The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.
It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.
A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.
A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.
For the Z-test, the test statistic is computed as
z = (x - μ) / (σ / √n)
where x = sample mean,
μ = population mean,
σ= population standard deviation,
and n = sample size.
The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.
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2. Write - (3i) in the form a + bi, where a and b are real numbers.
classify the different measurement systems into one of the four types
of scales. (Exercise)
1. Your checking account number as a name for your account.
2. Your checking account balance as a measure of the amount of money you
have in that account
3. The order in which you were eliminated in a spelling bee as a measure of your
spelling ability.
4. Your score on the first statistics test as a measure of your knowledge of
statistics.
5. Your score on an individual intelligence test as a measure of your
intelligence.
6. The distance around your forehead measured with a tape measure as a
measure of your intelligence.
7. A response to the statement "Abortion is a woman's right" where "Strongly
Disagree" = 1, "Disagree" = 2, "No Opinion" = 3, "Agree" = 4, and "Strongly
Agree" = 5, as a measure of attitude toward abortion.
8. Times for swimmers to complete a 50-meter race
9. Months of the year Meskerm, Tikimit…
10.Socioeconomic status of a family when classified as low, middle and upper
classes.
11. Blood type of individuals, A, B, AB and O.
12.Pollen counts provided as numbers between 1 and 10 where 1 implies there is
almost no pollen and 10 that it is rampant, but for which the values do not
represent an actual counts of grains of pollen.
13.Regions numbers of Ethiopia (1, 2, 3 etc.)
14.The number of students in a college;
15.the net wages of a group of workers;
16.the height of the men in the same town;
please help!! x-4.7y+9.1 + -x+5.8=12.4
The solution to the system of equations is x = 5 and y = 3.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.
To solve the system using addition, we want to add the two equations together in a way that eliminates one of the variables. In this case, we can add the two equations directly because the x term will cancel out:
X - 4.7y = -9.1
+(-x + 5.8 = 12.4)
1.1y = 3.3
Now we can solve for y by dividing both sides by 1.1:
y = 3.3 ÷ 1.1
y = 3
Substituting y = 3 back into one of the original equations, we can solve for x:
x - 4.7y = -9.1
x - 4.7(3) = -9.1
x - 14.1 = -9.1
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 3.
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WILL GIVE BRAINLIEST
Simplify the expression. Write the answer using scientific notation. (0.4x10^-6)(0.7x10^-2) 0.28 x 10^−9 2.8 x 10^−8 2.8 x 10^−9 2.8 x 10^−7
To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. So:
(0.4x10^-6)(0.7x10^-2) = (0.4)(0.7)x10^(-6-2) = 0.28x10^-8
Therefore, the answer is 0.28 x 10^−8 in scientific notation.
If a square has an area that is 49 square feet or less, what are the possible lengths x for the side of the square. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ft A. The possible lengths x for the side of the square is the interval, (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The possible lengths x for the side of the square is the list of values, x = ft. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) C. There are no possible lengths x for the side of the square.
The possible lengths x for the side of square A. The possible lengths x for the side of the square is the interval [-7,7].
Since the area of a square is given by the formula A = x^2, where x is the length of the side, we can solve for x to find the possible lengths of a square with area 49 square feet or less.
A ≤ 49
x^2 ≤ 49
|x| ≤ 7
So the possible lengths for the side of the square are any values of x between -7 and 7, inclusive.
Therefore, the answer is: A. The possible lengths x for the side of the square is the interval [-7,7].
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The equation of a circle is given below. ( � + 9 ) 2 + ( � − 46 ) 2 = 123 (x+9) 2 +(y−46) 2 =123left parenthesis, x, plus, 9, right parenthesis, squared, plus, left parenthesis, y, minus, 46, right parenthesis, squared, equals, 123 What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places.The equation of a circle is given below. ( � + 9 ) 2 + ( � − 46 ) 2 = 123 (x+9) 2 +(y−46) 2 =123left parenthesis, x, plus, 9, right parenthesis, squared, plus, left parenthesis, y, minus, 46, right parenthesis, squared, equals, 123 What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places.
According to the given question, the center of the circle is (-9, 46) and its radius is approximately 11.09.
What is equation of circle?The equation of a circle is a formula that describes the relationship between the x and y coordinates of any point on the circle.
The standard equation of circle is:
(x - h)²+(y - k)²=r²
This equation states that the sum of the squares of the differences between the x-coordinate and the center, and the y-coordinate and the center, is equal to the square of the radius.
The equation of the circle is given by (x+9)² + (y-46)² = 123.
Comparing this to the standard equation of a circle, (x-h)² + (y-k)² = r², we can see that the center of the circle is (-9, 46) and the radius is √(123) = 11.09.
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a sampling distribution is created using samples of the ages at which 48 children begin reading, what would be the mean of the sampling distribution of sample means? round to two decimal places, if necessary.
The mean of the sampling distribution of sample means is approximately 5.2 ± 0.1339.
When a sampling distribution is created using samples of the ages at which 48 children begin reading, the mean of the sampling distribution of sample means can be calculated by dividing the population mean by the square root of the sample size. This is known as the standard error of the mean and is denoted as SE.
The formula for calculating the standard error of the mean is:
SE = σ / √n
where σ is the population standard deviation and n is the sample size.In this case, the sample size is 48 children. Since the population standard deviation is not given, it is assumed that the sample standard deviation is used as an estimate of the population standard deviation. The formula for calculating the sample standard deviation is:
S = √[(Σ(x - μ)²) / (n - 1)]
where S is the sample standard deviation, Σ is the sum of the squared deviations from the mean, x is the value of each observation, μ is the mean of the sample, and n is the sample size.Using the data given, the sum of the squared deviations from the mean is:
Σ(x - μ)² = (6 - 5.2)² + (8 - 5.2)² + (7 - 5.2)² + (9 - 5.2)² + (4 - 5.2)² + (7 - 5.2)² + (6 - 5.2)² + (5 - 5.2)² = 2.56 + 5.76 + 1.44 + 12.96 + 1.44 + 1.44 + 0.36 + 0.04 = 26.4
The sample standard deviation is:S = √[26.4 / (48 - 1)] = 0.9197Using the formula for standard error of the mean, the mean of the sampling distribution of sample means is:
SE = σ / √n= 0.9197 / √48≈ 0.1339
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Jhonny has 87 apples, and 90 pears. he needs to make a smoothy for his friends. The resipide needs 45.8 ounces of pear juice and 50 ounces of apple juice. Does Jhonny have enough to make the smoothys for his friends if he has 5 friends? Why or why not.
No, Johnny does not have enough fruit to make smoothies for his 5 friends because he is short 383.51 ounces of juice.
When you dilate by a scale factor greater than 1 the figure shrinks.
True
False
Answer:
true
Step-by-step explanation:
Q5
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma negative 1, at 0 comma 2, at 1 comma 3, and at 5 comma 1 Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
The relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."
Why is the given relatiοn nοt a functiοn?Lοοking at the given pοints, we can see that the input x = -5 has an οutput y = 1, and the input x = 5 alsο has an οutput y = 1.
This means that there are twο different inputs (x-values) that cοrrespοnd tο the same οutput (y-value), viοlating the definitiοn οf a functiοn.
Tο determine if the relatiοn is a functiοn, we need tο check if fοr each input (x-value), there is exactly οne οutput (y-value).
Therefοre, the relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."
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every day, kymere takes the same street from his home to the university. there are multiple traffic lights with patterns along the way. if there is a green light while passing through an intersection, then 60% of the time the next light is also green and 25% of the time the next light is red. if the light is yellow, then there is a probability of 1 that the next light is red. if there is a red light, then 30% of the time the next light is green and 50% of the time the next light is red. (a) does this situation represent a markov chain? explain. (b) set up the transition probability matrix and diagram. (c) determine the number of classes and classify them. (d) the first light is green. compute and interpret all probabilities after three more lights. (e) if kymere has many street lights between home and the university, what proportion of these lights are green, yellow, and red? [no technology estimations permitted. solve this problem with a system of equations showing every step and fraction answers only.]
The proportion of green lights is 0.4286.
(a) Yes, this situation is a Markov chain since the probability of transitioning to a new traffic light state only depends on the current state.
(b) Transition probability matrix:
G Y R
[tex]G 0.60 0.00 0.40[/tex]
[tex]Y 1.00 0.00 0.00[/tex]
[tex]R 0.30 0.00 0.50[/tex]
(c) There is only one class, as all states can be reached from any other state.
(d) After three more lights, the probability of being in each state is:
G Y R
G 0.3240 0.0000 0.6760
Y 0.5000 0.0000 0.5000
R 0.3150 0.0000 0.6850
(e) The proportion of green lights can be found by solving the steady-state equation. Assuming there are n traffic lights, the system of equations would be:
[tex]0.60g + 0.30r[/tex]= g
[tex]0.00g + 0.00r[/tex] = r
[tex]0.40g + 0.50r[/tex] = r
g + y + r = 1
Solving this system gives g =[tex]0.4286[/tex], y = [tex]0.1429[/tex], and r = [tex]0.4286.[/tex]
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If Oscar the ostrich travels 215 miles in 5 hours on land, how fast does he travel?
HELP ASAP! Complete the square. Formula (b/2)²
a²+ 14a − 51 = 0
A. {-3,17}
B. {3,-17}
C. {-3,-17}
D. {3,17}
Answer:
B
Step-by-step explanation:
a² + 14a - 51 = 0 ( add 51 to both sides )
a² + 14a = 51
to complete the square
add ( half the coefficient of the x- term )² to both sides
a² + 2(7)a + 49 = 51 + 49
(a + 7)² = 100 ( take square root of both sides )
a + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )
a = - 7 ± 10
then
a = - 7 + 10 = 3
a = - 7 - 10 = - 17
The first quadrant is lava. the rest of the plane (including the x and y axes) is safe. to traverse the lava, you can place a board, which is a line segment of length at most 1, between two safe endpoints. once a board is placed, the line segment becomes safe, and points on it may be used as endpoints of a subsequent board. your goal is to reach the point (2023, 2023).
a. prove that one million boards aren't enough.
b. give a specific number of boards with which you can reach (2023, 2023).
c. prove that one billion boards aren't enough
Proof that one million boards aren't enough. .Therefore, one million boards are not enough to reach (2023, 2023).
A total of 2023 boards are needed to reach (2023, 2023).
How to explain the problemThis problem is a mathematical puzzle that involves traversing a hazardous area to reach a specific point using a limited number of resources.
The problem is set in the Cartesian plane, where the first quadrant (i.e., the region where both x and y coordinates are positive) is covered with lava, making it impossible to traverse.
Let's assume that we can reach (2023, 2023) with one million boards. We know that each board can cover a distance of at most 1. Therefore, the total distance we can cover with one million boards is at most one million. However, the distance between the origin (0, 0) and (2023, 2023) is ✓2023² + ✓2023² = 2855.9
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(i) Simplify the expression (p - 2q)² - p(p - 4q). (ii) Hence, by substituting a suitable value of p and of q, find the value of 5310² - 5330 × 5290.
After answering the presented question, we can conclude that expression Therefore, the value of 5310² - 5330 × 5290 when p = 5330 and q = 10 is 400.
what is expression ?An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
(i)
(p - 2q)² = p² - 4pq + 4q²
p(p - 4q) = p² - 4pq
(p - 2q)² - p(p - 4q) = (p² - 4pq + 4q²) - (p² - 4pq)
(p - 2q)² - p(p - 4q) = 4q²
(ii)
(5330 - 2×10)² - 5330(5330 - 4×10) = 4×10²
(5310)² - 5330 × 5290 = 400
Therefore, the value of 5310² - 5330 × 5290 when p = 5330 and q = 10 is 400.
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SOMEONE PLEASE HELP ME MY GRADE WILL GO DOWN IF I DONT GET THIS TURNED IN
will give brainliest 80 points
Answer: the value of x is 29
Step-by-step explanation:
Answer:
it's in the attachment
Step-by-step explanation:
the one that are the same value as the given value on the transversals are either opposite interior angles or opposite exterior angles
the ones that have different values as the given value on the transversal are subtracted from 180⁰
Line v has an equation of y=–10/9x–3. Perpendicular to line v is line w, which passes through the point (2,3). What is the equation of line w?
The equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).
What is an equatiοn οf the line?The definitiοn οf an equatiοn οf the line is a linear equatiοn with degree 1. X and Y are twο variables in the equatiοn fοr the line. The slοpe οf the line, which reflects the elevatiοn οf the line, is the third parameter.
The general fοrm οf the equatiοn οf the line:-
y = mx + c
m = slοpe
c = y-intercept
Given that Line, v has an equatiοn οf y=–109x–3. Perpendicular tο line v is line w, which passes thrοugh the pοint (2,3).
The slοpe οf the required line will be inverse and the οppοsite οf the given line,
m = 1/109
The intercept will be calculated as,
y = mx + b
3 = (1/109)2 + b
3 = 2/109 + b
327/109 = 2/109 + b
325/109 = b
The equatiοn οf the line is written as,
y = (1/109)x + (325/109)
Therefοre, the equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).
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Find all roots of the polynomial
p(x)= x^4 - 5x^3 + 7x^2 - 5x + 6 ; i
Answer:
The roots of p(z) are z = i, 2.91367 + 0.600499i, 1.22097 - 0.362212i, 0.306704 + 1.53771i.
The base of the parallelogram has a length of 10 cm what is the height 10 cm 12 cm or 14 cm 
The area of the parallelogram is 140 cm².
What is a parallelogram?A parallelogram is a quadrilateral having two pairs of parallel sides (a four-sided polygon). This indicates that opposing sides of a parallelogram are parallel, and opposite angles have the same size.
Given :
Base of parallelogram = 10 cm
Height of parallelogram = 14 cm
Area of Parallelogram = B × H
Area = 10 × 14
Area = 140 cm²
Area of parallelogram is 140 cm².
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The complete question is:
Franklin has a credit card with an APR of 28.2%. If he charges a purchase for $1,520, what is the estimated amount Franklin will pay in finance charges on that purchase?
The estimated amount Franklin will pay in finance charges on his $1,520 purchase is $35.07.
What is annual percentage rate?
Annual Percentage Rate (APR) is the annual rate charged for borrowing or earned through an investment and is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or investment.
The finance charges on a credit card purchase can be calculated using the following formula:
finance charges = (APR/365) * balance * number of days
Where APR is the annual percentage rate, balance is the amount of the purchase, and the number of days is the time period for which the finance charges are being calculated.
Assuming that Franklin does not make any payments towards his credit card balance during the billing period, the number of days for which finance charges will be calculated will be equal to the billing cycle. Let's assume a billing cycle of 30 days for this example.
Using the formula above, we can calculate the finance charges as follows:
finance charges = (28.2%/365) * $1,520 * 30
= (0.00077397) * $1,520 * 30
= $35.07 (rounded to the nearest cent)
Therefore, the estimated amount Franklin will pay in finance charges on his $1,520 purchase is $35.07.
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A path 2.5 M is running around a square field whose side is 45 M find area path
The area of the path running around the square field is 475 square meters.
To find the area of the path running around a square field with a side of 45 meters and a path width of 2.5 meters,
Calculate the area of the entire square (including the path):
Side of the larger square = 45 M (side of the field) + 2.5 M (width of the path on one side) + 2.5 M (width of the path on the opposite side) = 50 M
Area of the larger square = (Side of the larger square)²
= (50 M)²
= 2500 M²
Calculate the area of the square field (without the path):
Side of the field = 45 M
Area of the square field = (Side of the field)²
= (45 M)²
= 2025 M²
Subtract the area of the square field from the area of the entire square to find the area of the path:
Area of the path = Area of the larger square - Area of the square field
= 2500 M² - 2025 M²
= 475 M²
So, the area of the path running around the square field is 475 square meters.
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find the area of sector and the arc length. leave pi in answer; no decimals!
The arc length of the sector is 10π inches, and the area of the sector is 60π square inches.
What is the arc length and area of the sector of a circle?
Arc length = [tex] \frac{ \theta}{ {360}^{o} } \times 2\pi \: r[/tex]
Area of sector = [tex] \frac{ \theta}{ {360}^{o} } \times \pi \: {r}^{2} [/tex]
Where r is the radius of the circle, angle is the central angle in degrees, and π is the mathematical constant pi (approximately equal to 3.14159).
Given that the angle is 150° and the radius is 12 inches, we can substitute these values into the formulas to get:
Arc length
[tex]= \frac{150}{360} \times 2π(12) \\ = \frac{5}{12} \times 2π(12) \\ = 10π \: inches[/tex]
Area of sector
[tex]= \frac{150}{360} \times π(12)^2 \\ = \frac{5}{12} \times π(144) \\ = 60π \: square \: inches[/tex]
Therefore, the arc length of the sector is 10π inches, and the area of the sector is 60π square inches.
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How long must the brace be on a closet rod holder if the vertical side is 15 cm and the horizontal side must be attached 35 cm from the wall?
The brace must be approximately 38.1 cm long.
To find the length of the brace for the closet rod holder,
we can use the Pythagorean theorem,
which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the vertical side is 15 cm and the horizontal side is 35 cm.
Let's call the length of the brace (the hypotenuse) "c".
According to the Pythagorean theorem:
[tex]c^2 = (15 cm)^2 + (35 cm)^2[/tex]
[tex]c^2 = 225 cm^2 + 1225 cm^2[/tex]
[tex]c^2 = 1450 cm^2[/tex]
Now, to find the length of the brace, we need to take the square root of both sides:
[tex]c = \sqrt{(1450 cm^2)}[/tex]
c ≈ 38.1 cm.
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Please help me i dont know how to solve it
Answer:
25 + 55 + 45 + 10 = 135 runners.
B is correct.
Complete the following statement. Write your answer as a decimal or whole number.
__% of $5,000 = $3,750
I'm begging u PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
In a math class with 28 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 19 students who completed the assignment. There were 7 students who failed the test and also did not complete the assignment. What is the probability that a student who did not complete the homework passed the test?
Therefore, the probability that a student who did not complete the homework passed the test is 2/5 or 0.4 (or 40%).
What is Probability?Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 because there is one favorable outcome (getting heads) out of two possible outcomes (getting heads or tails).
Let's define the following events:
A: passing the test
B: completing the assignment
We know that:
[tex]P(A) = 18/28 = 9/14[/tex] (since 18 students out of 28 passed the test)
[tex]P(B) = 19/28[/tex] (since 19 students out of 28 completed the assignment)
P (A ∩ B) = P(B) = 19/28 (since every student who completed the assignment also took the test)
We want to find P (A | not B), which represents the probability of passing the test given that the student did not complete the assignment.
Using Bayes' theorem, we have:
P (A | not B) = P (not B | A) * P (A) / P (not B)
We know that:
P (not B | A) = P (A' ∩ B') / P(A') = 7/28 / 10/28 = 7/10 (since 7 students failed the test and did not complete the assignment)
P (not B) = 1 - P(B) = 9/28 (since not completing the assignment is the complement of completing the assignment)
Plugging in these values, we get:
[tex]P(A | not B) = (7/10) * (9/14) / (9/28)[/tex]
[tex]P(A | not B) = 2/5[/tex]
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I need an answer as soon as possible
Answer:
A. The rate of change of the table is equal to the rate of change of the graph.
I need help desperately I'll give 30 points any silly answers will be reported anyways PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
The solution to the operations of similar triangles are:
ΔABC is similar to ΔEDC
They are similar triangles by AAA Similarity rule
x = 24
How to Identify Similar Triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the given image, we can see that:
AB is parallel to DE
Thus:
∠BAE ≅ ∠DCA because they are both alternate angles
Similarly:
∠ABD ≅ ∠EDB because they are both alternate angles
We can also say that:
∠ACB ≅ ∠DCE because they are both opposite angles
Thus: ΔABC is similar to ΔEDC
They are similar triangles by AAA Similarity rule
Using similar triangles ratio, we can say that:
x/15 = 16/10
x = (16 * 15)/10
x = 24
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Please Help! No Silly Answers Please! I would appreciate correct answers. Thank you all! Please try and include Scratch Work, Thank you.
Answer:
y in (7,y) = 14
Step-by-step explanation:
A General Linear function is as the following:
y = mx + c, Where: m: slope of the line, c: y-intercept
Given that:
Point 1 (P1) = (1,5)
Point 2 (P2) = (3, 11)
Point 3 (P3) = (7,y)
By substituting in the linear function with P1:
5 = m + c ---> (1)
By substituting in the linear function with P2:
11 = 3m + c ---> (2)
By multiplying equation (1) times 3 and subtracting eq. (2) from it:
(15 = 3m + 3c) - (11 = 3m + c) =
4 = 2c
Then, c = 2
By substituting with "c" in eq. (1):
5 = m + 2
Then, m = 3
Hence,
the function of this line is:
y = 3x + 2
So,
to get "y" in P3, we are going to substitute with 7:
y = 3(7) + 2
then "y" in P3 = 23
Another Solution:
by getting the slope of the line:
[tex]Slope = \frac{\triangle y}{\triangle x}[/tex] Where: Δy: change in y points, Δx: change in x points
by utilizing P1 & P2 in slope formula:
[tex]slope = \frac{11 - 5}{3 - 1} = \frac{6}{2} = 3[/tex]
By substituting with P1 in the linear function:
5 = 3 + c
Then, c = 2
the function of the line is:
y = 3x + 2
So,
to get "y" in P3, we are going to substitute with 7:
y = 3(7) + 2
then "y" in P3 = 23
hope you find this easy to understand....
Have any questions? Write in the comments.
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Express cos � L as a fraction in simplest terms.
Answer:
cos(L) = (√46)/11
Step-by-step explanation:
You want cos(L) in simplest terms, given right triangle side lengths LK=√46 and JK=√75.
CosineThe cosine is the ratio ...
Cos = Adjacent/Hypotenuse
The side adjacent to vertex L is LK. The hypotenuse of the triangle is LJ. This means the desired ratio is ...
cos(L) = LK/LJ
Pythagorean theoremThe length of hypotenuse LJ can be found using the Pythagorean theorem.
LJ² = LK² +JK²
LJ² = (√46)² +(√75)² = 46 +75 = 121
LJ = √121 = 11
RatioThen the desired ratio is ...
cos(L) = (√46)/11