<---------------------------||----------------------------------------->
A B
50 mph 60 mph
so let's recall that d = rt, distance = rate * time.
both cars start out at the same time, say "t" hours.
after "t" hours car A has covered say "d" miles, since there's a total of 1320, then car B must surely had covered the slack, or 1320 - d.
[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ A&d&50&t\\ B&1320-d&60&t \end{array}\qquad \implies \begin{cases} ~\hfill \boxed{d}=50t\\ 1320-d=60t \end{cases} \\\\\\ 1320-\boxed{50t}=60t\implies 1320=110t\implies \cfrac{1320}{110}=t\implies 12=t[/tex]
At a baseball game, the probability that a fan brings a glove is 0.08. The probability that a fan is left-handed is 0.12. What is the probability that a randomly selected fan has a baseball glove and is left-handed? Round your answer to the nearest hundredth,
-Hello There-
If the probabilities are independent, the probability that a left-handed person will bring a glove is ...
0.08×0.12 = 0.0096 ≈ 0.01
Hope This Helped!
Have A Great Day!
Stay Safe,
TheBlueFox
the answer would be 0.1
What is the value of x in the linear equation below?
4+3x-ax=9-7x+bx
Answer:
x = 5/(10 - a - b)
Step-by-step explanation:
Solve for x:
4 + 3 x - a x = 9 - 7 x + b x
Collect in terms of x:
x (3 - a) + 4 = 9 - 7 x + b x
Collect in terms of x:
x (3 - a) + 4 = x (b - 7) + 9
Subtract (b - 7) x + 4 from both sides:
x (10 - a - b) = 5
Divide both sides by 10 - a - b:
Answer: x = 5/(10 - a - b)
Help asap 15 points!
What is the approximate area of a sector given Θ≈212 with a radius of 45 m?
Question 1 options:
2613.59 m²
3744.45 m²
3371.26 m²
2928.36 m
What is the approximate area of a sector given Θ≈92 degrees with a diameter of 9m?
Question 2 options:
60 m²
65 m²
15.6 m²
16.2 m
Final answer:
The approximate area of a 212-degree sector with a 45m radius is 3371.26 m², and the approximate area of a 92-degree sector with a 9m diameter (4.5m radius) is 16.2 m².
Explanation:
To find the approximate area of a sector of a circle, we use the formula for the area of a circle, A = πr², and then adjust it for the sector by multiplying by the ratio of the central angle to 360 degrees. For Question 1, the central angle θ is approximately 212 degrees and the radius is 45 m. The formula for the sector area becomes A = (π × (45 m)² × (212/360)). A quick calculation gives us the following area:
For the first sector with a 212-degree angle and a radius of 45m:
A = 3.1415927 × (45 m)² × (212/360) = 3.1415927 × 2025 m² × 0.5889 ≈ 3371.26 m²
For Question 2, the central angle θ is approximately 92 degrees and the diameter is 9m, which makes the radius 4.5m. The formula for the sector area then becomes A = (π × (4.5 m)² × (92/360)). The calculation yields the following area:
A = 3.1415927 × (4.5 m)² × (92/360) = 3.1415927 × 20.25 m² × 0.2556 ≈ 16.2 m²
Question VVVVVVVVVVVVVVVVVVVVVVVVVVVV
Answer:
{x| x≤ 1/2 or x ≥ 3/4}
Step-by-step explanation:
The values of x that make the factors zero are 3/4 and 1/2. The product of these factors will be positive when both factors are negative (for x < 1/2) or when both factors are positive (x > 3/4). The matching answer selection is the third one.
Theo is practicing for a 5 kilometer race. He runs 5 kilometers every day and records his time. His normal time is 25 minutes 15 seconds. Esterday it took him only 23 minutes 49 seconds. How much faster was his time yesterday than his normal time? What are you asked to find? What information do you know? How will you solve the problem? Solve the problem
2 minutes 21 seconds
In scalene triangle abc, m∠b=45° and m∠c=55°. what is the order of the sides in length, from longest to shortest?
The order of the sides of the triangle is bc>ab>ac as per the rule that side opposite to the larger angle is larger
According to the rule that the side opposite to the larger angle is larger. The order of the sides of the triangle is bc>ab>ac .
How do find if a triangle with a specific side length exists or not?Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
Then, if these three values satisfy the relation:
[tex]a < b +c\\b < a + c\\c < a + b[/tex]
Then they are for sure the side length of a triangle.
In scalene triangle ABC, m∠b=45° and m∠c=55°.
The order of the sides of the triangle is bc>ab>ac according to the rule that the side opposite to the larger angle is larger.
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You are a landlord, and your tenant complains that you are in violation of the ADA because your wheelchair ramp is too steep. An independent assessor finds that your ramp has an angle of incline of 4.65°. Explain whether or not your tenant’s complaints are justified
Answer:
Not justified
Step-by-step explanation:
ADA requirements are for a slope of 1 in 12 or less, an 8.3% grade, or an angle of 4.8° (actually, 4.764° when rounded to 3 decimal places). The ramp angle found by the assessor is compliant.
The tenant complaint does not seem justified.
the function f(t)= -5t^2+20t +60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the objects to hit the ground?
Answer:
t = 6: It takes 6 seconds for the object to hit the ground
Step-by-step explanation:
So, we need to find t when the height is 0. Since -5t² + 20t + 60 represents the height, that needs to equal 0.
Equation: -5t² + 20t + 60 = 0
Divide by -5: t² - 4t - 12 = 0
Find two numbers that add up to -4t and multiply to -12t²: -6t, 2t
Substitute: t² - 6t + 2t - 12 = 0
Factor: (t - 6)(t + 2) = 0
Answers: t = 6, t = -2
Since time can't be negative, t = 6.
To determine the time it takes for the object to hit the ground, the quadratic equation -5t^2 + 20t + 60 = 0 is solved, leading to the conclusion that it takes 6 seconds for the object to reach the ground.
The question asks, "How many seconds does it take for the object to hit the ground?" given the function f(t) = -5t2 + 20t + 60. To find when the object hits the ground, we need to determine when the height f(t) is equal to 0. This involves solving a quadratic equation.
Steps to Solve:
Set the equation equal to zero: -5t2 + 20t + 60 = 0.
Divide the entire equation by -5 to simplify: t2 - 4t - 12 = 0.
Use the quadratic formula: t = (-B ± √(B2 - 4AC)) / 2A, where A = 1, B = -4, and C = -12.
Calculate the discriminant: √((-4)2 - 4(1)(-12)) = √(16 + 48) = √64 = 8.
Substitute values into the formula: t = (4 ± 8) / 2, yielding t = 6 seconds or t = -2 seconds.
Dismiss the negative value, as time cannot be negative, leaving t = 6 seconds as the solution.
Therefore, it takes the object 6 seconds to hit the ground after it is launched.
Select all that apply. A point is reflected over the y-axis and translated up 3 units. How will the coordinates change? The x-coordinate will decrease by 3. The x-coordinate's sign will change. The y-coordinate's sign will change. The y-coordinate will increase by 3.
Answer:
Step-by-step explanation:
If the point is translated across the y axis then the x coordinate will change sign.
If the point is translated upwards then the y coordinate will increase by 3
So the answers are B and D.
Which product of prime polynomials is equivalent to 36x3 – 15x2 – 6x? x(3x – 2)(4x + 1) 3x(3x – 2)(4x + 1) 3(x2 + 1)(4x – 1) 3(x2 + 1)(4x + 1)
Answer:
3x (3x-2)(4x+1)
Step-by-step explanation:
36x^3 – 15x^2 – 6x
factor out the "3x"
3x (12x^2-5x-2)
3x(3x - 2) (4x + 1)
= 9x^2 - 6x (4x + 1)
= 36x^3 + 9x^2 + - 24x^2 - 6x
= 36x^3 - 15x^2 - 6x
hope this helps!
The product of prime polynomials is equivalent to Option (A) [tex]3x(3x - 2)(4x + 1)[/tex].
Concept of prime polynomial -In mathematics, an irreducible polynomial (or prime polynomial) is approximately a non-constant polynomial that cannot be factored into the product of two non-constant polynomials. The expression can be expressed in product of prime polynomial by converting it into the factored form.
How to solve the given polynomial expression into product of prime polynomials ?Given polynomial expression = [tex]36x^{3} - 15x^{2} - 6x[/tex]
Solving the polynomial expression in factored form -
⇒ [tex]3x(12x^{2} - 5x - 2)[/tex]
⇒ [tex]3x(12x^{2} - 8x + 3x - 2)[/tex]
⇒ [tex]3x[4x(3x - 2) + 1(3x - 2)][/tex]
⇒ [tex]3x(3x - 2)(4x + 1)[/tex]
Therefore the product of prime polynomial is [tex]3x(3x - 2)(4x + 1)[/tex]
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PLEASE HELP. The supply and demand curves reflect the availability and cost of a new gaming system. If the gaming system is currently at Demand and Supply 1, which change to the graph would have to occur to increase equilibrium price while lowering equilibrium quantity?
————————————
A. Add Demand 1 to left of Demand. (incorrect i already tried that)
B. Add Demand 1 to right of demand.
C. Add Supply 2 to left of Supply 1.
D. Add Supply 2 to right of Supply 1.
To increase equilibrium price while lowering equilibrium quantity, the supply curve needs to be shifted to the left.
Explanation:To increase equilibrium price while lowering equilibrium quantity in a supply and demand graph for a new gaming system, we need to shift the supply curve to the left. This can be done by adding a new supply curve, Supply 2, to the left of the original supply curve, Supply 1. Therefore, the correct answer is option C: Add Supply 2 to the left of Supply 1.
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Someone please help??
Answer:
[tex]\sqrt[3]{-0.064}=-0.4[/tex]
Step-by-step explanation:
An on-line calculator can do this if your own doesn't.
For a cube root, you may have to use the exponentiation function with an exponent of 1/3. Usually, that fraction will need to be put in parentheses. (See the second attachment for the result from a TI-84 calculator.)
A car traveling at 65 mph leaves a 25 foot skid mark. What is the ratio of the speed to length of skid mark? Give your answer in simplest form.
13:5 is the ratio of speed to skid mark
Which choice is equivalent to the expression below?
Answer: OPTION A
Step-by-step explanation:
We need to remember that Product of powers property, which states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Let's check the options:
A. For [tex]5^9*5^{\frac{9}{10}}*5^{\frac{6}{100}}*5^{\frac{9}{1000}}[/tex] you can apply the property mentioned before. Then:
[tex]5^{(9+\frac{9}{10}+\frac{6}{100}+\frac{9}{1000})=5^{9.969}[/tex]
(It is the equivalent expression)
B. Add the exponents:
[tex]5^9*5^{(\frac{9}{10}+\frac{9}{10}+\frac{6}{1000})=5^{10.806}[/tex]
(It is not the equivalent expression)
C. For [tex]5^9*5^{\frac{96}{10}}*5^{\frac{9}{100}}}[/tex] you can apply the property mentioned before. Then:
[tex]5^{(9+\frac{96}{10}+\frac{9}{100})=5^{18.69}[/tex]
(It is not the equivalent expression)
D. We know that [tex]5^{9.969}=9,290,347.808[/tex] and we maje the addition indicated in this option, we get:
[tex]5^9+5^{\frac{9}{10}}+6^{\frac{6}{100}}=1,953,130.37[/tex]
(It is not the equivalent expression)
Answer: A, i just took this test
Chris put $1,500 in a savings account at an annual interest rate of 5%. If Chris does not deposit or withdraw any money, what is the amount of interest Chris will earn the first year her money is in the savings account?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(1500)(0.05)(1)\implies I=75[/tex]
Chris will earn $75 in interest in the first year by depositing $1,500 into a savings account with an annual interest rate of 5%, calculated using the simple interest formula.
To calculate the amount of interest Chris will earn in the first year the money is in the savings account, we will use the formula for simple interest, which is Interest = Principal × Rate × Time. In this case, the principal amount is $1,500, the annual interest rate is 5% or 0.05 when expressed as a decimal, and the time is 1 year since we are looking for the interest for the first year only.
Therefore, the interest Chris will earn after one year is calculated as follows:
Interest = $1,500 × 0.05 × 1
Interest = $75
Thus, at the end of the first year, Chris will have earned $75 in interest.
