Answers
Step-by-step explanation:
remember the trigonometric triangle inside a circle.
sine is the up/down leg, cosine is the left/right leg.
the Hypotenuse (baseline) of the right-angled triangle is the angle-defining radius of the circle.
this is the basic definition inside the norm-circle with radius = 1.
for any other size sine and cosine need to be multiplied by the actual radius for the actual triangle side lengths.
I think you need the answer in simplified fraction and square root notification (you cut that off), but I give you also the decimal result, just in case.
so,
78 = cos(30)×y
78 = (sqrt(3)/2) × y
y = 78 / (sqrt(3)/2) = 2×78/sqrt(3) = 156/sqrt(3) =
= 90.06664199...
x = sin(30) × y = 0.5 × 156/sqrt(3) = 78/sqrt(3) =
= 45.033321...
Related Questions
If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + 5), what is the value of r?
F.:3
H. 7
J. 12
K. Cannot be determined from the given information
Answers
Answer:
H. 7
Step-by-step explanation:
Given x² + rx + 12 is equivalent to (x + 3)(x + s), equate the two expressions and expand the right side of the equation:
[tex]\begin{aligned}x^2+rx+12&=(x + 3)(x + s)\\ x^2+rx+12&=x^2 + sx + 3x + 3s\\x^2+rx+12&=x^2 + (s+3)x + 3s\end{aligned}[/tex]
To find the value of r, first find the value of s.
The constant term of the right-hand side must be equal to the constant term of the left-hand side. Therefore:
[tex]\implies 3s = 12[/tex]
Solve for s by dividing both sides of the equation by 3:
[tex]\implies s = 4[/tex]
Compare the coefficients of the terms in x:
[tex]\implies r = s + 3[/tex]
Substitute the value of s into the equation and solve for r:
[tex]\begin{aligned} \implies r &= s + 3\\&= 4 + 3\\&= 7\end{aligned}[/tex]
Therefore, the value of r is 7.
Answer:
[tex]\large\boxed{\sf r = 7 }[/tex]
Step-by-step explanation:
Correct question:- If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + s), what is the value of r?
Here we are given that , the expression (x+3)(x+s) is equal to r² + rx + 12 .
Firstly, expand the expression (x+3)(x+s) as ,
[tex]\implies (x+3)(x+s) \\[/tex]
[tex]\implies x(x+s)+3(x+s) \\[/tex]
[tex]\implies x^2 + xs + 3x + 3s \\[/tex]
Take out x as common,
[tex]\implies x^2 + (3+s)x + 3s \\[/tex]
Now according to the question,
[tex]\implies x^2 + (3+s)x + 3s = r^2 + rx + 12\\[/tex]
On comparing the respective terms , we get,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies 3s = 12 \\[/tex]
Solve the second equation to find out the value of s , so that we can substitute that in equation 1 to find "r" .
[tex]\implies 3s = 12 \\[/tex]
[tex]\implies s =\dfrac{12}{3}=\boxed{4} \\[/tex]
Now substitute this value in equation (1) as ,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies r = 3 + 4 \\[/tex]
[tex]\implies \underline{\underline{ \red{ r = 7 }}} \\[/tex]
and we are done!
In a large study designed to compare the risk of cardiovascular disease (CVD) between smokers and nonsmokers, random samples from each group were selected. The sample proportion of people with CVD was calculated for each group, and a 95 percent confidence interval for the difference (smoker minus nonsmoker) was given as (-0.01, 0.04). Which of the following is the best interpretation of the interval? We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the sample is between -0.01 and 0.04. We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the population is between -0.01 and 0.04. We are 95% confident that the proportion of all smokers with CVD is greater than the proportion of all nonsmokers with CVD because the interval contains more positive values. The probability is 0.95 that for all random samples of the same size, the difference in the sample proportions for smokers and nonsmokers with CVD will be between -0.01 and 0.04. long Pa Docs The probability is 0.95 that there is no difference in the proportions of smokers and nonsmokers with CVD because o is included in the interval -0.01 and 0.04 D Submit hips..
