The missing value is 33.
The median of a set of six ordered data values is the middle number, which is located in the third position.
To calculate the median, you need to add the numbers in the two middle positions and divide by two.
5 + 12 = 17, 21 + 33 = 54. 54 / 2 = 27.
Thus, the missing value is 33.
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8. A cook uses fifteen 2-litre bottles of cooking oil
in 4 weeks. If he decides to buy 5-litre tins of
cooking oil instead, how many tins of cooking
oil will he use over a 10-week period if the rate
at which he uses it remains unchanged?
Step-by-step explanation:
?
The cook uses 15 bottles of 2-litre cooking oil in 4 weeks. So, the total amount of cooking oil he uses in a week is:
15 bottles × 2 litres/bottle ÷ 4 weeks = 7.5 litres/week
Now, if the cook decides to buy 5-litre tins of cooking oil instead of 2-litre bottles, he will need to determine how many tins he will use in 10 weeks.
To do this, he needs to calculate the total amount of cooking oil he will need in 10 weeks, which is:
7.5 litres/week × 10 weeks = 75 litres
Each 5-litre tin contains more cooking oil than a 2-litre bottle, so the cook will need fewer tins than bottles to obtain the same amount of oil.
The number of 5-litre tins he needs is:
75 litres ÷ 5 litres/tin = 15 tins
Therefore, the cook will need 15 tins of cooking oil over a 10-week period if he decides to buy 5-litre tins of cooking oil instead of 2-litre bottles.
The number of tins of cooking oil he will use over a 10-week period if the rate at which he uses it remains unchanged is fifteen.
Since the cook uses Fifteen 2-liter bottles of cooking oil, the total will be 30 liters of cooking oil in the span of 4 weeks
In order to find the rate of oil usage, we divide the total amount of oil used by the number of weeks :
30 liters ÷ 4 weeks = 7.5 liters per week
As the rate of oil usage is constant the cook will need to use the same amount of cooking oil they used for 4 weeks over a 10 week period:
7.5 liters per week x 10 weeks = 75 liters of oil
If the cook decides to buy 5-liter tins of cooking oil instead of 2-litre tins, then the number of tins can be calculated by dividing the total amount of oil needed by the capacity of each tin:
75 liters ÷ 5 liters per tin = 15 tins of cooking oil
Hence the cook will need to buy fifteen tins of 5-liter cooking oil to cover the requirements over a 10-week period
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Write equivalent fractions for
4/5
and
7/12
using the least common denominator.
Answer: 35/60 and 48/60
Answer:
the answers are 35/60 and 48/60
Step-by-step explanation:
Prove that if events A and B are independent, then the complement events of A and B are also independent.
If A and B are independent, then the complements of A and B are also independent [proved]
The complement of an event A is the event not A, denoted A'. To prove that the complement events of A and B are independent if A and B are independent, we will use the definition of independent events.
The definition of independent events states that: If two events A and B are independent, then the probability of the intersection of A and B (P(A ∩ B)) is equal to the product of the probabilities of A and B (P(A)P(B)).
Therefore, if A and B are independent, then:
P(A ∩ B) = P(A)P(B)
Now, we will prove that the complements of A and B are independent.
The probability of the intersection of the complements of A and B (P(A' ∩ B')) is equal to the product of the probabilities of the complements of A and B (P(A')P(B')).
Since A and B are independent, we can conclude that A' and B' are independent since:
P(A' ∩ B') = P(A')P(B')
Therefore, if A and B are independent, then the complements of A and B are also independent.
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(1 point) find the area of the region outside r=10 10sinθ , but inside r=30sinθ.
To find the area of the region outside r = 10sinθ and inside r = 30sinθ, we must use polar coordinates, i.e., we need to find the area enclosed by the curve r = 30sinθ and subtract from it the area enclosed by the curve r = 10sinθ.
The equation for the area enclosed by a polar curve is given by:
A = 1/2∫αβr2dθ
For our problem, we will use the following equations:
α = 0
β = π/2
r = 10sinθ, and r = 30sinθ
Therefore, the required area of the region outside r = 10sinθ and inside r = 30sinθ can be found by evaluating the following integral:
A = 1/2∫0π/2302sin2θ - 102sin2θdθ
A = 1/2[900(π/2 - cosπ/2) - 100(π/2 - cosπ/2)]
A = 225π/2 - 50π/2 = 175π/2
Therefore, the area of the region outside r = 10sinθ and inside r = 30sinθ is 175π/2.
