A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is the skier's displacement from his starting point? (Use the graphical method to answer and include your scale on the graph paper.) Give both the magnitude and the angle in your answer.
Answers
The skier's displacement from his starting point is 127.179 m and makes an angle of 33.78°.
What is the law of cosine?The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.
Given A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º
base distance = 100 m
We will utilize the cosine rule to determine the magnitude of displacement because the triangle formed by the starting point, where he begins to ascend, and the ending point does not have a 90-degree angle. Cosine law requires a triangle with two sides and an angle between them, both of which are present.
a² = b² + c² - 2.b.ccos(α)
here a is the length of the third side,
b = base = 100m
c = 35 m
and α = 180 - 35 = 135°
so a² = b² + c² - 2.b.ccos(α)
a² = 100² + 35² - 2(100)(35)cos(135)
a² = 10000 + 1225 + 4949.74
a² = 16174.74
a = 127.179 m
and the angle between sides 100m and 127.179 m is given by
cosβ = (a² + c² - b²)/2a.c
cosβ = (127.179² + 35² - 100²)/2(127.179)(35)
cosβ = 0.831
β = cos⁻¹(0.831)
β = 33.78°
Hence displacement from the starting point is 127.179 m and forms an angle of 33.78°.
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Related Questions
What is the product of and ? Write your answer in standard form.
(a) Show your work.
(b) Is the product of and equal to the product of and ? Explain your answer.
Answers
Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]
Product of an Equation:
In mathematics, a product is a number or quantity obtained by multiplying two or more numbers. Example: 4 × 7 = 28, where the number 28 is said to be the product of 4 and 7. Another example: 6 times 4 is 24, so 6 multiplied by 4 is 24. The product of two positive numbers is a positive number, as if the product of two negative numbers is also positive (e.g., -6 × -4 = 24).
Now,
(A) We need to find the product of two given expressions.
[tex]\frac{1}{2x} -\frac{1}{4}[/tex] × [tex]5x^{2} -2x +6[/tex]
To multiply two given expressions, first multiply the first term in the first parenthesis by the entire expression in the second term, then do the same for the second term in the first parentheses.
[tex]\frac{1}{2x} -\frac{1}{4}[/tex] × [tex]5x^{2} -2x +6[/tex]
⇒ [tex]\frac{1}{2x} * [5x^{2} -2x +6] - \frac{1}{4} * [5x^2 - 2x +6][/tex]
⇒ [[tex]\frac{1}{2x} * 5x^2[/tex] - [tex]\frac{1}{2x} *2x[/tex] + [tex]\frac{1}{2x}* 6[/tex] ] - [ [tex]\frac{1}{4} * 5x^2 + \frac{1}{4} * 2x - \frac{1}{4}*6[/tex]]
Now, simplify the equation:
[tex]\frac{5x}{2} -1 + \frac{3}{x} - \frac{5x^2}{4} +\frac{x}{2} +\frac{3}{2}[/tex]
Rearranging the equation:
[tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]
Thus, the product of the two expressions is [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex].
(B) To compare the two expressions we will find the value of the two given expressions,
[tex]\frac{1}{2x} -\frac{1}{4} * 5x^{2} -2x +6[/tex] = [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]
For the value of:
[tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]
simplifying the equation:
[tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]
⇒ [tex][\frac{1}{4x} * (5x^{2} -2x +6)] - [\frac{1}{2} * (5x^{2} -2x +6)][/tex]
⇒ [tex]-\frac{5x^2}{2} + \frac{9x}{4} + 3.5 +\frac{3}{2x}[/tex]
As you can see, the result of the product of the two expressions is different.
Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]
Complete Question:
What is the product of 1/2x-1/4 & 5x^2-2x+6? Write your answer in standard form.
(A) show your work.
(B) is the product of 1/2x-1/4 & 5x^2-2x+6 equal to the product of 1/4x-1/2 & 5x^2-2x+6? Explain your answer
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a bag of fertilizer covers 2500 square feet of lawn how many bags of fertilizer should be purchased to cover a rectangular lawn 410 by 65 feet
Answers
Answer: 11
Step-by-step explanation:
410 * 65 = 26,650 sq ft
26,650/2500 = 10.66 bags
Answer:
11 bags.
Step-by-step explanation:
We know that the area is 410 x 65 = 26650
Now, we need to divide to find how many bags is needed.
26240/2500 = 10.66, which we round up cause we can't have a half bag.
A restaurant customer left $0.70 as a tip. The tax was 4% and the tip was 10% of the cost including tax.
Answers
Answer: The tip is 20% of the cost including tax. Thus .20 * X=3.50.Divide both sides of the equation by .20..20 divided into .20 = 1, so “X” = 1.And 3.50 divided by .20 = 17.50 So X = 17.50, cost of the meal plus the tax.The tax is .07, so we know that 100% of the meal cost PLUS 7% of the meal cost is 107% of the meal cost. That is 1.07 * Meal without tax = 17.50. Divide 17.50 by 1.07 and you get 16.355. Round up to 16.36.Is that right? Let’s see:7% tax on meal at 16.36 is 16.36 * .07 = 1.1452. Round up to 1.15.$1.15 + 16.36 = 17.51.And 20% (the tip) of 17.51 is .20 * 17.51 = 3.50Cost of the whole meal; food, tax and tip is 16.36+1.15+3.50 = 21.01.
Step-by-step explanation: my big brain
I need help with this last step.What do I put in the circles I'll give 50 points and brainliest for the first answer.
Answers
Answer: IS easy you only need to put your answer that you got when you multiply the numbers:)
Step-by-step explanation:
Help……………………………………..
Answers
Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x)
what is function ?Volumes and their variations, mathematics and supporting structures, types and their placements, and locations where they can be collected are all included in the study of mathematics. This same relationship between a group of inputs, each of which produces going support, is referred to as a "function.". Every function has a territory and a codomain, usually known as a scope. F is typically used to denote operations (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one operations, several more functions, within functions, and also on functions.
given
According to the table, the function's value at x = 10 is:
h(10) is not defined.
the values of the function change as x exceeds x = 10 to:
h(x+) = 18.5......
When roughly speaking, we have:
h(x+) = 18.5
Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x) .
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The complete question :-
What is Limit of h (x) as x approaches 10 plus?
four cards are dealt from a standard deck with 52 cards (w/o replacement), one at a time. what is the chance that a heart turns up on the fourth card, but not before? group of answer choices
Answers
The probability of getting a heart on the fourth card but not before that is 0.2278
The probability of getting a heart on the fourth card can be calculated by multiplying the probability of not getting a heart in the first three cards by the probability of getting a heart on the fourth card.
The probability of not getting a heart in the first three cards can be calculated as follows:
(39/52) * (38/51) * (37/50) = 0.862
where 39/52 is the probability of not getting a heart on the first card, 38/51 is the probability of not getting a heart on the second card (given that no heart was drawn in the first card), and 37/50 is the probability of not getting a heart on the third card (given that no heart was drawn in the first two cards).
The probability of getting a heart on the fourth card can be calculated as follows:
13/49 = 0.265
where 13/49 is the probability of getting a heart on the fourth card (given that no heart was drawn in the first three cards).
So, the probability of getting a heart on the fourth card, but not before, can be calculated as:
0.862 * 0.265 = 0.2278
So, the chance of getting a heart on the fourth card, but not before, is approximately 22.78%.
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PLS HELP I WILL GIVE BRAINIEST IF CORRECT I NEED HELP ASAP
An urn contains 8 red and 7 black balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are black? Round your answer to three decimal places.
Answers
Answer:
Step-by-step explanation:
Since the balls are drawn with replacement, the probability of drawing a black ball on any single draw is 7/15. The probability of drawing 6 black balls in succession is the product of the probabilities of each individual draw being a black ball. Therefore, the probability is:
(7/15)^6 ≈ 0.019
Rounding to three decimal places, the probability is 0.019.
Answer:
0.003
Step-by-step explanation:
The probability of drawing a black ball on any given draw is 7/15, since there are 7 black balls and 15 total balls in the urn. Because the balls are replaced after each draw, the probability of drawing a black ball on each of the 6 successive draws is (7/15) x (7/15) x (7/15) x (7/15) x (7/15) x (7/15) = (7/15)^6.
Therefore, the probability of drawing 6 black balls in succession is:(7/15)^6 = 0.0028 (rounded to three decimal places)
So the probability that all 6 balls drawn from the urn are black is approximately 0.003.
Solve the following:
a) 2(x + 3) = x - 4
b)
4(5x - 2) = 2(9x + 3)
Answers
Answer:
a. x= –10
b. x= 7
Step-by-step explanation:
a. 2(x+3)=x–4
2x+6=x–4
C.L.T
2x–x= –6–4
x= –10
b.4(5x–2)=2(9x+3)
20x–8=18x+6
C.L.T
20x–18x=6+8
2x=14
divide both sides by 2
x= 7
The first time Account # 1: was 1 year
account number # 2: was 10 years
Now just double it. Need help asap, thank you!!
Answers
For investment account 1, the balance doubles every year, so to find the time it takes to double again, we would need to solve for the time when the balance becomes $400 (double the starting balance of $200).
For investment account 2, the balance increases by $100 each year, so to find the time it takes to double again, we would need to solve for the time when the balance becomes $2,000 (double the starting balance of $1,000).
The pair of points lies on the same line with the given slope. Find x.
(3,1), (x,11); slope=2
Answers
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{11}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{x}-\underset{x_1}{3}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 2 }\implies \cfrac{10}{x-3}=2\implies 10=2x-6 \\\\\\ 16=2x\implies \cfrac{16}{2}=x\implies \boxed{8=x}[/tex]
find (-7x +1) + (4x-5)
Answers
Answer:
-3x -4
Step-by-step explanation:
(-7x +1) + (4x-5)
= -7x +1 + 4x-5 (brackets are unnecessary due to the commutative law of addition)
= -3x -4
in a given population, 11% of the likely voters are african american. a survey using a simple random sample of 600 landline telephone numbers finds 8% african americans. is there evidence that the survey is biased? explain.
Answers
There is an evidence that suggest that the survey is biased because the proportion of African Americans in the population, in our test, is less than 11%.
Is there evidence that the survey is biased?To determine if the survey is biased, we can use hypothesis testing. Let's define our null hypothesis as: "the proportion of African Americans in the population is 11%". Let's define our alternative hypothesis as "the proportion of African Americans in the population is less than 11%".
We can then use a one-tailed z-test to test our hypothesis, with a significance level of 0.05. The formula for the test statistic is:
z = (p - P) / sqrt(P(1-P)/n)
Plugging in the values, we get:
z = (0.08 - 0.11) / sqrt(0.11(1-0.11)/600)
x = -2.23
Looking up the critical value for a one-tailed test with a significance level of 0.05, we find it to be -1.645. Since our calculated z-value (-2.23) is less than the critical value (-1.645), we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of African Americans in the population is less than 11%.
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3/4(24x+28)-(4x-1)
I don't understand how to get the answer.
Answers
The expression evaluates to 14x + 22.
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
3/4(24x + 28) - (4x - 1)
We can start by simplifying the expression inside the parentheses:
3/4(24x + 28) - (4x - 1)
Remove the brackets
18x + 21 - 4x + 1
Evaluate the like terms
14x + 22
So, the value of the expression evaluates to 14x + 22.
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The expression 5x + 10 represents the amount of money in dollars the swim team earns by selling x school
spirit shirts.
If the team had to pay 2x + 3 in expenses, write and simplify an expression to represent their profit. Use
the vertical method. (NOTE: Profit = Income - Expenses)
PLS HELP ME SOMEONE!!!
Answers
The profit of the swimming club is 3x + 7 bucks, can be addressed by the articulation: 5x + 10 - (2x + 3),
Utilizing the upward technique:
5x + 10
2x + 3
=3x + 7
In this way, the benefit of the swimming club is 3x + 7 bucks.
The adage "5x + 10" addresses how much cash in dollars that the swimming club procures by selling x school soul shirts. To ascertain their benefit, the group's costs must be deducted from the pay. The saying "2x + 3" addresses the costs brought about by the group. To work on the articulation for benefit, the upward strategy can be utilized where the two articulations are thought of one over the other, with the comparing terms adjusted, and the subsequent articulation is deducted from the first. The last saying, "3x + 7", addresses the benefit of the swimming club in dollars, where every unit expansion in the quantity of shirts offered prompts an expansion in benefit by 3 bucks.
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6 divide by 222 long devision
Answers
Answer: 37
Step-by-step explanation:
6 divided into 2 is 0.
0 multiplied by 6 is 0.
2-0=2
bring down the other 2
6÷22=3
3×6= 18
23-18= 4
bring down the 3rd 2
now we have 44
44÷6 =43
42-42= 0
hence the answer is 37
Estefan brings two bags of sandwiches to a party. One bag contains 6 peanut butter sandwiches, 4 cheese sandwiches and 2 ham sandwiches. The other bag contains 4 peanut butter sandwiches, 2 cheese sandwiches, 4 ham sandwiches and 2 chicken salad sandwiches. If John picks one sandwich from each bag at random, what is the probability both will be peanut butter sandwiches? Express your answer as a common fraction
Answers
The number of peanut butter sandwiches in the first bag is 6 and in the second bag is 4. So, the probability of picking a peanut butter sandwich from each bag is 1/6.
The probability of an event happening is the number of successful outcomes divided by the number of total possible outcomes. In this case, there are two bags of sandwiches and John is picking one sandwich from each bag.
The first bag has 12 sandwiches in total, 6 of which are peanut butter. So, the probability of picking a peanut butter sandwich from the first bag is 6/12 or 1/2.
The second bag has 12 sandwiches in total, 4 of which are peanut butter. So, the probability of picking a peanut butter sandwich from the second bag is 4/12 or 1/3.
To find the probability of both sandwiches being peanut butter, you multiply the individual probabilities:
1/2 * 1/3 = 1/6.
So, the probability of both sandwiches being peanut butter is 1/6.
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The store sells 2-64 oz. bottles of liquid dish soap for $8.39 or 3 - 40 oz. bottles at $7.20. Which is the better buy?
Answers
It is better to buy 2-64 oz bottles of liquid dish soap for $8.39.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
Given that, the store sells 2-64 oz bottles of liquid dish soap for $8.39 or 3 - 40 oz bottles at $7.20.
2 pounds = 32 oz
So, 32+64=96 oz
Now, 8.39/96
= $0.087 per oz
Here, 3 - 40 oz = 88 oz
Unit rate = 7.20/88
= $0.081 per oz
Therefore, it is better to buy 2-64 oz bottles of liquid dish soap for $8.39.
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In the given, figure find y!
Answers
Answer:
i cant be botherd to help but
Step-by-step explanation:
use the knolage 180 degrees = full triangle
180 degress = 1 stright line
Answer:
40⁰
Step-by-step explanation:
Angles subtended by the same chord on the circumference
y= 40⁰
Please Help!!
(use the figure to answer questions 8,9 and 10)
The height ( in feet) of a ball thrown by a child is given by
= −^2 + 6 + 7,
where is the horizontal distance ( in feet) from where the ball is thrown ( see figure).
8. How high is the ball when it leaves the child’s hand? (Justify your answer)
9. What is the maximum height of the ball? ( must show work)
10. How far from the child does the ball strike the ground? ( must show work)
Answers
The ball is 7 feet high when it leaves the child’s hand
The maximum height is 16 feetIt lands 7 feet from the childHow high is the ball when it leaves the child’s hand?Given that
h(x) = -x^2 + 6x + 7
When it leaves his hand, we have
x = 0
This gives
h(0) = -(0)^2 + 6(0) + 7
Evaluate
h(0) = 7
What is the maximum height of the ball?Here, we have
h(x) = -x^2 + 6x + 7
Differentiate and set to 0
-2x + 6 = 0
So, we have
x = 3
The maximum height is
hmax = -3^2 + 6(3) + 7
hmax = 16
How far from the child does the ball strike the ground?This means that h(x) = 0
So, we have
-x^2 + 6x + 7 = 0
This gives
x^2 - 6x - 7 = 0
Expand
x^2 + x - 7x - 7 = 0
Factor
x(x + 1) -7(x + 1) = 0
So, we have
(x - 7)(x + 1) = 0
Solve for x
x = 7 or x = -1
Hence, the distance is 7 feet
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WILL GIVE brainliest
Answers
Answer:
Below
Step-by-step explanation:
y ( 5.98x - 5.81) - 2.19 y =
5.98xy - 5.81y - 2.19 y
5.98xy + ( - 5.81y - 2.19 y)
5.98xy + ( - 8y )
5.98xy - 8y or y ( 5.98x-8)
Kindred invested $38,976 into his first company. His investment decreased by 3. 5% each year over the first 3 years. Which exponential decay modle could kindred use ti determin the amount this investment will be worth if it continues to decrease at the same rate?
Answers
The exponential decay model for the investment of $38,976 with decreased rate 3.5% for 't' years is equal to option b. 38,976 (0.965 )^t.