Answers
The best interpretation of the confidence interval is We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the population is between −0.01 and 0.04 that is option B.
Confidence interval is estimate of Parameter were parameter is difference in proportion of smokers and non smokers in population.
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
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LetY1,Y2,Yn denote a random sample of size n from a population whose density is given by f(y)={αyα−1θα,0≤y≤θ0,elsewhere,where α>0 is a known, fixed value, but θ is unknown. Consider the estimator ˆθ=max(Y1,Y2,...Yn).(a) Show that ˆθ is a biased estimator for θ.(b) Find a multiple of ˆθ that is an unbiased estimator of θ.(c) Derive MSE(ˆθ).
Answers
(a) θ is a biased estimator for θ.
(b) (α+1)Y/α is an unbiased estimator of θ.
(c) MSE(θ) = αθ^2/[(α+1)^2(α+2)]
(a) To show that θ is a biased estimator for θ, we need to show that E(θ) ≠ θ.
Using the definition of the maximum function, we have
P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n
where F(y) is the cumulative distribution function of Y.
Differentiating both sides with respect to y, we get:
f(θ) = n(F(θ))^(n-1)f(θ)
Simplifying, we get
F(θ) = (1/n)^(1/(n-1))
Using this result, we can find the expected value of θ
E(θ) = ∫₀^∞ θf(θ)dθ = ∫₀^θ θαθ^α-1dθ = αθ/(α+1)
Thus, E(θ) ≠ θ, which means that θ is a biased estimator for θ.
(b) To find a multiple of θ that is an unbiased estimator of θ, we can use the method of moments.
We know that the population mean of Y is
μ = ∫₀^θ yf(y)dy = αθ/(α+1)
The sample mean is
Y = (Y1+Y2+...+Yn)/n
Equating these two expressions and solving for θ, we get
θ = (α+1)Y/α
Thus, (α+1)Y/α is an unbiased estimator of θ.
(c) The mean squared error (MSE) of θ can be written as
MSE(θ) = E[(θ - θ)^2]
Expanding the square and using the linearity of expectation, we have
MSE(θ) = E[θ^2] - 2θE[θ] + E[θ]^2
We already know that E[θ] = αθ/(α+1).
To find E[θ^2], we can use the fact that θ = max(Y1,Y2,...Yn)
P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n
Differentiating both sides with respect to y, we get
f(θ) = n(F(θ))^(n-1)f(θ)
Using this result, we can find E[θ^2]
E[θ^2] = ∫₀^∞ θ^2f(θ)dθ = ∫₀^θ θ^2αθ^α-1dθ = αθ^2/(α+2)
Substituting these expressions into the MSE formula, we get
MSE(θ) = αθ^2/(α+2) - 2θ(αθ/(α+1)) + (αθ/(α+1))^2
Simplifying, we get
MSE(θ) = αθ^2/[(α+1)^2(α+2)]
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Which expressions are equivalent to 8(3/4y -2)+6(-1/2+4)+1
Answers
Answer: 6y + 6
Step-by-step explanation:
To simplify the expression 8(3/4y -2) + 6(-1/2+4) + 1, we can follow the order of operations (PEMDAS):
First, we simplify the expression within parentheses, working from the inside out:
6(-1/2+4) = 6(7/2) = 21
Next, we distribute the coefficient of 8 to the terms within the first set of parentheses:
8(3/4y -2) = 6y - 16
Finally, we combine the simplified terms:
8(3/4y -2) + 6(-1/2+4) + 1 = 6y - 16 + 21 + 1 = 6y + 6
Therefore, the expression 8(3/4y -2) + 6(-1/2+4) + 1 is equivalent to 6y + 6.
2.35 [5] <$2.9> For the following code: Ibu $t0,($t1) sw $t0,($t2) Assume that the register $t1 contains the address 0x10000000 and the data at address is 0x11223344. 2.35.1 [5] <$2.3, 2.9> What value is stored in 0x10000004 on a big-endian machine? 2.35.2 [5] <$2.3, 2.9> What value is stored in 0x10000004 on a little-endian machine?
