Answer:
Step-by-step explanation:
Purplemath
To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. It is often simpler to work directly from the definition and meaning of exponents. For instance:
Simplify a6 × a5
The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together. That is:
MathHelp.com
Simplifying Expressions on MathHelp.com
Simplifying Expressions
a6 × a5 = (a6)(a5)
= (aaaaaa)(aaaaa)
= aaaaaaaaaaa
= a11
Thus:
a6 × a5 = a11
Simplify the following expression:
\mathbf{\color{green}{\dfrac{6^8}{6^5}}}
6
5
6
8
The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath.
\dfrac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}
6⋅6⋅6⋅6⋅6
6⋅6⋅6⋅6⋅6⋅6
How many extra 6's do I have, and where are they? I have three extra 6's, and they're on top. Then:
= \dfrac{6 \cdot 6 \cdot 6}{1} = \mathbf{\color{purple}{6^3}}=
1
6⋅6⋅6
=6
3
Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. If you're not sure, though, feel free to add "= 216", just to be on the safe side.
Simplify the following expression:
\mathbf{\color{green}{\dfrac{\mathit{t}^{10}}{\mathit{t}^8}}}
t
8
t
10
How many extra copies of t do I have, and where are they? I have two extra copies, on top:
\dfrac{t^{10}}{t^8} = \dfrac{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}
t
8
t
10
=
t⋅t⋅t⋅t⋅t⋅t⋅t⋅t
t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t
= \dfrac{t \cdot t}{1} = \mathbf{\color{purple}{\mathit{t}^2}}=
1
t⋅t
=t
2
Once you become comfortable with the "how many extras do I have, and where are they?" reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. The answers will start feeling fairly obvious to you.
Content Continues Below
Simplify the following expression:
\mathbf{\color{green}{\dfrac{5^3}{5^9}}}
5
9
5
3
This question is a bit different, because the larger exponent is on the term in the denominator. But the basic reasoning is the same.
How many extra copies of 5 do I have, and where are they? I have six extra copies, and they're underneath:
\dfrac{5^3}{5^9} = \dfrac{5 \cdot 5 \cdot 5}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5}
5
9
5
3
=
5⋅5⋅5⋅5⋅5⋅5⋅5⋅5⋅5
5⋅5⋅5
= \dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5} = \mathbf{\color{purple}{\dfrac{1}{5^6}}}=
5⋅5⋅5⋅5⋅5⋅5
1
=
5
6
1
Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for.
Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect.
Let's move on to expressions that are a bit more complex.
Simplify the following expression:
\mathbf{\color{green}{\dfrac{5\mathit{x}^5}{3\mathit{x}^3}}}
3x
3
5x
5
I mustn't forget that the "5" and the "3" are just numbers. Since 3 doesn't go evenly into 5, I can't cancel the numbers.
And I mustn't try to subtract the numbers, because the 5 and the 3 in the fraction "\frac{5}{3}
3
5
" are not at all the same as the 5 and the 3 in rational expression "\frac{x^5}{x^3}
x
3
x
5
". The numerical portion \frac{5}{3}
3
5
stays as it is.
For the variables, I have two extra copies of x on top, so the answer is:
\dfrac{5x^5}{3x^3} = \dfrac{5 \cdot x \cdot x \cdot x \cdot x \cdot x}{3 \cdot x \cdot x \cdot x}
3x
3
5x
5
=
3⋅x⋅x⋅x
5⋅x⋅x⋅x⋅x⋅x
= \dfrac{5 \cdot x \cdot x}{3}=
3
5⋅x⋅x
= \mathbf{\color{purple}{\dfrac{5\mathit{x}^2}{3} = \dfrac{5}{3}\mathit{x}^2}}=
3
5x
2
=
3
5
x
2
Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing.
Simplify (–46x2y3z)0
This is simple enough: anything to the zero power is just 1.
(–46x2y3z)0 = 1
Simplify –(46x2y3z)0
The parenthetical portion still simplifies to 1, but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. So the answer in this case is:
–(46x2y3z)0 = –1
Final answer:
The expression using only positive exponents is [tex]1/k^3[/tex].
