 B.18 C. -3 D.+ 3x
Answers
Add 9 to both side
-3x-9+9=-27+9
-3x=-18
divided -3 to each side
-3x/-3=-18/-3
x=6
Check:
-3x-9=-27
substitute x with 6
-3(6)-9=-27
-18-9=-27
-27=-27. As a result, the next step to isolate the variable is divided -3 to both side. Hope it help!
Next step to isolate the variable is to divide by -3 .
Given,
-3x-9=-27
Firstly,
Add 9 to both side of the equation,
-3x-9+9=-27+9
-3x=-18
Now,
Divide -3 to each side
-3x/-3=-18/-3
x=6
Now,
Check:
-3x-9=-27
Substitute x with 6
-3(6)-9=-27
-18-9=-2
Thus, the next step to isolate the variable is to divide -3 to both side of equation.
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Write a congruency statement for the pair of triangles.
Answers
Answer:
ΔABP is congruent to ΔBAQ
ΔABP ≡ ΔBAQ
Explanation:
We are given two triangles; ΔABP and ΔABQ
In these two triangles, we have:
AB as a common side
∠ABP = ∠BAQ
AQ = BP
We can conclude that these two triangles are congruent by SAS (side-angle-side) postulate which states that:
"When two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle, then the two triangles are congruent"
Note that when writing congruency statements, the order of the letters is critical as each angle/side in the first triangle must be congruent to its corresponding angle/side in the second triangle.
Based on the above, the congruency statement would be:
ΔABP is congruent to ΔBAQ
Hope this helps :)
Algebra 2
In a sample of 200 households, the mean number of hours spent on social networking sites during the month of January was 55 hours. In a much larger study, the standard deviation was determined to be 7 hours. Assume the population standard deviation is the same. What is the 99% confidence interval for the mean hours devoted to social networking in January?
A) The 99% confidence interval ranges from 53.73 to 56.27 hours.
B) The 99% confidence interval ranges from 7 to 55 hours.
C) The 99% confidence interval ranges from 54.51 to 55.49 hours.
D) The 99% confidence interval ranges from 55 to 60 hours.
Can i get an explanation?
All i know is that this question has something to do with the Margin of error.
The Margin of error has two different formulas
Please help :)
Answers
Confidence Interval is 53.73 to 56.27
Answer:
Step-by-step explanation:
n=sample size =200
Mean = x bar = 55 hours
Std deviation (Population) = 7 hours
For 99% confidence level
Z critical value = 2.58
Margin of error = ±2.58(std error)
Std error = [tex]\frac{7}{\sqrt{n} } =0.495[/tex]
Hence margin of error = ±0.495(258)=1.28
Confidence interval = (55-1.28, 55+1.28) = (53.72, 56.28)
~(53.73, 56.27)
Hence option A
(05.06)Bentley had $40 in birthday money in her piggy bank. She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week. Finally, she spent $15 on new sunglasses.
Which part of the scenario is best represented by a linear increasing interval?
Bentley has $40 in her piggy bank.
Bentley spent $10 on new flip flops.
Bentley got $20 for her allowance.
Bentley spent $15 on sunglasses.
Answers
linear increase would be something added to an equation.
she started with 40,
she spent 10 on flip flops and also spent 15 of sunglasses those are decreases
she added 20 for allowance which is an increase and we can assume she gets the same amount of allowance every week
so that would be the linear increase
Bentley had $40 in birthday money in her piggy bank. Bentley got $20 for her allowance which is represented by a linear increasing interval.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Bentley had $40 in birthday money in her piggy bank.
She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week.
Finally, she spent $15 on new sunglasses.
linear increase would be something added to an equation.
she started with $40 in her piggy bank.
She spent 10 on flip-flops and also spent 15 on sunglasses. This show decreases.
she added 20 for the allowance which is an increase and we can assume she gets the same amount of allowance every week.
So, that would be the linear increase.
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How to find if two equations are inverses of each other?
Answers
f(g(x)) takes the g function and plugs it into the x in the f function, like this:
[tex]f(g(x))=3[ \frac{(x+2)}{3} ]-2 [/tex]
cancel out the 3's to get
f(g(x))=(x+2)-2 which is just x. Now do it the other way: g(f(x))
[tex]g(f(x))= \frac{[(3x-2)+2]}{3} [/tex]
3x-2+2 is 3x, so we have
[tex]g(f(x))= \frac{3x}{3} =x[/tex]
See?
27 and 54 are side lengths of an isosceles triangle what is the shortest possible value for the other side
Answers
There is a 6 digit number consisting of the digits: 1, 1, 2, 2, 3 and 3. the 1's are one digit apart, the 2's are two digits apart and the 3's are three digits apart. what is the number?
Answers
Find the measure of each angle: Complementary angles with measures (5x)° and (4x−18)°.
Answers
so
5x+4x-18=90
9x-18=90
add 18 both sides
9x=108
divide both sides by 9
x=12
5x is one angle
5x=5(12)=60 degrees
the other one is 4x-18
4x-18=4(12)-18=48-18=30
the angles are 60 degrees and 30 degrees
and x=12 degree
The measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.
What are complementary angles?Complementary angles are a pair of angles whose sum is always equal to 90°.
If A and B are complementary angles, then A + B = 90°.
How to solve the given question?In the question, we are asked to find the measure of each angle, given that the angles (5x)° and (4x - 18)° are complementary angles.
As we know that these angles are complementary, we can write the equation to solve for x as,
5x + (4x - 18) = 90
or, 5x + 4x - 18 = 90
or, 9x = 90 + 18 = 108
or, x = 108/9 = 12.
Therefore, the value of these angles are:
(5x)° = (5*12)° = 60°.(4x - 18)° = (4*12 - 18)° = (48 - 18)° = 30°.Therefore, the measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.
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The excel function ________ would be used to find the lowest score on a series of student test scores. min median sum dmin
Answers
The Excel function you should use to find the lowest score in a series of test scores is the MIN function. It determines the smallest number in a set of values.
Explanation:The Excel function that should be used to find the lowest score on a series of student test scores is the MIN function. This function allows you to determine the smallest number in a set of values. For instance, if you have the scores in cells A1 to A10, you would write the formula as =MIN(A1:A10).
It's important to note that the other options provided, such as median, sum, and dmin, would not accurately find the lowest score. The median would find the middle score, sum would add all the scores together, and dmin is a database function that extracts the smallest number from a selected database column based on the specified conditions.
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PLEASE HELP!!!!!! picture inserted
Answers
1 revolution or 1 rotation is equivalent to 360 degrees
360 degrees/ 17 minutes = 21.16 rotation per minute or 21.16 rpm.
RPM or rotation per minute is the measure of the number of rotation completed per minute.
The amplitude is the distance from rest until the peak of its wave or crest. Since the rotation is completed in 17 minutes, therefore its amplitude is π/2
Pam and Meg each have a picture frame. Pam’s picture frame is a square with an area of 3 square feet. Meg’s picture frame is a circle with a radius of 1 foot. The circumference of Meg’s picture frame is the perimeter of Pam’s picture frame by approximately feet
Answers
Answer: So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 0.64 feet.
Step-by-step explanation:
Since we have given that
Area of Pam 's picture frame which is square in shape = 3 sq. ft.
As we know the formula for "Area of square ":
[tex]Area=Side^2\\\\3=Side^2\\\\\sqrt{3}\ ft=Side[/tex]
So, Perimeter of square frame would be
[tex]Perimeter=4\times side\\\\Perimeter=4\times \sqrt{3}\\\\Perimeter=6.93\ ft[/tex]
Radius of Meg's circular frame = 1 foot
So, Circumference of circular frame would be
[tex]2\pi r\\\\=2\times \dfrac{22}{7}\times 1\\\\=\dfrac{44}{7}\\\\=6.29\ ft[/tex]
So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 6.93-6.29=0.64 feet.
Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective. She decides to check several monitors and record if they are defective. Which of the following will make this process into a binomial experiment?
- Glenda checks the monitors until she has 300 defective monitors.
- Glenda checks 300 monitors and records the number that are defective until she gets greater than 0.5% defective monitors.
- Glenda checks the monitors until she has 300 non-defective monitors.
- Glenda chooses to check 300 monitors.
Answers
D is the correct answer.
Step-by-step explanation:
D. Glenda chooses to check 300 monitors.
A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.
Now, to know about the defects through binomial experiment Glenda must choose a number of computers or trials. So, option D is correct.
The statement that will make this process into a binomial experiment is that,
⇒ Glenda checks the monitors until she has 300 non-defective monitors."
Hence, Option C is correct.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective.
Since, A binomial experiment is defined as a statistical experiment which consists of n repeated trials.
Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.
Hence, For check several monitors and record if they are defective,
Glenda checks the monitors until she has 300 non-defective monitors."
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A triangle with sides of lengths 10, 24, and 27 is a right triangle.
True or false?
Answers
10^2 + 24^2 = 27^2
100 + 576 =/= 729
Let me know if you need any more help!
find the common ratio of the following geometric sequence: 3.512,12.292,43.022,150.577,527.020
A) 2.5
B) 3.5
C) 8.78
D) 0.29
Answers
Start from the right end and divide the by the previous term.
527.020/150.577 = 3.5
150.577/43.022 = 3.5
43.022/12.292 = 3.5
12.292/3.512 = 3.5
r = 3.5 LETTER B