Answers
The value stored in 0x10000004 on a big-endian machine is given by 0x00000011.
The word "endianness" refers to the arrangement of bytes as they are stored in computer memory. Endianness is classified as big or little depending on which value is stored first.
The "big end" (the most important item in the sequence) is put first and at the lowest storage address in a big-endian order. The "small end" (the least important item in the sequence) is put first in a little-endian order.
(1)In Big-endian Machine, first byte of multi-byte data will be stored first(at lower memory address)
Address Data
0x10000000 0x11
0x10000001 0x22
0x10000002 0x33
0x10000003 0x44
---------------------------------------------------------------------
lbu $t0, 0($t1)
Load unsigned byte in Register $t0 at address 0x10000000
Here byte at address 0x10000000 is 0x11
$t0 = 0x00000011
----------------------------------------------------
sw $t0, 0($t2)
Store a word(4 bytes) from Register $t0 to memory address 0x10000004
value stored in 0x10000004 is 0x00000011
--------------------------------------------------------------------------------
(2)In Little-endian Machine, last byte of multi-byte data will be stored first(at lower memory address)
Address Data
0x10000000 0x44
0x10000001 0x33
0x10000002 0x22
0x10000003 0x11
---------------------------------------------------------------------
lbu $t0, 0($t1)
Load unsigned byte in Register $t0 at address 0x10000000
Here byte at address 0x10000000 is 0x44
$t0 = 0x00000044
----------------------------------------------------
sw $t0, 0($t2)
Store a word(4 bytes) from Register $t0 to memory address 0x10000004
value stored in 0x10000004 is 0x00000044.
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Help pleaseeeeeeeeee!
Answers
Answer:
y = 0.8x
Step-by-step explanation:
machine fills 24 jars in 30 seconds , then
fills 1 jar in [tex]\frac{24}{30}[/tex] = 0.8 seconds
thus number of jars filled in x seconds is
y = 0.8x
divide 14 hours and 40 minutes by 5
you must give your answer in hours and minutes
Answers
Answer:
2 hours and 56 minutes.
Step-by-step explanation:
To divide 14 hours and 40 minutes by 5, we need to convert everything to minutes first.
14 hours is equal to 14 x 60 = 840 minutes.
So, 14 hours and 40 minutes are equal to 840 + 40 = 880 minutes.
Dividing 880 minutes by 5 gives us:
880 ÷ 5 = 176 minutes
Now, we need to convert the answer back to hours and minutes.
There are 60 minutes in 1 hour, so we can find how many hours are in 176 minutes by dividing by 60:
176 ÷ 60 = 2 with a remainder of 56.
So, the answer is 2 hours and 56 minutes.
When I first look at an equation, HOW DO I KNOW which method to use to solve it?
for example:
-4(7j+2) = 10
What do I look for (by looking at it) to know if I should start to solve it by distributing, or just use division?
Please help! I am really confused. Thank you
Answers
Answer:
j = - 9/14
Step-by-step explanation:
-4(7j+2) = 10
Distributing First
-28j - 8 = 10
Try to get the variable on one side.
-28j = 18
Divide both sides by -28
j = -18/28 = - 9/14
6TH GRADE MATH PLS HELP TYSM
Answers
Answer:
m = 1
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-1,0) (0,1)
We see the y increase by 1 and the x increase by 1, so the slope is
m = 1
Sorry if photo is side ways or upside down
Answers
1 gallon = 8 pints, therefore 2 gallons = 16 pints.
10 members = 10 pints drank, which means 16-10=6 pints left (A).
For question 5:
PART A
1 step = 1 meter
1km = 1,000 meter, hence
5km = 5,000 steps.
PART B
1 step = 0.5 meters
1km = 2,000 steps, hence
5km = 10,000 steps.
Hope this helped you!
Question 2 (2 points) ✓ Saved
In the news, you hear "tuition is expected to increase by 12% next year." If tuition
this year was $5,500 per year, what will it be next year?
