The data below shows the ratio of brown to green crayons in four kindergarten classrooms.
13 to 19
15 to 28
18 to 32
30 to 68
Which table below correctly shows these ratios in a three-column table?
Brown 13 15 18 30
Green 19 28 32 68
Total 32 43 50 98
Brown 19 28 32 68
Green 13 15 18 30
Total 32 43 50 98
Brown 13 28 18 30
Green 19 15 32 68
Total 32 43 50 98
Brown 32 43 32 30
Green 19 28 18 68
Total 13 15 50 98
Answers
Related Questions
dY For each matrix below, find the general solution for the system = AY , sketch the phase portrait dt for the system, then find the solution with the given initial condition. (1) A= (41) = ) Y(0) = (1,1) =
Answers
The solution with initial condition \($Y(0)=(1,1)$ is:$$Y(t) = \frac{\sqrt{5}+1}{2\sqrt{5}} e^{(2+\sqrt{5})t} \begin{pmatrix} 1 \\ -1+\sqrt{5} \end{pmatrix} + \frac{-\sqrt{5}+1}{2\sqrt{5}} e^{(2-\sqrt{5})t} \begin{pmatrix} 1 \\ -1-\sqrt{5} \end{pmatrix}$$\).
For each matrix below, find the general solution for the system = AY , sketch the phase portrait dt for the system, then find the solution with the given initial condition. (1) A= (41) = ) Y(0) = (1,1) =For the system of differential equations: Y'=AY, where A is a matrix, the general solution is given by:\($$Y(t)=ce^{At}$$\)where c is an arbitrary constant .In order to sketch the phase portrait, we first need to find the eigenvalues and eigenvectors of matrix A\(. $$\begin{pmatrix} 4&1\\ 1&0 \end{pmatrix}$$\)The characteristic equation is given by:\($$\lambda^2 - 4\lambda - 1 = 0$$\)Using the quadratic formula, we get:\($$\lambda = \frac{4 \pm \sqrt{16+4}}{2} = 2 \pm \sqrt{5}$$\)The eigenvalues are:\($$\lambda_1 = 2 + \sqrt{5}$$and$$\lambda_2 = 2 - \sqrt{5}$$\)
The eigenvector corresponding to \($\lambda_1$\) is given by\(:$$\begin{pmatrix} 1 \\ \lambda_1 - 4 \end{pmatrix} = \begin{pmatrix} 1 \\ -1 + \sqrt{5} \end{pmatrix}$$\)and the eigenvector corresponding to \($\lambda_2$ is given by:$$\begin{pmatrix} 1 \\ \lambda_2 - 4 \end{pmatrix} = \begin{pmatrix} 1 \\ -1 - \sqrt{5} \end{pmatrix}$$\)The phase portrait is shown below:The solution with initial condition \($Y(0)=(1,1)$ is:$$Y(t) = c_1 e^{(2+\sqrt{5})t} \begin{pmatrix} 1 \\ -1+\sqrt{5} \end{pmatrix} + c_2 e^{(2-\sqrt{5})t} \begin{pmatrix} 1 \\ -1-\sqrt{5} \end{pmatrix}$$\)Using the initial condition, we get:\($$\begin{pmatrix} 1 \\ 1 \end{pmatrix} = c_1 \begin{pmatrix} 1 \\ -1+\sqrt{5} \end{pmatrix} + c_2 \begin{pmatrix} 1 \\ -1-\sqrt{5} \end{pmatrix}$$\)Solving for \($c_1$ and $c_2$, we get:$$c_1 = \frac{\sqrt{5}+1}{2\sqrt{5}}$$$$c_2 = \frac{-\sqrt{5}+1}{2\sqrt{5}}$$\)
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using a z-table like the one found in lectures, or a z-score calculator, approximately what is the probability of randomly drawing a value greater than 3.0 from a z-distribution? question 3 options: .9995
Answers
The probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013
What does z-score mean?The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.
An element that is below the mean is indicated by a z-score that is less than 0.
An element bigger than the mean is indicated by a z-score greater than 0.
An element that is equal to the mean is represented by a z-score of 0.
