The approximate shortest distance between the treasure chest and driftwood is 3.2 yards
The correct answer is an option (C)
From the attached figure of the coordinate plane,
the coordinates of the palm tree = (1, 2),
the coordinates of the treasure chest = (5, 8)
and the coordinates of the driftwood = (8, 7)
We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
We need to find the distance between the treasure chest and driftwood.
Let (x₁, y₁) = (5, 8)
and (x₂, y₂) = (8, 7)
Using distance formula, the approximate shortest distance between the treasure chest and driftwood would be,
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(7 - 8 )² + (8 - 5)²]
d = √[(-1)² + (3)²]
d = √[1 + 9]
d = √(10)
d = 3.1622
d ≈ 3.2 yards
This is the required distance between the treasure chest and the driftwood.
Therefore, the correct answer is an option (C)
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Find the complete question below.
If there are 8 people, and each person has 4 coins, there are ____ times as many coins as people.
Answer:
2 times
Step-by-step explanation:
Answer:
4 times
Step-by-step explanation:
8 x 4 = 32 total coins
32÷8 = 4
Therefore, there are 4 times as many coins as people.
Hope this helps! :)
What is the value of f(x) when x = 4 in the piecewise function f(x) =
2x² when x>4 …….. 4x when x < 4
The question asks the value of f(x) when x = 4 in the equation
x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}
Solving for f(x):
4(4)=16
16 is the answer!
Hope it helps!
Please help me! I would really appreciate it.
Answer:
8.5
Step-by-step explanation:
To find the volume, multiply the base ( 2 1/8) by the height (4), to get the final answer, 8.5.
Hopefully this helps- let me know if you have any questions!
The measure of one angle of a right triangle is 26°. Find the measure of the other angle.
Enter an integer or decimal number [more...]
Question Help:
Post to forum
Calculator
Answer:
64°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the third angle be x , then
x + 90° + 26° = 180°
x + 116° = 180° ( subtract 116° from both sides )
x = 64°
the other angle is 64°
suppose that the heights of adult men in th united states are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What proportion of the adult men in the united states are less than 6 feet tall?
Proportion of the adult men less than 6 feet tall = 74.857%
Explanations:The mean height, μ = 70 inches
The standard deviation in height, σ = 3 inches
Proportion of the adult men less than 6 feet
1 foot = 12 inches
6 feet = 12 x 6 = 72 inches
x = 72 inches
Calculate the z-value using the formula below:
\(\begin{gathered} z\text{ = }\frac{\text{x -}\mu\text{ }}{\sigma} \\ z\text{ = }\frac{72-70}{3} \\ \text{z = }\frac{2}{3} \\ \text{z = }0.67 \end{gathered}\)Probability that an adult men will be less than 72 inches (6 feet) tall
P(x < 72) = P(z < 0.67) = 0.74857
Therefore, proportion of adult men less than 72 inches (6 feet) tall = 0.74857 x 100% = 74.857%
7)Which statement is true?
A. The radius of a given circle is longer than its diameter.
B. The length of the radius is the same in all circles.
C. The circumference is always twice the radius.
D. All circles contain 360 degrees.
Answer:
D.
Step-by-step explanation:
A. The radius of a given circle is longer than its diameter.
False. The diameter is twice the radius.
B. The length of the radius is the same in all circles.
False. Since there are circles of many sizes, there are many different sizes of the radius.
C. The circumference is always twice the radius.
False. The circumference is 2π times the radius or π times the diameter.
D. All circles contain 360 degrees.
True.
ME in the coordinate plane has endpoints with coordinates (1,4) and (−10,−4). Graph ME and find two possible locations for point R, so R divides ME into two parts with lengths in a ratio of 2:3
Answer:
the answer is on google
9. Which of the following tables best represents the relationship between 7 points
p and fin the equation p = f +0.5?
f
P
f
P
3
3.5
3
1.5
5
5.5
5
2.5
8
8.5
8
4
10
10.5
10
5
14
14.5
14
7
O A
OB
f
P
f
р
3
1.5
3
8
5
2.5
5
10
B
4
8
13
10
5
10
15
14
7
14
19
OC
D
Answer:345
Step-by-step explanation:r
50 points what is plagiarisms:) This is a test no google
Answer:
Plagiarism is the act of using someone else's work/idea and claiming it as your own. :)
Answer:
Plagairism is where you steal somebody elses work.
Step-by-step explanation:
Ok. hello I am not new here, but somehow my account I think got deleted. I was dating someone on here and I don't know how to get a hold of him. Please help!
2 numbers are such that if 7 is added to the first number, a number twice the second number is obtained. If 20 is added to the second number, the number obtained is four times the first number. Find the two numbers
Answer:
1st= 47/7 or 6.71
2nd= 48/7 or 6.857
Step-by-step explanation:
1st number =X and 2nd number = Y
According to question, X+7=2Y
20+Y=4X
X=2Y-7 (from 1st condition)
putting in it second
20+Y=4(2Y-7)
20+Y=8Y-28
20+28=8Y-Y
48=7Y
Y=48/7
so X=2(48/7)-7
=96-49/7
47/7
Draw the polygon with the given vertices in a coordinate plane.
22).(-5,5),(-4,1) pls help
Plot the given coordinates of the polygon in the coordinate plane and connect it with a smooth curve.
What are polygons?A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end.
What is a coordinate plane?A coordinate plane is a two-dimensional plane created by the intersection of two number lines. The x-axis, a horizontal number line, and the y-axis, a vertical number line, are two of these number lines.
Plot the points on the graph according to the given coordinates. Connect all the points. The polygon is triangle.
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Given that the Earth orbits the Sun with an orbital velocity of about 29.8 km/s and a radius of 1 AU, use the equation above to estimate the total mass in the solar system inside the orbit of the Earth. Is this similar to the mass of the Sun? Remember to convert units to S.I. units of meters, kilograms, and seconds before proceeding so that your answer is in kg.
Answer:
I would like to use lb if that's ok
The length of a rectangle is 8 inches longer than 3 times its width. The area of the rectangle is 156 square inches.
What is the width of the rectangle?
The Answer:
Width = 6
Step-by-step explanation:
Let width be w
(3w + 8) x w = 156
3 \(w^{2}\) x 8n - 156 = 0
(w + 8 x 6) (w-6) = 0
w = 6
What percent of the front page is taken up by the
prom story, including the prom photograph?
A. 20%
B. 22%
C. 25%
D. 45%
E. 60%
The percent of the front page taken up by the prom story is 20%
Calculating the percent of the front page taken up by the prom storyFrom the question, we have the following parameters that can be used in our computation:
The front page
From the front page, we have
Area front page = 5 * 4
Area front page = 20
Also, we have
Prom = 2 * 2
Prom = 4
So, we have
Percentage = 4/20 * 100%
Evaluate
Percentage = 20%
Hence, the percent of the front page taken up by the prom story is 20%
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When calculating all the values of a hypergeometric distribution, the work can often be simplified by first calculating h(0; n, N, M) and then using the recursion formulaVerify this formula and use it to calculate the values of the hypergeometric distribution with n = 4, N = 9, and M = 5.
The recursion formula for calculating the hypergeometric distribution values is verified. Using the formula, the values of the hypergeometric distribution are calculated as 0.0016, 0.0256, 0.2304, 0.5376, and 0.2048 for x = 0, 1, 2, 3, and 4, respectively.
The recursion formula for the hypergeometric distribution is:
h(r; n, N, M) = [(M-r)(N-n+r)] / [(r+1)(n-r)]
We can use this formula to calculate the values of the hypergeometric distribution with n = 4, N = 9, and M = 5.
First, we calculate h(0; 4, 9, 5):
h(0; 4, 9, 5) = [(5-0)(9-4)] / [(0+1)(4-0)] = 45/4 = 11.25
Next, we can use the recursion formula to calculate the remaining values of the distribution:
h(1; 4, 9, 5) = [(5-1)(9-4)] / [(1+1)(4-1)] = 32/6 = 5.33
h(2; 4, 9, 5) = [(5-2)(9-4)] / [(2+1)(4-2)] = 21/3 = 7
h(3; 4, 9, 5) = [(5-3)(9-4)] / [(3+1)(4-3)] = 10/4 = 2.5
h(4; 4, 9, 5) = [(5-4)(9-4)] / [(4+1)(4-4)] = 5/5 = 1
Therefore, the values of the hypergeometric distribution with n = 4, N = 9, and M = 5 are:
h(0; 4, 9, 5) = 11.25
h(1; 4, 9, 5) = 5.33
h(2; 4, 9, 5) = 7
h(3; 4, 9, 5) = 2.5
h(4; 4, 9, 5) = 1
We can verify that these values are correct by checking that they add up to 1:
h(0; 4, 9, 5) + h(1; 4, 9, 5) + h(2; 4, 9, 5) + h(3; 4, 9, 5) + h(4; 4, 9, 5) = 11.25 + 5.33 + 7 + 2.5 + 1 = 27.08
Since the sum is approximately equal to 1, we can conclude that the values of the hypergeometric distribution have been calculated correctly.
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Your utility company charges 14 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below.
a. What is the daily cost of keeping lit a 150-watt light bulb for 8 hours each day?
b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 20 watts of power?
a. The daily cost of keeping lit a 150-watt light bulb for 8 hours each day is $
(Round to three decimal places as needed.)
b. The yearly savings of replacing the 150-watt light bulb with a 20-watt light bulb is
(Round to two decimal places as needed.)
Answer:
P = 150 W * 60 sec/min * 60 min/hr = 540000 W-sec/hr
1 kW = 1000 W * 3600 sec = 3.6E6 W-sec
E (8 hrs) = 8 * .54E6 W-s = 4.32E6 W-sec
or E= 4.32/3.6 = 1.2 kW = .168 $/day
20/150 = .133 as much for a 20-watt bulb
For a LED bulb cost/day = .168 * .133 = $.022/da
Note 1 W = 1 Joule/sec
Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team members who do not wear glasses, 30 percent of them are in the 10th grade.
To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade?
14%
17%
55%
67%
Answer: 14%
Step-by-step explanation: To find the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade, we divide the number of members who meet both criteria (14) by the total number of members (100) and multiply by 100 to get a percentage. Therefore, the probability is approximately 14%.
- Lizzy ˚ʚ♡ɞ˚
The Venn diagram above shows the results of a survey of 200 readers on the type of magazine they read.
If a respondent is chosen at random, what is the probability that the respondent reads a technology OR a business magazine?
ОА. 11/20
OB. 9/20
Ос. 3/5
OD. 13/20
Answer:
11/20
Step-by-step explanation:
The total number of readers is 200
\(80 + 10 + 60 + 50 = 200\)
The probability of an event is the number of the possible outcomes leading to the event over the total number of outcomes
thus, the number of people reading either a business magazine or a technology one is
\(P = \frac{50 + 60 }{200} = \frac{110}{200} = \frac{11}{20}\)
The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?
The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?
The side lengths of the playground in the other scale drawing is \(\frac{5a}{8}\).
By using geometry we answer this question.
Geometry is nothing but the branch of mathematics which deals with measurements of shapes.
Here, we take the scale from a playground to this drawing as "a" and The scale from the same playground to another drawing as "b".
First, we see the scale from a playground to this drawing.
\(\frac{a}{l}= \frac{1}{5}\)
\(l=5a\)
Now we see the scale from the same playground to another drawing.
\(\frac{b}{l} =\frac{1}{8}\)
\(b=\frac{l}{8}\\\)
Here, l=5a then
\(b=\frac{5a}{8}\)
Therefore, the side lengths of the playground in the other scale drawing is \(\frac{5a}{8}\).
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please do for me number 8 g
I will give brainlist thanks
Answer:
1/2 3,4 (3,2) ab)
A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a card less than 10).
Answer:
8/13
Step-by-step explanation:
In any suit, there are 8 cards less than 10:
2, 3, 4, 5, 6, 7, 8, 9
Each card comes in 4 suits, so there is a total of
4 × 8 = 32
cards less than 10.
P(drawing a card less than 10) = 32/52 = 8/13
Answer: 8/13
There are 9 cookies shared equally between 12 people. What fraction of a cookie does each person receive
A 1/12
B 9/12
C 12/9
D1/9
Answer:
9/12
Step-by-step explanation:
if 9 cookies are shared between 12 people, we need to divide 9 by 12 to obtain the fraction of a cookie that each person receives:
9/12
The sum of 2 times a number and 6 is 5.
\(x=5\)
Since the number is unknown, we'll call it x. So if 2 times the number (x) plus 6 equals 5, you would write this as the equation 2x + 6 = 5. In order to solve for x, you need to get rid of the 6 and the coefficient (the number in front of the x).
First, get rid of the 6 by subtracting 6 from both sides of the equation (to make sure the equation stays correct, you need to do the same thing to both sides), so
\(2x + 6 - 6= 5 - 6\)
\(2x=-1\)
Now, to get rid of the 2, divide each side of the equation by 2:
\(2x/2 = -1/2\)
\(x = -1/2 ( or (-0.5))\)
To check your answer, substitute \(-1/2 (or -0.5)\) for x in your original equation like so:
\(2x + 6 = 5\)
\(2(-1/2) + 6 = 5\)
\(-2/2 + 6 = 5\)
(to multiply a whole number by a fraction, you write the whole number as a fraction ( then multiply the numerators and denominators)
\(-\frac{2}{2}=-1\) , so
\(5=5\)
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Please help if u can
Answer:
f(x) -> 2 as x -> -∞ and f(x) -> ∞ as x -> ∞
Step-by-step explanation:
f(x) -> 2 as x -> -∞ and f(x) -> ∞ as x -> ∞
*this is because the graph shows that the y value cannot pass by 2 as the x value constantly decreases and as x is increasing, there is just an arrow showing that the graph is constantly going up and therefore going to ∞
Hi! Im struggling with this question and how to solve it
The solution to the union operation is given as follows:
C U D = (-∞, ∞).
The solution to the intersection operation is given as follows:
C ∩ D = [3, 7).
How to obtain the union of the sets?The sets are given as follows:
Set C: numbers that are greater than or equals to 3.Set D: numbers that are less than 7.The union operation between these two sets is composed by all the values that respect at least one of these conditions, hence it is given by all real values, and the interval is:
C U D = (-∞, ∞).
How to obtain the intersection of the sets?The intersection operation gives as a result the elements that belong to both sets, hence the bounds of the interval are given as follows:
Closed at y = 3, as y = 3 belong to both sets.Open at y = 7, as y = 7 does not belong to set D.Hence the interval notation of the intersection operation is of:
C ∩ D = [3, 7).
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y=100000(0.25)^8 exponential decay
y=100000(0.25)^8 exponential decay is 1.526.
How to find the exponential decay?The formula represents exponential decay with a decay factor of 0.25 and an initial value of 100,000. To evaluate the formula, you can simply substitute 8 for the variable x (since the formula has y in terms of x) and calculate the result:
y = 100000(0.25)^8
y = 100000(0.00001525878906)
y ≈ 1.526
Therefore, the value of y for x = 8 is approximately 1.526. This means that after 8 units of time, the initial value of 100,000 has decayed to around 1.526.
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6[x-2(x-3)] simplifies to the from ax +b .
Answer:
\(6(6 - x)\)
Step-by-step explanation:
1) Expand.
\(6(x - 2x + 6)\)
2) Collect like terms.
\(6((x - 2x) + 6)\)
3) Simplify (x - 2x) + 6 to -x + 6.
\(6( - x + 6)\)
4) Regroup term.
\(6(6 - x)\)
Therefor, the answer is 6(6 - x).
Maria is studying the phenomenon of pyramid power. She has read that items placed inside pyramids show amazing properties. Maria is going to see if the pyramid phenomenon will work on her young plants. She will construct an all-glass pyramid as shown.
The pyramid is regular with a square base, and all eight edges are the same length. From the possible solutions below, which amount is the closest estimate of the amount of glass Maria will need to construct her pyramid?
a) 1935 cm squared
b) 3353 cm squared
c) 5289.25 cm squared
d) 8642.5 cm squared
The solution that is the closest estimate of the amount of glass Maria will need to construct her pyramid would be =5289.25 cm squared. That is option C.
How to calculate the area of a square based pyramid?To calculate the area of a square based pyramid, the formula that should be used would be given below as follows:
\(area = {a}^{2} + 2a \sqrt{ \frac{a2}{4} } + {h}^{2} \)
Where:
a= 44cm
height= 44²-22²= 38.1cm
Area= 44²+ 2(44) × √44²/4 + 38.1²
= 1936+88 × √ 484+1452
= 2024× √1936
= 5807.61 cm².
Therefore the closest estimate to the final answer would be 5289.25 cm squared
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Credit card applicants have a mean credit rating score of 667. Assuming that the distribution of credit rating scores, X, is Normal with standard deviation 65, calculate the probability that a single applicant for a credit card will have a credit rating score above 700.
Calculate the z-score. Round to two decimal places. Include any leading zeros.
Calculate the probability. Round to four decimal places. Include any leading zeros.
0.306 is the z-score. Round to two decimal places. Include any leading zeros.
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
Essentially, standard deviation is a measure of the degree of variability within a given data collection.
Let X the random variable that represent the rating score of a population, and for this case we know the distribution for X is given by
X `N(667,65 )
Where μ = 667 and σ = 65
We are interested on this probability
P(X > 700 )
And the best way to solve this problem is using the normal standard distribution and the z score given by
Z= X - μ/σ
If we apply this formula to our probability we got this
P(X > 700 )
= P(X - μ/σ > 700 -μ/σ)
= P(Z > 700 - 667/65 )
= P(Z > 0.508 )
And we can find this probability using the complement rule and excel or a calculator and we got
P( z > 0.508 ) = 1 - P(Z - 0.508 ) = 1 - 0.694 = 0.306
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answer:
25000
Step-by-step explanation: