Usain's speed in miles per hour is 22.72 mph.
What is Speed Distance Formula?Speed = Distance/Time
Distance = Speed X Time
Time = Distance / Speed
Given:
Usain run 100 yards in 9 sec.
So, he can 1760 yards in
= 9/100 x 1760
= 158.4 sec
As, his speed in yards/ sec= 100/9
So, 1760 yard= 1 mile and 3600 sec = 1 hour
Now, the speed in miles per hour
= 100/ 9 x 3600/1760
= 100/9 x 2.045
= 22.72 mph
Hence, the speed is 22.72 mph.
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Kayla had a balance of $65 in her savings account before withdrawing $28. What is her new balance? $83 $93 $43 $37
Which figure below shows the correct vector relationship between voltage and current in a parallel LC circuit?
Therefore , solving the provided vector question we can say that Figure B best describes the voltage and current in parallel LC circuit
what is vector?In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow.
Given :
Vector as given :
Figure A, Figure B , Figure C and Figure D
Voltage and current
parallel LC circuit
=>Iₙ * Eₙ = Iₙ
Size and direction are two independent characteristics of a quantity or phenomena known as a vector.
The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.
Here,
From observation we can say that ,
Figure B best describes the voltage and current in parallel LC circuit
Figure B
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You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 500 eggs and 1,050 cups of cream. How many quarts of each flavor should you make in order to use up all the eggs and cream?
Creamy Vanilla
qt
Continental Mocha
qt
If I manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. Where I have in stock 500 eggs and 1,050 cups of cream. The number of quarts of each flavor that I would make in order to use up all the eggs and cream is: 150 quarts of Vanilla and 200 Quarts of Mocha.
Let x and y be the number of Quarts of Vanilla and Mocha respectively.
The total number of eggs used is given as:
2x+y = 500
And the total cups of cream is:
3x + 3y = 1050
Removing the second equation from three times the first, we get:
3(2x + y) - (3x + 3y) = 3(500) -1050
6x + 3y - 3x - 3y = 1500 - 1050
⇒ 3x = 450
⇒ x = 450/3
x = 150
By substituting x back in tot he first equation we find:
2x+y = 500
2 (150) + y = 500
300 + y = 500
y = 500 - 300
y = 200.
Thus, to use up al the eggs and cream, 150 quarts of Vanilla and 200 quarts of Mocha should be produced.
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Jasmine claims “to find the lowest common multiple of two numbers, you can multiply them together. For example, 5 × 8 = 40 and the LCM of 5 and 8 is 40”
Is Jasmine correct? Justify your answer.
Answer:
No, Jasmine is not correct. The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. Multiplying the two numbers together is not always the correct method to find the LCM.
For example, the LCM of 5 and 8 is 40, but the product of 5 × 8 = 40 is not the LCM.
A more accurate way of finding the LCM is by using the prime factorization of the numbers. By finding the prime factorization of the two numbers, you can take the highest exponent of each prime factor and multiply them together. The result of that multiplication is the LCM of the two numbers.
In this case, the prime factorization of 5 is 5 and 8 is 2^3. The LCM of 5 and 8 is 2^3*5 = 40. So Jasmine's claim that 5 x 8 = 40 and the LCM of 5 and 8 is 40 is not correct.
A bakery produces 280 loaves of bread and 95 cakes daily.
explain how you would compute the percent of the baked foods that are cakes.
The percent of the baked foods that are cakes will be 25.33%
How to calculate the percentage?It should be noted that a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %. In this situation, the bakery produces 280 loaves of bread and 95 cakes daily.
The percent of the baked foods that are cakes will be:
= Number of cakes / Number produced daily × 100
= 95 / (280 + 95) × 100
= 95 / 375 × 100
= 25.33%
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Simplify the following expression.
4√72
O A. 6√24
B.
144√6
OC. 24√6
D. 24√/2
O D.
The expression 4√72 can be simplified by first taking the square root of both sides, which gives us 2√72. Then, we can factor out a 6 from both sides, which gives us 24√6. Therefore, the simplified expression is 24√6.
What is expression?Expression is the process of conveying one’s thoughts, emotions, ideas, and beliefs through speech, writing, art, or any other form of communication. Expression is a form of communication that allows people to express themselves in a way that is meaningful and personal to them. It is a powerful way for individuals to express their thoughts, feelings, and opinions without fear of judgement or criticism. Expression is an important part of self-expression, and it can be used to connect with others through shared experiences, to create a sense of community, and to grow and learn from one another. Expression is an invaluable tool for self-expression, creativity, and communication.
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Consider parallelogram JKLM below.
Use the information given in the figure to find mLNJK, x, and mLNKJ.
K
N
4x - 3
13
AL
50°
42°
M
Answer:
∠NJK = 50°x = 4∠NKJ = 42°Step-by-step explanation:
You want a couple of interior angles and the value of x given the parallelogram in the figure.
AnglesThe diagonals of a parallelogram bisect each other, and divide the figure into two pairs of congruent triangles. Here, the congruent triangles of interest are ...
∆NKJ≅∆NML
In these triangles, that means ...
∠J ≅ ∠L = 50° = ∠NJK
∠K ≅ ∠M = 42° = ∠NKJ
SegmentsThe halves of diagonal JL are congruent, so we have ...
4x -3 = 13
4x = 16 . . . . . . . . add 3
x = 4 . . . . . . . . . divide by 4
Write and solve an equation.
A drink and 7 pizzas cost $94.25. The cost of the drink was $1.50. What was the cost, c, of one pizza?
Answer:
13.25
Step-by-step explanation:
1. you have to subract the cost of the drink:
94.25-1.50=92.75
2.you have to divide to get the individual cost of pizzas by doing
92.75÷7=13.25
so therefore your answer is 13.25 per pizza
how do you find the distance formula to find the distance between each of the specified points. (ie pythagorean theorem)?
Answer: The distance formula is a mathematical formula used to find the distance between two points in a plane. One way to find the distance formula is by using the Pythagorean theorem.
The Pythagorean theorem 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.
The distance formula can be derived from the Pythagorean theorem by considering the two points as the two endpoints of a line segment. The formula is as follows:
Distance = √(x2 - x1)^2 + (y2 - y1)^2
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this formula, the difference in the x-coordinates is squared and the difference in the y-coordinates is also squared. Then, these two values are added and the square root of the result gives the distance between the two points.
For example, if we have two points (x1, y1) = (2, 3) and (x2, y2) = (5, 8), we can use the distance formula to find the distance between these two points:
Distance = √((5 - 2)^2 + (8 - 3)^2)
Distance = √(3^2 + 5^2)
Distance = √(9 + 25)
Distance = √(34)
Distance = 5.83
Therefore, the distance between the two points is 5.83 units.
Step-by-step explanation:
How do I divide with rational expressions.
The value of the rational expression is q⁴ / 14p⁴
What are rational expressions?A rational expression is the ratio of two polynomials. If f is a rational expression, then f can be written in the form p/q where p and q are polynomials.
Given are rational expressions,
5pq / 16p³ ÷ 35p²q² / 8q⁵
Using identity, a/b ÷ c/d = a/b × d/c
5pq / 16p³ × 8q⁵ / 35p²q²
= 40q⁴ / 560p⁴
= q⁴ / 14p⁴
Hence, the value of the expression is q⁴ / 14p⁴
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3) The area and
diagonal of a
Kite are 144cm and 8cm respectively, find the other diagonal
Answer:
Step-by-step explanation:
Let the other diagonal be d.
From the Pythagorean theorem,
d2 = 82 + 1442
d2 = 64 + 20736
d2 = 20800
d = √20800
d = 144 cm
I need help with this
Answer:
Step-by-step explanation:
the answer will be option 4
What is the equation of this line? y>1/2x−3 y<1/2x−3 y>2x−3 y<2x−3
Answer:
The equation of this line is y>1/2x-3
Step-by-step explanation:
This is an inequality equation that represents a line that is greater than 1/2x-3. The inequality symbol ">" indicates that all the y-coordinates that are on the same side of the line as the y-axis are greater than 1/2x-3.
In other words, all the points that lie above the line will satisfy the inequality, while all the points that lie below the line will not.
It's worth noting that the line y<1/2x-3 represents the same line but the inequality symbol "<" indicates that all the y-coordinates that are on the same side of the line as the x-axis are less than 1/2x-3.
y>2x-3 and y<2x-3 represent different lines, the first one represents a line with a slope of 2 and the second one represents a line with a slope of -2.
The debt-to-assets ratio formula is: Debt-to-assets ratio = total liabilities/total assets. If your total liabilities are $3,228 and your total assets are $5,091. What is your debt-to-assets ratio?
The debts to assets ratio is 0.63
How to calculate the debts to assets ratio ?The formula for calculating debts to assets ratio is
total liabilities/total assets
The total liabilities is $3,228
The total assets is $5,091
Therefore the debts to assets ratio is
3228/5091
= 0.63
Hence the debts to assets ratio is 0.63
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Twenty less than a number is more than twice the same number . Find the smallest possible value of the number.
The smallest possible value of the number that is an integer is -21
Determining the value of a numberFrom the question, we are to determine the smallest possible value of the number
From the given information, we have that
"Twenty less than a number is more than twice the same number"
Let the number be x
Then,
we can write that
x - 20 > 2x
Now, we will solve for x
x - 20 > 2x
-20 > 2x - x
-20 > x
Therefore,
x < -20
The possible integers are -21, -22, -23, -24, -25, -26, ...
Then,
The smallest integer is -21
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Write the sentence as an equation.
106 more than the quantity 68 times y is the same as 36 decreased by y
Answer: 68y+106=36-y
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 9 cm long. A second
side of the triangle is 22.5 cm long. Find all possible lengths for the third side of the triangle.
The Angle Bisector Theorem states that in a triangle, if a line bisects one angle of a triangle and is also a median to the side opposite of that angle, then the ratio of the length of the median to the length of the side opposite the angle bisected is equal to the ratio of the length of the other two medians.
Therefore, if the angle bisector divides the opposite side into segments 6 cm and 9 cm long, the ratio of the length of the median to the length of the side opposite the angle bisected is 6/9.
Let x be the length of the third side of the triangle.
The Angle Bisector Theorem states: (x/22.5) = (6/9)
Solving for x, we get: x = (22.5 * 6/9) = 15
So the length of the third side of the triangle is 15 cm.
This is the only possible length for the third side of the triangle because the Angle Bisector Theorem only holds if the angle bisector is also a median to the side opposite of that angle.
The table of values represents a quadratic function f(x).
x f(x)
−8 13
−7 6
−6 1
−5 −2
−4 −3
−3 −2
−2 1
−1 6
0 13
What is the equation of f(x)?
f(x) = (x + 5)2 − 2
f(x) = (x + 4)2 − 3
f(x) = (x − 4)2 − 3
f(x) = (x − 5)2 − 2
The correct equation of quadratic equation is,
⇒ f (x) = (x + 4)² - 3
We have to given that;
The table of values represents a quadratic function f(x).
And, Values are,
x f(x)
−8 13
−7 6
−6 1
−5 −2
−4 −3
−3 −2
−2 1
−1 6
0 13
Now, By given options;
f (x) = (x + 5)² - 2
Put x = - 8, f (x) = 13;
13 = (- 8 + 5)² - 2
13 = 9 - 2
13 ≠ 7
From (ii);
f (x) = (x + 4)² - 3
Put x = - 7, y = 6;
6 = (- 7 + 4)² - 3
6 = 9 - 3
6 = 6
Hence, The correct equation of quadratic equation is,
⇒ f (x) = (x + 4)² - 3
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Find the measure of < 6.
Answer:
Angle 6 = 70
Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.
After playing 5 games, you have 33 credits left. You play 4 more games and have 21 credits left. Write an equation that represents the number of credits y on the card after x games
Answer:
5x=33y,4x=21y I hope this is helpful
5. An engineer typically makes 50% more than a school teacher. What is the engineer's income as a percentage of the school teacher's income. How many times as large as the teacher's income is the engineer's?
Answer:
If an engineer typically makes 50% more than a school teacher, then the engineer's income is 150% of the school teacher's income. Because 100% represents the school teacher's income, and 50% represents the engineer's additional income, the sum is 100%+50% = 150%.
The engineer's income is also 1.5 times as large as the school teacher's income. This can be found by dividing the engineer's income percentage (150%) by the school teacher's income percentage (100%), which gives 150% / 100% = 1.5.
So the engineer's income is 150% of the school teacher's income, and it is 1.5 times as large as the school teacher's income.
- C
Serena added 10 grams of sugar to 20 grams of water.
She made
grams of
%
sugar syrup.
Serena added 10 grams of sugar to 20 grams of water to make a sugar syrup.
The total amount of sugar syrup made is the sum of the weight of sugar and the weight of water, so:
10 grams (sugar) + 20 grams (water) = 30 grams (sugar syrup)
To find the percentage of sugar in the syrup, we can divide the weight of the sugar by the total weight of the syrup and multiply by 100.
% sugar = (weight of sugar / total weight of syrup) * 100
% sugar = (10 / 30) * 100 = 33.333 %
So the sugar syrup made by Serena contains 33.333% sugar by weight.
It's important to note that the sugar syrup doesn't have only sugar, it also have water, the sugar is just the main ingredient and the percentage of sugar is just the proportion of sugar within the syrup.
The output voltage of an amplifier is calculated by multiplying the input voltage by the voltage gain of the amplifier. Calculate the output voltage, in millivolts (mV), for a circuit if the input voltage is 45 mV and the gain is 30.
The output voltage, in millivolts (mV), for the circuit would be equal to 1,350 millivolts.
What is an amplifier?An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.
The output voltage of an amplifier= input voltage × gains.
We have been given that input voltage = 45 mV
The gain = 30
Therefore, the output voltage= 45×30
= 1350millivolts.
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What is AE?
Enter you answer in the box.
Answer:It means almost everywhere
Step-by-step explanation:
The value of AE is, 10 units.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Here, From the given figure we can see that two triangle ABE and DEC are similar.
Therefore, The ratio of corresponding sides are equal.
Hence, From figure we get,
⇒ ED/AE = CD/AB
Substitute all the values, we get;
⇒ (x + 6)/(2x + 6) = 8/10
⇒ 10(x + 6) = 8(2x + 6)
⇒ 10x + 60 = 16x + 48
⇒ 16x - 10x = 60 - 48
⇒ 6x = 12
⇒ x = 2
So, The value of AE is,
AE = 2x + 6
AE = = (2 × 2 ) + 6
AE = 4 + 6
AE = 10
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Is 6 inches in 10 seconds proportional to 12 inches in 60 seconds?
Answer: No
Step-by-step explanation:
to be proportional, both numbers have to increase by the same number
because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in
When a number is decreased by 10% of itself, the result is 99. What is the number?
Answer:990
Step-by-step explanation:10%=0.1
X*0.1=99
99/0.1=990
x=990
PLEAE HELPP WILL MARK BRAINLIEST
Given that my=34°, find the value of the angle b
A 146°
B 56°
C 34°
D 124°
E 68°
Answer: D - 124°
Step-by-step explanation: Since y and a are vertical angles, we can determine that angle a is equal to 34°
90° + 34° = 124°
180° - 124° = 56°
Now we know the last angle in the triangle. Since this angle is on the same line as angle b, subtracting it from 180 would give us angle b
180° - 56° = 124°
Place value of the 4 in 2, 487, 492
HELPPPP ???
Select the correct statement about the system of equations.
the answer is letter d)
if u arrange it correctly it will be -x +2y=2
-½x+y=1
then multiply -½ by the first equation and multiply -1 by the second equation..
then change the signs of the second equation
then cancel x .. then y =1
then substitute y with 1
..it won't be correct
What Income tax should be on 400 naira at the rate of 2¹/2 kobo per Naira? A. 2 Naira B. 4 Naira C. 5 Naira D. 10 Naira E. 15 Naira
Step-by-step explanation:
A. Hawa Enterprise is a small retail business located in Changlun, Kedah. Follows are information on bank transactions of Hawa Enterprise as at 31 July 2022:
a. Cash on the book was RM34,635.
b. Cash as shown on the bank statement was RM35,296.
c. A deposit of RM3,500, representing cash receipts on 31 July, did not appear on the bank statement.
d. Outstanding cheque include cheques No 2031, No 2558, and No 2783 with the amount respectively RM530, RM1,551 and RM2,100.
e. The bank collected RM810 on a note receivable for Hawa Enterprise. The bank charged a collection fee of RM10 which was credited to Hawa Enterprise’s account.
f. An NSF cheque for RM950 from a customer, En Mansor, was returned with the bank statement.
g. The bank paid correctly an amount of RM3,680 for cheque No 2805 which was recorded in a book as RM3,860. h. Bank service charges for July 2022 amounted to RM50.
REQUIRED:
Prepare the bank reconciliation statement for Hawa Enterprise as at 31 July 2022.
B. Beginning July 2022, Hawa Enterprise has established a petty cash fund for its small expenditures. The following transactions took place during the month of July:
5/7 Established a RM300 petty cash fund with cash withdrawn from the company’s current account.
30/7 The petty cash fund has RM12 remaining and is replenished. Expenditures for July were RM75 for supplies, RM60 (meals), RM80 (postage), RM50 (amenities) and RM25 (freight-in).
REQUIRED:
Prepare the journal entries for the above transactions.