Invested amount by Kindred = $38,976
Each year investment decreased by 3.5%
Number of years represented by 't' = 3 years
Amount decreased by 100 - 3.5% = 96.5%
= 0.965
Total amount decreased in three years = $38,976 × ( 0.965 )³
= $35,025.085
Exponential decay model for 't' years at the same rate is given by the equation :
= 38,976 × ( 0.965 )^t
Therefore, the exponential decay model for the given situation of investment with decreasing rate is given by option b. 38,976 (0.965 )^t.
The above question is incomplete , the complete question is:
Kindred invested $38,976 into his first company. His investment decreased by 3.5% each year over the first 3 years. Which exponential decay model could Kindred use to determine the amount his investment will be worth if it continues to decrease at the same rate?
a. 38,976 (1.035 )^t
b. 38,976 (0.965 )^t
c. 38,976 (1 -r )^3.5
d. 38,976 (1 -r )^0.035
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i have a question.
0,2 2,3 4,4 6,5 8,6 10,7
(coordinates ^)
Q. first, complete the table of x and y coordinates.
x. y
----------
3. _
5. _
7. _
Answers
Answer:
x | y
0 | 2
2 | 3
3 | 4
4 | 5
5 | 6
6 | 7
7 | 8
So, completing the table:
x | y
3 | 4
5 | 6
7 | 8
Step-by-step explanation:
Please study well it is a very easy question
7. to survey the opinions of bleacher fans at wrigley field, a surveyor plans to select every one-hundredth fan entering the bleachers one afternoon. will this result in a simple random sample of cub fans who sit in the bleachers?
Answers
The survey does not result in a simple random sample of Cubs fans who sit in the bleachers. So, option E) is correct.
Simple random sampling is a method of selecting a sample from a population such that each element in the population has an equal chance of being selected. This is achieved by using a random number generator or by randomly assigning a number to each element in the population and then selecting a sample based on those numbers.
In this case, the survey plan to select every one-hundredth fan entering the bleachers is not a simple random sample because not every sample of the intended size has an equal chance of being selected. For example, the first fan entering the bleachers has a 1 in 100 chance of being selected, while the second fan has a 2 in 100 chance of being selected. This creates a non-uniform selection process, which is not representative of simple random sampling.
Therefore, the survey plan to select every one-hundredth fan entering the bleachers results in a form of systematic sampling, which is not a simple random sample.
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Complete Question: One afternoon, a surveyor intends to pick every fan entering the bleachers to get the views of those who sit in them at Wrigley Field. Will this lead to a straightforward random sample of Cubs supporters seated in the stands?
A. Yes, as each bleacher spectator has an equal chance of getting chosen.
B. The answer is yes, but only if the bleachers have a single entrance.
C. The control group will consist of the 99 out of 100 bleacher spectators who were not chosen.
D. The answer is "yes," as this is an illustration of systematic sampling, a subset of basic random sampling.
E. No, since there are unequal odds of selecting each sample of the intended size.
23 equals x minus 9; x minus 14
Answers
The value of 'x' satisfying the statement is x = 32 or x = 27.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A statement 23 equals x - 9, x - 14 which can be numerically expressed as, 23 = x - 9 or 23 = x - 14.
Therefore,
x - 9 = 23 or x - 14 = 23.
x = 23 + 9 or x = 23 + 14.
x = 32 or x = 37.
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the variance of a sample of 169 observations equals 576. the standard deviation of the sample equals:
Answers
If the variance of a sample of 169 observations equals 576, then the standard deviation of the sample equals to 24.
It is given that number of observations are 169 and their variance is 576,
now we have to find the standard deviation of the sample :
The Standard Deviation is a measure of how spread out numbers are. It's symbol is σ. It is the square root of the Variance. Variance is the average squared deviations from the mean.
Standard deviation (σ) = [tex]\sqrt{variance}[/tex]
Standard deviation (σ) = [tex]\sqrt{576}[/tex]
Standard deviation (σ) = 24
so the standard deviation of the sample is 24.
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suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. what is the expected value of his or her total winnings for the four spins?
Answers
Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. The expected value of his or her total winnings for the four spins is $800.
Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again.
We have to determine the expected value of his or her total winnings for the four spins.
Total winning depends on the fourth term.
Outcome Skunk 100 200 500
Probability 1/4 1/4 1/4 1/4
Total Winning 0 900 1000 1300
Expected Total Winning = 1/4 (0 + 900 + 1000 + 1300)
Expected Total Winning = 1/4 × 3200
Expected Total Winning = 800
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The complete question is:
Contestants on a game show spin a wheel like the one shown in the figure above. Each of the four outcomes on this wheel is equally likely and outcomes are independent from one spin to the next.
