Answer:
70
Step-by-step explanation:
If you use Pascal's Triangle, you will need 9 lines, since there are 9 terms in a binomial raised to the 8th power. Those 9 terms are:
1, 8, 28, 56, 70, 56, 28, 8, 1
The first expansion through the one we need are below (I hope you know how to use Pascal's Triangle!):
[tex]1(x^8)(y^0)+8(x^7)(y^1)+28(x^6)(y^2)+56(x^5)(y^3)+70(x^4)(y^4)+...[/tex]
Answer:
70
Step-by-step explanation:
apex
Bob uses 2/5 of a cup of vinegar in his salad dressing recipe. How much vinegar would Bob use to make 2 3/4 recipes?
Final answer:
To find out how much vinegar Bob needs for 2 3/4 recipes, simply multiply 2/5 cup (the amount used for one recipe) by 2 3/4. The answer is 1.1 cups of vinegar.
Explanation:
To calculate the amount of vinegar Bob would use to make 2 3/4 of his salad dressing recipes, we first need to determine how much vinegar is used in one full recipe. We then multiply that amount by 2 3/4 to find the total vinegar needed for the larger batch.
Bob uses 2/5 of a cup of vinegar for one recipe. To make 2 3/4 recipes, we perform the following calculation:
Multiply the amount of vinegar for one recipe by the number of recipes: (2/5) cup * (11/4) recipes.Convert 2 3/4 into an improper fraction, which is 11/4.Calculate: (2/5) * (11/4) = (2*11) / (5*4) = 22 / 20 = 1 1/10 or 1.1 cups of vinegar.Therefore, Bob would use 1.1 cups of vinegar to make 2 3/4 of his salad dressing recipes.
Divide.
refer to the picture
Bluesky air has the best on-time arrival rate with 80% of its flights arriving on time. a test is conducted by randomly selecting 16 bluesky air flights and observing whether they arrive on time. what is the probability that 2 flights of bluesky air arrive late? (please carry answers to at least six decimal places in intermediate steps. give your final answer to the nearest four decimal places).
The problem can be solved by using the binomial probability formula. We know that the binomial model deals with the probability of success of an event in a series of experiments. Plug the values into the binomial formula to find the probability that 2 flights out of 16 selected flights will arrive late.
Explanation:This problem can be solved using the binomial probability formula. The binomial distribution model deals with finding the probability of success of an event that has only two possible outcomes in a series of experiments, such as a coin toss.
Given that the probability of a flight arriving on time is 80%, the probability (p) for a flight arriving late is 20% or 0.2. We are looking for the probability that 2 out of 16 flights arrive late. This is a binomial problem where n=16 (the number of trials), k=2 (the number of successes), and p=0.2 (probability of success).
The binomial formula is P(X=k) = C(n, k) * (p^k) * (1-p)^(n-k)
where C(n, k) is a combination that calculates the number of possible combinations of n items taken k at a time, without regard to the order of selection.
So, to solve this problem:
First, calculate C(16, 2).Second, calculate (0.2^2).Third, calculate ((1-0.2)^(16-2)).Lastly, multiply those three results together to get the final probability.The probability that 2 flights out of 16 selected flights will arrive late can be computed by plugging these values into the binomial formula.
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A pizza place is offering 20% discount off all it's pizzas Ali orders a pizza for the reduced price of £5.60 Work out the original price
F(x) = 2x2 – 4x – 3
0 = 2x2 – 4x – 3
3 = 2(x2 – 2x)
3 + 1 = 2(x2 – 2x + 1)
4 = 2(x – 1)2
2 = (x – 1)2
± = x – 1
1 ± = x
Mica is solving for the zeros of a quadratic function by completing the square. Her work is shown. What error did Mica make?
ANSWER CHOICES
Mica should have set each x = 0 instead of f(x).
Mica should have added 2 to 3 instead of 1.
Mica should have multiplied both sides by 2 instead of dividing.
Mica should have subtracted 1 from both sides instead of adding.
The length of a rectangle is 5 more than 3 times its width. Find the length and width of the rectangle with an area of 182 square units.
PLEASE EXPLAIN.
The length and width of the given rectangle with area of 182 square units is; Length = 26 units and width = 7 units
Area of a Rectangle
Let the length of the rectangle be x
Let the width of rectangle be y
Let the area of rectangle be A
Formula for area of rectangle is;
A = length * width
Thus;
A = xy
We are told that area is 182 square units. Thus;
xy = 182 sq.units -----(eq 1)
Also the length of the rectangle is 5 more than 3 times its width. Thus;
x = 3y + 5 ------(eq 2)
Put 3y + 5 for x in eq 1 to get;
y(5 + 3y) = 182
3y² + 5y = 182
3y² + 5y - 182 = 0
Using online quadratic equation calculator gives; y = 7
Thus; x = 182/7
x = 26
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1. is not consided a high risk investment
A- investing in stocks
B- inversting in cds
C- investing in start up ventures
D-investing in entrepreneurial activities
2. the dow is where are exchanged
A-certificates of deposit
B-bonds
C-stocks
D-companies,
Erika bought 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears for $21.00. Meanwhile, Irene bought 3 kilograms of cinnamon red hots and 3 kilograms of gummy bears for $39.00. What is the cost of one kilogram of each type of candy?
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Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin. Naturally, she wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle. What is the angle of elevation, in degrees, of the roof beams?
The angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
Width of the cabin = 42 meters
Wooden beam length = 27 meters
Since opposite beams would meet exactly in the middle.
The half of the beam width = 42/2 ⇒ 21 meters
As we can see in the right angle triangle:
[tex]\rm cosx = \frac{21}{27}[/tex]
[tex]\rm x = cos^{-1}(\frac{21}{27} )[/tex]
x = 38.9°
Thus, the angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.
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please help I don't understand this
Solve for x
2/(9x) = 4/7
18/7
I don't know
- 18/7
7/18
- 7/18
PLEASE HELP >.<
Use Pascal's triangle to expand the binomial (d-5)^6
please solve step by step
Answer:
what that guy said
Step-by-step explanation:
What is the perimeter of this equilateral triangle?
The figure below shows a right triangle:
What is r ÷ q equal to? (6 points)
sin y°
sin x°
tan x°
tan y°
The value based on the information given about the right angle will be such that r ÷ y is sin y°.
It should be noted that the sine of an angle is calculated as:
Sine = Opposite / Hypotenuse
Based on the information given, it can be seen that r is the angle that's facing y° while q units is hypotenuse. Therefore, the value based on the information given that r ÷ y will be sin y°.
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f a plane slices horizontally through the solid cube, what is the shape of the cross-section?
(Sin3 theta + cos 3 theta / sintheta + cos theta) + sin theta cos theta
A cube with side length 2f is stacked on another cube with side length 3g2. Choose the expression that represents the total volume of the cubes.
Answer:
the answer is c
Step-by-step explanation:
Write an expression for "9 multiplied by t''.
What is the measure of AU
Answer:
Step-by-step explanation:
Given: The measure of the arc QU=88°, ∠QUA=111°.
To find: The measure of the arc AU.
Construction: Join QX and UX and AX, where X is the center of the circle such that ∠UXA=x.
Solution: It is given that The measure of the arc QU=88°, ∠QUA=111°.
Now, we know that The measure of a minor arc is the same as the measure of the central angle that corresponds to it, therefore
If the minor arc QU=88°, then ∠QXU=88°.
Also, we know that the major central angle is double of the inscribed angle, thus
∠QXA=2(∠QUA)
⇒∠QXA=2(111°)
⇒∠QXA=222°
Using the angle sum property for a point X, we have
∠QXA+∠QXA=360°
⇒222°+88+x=360°
⇒310°+x=360°
⇒x=50°.
Again, The measure of a minor arc is the same as the measure of the central angle that corresponds to it, thus
The measure of the arc AU is same as ∠UXA that is 50°,therefore, the measure of AU is 50°.
Hence, option B is correct.
At a local store you find the following prices listed:
Tape 2 rolls for $1.28
Notepads 3 pads for .87
Highlighters 1 for 1.59
Pens 2 for 1.98
How much would you pay for one roll of tape, two note pads, two highlighters, and two pens?
A. $4.50
B. $6.38
C. $8.07
D. $5.72
Una was asked to write about predicting population means by taking the means of samples. She recorded a list of some statements generated from her classmates. Which statements are true? Check all that apply. The best prediction of the population mean is the value that falls between the least and greatest sample means. It is unlikely that the population mean will be the least or greatest mean from the samples. If the means of different samples are close in number, or have small variation, then they cannot be used to make predictions for the actual population. A more accurate prediction of the population mean can be made by decreasing the number of random samples. Samples are a random selection of data values from a population. To find the range of the sample means, subtract the least value from the greatest value.
Answer:
1, 2, and 5.
Step-by-step explanation:
The best prediction of the population mean is the value that falls between the least and greatest sample means.
It is unlikely that the population mean will be the least or greatest mean from the samples.
To find the range of the sample means, subtract the least value from the greatest value.
Hope that is helpful ¯\_(ツ)_/¯
The correct statements for the population mean are 1, 2, and 5.
What is the population mean?The population mean formula basically calculates the group's arithmetic mean by adding up all the data points and dividing the result by the total number of items in the sample.
The correct statements are given below:-
The best prediction of the population mean is the value that falls between the least and greatest sample means.It is unlikely that the population mean will be the least or greatest mean from the samples.To find the range of the sample means, subtract the least value from the greatest value.To know more about the population mean follow
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How do I find X in this math problem?
The diameter of a sphere is 4 centimeters. What is the volume of the sphere? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth.
Answer:
Volume of the sphere(V) is given by:
[tex]V = \frac{4}{3} \pi r^3[/tex] ....[1]
where,
r is the radius of the sphere.
As per the statement:
The diameter of a sphere is 4 centimeters.
Formula for the diameter(d) is given by:
[tex]d = 2r[/tex]
⇒[tex]4 = 2r[/tex]
Divide both sides by 2 we have;
2 = r
or
r = 2 cm
Substitute in [1] and use 3.14 for pi. we have;
[tex]V = \frac{4}{3} \cdot 3.14 \cdot 2^3 = \frac{4}{3} \cdot 3.14 \cdot 8[/tex]
Simplify:
V = 33.4933333 cubic cm
therefore, the volume of the sphere to the nearest tenths is, [tex]33.5 cm^3[/tex]
Given f(x)=4x2−5 and g(x)=x+3 .
What is (fg)(x) ?
Answer:
[tex](fg)(x)=4x^3+12x^2-5x-15[/tex]
First option is correct.
Step-by-step explanation:
We have been given that
[tex]f(x)=4x^2-5[/tex]
[tex]g(x)=x+3[/tex]
We know that [tex](fg)(x)=f(x)g(x)[/tex]
Hence, we have to find the product of f(x) and g(x)
[tex](fg)(x)=(4x^2-5)(x+3)[/tex]
Apply distributive property
[tex](fg)(x)=4x^2\cdot x+4x^2\cdot3-5x-5\cdot3[/tex]
Simplifying, we get
[tex](fg)(x)=4x^3+12x^2-5x-15[/tex]
First option is correct.
A rectangle has a length of 4 centimeters and a width of 7 centimeters. What is the effect on the perimeter when the dimensions are multiplied by 5?
in one u.s city, the taxi cost is $2 plus 0.08 per mile. if you are traveling from the airport, there is and additional charge of $4.50 fir tolls. How far can yoh travel from the airport by taxi for 34.50?
How many arrangements of 3 types of flowers are there if there are 6 types to choose from?,
Martina's gross weekly pay is $1168
To maintain her current lifestyle, how much should she save up by the time she retires?
A.) $303,680
B.) $607,360
C. $672,768
D. $789,568
Martina would need $1,214,720 to maintain her current lifestyle for 20 years post-retirement, based on a gross weekly pay of $1,168. None of the provided options match this calculated amount, suggesting a need for a reassessment.
To determine how much Martina should save by the time she retires, we must first understand her annual consumption.
If Martina's gross weekly pay is $1168, her annual income is calculated as follows:
Annual Income = 52 weeks/year × $1168/week = $60,736/year.
Assuming Martina plans to spend the entire amount to maintain her current lifestyle during retirement, and assuming she lives 20 years post-retirement, the total amount she would need is:
Total Retirement Savings Needed = $60,736/year × 20 years = $1,214,720.
Given the provided options:
A) $303,680B) $607,360C) $672,768D) $789,568None of the provided choices match the calculated amount of $1,214,720 needed for maintaining her current lifestyle over 20 years of retirement. Therefore, additional context is needed, or a reassessment of Martina's retirement duration and lifestyle costs should be considered.
Julia and Maya are walking towards each other. When they started, the distance between them was 1600 feet. What will be the distance between them in 2.5 minutes, if they walk with the same speed: 80 feet per minute?