By setting up a system of equations, we find that the larger and smaller numbers in question are 31 and 12, respectively. We solve for the larger number first and then use it to find the smaller number.
Explanation:To solve this problem, we can use variables to represent the two unknown numbers. Let's call the larger number x and the smaller number y. We have two pieces of information that can be turned into mathematical equations:
Now we can substitute the second equation into the first one to solve for x:
x + (x - 19) = 43
Simplifying the equation, we get:
2x - 19 = 43
Adding 19 to both sides gives us:
2x = 62
Dividing both sides by 2 gives us:
x = 31
Now that we have the value of x, we can find y:
y = 31 - 19
This gives us:
y = 12
Therefore, the larger number is 31 and the smaller number is 12.
In professor shannon's economics class there are 12 male students. females represent 60% of the class total. how many students does professor shannon have in his economics class?
Answer:
There are total 30 students in the class.
Step-by-step explanation:
Let the total number of students in class = x
Number of males in the class = 12
Number of females in the class = 60% of Total students = 60% of x = 0.6x
So, we get that,
Number of males + Number of females = Total students
i.e. [tex]12+0.6x=x[/tex]
i.e. [tex]12=x-0.6x[/tex]
i.e. [tex]12=0.4x[/tex]
i.e. [tex]x=\frac{12}{0.4}[/tex]
i.e. x = 30
Thus, there are total 30 students in the class.
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
Compare 7 x 103 and 2 x 103.
A) 7 x 103 is 3.5 times larger than 2 x 103
B) 7 x 103 is twice as large as 2 x 103
C) 7 x 103 is 3 times larger than 2 x 103
D) 7 x 103 is 5 times larger than 2 x 103
The expression 7 x 10³ is 3.5 times larger than 2 x 10³ because the power of 10 is the same in both, so we simply compare the coefficients 7 and 2.
Explanation:The student is asking to compare two expressions written in scientific notation: 7 x 10³ and 2 x 10³. Scientific notation allows us to write very large or very small numbers conveniently and is commonly taught in middle school math.
To compare these two expressions, we can look at the coefficients (7 and 2) because the powers of 10 are the same in both expressions (10³). Since these powers are the same, comparing the coefficients directly will give us the relationship between the two expressions. Here, 7 is simply 3.5 times as large as 2, so we can say that 7 x 10³ is 3.5 times larger than 2 x 10³.
In terms of the answer choices provided by the student, we can thus conclude that the correct answer is:
A) 7 x 10³ is 3.5 times larger than 2 x 10³1/2 (4-k)=2/5
Distribute and find LCM
Answer:
20 -5k = 4the LCM of the denominators is 10Step-by-step explanation:
I find it convenient to do the problem in the reverse order: find the LCM, then distribute. That way, I'm not distributing a fraction.
The LCM of 2 and 5 is their product: 2·5 = 10. Multiplying the equation by 10 gives ...
5(4 -k) = 4
Now, distributing, we get ...
20 -5k = 4
What is the slope of the function
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
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.
Find the range of the following list of numbereally -9, 17, -12, 15, 8, 0,16,
The Tigers won twice as many football games as they lost. They played 96 games. How many games did they win?
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.
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.
WILL GIVE A BRAINLEST AND 20PTS
A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Answer:- R(0, 360°) is the right answer.
Given: A parallelogram is transformed according to the rule (x, y) → (x, y).
⇒The points of the image is same as the points of the original figure.
⇒ The given mapping create an image onto itself.
We know that the mapping of all points of a figure in a plane is done by basic rigid transformations such as translation, reflection or rotation.
In rotation to create a image that is onto itself , then the rotation must be about 360°, so that the rotation will take a complete turn to get back the original figure with the same points.
Thus in rotation the another way to state the transformation is R(0, 360°).
Jason draws a line in the sand at the beach the line is 7/8 feet long he wants to divide the line into sections that are 1 8 feet long how many sections with a line be divided into?
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
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
Find the equation of a cosine curve that is obtained by shifting the graph of y=cos(x) to the left 5 units and upward 9 units and vertically compressed by a factor of 4 and vertically flipped
We want to find the equation of a cosine function after we apply some given transformations to it.
The equation of the resulting cosine curve is:
g(x) = -(1/4)*cos(x + 5) - 9/4.
Let's see how we got that equation:
First, we need to define all the transformations that we will be using:
Vertical shift:
For a given function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N.
If N is positive the shift is upwards.IF N is negative the shift is downwards.Horizontal shift:
For a given function f(x) a horizontal shift is written as:
g(x) = f(x + N).
If N is positive the shift is towards the left.If N is negative the shift is towards the right.Vertical compression.
For a function f(x) a vertical compression by a factor k is written as:
g(x) = (1/k)*f(x).
Vertical flip (or vertical reflection).
For a general function f(x) a vertical reflection is written as:
g(x) = -f(x).
So we start with:
f(x) = cos(x).
First we shift it to the left 5 units, so we get:
g(x) = f(x + 5)
Then we shift it up 9 units, then we get:
g(x) = f(x + 5) + 9
Then we compress it vertically by a factor of 4:
g(x) = (1/4)*(f(x + 5) + 9)
Then we flip it vertically:
g(x) = -(1/4)*(f(x + 5) + 9)
Replacing f by the cosine function we get:
g(x) = -(1/4)*( cos(x + 5) + 9)
g(x) = -(1/4)*cos(x + 5) - 9/4.
This is the equation of the resulting cosine curve.
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Which of the following shows 12⁄28 written in prime factored form to help in reducing the fraction to simplest form? A. 7×2×2⁄3×2×2 B. 3⁄7 C. 3×2×2⁄7×2×2 D. 6×2 ⁄7×4
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.
2 divided by 880 = ?
Two consecutive numbers whose square differ by 25
To get to a dog show, Mr. Luna first drives 7 miles west from his home and then 3 miles north. Next, he turns east and drives 11 miles. Finally, he turns north and drives 4 miles to the dog show. How far north of Mr. Luna's home is the dog show?
Answer:
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.
If X and Y vary directly, as x decreases, what happens to the value of y?
what is 31 billion in scientific notation
we know that
[tex] 1 billion=1,000,000,000 [/tex]
In scientific notation
[tex] 1,000,000,000=1*10^{9} [/tex]
To find the value of [tex] 31 billion [/tex]
Multiply the value of one billion for [tex] 31 [/tex]
so
[tex] 31*1*10^{9} =31*10^{9}\\ =3.1*10^{10} [/tex]
therefore
the answer is
[tex] 3.1*10^{10} [/tex]
The scientific notation of [tex]31 \text{billion}[/tex] is [tex]\boxed{3.1 \times \left( {{{10}^{10}}} \right)}[/tex].
Further explanation:
Scientific notation is also called as the standard form of writing a number.
The number has two parts in the scientific notation.
First part is digits or digit with decimal and the second part is 10 to the power.
If the number is greater than 10, move the decimal point to the left.
If the number is less than 10, move the decimal point to the right.
Calculation:
One billion is equal to [tex]1000000000[/tex].
In scientific notation one million can be expressed as,
[tex]\boxed{{\text{1}}\,{\text{billion}} = {10^9}}[/tex]
Thirty one billion is equal to [tex]31000000000[/tex].
Now find the scientific notation SN of 31 billion.
[tex]\begin{aligned}\text{SN} &= 31000000000 \\&= 31 \times \left( {{{10}^9}} \right) \\&= 3.1 \times \left( {{{10}^{10}}} \right) \\ \end{aligned}[/tex]
The first part of the scientific notation is [tex]\boxed{3.1}[/tex].
The second part of the scientific notation is [tex]\boxed{{10^{10}}}[/tex].
Hence, the scientific notation of [tex]31 \text{billion}[/tex] is [tex]\boxed{3.1 \times \left( {{{10}^{10}}} \right)}[/tex].
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Scientific notation
Keywords: scientific notation, one billion, thirty one billion, million, standard form, first part of scientific notation, second part of scientific notation, power.
What is the remainder when 1,095 is divided by 7?
A) 3
B) 4
C) 5
D) 6
What is the zero r(x)=3/8x-16 ?
What is the side length of a cube that has a volume of 24 cm 3?
17.50 with a 7% sales tax?
To find the total cost of an item with sales tax, convert the tax rate to a decimal, multiply by the item's price, add the result to the original price, and round to the nearest cent. A $17.50 item with a 7% sales tax would cost a total of $18.73 after tax.
To calculate the total cost of an item with sales tax, you first need to determine the amount of sales tax by converting the percentage to a decimal and then multiplying by the item's cost. For an item priced at $17.50 with a 7% sales tax, you would convert 7% to a decimal (0.07) and then multiply this by $17.50. Therefore, the calculation would be:
Sales Tax = $17.50 x 0.07 = $1.225
Once you have the sales tax amount, you add it to the original price to find the total cost:
Total Cost = Original Price + Sales Tax
$17.50 + $1.225 = $18.725. After rounding to the nearest cent, the total cost would be $18.73.
Is 4/25 greater than 0.28