Answer:
0.96
Step-by-step explanation:
Bella owns a small business selling ice-cream. She knows that in the last week 50 customers paid cash, 2 customers used a debit card, and 4 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.
50 cash, 2 debit card, and 4 credit card.
50+2+4= 56
There were a total of 56 customers. 50+4=54 customers paid with cash or a credit card.
Probability the next customer will pay with cash or a credit card:
54
56
= 0.964285...
≈ 0.96
Round to the nearest hundredth
The probability as a decimal to the nearest hundredth is
0.96
Simplify and answer fast please
The value of the expression 6 3/4 - 2 3/20 is -91/12.
How to convert improper fraction to mixed fraction?An improper fraction is a fraction that cannot be further simplified and has a numerator higher than or equal to the denominator. For instance, 13/5 is a bad fraction. Let's find the mixed fraction equivalent of this incorrect fraction.
Divide the denominator by the numerator in step 1. Step 2: Track down the rest. In step 3, arrange the numbers as follows: quotient, followed by a portion of the remainder or divisor.
The given expression are:
6 3/4 - 2 3/20
Convert the mixed fraction into improper fraction:
27/4 - 43/3
Take the LCM of the two:
81/12 - 172/12
-91/12
Hence, the value of the expression 6 3/4 - 2 3/20 is -91/12.
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What are the answrrs
For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.
Purple 1 is thus a redder hue of purple than Purple 2.
Purple 2 is a more blue-based purple than Purple 1.
What is the ratio?The utilization of two or more additional numbers that compares is known as the ratio.
The ratio of red to blue in purple 1 and purple 2 will be 1:2 and 1:3, respectively. The table is given below.
Purple #1 Purple #2
Red: Blue Red: Blue
1 2 1 3
2 4 2 6
3 6 3 9
For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.
Purple 1 is thus a redder hue of purple than Purple 2.
Purple 2 is a more blue-based purple than Purple 1.
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you need a plan. you know this radius using the formula formula for circumference. but you do not know the circumference. you know that 75% of the circumference is 6 in. next use the formula for the circumference of a circle to determine the radius. whT is the radius of the frame? round your awnser to the nearest tenth
The radius of the frame is approximately 1.27 inches
How to find the radius of the frame?
First, we can start by using the formula for the circumference of a circle:
C = 2πr
Where
C is the circumference and r is the radius.We know that 75% of the circumference is 6 inches, so we can set up the following equation:
0.75C = 6
Simplifying this equation by dividing both sides by 0.75, we get:
C = 8
Now we can use this value of the circumference and the formula for the circumference to solve for the radius:
C = 2πr
8 = 2πr
Dividing both sides by 2π, we get:
r = 8/(2π)
Using a calculator, we can evaluate this expression to get:
r ≈ 1.27
Therefore, the radius of the frame is approximately 1.27 inches.
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Find the future value (in dollars) of a 2-year investment of $6,525 into a simple interest rate account that has an annual simple interest rate of 3.7%.
$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The formula to calculate the future value of an investment with simple interest is:
FV = P(1 + rt)
where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.
P = $6,525
r = 0.037
t = 2 years
Plugging these values into the formula, we get:
FV = $6,525(1 + 0.037×2)
FV = $6,525(1.074)
FV = $7,008.
Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.
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fx=x square -4 find codomain
So, the codomain of the function is the set of all real numbers: codomain = R.
What is function?In mathematics, a function is a rule that maps a set of inputs (domain) to a set of outputs (codomain) in such a way that each input is associated with exactly one output. A function can be represented using various notations, including equations, graphs, and tables. A function can be thought of as a machine that takes an input and produces an output. The input is usually represented by the variable x, and the output is represented by the variable y. The relationship between the input and output is defined by the function rule. Functions are used in many areas of mathematics, science, and engineering to describe various phenomena, such as motion, growth, and decay. They are also used to model and analyze data in statistics and economics, and to design and control systems in engineering and computer science.
Here,
The codomain is the set of all possible output values of a function.
For the given function, f(x) = x² - 4, we can see that the output values are obtained by squaring the input value, subtracting 4, and therefore can be any real number.
To find the codomain of the function f(x) = x² - 4, we need to determine the range of the function, which is the set of all possible output values.
Let y = f(x) = x² - 4.
To find the range, we need to solve for y:
y = x² - 4
y + 4 = x²
Taking the square root of both sides, we get:
x = ±√(y + 4)
Therefore, the range of the function is the set of all real numbers greater than or equal to -4, since y + 4 must be non-negative for real values of y:
range = {y | y + 4 ≥ 0} = {y | y ≥ -4}
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a) If the slant range of the plane in the image is 14.5 km, and the ground range is 10.15 km, find the altitude of the plane to the nearest meter. Show your work and explain your thinking.
b) If this plane loses power and descends suddenly at a rate of 750 meters per minute, how much time will the pilot have before he has to land?
a) The altitude of the plane is approximately 8.4 kilometers.
b) The pilot has approximately 11.2 minutes before he has to land.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the lengths of the other two sides (the legs).
In mathematical terms, if we have a right triangle with legs a and b and hypotenuse c, the Pythagorean theorem can be written as:
[tex]a^2 + b^2 = c^2[/tex]
This theorem is named after the ancient Greek mathematician Pythagoras, who was the first to prove it. The Pythagorean theorem has numerous applications in geometry, trigonometry, physics, and engineering, among other fields.
The Pythagorean theorem can also be used to determine whether a triangle is a right triangle or not. If the lengths of the three sides of a triangle satisfy the equation [tex]a^2 + b^2 = c^2,[/tex] then the triangle is a right triangle with sides a and b and hypotenuse c.
a) In the given image, we can see that the slant range, ground range, and altitude form a right triangle. We can use the Pythagorean theorem to find the altitude of the plane.
Pythagorean theorem: In a right triangle, the square of the hypotenuse (slant range in this case) is equal to the sum of the squares of the other two sides (ground range and altitude in this case).
Therefore, we can write:
[tex]Slant range^2 = Ground range^2 + Altitude^2[/tex]
Substituting the given values, we get:
[tex]14.5^2 = 10.15^2 + Altitude^2[/tex]
Simplifying and solving for altitude, we get:
Altitude ≈ 8.4 km (rounded to the nearest meter)
Therefore, the altitude of the plane is approximately 8.4 kilometers.
b) If the plane descends suddenly at a rate of 750 meters per minute, we can use the altitude of the plane (calculated in part a)) to find the time the pilot has before landing.
Time = Altitude/Descent rate
Substituting the values, we get:
Time = [tex]\frac{8.4 }{0.75}[/tex] ≈ 11.2 minutes
Therefore, the pilot has approximately 11.2 minutes before he has to land.
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you heard that the Math munch cafre runs a cookie special one a month. For $1.50 you can get 6 cookies at this rate how many cookies could you get for $1.00
In linear equation, you can get 4 cookies for $1.00 at the Math munch cafe.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
If you can get 6 cookies for $1.50, then the cost of each cookie is:
$1.50 ÷ 6 = $0.25
This means that for $1.00, you can get:
$1.00 ÷ $0.25 per cookie = 4 cookies
Therefore, you can get 4 cookies for $1.00 at the Math munch cafe.
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Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.
The answer of the given question based on to determine that the quadrilateral must be a parallelogram the answer is given below.
What is Parallelogram?A parallelogram is type of quadrilateral ( polygon with four sides) with two pairs of parallel sides. This means that the opposite sides of parallelogram are parallel and congruent.
Yes, we can determine that the given quadrilateral is a parallelogram based on the information given.
We are told that opposite sides of the quadrilateral are congruent (that is, AB is congruent to CD, and BC is congruent to DA), which is a property of parallelograms. We are also told that opposite angles of the quadrilateral are congruent (that is, angle A is congruent to angle C, and angle B is congruent to angle D), which is another property of parallelograms.
Therefore, based on these two pieces of information, we can conclude that the quadrilateral must be a parallelogram. This is because these properties are unique to parallelograms and do not apply to other types of quadrilaterals, such as rectangles, rhombuses, or trapezoids.
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Find Growth/Decay Percentage for y=990(1.922)
The growth percentage for the given function is 92.2%.
What is the percentage?
A number can be represented as a fraction of 100 using a percentage. "%" is used to represent it.
For instance, when we state that 20% of a class is made up of guys, we mean that 20 of the class's 100 pupils are male. In other words, there are 20 out of 100 boys in the class, or 0.2.
We can multiply by 100 to change a fraction or decimal into a percentage. For instance, we can multiply the fraction 3/5 by 100 to achieve the following percentage conversion:
3/5 × 100% = 60%
Now,
The given function is [tex]y = 990^{(1.922)}[/tex]
We can compare this to the standard form of an exponential function y = abˣ, where "a" represents the initial value or starting point, "b" represents the growth or decay factor, and "x" represents the time or number of periods.
In this case, we have:
a = 990 (the initial value)
b = 1.922 (the growth factor)
To find the growth percentage, we can subtract the initial value from the final value and divide by the initial value:
(1.922 - 1) / 1 × 100% = 92.2%
Therefore, the growth percentage for the given function is 92.2%.
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2. Themba decides to draw a bar graph. Use graph 2 below to answer the questions that follow: 25 20 No. 15 of Customers 10 5 0 Graph 2: Favourite Sandwiches Ham Favourite Sandwiches Cheese Egg Chicken Polony Sandwich Choice
The probability both will be peanut butter sandwiches will be 1/6.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true.
here, we have,
The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
The probability that John picks a peanut butter sandwich from the first bag is 6/12 = 1/2.
The probability that John picks a peanut butter sandwich from the second bag is 4/12 = 1/3.
The probability that John picks a peanut butter sandwich from both bags is (1/2) * (1/3) = 1/6.
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6.)Walmart is running a sale on baseball hats. Sergio bought one on sale for 25% off its regular price of $45. If sales tax is 10.25%, what is the total cost of the hat?
Answer: 37.21 dollars
Step-by-step explanation: 25% of 45 is 11.25 so after the sale it is 33.75 then you multiply by .1025 which gives you 3.46 rounded then add it
33.75+3.46= 37.21
simplify (2)/(3)(3x-1)+4x+3^(2)-10x+5
find the value of each variable using sine and cosine.
Answer:
p ≈ 11.3 , q ≈ 4.1
Step-by-step explanation:
using the cosine ratio in the right triangle
cos20° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{p}{12}[/tex] ( multiply both sides by 12 )
12 × cos20° = p , then
p ≈ 11.3 ( to 1 decimal place )
using the sine ratio in the right triangle
sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{12}[/tex] ( multiply both sides by 12 )
12 × sin20° = q , then
q ≈ 4.1 ( to 1 decimal place )
Suppose that you put 2 dimes, 2 nickels, and 1 penny into a bag. a coin will be drawn from the bag and replaced 175 times. what is a reasonable prediction for the number of times a dime will be drawn?
A reasonable prediction for the number of times a dime will be drawn is approximately 90.
What is probability?Probability is the measure of how likely it is that an event will happen. The event is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. Probability is used in many areas, such as mathematics, science, engineering, and finance. For example, in mathematics, probability is used to determine the likelihood of an event occurring or a certain outcome occurring.
When 2 dimes, 2 nickels, and 1 penny are placed into a bag, there are 5 total coins. Therefore, the probability of drawing a dime is 2/5. When a coin is drawn and replaced 175 times, the probability of drawing a dime will remain the same (2/5) and the expected value of drawing a dime is 175*2/5 = 90. Since this is a reasonable prediction, it is a valid solution.
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3. Sergio's savings account statement showed a previous balance of $234.95 and interest of $1.06. The statement also showed deposits of $123.42 and $50.66 and withdrawals of $323.09. What is his new balance?
Sergio's new balance is $87
How to calculate the new balance?Sergio's savings showed a previous balance of $234.95 and interest of $1.06
The statement also showed deposits of $123.42 and $50.66 and withdrawals of $323.09
The new balance can be calculated by adding the previous balance, interest, deposits in the statement and then subtract the sum total from the withdrawal amount
234.95 + 1.06 + 123.42 + 50.66 - 323.09
= 410.09 - 323.09
= 87
Hence Sergio's new balance after adding the deposits, previous balance then subtracting from the withdrawal is $87
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You want to have $800,000 when you retire in 25 years. If you can earn 5% interest compounded monthly, how much would you need to deposit now into the account to reach your retirement goal?
Answer:
We can use the formula for the future value of an annuity to solve this problem. An annuity is a series of equal payments made at regular intervals. In this case, we are making a single lump-sum deposit now to grow into the desired future value.
The formula for the future value of a lump-sum deposit is:
FV = PV x (1 + r/n)^(n*t)
Where:
FV = future value
PV = present value (the amount to be deposited now)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, we want to find the present value (PV) required to grow into the future value (FV) of $800,000 in 25 years with an annual interest rate of 5% compounded monthly, so:
FV = $800,000
r = 5% = 0.05 (annual interest rate)
n = 12 (monthly compounding)
t = 25 (number of years)
Substituting these values into the formula, we get:
$800,000 = PV x (1 + 0.05/12)^(12*25)
Simplifying the exponent on the right-hand side, we get:
$800,000 = PV x (1.004167)^300
Dividing both sides by (1.004167)^300, we get:
PV = $800,000 / (1.004167)^300
Using a calculator or spreadsheet, we can evaluate this expression to find:
PV ≈ $267,227.92
Therefore, you would need to deposit approximately $267,227.92 now into the account to reach your retirement goal of $800,000 in 25 years with an annual interest rate of 5% compounded monthly.
A survey was conducted of 1000 household in Texas 670 household responded that the household included an Aggie fan while 450 household responded that the household included a Longhorns and 90 household responded that the household and I include an Aggie or a longhorn fan using the given information construct the corresponding Venn diagram to include the number of household surveyed and each mutually exclusive region
The circle in the middle represents the number of households with an Aggie or a Longhorn fan and it is 90.
What is household?Household refers to a single dwelling unit occupied by a family or other group of people who share common living arrangements. This includes a home, apartment, condominium, or other dwelling. Households can be single-family, multi-family, or even a group of unrelated people. They are typically headed by one or more adults, and may include children, elderly family members, and other dependents.
The total number of households surveyed is 1000 and is represented by the circle outside the two others. The circle on the left represents the number of households with an Aggie fan and it is 670. The circle on the right represents the number of households with a Longhorn fan and it is 450. The circle in the middle represents the number of households with an Aggie or a Longhorn fan and it is 90.
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Find the probability that the sum is as stated when a pair of dice is rolled. Odd or doubles
There is approximately a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
There are 3 odd numbers among the possible outcomes of each die (1, 3, 5), so there are 3 x 3 = 9 ways to obtain an odd sum:
(1,2), (1,4), (1,6), .... (6,1), (6,3), (6,5)
There are 6 possible outcomes for rolling the same number on both dice, so there are 6 ways to obtain doubles:
(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
We counted (1,1), (3,3), and (5,5) twice in the above two categories, so we need to subtract 2 from the total count.
Therefore, there are 9 + 6 - 2 = 13 ways to obtain an odd sum or doubles.
Therefore, the probability of rolling an odd sum or doubles is:
P(odd sum or doubles) = 13/36
Thus, there is about a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.
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bill is in the process of installing an above ground swimming pool in his yard. if the diameter of the pool is 35 feet what is the approximate circumference of the pool\
PLEASE HELP, WILL GIVE BRAINLIEST!!!!
see image bellow
Answer:
onomatopoeia
Step-by-step explanation:
onomatopoeia are words that are sounds
Answer:
Onomatopoeia
Step-by-step explanation:
The guitar Francisca wants is on sale at two different stores. The original price of the guitar at both stores is $160. At which store is the guitar less expensive? How much less expensive?
Answer:
The guitar Francisca wants is on sale at two different stores. The original price of the guitar at both stores is $160. At which store is the guitar less expensive? How much less expensive?
Find the slope of the line shown below?
The slope of the line passing through (- 1, 3) and (1, - 2) is - 5/2.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the steeper its graph or the rate of change is large.
From the given line we can identify two coordinate points,
(- 1, 3) and (1, - 2).
Now, We know slope(m) = (y₂ - y₁)/(x₂ - x₁).
slope(m) = (- 2 - 3)/(1 + 1).
slope(m) = - 5/2.
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Question 3
Joanne's Printing Services charges $49.95 to print 200 business cards. Each additional set of
100 cards costs $14. This is represented in the piecewise function below, where x is 1 set of
100 cards:
r(x) =
5 pts
29.95
when x is an integer and x < 2
29.95 + 14(x - 2) when x is an integer and x > 2
Determine the cost of 6 sets of cards.
The cost of 6 sets of cards is $105.95
How to get the cost of 6 sets of cards?Each set has 100 cards, then in 6 sets there are 6*100 = 600 cards.
We know that the first 200 cards costs $49.95, and from then, the cost per set is $14.
So we have a piecewise function which can be written as:
y = $49.95 if x ≤ 200
y = $49.95 + $14*(x - 200) if x > 200.
Then we have 200 cards and 4 sets, then the total cost will be:
$49.95 + 4*$14 = $105.95
That is the cost of the 6 sets.
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30. When the polynomial f(x) = (p-1)x³ + px² + qx +r, where p, q and r are constants, is divided by (x + 2) and (x - 1), the remainders are - 5 and 4 respectively. If (x + 1) is a factor of f(x), find the values of p, q and r. Hence, factorize f(x) completely.
Answer:
Step-by-step explanation:
Using the remainder theorem we get:
[tex]f(-2)=-5[/tex], [tex]f(1)=4[/tex], and [tex]f(-1)=0[/tex]
So we get
[tex]f(-2)=(-8)(p-1)+4p-2q+r=-5[/tex]
[tex]-8p+8+4p-2q+r=-5[/tex]
[tex]-4p-2q+r=-13[/tex] [tex](a)[/tex]
[tex]f(1)=(p-1)+p+q+r=4[/tex]
[tex]2p+q+r=5[/tex] [tex](b)[/tex]
[tex]f(-1)=-(p-1)+p-q+r=0[/tex]
[tex]-q+r=-1[/tex] [tex](c)[/tex]
We need to solve (a), (b) and (c) simultaneously to find p,q, and r.
from [tex](c)[/tex] [tex]r=q-1[/tex]. Sub this into (a) and (b):
[tex]-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12[/tex] [tex](d)[/tex]
[tex]2p+q+(q-1)=5 \rightarrow q=3-p[/tex] [tex](e)[/tex]
Sub (e) into (d) we get
[tex]-4p-(3-p)=-12 \rightarrow p=3[/tex]
Sub [tex]p=3[/tex] into [tex](e) \rightarrow q=0[/tex]
Sub [tex]p=3,q=0[/tex] into [tex](c) \rightarrow r=-1[/tex]
SOLUTION: [tex]p=3,q=0,r=-1[/tex]
So [tex]f(x)=2x^3+3x^2-1[/tex]
by dividing (x+1) into f(x) we get (I am not showing working for this division)
[tex]f(x)=(x+1)(2x^2+x-1)[/tex]
[tex]\rightarrow f(x)=(x+1)(2x-1)(x+1)[/tex]
In triangle LMN, m = 4.1 inches, I = 3.9 inches and to the nearest 10th of a degree.
The possible value of angle M is 30.6°.
What is Law of Sines?Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.
That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Given is a triangle LMN.
Given, m = 4.1 inches, I = 3.9 inches
∠L = 151°. We have to find ∠M.
Using law of sines,
l / sin L = m / sin M
3.9 / sin (151°) = 4.1 / sin (M)
sin (M) = [4.1 × sin (151°)] / 3.9
= 0.5097
M = sin⁻¹ (0.5097) = 30.64° ≈ 30.6°
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The question is incomplete. The complete question is,
In triangle LMN, m = 4.1 inches, I = 3.9 inches and ∠L = 151°. Find all possible values of ∠M to the nearest 10th of a degree.
The beach is 141 miles away. Your gas tank hold 18 gallons, and you use 3/8 of a tank to get to the beach.
a) What is your mpg (Miles per gallon)?
b) If gas costs $3.15 per gallon, how much did you spend to get to the beach?
*NEED ANSWERS NOW* FOR 28 POINTS im in 8th grade
You therefore paid $21.26 to travel to the beach.
How is a mile calculated?One mile is 5,280 feet long. To determine how many steps this should require walking a mile, simply split 5,280 feet by the length of your typical stride. For instance, if your typical stride is 2 feet, walking a mile will need 2,640 steps.
a) We must divide the total amount of miles travelled by the quantity of gas consumed in order to compute mpg (miles per gallon). If 141 miles are covered by 3/8 of a tank, we may calculate the tank's total capacity as follows:
18 gallons = 8/8 tank (full tank)
So, 3/8 tank = (3/8) x 18 = 6.75 gallons
Therefore, the mpg is:
mpg = distance traveled ÷ gas used
mpg = 141 miles ÷ 6.75 gallons
mpg = 20.89 miles per gallon (rounded to two decimal places)
b) The entire amount of gas consumed must be multiplied by the gallon price in order to get the cost of gas. Gas is expensive at:
Cost of gas = gas used x price per gallon
Cost of gas = 6.75 gallons x $3.15/gallon
Cost of gas = $21.26
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On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 12. The scores were normally distributed. Complete the following statements.
(a) Approximately 68% of the students scored between blank and blank
.
This is happening because the standard deviation of the scores is 12.
What is standard deviations?Standard deviation is a measure of how spread out a set of data is. It is a measure of how far each data point is from the mean of the data set. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Standard deviation is an important concept in statistics and is used to measure the variability of a data set. It is used to assess the risk associated with investments, as well as to determine the accuracy of an estimate.
(a) Approximately 68% of the students scored between blank and blank.
39 and 63
(b) Approximately 95% of the students scored between blank and blank.
27 and 75
This is happening because the standard deviation of the scores is 12. When the scores are normally distributed, roughly 68% of them will fall within 1 standard deviation of the mean, which is between 39 and 63. Similarly, 95% of the scores will fall within 2 standard deviations of the mean, which is between 27 and 75.
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Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds. (For example, they should do their first squat 30 seconds into the drill.) How many times during the 200 second drill should the little monsters do an overhead press and a squat at the same instant?
The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilising operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds.
The prime factorization of 12 is 2² x 3, and the prime factorization of 30 is 2 x 3 x 5.
To find the smallest common multiple, we need to take the highest power of each prime factor that appears in either factorization. Thus, the smallest common multiple of 12 and 30 are:
2² x 3 x 5 = 60
This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.
To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:
200 ÷ 60 = 3 remainder 20
This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.
Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.
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Percent Change
if I used $332.03 from $1 000 what percentage is that
So, by resolving the given, we obtain the : As a result, subtracting As a percentage result, subtracting $332.03 from $1,000 results in a loss of 66.797%.$332.03 from $1,000 results in a loss of 66.797%.
What is percentage?A ratio or value stated as a percentage of 100 is referred to as a percentage in mathematics. The abbreviations "pct.," "pct," and "pc" are also sporadically used. Nonetheless, the percentage symbol "%" is frequently used to denote it. The percentage amount is dimensionally empty. When the denominator is 100, percentages are essentially fractions. To show that a number is a percentage, a percent symbol (%) should be used next to it. For instance, you receive a 75% grade if you correctly answer 75 out of 25 questions (75/100) on a test. For percentage calculations, multiply the outcome by 100 after dividing the amount by the total. The percentage is calculated by multiplying (value/total) by 100%.
You may use the following calculation to get the percentage change between $1,000 and $332.03:
(|new value - old value| / old value|) x 100% represents the percentage change.
In this instance, the new value is $332.03 while the previous value was $1,000.
percentage change = (|332.03 - 1000| / 1000| x 100% = f 66.797%.
As a result, subtracting $332.03 from $1,000 results in a loss of 66.797%.
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A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 90 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 20 cm deep?
The speed at which the water level is rising when the water is 20 cm deep is 0.04285 m/min
How to solve thisUsing differentiation:
dV/dt = 0.3
find dh/dt
the width of the water level is dependent on the height
at height 0, width of 20
height 60, width of 80
when height increases by 1, width increases by 1
dh/dt = dw/dt
V = 0.5*(0.2 + (0.2+h))*h*10
V = 5*(0.4 + h)*h
V = 5h^2 + 2h
dV/dt = 5*2h(dh/dt) + 2(dh/dt)
when h = 0.5
0.1 = 5*2*0.5*(dh/dt) + 2(dh/dt)
0.1 = 5(dh/dt) + 2(dh/dt)
7(dh/dt) = 0.3
dh/dt = 0.04285 m/min
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