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g you are executing linear sequential search algorithm on an array of size n. suppose that the key you are searching for is included in the array. also you know that the probability of finding the key at the last position of the array is 1/3, and the probability of finding the key at the second last position is 1/3 as well. furthermore, the probability of finding the key at every other positions are all equal to each other.
The expected number of comparisons for linear sequential search algorithm in an array of size n with a key having equal probability in every position (except for the last two) is (2n-5)/(3(n-2)).
The probability of finding the key in any position of the array (except for the last two positions) is (1/3)/(n-2), since there are n-2 such positions in the array.
Therefore, the probability of finding the key in the first position is also (1/3)/(n-2), since all positions have equal probability of containing the key (except for the last two positions).
In this case, the algorithm would have to search through the entire array before finding the key, resulting in n comparisons.
On average, the algorithm would have to search through (n+1)/2 positions to find the key, since all positions have equal probability of containing the key (except for the last two positions).
However, the expected number of comparisons for the linear sequential search algorithm can be calculated as follows:
(1/3) * (n-1) + (1/3) * (n-2) + (n-4) * (1/3) * (1/(n-2)) + 1 * (1/3)/(n-2)
= (2n-8)/(3(n-2)) + 1
= (2n-5)/(3(n-2))
Therefore, the expected number of comparisons required by the linear sequential search algorithm is (2n-5)/(3(n-2)).
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Alexa and Tara were selling bracelets to raise money for charity. Alexa sold 4 bracelets for every 3 bracelets Tara sold. Together they sold 49 bracelets. How many did they each sell?
Answer: Alexa sold 28 and Tara sold 21.
Step-by-step explanation: Refer to photo :)
consider a goodness-of-fit test with a computed value of chi-square27.385 and a critical value13.388, the appropriate decision would be to __________.
The null hypothesis is accepted since the chi-square at the supplied critical value level value is greater than 13.388 (27.385).
In five to six key stages, the hypothesis test announces the conclusion of an assumption.
The approach to be utilized is predicated on the notion of correlating a parameter's standardized sample equivalent to the crucial boundary that permits the null hypothesis to be accepted.
For this particular question,
The value of the chi-square is 27. 385.
The crucial number is 13.388.
The following are the hypotheses for the goodness of fit test : If an expected value and the observed values are identical, the value is considered null. Alternative: The expected value and the observed values differ substantially. One tail exists in the chi-square test.
The standard is as follows:
If the test statistic is higher than the threshold value, the null hypothesis is rejected. The same null hypothesis is rejected if the test statistic is below the crucial value. Because the chi-square is greater than 13.388 and the critical value is provided, the null hypothesis is therefore accepted at that level.
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pls help me!!!!!
Simplify completely quantity 12 x plus 36 over quantity x squared minus 4 x minus 21 and find the restrictions on the variable.
12 over quantity x minus 7, x ≠ 7
12 over quantity x minus 7, x ≠ 7, x ≠ −3
quantity x plus 3 over quantity x minus 7, x ≠ 7
quantity x plus 3 over quantity x minus 7, x ≠ 7, x ≠ −3
The simplified expression is 12 over x minus 7 and x ≠ 7
Simplifying an expression:
Simplifying an expression means manipulating it into a simpler form by performing operations such as combining like terms, factoring, expanding, and canceling out terms or factors.
The goal of simplification is to make the expression easier to work with, understand, and analyze.
Here we use factoring to simplify the expression.
Here we have
Quantity 12 x plus 36 over quantity x squared minus 4 x minus 21
The above expression can rewrite as
(12x + 36) / (x² - 4x - 21)
To simplify the above equation
Factorize the denominator as follows
=> x² - 4x - 21
=> x² - 7x + 3x - 21
=> x(x - 7) + 3(x - 7)
=> (x - 7) (x + 3)
The numerator can rewrite as follows
(12x + 36) = 12 [x + 3]
Hence,
The expression (12x + 36) / (x² - 4x - 21)
= 12 [x + 3]/(x - 7) (x + 3)
= 12/(x - 7)
Therefore,
The simplified expression is 12 over x minus 7 and x ≠ 7
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The recipe says it makes 6 servings. How many cups of dressing are there in one serving? Show your answer in pictures, equations, and words.
According to the given information, one serving of the dressing contains 1/2 cup of the mixture, along with a pinch of herbs and salt.
What is a ratio?
A ratio is a comparison of two quantities or values, often expressed as a fraction. Ratios can be used to express the relationship between two or more quantities.
To find out how many cups of dressing are in one serving, we can use the given recipe and the concept of ratios.
The total amount of dressing made by the recipe is the sum of the amounts of each ingredient:
Total amount = 1/3 cup + 1/6 cup + a pinch + a pinch
We can simplify the equation by combining the pinches into a single value:
Total amount = 1/3 cup + 1/6 cup + a pinch of herbs and salt
To find out how much dressing is in one serving, we divide the total amount by the number of servings:
Amount per serving = Total amount / Number of servings
Amount per serving = (1/3 cup + 1/6 cup + a pinch of herbs and salt) / 6
To simplify this equation, we can first add the fractions:
Amount per serving
= (2/6 cup + 1/6 cup + a pinch of herbs and salt) / 6
= (3/6 cup + a pinch of herbs and salt) / 6
= (1/2 cup + a pinch of herbs and salt) / 6
Now we can divide the total amount by the number of servings:
Amount per serving = (1/2 cup + a pinch of herbs and salt) / 6
This means that each serving contains 1/2 cup of dressing plus a pinch of herbs and salt. In pictures, we can show this as:
1/2 cup of dressing and a pinch of herbs and salt
Therefore, one serving of the dressing contains 1/2 cup of the mixture, along with a pinch of herbs and salt.
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The speed of the plane is 380 miles per hour. Find dθ/dt when x = 10 and x = 3. (Round your answers to three decimal places.)
When the speed of the plane is 380 miles per hour:
dθ/dt = -0.0172 radians per minute for x = 10
dθ/dt = -0.0516 radians per minute for x = 3
To find the derivative of the given equation with respect to time t:
dθ/dt = 1/(x secθ) * dx/dt
For x = 10; dθ/dt = 1/(10 secθ) * dx/dt
For x = 3;dθ/dt = 1/(3 secθ) * dx/dt
dx/dt = x² + y² = r²
Differentiate both sides with respect to time t; 2x dx/dt + 2y dy/dt = 0
Simplify this equation using trigonometric identities;
x = r cosθ
dx/dt = - r sinθ (dθ/dt)θ = arccos(3/5)
θ = 53.13°x = 10 miles
r = 10 / cos 53.13° = 18.44 miles
dy/dt = - (x/y) dx/dt
dy/dt = - (10 / 4) * (- 18.44 sin 53.13° / 380) = 0.4053 miles per minute
For x = 10;
dθ/dt = 1/(10 secθ) * dx/dt
dθ/dt = 1 / (10 sec 53.13°) * (- 18.44 sin 53.13° / 380) = -0.0172 radians per minute (rounded to 3 decimal places)
Similarly, for x = 3;
dθ/dt = 1/(3 secθ) * dx/dt
dθ/dt = 1 / (3 sec 53.13°) * (- 18.44 sin 53.13° / 380) = -0.0516 radians per minute (rounded to 3 decimal places)
Therefore, the value of dθ/dt is -0.0172 radians per minute for x = 10 and -0.0516 radians per minute for x = 3.
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prove the following: for any set x and any indexed collection of sets {aα}α∈λ the following hold: x ∪α∈λ aα = ∩α∈λx\aα, and x ∩α∈λ aα = ∪α∈λx\aα.
To prove the following: for any set x and any indexed collection of sets {aα}α∈λ the following hold: x ∪α∈λ aα = ∩α∈λx\aα, and x ∩α∈λ aα = ∪α∈λx\aα is x ∪α∈λ aα = ∩α∈λx\aα, and x ∩α∈λ aα = ∪α∈λx\aα.
we must use set theory.
The De Morgan’s Laws states that: (A U B)' = A' ∩ B' and (A ∩ B)' = A' U B'.
Using this, we can prove the first part of the statement: x ∪α∈λ aα = ∩α∈λx\aα.
Using De Morgan's Laws, we can rewrite x ∪α∈λ aα as (x \ aα)'.
Then, using the distributive law of union over intersection, we can rewrite (x \ aα)' as ∩α∈λ (x \ aα)'.
Now, using De Morgan's Laws again, we get: ∩α∈λ (x \ aα)' = ∩α∈λx\aα.
Thus, we can prove that x ∪α∈λ aα = ∩α∈λx\aα.
We can similarly prove the second part of the statement, x ∩α∈λ aα = ∪α∈λx\aα, using De Morgan's Laws and the distributive law of intersection over union. Therefore, for any set x and any indexed collection of sets {aα}α∈λ the following hold: x ∪α∈λ aα = ∩α∈λx\aα, and x ∩α∈λ aα = ∪α∈λx\aα.
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(769x 769-231 x 231)x (342 x 342-658 x 658) (769 +231)x (342-658)
The simplified form of the expression (769x 769-231 x 231)x (342 x 342-658 x 658) (769 +231)x (342-658) is 53,764,768,000,000
To simplify this expression, we'll need to perform a series of arithmetic operations according to the order of operations
Let's start with the first set of parentheses
(769x 769-231 x 231)
Here, we can simplify the expression inside the parentheses using the distributive property of multiplication:
769 x 769 - 231 x 231
= (769 + 231) x (769 - 231)
= 1000 x 538
= 538,000
So the first set of parentheses simplifies to 538,000.
Moving on to the second set of parentheses
(342 x 342-658 x 658)
Again, we can use the distributive property of multiplication to simplify the expression inside the parentheses
342 x 342 - 658 x 658
= (342 - 658) x (342 + 658)
= -316 x 1000
= -316,000
So the second set of parentheses simplifies to -316,000.
Next, we'll multiply the results of the first two sets of parentheses
538,000 x (-316,000)
= -170,008,000,000
So the first two sets of parentheses multiplied together simplify to -170,008,000,000.
Moving on to the third set of parentheses
(769 + 231)x (342-658)
We can simplify this expression using basic addition and subtraction
(769 + 231)x (342-658)
= 1000 x (-316)
= -316,000
So the third set of parentheses simplifies to -316,000.
Finally, we'll multiply the result of the first two sets of parentheses by the result of the third set of parentheses
-170,008,000,000 x (-316,000)
= 53,764,768,000,000
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PLEASE HELP! I will give brainliest for this question!
Write a value in each region that makes the inequality or inequalities true.
The values that make both inequalities true are: 2 < x < 3
What is inequalities?Inequalities are mathematical expressions that describe the relative size or magnitude of two values. An inequality is typically written with one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
To solve the inequality 2x - 1 > 3, we first add 1 to both sides to get:
2x > 4
Then, we divide both sides by 2 to get:
x > 2
Therefore, any value of x greater than 2 will make the inequality 2x - 1 > 3 true. For example, x = 3 makes the inequality true:
2(3) - 1 = 5 > 3
3x - 9 < 0
3x < 9
x < 3
Therefore, any value of x less than 3 will make the inequality 3(x - 3) < 0 true. For example, x = 2 makes the inequality true:
3(2 - 3) = -3 < 0
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The complete question is -
Write a value in each region that makes the inequality or inequalities true. 2x-1>3 and 3(x-3)<0
Name: 6-4 Additional Practice In 1 and 2, use the graph to complete the statements. 1. The measure of variability that best describes the data is the 2. The typical number of visits to the library is represented by the 16 DHRD GANO 14 12 10 8 0 Library Visits Por Year 0-9 10-19 20-29 30-49 40-49 Frequency
The appropriate measure of variability is the range and the appropriate measure of center is the mean
How to determine the appropriate measuresMeasure of variability
The range would be a suitable measure of variability for the stem and leaf plot when the data set is uniformly distributed.
Simply said, the range is the difference between the greatest and smallest values in the data set.
Measure of center
The mean is a suitable measure of center to use in a stem and leaf plot when there are no outliers in a dataset.
The dataset's values are added up to determine the mean, which is then divided by the total number of values.
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Rectangle ABCD has a perimeter of 22 units. The coordinates of the rectangle’s vertices are A(−4, 5) , B(3, 5), C(3, x), and D(−4, x). Which could be the value of x?
