A caterpillar eats 75 leaves in 5 hours. How many leaves will the caterpillar eat in 8 hours if it continues to eat at the same rate?
Georgle is three times older than Maddle. If Georgle is 39 years old, which equation can be used to find m, Maddie's
age?
Examine this set of Pythagorean triples. Look for a pattern that is true for each triple regarding the difference between the three values that make up the triple.
Describe this pattern. Then see if you can think of another Pythagorean triple that doesn’t follow the pattern you just described and that can’t be generated using the identity . Explain your findings.
x-value Pythagorean Triple
3
4
5
6
The pattern is that two larger numbers differ by 2 and the smaller is the root of twice the sum of the larger two.
How to explain the pattern?The given formula gives rise to the above observations. it tells you
a = 2x
b = x^2 -1
c = x^2 +1
This is a special case of Euclid's formula ...
a = 2mn
b = m^2 -n^2
c = m^2 +n^2
for n=1.
Since m and n can be any integer values, there are certainly many other. Pythagorean triples that do not match the formula given in the problem. Using n=2, for example, the triples are:
a = 4x
b = x^2 -4
c = x^2 +4
Some triples from this set of formulas are (5, 12, 13), (20, 21, 29), (28, 45, 53), (36, 77, 85).
It should bm be noted that triples from this set of formulas will not match directly those from the formulas in the problem statement, but triples from both lists may reduce to the same primitive triple.
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Complete question
Examine this set of Pythagorean triples from part C. Look for a pattern that is true for each triple regarding the difference between the three values that make up the triple.
Describe this pattern. Then see if you can think of another Pythagorean triple that doesn’t follow the pattern you just described and that can’t be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings.
x-value Pythagorean Triple
3 (6,8,10)
4 (8,15,17)
5 (10,24,26)
6 (12,35,37)
1. Amy is practicing target shooting at a special facility. A target projectile is launched
into the air from a platform 10 feet above the ground at a rate of 96 feet per second.
Amy aims and shoots at her target. Her bullet follows a linear path with a slope of 17
feet per second and she fires from a height of 5 feet.
The equation used to determine height and time is y = 16x² + 96x + 10 and y = 17x + 5
What is Projectile Motion ?
A projectile is something that has only one force acting on it the entire time, which is gravity, with the exception of the beginning.There are numerous types of projectiles.A projectile is something that is launched from the position of rest.A projectile is also any object that is hurled vertically upward as long as air resistance has no effect. Additionally, a projectile is any object that is fired upward at an angle to a horizontal plane.
The height of projectile after t seconds is given,
h(t) = 1/2 gt² + v₀t + s₀
where,
v₀ ( initial velocity ) = 96 feet per second
s₀ ( initial height ) = 10 feet
g = 32 feet per second²
put the values,
h(t) = 1/2 (32)t² + 96 t + 10
h(t) = 16 t² + 96 t + 10
so, let h(t) = y and t = x
y = 16x² + 96x + 10
We know, Amy's bullet follows a linear path,
The linear equation is,
y = mx + b
where, slope (m) = 17 feet per second and,
y-intercept (b) = 5 feet
plug in the values in linear equation,
y = 17x + 5
Therefore, The equation used to determine height and time is y = 16x² + 96x + 10 and y = 17x + 5
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Levine Labs used 50,000 ounces of specimen adhesive during the year. The direct materials standard allows 1.50 ounces of adhesive at a price of $0.40 per ounce for each pathology test. The direct materials quantity variance was $880 Favorable.
How many pathology tests did Levine Labs complete during the year?
(Round per unit value to 2 decimal places, e.g. 15.25 and final answer to O decimal places, e.g. 125.)
Pathology tests ____?
The number of pathology tests that were completed during the year by Levine Labs are 34,800 tests.
What is the calculation showing the above answer?Note that Material quantity variation - Material quantity variation describes the cost difference caused by variations in the actual material used and the standard material to be utilized.
Material quantity Variance =
(Actual material used- Standard material used) x Standard cost
(50000-no of test x 1.5) x 0.4 = -880
-2200 = 50000-(No of test*1.5)
No of test x 1.5 = 52,200
No of test = 52,200/1.5
No of test = 34,800
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Find the unit rate
Rahul travelled 348 miles in 6 hours
Answer:
Step-by-step explanation: 348 miles and 6 hours
if a box of pens is given to 25 children, they will get 2 pens each. how many pens would each get, if the number of children is reduced to 15?