Explanation:
To simplify the expression [tex]k^0 * k^-3[/tex] and write it using , we need to apply the laws of exponents.
The expression can be broken down into two parts.
Therefore,
[tex]k^0 = 1[/tex] (anything raised to the power of 0 is 1).
[tex]k^-3 = 1/k^3[/tex] (negative exponent indicates reciprocal).
Therefore,
[tex]k^0 * k^-3[/tex] [tex]= 1 * 1/k^3[/tex]
[tex]= 1/k^3.[/tex]
1) Ivy, Dylan, and Tyrone shared 100 personalized pencils. Ivy received 8 more pencils than Dylan. Tyrone received twice as many pencils as Ivy. How many pencils did each child receive?
Answer:
Number of pencils received by Dylan = 19
Number of pencils received by Ivy = [tex]27[/tex]
Number of pencils received by Tyrone = [tex]54[/tex]
Step-by-step explanation:
Given:
Ivy, Dylan, and Tyrone have together 100 pencils.
Ivy has 8 more pencils than Dylan.
Tyrone has twice as many pencils as Ivy.
To find: Number of pencils received by Ivy, Dylan, and Tyrone
Solution:
Let number of pencils received by Dylan = x
So, number of pencils received by Ivy = [tex]x+8[/tex]
number of pencils received by Tyrone = [tex]2(x+8)=2x+16[/tex]
Total number of pencils with Ivy, Dylan, and Tyrone = 100
So,
[tex]x+8+x+2x+16=100\\4x+24=100\\4x=76\\x=\frac{76}{4}\\ =19[/tex]
Number of pencils received by Dylan = 19
Number of pencils received by Ivy = [tex]19+8=27[/tex]
Number of pencils received by Tyrone = [tex]2(19)+16=38+16=54[/tex]
Dylan received 21 pencils, Ivy received 29 pencils, and Tyrone received 58 pencils. This conclusion was reached by setting up equations based on the relationships provided and solving for the variables.
To determine how many pencils each child received, let's define variables for each child's pencils:
Dylan: Let's represent the number of pencils Dylan received as D.Ivy: Ivy received 8 more pencils than Dylan, so we can represent Ivy's pencils as D + 8.Tyrone: Tyrone received twice as many pencils as Ivy, so we'll represent Tyrone's pencils as 2(D + 8).Now we know that the total number of pencils shared is 100, so we can create an equation:
D (Dylan's pencils) + (D + 8) (Ivy's pencils) + 2(D + 8) (Tyrone's pencils) = 100
Simplifying the equation:
D + D + 8 + 2(D + 8) = 100
Combine like terms:
D + D + 2D + 16 = 100
4D + 16 = 100
Subtract 16 from both sides to isolate the term with D:
4D = 84
Divide both sides by 4:
D = 21
So, Dylan received 21 pencils. Using this value, we can now find the number of pencils for Ivy and Tyrone:
Ivy: D + 8 = 21 + 8 = 29Tyrone: 2(D + 8) = 2(29) = 58Therefore, the number of pencils each child received are:
Dylan: 21 pencilsIvy: 29 pencilsTyrone: 58 pencilsWhich situations can be simulated using this spinner? Select three options.
A spinner with 6 equal sections.
A: Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female
B: Predicting the gender of a randomly chosen history teacher if 12 of 15 history teachers are female
C: Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female
D: Predicting the gender of a randomly chosen chemistry teacher if 4 of 9 chemistry teachers are female
E: Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female
Answer:
A: Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female.C: Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female.E: Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female.Step-by-step explanation:
Notice that the spinner has 6 equal sections.
So, all situations that can be simulated with such spinner must be multiples, divisors of 6, or a number least than 6, that way, we could use the 6 equal-section spinner.
Option A uses 1 of 3, Option B uses 8 of 12, and Option E uses 2 of 4.
Therefore, the anwers are A, C and E.
Answer: A C E
Step-by-step explanation:
A walker and a cyclist are 45 miles apart. They move towards each other with speeds of 5 mph and 10 mph respectively. In how many hours will they meet?
Answer: they will meet after 3 hours.
Step-by-step explanation:
Let t represent the number of hours it will take them to meet.
A walker and a cyclist are 45 miles apart. If they move towards each other, in t hours, they would have covered a total of 45 miles
Distance = speed × time
They move towards each other with speeds of 5 mph and 10 mph respectively. It means that the distance covered by the walker in t hours is 5 × t = 5t
Also, the distance covered by the cyclist in t hours is 10 × t = 10t
Since the total distance covered us 45 miles, then
5t + 10t = 45
15t = 45
t = 45/15
t = 3 hours
Which dimensions cannot create a triangle? Three sides measuring 6 cm, 8 cm, and 10 cm three angles measuring 10 degrees, 25 degrees, and 145 degrees three sides measuring 9 m, 15 m, and 9 m three angles measuring 40 degrees, 70 degrees, and 65 degrees
Answer:
c
Step-by-step explanation:
its correct no neef for an explanation
How can you tell if a fraction is a perfect square?
Answers: A fraction is a perfect square if it's reduced version (of an improper fraction if the number is greater than 1) has both numerator and denominator numbers that are perfect squares. IE: 25/36 is a perfect square because both 25 and 36 are perfect squares.
Step-by-step explanation:
So for example 5/25 is a perfect square but 2/5 wouldn't be a perfect square.
Tell me if this helped you
If a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
A fraction is a perfect square if both the numerator and the denominator of its reduced version, which is an improper fraction if the integer is greater than 1, are perfect squares. To put it another way, 25/36 is a perfect square as 25 and 36 are both perfect squares.
Thus, if a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
You want to go on a trip to Disney World with your friends. The trip costs $1450 and they have a special discount of 35% off. The tax rate for the package is 10%. What is the total price of the trip?
Answer: the total price of the trip is
$1087.5
Step-by-step explanation:
The trip costs $1450 and they have a special discount of 35% off. It means that the amount that would be taken off is
35/100 × 1450 = $507.5
The cost of the trip would be
1450 - 507.5 = $942.5
The tax rate for the package is 10%. It means that the amount of tax to be paid is
10/100 × 1450 = $145
Therefore, the total price of the trip would be
942.5 + 145 = $1087.5
can u pls help i have a few mins left
What is the common denominator of 1/a + 1/b in the complex fraction 1/a-1/b divided by 1/a+ 1/b?
Answer:
common denominator of 1/a + 1/b is ab
however simplifying the complex fraction gives: (b-a)/(b +a)
Step-by-step explanation:
common denominator of 1/a + 1/b
should be the product of the denominators
a*b
so 1/a + 1/b = (b + a)/ab
ao
( 1/a - 1/b) divided by (1/a + 1/b) = (b - a)/(ab) divided by (b+a)/ab
To find the common denominator for 1/a and 1/b within a complex fraction, we use ab. The complex fraction (1/a - 1/b) divided by (1/a + 1/b) can be simplified by multiplying the numerator and denominator by ab, leading to a simplified form of (b² - a²) / (a² + b²).
When finding the common denominator for complex fractions like 1/a and 1/b, it's similar to dealing with real numbers. Given the complex fraction (1/a - 1/b) divided by (1/a + 1/b), we can identify a and b as the denominators. To combine the fractions within the complex fraction, we need a common denominator, which is ab. Thus, the fractions would become (b/a - a/b) and (a/b + b/a), both with a common denominator of ab.
In the complex fraction ((1/a - 1/b) / (1/a + 1/b)), by finding the common denominator, we then rewrite the equation as (b/a - a/b) / (a/b + b/a), which simplifies to (b² - a²) / (a² + b²) when multiplied by ab in both the numerator and the denominator. This process of finding the common denominator allows us to combine and simplify the complex fraction.
You are solving 5 – 83 = y3. Which equation will you get if you multiply both sides by 3?
Answer:
15 - 3(8³) = 3y³
Step-by-step explanation:
5 – 8³ = y³
3(5 - 8³) = 3(y³)
15 - 3(8³) = 3y³
Answer:
15-8=y
Step-by-step explanation:
The students put recycling bins for cans for bottles in the cafeteria in the teachers lounge. They split them easily into 3 bags how many pounds were in each bag
Answer:
There were 16.3 pounds in each of the bags
Step-by-step explanation:
The complete question is as follows;
The students put recycling bins for cans and bottles in the cafeteria and teachers lounge. At the end of last week, there was a total of 48.9 pounds of cans and bottles. They split them evenly into 3 bags. How many pounds were in each bag?