Answer:
x = 1 or x = 9-----------------------------------------
The distance between A and B is the difference of x-coordinates, as y-coordinates are same:
3 - (-4) = 3 + 4 = 7 unitsIt means parallel side has same length.
Using perimeter we can find the adjacent side length:
AD = BC = (22 - 2*7)/2 = 8/2 = 4 unitsSince AB is horizontal, AD and BC are vertical segments.
Position of C and D could be above or below the segment AB.
If above AB, then coordinates are:
C(3, x) = C(3, 5 + 4) = C(3, 9)D(-4, x) = D(-4, 5 + 4) = D(-4, 9)If below AB, then coordinates are:
C(3, x) = C(3, 5 - 4) = C(3, 1)D(-4, x) = D(-4, 5 - 4) = D(-4, 1)See attached for better visual.
Michael will randomly choose 1 candy from the jar. What is the probability that he will choose an orange candy?
The probability of randomly selecting an orange candy is 1/3.
How to get the probability?We assume that all the candy have the same probability of being randomly selected. Then the probability of randomly selecting an orange candy is equal to the quotient between the number of orange candy and the total number of candy in the jar.
There are 6 orange ones, and the total number is:
T = 3 + 5 + 6 + 4
T = 18
Then the probability will be:
P = 6/18 = 1/3
The correct option is D.
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what is 1+1? need help asap
Answer:
its 11
Step-by-step explanation:
hope this helped bro!
5. You loan a friend $2500 and charge them 43/8% simple interest. What will be the total amount that they must repay you after 18 months?
The total amount that they must repay after 18 months is $2582.03
To calculate the total amount that your friend must repay you after 18 months, we need to first calculate the interest charged on the loan.
The interest rate is 43/8%, which can also be written as 0.04375 in decimal form.
To calculate the interest charged on the loan, we can use the formula:
Interest = Principal x Rate x Time
Where:
Principal = $2500 (the amount of the loan)
Rate = 0.04375 (the interest rate per year in decimal form)
Time = 18/12 (18 months expressed in years)
Plugging in the values, we get:
Interest = $2500 x 0.04375 x 18/12 = $82.03
So your friend will be charged $82.03 in interest.
To calculate the total amount that your friend must repay, we simply add the principal and interest together:
Total amount = Principal + Interest
Total amount = $2500 + $82.03 = $2582.03
Therefore, your friend must repay you a total of $2582.03 after 18 months.
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Solve 3x+9y=24 and x+3y=8 by elimination
I think I know the answer I just need clarification
Answer:
these equations are the same thing just multiply x+3y=8 by -3
Step-by-step explanation:
Marvin saw a rug in a store that he would like to purchase. It has an area represented by the expression shown on the rug. He cannot remember the length and width, but he remembers that the length and the width were the same. a. Factor the expression that represents the area of the rug. b. What do the factors in the factored expression represent. ( x²-16x + 64)
The area of the rug, represented by the quadratic expression, x² - 16·x + 64, indicates;
a. The factored expression is; x² - 16·x + 64 = (x - 8)·(x - 8)
b. The factors (x - 8) and (x - 8) in the factored expression represent the length and the width of the rug.
What is a quadratic expression?A quadratic expression is an expression of the form; a·x² - 16·x + 64, where a ≠ 0, and a, b, and c are numbers.
The possible expression for the area of the rug is the quadratic expression; (x² - 16·x + 64)
The length of the rug = The width of the rug
a. The factor of the expression in the question, (x² - 16·x + 64), can be obtained by finding the numbers that have a product of 64 and a sum of -16
The possible number is therefore; 8
-8 × -8 = 64
-8 - 8 = -16
Therefore, we get; (x - 8) × (x - 8) = (x² - 16·x + 64)
The factored expression is therefore; (x² - 16·x + 64) = (x - 8) × (x - 8)
b. The measure of the factors are the same; (x - 8) = (x - 8)
Whereby; x² - 16·x + 64 represents the area of the carpet and the lengths and the width of the of carpet are the same, therefore;
The length of the carpet = (x - 8)
The width of the carpet = (x - 8)
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Please help! I've tried but I just cant seem to get it.
Help would be gravely appreciated.
Answer:
58 degrees
Step-by-step explanation:
The vertical angles are equal
(2x + 6) + (2x +6) + X + X = 360
6x +12 =360
6x = 360 - 12
6x = 348
X = 58
Answer:
58°
Step-by-step explanation:
to solve <GLK
(2x+6)+(2x+6)+x+x=360
6x+12=360
6x=360-12
6x=348
Divide both sides by 66x/6=348/6
x=58°
the ratio of 7th graders to 8th graders on the tennis team is 3 to 5. what percent of the players on the tennis team are 8th graders?
The percentage of the players on the tennis team belongs to 8th graders from the given ratio is equal to 62.5%.
Ratio of the players of 7th graders to 8th graders on the tennis team = 3 : 5
Let the number of 7th graders on the tennis team be represented by 3x.
And let the number of 8th graders on the tennis team be represented by 5x.
Then,
The total number of players on the tennis team is 3x + 5x = 8x.
Percentage of players who are 8th graders,
= (the number of 8th graders (5x))/(the total number of players (8x)) × 100
Substitute the values we have,
⇒Percentage of players who are 8th graders = (5x / 8x) x 100%
⇒Percentage of players who are 8th graders = 62.5%
Therefore, percentage of the players on the tennis team are 8th graders is equal to 62.5%.
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Given tan θ = −1 and 90 ≤ θ ≤ 180°, what is csc θ? (2 points)
1
2
radical 2
2 times radical 3 over 3
Answer:22
Step-by-step explanation:Do the math then do more math
Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
if tan(θ) = -1, then θ = 135° or 315°.
Because theta is bound by 90 and 180 degrees, θ = 135°.
csc (θ) = 1 / sin(θ)
sin (θ) = sin (135°) = [tex]\frac{\sqrt{2} }{2}[/tex]
Because cosecant is the reciprocal of sine, our answer is [tex]\frac{2\sqrt{2} }{2}[/tex], or [tex]\sqrt{2}[/tex].
HELP ASAP !!!!!!!!,,,
-3x³ + 26x² - 18x + 16
Step-by-step explanation:We can multiply factors out to create a singular polynomial.
Multiplication
The first step of simplification is to multiply the factors. To keep our work neat, let's multiply the trinomial (polynomial with 3 three terms) by -x. Then, afterward, multiply the trinomial by 8. Then, we can add these answers together.
-x * (3x² - 2x + 2)We can multiply each term individually and then combine at the end. Let's work from left to right.
-x * 3x² = -3x³-x * -2x = 2x²-x * 2 = -2xNow, let's combine: -3x³ + 2x² - 2x. Then, let's move on to 8.
8 * (3x² - 2x + 2)Once again we can work from left to right.
8 * 3x² = 24x²8 * -2x = -16x8 * 2 = 16We can combine again: 24x² - 16x + 16. Finally, let's combine all of our answers: -3x³ + 2x² - 2x + 24x² - 16x + 16.
Standard Form
Now that we have one form of the answer, we can further simplify and change to standard form. The last step of simplification is to combine like terms. Like terms are terms with the same variable and exponent.
-3x³ + 2x² - 2x + 24x² - 16x + 16 = -3x³ + 26x² - 18x + 16Now, we need to make sure we're in standard form. Standard form is when the terms are written in descending order of degree. This means that the term with the highest exponent should be written first and the constant last. Note that constants are considered to have an exponent of 0. The answer above is actually already in standard form. But, we can check by just making sure the exponents are decreasing from left to right.
The final answer is -3x³ + 26x² - 18x + 16.
Given Triangle ABC where A and B are complementary angles. What is the equivalent to cos 25?
Answer:
0.9063
Step-by-step explanation:
Complementary angles are two angles whose sum is 90 degrees. In triangle ABC, if angle A and angle B are complementary, then we can write:
angle A + angle B = 90 degrees
Since this is a right triangle, we can use the trigonometric functions to find the lengths of the sides. The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse:
cos A = adjacent/hypotenuse
cos B = adjacent/hypotenuse
Since angles A and B are complementary, we can substitute 90 - A for B:
cos (90 - A) = adjacent/hypotenuse
sin A = adjacent/hypotenuse
So, to find the value of cos 25 degrees in this triangle, we need to find the sine of the complementary angle 65 degrees. Using the same logic as above, we can write:
sin (90 - 25) = adjacent/hypotenuse
cos 25 = adjacent/hypotenuse
We know that sin 65 = cos 25, so we can write:
cos 25 = sin 65
We can use a calculator to find that sin 65 is approximately 0.9063. Therefore, cos 25 is equivalent to approximately 0.9063.
Lacy and Emma are walking a trail Emma walks 5.4 kilome
ters farther than Lacy. Which equations represent the
number of kilometers Lacy walks, Lif Emma walks 6
The required distance Lacy walks 0.6 kilometers or 600 meters.
What is Equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.
According to question:We can start by assigning a variable to the number of kilometers that Lacy walks. Let's use "L" for Lacy's distance.
Since Emma walks 5.4 kilometers farther than Lacy, we can express
Emma's distance in terms of Lacy's distance as:
E = L + 5.4
where "E" represents Emma's distance.
If Emma walks 6 kilometers, we can set E equal to 6 and solve for L:
E = L + 5.4
6 = L + 5.4
Subtracting 5.4 from both sides, we get:
0.6 = L
So Lacy walks 0.6 kilometers or 600 meters.
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If a1 =5 and an =an−1 +4 then find the value of a4 .
Answer:
17
Step-by-step explanation:
You want to know the value of a4, given that a1 = 5 and a(n) = a(n-1) +4.
Arithmetic sequenceWhen a constant is added to each term to get the next term, the sequence is an arithmetic sequence. The terms can be found using the given equation:
a1 = 5
a2 = a1 +4 = 9
a3 = a2 +4 = 13
a4 = a3 +4 = 17
The value of a4 is 17.
find the limit, if it exists. (if an answer does not exist, enter dne.) lim x→[infinity] 81x2 x − 9x incorrect: your answer is incorrect.
The limit of the given function as x approaches infinity is infinity.
To find the limit of the given function as x approaches infinity, we need to apply the rules of limits.
The given function is:
lim x→[infinity] 81x2 x − 9x
We can simplify the function by dividing each term by x:
lim x→[infinity] 81x - 9
As x approaches infinity, the term 81x will also approach infinity, and the term -9 will become insignificant in comparison. Therefore, the limit of the function as x approaches infinity is infinity.
The final answer is:
lim x→[infinity] 81x2 x − 9x = infinity
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If B = [a b c d], find conditions on a, b, c, and d such that AB = BA. (Select all necessary conditions.) A = [1 1 0 1] A. a = b B. a = d C. c = 0 d = 0 D. b = c
A is a 1 x 4 matrix, the columns of B must be equal in order for the matrix product to be the same.
In order for AB to be equal to BA, all of the conditions below must be true:
A. a = b B. a = d C. c = 0 d = 0 D. b = c.
This is because the matrix B contains a, b, c, and d as entries,
and since A is a 1 x 4 matrix, the columns of B must be equal in order for the matrix product to be the same.
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(Identify the controllable and uncontrollable inputs for this model.(Select all that apply.)(i) controllableO xO yO labor hoursO labor availabilityO unit profit(ii) uncontrollableO xO yO labor hoursO labor availabilityO unit profit
The inputs that can be controlled in a model and those that cannot be controlled are referred to as controllable and uncontrollable inputs, respectively.
(i) controllable inputs: labor hours, labor availability, and unit profit
(ii) uncontrollable inputs: weather, natural disasters, or fluctuations
The controllable and uncontrollable inputs in a model are the inputs that the modeler can or cannot control, respectively. The controllable inputs are the inputs that can be manipulated by the modeler to achieve the desired output.
The controllable inputs are labor hours, labor availability, and unit profit. The labor hours can be modified to increase or decrease the level of production, while the labor availability can be altered to adjust the number of workers needed. The unit profit, on the other hand, can be modified to increase the profitability of the business.
The uncontrollable inputs, on the other hand, are the inputs that the modeler cannot control. The uncontrollable inputs in this case are x and y. These inputs could be external factors such as the weather, natural disasters, or fluctuations in market conditions that can affect the production output of a business.
The controllable inputs are labor hours, labor availability, and unit profit and uncontrollable inputs are external factors.
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