660
6160
4840
Cannot be solved.
Answers
Answer: 6,160
Step-by-step explanation:
Immediately, without even doing any math, the only logical answer would be 6160. This is because the current tuition is 5,500 and it is increasing so the answer cannot be lower.
However, mathematically you can prove this by turning 12% into a decimal and multiplying it by 5,500. 12% could be converted to .12 and because it is increasing you must add 1, or 100%, since that is what it started with. 5,500 x 1.12 = 6,160.
5 Mrs. Newsome bought a piece of fabric 142 centimeters long to make a quilt for her son's bedroom. She bought a piece of fabric 2 meters long for curtains. How could Mrs. Newsome find the total length, in centimeters, of both pieces of fabric? Multiply 2 by 2,000, then add 142. Add 2 and 142, then multiply by 100. Divide 142 by 100, then add 2,000. O Multiply 2 by 100, then add 142. B C
Answers
Answer:
Step-by-step explanation:
To find the total length of both pieces of fabric in centimeters, we need to add the length of the first piece of fabric (142 cm) and the length of the second piece of fabric (2 meters).
However, we need to make sure that the units are consistent before we add the lengths. We can convert the length of the second piece of fabric from meters to centimeters by multiplying by 100. Therefore, the total length in centimeters is:
142 cm + 2 meters * 100 cm/meter = 142 cm + 200 cm = 342 cm
The option that correctly gives the answer is "Multiply 2 by 100, then add 142" (Option C).
11/12 x 8/25 x 15/16 x 9/44
Answers
9/160
Decimal form:
0.05625
The area of a trapezium is 156cm2, the parallel sides are 17cm and 35cm respectively. What is the height of the trapezium
Answers
Answer:
6 cm
Step-by-step explanation:
You want the height of a trapezium with bases 17 cm, 35 cm and area 156 cm².
Area formulaThe formula for the are of a trapezium is ...
A = 1/2(b1 +b2)h
Filling in the given values, we have ...
156 = 1/2(17 +35)h = 26h
6 = h . . . . . . . . . . divide by 26
The height of the trapezium is 6 cm.
Answer:
6cm
Step-by-step explanation:
To find:-
The height of the trapezium.Answer:-
We are here given that the area of the trapezium is 156cm² and two of the parallel sides are 17cm and 35cm .We are interested in finding out the height of the trapezium.
The area of the trapezium is given by the formula,
[tex]:\implies \sf Area =\dfrac{1}{2}\times (s_1+s_1)\times h \\[/tex]
where s1 and s2 are the || sides of the trapezium and h is the height of the trapezium.
Now on substituting the respective values in the given formula, we have;
[tex]:\implies \sf 156cm^2 =\dfrac{1}{2} (17cm+35cm)\times h \\[/tex]
[tex]:\implies \sf 156cm^2(2) = 52cm (h) \\[/tex]
[tex]:\implies \sf h =\dfrac{156(2)}{52} cm\\[/tex]
[tex]:\implies \sf \pink{ height = 6 cm }\\[/tex]
Hence the height of the trapezium is 6cm .
the solution set is
5r+20/10=3r-6/3
Answers
Answer:
r = -2
Step-by-step explanation:
5r + 20/10 = 3r -6/3
5r + 2 = 3r - 2
2r + 2 = -2
2r = -4
r = -2
Answer: r = -2
Step-by-step explanati
f(s) = 3s + 2
p(s) = s^3+ 4s
Find (f • p)(-5)
Answers
The value of (f • p)(-5) is 1885 when functions are given as f(s) = 3s + 2 and p(s) = s³+ 4s.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is often represented by an equation or formula, and can be visualized as a graph. Functions are widely used in various areas of mathematics, science, engineering, and other fields to model real-world phenomena and solve problems.
Here,
f(s) = 3s + 2
p(s) = s³+ 4s
To find (f • p)(-5), we need to first find f(-5) and p(-5), and then multiply them together. To find f(-5), we substitute -5 into the function f(s) and simplify:
f(-5) = 3(-5) + 2
= -13
To find p(-5), we substitute -5 into the function p(s) and simplify:
p(-5) = (-5)³ + 4(-5)
= -125 - 20
= -145
Now we can multiply f(-5) and p(-5) together to find (f • p)(-5):
(f • p)(-5) = f(-5) * p(-5)
= (-13) * (-145)
= 1885
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I need the answer to this problem
Answers
Answer:
x = 4
Step-by-step explanation:
If we use A*B = C*D we get 2*6 = 3*x which is 12 = 3x. Dividing both sides by 3 you get 4 = x
Using a different map that is missing any indication of scale, you measure the distance from Point C
to Point D as five inches, but it is 500 miles on the ground. Prepare the following two expressions
of scale for the map:
(a) Fractional
(b) Written
SHOW YOUR WORK! This includes the potential for partial value, if incorrect.
Simplify your scale (e.g., reduce to 1 inch = x miles, not 5 inches = 250 miles).
Answers
Answer:
To calculate the scale of the map, we can use the following formula:
Scale = Actual distance / Map distance
(a) Fractional scale:
The actual distance between Point C and Point D is 500 miles, and the distance on the map is 5 inches. Therefore, the fractional scale can be calculated as:
Scale = 500 miles / 5 inches
Scale = 100 miles per inch
So the fractional scale of the map is 1 inch = 100 miles.
(b) Written scale:
To express the scale in written form, we can use the ratio of inches to miles. Since 1 inch represents 100 miles, we can write the scale as:
1 inch represents 100 miles
Alternatively, we can simplify the scale to a more common ratio by dividing both sides by 100:
1/100 inch represents 1 mile
Therefore, the written scale of the map is 1/100 inch = 1 mile.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
The true statements are:
The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph does not contain the point (20, -8).
How to deal with quadratic equation?The quadratic function is f(x) = x^2 - 5x + 12. Here are the statements that are true:
The value of f(-10) = 82:
To find f(-10), we substitute -10 for x in the function:
[tex]$$f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162$$[/tex]
Therefore, the statement "The value of f(-10) = 82" is false.
The graph of the function is a parabola:
Since the highest power of x in the function is 2, the graph of the function will be a parabola. Therefore, the statement "The graph of the function is a parabola" is true.
The graph of the function opens down:
The coefficient of [tex]$x^2$[/tex] in the function is positive (+1), which means the parabola opens upwards. Therefore, the statement "The graph of the function opens down" is false.
The graph contains the point (20, –8):
To see whether the point (20, -8) is on the graph of the function, we substitute x=20 into the function:
[tex]$$f(20) = (20)^2 - 5(20) + 12 = 400 - 100 + 12 = 312$$[/tex]
Since the y-coordinate of the point (20, -8) is not equal to 312, the statement "The graph contains the point (20, –8)" is false.
The graph contains the point (0, 0):
To see whether the point (0, 0) is on the graph of the function, we substitute x=0 into the function:
[tex]$$f(0) = (0)^2 - 5(0) + 12 = 12$$[/tex]
Since the y-coordinate of the point (0, 0) is equal to 12, the statement "The graph contains the point (0, 0)" is true.
Therefore, the true statements are:
The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph does not contain the point (20, -8).
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can someone help me please!
Answers
The median is the middle value of a data set when the values are arranged in order from lowest to highest (or highest to lowest). If there is an even number of values, then the median is the average of the two middle values. The median divides the data set into two halves, with half of the values being below the median and half of the values being above the median.
The first quartile, denoted as Q1, is the value that separates the lowest 25% of the data from the rest of the data. The second quartile, denoted as Q2, is the median of the data set. The third quartile, denoted as Q3, is the value that separates the lowest 75% of the data from the rest of the data.
The data-set has in this problem has two-halves of five elements, divided by the number 21, hence the median and the quartiles are given as follows:
The median of the data-set is of: 21 minutes.The lower quartile of the data-set is of 13 minutes. -> Median of the first five elements.The upper quartile of the data-set is of 27 minutes. -> Median of the last five elements.More can be learned about the median of a data-set at https://brainly.com/question/3514929
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Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 1,557 pounds to 4,665 pounds.(e) What is the probability that a vehicle will weigh between 1,946 and 4,455 pounds? (Round your answer to 4 decimal places.)
Answers
The probability that a vehicle will weigh between 1,946 and 4,455 pounds is 0.8076.
To solve this problem, we need to find the probability that a randomly chosen car weighs between 1,946 and 4,455 pounds. Since weight is uniformly distributed, we know that the probability density function is constant over the entire range of possible values.
First, we need to find the total range of possible values:
Range = maximum weight - minimum weight
Range = 4,665 - 1,557
Range = 3,108
Next, we need to find the range of values that fall between 1,946 and 4,455:
Target range = 4,455 - 1,946
Target range = 2,509
Finally, we can calculate the probability of a randomly chosen car falling within this target range:
Probability = Target range / Range
Probability = 2,509 / 3,108
Probability = 0.8076 (rounded to 4 decimal places)
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please help!!! i really need it
Answers
Step-by-step explanation:
Lisa started with $25 on her prepaid debit card. After her first purchase, she had $22.90 left. Therefore, she spent:
$25 - $22.90 = $2.10
We know that the price of the ribbon was 14 cents per yard. To find out how many yards Lisa bought, we can set up an equation:
$2.10 ÷ $0.14/yd = 15 yards
Therefore, Lisa bought 15 yards of ribbon with her prepaid debit card.
i hope this helps
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
Step-by-step explanation:
it was not clear if an average change rate would be sufficient, or if you needed an immediate change rate (as I also don't know if you covered derivatives already or not).
so, it would be helpful, if you could put a message to an answer that was not giving you what you need.
so, here now an answer for an immediate change rate (hopefully that is what you need) :
we have a right-angled triangle.
the direct line of sight (the direct distance between police and red car) is the Hypotenuse (the baseline opposite of the 90° angle).
the 50 ft and 180 ft are the legs.
Pythagoras gives us the length of the Hypotenuse :
Hypotenuse² = 50² + 180² = 2500 + 32400 = 34,900
Hypotenuse = sqrt(34900) = 186.8154169... ft
in general terms let's say x is the distance of the cop to the road, y is the distance on the road to the crossing point with the distance cop to road, and z is the line of sight distance between the red car and the cop (the Hypotenuse).
x² + y² = z²
now, the first derivative of distance is the change of distance = speed.
then dy/dt (= y') is how fast the car is traveling down the road. dx/dt (= x') is how fast the cop is traveling toward the road. and dz/dt (= z') is how fast the distance between the cop and the car is changing.
now, we take the derivative of our equation
x² + y² = z² with respect to time, variable by variable :
d(x² + y² = z²)/dt =
dx²/dx × dx/dt + dy²/dy × dy/dt = dz²/dz × dz/dt
that gives us the equation
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
x(dx/dt) + y(dy/dt) = z(dz/dt)
from the problem we know x (50 ft), y (180 ft), dz/dt (85 ft/s). we calculated z (the Hypotenuse = sqrt(34900), and since the cop is not moving, we know dx/dt = 0.
and we get
50ft×0ft/s + 180ft×(y') = sqrt(34900)ft×(85)ft/s
we solve for y' (the speed of the car on the road)
y' = sqrt(34900)×85/180 = 88.21839132... ft/s
≈ 88.22 ft/s
and now here the difference for an average change rate over the unrevealed of 1 second :
the radar measured the change of the distance (Hypotenuse) from 1 second ago to now.
so, 1 second ago, the distance was
186.8154169... + 85 = 271.8154169... ft
the 50 ft leg stays the same, but the 180 ft leg was (again via Pythagoras)
271.8154169...² = 50² + leg²
leg² = 271.8154169...² - 50² = 71,383.62088...
leg = 267.1771339... ft
so, the red car traveled
267.1771339... - 180 = 87.1771339... ft/s
as you can see, it is close, but there has to be a difference, as the average change rate is only an approximation to the immediate change rate.
Which set of ordered pairs does not represent a function?
1. {(6,5), (3, 5), (−2, 8), (-9,4)}
2. {(-6, -1), (3, 1), (4, −4), (8, 1)}
3. {(-1,9), (-8, 5), (-1, 3), (-9, 1)}
4. {(5,9), (2,-5), (-1,-5), (0, 1)}
Answers
The set of ordered pairs does not represent a function is the one in the third option.
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
Which set of ordered pairs does not represent a function?A relation maps elements from one set, the domain, into elements of other set, the range.
Such that these mappings are of the form (x,y).
A function is a relation where each input is mapped into a single one output, then if you see a relation that has two points with the same value of x and different values of y, then that relation is not a function.
Particularly, if you look at the third option:
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
You can see that the first and second points have the same input and different outputs, then this is not a function, and that is the correct answer.
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Which ordered pair maximizes the objective function p=3x+8y
(0,0)
(2,7)
(5,6)
(8,1)
Answers
Answer:
P(5,6) = 63
Step-by-step explanation:
Test each point to see which ordered pair maximizes the objective function:
(0,0): p = 3(0) + 8(0) = 0
(2,7): p = 3(2) + 8(7) = 6 + 56 = 62
(5,6): p = 3(5) + 8(6) = 15 + 48 = 63
(8,1): p = 3(8) + 8(1) = 24 + 8 = 32
Hence, (5,6) is the ordered pair that maximizes the objective function.
Last years freshman class at Big State university totaled 5,324 students
URGENT
Answers
The amount a student received in merit scholarships was $3,456 ($478 per student). The cost of full tuition was $4,200. This means that the difference between the amount of the scholarship and the cost of tuition was $744.
What is amount ?Amount is a numerical value that represents a quantity of something. It is used to measure the size, amount, or degree of something, often in terms of money, time, or distance. Amounts are usually expressed in a specific unit, such as dollars, minutes, or kilometers. Amounts can also refer to the total number of something, such as the amount of people in a room or the amount of items in a box. Amounts can also be used to describe a portion or percentage of something, such as the amount of a discount or the amount of interest earned.
To find the percentage of students who did not receive enough to cover full tuition, we need to divide the difference ($744) by the amount of the scholarship ($3,456). This gives us a percentage of 21.5%.
Rounded to the nearest whole percent, the answer is 22%. This means that 22% of students who received a merit scholarship did not receive enough to cover full tuition.
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a friend has an 81% average before a final exam. The score includes everything but the final, which counts for 15% of the grade. What is the minimum to earn 75% for the course?
Answers
Answer:
57
Step-by-step explanation:
Okay, So we have this person That has 81% average before the quiz. For a course That score includes everything, but the final, which counts for 25% of the course grade, was the best course grade you your friend can earn. Okay, The best course grade given to me makes me. Mhm. 100. So we have .81 times. Actually we'll keep this as 81, times .75 right Plus 100 times. Excuse ME, Time 0.25. This is equivalent to 81 times 0.75. Mhm. This is equivalent to 81 times .75 plus 100 times 0.25, Which equals 85.75%. Now that's for part one. Report to we have what is the minimum score? Turn to 75%. So we have 75 equal to 81 times 0.75 Plus X. Times zero 25. So 81 times 0.75 equals 60.75 75- is value mhm. Is equal to 14.25. So we have 0.25 x. And if we divide 14.25 over 0.25, we isolate X. So the minimum score to get a 75 is a 57
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A poster is to have a total area of 245 cm2. There is a margin round the edges of 6 cm at the top and 4 cm at the sides and bottom where nothing is printed.
What width should the poster be in order to have the largest printed area? **answer does not contain variables**
Answers
The largest printed area of the poster would be when the width and height of the poster are equal. To find the width of the poster, we need to subtract the total area of the margins from the total area of the poster.
The total area of the margins is 6 cm x 4 cm + 4 cm x 6 cm = 88 cm2.
Therefore, 245 cm2 - 88 cm2 = 157 cm2.
We can then use the formula A = W x H, where A is the area and W and H are the width and height of the poster, respectively.
Therefore, 157 cm2 = W x W.
We can solve for W by taking the square root of both sides.
Therefore, W = √157 = 12.5 cm.
Therefore, the width of the poster should be 12.5 cm in order to have the largest printed area.
Can the binomial distribution be approximated by a normal distribution? n = 31, p = 0.9 Explain why or why not.
Answers
Therefore, we can use the normal distribution with mean 27.9 and standard deviation 1.67 to approximate the binomial distribution with n = 31 and p = 0.9.
What is binomial distribution?The binomial distribution is characterized by two parameters: the number of trials, denoted by n, and the probability of success on each trial, denoted by p. The probability of obtaining exactly k successes in n trials is given by the binomial probability mass function:
P(k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{(n-k)}[/tex],
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Given by the question.
Yes, the binomial distribution with n = 31 and p = 0.9 can be approximated by a normal distribution.
The conditions for a binomial distribution to be approximated by a normal distribution are as follows:
n*p >= 10
n*(1-p) >= 10
In this case, n = 31 and p = 0.9, so:
np = 310.9 = 27.9 >= 10
n*(1-p) = 31*0.1 = 3.1 >= 10
Condition 1 is satisfied, but condition 2 is not. Therefore, it is recommended to use a correction factor to improve the approximation.
The correction factor is given by:
[tex]\sqrt[2]{np(1-p)}[/tex]
Substituting the values, we get:
[tex]\sqrt[2]{310.90.1}[/tex]= 1.67
The corrected values for mean and standard deviation are:
mean = np = 310.9 = 27.9
standard deviation = [tex]\sqrt[2]{np(1-p)}[/tex] = 1.67
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Question 4 X Suppose that starting today, you make deposits at the beginning of each quarterly period for the next 40 years. The first deposit is for 400, but you decrease the size of each deposit by 1% from the previous deposit. Using an nominal annual interest rate of 8% compounded quarterly, find the future value (i.e. the value at the end of 40 years) of these deposits. Give your answer as a decimal rounded to two places (i.e. X.XX).
Answers
if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
The first step in solving this problem is to calculate the amount of each quarterly deposit. We know that the first deposit is $400, and each subsequent deposit decreases by 1% from the previous deposit. This means that each deposit is 99% of the previous deposit. To calculate the size of each deposit, we can use the following formula:
deposit_ n = deposit_(n-1) * 0.99
Using this formula, we can calculate the size of each quarterly deposit as follows:
deposit_1 = $400
deposit_2 = deposit_1 * 0.99 = $396.00
deposit_3 = deposit_2 * 0.99 = $392.04
deposit_4 = deposit_3 * 0.99 = $388.12
...
We can continue this pattern for 40 years (160 quarters) to find the size of each quarterly deposit.
Next, we need to calculate the future value of these deposits using an nominal annual interest rate of 8% compounded quarterly. We can use the formula for compound interest to calculate the future value:
[tex]FV = PV * (1 + r/n)^(n*t)[/tex]
where FV is the future value, PV is the present value (which is zero since we are starting with deposits), r is the nominal annual interest rate (8%), n is the number of times the interest is compounded per year (4 since we are compounding quarterly), and t is the number of years (40).
We can substitute the values into the formula and solve for FV:
[tex]FV = $400 * (1 + 0.08/4)^(440) + $396.00 * (1 + 0.08/4)^(439) + $392.04 * (1 + 0.08/4)^(4*38) + ... + $1.64 * (1 + 0.08/4)^4[/tex]
After solving this equation, we get a future value of $143,004.54, rounded to two decimal places. This means that if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
This calculation highlights the power of compound interest over long periods of time. By making regular contributions and earning interest on those contributions, our investment grows exponentially over time. It also shows the importance of starting early and consistently contributing to an investment over time in order to achieve long-term financial goals.
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