P(Z > a) = 1-P(Z<a)
Let's say we want to know, for instance, the likelihood that a z-score will be higher than 3.00.
We learn from the table, that
P(Z < 3.00) = 0.9987.
Therefore,
P(Z > 3.00) = 1 - P(Z < 3.00)
= 1 - 0.9987
= 0.0013.
Therefore, the probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013
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3) 8x = 72
It’ll help
Answers
Answer:
9
Step-by-step explanation:
×=72/8
×=9
Hope it helps
Answer: 9
Step-by-step explanation: First, look for the value of x. A number with a variable in front of it means that you’ll be multiplying, but you can use division which makes it easier to find x. SO, DIVIDE 72 by 8 (82 ÷ 7), which equals to 9. (8 x 9 = 72)
You deposit $2700 in a long-term investment fund in which the interest is compounded monthly. After 4 years, the balance is $2983.65. What is the annual interest rate?
Answers
Answer: The annual interest rate is $70.9125.
Step-by-step explanation: To get the interest rate after 4 years, subtract 2700 from 2983.65. The answer to that is $283.65.
To get the ANNUAL interest rate, divide $283.65 by 4.
The answer to that is $70.9125.
Therefore, your answer is $70.9125.
Hope this helped :D
Determine the derivative with quotient rule and find the equation of the tangent to f(x) at x=0
Answers
ANSWER
\(\text{ The derivative of the function is; }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ -2x}^2\text{ + 2}}{\text{ \lparen x}^2\text{ + 1\rparen}^2}\)EXPLANATION
Given that;
\(\text{ f\lparen x\rparen = }\frac{\text{ 2x}}{\text{ x}^2\text{ + 1}}\)Let U(x) = 2x and V(x) = x^2 + 1
Apply the quotient rule to find the derivative of f(x)
\(\text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ V}\frac{\text{ dU}}{\text{ dx}}\text{ - U }\frac{dv}{\text{ dx}}}{\text{ V}^2}\)Differentiate U and V with respect to x
\(\begin{gathered} \text{ U\lparen x\rparen = 2x} \\ \text{ }\frac{\text{ du}}{\text{ dx}}\text{ = 2} \\ \\ \\ \text{ V\lparen x\rparen= x}^2\text{ + 1} \\ \text{ }\frac{dv}{\text{ dx}}\text{ = 2x} \end{gathered}\)Hence, we have
\(\begin{gathered} \text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{(x^2\text{ + 1\rparen}\times2\text{ - 2x\lparen2x\rparen}}{(x^2\text{ + 1\rparen}^2} \\ \\ \text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ 2x}^2\text{ + 2 - 4x}^2}{(x^2\text{ + 1\rparen}^2} \\ \\ \text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ -2x}^2\text{ + 2}}{\text{ \lparen x}^2\text{ + 1\rparen}^2} \end{gathered}\)Find the center of a circle whose end points of a diameter are A (-5,6) and B (3,4)
pls answer fast
Answers
Answer:
(-1, 5)
Step-by-step explanation:
The center of a circle is the midpoint of the diameter.
So we have to calculate the midpoint of the diameter, using this formula:
midpoint = ( \(\frac{x_{2 }+x_{1} }{2}\) , \(\frac{y_{2} + y_{1} }{2}\) )
= (\(\frac{3 + (-5)}{2}\) , \(\frac{4 + 6}{2}\) )
= (-1, 5)
∴ The center of the circle lies at the point (-1, 5).
Exercise 10
You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. What is the probability of the compound event? Write your answer as a fraction or percent rounded to the nearest tenth.
Answers
The probability of choosing a 5 and then a 6 is 1/49
Finding the probability of the compound eventFrom the question, we have the following parameters that can be used in our computation:
The tiles
Where we have
Total = 7
The probability of choosing a 5 and then a 6 is
P = P(5) * P(6)
So, we have
P = 1/7 * 1/7
Evaluate
P = 1/49
Hence, the probability of choosing a 5 and then a 6 is 1/49
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Question
You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6
when constructing a confidence interval for a population proportion, we check that the sample size is less than 10% of the population size.why is it necessary to check this condition?
Answers
The condition that the sample size should be less than 10% of the population size is important when constructing a confidence interval for a population proportion.
Suppose the sample size is too large relative to the population size. In that case, the sample may not be truly random as it could become biased towards certain groups or characteristics within the population. Additionally, the normal approximation may not hold for the sample proportion, which could lead to inaccurate confidence intervals.
By ensuring that the sample size is less than 10% of the population size, we can assume that the sample was drawn randomly from the population and that the normal approximation is appropriate. This allows us to use the standard normal distribution to construct the confidence interval for the population proportion.
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What is the difference between quadratic equations and equations?
Answers
Answer:
A quadratic function is a function of a single variable x, with a value y determined by a formula of the form:
y = ax^2 + bx + c, where a, b and c are constants.
On the other hand, an equation is a mathematical statement saying that something is equal to something else. In particular, a quadratic equation is a an equation that says that a quadratic function has a particular value. If that value is a constant, then a quadratic equation can be expressed in the form ax^2 + bx + c = 0. There are normally two values of x that solve this equation. Sometimes there is only one (i.e. the two solutions are equal).
def:This is what we call the money you get back when you pay for something.
term:
Answers
Answer:
Change
Step-by-step explanation:
I call what I get back in return, change. The money we get back if you pay extra for something you buy.
Hope this helps!
a prism and a pyramid have congruent bases and equal heights the volume of the prisms is twice the volume of the pyramid'
Answers
To find the relationship between the volume of a prism and a pyramid with congruent bases and equal heights, we need to consider their formulas.
The volume of a pyramid is given by the formula V = (1/3)Bh,
where B represents the area of the base and h represents the height. Since the bases of the prism and pyramid are congruent and their heights are equal, we can write the equation:
Volume of Prism = 2 × Volume of Pyramid Using the formulas mentioned earlier, we can substitute the expressions for the volumes:
Bh = 2 × (1/3)Bh
Simplifying this equation, we can cancel out the B's:
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The statement "a prism and a pyramid have congruent bases and equal heights, and the volume of the prism is twice the volume of the pyramid" is FALSE.
To understand why, let's consider a simple example. Imagine we have a triangular prism and a triangular pyramid with congruent bases and equal heights. The base of both shapes is a triangle, and their heights are the same.
The volume of a prism can be calculated by multiplying the area of its base by its height. Similarly, the volume of a pyramid can be calculated by multiplying the area of its base by one-third of its height.
Since the prism and the pyramid have congruent bases and equal heights, the only difference in the volume calculation is the factor of 1/3 for the pyramid.
This means that the volume of the pyramid is one-third the volume of the prism, not half. Therefore, the statement that the volume of the prism is twice the volume of the pyramid is false.
Therefore, the statement is incorrect, and the volume of the prism is not twice the volume of the pyramid, but rather three times as much.
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Abama Math-5th Grade 1. James is starting a new business in Sitka, AK. He will need to fly from his home in Montgomery to Sitka and back 15 times in the next year. The trip is 2,856 miles one-way. How many miles will James be flying in the next year? (multiplication) Megan's aquarium measuron miles
Answers
James will be flying a total of 85,680 miles in the next year.
To find out how many miles James will be flying in the next year, we need to multiply the distance of one round trip by the number of round trips he will make in a year.
The distance of one round trip is twice the one-way distance, so:
2 x 2,856 miles = 5,712 miles per round trip
Since James will make 15 round trips in a year, we can multiply the distance of one round trip by 15:
5,712 miles/round trip x 15 round trips = 85,680 miles
Therefore, James will be flying a total of 85,680 miles in the next year.
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What is the solution set for this inequality?
20 + x < 64
Answers
Answer:
x<44
Steps:
Step 1: Simplify both sides of the inequality.
x+20<64
Step 2: Subtract 20 from both sides.
x+20−20<64−20
x<44
Answer:
x<44?