Solution;
This is a straightforward question that borders on one of the arithmetic operations which is division.
To properly understand this question, we can reframe it to mean if you have three bags containing cans and bottles with a total weight of 48.9 pounds, what is the weight of each bag if they have the same weight?
we can see we have succeeded in making the question look simpler while meaning the same thing.
To get the weight of each of the bags, what we simply do is to divide the total weight of the bags by 3
Mathematically that would be 48.9/3 = 16.3
This means that each of the bags weigh 16.3 lbs
Anthony is running a lemonade stand. He expects to make $108 for the day, but ends up making 204% of that amount. How much money did Anthony make that day?
Answer:
$220.32
Step-by-step explanation:
108 x 2.04 = 220.32
What is the volume of the pyramid?
A rectangular pyramid with a base of 10 inches by 8 inches and height of 12 inches.
A. 120 inches cubed
B. 320 inches cubed
C. 480 inches cubed
D. 960 inches cubed
Answer:
b) i got it right in edg
Step-by-step explanation:
Credit card A is running a promotion where they will charge 0% interest for the first year, and then 0.8% interest compounded continuously after that. Credit card B has an interest rate of 0.7%, also compounded continuously. If you are going to make a $500 dollar purchase and plan to not make a single payment for 2.5 years, which credit card would you go with? Explain for answer in 1-2 sentences.
Answer:
Since the total amount you have to pay for the purchase on the credit card A is lower, then it's the best option.
Step-by-step explanation:
For credit card A the ammount will only be compounded after 1 year, so the total time elapsed for the laon is 1.5 years, while for the credit card B it'll be the full 2.5 years. To compute the total amount of a interest compounded continuously we must apply the formula:
M = C*e^(r*t)
Where M is the total amount, C is the initial amount, r is the interest rate and t is the time elapsed.
For credit card A:
M = 500*e^(0.008*1.5) = 506.03614
For credit card B:
M = 500*e^(0.007*2.5) = 508.8270
Since the total amount you have to pay for the purchase on the credit card A is lower, then it's the best option.
Answer:
hey
Step-by-step explanation:
what was your answer?
Shota invests $2000 in a certificate of deposit that earns 2% in interest each year.Write a function that gives the total v(t) in dollars of the investment t years from now
Answer:
The correct answer is v(t) = (principal × time × 0.02) if calculated simply and v(t) = Principal × [tex]( 1.02) ^ {time}[/tex] where v(t) is the interest after t years .
Step-by-step explanation:
Principal amount invested by Shota is $2000.
Interest is earned at 2% per year.
Time for which the principal is invested is t years.
Therefore let the total interest be v(t) dollars in t years.
Case 1: Simple Interest.
v(t) = (principal × time × [tex]\frac{r}{100}[/tex] ) = (2000 × t × 0.02) = 40t
Case 2: Compound Interest.
v(t) = Principal × [tex]( 1+ \frac{r}{100}) ^ {t}[/tex] - Principal = 2000 × [tex]( 1.02) ^ {t}[/tex] - 2000.
A car moves at a constant speed of 50 miles per hour. How long does it take the car to go 200 miles?
Answer: 4 hours
Step-by-step explanation: If you take 50 times 4 it will get you 200. Another way to look at it is the car is going 50 miles per hour, so in one hour the car has gone 50 miles, in two hours it’s gone 100, three hours it’s gone 150, so in four hours it’s gone 200 miles
Final answer:
To calculate how long it takes to travel 200 miles at a constant speed of 50 miles per hour, divide the distance by the speed. The car will take 4 hours to cover the distance.
Explanation:
To determine how long it takes a car moving at a constant speed to cover a certain distance, we use the formula time = distance \/ speed. In this case, the car is moving at a constant speed of 50 miles per hour and needs to cover a distance of 200 miles.
