If X and Y vary directly, as x decreases, what happens to the value of y?
Find the range of the following list of numbereally -9, 17, -12, 15, 8, 0,16,
Write an application to simulate the rolling of two dice. the application should use an object of class random once to roll the first die and again to roll the second die. the
Final answer:
The answer explains how to create a Python application to simulate rolling two dice using the random module.
Explanation:
application
To simulate the rolling of two dice using an object of class random, you can create a Python application. Here's an example of how you can achieve this:
Import the random module.
Create a function to simulate rolling a die.
Call the function twice to simulate rolling two dice.
Does anybody know a rule that will work for all of these?
y = something x plus or minus a number
going through each line it isn't a linear pattern ( they don't all have the same difference when subtracted or added together)
so now you play around with quadratic equations ( square roots, powers, etc.)
and you will see that y = x^2 -5
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.
The requried fraction of the bouquet that is pink roses is 7/12, as of the given proportion.
If Angelica's bouquet of a dozen roses contains 5 white roses, then the remaining roses must be pink. Since there are 12 roses in a dozen, the number of pink roses in the bouquet would be 12 - 5 = 7.
To find the fraction of the bouquet that is pink roses, we divide the number of pink roses by the total number of roses:
Fraction of pink roses = Number of pink roses / Total number of roses
Fraction of pink roses = 7 / 12
Therefore, the fraction of the bouquet that is pink roses is 7/12.
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What is the answer to 2/7 x 4 4/9
Find the time required for $5000 to be equal to $14,000 when deposited at 7% compounded monthly
In the circle graph above, you can see that 47% of the company's monthly income is used to pay the owner's personal salary. If the amount of the owners's personal salary was $2,176.10 this month, what was the company's total monthly income this month?
Final answer:
To find the total monthly income, set up a proportion using the percentage of the owner's salary with the given amount. Solve for the total income to find the answer.
Explanation:
In the circle graph above, the owner's personal salary represents 47% of the company's monthly income. This means that $2,176.10 is 47% of the total monthly income. To find the total income, you can set up a proportion: $2,176.10 is to 47% as X is to 100%. Solving this equation gives you the company's total monthly income as $4,635.
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Jasmine earns $36 for 4 hours of baby-sitting. She charges a constant hourly rate. Which table correctly shows the amount Jasmine earns baby-sitting for different numbers of hours?
Answer:
A
Step-by-step explanation:
A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x) = x + 30. How will the graph of this function change if the coal car weight is changed to 26 tons? The line will shift vertically up by 4 tons. The line will shift vertically up 26 tons. The line will shift vertically down by 4 tons. The line will shift vertically down by 26 tons.
The line will shift vertically down by 4 tons.
What is the slope of the function
Two consecutive numbers whose square differ by 25
Ben earns $1500 each summer and puts the money in a savings account with a 6% simple interest rate. If he deposits the same amount each year, how much money will he have at the end of his third summer
$4770
$3250
$3175
$2850
find the measure of <ghk <hki and <hkj show your work or wite and explanation
The function g(x) = –x2 + 16x – 44 written in vertex form is g(x) = –(x – 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –x2 + 16x – 44?
Answer:
the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)
Step-by-step explanation:
The function [tex]g(x) = -x^2 + 16x - 44[/tex] written in vertex form is [tex]g(x) = -(x - 8)^2 + 20[/tex]
The parent function is f(x)=x^2
Now we compare parent function f(x) and g(x)
In g(x), negative sign at first
f(x) ----> -f(x) , the graph is reflected across x axis
f(x)-----> f(x-h), the graph will be transformed h units to right
f(x)----> f(x) +k , the graph will be transformed k units up
[tex] g(x) = -(x - 8)^2 + 20[/tex], the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)
Which expression is equivalent to (5x^3)(2x)^3?
A. 10x^6
B. 30x^6
C. 40x^6
D. 1000x^12
What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16
Answer:
y = 8Step-by-step explanation:
[tex]Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================[/tex]
[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}[/tex]
[tex]\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}[/tex]
[tex]4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D[/tex]
Answer:
6
Step-by-step explanation:
The basal diameter of a sea anemone is an indicator of its age, and in a certain population of anemones, the distribution of basal diameters is approximately normal with a mean of 5.3 cm and a standard deviation of 1.8 cm. suppose you randomly select five anemones from this population.
a. what is the probability that all five anemones have a basal diameter more than 5.5 cm? (2pt)
The probability that all five randomly selected sea anemones from a population with normally distributed basal diameters have a diameter more than 5.5 cm is approximately 4.5%.
Explanation:To solve this problem, we first need to find the probability that one sea anemone has a basal diameter more than 5.5 cm, given the population's mean basal diameter is 5.3 cm with a standard deviation of 1.8 cm. We calculate the Z-score for a diameter of 5.5 cm to see how many standard deviations this value is away from the mean. The Z-score formula is Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation.
The Z-score for a diameter of 5.5 cm is Z = (5.5 - 5.3) / 1.8 ≈ 0.11. Looking this up in a standard normal distribution table, we find that the probability of selecting an anemone with a diameter larger than 5.5 cm is approximately 0.5438. Since the selections are independent, the probability of all five having a diameter more than 5.5 cm is (0.5438)⁵ ≈ 0.045, or 4.5%.
The probability that all five randomly selected anemones have a basal diameter more than 5.5 cm is approximately 0.0056.
To solve this problem, we can use the standard normal distribution. First, we need to standardize the diameter value using the z-score formula:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
where:
- x is the value of the basal diameter,
- [tex]\mu[/tex] is the mean of the basal diameters (5.3 cm),
- [tex]\sigma[/tex] is the standard deviation of the basal diameters (1.8 cm), and
- z is the standardized score.
For a basal diameter of 5.5 cm, the z-score would be:
[tex]z = \frac{5.5 - 5.3}{1.8} = \frac{0.2}{1.8} \approx 0.1111[/tex]
To find the probability that an anemone has a basal diameter more than 5.5 cm, we need to find the area to the right of z = 0.1111 under the standard normal curve.
Using a standard normal table or calculator, we find that this area is approximately 0.4562.
Since each selection is independent (assuming replacement), the probability that all five anemones have a basal diameter more than 5.5 cm is the probability raised to the power of 5:
[tex]P(\text{all five} > \text{ 5.5 cm}) = (0.4562)^5 \approx 0.0056[/tex]
So, the probability that all five randomly selected anemones have a basal diameter more than 5.5 cm is approximately 0.0056.
you drink one fourth of a pitcher of Kool-Aid your friend drinks 7/12 of the pitcher what fraction of the pitcher do you and your friend drink
Consider the equation log (3x-1)=log base 2 of 8. Describe the steps you would take to solve the equation, and state what 3x-1 is equal to.
The bases are not the same, so you cannot set 3x - 1 equal to 8.
You can evaluate the logarithm on the right side of the equation to get 3.
You can use the definition of a logarithm to write 3x - 1 = 1000.
Answer: The solution of the given equation is [tex]x=333\dfrac{2}{3}[/tex] and the value of (3x - 1) is 1000.
Step-by-step explanation: We are given to describe the steps in solving the following logarithmic equation:
[tex]\log(3x-1)=\log_28.[/tex]
Also, we are to find the value of [tex](3x-1).[/tex]
We will be using the following logarithmic properties:
[tex](i)~\log_ba=x~~~\Rightarrow a=b^x,\\\\(ii)~\log_ba=\dfrac{\log a}{\log b},\\\\(iii)~\log a^b=b\log a.[/tex]
We note here that if the base of logarithm is not mentioned, then we assume it to be 10.
The solution is as follows:
[tex]\log(3x-1)=\log_28\\\\\Rightarrow \log(3x-1)=\dfrac{\log8}{\log2}\\\\\Rightarrow log(3x-1)=\dfrac{\log2^3}{\log2}\\\\\Rightarrow \log(3x-1)=\dfrac{3\log2}{\log2}\\\\\Rightarrow \log(3x-1)=3\\\\\Rightarrow 3x-1=10^3\\\\\Rightarrow 3x-1=1000\\\\\Rightarrow 3x=1001\\\\\Rightarrow x=\dfrac{1001}{3}\\\\\Rightarrow x=333\dfrac{2}{3}.[/tex]
Thus, the solution of the given equation is [tex]x=333\dfrac{2}{3}[/tex] and the value of (3x - 1) is 1000.
x+4, -x+64. Use the expressions that represent the length and width of the game board to write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y=ax²+bx+c, where a,b, and c are real numbers.
Jed took 2 free throws in 5 seconds. Alex took 4 free throws in 12 seconds did the two shoot free throws at the same rate? Explain
Jed and Alex do not shoot free throws at the same rate, Jed is faster by 0.5 seconds.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Jed took 2 free throws in 5 seconds.
∴ Jed can do 1 free throw in (5/2) = 2.5 seconds.
Alex took 4 free throws in 12 seconds.
∴ Alex can do 1 free throw in (12/4) = 3 seconds.
No, Jade and Alex do not shoot free throws at the same rate Jed is faster by 0.5 seconds.
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A chicken breast weighs 1.375 pounds on a digital scale. What is that same weight as a mixed number?
Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.
Which statements are true about the parallelograms? Check all that apply.
The length of side MN is 2 units.
The length of side M'N' is 5 units.
The image is smaller than the pre-image.
Sides MQ and M'Q' both have the same slope, 1.
The scale factor is 2/5
Answer:
Options 1,2 and 4 are correct.
Step-by-step explanation:
We have been given a parallelogram MNPQ was dilated to create parallelogram M'N'P'Q' and we asked to find out which of the given options are correct.
Let us see all the options one by one.
On using distance formula we can see that side MN is 2 units.
[tex]MN=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]
[tex]MN=\sqrt{(4-2)^{2} +(-2-(-2))^{2} }[/tex]
[tex]MN=\sqrt{(2)^{2} } =2[/tex]
Therefore,option 1 is correct.
We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.
Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.
Now look at our option 4.
Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.
Therefore, option 4 is correct indeed.
Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.
Therefore, our fifth option is false.
Considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.
How to find SlopeSlope = vertical distance / horizontal distance = change in y / change in x.
How to find Scale FactorScale factor = length of image/corresponding length of pre-image.
Find the length of MN:
MN = |4 - 2| = 2 units (Option A is true).
Find M'N':
M'N' = |10 - 5| = 5 units (Option B is true).
MNPQ is the pre-image, while M'N'P'Q' is the image, therefore, the image is bigger than the pre-image. (Option C is NOT true).
Find Slope of MQ:
Slope = 1/1 = 1
Find Slope of M'Q':
Slope = 2/2 = 1 (Option D is true).
Find the scale factor:
Scale factor = dimension of image/dimension of pre-image = M'N'/MN
Scale factor = 5/2 (Option E is NOT true).
Therefore, considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.
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The rectangular box shown in the figure has dimensions 9" × 5" × 3" (a = 9, b = 5, c = 3). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 5" × 3" side. (Round your answer to two decimal places.)
The simplest method to do this is with the vector dot
product. Let the vector A = <9i + 5j> with magnitude √106 be the base
diagonal, and B = <5j + 3k> be the diagonal vector on the side, with
magnitude √34. Then cos θ = (A dot B) divided by the product of the magnitudes.
A dot B =30, so
cos θ = 30 / √(34 x 106)
= 0.4997 ==>
θ = 49.19° is the answer
For any normal distribution, the probability of randomly selecting a z-score less than z = 1.40 is p = 0.9192.
a. True
b. False
VERY IMPORTANT
which series of transformations take the graph of f(x)=4x+9 to the graph of g(x)=-4x+7?
1. reflect the graph about the x axis and translate 2 units down?
2. reflect the graph about the y axis and translate 2 units up?
3. reflect the graph about the x axis and translate 2 units up?
4. reflect the graph about the y axis and translate 2 units down?
The correct transformation is to reflect the graph about the y-axis and then translate it 2 units down, corresponding to option 4.
The correct transformation is therefore to reflect the graph about the y-axis to change the slope from positive to negative and then translate 2 units down to change the y-intercept from +9 to +7. This corresponds to option 4 from the question.
Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A is 4% interest over 6 years. Plan B is 5% interest over 4 years. Using the formula mc024-1.jpg for payment, m, which statement best compares the plans?
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B
To determine which payment plan is better for borrowing $3,000, Plan A or Plan B, one must calculate both the monthly payments and total interest charges using the given annual interest rates and compounding periods for each plan and compare the results accordingly.
Peter wants to borrow $3,000 and is considering two different payment plans. To compare these plans, we need to calculate the monthly payment and total interest charge for each.
Plan A has an annual interest rate of 4%, compounded monthly over 6 years (or 72 months). Using the formula for monthly payment (m), we can find the monthly payment for Plan A:
m = P[r(1+r)^n] / [(1+r)^n-1]
Where:
Similarly, Plan B has an annual interest rate of 5%, compounded monthly over 4 years (or 48 months). We use the same formula to calculate the monthly payment for Plan B.
After calculating m for both plans, we can also calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal amount from the result for each plan. Then, we can compare the monthly payments and total interest charges between Plan A and Plan B.
Which linear system has a solution of
[tex]x = 2 \: and \: y = - 3[/tex]