Step-by-step explanation:
I'm new to this and I dont really understand this
Answers
Answer:
So starting off with 1a f(4)
We simply substitute x with 4 for the function
f(4)=2(4)-5
f(4)=8-5
f(4)=3
Next 1b, here it's a little different since you have to multiply the functions I think ( please correct me if I'm wrong).
gf(4), basically means functions g and f are being multiplied and their variables are being substituted with 4.
g(4)=4^2+3
g(4)=16+3
g(4)=19
and we also know from before that f(4)=3, so we'll do 19 times 3 which is 57
For the next two, I may be wrong, but I'm still going to try:
anything to the power of a negative is a fraction so for f^-1(x)=2x-5 we'll have 1/f(x)=x/2+5/2
And then for g^-1, we'll have 1/g(x)=\(\sqrt{x-3} \sqrt{x-3}\)
Hope I helped :)
Expand.
Your answer should be a polynomial in standard form.
(7g+2)(5g+4)=
Answers
Answer:
35g^2 +38g +8
Step-by-step explanation:
3| -8x | +8 = 80
helpp
Answers
Answer:
x=8.625
Step-by-step explanation:
ok so the lines mean absolute value so its actuall positive soyou get 3+8x+8=80
so add 3 and 8 to get 11+8x=80
subtract 11 to get 8x=69
then divide it by 8 so x is by itself
x=8.625 hope this helped :)
Answer:
x = 3 , x = -3
Step-by-step explanation:
3 | -8x | + 8 = 80
3 | -8x | = 72
Solve the negative and positive case:
Negative-
-3 ( -8x ) = 72
24x = 72
x = 3
Positive-
3 (-8x ) = 72
-24 = 72
-x = 3
x = -3
A computer processes information in nanoseconds. A nanosecond is one-billionth of a second. Write this number as a decimal.
Answers
Answer:
0.000000001
Step-by-step explanation:
Let's convert this :
0.000000001
tHT M B
t=tenths
H=Hundredths
T=Thousandths
M=millionths
B=Billionths
Solve and show your work.
The garden has 3 times as
many cabbages as carrots. If
there are 36 cabbages, how
many carrots are there? [easy points]
Answers
Answer:
12 carrots
Step-by-step explanation:
If there is 3 times as much cabbages as there is carrots, and there is 36 cabbages then you would do 36/3 because of the 3 times as much. The answer would be 12 carrots.
36/3=12
the square of 1/4 equal the square root of
Answers
Answer:
\(\frac{1}{256}\)
Step-by-step explanation:
(¼)²=√x
√x=1/16
x=(1/16)²
x= 1/256
Roseann is spending money at the average rate of Php 75 per day. After 10 days, she has Php 50 left. The amount left depends on the number of days that have passed.
Answers
Answer: She started with 800, since 75 x 10 is 750 and she was left with 50 simply add 750 + 50 = 800
how many solutions are there to the equation 7x+12=5x-8
Answers
I need some help with this
Answers
825317
Write the equation of the line in fully simplified slope-intercept form.
11
1998 6543 N
10
2
1
-12-11-10-9-8-7-6-5-4-3-2-11
~
-2
3
-4
-6
-9
-10
-11
-12
1 2 3 4 5 6 7 8 9 10 11 12
Answers
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
Need quick help with this math
Answers
Answer:
Eleanor and Harold
Step-by-step explanation:
The decimal \(0.13\overline{7}\) consists of the sum of two terminating decimals and one non-terminating decimal:
\(0.13\overline{7}=0.1+0.03+0.00\overline{7}\)
Therefore, we have:
\(0.13\overline{7}=\frac{1}{10}+\frac{3}{100}+\frac{7}{900},\\\\0.13\overline{7}=\frac{10}{100}+\frac{3}{100}+\frac{7}{900},\\\\0.13\overline{7}=\frac{13}{100}+\frac{7}{900}=\frac{117}{900}+\frac{7}{900}=\boxed{\frac{124}{900}}\)
Hector's answer is equivalent but not simplified. However, they are both technically correct.
Frank is going to plant d vegetable seeds in one garden and 4d + 4 vegetable seeds in another.
How many seeds is Frank going to plant?
Frank is going to plant seeds.
(Simplify your answer.)
Answers
Answer:
5d+4
Step-by-step explanation:
\(Total = d + (4d + 4)\\Total = 5d + 4\)
Hope it helps ;P
Determine the force in members gf, fc, and cd of the bridge truss using method of sections. state if the members are in tension of compression. assume all members are pin connected 15 ft 30 ft 40 ft-40 ft40 ft40 ft 10 k 15 k
Answers
While fc is in compression, members gf and cd are in average tension. Gf has a force of 10k, fc of 15k, and cd of 5k.
The method of sections can be used to calculate the force in members gf, fc, and cd of the bridge truss. While members fc and cd are in compression, member gf is in tension. In comparison to fc's 15k and cd's 5k, the force in gf is 10k. By assuming that the total sum of the forces in each part is equal to zero, this may be ascertained. The force on gf is 10k and the force on fc is 15k for the left section, the middle section has a 15k fc and a 5k cd force, and the right section has a 5k cd force. The dimensions of each member—15 feet, 30 feet, 40 feet, 40 feet, and 40 feet—are considered to be pin linked.
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a car is driving at 55 kilometers per hour. how far, in meters, does it travel in 3 seconds? myopenmath
Answers
The car travels 45.84 meters in 3 seconds.
To solve this problem, we need to convert the speed of the car from kilometers per hour to meters per second since the time given is in seconds.
To do this, we can use the conversion factor that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.
So, 55 kilometers per hour is equal to (55 x 1000) / 3600 = 15.28 meters per second.
Now, we can use the formula: distance = speed x time
Plugging in the values, we get distance = 15.28 meters per second x 3 seconds = 45.84 meters.
Therefore, the car travels 45.84 meters in 3 seconds.
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Tina bikes 3 miles
Mark bikes 3 times as far as Tina
Kai bikes 3 times as far as Mark
What exponential expression represents the distance Kai bikes?
A. (3)4miles
B. (2)3 miles
C. (3)3 miles
D. (3)2 miles
Answers
Answer:
\(c. \: {3}^{3} \)
Step-by-step explanation:
\( {3}^{3} \)
please help please
use the distributive property to solve the equation
28 - (3x+4) = 2(x+6) + x
and
use the distributive property to solve the equation
3(x-6) + 6 = 5x - 6
PLEASE SHOW STEPS
THANK YOU
Answers
Answer:
1. x = 2
2. x = -3
Step-by-step explanation:
1.
28 - (3x + 4) = 2(x + 6) + x
28 - 3x - 4 = 2x + 12 = x
24 - 3x = 3x + 12
-3x -3x
-------------------------
24 - 6x = 12
-24 -24
---------------------
-6x = -12
÷-6 ÷-6
---------------
x = 2
----------------------------------------------------------------------------------------------------------
2.
3(x - 6) + 6 = 5x - 6
3x - 18 + 6 = 5x - 6
3x - 12 = 5x - 6
-5x -5x
--------------------------
-2x - 12 = -6
+12 +12
----------------------
-2x = 6
÷-2 ÷-2
--------------
x = -3
I hope this helps!
-84+112=2x+12+x
28=3x+12
28-12=3x
16=3x
16/3=x
5.3=x
It is possible to compute the theoretical density of a crystalline ceramic material using following equation, which of the statements for the equation is incorrect. p=π'(Σ Αc+Σ Α.) /VcNA (a) n' is the total number of atoms within the unit cell (b) Σ Ac is the sum of the atomic weights of all cations in the formula unit (c) Vc is the unit cell volume
Answers
The statement which is incorrect for the equation: \(p = \pi' \left( \sum_{c=1}^{n_c} A_c + \sum_{a=1}^{n_a} A_a \right) / (V_c N_A)\) is (a) n' is the total number of atoms within the unit cell.
What is the formula to compute the theoretical density of a crystalline ceramic material?
The formula used to compute the theoretical density of a crystalline ceramic material is:
\(p = \pi' \left( \sum_{c=1}^{n_c} A_c + \sum_{a=1}^{n_a} A_a \right) / (V_c N_A)\)
Where
p is the theoretical density
π' is a constant equal to 1.38
Σ Ac is the sum of the atomic weights of all cations in the formula unit
Σ A is the sum of the atomic weights of all anions in the formula unit
Vc is the unit cell volume n' is the total number of atoms within the unit cell
NA is Avogadro's number So, the answer is option a. (a) n' is the total number of atoms within the unit cell.
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