The contestant spins the wheel.
If the result is a skunk, no money is won and the contestant's turn is finished.
If the result is a number, the corresponding amount in dollars is won.
The contestant can then stop with those winnings or can choose to spin again, and his or her turn continues.
If the contestant spins again and the result is a skunk, all of the money earned on that turn is lost and the turn ends.
The contestant may continue adding to his or her winnings until he or she chooses to stop or until a spin results in a skunk.
Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. What is the expected value of his or her total winnings for the four spins?
Measured in meters, the wavelength of red light is about 8x10 to the -7 power, and the wavelength of violet light is 8x10 to the -7 power. The wavelength of red light is how many times longer than the wavelength of violet light
Answers
The wavelength of red light is exactly the same as the wavelength of violet light, so it is not longer or shorter.
1. First, we need to identify the wavelengths of red light and violet light.
2. Red light has a wavelength of 8x10 to the -7 power meters and violet light has a wavelength of 8x10 to the -7 power meters.
3. Since both wavelengths are the same, the wavelength of red light is not longer or shorter than the wavelength of violet light.
The wavelength of light is measured in meters, and the wavelength of red light is 8x10 to the -7 power meters, while the wavelength of violet light is 8x10 to the -7 power meters. This means that both the wavelengths are exactly the same and the wavelength of red light is not longer or shorter than the wavelength of violet light. This is because the wavelength of light is a fundamental property that determines the color of light and the wavelength of red light and violet light are both the same.-
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Class A, B and C were given some chocolate bars to sell for their fundraising event. The average number of chocolate bars the 3 classes had at first was 225. After Class B sold twice as many chocolate bars as Class A and Class C sold 3/4 as many chocolate bars as Class B, the average number of chocolate bars the 3 classes had left was 45. How many chocolate bars did Class A and Class C sell altogether?
Answers
Class A and Class C sell 187.5 altogether
How many chocolate bars did Class A and Class C sell altogether?Represent the classes with their initials
So, we have
B = 2A
C = 3/4 * B = 3/4 * 2A
C = 3/2A
The total number of bars they had initially was
A + B + C = Total
A + 2A + 3/2A = Total
Total = 4.5A
The average number of bars the 3 classes had initially was 225,
So
4.5A = 225
A = 75
For Class A and Class C together, we have
Class A and C = A + 3/2A
Class A and C = 75 + 3/2 * 75
Class A and C = 187.5
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At a basketball game a team made 51 successful shots. They were a combination of 1- and 2- point shots. The team scored a total of 84 points in all.
Answers
If the equation be x + 2(51 - x) = 83 then the value of x be 19.
What is meant by expressions?A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.
In mathematics, a numerical expression is a mixture of numbers and integers combined using addition, subtraction, multiplication, or division.
Let x be the number of 1 point shots.
51 - x be the number of 2 point shots
Let the equation be x + 2(51 - x) = 83
Expanding the above equation as
x + 2(51 - x) = -x + 102
simplifying the above equation, we get
-x + 102 = 83
-x = -19
Divide both sides by -1
[tex]$\frac{-x}{-1}=\frac{-19}{-1}[/tex]
x = 19
Therefore, the value of x be 19.
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Solve for a 7x - 5 < 13 Give your answer as an improper fraction in its simplest form.
Answers
Answer:
[tex]x < \dfrac{18}{5}[/tex]
Step-by-step explanation:
Solving inequalities:7x - 5 < 13
Add 5 to both sides
7x < 13 + 5
7x < 18
Divide both sides by 7,
[tex]\sf x < \dfrac{18}{7}[/tex]
Answer:
[tex]x < \dfrac{18}{7}[/tex]
Step-by-step explanation:
We are being asked to solve for x as an improper fraction in simplest form given the equation: [tex]7x - 5 < 13[/tex].
First, we must isolate the variables (x's) from the constants (numbers). We can achieve this by adding 5 to both sides.
[tex]7x - 5 + 5 < 13 + 5[/tex]
[tex]7x < 18[/tex]
Then, we can solve for one multiple of x by dividing both sides by x's coefficient, which is 7.
[tex]7x < 18\\\overline{\ 7\ } \ \ \ \: \overline{\ 7\ }[/tex]
[tex]x < \dfrac{18}{7}[/tex]