This simplified form of given expression is: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.
Here,
Now, we can multiply this result by the original expression raised to the power of 3:
(4s⁵t⁻⁷/−2s⁻²t⁴)³ * (1/(-8s⁶t¹²)) = (4s⁵t⁻⁷)³ / (-8s⁶t¹²)
Finally, we'll simplify the numerator by raising 4s⁵t-7 to the power of 3:
(4s⁵t-7)³ = (4s⁵t)³ * (-7)³ = 64s¹⁵t³ * 343 = 21952s¹⁵t³
Putting it all together, we get the abbreviated version of the given expression: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹
To know more about expression,
https://brainly.com/question/30091997
#SPJ1
Each of the 23 students in Ms.Evan's class raised $45 for the school by selling coupon books. How much money did the class raise?
Please help me
Answer:
The class raised $45 x 23 = $1035.
Step-by-step explanation:
To find the total amount of money raised by the class:
Identify the amount raised by one student: $45.
Multiply the amount raised by one student by the number of students: $45 * 23.
The total amount raised by the class is $45 * 23 = $1035.
Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the
explicit formula, and the recursive formula.
Hence Sequences 4, 16, 36, 64,.. are not arithmetic, however 40, 30, 20, 10,... are, with a common difference of -10 and the 52nd term being -490.
what is arithmetic progression ?An arithmetic progression is defined as a constant discrepancy between terms that follow one another through a series. For instance, the number sequence 5, 7, 9, 11, 13, and 15 is an example of either an exponential manner with a limitation of two. A progression with a set tolerance between any consecutive numbers is referred to as a "arithmetic progression" (A.P.). Two types of mathematical progression are possible: series in mathematics with a finite length A finite geographic progression is a serie with a finite number of terms. The early, delayed, tolerance, and frequency of terms may all be calculated using the terms in the series.
given
First succession
4, 16, 36, 64,
The common difference must be the same for it to be considered AP.
It is not AP since 16 - 4 ≠ 36 - 16.
Second succession;
40, 30, 20, 10, ...
common distinction =30 - 40 = 20 - 30 = 10 - 20 = -10
As a result, it will be an AP because the common difference is -10 and the same.
Now, The nth phrase of AP equals a plus (n - 1) d, where d is a typical difference and an is the initial term.
So, 52nd term = 40 + (52 - 1) (-10), which is -490.
Hence Sequences 4, 16, 36, 64,.. are not arithmetic, however 40, 30, 20, 10,... are, with a common difference of -10 and the 52nd term being -490.
To know more about arithmetic progression visit:
https://brainly.com/question/16947807
#SPJ1
A survey of 1,029 tourists visiting Orlando was taken. Of those surveyed:
258 tourists had visited the Magic Kingdom
299 tourists had visited Universal Studios
100 tourists had visited both the Magic Kingdom and LEGOLAND
82 tourists had visited both the Magic Kingdom and Universal Studios
76 tourists had visited both LEGOLAND and Universal Studios
12 tourists had visited all three theme parks
68 tourists did not visit any of these theme parks
How many tourists only visited the LEGOLAND (of these three)?
44 tourists only visited LEGOLAND (of these three).
Solving for the tourists only visited the LEGOLAND only:Let's call the number of tourists who visited only LEGOLAND x.
From the information given, we know that:
258 tourists had visited the Magic Kingdom
299 tourists had visited Universal Studios
100 tourists had visited both the Magic Kingdom and LEGOLAND
82 tourists had visited both the Magic Kingdom and Universal Studios
76 tourists had visited both LEGOLAND and Universal Studios
12 tourists had visited all three theme parks
68 tourists did not visit any of these theme parks
We can calculate x as follows:
x = number of tourists who visited LEGOLAND only
number of tourists who visited LEGOLAND - number of tourists who visited LEGOLAND and Magic Kingdom - number of tourists who visited LEGOLAND and Universal Studios + number of tourists who visited all three parks
= 100 - 82 - 76 + 12
= 44
Hence, 44 tourists only visited LEGOLAND (of these three).
Learn more about Quantitative reasoning on
https://brainly.com/question/28715751
#SPJ1
1. Starting at the initial side, make 3.3 rotations counterclockwise.
a. What is the angle measure?
b.Name a positive angle and a negative angle that are both coterminal to the angle
c. In what quadrant is the terminal side of the angle?
d. What is the reference angle?
Answer:
(+7)[(-12)-(+8)]
Step-by-step explanation:
(+7)[(-12)-(+8)
Find the value of x.
Answer:
x=65°
Step-by-step explanation:
Solution Given:
let the point having angle 115° be e.
and point having side containing a and c be f.
we have
∡bec+115°= 180° being linear pair
∡bec=180°-115°=65°
again
∡bec= ∡afc=65° being corresponding angle
again
∡afc=x°=65° being corresponding angle
I need a answer with solution please help
Answer: b because i searched it up and thats what it is
simple and compound interest
pls tell me answer , asap
The value of interest after 3 years is £2,304.
What is simple interest?Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it is the kind of interest that banks give their customers on their savings accounts.
Given amount invested = principal = £9600
rate = 8% per year
time = 3 years
simple interest is,
SI = (Prt)/100
SI = (9600*8*3)100
SI = £2,304
Hence value after 3 years is £2,304.
Learn more about simple interest;
https://brainly.com/question/25845758
#SPJ1
Which of the following functions is most likely to have the smallest value for y if x is large? (Assume k is positive.) a. a direct variation function with a small value for k c. an inverse variation function with a small value for k b. a direct variation function with a large value for k d. an inverse variation function with a large value for k
An inverse variation function with a small value for k. Therefore, option C is the correct answer.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
The association between x and y can be classified in two ways, as follows:
Direct proportional: when the input x increases, the output y also increases.
Inverse proportional: when the input x increases, the output y decreases.
For this problem, we need an inverse proportional function, that has the following format:
y = k/x.
The lower the value of k, the lower the value of y when x goes to infinity.
Therefore, option C is the correct answer.
To learn more about the proportional relationship visit:
brainly.com/question/12917806.
#SPJ1
Land O' Lake's average annual household income in 2021
A) ~$62,000
B) ~$84,000
C) ~$96,000
D) ~$71,000
According to statistics, Land O' Lake's 2021 average annual household income was given at $84,146. Thus, the correct answer is Option B which indicates that the amount is approximately $84,000.
What is Average Annual Household Income?Average Annual Household Income is the average amount of money earned annually by a household, calculated by dividing the total household income by the number of households. It provides a measure of the economic well-being of a particular group or population.
Average Annual Household Income is useful because it provides a broad overview of the economic well-being of a population and can be used to compare the standard of living across different regions, demographic groups, and over time. It is an important indicator of the economy's health and the distribution of wealth.
Learn more about Average Annual Household Income:
https://brainly.com/question/17100688
#SPJ1
shape y is an enlargement of shape x by a scale factor of 4
work out lengths a and b
Answer:
ehhhh
Step-by-step explanation:
Elizabeth is thinking of a two-digit number. When the tens digit is subtracted from the ones digit, the difference is 2. One-fifth of the number is 1 less than the sun of the digits. What is the number?
The two digit number is 35.
What is equation modelling?Writing a mathematical statement in the form of a mathematical equation for the correct analysis, measurement and solutions.
Given is that Elizabeth is thinking of a two - digit number. When the tens digit is subtracted from the ones digit, the difference is 2. One-fifth of the number is 1 less than the sun of the digits.
Let the number be (xy).
We can write the two digit number as -
xy = 10x + y ... Eq { 1 }
Now, it is given that when the tens digit is subtracted from the ones digit, the difference is 2. We can write -
y - x = 2 ... Eq { 2 }
Also, one - fifth of the number is 1 less than the sun of the digits. We can write -
(1/5)(10x + y) = (x + y) - 1 ... Eq { 3 }
Now, from eq { 1 } and eq { 2 }, we have -
y - x = 2
y = x + 2
and
(1/5)(10x + y) = (x + y) - 1
(1/5)(10x + x + 2) = (x + x + 2) - 1
(1/5)(11x + 2) = 2x - 1
11x + 2 = 10x - 5
x = - 7
y = -5
So, the number would be -
xy = 35
Therefore, the two digit number is 35.
To solve more questions on equation modelling, visit the link below -
https://brainly.com/question/13202514
#SPJ1
Which of the values listed is a prime number?
A. 10
B. 15
C. 27
D. 29
Answer:
D. 29
Step-by-step explanation:
A. 10 = 2 × 5 not prime
B. 15 = 3 × 5 not prime
C. 27 = 3³ not prime
D. 29 = 1 × 29 prime
Answer:
29
Step-by-step explanation:
A prime number is a number that can't be divided by any number other than itself or 1.
10
1*10
2*5
5*2
10*1
NOT A PRIME NUMBER
15
1*15
3*5
5*3
15*1
NOT A PRIME NUMBER
27
1*27
3*9
9*3
27*1
NOT A PRIME NUMBER
29
1*29
29*1
PRIME NUMBER
Carry your intermediate computations
to at least four decimal places, and round your answer to at least one decimal place.
The mean of the histogram is 904.8
How to determine the mean of the histogramThe mean of the histogram is calculated as
Mean = Sum of the product of carrying load and frequency/Sum of frequency
Using the above as a guide, we have the following:
Mean = (870 * 5 + 890 * 7 + 910 * 8 + 930 * 4 + 950 * 3)/(5 + 7 + 8 + 4 + 3)
Evaluate
Mean = 904.8
Hence, the mean is 904.8
Read more about mean at
https://brainly.com/question/14532771
#SPJ1
cost price R600 profit R150 what is loss and selling price?
The loss is given as difference of cost price and selling price and the selling price is R750.
What is profit and loss?Mathematicians use the profit and loss formula to calculate market prices for goods and to assess how lucrative a company is. There is a selling price and a cost price for every goods. We can determine the profit made or loss suffered for a certain product based on the values of these prices. Cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc. are some of the key words that are addressed in this article.
Given that the cost price is R600, and the profit is R150.
The profit is given as:
P = SP - CP
150 = SP - 600
SP = 150 + 600
SP = 750
The loss is given as:
L = CP- SP
Hence, the loss is given as difference of cost price and selling price and the selling price is R750.
Learn about profit and loss here:
https://brainly.com/question/13934673
#SPJ1
Every day last week, Lily biked 7 miles and Charlotte biked 9 miles.
On one day, how many miles did Lily and Charlotte bike together?
• If they biked the same number of miles each day for 3 days, how many miles did they bike in all?
Both Lily and Charlotte biked 9 miles in a day. They biked 48 miles within the space of 3 days
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Every day last week, Lily biked 7 miles and Charlotte biked 9 miles.
The total distance both biked in a day = 7 miles + 9 miles = 16 miles
Both Lily and Charlotte biked 9 miles in a day
They biked the same number of miles each day for 3 days, hence:
Total distance biked = 16 miles per day * 3 days = 48 miles
They biked 48 miles within the space of 3 days
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
This picture is what i need help with
Answer: [tex]80\%[/tex]
Step-by-step explanation:
[tex]\frac{90-50}{50} \times 100=80\%[/tex]
5. Health and Fitness Tyler does squats and pushups. He wants to increase the number of each type of exercise by 20% by the end of the month. He currently does 25 pushups. If Tyler meets his goal, he will do a total of 13 more squats and pushups than he does now. Write an equation to find how many squats Tyler does now?
If Health and Fitness Tyler does squats and pushups. He wants to increase the number of each type of exercise by 20% by the end of the month. The equation is 0.2(x+25)=13 and the number of squats is 40.
How to find the number of squats?Let x represent the number of squats Tyler currently have
Given the equation:
0.2(x + 25) = 13
Expanding the parentheses on the left side:
0.2x + 5 = 13
Subtracting 5 from both sides:
0.2x = 8.
Dividing both sides by 0.2 to isolate x:
x = 8/0.2
x = 40
Therefore Tyler currently does 40 squats.
Learn more about number of squats here: https://brainly.com/question/14155010
Please help!!
Thankyou!!
The scale factor is: 1.8
because of :
[tex]\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8[/tex]
The value of log 3 5 × log 25 9 is
The value of [tex]log_35 \times log_{25}9[/tex] is 1.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]log_35 \times log_{25}9[/tex]
[tex]log_ab = \frac{logb}{loga}[/tex]
So,
= log 5 / log 3 x log 9 / log 25
= log 5 / log 3 x log 3² / log 5²
[tex]logm^n = n~logm[/tex]
So,
= log 5 / log 3 x log 3² / log 5²
= (log 5 / log 3) x (2 log 3 / 2 log 5)
= (log 5 / log 3) x (log 3 / log 5)
= 1
Thus,
1 is the value.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
To isolate the variable on one side of the equal sign, divide both sides of the equation by .
To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.
Gabriella went to Tiers of Joy Bakery to buy her mom’s birthday cake. The cake was $25.52, which left Gabriella with $24.48 to spend on her mom’s present. Let a be the amount of money Gabriella had before buying the cake. Write and solve an equation to find a.
Answer: $50
Step-by-step explanation:
Let's denote the amount of money Gabriella had before buying the cake as "a". Then we can write an equation to find "a":
a - $25.52 = $24.48
Adding $25.52 to both sides:
a = $25.52 + $24.48
So,
a = $50
Therefore, Gabriella had $50 before buying the cake.
What is the slope of the linear relationship? a graph of a line that passes through the points 0 comma 3 and 2 comma negative 2 negative five halves five halves negative two fifths two fifths
The slope of the linear relationship is equal to: A. negative five halves.
How to calculate the slope of a line?In Mathematics, the slope of a linear relationship can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following slope and data points on the line:
Points on x-axis = (0, 2).Points on y-axis = (3, -2).Substituting the given data points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-2 - 3)/(2 - 0)
Slope, m = -5/2
Note: -5/2 is negative five halves.
Read more on slope here: brainly.com/question/3493733
#SPJ1
Answer: The Answer is A. -5/2
Step-by-step explanation: I took the test.
A model is made of a car. The car is
feet long and the model is
inches long. What is the ratio of the length of the car to the length of the model?
A
131313: 101010
B
101010: 156156156
C
156156156: 101010
D
101010: 131313
The car is 7 feet long and the model is 16 inches long, the ratio of the length of the car to the length of the model is, 21:4 So Option D is correct
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
The car is 7 feet long
The model is 16 inches long
The ratio of the length of the car to the length of the model = ?
It is known that,
1 feet = 12 inches
Now, converting length of car into inches
⇒ 7 feet = 7×12 inches = 84 inches
So, Ratio of lengths
⇒ 84/16
⇒ 21/4
Hence, the ratio is 21:4
To know more about Ratio check:
https://brainly.com/question/13419413
#SPJ1
Complete question:
A model is made of a car. The car is 7 feet long, and the model is 16 inches long. What is the ratio of the length of the car to the length of the model?
a) 4:21
b) 7:16
c) 16:7
d) 21:4
The amount of liquid in three containers is shown below
Order the liquid measurements from least to greatest.
how your work.
The equivalent of a gallon (gal) is 16 cups, 8 pints, or 4 quarts. The biggest liquid measurement is this one.
What liquid has the largest measurement?The equivalent of a gallon (gal) is 16 cups, 8 pints, or 4 quarts. The biggest liquid measurement is this one.There are various units of measurement that can make your recipes easier to follow, especially when measuring in greater quantities. We typically refer to volume in terms of teaspoons, tablespoons, cups, millilitres, and fluid ounces.A millilitre, which is one thousandth of a litre, is the smallest metric unit for measuring the smallest amount of liquid. Thus, we may state that 1 litre equals 1000 millilitres.The most precise tools for measuring small volumes of liquid are volumetric flasks, burettes, and pipettes, which have tolerances of less than 0.02.The complete question is
What is the biggest measurement of liquid?
To learn more about liquid measurements refer to:
https://brainly.com/question/7744911
#SPJ1
Lydia has money in two savings accounts. One rate is 12% and the other is 13%. If she has $850 more in the 13% account and the total interest is $388, how much is invested in each savings account?
Lydia invested an amount of $1110 in the 12% savings account and $1960 in the 13% savings account.
Let's assume the amount invested in the 12% savings account "x". Then, the amount invested in the 13% savings account would be "x + 850".
The total interest earned is $388, so we can write the following two equations to represent the interest earned in each account:
0.12x + 0.13(x + 850) = 388
Expanding the second equation, we get:
0.12x + 0.13x + 110.5 = 388
Combining like terms and simplifying, we get:
0.25x = 277.5
Dividing both sides by 0.25, we get:
x = 1110
So, she invested $1106 in the 12% savings account and $1110 + 850 = $1960 in the 13% savings account.
Learn more about the simple interest here:
brainly.com/question/22621039
#SPJ1
You purchase 200 shares for $70 a share ($14,000), and after a year the price falls to $80. Calculate the percentage return on your investment if you bought the stock on margin and the margin requirement was (ignore commissions, dividends, and interest expense): 20 percent
Answer: First, calculate the total value of the shares after the price fall to $80:
value = 200 shares * $80/share = $16,000
Then, calculate the amount of money borrowed:
borrowed = $14,000 / (1 - margin requirement)
= $14,000 / (1 - 0.20)
= $14,000 / 0.80
= $17,500
Finally, calculate the percentage return on investment:
return = (value - borrowed) / borrowed * 100%
= ($16,000 - $17,500) / $17,500 * 100%
= -6.06%
The return on investment is -6.06%, meaning that the investment lost 6.06% of its value.
Step-by-step explanation:
The blueprint for a circular gazebo has a scale of 2 inches=5 feet. The blueprint shows that the gazebo has a diameter of 5.1 inches. What is the actual diameter of the gazebo? What is its area? Use 3.14 for π.
The actual diameter of the gazebo is 12.75 feet and has an area of
127.6 square inches.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The blueprint for a circular gazebo has a scale of 2 inches = 5 feet.
So, The scale factor is (5/2) = 2.5 or 1 inch = 2.5 feet.
Also given, The gazebo has a diameter of 5.1 inches.
Therefore, The actual diameter of the gazebo is = 5.1×2.5 = 12.75 feet.
The area of the gazebo is π(12.75/2)² = 127.6 square inches.
learn more about scale factors here :
https://brainly.com/question/30215119
#SPJ1
Find the total surface area of this cuboid. 6 cm 5 cm 4 cm
Answer:
solution
given,
length =6cm
breadth =5cm
height =4cm
Now,
area of cuboid =l×b×h
=6cm ×5cm×4cm
=120cm^3
Hence, the total surface area of the given figure of cuboid is 120cm^3
Step-by-step explanation:
given above
How can you rewrite -8
−
− 10 as an addition problem
Answer:
When using inverse operations with negative numbers, when you change subtraction to addition, the negative turns to a positive.
-8 - -10 can be changed to:
8 + 10
8 + 10 = 18
Step-by-step explanation:
Hope it helps! =D
Sorry took so log to answer. My internet is being slow some reason. -_-
A catapult launches a pumpkin from the base of a hill. The
hill follows an incline with the height in meters, y, in terms
of horizontal distance in meters, x, given by the equation
y=0.9x. The height of the pumpkin, as it is launched up-
hill, is given by the function y = -0.1x² +4.9x¸
What is the height, in meters, where the pumpkin lands on
the hill?
The height where the pumpkin lands on the hill is given as follows:
36 meters.
How to obtain the height where the pumpkin lands on the hill?The equation for the pumpkin's height is given as follows:
y = -0.1x² + 4.9x.
The equation for the hill's height is given as follows:
y = 0.9x.
Hence the pumpkin will land on the hill at a time of:
-0.1x² + 4.9x = 0.9x.
Hence:
0.1x² - 4x = 0.
x(0.1x - 4) = 0.
0.1x - 4 = 0
x = 40.
The height is then given as follows:
y = 0.9(40)
y = 36 meters.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1