Answer: 8 teas were caffeinated
Step-by-step explanation:
To solve is to turn 25% into a decimal:
This is 25/100 turned into 0.25
*Multiply this by 32
This gives the number 8
*To do this, multiply without the decimal: 25 x 32 = 800
Then place the decimal back 2 places to the left of the last number:
8.00
Solve the equation below by factorising.
2x^2- 10x= 0
Answer:
x = 0 , x = 5
Step-by-step explanation:
2x² - 10x = 0 ← factor out 2x from each term on the left side
2x(x - 5) = 0
equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x - 5 = 0 ⇒ x = 5
Write the function for the graph A. f(x) =2•(4) x B.f(x) = 4 •(2) x C. f(x) = 4•(8) x D. f(x) =2•(8) x
The exponential equation that represent the graph is y = 2(4)^x
Exponential functionsThe standard exponential function is expressed as
y = ab^x
Given the coordinate points (1, 8) and (0,2), the equivalent equations are;
8 = ab^1
2 = ab^0
from equation 2, a = 2
8 = 2b
b = 4
Hence the exponential equation that represent the graph is y = 2(4)^x
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Which is the best estimate of -14 1/9 (-2 9/10) ?
Answer:
42
Step-by-step explanation:
-14 1/9 is about -14.
-2 9/10 is about -3.
Multiplying these, we get (-14)(-3)=42.
Because computers operate so quickly, developers often measure time in milliseconds (which are 1000th of a second). Which operation could we perform in order to find the number of milliseconds in a year
The operation is 365*24*60*60*1000 = 31536*10^6.
As we know the year has 365 days.
Each day has 24 hours.
Each hour has 60 minutes.
Each minute has 60 seconds.
Each second has 1000 millisecond.
Therefore number of milliseconds in a year is
365*24*60*60*1000 = 31536*10^6.
Hence we get the The operation is 365*24*60*60*1000 = 31536*10^6.
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A: Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship.
B: Identify and interpret the key features of the function in the context of the situation you described in part A.
The function represented is analyzed below.
How to illustrate the function?The function represented by the graph is related to a piecewise function.
The key features of the function include:
The function has a constant value in interval (0, 15) which is 40.
It decreases at first and then increases from 45 to 65.
It increases linearly from 65 to 90.
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PLS HELP PLSSS HELP
I NEED THIS SOLVED
PLSS DO IT
PLSSSS HELPP
ITS SO HARD
I WILL FAIL
HELP PLSSS
Answer:
x² + 5x - 14 = (x + 7)(x - 2)
x² - 3x - 54 = (x - 9)(x + 6)
x² + 8x + 12 = (x + 2)(x + 6)
x² - 11x + 30 = (x - 5)(x - 6)
x² - 25 = (x + 5)(x - 5)
x² + 8x - 9 = (x - 1)(x + 9)
Step-by-step explanation:
To factor x² + ax + b, look for two numbers whose sum is a and whose product is b.
The factorization of x² - a² is (x + a)(x - a).
x² + 5x - 14 = (x + 7)(x - 2)
x² - 3x - 54 = (x - 9)(x + 6)
x² + 8x + 12 = (x + 2)(x + 6)
x² - 11x + 30 = (x - 5)(x - 6)
x² - 25 = (x + 5)(x - 5)
x² + 8x - 9 = (x - 1)(x + 9)
The factored form of the given expressions are
y = (x -2)(x +7)
y = (x +6)(x -9)
y = (x +2)(x +6)
y = (x -5)(x -6)
y = (x +5)(x -5)
y = (x -1)(x +9)
y = (x +4)(x -4)
Factoring quadratic expressionsFrom the question we are to factor the given quadratic expressions
y = x² + 5x - 14y = x² +7x -2x - 14
y = x(x +7) -2(x +7)
y = (x -2)(x +7)
y = x² -3x - 54y = x² -9x +6x - 54
y = x(x -9) +6(x -9)
y = (x +6)(x -9)
y = x² +8x + 12y = x² +6x +2x +12
y = x(x +6) +2(x +6)
y = (x +2)(x +6)
y = x² -11x +30y = x² -6x -5x +30
y = x(x -6) -5(x -6)
y = (x -5)(x -6)
y = x² - 25y = (x +5)(x -5)
y = x² + 8x - 9y = x² +9x -x -9
y = x(x +9) -1(x +9)
y = (x -1)(x +9)
y = x² - 16y = (x +4)(x -4)
Hence, the factored form of the given expressions are
y = (x -2)(x +7)
y = (x +6)(x -9)
y = (x +2)(x +6)
y = (x -5)(x -6)
y = (x +5)(x -5)
y = (x -1)(x +9)
y = (x +4)(x -4)
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Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f _________.
The differentiation of the stated series expansion of f term-by-term to obtain the corresponding series expansion for the stated derivative of f is [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)Xⁿ⁻¹
What are the steps to arrive at the above solution?f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ
⇒ f'(x) = d/dx [[tex]\sum_{n=0}^{\infty}[/tex](-1)ⁿ 3ⁿXⁿ]
= [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿ d/dx (xⁿ)
= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿ(nxⁿ⁻¹)
= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿnxⁿ⁻¹
= [tex]\sum_{n=1}^{\infty}[/tex] ((-1)ⁿnxⁿ⁻¹)3ⁿ
= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)xⁿ-1
What is differentiation?In mathematics, differentiation is used to calculate rates of change. In mechanics, for example, velocity is the rate of change of displacement (with regard to time).
The acceleration is the rate of change of velocity (with respect to time).
What is the practical use of Differentiation in real life?They are employed in many fields, including
biologyeconomicsphysicschemistry, and engineering.They can be used to represent:
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Full Question:
Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f.
If f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ
The chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week. The number of students is modeled by f(x) = 4(1.0256)x.
A: Create a question you could ask that could be answered only by graphing or using a logarithm.
The question that could be answered by using a logarithm is explained below
How to explain the logarithm?The question is: Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.
The question is asking you to solve y = f(x)
You already did this using a constant for y. Do the same thing with y instead of the constant.
y = 4(1.0256^x)
y/4 = 1.0256^x . . . . . . . divide by 4
log(y/4) = x·log(1.0256) . . . . . take logs
log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x
Now, you have a model for x in terms of y, which is what the question is asking for.
x = log(y/4)/log(1.0256)
When y=12, this is .x = log(12/4)/log(1.0256) ≈ 43.46 weeks
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Select the correct answer.
Which expression and quotient does the diagram model?
The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.
Which expression and quotient is depicted by the diagram model as in the task content?It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).
Additionally, the dividend in the quotient by observation is the sum of terms as follows;
x² + x +x -x -1 -1 = x²+x -2.
Ultimately, the result of the division according to the model is; (x +2).
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Hi! It’d be really helpful if someone could explain he two questions below, thanks!
how to solve for problem 14
m∠ AEM = 20°
How to determine the angle
From the given figure, we can see that m∠ AEM is alternate to m∠ ACE
Note that m∠ ACE = 20°
Alternate angles are equal.
If m∠ ACE is alternate to m∠ AEM
Then, m∠ AEM = 20°
Hence, m∠ AEM = 20°
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PLEASE HELP IM STUCK
The slope-intercept equation for the given line is y = 2x + 3
Equation of a straight lineFrom the question, we are to determine the equation for the line
The slope-intercept form of the equation of a straight line is
y = mx + b
Where m is the slope
and b is the y-intercept
First, we will determine the slope
Slope of the line = (3 - 0) / (1.5 - 0)
Slope of the line = 3/1.5
Slope of the line = 2
∴ m = 2
On the graph, we can observe that the y-intercept is 3
∴ b = 3
Thus,
The equation becomes
y = 2x + 3
Hence, the slope-intercept equation for the given line is y = 2x + 3
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Find the area of the polygon formed whe these points are connected a(3,7)b(3,3)c(7,3)d(7,7)
Here, given
sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)
Let, 3 = x1 & 7= y1 , 3= x2 & 7= y2 , 7= x3 & 3= y3 , 7= x4 & 7= y4
[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}
[tex]\frac{1}{2}[/tex] (32)
16cm^2
Hence, the area of the polygon is 16cm2.
The formula for calculating the area of a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].
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Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −3x^2 + 150 − 1200, where x is the amount he charges per tree.
1. How much does he need to charge if he wants to break even?
2. How much does he need to charge if he wants to make a profit of $600?
He need to charge 24$ per tree if he wants to make a profit of $600.
According to statement
Noah knows that his profit, P, in dollars, are P= −3x^2 + 150 − 1200.
Now, we find the value of x when the profit is $600
Where X represent the Amount he charges per tree.
The given equation is P= −3x^2 + 150 − 1200.
Substitute the value of p is $600 in the above written equation
Then
600 = −3x^2 + 150 − 1200.
After solving the equation by a substitution method the value of X becomes
600+1200-150 = -3(x)^2
x = (1650/3)^1/2
x= 24$
it means the charge per tree is 24$.
So, He need to charge 24$ per tree if he wants to make a profit of $600.
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Your ship has steamed 1651 miles at 20 knots using 580 tons of fuel oil. The distance remaining to your next port is 1790 miles. If you increase speed to 25 knots, how much fuel will be used to reach that port
The 680 tons of fuel needed to cover the next 1790 miles distance.
According to the statement
We have given that the ship covered a 1651 miles distance at 20 knots by a 580 tons of fuel oil.
And distance remaining to next port is 1790 miles and speed increases to 25 knots.
And we have to find that how much fuel used to reach that port.
So, Distance covered = 1651 mile
fuel used = 580 tons
distance covered with 1 tons fuel = 1651/580
distance covered with 1 tons fuel = 2.85 mile at a speed of 20 knots.
so, The fuel consumption for 1790 mile is = 1790/2.85
The fuel consumption for 1790 mile is = 628 tons of fuel needed.
So, The 680 tons of fuel needed to cover the next 1790 miles distance.
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(x)/(12)=(y)/(13)=(z)/(15 )3x+2y=35 tìm x , y , z
Step-by-step explanation:
z is the answer of your question 15 is correct answer
John is looking at the top of a building and thinking it would be great to make a zipline from the top to your current location. He measures the angle of elevation as 28and is 182 feet from the base of the buildingHow long a zipline is needed if John is 71.5 inches tall? Include a sketch that shows all known information and clearly shows what you need to findShow all work and give the answer rounded to the nearest tenth of a foot
Answer:
Step-by-step explanation:
sin(28) = 2184 / x
x= 2184/ sin(28) = 2184 / 0.4694 = 4652.75
4652.75 / 12 = 387.7 ft
ANSWER: 387.7ft
In the given case, The length of the zipline needed is approximately 96.7 feet.
To find the length of the zipline needed, we can use trigonometry. Let's start by drawing a sketch to visualize the problem. | | zipline | | | | | | | | | | John | Building 28°
John's location, with the angle of elevation labeled as 28°. John is 182 feet away from the base of the building, and he is 71.5 inches tall.
To find the length of the zipline, we can use the tangent function.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is John's height, and the adjacent side is the distance between John and the building. Using the tangent function, we have: tan(28°) = opposite / adjacent
We want to find the length of the zipline, which is the hypotenuse of the right triangle formed by John, the building, and the zipline. Let's call this length "x".
Therefore, we can rewrite the equation as: tan(28°) = 71.5 inches / 182 feet To solve for x, we need to convert the units so that they match.
Let's convert inches to feet: 71.5 inches = 71.5 inches * (1 foot / 12 inches) ≈ 5.96 feet (rounded to the nearest hundredth)
Now, let's solve for x: tan(28°) = 5.96 feet / 182 feet
To isolate x, we can multiply both sides by 182 feet: x ≈ tan(28°) * 182 feet Using a calculator, we find that tan(28°) ≈ 0.5317.
Multiplying this by 182 feet, we get: x ≈ 0.5317 * 182 feet ≈ 96.7 feet (rounded to the nearest tenth) .
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each of 16 students in a class made a poetry book. each book contained 24 poems. how many poems are in 16 books
In trapezoid LOVE, the length of the midsegment is 2x inches. If one
parallel side is x inches, what is the length of the other parallel side?
The length of the other parallel side is 3x
How to determine the other parallel side?The given parameters are:
Midsegment= 2x
One parallel side = x
The midsegment is calculated as:
Midsegment = 0.5 * (sum of parallel sides)
So, we have
2x = 0.5 *(x + Other side)
Divide by 0.5
4x = x + Other side
Evaluate the like terms
Other side = 3x
Hence, the length of the other parallel side is 3x
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PLEASE HELP ME IM STUCK
The slope-intercept formula of the linear equation is:
[tex]y = \frac{3}{7}x + 7[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The y-intercept is of b = 7. The line also goes through point (0,-3), hence the slope is:
m = 3/7.
Thus the equation is:
[tex]y = \frac{3}{7}x + 7[/tex]
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HELP PLS 5. Find the missing side lengths. Leave the answers as radicals in simplest form.
Answer:
[tex]a=22, b=11\sqrt{3}[/tex]
Step-by-step explanation:
Given a 30-60-90 triangle, the shortest side is always opposite of the smallest angle, in this case 11 is opposite the 30° angle. The largest side of a 30-60-90 triangle will always be twice the smallest, giving [tex]a[/tex] a measure of [tex]22[/tex]. To get the side across the 60° angle we multiply the smallest side by the square root of 3. Meaning [tex]b=11\sqrt{3}[/tex]
The volume of this cylinder is 7500cm3.
find the missing length x.
give your answer rounded to 1 dp.
V = π r2h. Volume Calculations. Round ( Cylinder) Tanks. Example 1. Find the Volume in cubic feet of a tank having a radius of 10 feet and ...
Missing: 7500m Give SF.
In the case of a hollow cylinder, we measure two radii, one for the inner circle and one for the outer circle formed by the base of a hollow cylinder. Suppose, r1 and r2 are the two radii of the given hollow cylinder with 'has the height, then the volume of this cylinder can be written as; V = πh(r12 – r22).
To find the volume of a box, simply multiply the length, width, and height — and you're good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters.
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Select the correct answer.
(1, √3) to polar form.
A. (√3, 30°)
B. (2,60°)
C. (4,30°)
D. (2,240°)
Answer:
(2, 60°)
Step-by-step explanation:
A point in polar form (a,b) is represented by a radius and an angle (r, ϴ). To convert, use the formula r² = a² + b² to get r, and [tex]tan^{-1}[/tex](b/a) = ϴ
[tex]r = \sqrt{1^{2} + \sqrt{3} ^{2} }[/tex]
[tex]r = \sqrt{1+3}[/tex]
[tex]r = \sqrt{4}[/tex]
= 2
[tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]/1) = ϴ
= 60°
Jenny draws the path to walk from her house over to her grandmother's house. She knows that she has to avoid the end of the segment where construction is taking place. If she wants to use equations to identify her path on the coordinate plane, what should her answer look like?
Her answer should look like y = x + 2, x ≤ 2
How to determine the equation?The complete question is added as an attachment
From the attached graph, we have the following points
(x, y) = (2, 4) and (0, 2)
See that the difference between the y and x values is 2 where y > x
So, we have
y - x = 2
Add x to both sides
y = x + 2
The highest value of x in the graph is 2.
So, we have
x ≤ 2
Hence, her answer should look like y = x + 2, x ≤ 2
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A rectangular piece of land measures 4.5 km long and 2.5 km wide
Calculate the ratio of
1.It's width to its length
2.Its length to its perimeter
The ratio of its width to its length is; 5 :9.
The ratio of its length to its perimeter is; 9: 28.
What is the ratio of its width to its length?1). From the task content, the land measures 4.5 km long and 2.5 km wide. Hence, the ratios is; 2.5: 4.5.
Therefore, we have; 5: 9 by expression as whole number ratios.
2) Since the perimeter of the rectangle is; 2(2.5+4.5) = 14.
The ratio of length to perimeter expressed simply is therefore; 9: 28.
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Rearrange the equation so a is the independent variable.
−3a+6b=a+4b
Answer:
6b-4b=a+3a
2b=4a
4a=2b
a=2b/4
a=b/2
Instructions: Find the measure of the indicated angle to the nearest degree.
The number (2^22-2^20) (3^24-3^22) (4^26-4^24) is equal to 2^x × 3^y × 5^z. Determine the value of x+y+z.
Answer:
96
Step-by-step explanation:
(2^22-2^20) (3^24-3^22) (4^26-4^24)
=[(2^2-1)2^20][(3^3-1)3^22][(4^2-1)4^24]
=3*2^20*8*3^22*15*4^24
=2^23*3^23*4^24*15
=2^23*3^23*2^48*3*5
=2^71*3^24*5.
∵(2^22-2^20) (3^24-3^22) (4^26-4^24)=2^x × 3^y × 5^z，
∴x=71, y=24, z=1,
∴x+y+z=71+24+1=96.
find the values of A and B
PLEASE HELP GIVING BRAINLIEST
Factoring the roots, the values of A and B are given as follows:
A = 3z.B = 2.What are the values of A and B?The expression is:
[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]
We have that:
[tex]\frac{45}{40} = \frac{9}{8}[/tex]
Hence:
[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \sqrt{\frac{9\alpha z^3}{8}} = \sqrt{\frac{9\alpha z^2 \times z}{4 \times 2}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]
Hence, comparing the last two equalities:
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9 boys can paint a basketball court in 3 hours how long should 5 boys take working at the same rate
Answer:
100 minutes
Step-by-step explanation:
3 hours= 180 min
180/9 = 20
20 x 5 =100 min