We can calculate the time it will take as follows:
Time = Distance \/ Speed
Time = 200 miles \/ 50 miles per hour
Time = 4 hours
Therefore, it will take the car 4 hours to travel 200 miles at a constant speed of 50 miles per hour.
A researcher selects two samples of equal size and computes a mean difference of 1.0 between the two sample means. If the pooled sample variance is 4.0, then what is the effect size using the estimated Cohen’s d formula?
Answer:
The Cohen's D is given by this formula:
[tex] D = \frac{\bar X_A -\bar X_B}{s_p}[/tex]
Where [tex] s_p[/tex] represent the deviation pooled and we know from the problem that:
[tex] s^2_p = 4[/tex] represent the pooled variance
So then the pooled deviation would be:
[tex] s_p = \sqrt{4}= 2[/tex]
And the difference of the two samples is [tex] \bar X_a -\bar X_b = 1[/tex], and replacing we got:
[tex] D = \frac{1}{2}= 0.5[/tex]
And since the value for D obtained is 0.5 we can consider this as a medium effect.
Step-by-step explanation:
Previous concepts
Cohen’s D is a an statistical measure in order to analyze effect size for a given condition compared to other. For example can be used if we can check if one method A has a better effect than another method B in a specific situation.
Solution to the problem
The Cohen's D is given by this formula:
[tex] D = \frac{\bar X_A -\bar X_B}{s_p}[/tex]
Where [tex] s_p[/tex] represent the deviation pooled and we know from the problem that:
[tex] s^2_p = 4[/tex] represent the pooled variance
So then the pooled deviation would be:
[tex] s_p = \sqrt{4}= 2[/tex]
And the difference of the two samples is [tex] \bar X_a -\bar X_b = 1[/tex], and replacing we got:
[tex] D = \frac{1}{2}= 0.5[/tex]
And since the value for D obtained is 0.5 we can consider this as a medium effect.
Katarina bought a package of 500 stickers. Each sheet in the package has 20 stickers.
25% of the stickers on each sheet are hearts. The remaining stickers are stars.
The correct options are: B and D. The true statements about stickers are: Katarina has 375 star stickers and 75% of the stickers are stars.
Let's analyze each statement given the information that 25% of the 500 stickers are hearts, and the remaining stickers are stars.
1. Total number of stickers: 500
2. Percentage of heart stickers: 25%
3. Percentage of star stickers: 100% - 25% = 75%
Now, let's calculate the actual numbers:
- Number of heart stickers:
[tex]\[ 25\% \text{ of } 500 = \frac{25}{100} \times 500 = 0.25 \times 500 = 125 \][/tex]
- Number of star stickers:
[tex]\[ 75\% \text{ of } 500 = \frac{75}{100} \times 500 = 0.75 \times 500 = 375 \][/tex]
Now, let's evaluate each statement:
A. Katarina has 100 heart stickers.
- False. Katarina has 125 heart stickers.
B. Katarina has 375 star stickers.
- True. Katarina has 375 star stickers.
C. The package contains 20 sheets of stickers.
- Not enough information is given to determine this. This statement is irrelevant without knowing how many stickers are on each sheet.
D. 75% of the stickers are stars.
- True. 75% of 500 stickers are stars.
E. The number of heart stickers is the same as the number of star stickers.
- False. The number of heart stickers (125) is not the same as the number of star stickers (375).
So, the true statements are:
B. Katarina has 375 star stickers.
D. 75% of the stickers are stars.
The complete question is:
Katarina bought a package of 500 stickers. 25% of the stickers are hearts. The remaining stickers are stars. Select all the statements that are true.
A.Katarina has 100 heart stickers.
B.Katarina has 375 star stickers.
C.The package contains 20 sheets of stickers
D.75% of the stickers are stars.
E.The number of heart stickers is the same as the number of star stickers.
On a coordinate plane, a parabola opens down with solid circles along the parabola at (negative 3, negative 5), (negative 2, 0), (negative 1, 3), (0, 4), (1, 3), (2, 0), (3, negative 5). Use the drop-down menus to identify the values of the parabola. Vertex = Domain = {x| } Range = {y| y ≤ }
Answer:
vertex: (0,4) // domain: x is a real number // