Answer: Assuming the student walks along a rectangular grid and not diagonally, the possible locations the student could end up after walking 4 miles in any direction would be the points that are 4 units away from the starting point in a north, south, east, or west direction.
Using this information, we can determine that the possible locations the student could end up at are:
(-2, 10)
(-6, 14)
(-10, 10)
(-6, 6)
Therefore, the answer is:
All of the above locations are possible endpoints.
Step-by-step explanation:
If the student walks 4 miles north, south, east, or west, the location at the end of the walk are respectively, (-6, 14). (-6, 6), (-2,10). (-10, 10).
What is a coordinate plane?The Cartesian plane, named after the mathematician René Descartes (1596 - 1650), is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.
Given that,
A student starts a walk at (-6, 10)
If the student walks 4 miles north, south, east, or west,
The location at the end of the walk =
Plotting dotted diagram,
East
|
North --------- |-------------- South
|
West
Suppose, he goes to north direction
Then, 4 will be added to y coordinate,
It can be written as,
(-6, 14)
Similarly, for South, (-6, 6),
East, (-2,10).
West, (-10, -10)
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what is the value of f(40,20) and what does it represent? find an estimate for fv(40,20) and ft(40,20).
fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1 , ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05 are the required functional estimations of a given representations.
However, we can estimate the partial derivatives with respect to x (fv) and y (ft) at the point (40,20) using the definition of partial derivatives:
fv = ∂f/∂x ≈ (f(40+h,20) - f(40,20))/h
where h is a small increment in the x direction. Similarly,
ft = ∂f/∂y ≈ (f(40,20+k) - f(40,20))/k
where k is a small increment in the y direction.
To estimate fv(40,20) and ft(40,20), we need to choose small values of h and k and evaluate the function at the corresponding points. Let's say h = 0.1 and k = 0.05:
fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1
ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05
We can then use these estimates to approximate the value of f(40.1,20.05) using the first-order Taylor approximation:
f(40.1,20.05) ≈ f(40,20) + fv(40,20)0.1 + ft(40,20)0.05
Note that this is an approximation and may not be very accurate if the function is highly nonlinear or has discontinuities. However, it can give us a rough idea of the value of f(40,20) and how it changes with small variations in x and y.
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what is the difference of (4m^2-5) -(5m-20)
Answer:
4m^2+15-5m
Step-by-step explanation:
Remove parentheses.
4m^2-5-5m+20
Collect like terms.
4m^2+(-5+20)-5m
Simplify
4m^2+15-5m
What is the base, rate of change (incr/decr), and is it growth or decay
Y=3000(0.72)^x
The key features of the function are Base = 0.72, Rate = decrement and it decays
identifying the key features of the functionGiven that
y = 3000 * (0.72)ˣ
The given equation is in the form of exponential decay:
Base: The base of the exponential function is the constant term that is being raised to a power. In this case, the base is 0.72.
Rate of change: The rate of change is the factor by which the function is being multiplied or divided as the input variable increases.
Since the base is less than 1, the function is decreasing as x increases. The rate of decrease is given by the base, which is 0.72.
Growth or decay: As the base is less than 1, the function is decreasing, which means it is a decay function.
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PLS HELP ASAP .a vacuum cleaner costs the owner $220 to buy. They then mark up the cost to sell it by 30%. What as the amount of the mark up? What is the selling price?
The amount of the mark up is $66 and the selling price is $286.
What is markup percentage?The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:
Markup percentage = (Selling price - Cost price) / Cost price x 100%
Given that, the mark up is 30%.
Thus,
Mark up = 0.3 x $220 = $66
The selling price is:
Selling price = $220 + $66 = $286
Hence, the amount of the mark up is $66 and the selling price is $286.
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Write ^4√11^5 without radicals.
Answer: ^4√11^5 = 11^(5/4)
Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.
So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:
^4√11^5 = (11^5)^(1/4) = 11^(5/4)
Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.
Hope this helps, and have a great day!
Any number that can be written as a decimal, write as a decimal to the tenths place.
Given A = (-3,2) and B = (7,-10), find the point that partitions segment AB in a 1:4 ratio.
The point that partitions segment AB in a 1:4 ratio is (
).
The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].
How to find the ratio?To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.
Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:
[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]
and
[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]
Using the distance formula, we can find the lengths of AP, PB, and AB:
[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]
Substituting these into the section formula, we have:
[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]
Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].
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A primary credit card holder has a current APR of 16.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent?
To calculate the monthly periodic interest rate from an annual percentage rate (APR), we need to divide the APR by 12 (the number of months in a year). We can use the following formula:
Monthly periodic interest rate = APR / 12
In this case, the APR is 16.75%, so we can plug it into the formula and simplify:
Monthly periodic interest rate = 16.75% / 12
Monthly periodic interest rate = 1.395833...%
Rounding to the nearest hundredth of a percent, we get:
Monthly periodic interest rate = 1.40%
Therefore, the monthly periodic interest rate for the primary credit card holder is 1.40%.
A candy store uses 10. 3 grams of sugar each hour. How many grams of sugar will the store use in 10 hours?
The candy store will use 103 grams of sugar in 10 hours.
To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).
To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.
We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.
So the calculation would be:
10.3 grams/hour x 10 hours = 103 grams
Therefore, the candy store will use 103 grams of sugar in 10 hours.
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number 5 goes through the device and the result is 25 . what would a possible rule for machine B be ?
Answer: multiplied by 5 or squared
Step-by-step explanation:
If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).
5 x 5 = 25
5^2 = 25.
No idea how to use this app tbh
Answer:
-10
Step-by-step explanation:
I added a photo of my solution
Answer:
Answer is -10
Step-by-step explanation:
What is the sum of A+C?  a.the matrices b -2,11,5,0,-2,1 c.12,3,1,-2,2,-1 d. -35,28,6,-1,0,12
Answer:on edge B)-2,11,5,0-2,1
The sum of the matrices A and C from the list of options is the matrix B
Calculating the sum of the matricesGiven the following matrices
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
To find the sum of matrices A and C, we add the corresponding elements in each matrix:
So, we have: A + C
| 0 - 2 6 + 5 2 + 3 |
| 1 - 1 5 - 7 -2 + 3|
Evaluate the sum
| -2 11 5 |
| 0 -2 1 |
This represents option B
Therefore, the sum of matrices A and C is (B)
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Complete question
What is the sum of A+C?
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
HELP IS DUE TODAY!!!!!!!!!!!!!!!!!!
Using expressions,
4a. x= 0 is not possible.
4b. x= 1 is not possible.
5a. (9x-5)(9x+5)
5b. (x-3)(2x+1)
6. 1/(3x-7)
7a. x = (-5,∞)
7b. x = (∞,2]
7c. x = (-3,7]
What are expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let's examine the writing of expressions.
The other number is x, and a number is 6 greater than half of it.
As a mathematical expression, this proposition is denoted by the expression x/2 + 6.
Here the values of x has to be such that the denominator is not equal to zero.
So, x cannot be zero and x cannot be 1 as these two values in the respective questions will make the denominator zero.
a. 81x²-25
= 81x² + 45x-45x-25
=9x(9x+5)-5(9x+5)
= (9x-5)(9x+5)
b. 2x²-5x-3
= 2x² + x - 6x -3
= x(2x+1)-3(2x+1)
=(x-3)(2x+1)
Next, the intervals for x are as follows:
x = (-5,∞)
x = (∞,2]
x = (-3,7]
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Find 7/8(3. 5) write your answer as a mixed number in the simplest form
to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.
To find 7/8 of 3.5, we can simply multiply 7/8 and 3.5 together.
7/8 x 3.5 = (7/8) x (7/2) = 49/16
So, the answer is 49/16. However, we need to write the answer as a mixed number in the simplest form.
To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. In this case, 49 divided by 16 is 3 with a remainder of 1.
So, the mixed number is 3 1/16.
To simplify the mixed number, we need to check if we can reduce the fraction part (1/16) further. 1 is not divisible by any number other than 1 itself, so it is already in its simplest form.
Therefore, the final answer is 3 1/16.
In summary, to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.
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Determine the value of X
Answer:
x = 26.
Step-by-step explanation:
Given: 2x + 3x + 50 = 180
First, write it down:
2x + 3x + 50 = 180
Then, collect like terms:
2x + 3x = 180 - 50
Then calculate:
5x = 130 (Divide both sides by 5)
x = 26
A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Which of the following is the best interpretation of the interval? Five percent of the time, the time for response is less than 2.8 minutes or greater than 12.3 minutes. B The probability is 0.95 that a randomly selected time for response will be between 28 minutes and 12.3 minutes Ninety-five percent of the time the mean time for response is between 2.8 minutes and 12.3 minutes. (D) We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes We are 95% confident that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.
The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct
A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.
Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.
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2x^4 −15x^3 +27x^2 +2x +8 is divided by x−4
Answer:
Step-by-step explanation:
Standard: 2x^3 - 7x^2 -x-2
Quotient: 2x^3- 7x^2 -x-2
remainder: 0
miguel rode his bicycle 4 miles less than 5 times the number nathen rode. if Miguel rode his bicycle 6 miles, how many miles did nathan ride?
Answer:Hence, Nathan rode 2 miles
Step-by-step explanation:ask if you need any questions
Pls Help I am stuck on this and i don't know how to do this
Men will have completed oil changes in hours Therefore, Will and Gabriel will each have done 12 oil changes after 4 hours.
What is hours?Hours is a unit of time measurement. It is used to measure a specific amount of time and is usually denoted by the symbol “h”. There are 24 hours in a day, 60 minutes in an hour and 60 seconds in a minute. Hours are used to measure both short and long periods of time. Commonly, hours are used to measure the length of a workday, the length of a school day, or the length of a movie. Hours are also used to measure how long a person has been alive, how long an event has been going on, or how long an item has been in use.
Let W be the total number of oil changes Will has completed, and G be the total number of oil changes Gabriel has completed.
System of equations:
W = 8 + 2t
G = 3t
Since they will be tied at some point during the day, W = G.
Substituting W into G's equation:
8 + 2t = 3t
Solving for t:
2t = 8
t = 4
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at the farmers market there is a large pile of small cauliflowers. the mean weight of these cauliflowers is 400 grams with a standard deviation of 20 grams. assume the weight of theses cauliflowers is normally distributed. which has a greater probability, the mean weight of an individual cauliflower being between 400 and 409 grams or the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams?
The mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability.
Standard deviation of the given data is 20 grams. The mean weight of the cauliflower is 400 grams. Now, for calculating the probability, we need to standardize the given mean weight of cauliflower. It will be as follows. Z-score for the mean weight of cauliflower is given as:
z = (X - μ) / σwhere X = 400 grams (mean weight of cauliflower)
μ = 400 grams (mean weight of the population)
σ = 20 grams (standard deviation)z = (400 - 400) / 20 = 0
Now, the probability of the mean weight of an individual cauliflower being between 400 and 409 grams is as follows:
P(400 < X < 409) = P(0 < Z < 0.45)
Using the standard normal distribution table, the probability is 0.1745.
The mean weight of a random sample of 36 of the cauliflowers is between 400 and 409 grams. The mean weight of a random sample of 36 of the cauliflowers is given by:
(X-μ)/ (σ/√n)where μ = 400 grams (mean weight of cauliflower)
σ = 20 grams (standard deviation)
n = 36 (number of samples)
Now, we need to standardize the sample mean. It will be as follows:
z = (X - μ) / (σ/√n)z = (400 - 400) / (20 / √36)
z = 0
As the z-score is zero, the probability will be equal to 0.5. Hence, the mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability than the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams.
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I Really want this pleaseeeeeeeeeeeeeeeeeee
Answer:
no
Step-by-step explanation:
using Pythagorean theorem:
[tex]26^{2} +42^{2}=50^{2}[/tex]
676+1764=2500
2440=2500
2440<2500
Answer:no
Given mn, find the value of x.
t
(7x-4)º
(3x+28)°
Hence, the value of variable in the given expression x is 8
What is Angle?An angle is formed when two straight lines meet at a common endpoint.
given:∠1 = 7x - 4
∠2 = 3x + 28
A secant line that crosses two parallel lines produces these angles. After that, these angles were congruent, which means that their measures are equal.
Then, equaling both given expressions and solving for x, we get:
Step1: subtract 3x both sides
7x - 4 = 3x + 28
Step2: add 4 both sides
7x - 3x - 4 = 28
Step2: simplify like terms
7x - 3x = 28 + 4
Step3: divide by 4 both sides
4x = 32
x = 32/4
x = 8
Hence, the value of x is 8.
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Write an equation that describes the function.
4. Input, x Output, Y
0 0
1 4
2 8
3 12
Answer:
Y = 4x
Step-by-step explanation:
In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.
Borachio eats at the same fast-food restaurant every day. Suppose the time X between the moment Borachio enters the restaurant and the moment he is served his food is normally distributed with mean 4. 2 minutes and standard deviation 1. 3 minutes. A. Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served. B. Find the probability that average time until he is served in eight randomly selected visits to the restaurant will be at least 5 minutes
The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is 0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.
Given that mean μ = 4.2 , standard deviation σ = 1.3
1. P(X >= 5) = P((X - μ)/σ >
= (5 - 4.2) /1.3
= P(Z ≥ 0.6154)
= 1 - P(Z < 0.6154)
= 1 - 0.7324
= 0.2676
The required probability is 0.2676.
2.Given that n = 8 then [tex]\bar x[/tex] = σ/[tex]\sqrt{(n)[/tex] = 1.3/√(8) = 0.4596
P(x-bar ≥ 5) = P(([tex]\bar x[/tex] - μ)/σx-bar ≥ (5 - 4.2)/0.4596)
= P(Z ≥ 1.7406)
= 1 - P(Z < 1.7406)
= 1 - 0.9591
= 0.0409
The required probability is 0.0409.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
(9x-1)º
74°
62°
PLS HURRY!!
In the given triangle, the value of x = 5.
What is a triangle's definition?
A triangle is a geometrical shape that is defined as a polygon with three sides and three angles. It is a closed figure with three line segments as its sides, and these sides intersect at three points, which are called vertices. When we add all the angles of a triangle then the result will always be 180°.
Now,
As we know the property of a triangle that
sum of all angles of triangle=180°
given angles are (9x-1)°, 74° and 62°
then,
9x-1+74+62=180°
9x+135=180
9x=45
x=5
Hence,
the value of x is 5.
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in a congressional district, 55% of the registered voters are democrats. which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?
A. P( z< 50 — 55/ 100 )
B. P( z< 50 — 55/ √55(45)/100)
C. P( z< 55 — 5 / √55(45)/100)
D. P( z< 50 — 55/√100(55) (45))
The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).
To find the probability, we first calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.
The standard deviation can be calculated as:
σ = √(np(1-p))
where n is the sample size (100) and p is the proportion of democrats (0.55).
Now, plug in the values into the z-score formula:
z = (50 - 55) / √(100 * 0.55 * 0.45)
The probability is then found as P(z < z-score), which is represented by the option B.
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What percentage of people would exed to score higher than a 2.5, but lower than 3.5? The mean: X=3.00 The SDis= + 0.500 18% 999 o 50% 03%
Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.
Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.
First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]
Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).
To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:
Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]
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in a test measuring the life span of a certian brand of tire, 100 tires are tested. the results showed an averaged lifetime of 50,000 miles, with a standard deviation of 5,000 miles. estimate the 95% confidence interval on the mean: 50,000 - miles (round up all decimal places)
We can say with 95% confidence interval that the true mean lifetime of the tires is between 49,020 and 50,980 miles.
To calculate the confidence interval, we use the formula:
CI = x-bar ± z* (σ/√n)
where x-bar is the sample mean (50,000 miles), z is the z-score associated with the desired confidence level (in this case, 1.96 for 95% confidence level), σ is the standard deviation (5,000 miles), and n is the sample size (100).
Plugging in the values, we get:
CI = 50,000 ± 1.96*(5,000/√100)
Simplifying the expression, we get:
CI = 50,000 ± 980.
Therefore, we can say with 95% confidence that the true mean lifetime of the tires is between 49,020 and 50,980 miles.
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Find the linear measure of arc KML on OO, where line segment KM is a diameter, OM=36, and angle KOL-145. Use 3. 14 for pie and estimate your answer to two decimal places
The linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.
Since KM is a diameter, angle KOM is a right angle. Therefore, angle KOL is a straight angle, which means that angle MOL is 180 - 145 = 35 degrees.
Now, we can use the fact that the measure of an arc is proportional to the measure of the angle it subtends. In particular, if the measure of an angle in degrees is θ and the radius of the circle is r, then the length of the arc it subtends is given by:
length of arc = (θ/360) * 2πr
In this case, the radius of the circle is half of the diameter KM, which is 36/2 = 18. So we have:
length of arc KML = (35/360) * 2 * 3.14 * 18
≈ 3.33
Therefore, the linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.
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50 Points
Janey paints a block of wood with gold glitter for an art project. The block measures
8 inches by 10 inches by 20 inches.
After she's done, she decides to make two blocks by cutting through the block on the
red line. She still wants each block to be covered with gold glitter.
What is the total area of the cut surfaces she still needs to paint?
Answer the questions to find out.
1. What is the shape of each cut surface? what are its dimensions?
2. What is the area of each cut surface?
3. What is the total area Jenny needs to paint? Explain how you found your answer.
Answer:
The shape of each cut surface is a rectangle. The dimensions of the first cut surface are 8 inches by 10 inches, and the dimensions of the second cut surface are 10 inches by 20 inches.
The area of the first cut surface is 8 inches x 10 inches = 80 square inches. The area of the second cut surface is 10 inches x 20 inches = 200 square inches.
To find the total area Jenny needs to paint, we need to add the area of the first cut surface to the area of the second cut surface.
Total area = Area of first cut surface + Area of second cut surface
Total area = 80 square inches + 200 square inches
Total area = 280 square inches
Therefore, Jenny needs to paint a total area of 280 square inches.
At a basketball game, a team made 53 successful shots. They were a combination of 1- and 2-point shots. The team scored 90 points in all. Write and solve a system of equations to find the number of each type of shot.
Answer: the team amassed 88i points total, by shooting t two-point baskets and u 1-point free throws.
t+u = 53
total is: 2t + u = 88.
Step-by-step explanation:
hope i makes sense