When the students get reduced to 15 then each student will get 3 pens.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total students = 25
Each Student get 2 pens.
So, 25 students get = 25 x 2= 50 pens
Now, number of children reduced = 25 -10= 15
So, each student get = 50/ 15 = 3.333 = 3 pens
Hence, each student will get 3 pens.
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The marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation.
-3/4
C'(x)=x
Find the cost of printing 133 more posters when 17 have already been printed.
The cost of printing 133 more posters when 17 have already been printed is $.
(Round to the nearest cent as needed.)
When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.
How to calculate cost of painting?A mathematical formula known as a cost function is used to visualise how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.
The following equation, C'(x)=x-3/4, tells us the marginal cost (in dollars) of printing a poster after x posters have been printed.
The given equation is :C'(x)=x-3/4
The cost of printing 133 more posters when 17 have already been printed is given by;
applying the limitations we obtain and integrating both sides of the equation;
[tex]$$\int_a^b C^{\prime}(x) d x=\int_{17}^{133} x^{\frac{-3}{4}} d x$$[/tex]
As we know that [tex]$\int x^n d x=\frac{x^{n+1}}{n+1}$[/tex], so;
[tex]$&=4\left[x^{\frac{1}{4}}\right]_{17}^{133} \\[/tex]
[tex]$&=4\left[(133)^{\frac{1}{4}}-(17)^{\frac{1}{4}}\right] \\[/tex]
= $ 5.4616
Therefore When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.
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40
100%
Complete the table to show different percentages of the steaming time.
Time (min)
Percentage
100% of 40 min
50% of 40 min
250% of 40 min
The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively
How to complete the table to show different percentages of the steaming time?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min
100% of 40 min:
100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min
50% of 40 min:
50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min
250% of 40 min:
250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min
Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.
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its in the picture♡
Answer:A. (10 x 3) + 8
Answer:
A : ( 10 * 3 ) + 8
Hope this helps!
Step-by-step explanation:
10 friends, each donate 3 pieces of clothing, ( 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 ) or ( 10 * 3 ), plus the 8 pieces of clothing Emily is donating. ( 10 * 3 ) + 8.
The number of carbon atoms in a fossil is given by the function y = 51000(0.85), where t represents the number of
years since being discovered. What is the percent of change each year? Explain how you arrived at your answer.
The percent of change each year is 15%.
How to calculate percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
It is given that The number of carbon atoms in a fossil is given by the function y = [tex]51000(0.85)^t[/tex], where t represents the number of years since being discovered.
Here , y = [tex]51000(0.85)^t[/tex]
t = number of years
y = number of carbon atoms in a fossil.
For t = 1 year
y = 51000[tex](0.85)^1= 51000(0.85) = 43350[/tex]
For t = 2 years
y = 51000[tex](0.85)^2= 36847.5[/tex]
For t = 3 years
y = 51000[tex](0.85)^3=31320.375[/tex]
Percentage change in one year = [tex]\frac{36847.5-43350}{43350}[/tex] × 100 = -15%
Percentage change in second year = [tex]\frac{31320.375-36847.5}{36847.5}[/tex] × 100 = -15%
here, negative sign shows decrement. In this way, every year carbon atom in fossil decreases by 15%.
Therefore, the percent of change each year is 15%.
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Find the square root that is a real number
The square root of √-36 is 0.
What is square root?A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol "sqrt"—square root of, end square root. The opposite of squaring an integer is finding its square root. In mathematics, a square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.So, √-36:
Calculate the square root as follows:
Therefore, the square root of √-36 is 0.
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Pls help giving brainliest
Answer:5) gcf=6 lcm=42 | 6) gcf=2 lcm=270 | 7) gcf=2 lcm=224
Step-by-step explanation:
f(x)=x^2-1, g(x)=x+2
The composite function ( f. g(x)) is x² + 4x + 3
What is a function?A function can be described mathematically as a rule, law or equation that explains, shows and elaborates the relationship between to variables.
The variables are known as;
The independent variableThe dependent variableFrom the information given, we have the functions as;
f(x)=x^2-1g(x)=x+2To determine the composite function ( f. g(x)), we have to substitute the value of g(x) as a function in the function f(x) as the variable 'x', we get;
( f. g(x)) = (x + 2)² - 1
Now, let's expand the square
( f. g(x)) = (x + 2) ( x+ 2) - 1
Expand the bracket
( f. g(x)) = x² + 2x + 2x + 4 - 1
Now, let's collect like terms, we get
( f. g(x)) = x² + 4x + 3
Thus, the function is x² + 4x + 3
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The complete question:
Find ( f. g(x)) if f(x)=x^2-1, g(x)=x+2
A sample of 39 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are
summarized in the following table.
Number of computers Price (in dollars)
13 - 2300
11 - 1800
15 - 2150
Find the mean price for this sample. Round your answer to the nearest dollar.
The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
What is mean?A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilizes the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.acc to our question-
Mean price = total amount spent on computers / number of computers= (6*900 +18*800+14*2600+5*1750)/(6+18+14+5) =64,950/43 = 1510.47x f fx900 6 5400800 18 144002600 14 364001750 5 875043 64950xbar = Σxf/Σf = 64,950/43 = 1510.47hence,The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
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A teacher runs each morning before school. Last week, he ran a total of 5 3/4 miles. This week, he ran 4/5 of the total number of miles he ran last week. What is the total number of miles that the teacher ran last week and this week?
The total number of miles that the teacher ran both last week and this week was 10.35 miles
How to find the total number of miles?Last week, the teacher ran a total of 5 3/4 miles. For easier calculation, convert this to a decimal:
= 5 + 3/4
= 5 + 3 ÷ 4
= 5 + 0.75
= 5.75 miles
This week, the teacher ran 4 / 5 of the miles he ran the previous week:
= 5. 75 x 4/5
= 4.6 miles
The total number of miles the teacher ran both last week and this week were:
= 5.75 + 4.6
= 10.35 miles
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Answer:
10 7/20 miles
Step-by-step explanation:
NO LINKS!! Please help me with these graphs Part 4a
Answer:
a. x = 1.75, x = 4.25
b. y = -7
c. Maximum point at (3, 5).
d. Domain: (-∞, ∞)
e. Range: (-∞, 5]
f. See attachment.
Step-by-step explanation:
Given function:
[tex]\text{f}(x)=-4|x-3|+5[/tex]
As per the question, use a graphing calculator to graph the given function.
Part aThe x-intercept(s) are the points at which the curve crosses the x-axis.
x-intercepts: x = 1.75, x = 4.25Part bThe y-intercept is the point at which the curve crosses the y-axis.
y-intercept: y = -7Part cFrom inspection of the graph:
Maximum point at (3, 5).Part dThe domain of a function is the set of all possible input values (x-values).
The domain of the given function is unrestricted.
Domain: (-∞, ∞)Part eThe range of a function is the set of all possible output values (y-values).
As the function has a maximum point at y = 5, the range is restricted.
Range: (-∞, 5]Part fGraph label the axes using a scale of 1 (see attachment).
Plot the maximum point (3, 5). Plot the y-intercept: (0, -7).Draw a straight line from the maximum point through the y-intercept.Substitute x = 5 into the function to find the value of y at that point:
[tex]\begin{aligned}\implies \text{f}(5)&=-4|5-3|+5\\&=-4|2|+5\\&=-4(2)+5\\&=-8+5\\&=-3\end{aligned}[/tex]
Plot found point (5, -3).Draw a straight line from the maximum point through point (5, -3).The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Find
(a) the co-ordinates of the mid-point of the line PQ,.
The co-ordinates of the mid-point of the line PQ are (6,4).
From the question, we have
The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Mid-point of the line PQ =(10+2)/2 , (12-4)/2
= (6,4).
Midpoint:
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.
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for a given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" find the value of the 15th term
For the given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" the value of the 15th term is 1539.
What is a geometric sequence?
One particular sort of sequence is a geometric sequence. It is a sequence in which each term, with the exception of the first, is multiplied by a fixed integer to obtain the following term. The common ratio must be multiplied by the current term in the geometric sequence to obtain the next term, and the common ratio must be divided by the current term to obtain the previous term.
Solution Explained:
We know, a7 = 19/81, a12 = -57
So, ar^7 = 19/81 and ar^12 = -57 (r= common ratio)
Since r< a15 < 0 [the sign alternate]
Ignoring the signs,
r^12 = r^7 X r^5
57 = 19/81 X r^5
(57 X 81)/19 = r^5
243 = r^5
r = the fifth ratio of 243 = 3
therefore, r = -3
So, a15 = a12 X r^3
= -57 X (-3)^3
= 1539
Hence, the value of the 15th term is 1539.
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Solve for x.
5^x +25^x+125^x=-5
Answer:
No solutionStep-by-step explanation:
Given5ˣ + 25ˣ + 125ˣ = - 5Each exponent on the left side is a positive number and therefore their sum is positive too.
But we have a negative value on the right.
This is not possible, hence no solutions.
Use the equation below to find v, if u = 18, a = 6, and t = 4
v = u + at
The value of v from the given equation v=u+at is 42
What is an equation?An equation is a mathematical expression that contains an equals symbol
From the given equation v=u+at
u=18
a=6
t=4
Substituting for u,a and t in the equation
v=18+6(4)
expanding the bracket
v=18+24
v=42
Hence, the the v in the equation v=u+at is 42
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x-6=-[tex]\frac{1}{6}[/tex]y²
2x+y=6
Solve algebraically
PLEASE ANSWER AS SOON AS POSSIBLE WITH EXPLANATION!!!!! THANK YOU!!!
Bob’s bank charges him a $3.15 service fee every time he uses an out-of-network ATM. If Bob uses an out-of-network ATM an average of three times every two weeks, how much will he pay in service fees over the course of a year?
a.
$327.60
b.
$109.20
c.
$491.40
d.
$245.70
Please select the best answer from the choices provided
A
B
C
D
answer:
$245.70
why?:
1 year = 52 weeks
52/2= 26
26*3 = 78 times
78*3.15= 245.70
What is 9.65+0.4, 16.058- 1.2
Answer:
Step-by-step explanation:
9.65+0.4=10.05
16.058-1.2=14.858
what is -3 > -2x + 7 ?
Find function which gives the slope of the line tangent to j(x).
j(x)=4x55−x4+x2
A. 3x4−12x3+2x
B. 16x3−12x2+2
C. 4x4−4x3+2x
D. 4x4−4x3+2
Please help me thank you so much!
Answer:
please write it more clearly or take a pic
the graph of f(x)=x^3+3x^2-4 is shown. what is the value of f^-1(-4)
Since the function is not one-to-one, the inverse function of f(x) = x³ + 3x² - 4 is not defined at x = -4.
How to obtain the numeric value of the inverse function?An original function is composed by a set of points in the following format:
(x,y).
On the graph of the function, we have that:
The x-coordinate represents the input of the function, being the horizontal axis of the graph.The y-coordinate represents the output of the function, being the vertical axis of the graph.On the inverse function, the input and the output are exchanged, hence the format of the point is:
(y,x).
To find the numeric value of the inverse function at x = -4, we need to identify the value of x on the original function where y = -4.
However, looking at the graph of the function given at the end of the answer, the function is not one-to-one at y = -4, since f(-3) = f(0) = 4, thus the inverse function is not defined at x = -4.
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Deshaun drove 469 miles in 7 hours.
At the same rate, how long would it take him to drive 335 miles?
We're assuming Deshaun is driving at a constant speed/at the same rate,
He drove 469 miles in 7 hours -> his speed = 469 : 7 = 67 (mph)
Therefore, it would take him 335 : 67 = 5 hours to drive 335 miles.
A letter is chosen at random from the word MATHEMATICS. Find the probability that it will be
a) an H
b) an M
c) a B
d) a vowel,
e) a letter other than an A
Answer:
a) 1/11
b) 2/11
c) 0/11
d) 4/11
e) 9/11
Step-by-step explanation:
'MATHEMATICS' has 11 letters.
a) there is only one H out of the 11 letters meaning the probability is 1/11
b) there are two M s out of the 11 letters meaning the probability is 2/11
c) there is no B in the word meaning the probability is 0/11
d) there are four vowels (2 A s, 1 E and 1 I) out of the 11 letters meaning the probability is 4/11
e) there two A s in the word and 11-2=9 meaning the probability is 9/11
Hope this helps :)
What is the last digit of the number 4^2016?
Answer:
The last number is 4
Step-by-step explanation:
