The particle is speeding up after 1.67 seconds.
What is displacement ?
In physics, displacement refers to the distance and direction of an object's change in position from its starting point to its ending point. It is a vector quantity, which means that it has both magnitude and direction.
Displacement is different from distance, which is the total length of the path an object has traveled, regardless of direction. Displacement only considers the straight-line distance and direction between the starting and ending points.
According to given conditions :
To determine when the particle is speeding up, we need to find the acceleration of the particle.
The acceleration of the particle is given by the second derivative of its position function:
a(t) = s''(t) = 6t - 10
The particle is speeding up when its acceleration is positive. So, we need to find the values of t for which a(t) > 0.
Setting a(t) > 0, we have:
6t - 10 > 0
6t > 10
t > 10/6
t > 1.67
Since t ≥ 0, the particle is speeding up when t > 1.67.
Therefore, the particle is speeding up after 1.67 seconds.
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the length of the hypotenuse is 51 cm, and one leg measure 24 cm. Find the length of the other leg of the triangle
c²=a²+b²
(51)²=(24)²+b²
2601=576+b²
2601-576=b²
2,025=b²
√2025=√b²
b= 45
the length of the other leg of the triangle is 45 cm
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
To find the volume of a triangular prism, you need to calculate the area of the triangular base and then multiply it by the height of the prism. First, calculate the area of the base by finding the length of the triangle's sides and then using the Heron's Formula. Then, multiply the area of the base with the height of the prism to get the volume of the triangular prism. For example, if the length of the sides of the triangle is 3, 4 and 5, then the area of the base is 6 and the height of the prism is 8, then the volume of the prism is 48.
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The length of the other leg of the triangle is 45 cm.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
To find the volume of a triangular prism, you need to calculate the area of the triangular base and then multiply it by the height of the prism. First, calculate the area of the base by finding the length of the triangle's sides and then using the Heron's Formula. Then, multiply the area of the base with the height of the prism to get the volume of the triangular prism. For example, if the length of the sides of the triangle is 3, 4 and 5, then the area of the base is 6 and the height of the prism is 8, then the volume of the prism is 48.
According to Pythagoras theorem.
c² = a²+b²
(51)² = (24)²+b²
2601 = 576+b²
2601-576 = b²
2,025 = b²
√2025 = √b²
b = 45
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What is the conversion of 28 f to c ?
The conversion of 28 Fahrenheit to Celsius is -2.22.
To convert 28 degrees Fahrenheit (28°F) to Celsius (°C), you can use the formula:
°C = (°F - 32) x 5/9
Substituting 28 for °F in the formula, we get:
°C = (28 - 32) x 5/9
Simplifying the expression inside the parentheses and performing the arithmetic operations, we get:
°C = (-4) x 5/9
°C = -2.22
Therefore, 28°F is equal to -2.22°C (rounded to two decimal places).
Celsius and Fahrenheit are two scales used to measure temperature.
Celsius, also known as the centigrade scale, is a temperature scale where the freezing point of water is 0 degrees Celsius and the boiling point of water is 100 degrees Celsius at standard atmospheric pressure.
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Correct Question :
What is the conversion of 28 Fahrenheit to Celsius?
Can somebody help me pls? 20 PTS + will mark brainliest, please
The number 1.07 × 10⁸ in standard form is 107,000,000.
How to write a number in standard form?To write 1.07 × 10⁸ in standard form, we need to move the decimal point to the left or right such that there is only one non-zero digit to the left of the decimal point.
In this case, we have 1.07 × 10⁸, which means we have a value of 1.07 times 10 raised to the power of 8. To convert this to standard form, we need to move the decimal point 8 places to the right since 10 is being raised to the power of 8.
1.07 × 10⁸ = 107,000,000
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Let’s go Shopping!
You and your friend have decided a day to the mall is in order. Answer the following questions regarding some purchases you make. Be sure to read the directions carefully and answer the questions fully to what the directions are asking you to do. This means you must prep for the day. This includes what you will wear and how your travel will look.
1. Your first plan of action is to decide what to war for the day.. You will be shopping all day. The temperature at 8 am this morning is 45 degrees. The weather man says the temperature will increase by 32 degrees by 12 pm then decrease by 14 degrees at 6pm where it remains constant. Setup an expression for finding temperature throughout the day. Find the final temperature from your expression. (Optional-Attach a picture of your favorite shirt, sweatshirt, etc.)
2:Your next decision is deciding on how many 5-minute songs you can listen to while driving to the mall, which is 45 minutes away. Setup an expression to find the number of songs you can listen to on the way to the mall. Find the total number of songs you can listen to. (Optional- list your favorite song currently.)
3:After listening to all your favorite tunes, you finally arrive at the mall. You can’t remember how much money you have. You pull out your money. You have seven twenty dollar bills, four ten dollar bills, three five dollar bills, and eight one dollar bills. Setup an expression for the total amount of money you have. Find the total amount of money you have.
4:After counting your money. The first store you go to is a video game store. You see 4 games you would like to purchase. The first is $19.99, the second is $21.59, the third is $9.92, and the last one is $22.88. You purchase all four games. You get talking with your friend and remember that the last one you bought for $22.88 is a game your friend already has. You take that game back to the store and they charge a fee of $2.99 for returned games. Setup an expression for the amount you paid for the 4 games, the game you returned and the fee you had to pay. Find the total after you paid for the 4 games, the returned game, and the fee. (Optional – list your favorite video game)
5:Your friend decides you should go a clothes store next. Your friend has one hundred dollars. They pick out 10 items. The first three are $15.99, the second three are $10.40 and the last four are $4.50. Explain how you would estimate if your friend has enough money to buy all the items. Then setup an expression to find out if your friend has enough money to buy all the items. Lastly, find the total from your expression.
6:After you both have bought some items you decide it is time for some candy at the candy store. You decide to buy 5 and 1/2 pounds of jelly beans. Your friend suggests that you share your jelly beans with your other friends tomorrow. You decide to give each friend ¼ of a pound. How many friends can you share your jelly beans with? Set up an expression to find the number of friends you can share it with. (Optional what is your favorite candy?)
7:Giving to your church is part of God’s will. Genesis 14:19-20 says,” And he blessed him and said, “Blessed be Abram by God Most High, Possessor of heaven and earth; and blessed be God Most High, who has delivered your enemies into your hand!” And Abram gave him a tenth of everything.” Before you went to the mall you should have set side 10% or 0.1 of your money you had. From question three, how much money should you bring to church? Setup an expression to show the amount you should bring.
The total amount spent when the 10 items are bought is $97.17.
The final temperature given the increase in temperature and the decrease in temperature is 18 degrees.
What is the total amount spent and the final temperature?In order to determine if your friend has enough money to buy all the items, the total cost of the items have to be determined. The total cost is the sum of all the items bought.
here, we have,
Total cost = total cost of the first three items + total cost of the second three + total cost of the last three
Total cost = (3 x 15.99) + (3 x 10.40) + (4 x 4.50)
Total cost = $47.97 + $31.20 +18
Total cost = $97.17
An increase in temperature would be represented with a positive number. While, a decrease in temperature would be represented with a negative number. The final temperature can be determined by adding the temperature increase and decease together.
Final temperature = increase in temperature - decrease in temperature
Final temperature = 32 - 14 = 18 degrees
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HELP MEE PLEASEEEEEE
The third term in the recursive sequence is 9
How to find the third term in the recursive sequence?
A recursive sequence is a sequence of numbers where each term is defined by a formula that uses one or more of the previous terms in the sequence. In other words, each term depends on the term(s) that come before it.
Since a₁ = 3 and [tex]a_{k+1}[/tex]= 2a[tex]_{k}[/tex] - 1
a₂ = 2a₁ - 1
a₂ = 2(3) - 1 = 6 - 1 = 5
a₃ = 2a₂ - 1
a₃ = 2(5) - 1 = 10 - 1 = 9
Thus, the third term in the recursive sequence will be 9
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If you draw a radius from the center of the circle to the point of tangency, what is the measure of the angle formed by the radius and the tangent line?
Responses
A Cannot be determined
B 45°
C 90°
D 180°
IMAGE ATTACHMENT
Answer:
c 90 degrees
Step-by-step explanation:
i took the test
Airline passengers arrive randomly and independently at the pass nger-screening facility at major international airport: The mean arrival rate 10 passengers per minute (Round your answers to six decimab places_ (a) Compute the probability of no arrivals in one-minute period_ 000045 (b) Compute the probability that three or fewer passengers arrive in one-minute period. 0.010336 Compute the probability of no arrivals in 21-second period Compute the probability of at least one arrival 21-second period.
The probability of at least one appearance in a 21-alternate period is 0.969803
(a) The appearance rate is 10 passengers nanosecond , so the anticipated number of advents in nanosecond is also 10. The probability of no advents in one minute is given by the Poisson distribution with parameter lambda = 10:
P(X = 0) = [tex]e^{(-lambda)}[/tex] [tex]lambda^{0}[/tex] / 0! = [tex]e^{(-10)}[/tex]* [tex]10^{0}[/tex] / 1! = 0.000045 (rounded to 6 decimal places)
Therefore, the probability of no arrivals in one-minute period is 0.000045.
(b) To compute the probability that three or fewer passengers arrive in one-minute period, we can use the cumulative distribution function (CDF) of the Poisson distribution:
P(X <= 3) = sum from i=0 to 3 of P(X = i)
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= [tex]e^{-10}[/tex] *[tex]10^{0}[/tex] / 0! + [tex]e^{(-10)}[/tex] * [tex]10^{1}[/tex]/ 1! + [tex]e^{(-10)}[/tex] * [tex]10^{2}[/tex] / 2! + [tex]e^{(-10) }[/tex]* [tex]10^{3}[/tex]/ 3!
= 0.010336 (rounded to 6 decimal places)
Therefore, the probability that three or fewer passengers arrive in one-minute period is 0.010336.
(c) The arrival rate is 10 passengers per minute, which is equivalent to 10/60 = 1/6 passengers per second. Therefore, the expected number of arrivals in a 21-second period is (1/6) * 21 = 3.5 passengers. The probability of no arrivals in a 21-second period is given by the Poisson distribution with parameter lambda = 3.5:
P(X = 0) = [tex]e^{(-lambda)}[/tex] * l[tex]lambda^{0}[/tex] / 0! = [tex]e^{(-3.5)}[/tex] * [tex]3.5^{0}[/tex]/ 1! = 0.030197 (rounded to 6 decimal places)
Therefore, the probability of no arrivals in a 21-second period is 0.030197.
(d) The probability of at least one arrival in a 21-second period is equal to 1 minus the probability of no arrivals:
P(at least one arrival) = 1 - P(no arrivals)
= 1 - 0.030197
= 0.969803 (rounded to 6 decimal places)
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Write a function in terms of t that represents the situation.
A stock valued at $100 decreases in value by 9.5% each year.
Y=
Answer:
100-0.095x
Step-by-step explanation:
What is factorization of 105 ?
The prime factorization of 105 is 3 × 5 × 7. We can also write this as 3 × [tex]5^1[/tex] × [tex]7^1[/tex], where the exponents indicate the number of times each prime factor appears in the factorization.
To find the prime factorization of 105, we can use the following steps:
Find a factor of 105. One way to do this is to try dividing 105 by prime numbers (2, 3, 5, 7, 11, ...) until we find a factor. We can also notice that 105 is divisible by 3 since the sum of its digits (1 + 0 + 5) is a multiple of 3.
Divide 105 by the factor we found in step 1 to get a smaller number.
Repeat steps 1 and 2 with the smaller number until we get a prime number.
Using this method, we can find the prime factorization of 105 as follows:
105 ÷ 3 = 35
35 ÷ 5 = 7
Since 7 is a prime number.
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you buy a new car for $22,500. the value of the car decreases by 25% each year. write an exponential decay model giving the car's value v (in dollars) after t years. what is the value of the car after three years to the nearest dollar amount?
Therefore, the value of the car after three years is approximately $9,484.
What is percent?Percent is a term used to represent a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express proportions, ratios or fractions in terms of parts per hundred. The word "percent" comes from the Latin phrase "per centum," which means "by the hundred." Percentages are commonly used in everyday life, such as in calculating taxes, discounts, interest rates, and in comparing statistics, among others.
Here,
The exponential decay model for the value of the car after ⁿ years can be written as:
v = 22500 * (0.75)ⁿ
where 22500 is the initial value of the car, and (0.75)ⁿ represents the value after ⁿ years with a 25% annual decrease.
To find the value of the car after three years, we can substitute n = 3 into the equation:
v = 22500 * (0.75)³
v = 22500 * 0.421875
v = 9484.375
Rounding this to the nearest dollar amount, we get:
v ≈ $9,484
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Two vertices of a right triangle have coordinates (5, 12) and (11, 12). The segment that connects these points is a leg of the triangle.
Which coordinate pair for the third vertex would create a right triangle?
Responses
(19, 12)
, left parenthesis 19 comma 12 right parenthesis,
(8, 20)
, left parenthesis 8 comma 20 right parenthesis,
(8, 12)
, left parenthesis 8 comma 12 right parenthesis,
(11, 4)
, left parenthesis 11 comma 4 right parenthesis,
The answer is (A) (11, 4).
Step-by-step explanation: Given that two vertices of a right-angled triangle are A(5, 12) and B(11, 12).
We can plot the given points on the co-ordinate plane as shown in the attached figure.
We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse.
The lengths of the three sides are
[tex]AB = 11 - 5 = 6\\\\BC = 12 - 4 = 8\\\\AC = \sqrt{AB^{2} +BC^{2} } = \sqrt{6x^{2}+8^{2} } = \sqrt{100} = 10[/tex]
Thus, the correct option is (A).
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x-values containing values negative 8, negative 5, negative 1, 1, and 12 and another circle labeled y values containing values negative 4 and negative 2 and arrows from negative 8 to negative 4, negative 5 to negative 2, negative 1 to negative 2, 1 to negative 2, 12 to negative 4, and 12 to negative 2. Is the relation a function? Explain.
To determine whether the relation is a function, we need to check if each x-value is associated with only one y-value in the mapping diagram.
Identify the mapping diagram.A mapping diagram is a picture of two circles that shows the connection between input and output values. Illustration of a mapping diagram. The x-values (inputs) in the image are converted to the associated y-values by drawing an arrow from one x-value to its corresponding y-value (outputs).
From the given mapping diagram, we can see that the x-value -8 is associated with the y-value -4, the x-value -5 is associated with the y-value -2, the x-value -1 is associated with the y-value -2, the x-value 1 is associated with the y-value -2, the x-value 12 is associated with both the y-value -4 and -2.
Since the x-value 12 is associated with two different y-values, the given relation is not a function. To be a function, each x-value must be associated with only one y-value in the mapping diagram.
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Answer: I think its C lmk if I'm wrong
Explanation:
in a regression model, outliers may be identified by examining the?
in a regression model, outliers may be identified by examining the Residual. Seeing how far the data points are away from the regression is how you can determine outliers.
What's a residual in finance?
A residual or balloon payment is a final lump sum you're needed to pay at the end of your loan term to enjoy an asset outright. generally, the lump sum is original to – or lower than – the downgraded value of the asset.
What are exemplifications of residual?
Residual describes what remains after utmost of commodity is gone. It's an nearly formal word for what is leftover. However, also you have some residual bitterness, If you've gotten over your bifurcation but you still have the appetite to protest your partner.
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Mrs. Milton travels 60 miles round-trip to work. She works five days a week. Her car gets about 25
miles per gallon of gasoline. About how many gallons of gasoline does Mrs. Milton's car use during her
weekly commute?
Answer:
Mrs. Milton's car uses about 12 gallons of gasoline each week for her commute.
If all real numbers are solution, click on All reals. If there is no solution, click on the no solution.
We can write the solution set as -
v < 11 {v > 0}v > - 11 {v < 0}What is inequality?An inequality is used to compare two numbers or expressions.
Given is the linear inequality as -
|v| - 16 < - 5
The given linear inequality is -
|v| - 16 < - 5
|v| < - 5 + 16
|v| < 11
Now -
v < 11 {v > 0}
&
- v < 11 {v < 0}
v > - 11 {v < 0}
Therefore, we can write the solution set as -
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what is 86 cm in inches ?
86 centimeter is approximately equal to 33.8583 inches.
We may use the conversion factor of 1 inch = 2.54 cm to convert 86 cm to inches.
To obtain the corresponding measurement in inches, divide 86 cm by 2.54:
86 cm ÷ 2.54 inches = 33.8583 inches (rounded to four decimal places)
To comprehend this conversion, we must first realise that centimetres (cm) and inches (in) are both length units, but they are measured using distinct systems. Centimeters are part of the metric system, which is widely used in most nations worldwide, whereas inches are part of the Imperial system, which is widely used in the United States, the United Kingdom, and a few other countries.
The precise connection between the two measurement systems yielded the conversion factor of 1 inch = 2.54 cm. To translate a length from centimetres to inches, divide the value by 2.54, and to convert from centimetres to inches, multiply the value by 2.54.
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Rashon bought a pair of sunglasses online for $34. He used a coupon code to get a 30% discount. The website also applied a 20% processing fee to the price after the discount. How much was the processing fee? Round to the nearest cent.
Answer:
$4.80
Step-by-step explanation:
The processing fee was 20% of the price after the discount, which would be 20% of $34 minus 30%, or 20% of $23.80. This is equal to $4.76, which rounded to the nearest cent is $4.80.
i need help with this question
Answer:
Below
Step-by-step explanation:
Volume of a cone = 1/3 pi r^2 h
4125 pi = 1/3 pi r^2 h
4125 = 1/3 r^2 h <===if diameter =30 then radius = 15 units
4125 = 1/3 (15)^2 h
4125 / (1/3 * 15^2) = h = 55 units
does anyone know how to do this i’m stuck
Answer:
yes I know but how should I show u dude
Answer: look at the image for the answer and explanation
Step-by-step explanation:
what is 1.78 m to feet?
According to the standard conversion rates 1.78 is equal to 5.696 feet.
We measure the distance between any two bodies in the terms of meter but when the distance is a small one, we can also use the unit called foot and these two units are interconvertible.
According to the standard us conversion rates one meter is equal to 3.2 ft.
We can use this same conversion rate to find the measurement of 1.78 m into ft.
So, we will write,
1 m = 3.2ft
1.78m = 1.78 x 3.2 ft
1.78m = 5.696 ft.
So, we have found that 1.78 m is equal to 5.696 feet.
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9. 12 in. 24 in. 8 in. 20 in.
The two dimensions that should follow the sequence, 12 in. 24 in. 8 in. 20 in., are 4 in. and 16 in.
What is a sequence?A sequence is an ordered list of numbers that follow a specific pattern.
Related events or things that follow each other in an orderly form are described as sequences.
24 inches are 12 inches more than 12 inches (24 -12).
20 inches are 12 inches more than 8 inches (20 - 8).
16 inches are 12 inches more than 4 inches (16 - 4).
The common difference between the dimensions is 12 inches and the sequence reduces in value by 4 inches from the previous length and width to the next.
Thus, we can identify some patterns in any sequence, whether they are arithmetic, geometric, quadratic, or special sequences.
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Question Completion:Which two dimensions should follow this sequence?
PLS ANSWER QUICKLY!!!! ILL GIVE BRAINLEST AND 50 POINTS!!!!!
Make sure to find the missing angle measure AND the 2 missing side lengths.
Answer:
we can assume that m = 90% cause the square so the we know that all the angles add up to 180° so ad 30 +90 and then subtract you sum from 180 and that is the angle of x
Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 2/7 x^2, y = 9/7 - x^2 Find the volume V of this solid. V = Sketch the region, the solid, and a typical disk or washer. (Do this on paper. Your instructor may ask you to turn in this work.)
Take into consideration the solid that results from rotating the area enclosed by the provided curves about the x-axis. y = 2/7 x^2, y = 9/7 - x^2 . the volume of the solid is approximately 1.412 cubic units.
To find the volume of the solid obtained by rotating the region bounded by the curves y = 2/7 [tex]x^{2}[/tex] and y = 9/7 - [tex]x^{2}[/tex] about the x-axis, we can use the method of disks or washers.
First, we need to find the limits of integration. The curves intersect when:
2/7[tex]x^{2}[/tex] = 9/7 - [tex]x^{2}[/tex]
Multiplying both sides by 7, we get:
2[tex]x^{2}[/tex] = 9 - 7[tex]x^{2}[/tex]
9[tex]x^{2}[/tex] = 9
[tex]x^{2}[/tex] = 1
x = ±1
Therefore, the limits of integration are x = -1 and x = 1.
Next, we need to express the curves in terms of y. Solving for x in each equation, we get:
x = ±√(7/2 y)
x = ±√(9/7 - y)
Using the method of disks, we can find the volume of the solid by integrating the areas of circular disks with radius y from y = 0 to y = 9/7.
The radius of each disk is given by the difference between the upper and lower curves evaluated at y:
r = √(9/7 - y) - √(7/2 y)
The area of each disk is given by:
A = π[tex]r^{2}[/tex]
Substituting for r, we get:
A = π [√(9/7 - y) - √(7/2 y)]
Expanding and simplifying, we get:
A = π [9/7 - y + 7/2 y - 2√(9/7 y)]
A = π [9/7 + 3/2 y - 2√(9/7 y)]
Integrating with respect to y, we get:
V = ∫[0, 9/7] π [9/7 + 3/2 y - 2√(9/7 y)] dy
V = π [(9/7) y + (3/4) - (4/9) [tex]9/7^{3/2}[/tex] [tex]y^{3/2}[/tex]] [0, 9/7]
V = π [81/28 - (64/81) [tex]9/7^{3/2}[/tex]]
V ≈ 1.412
Therefore, the volume of the solid is approximately 1.412 cubic units.
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Question 5: In an examination in which full marks were 500. A got 10% less than
B. B got 25% more than C, C got 20% less than D. If A got 360 marks, what
percentage of full marks was obtained by D?
(a) 90%
(b) 80%
(c) 50%
(d) 60%
The percentage of full marks was obtained by D is (d) 60%.
What is percentage ?
Let's start by using the given information to find out how many marks B, C, and D got in the exam.
We know that A got 10% less than B, so if A got 360 marks, then B got 10% more than that, which is:
B = 360 + 10% of 360
= 360 + 36
= 396
We also know that B got 25% more than C, so if B got 396 marks, then C got 25% less than that, which is:
C = 396 - 25% of 396
= 396 - 99
= 297
Finally, we know that C got 20% less than D, so if C got 297 marks, then D got 20% more than that, which is:
D = 297 + 20% of 297
= 297 + 59.4
= 356.4
So D got 356.4 marks out of 500. To find out what percentage of full marks D obtained, we can use the formula:
percentage = (marks obtained / full marks) x 100
Therefore, the percentage of full marks obtained by D is:
percentage = (356.4 / 500) x 100
= 71.28%
Rounded to the nearest integer, the answer is approximately 71%, which is closest to option (d) 60%. Therefore, the answer is (d) 60%.
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Encontrar el coeficiente de y en (3 xy+2)4
The required coefficient of y in [tex](3xy + 2)^4[/tex] is 96x.
What is binomial expansion?The binomial expansion is a formula for expanding a binomial expression of the form [tex](a + b)^n\\[/tex], where "a" and "b" are constants and "n" is a positive integer. The expansion gives the coefficients of each term in the expansion.
Here,
We can use the binomial theorem to expand the expression,
[tex](3xy + 2)^4 = C(4,0) (3xy)^4 (2)^0 + C(4,1) (3xy)^3 (2)^1 + C(4,2) (3xy)^2 (2)^2 + C(4,3) (3xy)^1 (2)^3 + C(4,4) (3xy)^0 (2)^4[/tex]
where C(n,k) represents the number of combinations of k objects that can be chosen from a set of n objects.
The coefficient of y in the fourth term is given by the coefficient of ([tex]3xy)^1 (2)^3[/tex]. That is, we need to find the coefficient of y in the term:
[tex]C(4,3) (3xy)^1 (2)^3 = 4 * 3xy * 2^3 = 96xy[/tex]
Therefore, the coefficient of y in [tex](3xy + 2)^4[/tex] is 96x.
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In ΔXYZ, ∠Y=90° and ∠X=58°. ∠ZWY=70° and XW=120. Find the length of ZY to the nearest 10th.
The length of ZY to the nearest 10th is 69.5 units.
What is the triangle?
A triangle is a closed figure made of 3 line segments.
It has 3 sides, 3 vertices and 3 angles.
The sum of two sides is always Greater than the third side.
The sum of all angles is 180°.
We can start by finding the measure of angle YXZ:
m∠YXZ = 180° - m∠Y - m∠X = 180° - 90° - 58° = 32°
Now we can use the tangent ratio to find ZY:
tan(32°) = ZY / XW
ZY = XW * tan(32°) = 120 * tan(32°) ≈ 69.5
Hence, the length of ZY to the nearest 10th is 69.5 units.
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Answer:459.9
Step-by-step explanation:
I got this from Khan academy.
Rewright the equation by completing the square. x^2 −14x+33=0
(x+_)^2
HELP!
what is the nominal ordinal interval ratio?
Nominal, ordinal, interval, and ratio are measurement scales used in statistics to categorize and rank data.
Nominal, ordinal, interval, and ratio are four sorts of information estimation scales utilized in measurements.
Nominal scales are utilized to mark or classify information into particular gatherings, where each gathering is fundamentally unrelated and altogether comprehensive. Instances of ostensible information incorporate orientation, race, and occupation.
Ordinal scales include positioning information in a particular request, however the distinctions between values are not significant. Instances of ordinal information incorporate positioning motion pictures in view of their prominence or understudy execution on a test.
interval scales include positioning information in a particular request, however the distinctions between values are significant, and there is no obvious zero point. Instances of stretch information incorporate temperature, intelligence level scores, and time.
ratio scales are like span scales, however they have a genuine zero point, implying that values can be duplicated and partitioned. Instances of proportion information incorporate weight, level, and pay.
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The complete question is:
what is the nominal, ordinal, interval and ratio?
a normal distribution has a mean of µ = 70 with σ = 12. if one score is randomly selected from this distribution, what is the probability that the score will be less than x = 76?
The probability that a randomly selected score from this normal distribution is less than x = 76 is 0.6915
To find the probability that a randomly selected score from a normal distribution with mean µ = 70 and standard deviation σ = 12 is less than x = 76,
we need to use the standard normal distribution and calculate the z-score corresponding to x = 76, and then look up the corresponding area under the standard normal curve using a standard normal distribution table.
The z-score is calculated as:
z = (x - µ) / σ
z = (76 - 70) / 12
z = 0.5
By using a standard normal distribution table, we can find the area under the curve to the left of z = 0.5, which is 0.6915.
Therefore, the probability that a randomly selected score from this normal distribution is less than x = 76 is 0.6915 or approximately 69.15%.
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What is the equation of the line that passes through the point (2, 1) and has a slope
of -5/2
The equation of the line that passes through the point (2, 1) and has a slope of -5/2 is y=(-5/2)*x+6.
Linear EquationAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=3x+4. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=3 and b=4.
The question gives:
Point : (2,1) , where x=2 and y=1
Slope= -5/2
From the standard form of the linear equation ( y= mx+b) and the given point and the slope, you can write:
y=mx+b
1=-5/2*(2)+b , thus you can find b.
1=-5+b
-b=-5-1
-b=-6
b=6
If b=6 and m=-5/2, you can write the linear equation:
y=mx+b
y=(-5/2)*x+6
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The equation of line that models this is y = -5/2x + 6
What is the equation of lineThe equation of a line is typically written in slope-intercept form, which is y = mx + b, where m is the slope of the line, and b is the y-intercept.
The slope (m) is a measure of how steep the line is, and it can be calculated using the formula:
y = mx + c
In the given question, the slope is -5/2 and the points are (2, 1)
Substituting the values into the formula of equation of line;
y = mx + c
1 = -5/2(2) + c
1 = -5 + c
c = 1 + 5
c = 6
The equation is y = -5/2 + 6
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