Enrique needs to buy hamburgers and hot dogs for a picnic. He has only $16.50 to spend and must buy AT LEAST 44 hamburgers or hot dogs. A store charges $.50 per hamburger and $0.25 per hot dog. Which of the following is a possible way Enrique might buy the hamburgers and hot dogs?
29 hamburgers and 15 hot dogs
25 hamburgers and 18 hot dogs
22 hamburgers and 23 hot dogs
20 hamburgers and 25 hot dogs
Answer: D.
Step-by-step explanation:
The answer is 20 hamburgers and 25 hot dogs.
20(.5)+25(.25)<16.5
10+6.25<16.5
16.25<16.5
The budget is $16.50 and $16.25 is $.50 less therefore making it a possible option for Enrique.
With his budget of $16.50, Enrique can afford to buy the fourth option, 20 hamburgers and 25 hot dogs, which totals $16.25.
Explanation:Let's calculate the cost of each option and see which ones Enrique can afford with his $16.50:
29 hamburgers and 15 hot dogs: (29 x $0.50) + (15 x $0.25) = $14.75 + $3.75 = $18.5025 hamburgers and 18 hot dogs: (25 x $0.50) + (18 x $0.25) = $12.50 + $4.50 = $1722 hamburgers and 23 hot dogs: (22 x $0.50) + (23 x $0.25) = $11.0 + $5.75 = $16.7520 hamburgers and 25 hot dogs: (20 x $0.50) + (25 x $0.25) = $10.0 + $6.25 = $16.25Looking at these calculations, we can see that Enrique could only afford to buy the fourth option, 20 hamburgers and 25 hot dogs, with his $16.50 as that totals $16.25, which is within his budget.
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Maureen is making trail mix. She uses 8 ounces of granola and 2 ounces of raisins in her recipe. Fill in each statement. For every 1 oz of granola, Maureen uses oz of raisins. If she uses 24 oz of granola, she would need oz of raisins.
Answer:
So for every ounce of granola she uses a quarter ounces of raisins so a quarter of 24 is 6
Answer:6
Step-by-step explanation:
What is this half circles radius and how do you find it?
Answer:
The radius of the semicircle is 4 cm
Step-by-step explanation:
The diameter of the semicircle is 8 cm
The radius is 1/2 of the diameter
1/2 *8 = 4 cm
The radius of the semicircle is 4 cm
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you to find the radius of the circle (in this equation you would)}[/tex] [tex]\text{have to multiply one half from the number 8}[/tex]
[tex]\frac{1}{2}\times8=?\\ \frac{1}{2}\times\frac{8}{1} \\ \\1\times8=8\\2\times1=2\\\\8\div2=4[/tex]
[tex]\boxed{\boxed{\text{Answer: 04 cm}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Question 2(Multiple Choice Worth 5 points)
(08.06 LC)
Which numbers should be multiplied to obtain 1652 − 1232?
42 and 42
42 and 288
1,764 and 1,764
4,202 and 4,248
I believe the correct answer to this question is 42 and 288. If im not wrong.
Answer:
the answer is 42 and 228
Step-by-step explanation:
165x165=27,225 and 123x123=15,129
27,225-15,129=12,096
if you multiply 4x288 you get 12,096 which is your answer from before.
HELP PLEASE ASAP - 40 POINTS
WILL AWARD BRAINLIEST
The lunch special at Mrs. Tucker’s Country Buffet has a choice of:
2 appetizers
5 main courses
5 desserts
3 drinks
How many lunch meals are possible?
Answer: 2
Step-by-step explanation:
The reason is for each meal to have one thing of food for every lunch special. So then you would go one by one, theres 2 appetizers so that means it'll only reach to 2 lunches. Then theres 5 main courses and you seperate those having 2 of the 5 with the appetizers. Onto the desserts, there are 5 desserts and 2 out of the 5 you put it together with the lunches that have a main course and appetizers. Next, there are 3 drinks and 2 of those 3 you would put it with the 2 meals that has an appetizer,main course,dessert, and now a drink. In the end, Its only possible that there are 2 lunch special being able to be made. With all the food
Answer: 150
Step-by-step explanation:
We know that a complete lunch meal consist of an appetizer , a main course , a dessert and a drink.
Given: The number of appetizers=2
The number of main courses=5
The number of desserts=5
The number of drinks=3
Therefore, the number of possible lunch meals will be :
[tex]2\times5\times5\times3=150[/tex]
Hence, there are 150 lunch meals are possible.
Rectangular prism has a length of 214 feet, a width of 6 feet, and a height of 312 feet. what is the volume of the prism? enter your answer in the box. ft³
The answer is V≈4.01×105
Best answer gets brainliest!
What are some equivalent expressions of 6(m + 2 + 7m)?
Answer:
See Explanation
Step-by-step explanation:
To write an equivalent expression, we can combine like terms. So m +7m is 8 and we get 6(8m+2).
Here are a few others:
48m+12
6(m+m+m+m+m+m+m+m+2)
3(16m+4)
6m+12+42m
6m+6m+6m+6m+6m+6m+6m+6m+2
and the list goes on...
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you to solve this equation, you need to DISTRIBUTE}[/tex]
[tex]\text{Formula: a(b + c) = ab + ac / if this equation: a(b + c + d) = ab + ac + ad}[/tex]
[tex]\text{6(m + 2 + m)}[/tex]
[tex]\text{6(m) = 6m}[/tex]
[tex]\text{6(2) = 12}[/tex]
[tex]\text{6(7m) = 42m}[/tex]
[tex]\text{Next, combine your like terms}\downarrow \\ \text{6m + 42m}\\ \text{The 12 stays the same because they AREN'T any like terms to compare it with}[/tex]
[tex]\text{6m + 42m = 48m}[/tex]
[tex]\text{12 = 12}[/tex]
[tex]\boxed{\boxed{\text{Answer: 48m + 12}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Given ΔABC, m∠A = 50°, m∠B = 60°, and a = 7. Find c.
Answer:
D) 8.6
Step-by-step explanation:
The Law of Sines tells you ...
c/sin(C) = a/sin(A)
The sum of angles in a triangle tells you ...
C = 180° -A -B = 180° -50° -60° = 70°
Then ...
c = a·sin(C)/sin(A) = 7·sin(70°)/sin(50°) ≈ 8.6 . . . . . above equation multiplied by sin(C)
_____
There are apps available for phone or tablet for solving triangles. Many graphing calculators have functions that will do the same. Also, there are on-line triangle solvers that will give you the answer.
We include the working here because you're supposed to know how to work the problem. If all you want is the answer, that can be found faster a number of different ways.
Determine the angle measure between vectors u and v: u = – 3i + 3j and v = 3i + 2j .
Answer:
[tex]\theta=101.3\degree[/tex] to the nearest tenth
Step-by-step explanation:
The given vectors are;
u = – 3i + 3j and v = 3i + 2j
We use the dot product to find the angle between the two vectors.
[tex]u\bullet v=|u| |v|\cos \theta[/tex]
[tex](-3i+3j)\bullet (3i+2j)=|-3i+3j| |3i+3j|\cos \theta[/tex]
[tex](-3i+3j)\bullet (3i+2j)=\sqrt{(-3)^2+3^2} \sqrt{3^2+2^2}\cos \theta[/tex]
[tex]-9+6=3\sqrt{2} \sqrt{13}\cos \theta[/tex]
[tex]-3=3\sqrt{2} \sqrt{13}\cos \theta[/tex]
[tex]-1=\sqrt{26} \cos \theta[/tex]
[tex]-\frac{1}{\sqrt{26}}= \cos \theta[/tex]
[tex]\cos^{-1}(-\frac{1}{\sqrt{26}})= \theta[/tex]
[tex]\theta=101.3\degree[/tex]
Which even number is not a composite number
Answer:
2
Step-by-step explanation:
The only factors for this even numbers is itself and one. Other even numbers are composite because they can be divided by 2, but this number is 2 so it can only be divided by two numbers.
The circumference (C) of a circle is 16cm. Which formula can you use to find the diameter (d) if you know that C= πd?
The formula is d=C/π.
The diameter is 2 times the radius
The formula for the circumference using the radius is 2πr.
in order to do this backwards, we would have to do 16÷2÷π, but we're not looking for the radius.
Therefore, we take out the ÷2 part, which would be 16÷π
16 is the circumference
16÷π=d
d=C÷π
Answer:
d = /π
Step-by-step explanation:
A small factory planned to produce a batch of men’s shirts in 8 days. But producing 10 more shirts per day than planned, they finished the task one day early. How many shirts per day was the factory planning to produce?
70 shirts per day
We simply need to find how many shirts would have been produced on the 8th day. This can be done by multiplying the number of extra shirts produced per day by the number of days extra shirts were produced. Since one day was skipped due to finishing early, there were 7 days of producing extra shirts.
7 times 10 equals 70. This means that 70 shirts would have been produced on the 8th day, which means the factory was planning on producing 70 shirts for every other day as well.
Identify the angle measures of PQRS. I'm so confused, please help me! SHOW YOUR WORK!!
10y + 7 + 3(3y + 7) = 180
10y + 7 + 9y + 21 = 180
19y + 28 = 180
19y = 180 - 28
19y = 152
y = 152/19
y = 8
Plug back into Q and S.
Q = 10y + 7
Q = 10(8) + 7
Q = 80 + 7
Q = 87
S = 3(3y + 7)
S = 9y + 21
S = 9(8) + 21
S = 72 + 21
S = 93
Without solving for x to find the other angles, we can easily see that the answer is choice C.
Answer:
P = 61°
Q = 87°
R = 119°
S = 93°
Done!
What is the domain and range for the following function and its inverse?
f(x) = x2 + 3
f(x)
domain:
f–1(x)
domain:
Answer:
Step-by-step explanation:
The domain of that function is all real numbers. The x values will drop into negative infinity and will grow to positive infinity.
The range is found from the vertex form of a parabola, which is
[tex]y=(x-h)^2+k[/tex]
where h indicates side to side movement of the vertex and k indicates up or down. Our function has a +3 at the end of it and is positive (so it opens upwards), so the range is y ≥ 3.
To find the inverse of that function, switch the x and y coordinates and solve for the new y. Let f(x) be y, then switch the x and y:
[tex]x=y^2+3[/tex]
Now solve for the new y:
y = ±[tex]\sqrt{x-3}[/tex]
To find the domain of a radical, set the radicand greater than or equal to 0 and solve for x (this is because the radicand cannot be a negative number or we are dealing with imaginary numbers and that's not what you want. BTW, a radicand is the term under the radical sign).
x - 3 ≥ 0 so x ≥ 3. The domain of the inverse is all real numbers greater than or equal to 3.
This is a sideways parabola (the inverse is), and it opens to the right starting at the x value of 3. It will grow into positive values of y to infinity and will drop into negative values of y into negative infinity.
Just a little trick here to remember, and it ALWAYS holds true: the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse. Look to our solution for your problem here and you'll see that it is true.
The formula for the nth term b of a geometric series is b=arn-1. Find n when b=1,024, a=16 and r=2.
[tex]\bf b=ar^{n-1}~~ \begin{cases} b=1024\\ a=16\\ r=2 \end{cases}\implies 1024=16(2^{n-1})~~ \begin{cases} 1024=&2^{10}\\ 16=&2^4 \end{cases} \\\\\\ 2^{10}=2^4(2^{n-1})\implies \cfrac{2^{10}}{2^4}=2^{n-1}\implies 2^{10}\cdot 2^{-4}=2^{n-1}\implies 2^{10-4}=2^{n-1} \\\\\\ 2^6=2^{n-1}\implies \stackrel{\textit{same base, the exponents must be the same}}{6=n-1\implies 7=n}[/tex]
The value of n when b = 1,024, a = 16, and r = 2 is 7.
The student is asking to solve for n in the formula of the nth term of a geometric series given the formula b = ar^(n-1) and the values of b, a, and r. To find the value of n, we can substitute the known values into the formula and solve for n.
b = 1,024
a = 16
r = 2
Using these values:
Substitute the known values into the formula: 1,024 = 16 imes 2^(n-1)
Divide both sides by 16: 64 = 2^(n-1)
Recognize that 64 is 2 to the power of 6: 2^6 = 2^(n-1)
Therefore, n - 1 = 6
Add 1 to both sides to find n: n = 7
The value of n when b = 1,024, a = 16, and r = 2 is 7.