Write an expression to show the sum of fourteen and triple eight.
Find the nth term of the sequence
-3, 0, 5, 12
Work out the reciprocal of 2 x 10(9,as a power). Give your answer in standard form.
A chef has less than 25.8 pounds of rice. She takes out 5 pounds to use during the day and stores the rest in containers. Each container has 2.5 pounds of rice. Let x represent the number of containers. What is the maximum number of containers the chef will be able to fill with rice? 13 12 8 7
The chef has less than 25.8 pounds of rice.
She takes out 5 pounds to use during the day and stores the rest in containers.
Quantity of rice stored = 25.8 - 5 = 20.8 pounds
Each container can store 2.5 pounds of rice.
Let x represent the number of containers.
The number of containers that can be filled = 20.8/2.5 = 8.32
So, the maximum number of containers the chef will be able to fill with rice is 8
what Is the product? 4n/4n-4*n-1/n+1
Answer:
n/(n+1) . . . . n ≠ 1
Step-by-step explanation:
As written, there is no product. There is ony the sum ...
[tex]4\dfrac{n}{4}-4n-\dfrac{1}{n}+1[/tex]
With appropriate parentheses, this becomes the product of rational functions ...
... (4n)/(4n-4)·(n-1)/(n+1)
[tex]=\dfrac{4n(n-1)}{4(n-1)(n+1)}=\dfrac{n}{n+1}[/tex]
_____
At n=1, the product has a "hole" where the denominator of the original expression is zero, so the expression is undefined. Hence the domain of the product must be restricted to n≠1 (as well as n≠-1).
Eight more than the quotient of a number and 4 equals 5
The perimeter of the rectangle is 34 cm. Find the value of x.
A. 2
B. 17
C. [tex] \frac{34}{33} [/tex]
D. 20
Ninas car exponentially depreciates at a rate of 7 percent per year. If nina bought the car when it was 6 years old for 12000, what was the original price of the car
Answer:
[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]
And solving for the initial amount [tex] A_o[/tex] we got:
[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]
So then the original price for the car would be approximately 18263.539$
Step-by-step explanation:
For this case we can use the exponential model given by:
[tex] A(t) = A_o e^{bt}[/tex]
Where:
[tex]A_o[/tex] represent the initial amount for the car
[tex]b=-0.07[/tex] represent the exponential growth/decay rate
t represent the number of years. With t =0 at the begin
After 6 year we have that t =6, and we know this condition:
[tex] A(6) = 12000[/tex]
So then we can use the exponential model formula and the condition given and we have this:
[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]
And solving for the initial amount [tex] A_o[/tex] we got:
[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]
So then the original price for the car would be approximately 18263.539$
Write an equation for the translation of y = 4 x that has the given asymptotes. 15. x = 0, y = 3
Simplify. −5x4(−3x2+4x−2)
1:−8x^6−x^5−7x^4
2:15x^8−20x^4+10
3:15x^6−20x65+10x64
4:−15x^8−20x^5+10x^4
Answer:
[tex]15x^{6}-20x^{5}+10x^4)[/tex]
Step-by-step explanation:
We have been given an expression [tex]-5x^4(-3x^2+4x-2)[/tex] and we are asked to simplify our given expression.
We will use distributive property [tex]a(b+c)=a*b+a*c[/tex] to simplify our given expression.
Upon distributing [tex]-5x^4[/tex] we will get,
[tex](-5x^4*-3x^2)+(-5x^4*4x)-(-5x^4*2)[/tex]
Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,
[tex](15x^{4+2})+(-20x^{4+1})-(-10x^4)[/tex]
[tex](15x^{6})+(-20x^{5})-(-10x^4)[/tex]
[tex]15x^{6}-20x^{5}+10x^4)[/tex]
Therefore, our given expression simplifies to [tex]15x^{6}-20x^{5}+10x^4)[/tex].
The original price of sn item is $25, but after the discount, you only have to pay $18.50. what is the discount (as a percent)?
The discount is 26%.
What is Discount?The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
Given:
Marked price = $25
Selling price = $18.50
So,
Discount = MP - SP
Discount = 25-18.50
Discount = 6.50
Now,
D% = D/MP *100
D% = 6.5 /25*100
D% = 26%
Hence, the discount percent is 26%.
Learn more about discount here:
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Which rule describes a translation that is 8 units to the right and 2 units up?
x, y (x + 8, y + 2)
maxine hosted a dinner party at her favorite restaurant. she had to pay $12 per guest. the restaurant took $72 off the bill due to a mistake in the order. if the finale bill is $300, which equation will help the restaurant determine the number of guests at the dinner party
If the radius of the circle is doubled, by what number is the circumference multiplied?
The number by which the circumference is multiplied is:
2
Step-by-step explanation:We know that the circumference of the circle in terms of the radius r is given by:
[tex]\text{Circumference}=2\pi r[/tex]
Now, if the radius is doubled.
i.e.
[tex]r'=2r[/tex]
Hence, the circumference of the new circle is given by:
[tex]\text{Circumference of new circle}=2\pi (2r)\\\\i.e.\\\\\text{Circumference of new circle}=2(2\pi r)[/tex]
i.e.
[tex]\text{Circumference of new circle}=2\times \text{Circumference of original circle}[/tex]
The constant by which the circumference is multiplied is: 2
jake plans to use a ramp to make it easier to move a piano out of the back of his truck the back of the truck is 33 inches tall and the ramp is 65 inches long. what is the horizontal distance from the end of the ramp to the back of the truck
Answer:
56 inches is the horizontal distance from the end of the ramp to the back of the truck.
Step-by-step explanation:
Height of the back of the truck =33 inches
Length of the ramp = 65 inches
Length of the end of ramp to the back of the truck =?
In triangle ABC:
AB = 33 inches
BC = ?
AC = 65 inches
[tex]AB^2+BC^2=AC^2[/tex] (Pythagoras theorem)
[tex](33 inches)^2+(BC)^2=(65 inches)^2[/tex]
BC = 56 inches
I need Geometry help!!!
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If the circumference of a circle is 11inches, which is closest to its area?a.380 square inchesb.95 square inchesc.17 square inchesd.35 square inches
look at the pictures bellow
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
The perimeter of the first figure is [tex]6\pi +12\sqrt{2}[/tex]
Step-by-step explanation:
Besides that, they got everything right.
What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
80.47
Step-by-step explanation:
This is correct! :D
What is 6/7 as a recurring decimal?
A rhombus exists. This rhombus has 2 diagonals. The diagonals touch the side forming angles. These angles are in the ratio 4:5. Solve for all the angles in this rhombus based on the theorems for rhombuses and parallelograms.
A clock is constructed using a regular polygon with 60 sides. The polygon rotates everybody minute. How much has the polygon rotated after 7 minutes
•14 degrees
•21 degrees
•35 degrees
•42 degrees
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.
Please solve these for me. I need them for a quiz.
HELP QUICK PLEASE!!!!!
A proof for the Corresponding Angles Theorem is shown below. Next to each reason, choose the statement to which it applies.
How are the functions y=x and y=x+5 related? How are their graphs related?
Final answer:
The functions y=x and y=x+5 have the same slope but different y-intercepts. Their graphs are straight lines.
Explanation:
The functions y=x and y=x+5 are related in that they have the same slope of 1. This means that for every increase of 1 in the value of x, the value of y will also increase by 1. However, they have different y-intercepts. The function y=x has a y-intercept of 0, while the function y=x+5 has a y-intercept of 5.
Their graphs are related in that they are both straight lines. The graph of y=x is a line passing through the origin (0,0), while the graph of y=x+5 is a line shifted upward by 5 units compared to the graph of y=x.
How many sets of 7 questions can be chosen from a file of 25 questions?
6) Ethan uses the function f(x) = 2x2 + 2x + 4 to track the temperature of a substance over 8 hours. You know that f(3) = 28 meaning that the temperature of the substance is 28°C when you plug in a 3 for x. What is the domain of Ethan’s function?
The domain of Ethan's function f(x) = 2x² + 2x + 4 is all real numbers as it is a quadratic function.
Explanation:The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = 2x² + 2x + 4 represents the temperature of a substance over time. Since temperature is a physical quantity and cannot be negative, the domain of the function must be restricted to non-negative values of x.
To determine the exact domain of the function, we can analyze the expression 2x² + 2x + 4. This expression is always non-negative for any real number x. Therefore, the domain of f(x) = 2x² + 2x + 4 is all real numbers x ≥ 0.
In mathematical notation, the domain of the function can be expressed as:
{x ∈ ℝ | x ≥ 0}
This indicates that the function is defined for all real numbers (ℝ) as long as the value of x is greater than or equal to 0 (x ≥ 0).