To simplify the expression (3b^3)^4, raise the base to the fourth power and simplify the exponent.
Explanation:To simplify the expression (3b^3)^4, we need to raise the base, 3b^3, to the fourth power. This can be done by multiplying the exponents. The result is 3^4 * (b^3)^4, which simplifies to 81b^12.
Learn more about Simplifying expressions here:https://brainly.com/question/29003427
#SPJ2
2 divided by 880 = ?
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.
If you want to learn more, you can read:
https://brainly.com/question/13810353
A trial has markers every 1/8 mile. Jody starts at the 2 1/4-mile marker, hikes to the 4 3/8-mile marker, and then hikes back to the 1 1/2 mile marker. Did Jody hike more than 4 miles? Explain.
What is the remainder when 1,095 is divided by 7?
A) 3
B) 4
C) 5
D) 6
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.
Find the range of the following list of numbereally -9, 17, -12, 15, 8, 0,16,
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.
The Tigers won twice as many football games as they lost. They played 96 games. How many games did they win?
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?
Kersha has two jobs. During the day she works as an office clerk, and in the evening she works as a cashier. Her office job pays her $12.00 per hour. Her cashier job pays her $8.25 per hour. In one week, Kersha worked 55 hours. She earned a total of $585.
How many hours did Kersha work in each job?
a.) Office clerk: 35 hours; cashier: 20 hours
b.) Office clerk: 31 hours; cashier: 24 hours
c.) Office clerk: 20 hours; cashier: 35 hours
d.) Office clerk: 28 hours; cashier: 27 hours
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
(choices in picture)
Answer:
Yep the answer is −3x+y=−7
Step-by-step explanation:
Find the time required for $5000 to be equal to $14,000 when deposited at 7% compounded monthly
Is 4/25 greater than 0.28
Worth 37 points answer asap
this is a college question
a farmer is given 500 ft of fencing. He will be constructing a rectangular coral to keep pigs and sheep, however he wants to keep them separate so there will be a wall of fence in the middle of the coral as well (the dividing wall will be parallel to 2 of the sides). What are the dimensions of the coral that will maximize the area, and what is the area?
hi therrre you are an awesome person
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°).
What is the zero r(x)=3/8x-16 ?
Ingrid collected 6 cans of food and 18 boxes of food for the food bank. Which describes the relationship between cans of food and boxes of food?
The relationship between the cans of food and boxes of food that Ingrid collected can be determined by the mathematical equations involving addition/subtraction and multiplication/division.
For addition/subtraction:
D = x – y
Where D is difference, x is the number of cans of food, and y is the boxes. Substituting the known values,
D = 6 – 8 = -2
For multiplication/division:
R = x/y
Where R is the ratio. Substituting the known
values,
R = 6/8 = ¾ = 0.75
The relationship between the number of cans of food and boxes of food collected by Ingrid is a ratio of 1 can to 3 boxes after simplification. This means there is 1 can for every 3 boxes.
Ingrid collected 6 cans of food and 18 boxes of food for the food bank. To describe the relationship between cans of food and boxes of food, we can use a mathematical ratio.
The ratio of cans to boxes is calculated by dividing the number of cans by the number of boxes. This gives us:
6 cans : 18 boxes
To simplify this ratio, we divide both numbers by their greatest common divisor, which is 6:
6 ÷ 6 = 1
18 ÷ 6 = 3
Therefore, the simplified ratio is:
1 can : 3 boxes
This means there is 1 can of food for every 3 boxes of food. This ratio helps us understand the proportional relationship between the two quantities.
Which expression is equivalent to ? m-4/m+4 / (m+2)
Answer:
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
Step-by-step explanation:
Given Parameters;
(m-4)/(m+4) and (m+2)
Required:
To divide and write out the equivalent expression.
Two or more expressions are said to equivalent if and only if they give the same result.
Solving (m-4)/(m+4) divided by (m+2)
We have
[tex]\frac{m - 4}{m + 4}[/tex] divided by [tex]m + 2[/tex]
[tex]= \frac{m - 4}{m + 4} / (m + 2)[/tex]
Convert division to multiplication
[tex]= \frac{m - 4}{m + 4} *\frac{1}{(m + 2)}[/tex]
= [tex]\frac{(m - 4) * 1}{(m + 4) * (m + 2)}[/tex]
[tex]= \frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
We can't simplify any further;
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
To check if this is true
Let m = 1
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] becomes
[tex]\frac{1 - 4}{1 + 4} / (1 + 2)[/tex]
[tex]\frac{-3}{5} / (3)[/tex]
[tex]\frac{-3}{5} * \frac{1}{3}[/tex]
[tex]\frac{-1}{5}[/tex]
And
[tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex] becomes
[tex]\frac{(1 - 4)}{(1 + 4)(1 + 2)}[/tex]
[tex]\frac{(-3)}{(5)(3)}[/tex]
[tex]\frac{-1}{5}[/tex]
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
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
A box of crayons costs $1.75, including tax. Mr. Valentino wants to purchase boxes of crayons for his class and has a $25 budget. Write an inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget
a.$1.75x ≤ $25
b.$1.75x ≥ $25
c.$25x ≤ $1.75
d.$25x ≥ $1.75
it is multiple choice
The correct inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget is $1.75x ≥ $25.
Explanation:The correct inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget of $25 is b. $1.75x ≥ $25.
This inequality states that the product of the cost per box, $1.75, and the number of boxes, x, must be greater than or equal to $25 to remain within his budget.
You can solve this inequality by dividing both sides by $1.75 to find the minimum number of boxes he can buy and still stay within his budget.
Learn more about Solving Inequalities here:https://brainly.com/question/26855203
#SPJ2
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
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].
Learn more:
1. Learn more about slope intercept form https://brainly.com/question/1473992
2. Learn more about unit period https://brainly.com/question/558692
3. Learn more about unit conversions https://brainly.com/question/4837736
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.
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:
1/2 (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
The price of an item selling at 150% of its $63 value is
Answer:
94.50
Step-by-step explanation:
i used a calculator
The equations for two lines in the coordinate plane are 2dx - y = -4 and 4x - y = -6, where d represents an unknown value. What value(s) of d would make these lines perpendicular?
The value of d that makes the lines 2dx - y = -4 and 4x - y = -6 perpendicular is -1/8, as this value makes the product of their slopes equal to -1.
Explanation:To determine which value(s) of d would make the two lines perpendicular, we have to evaluate the slopes of the two lines and set their product to be -1, since perpendicular lines have slopes that are negative reciprocals of each other. Rearranging the first equation, 2dx - y = -4, we get y = 2dx + 4, which has a slope of 2d. For the second equation, 4x - y = -6, rearranging gives y = 4x + 6, with a slope of 4.
The product of the slopes of two perpendicular lines should be -1, so:
(2d) * 4 = -1
Solving for d: d = -1/8.
Thus, when the value of d is -1/8, the two lines are perpendicular.
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 10³VERY 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.
if 5 doses of medicine weigh 29.925 grams, how much would 1 dose weigh?
What is the side length of a cube that has a volume of 24 cm 3?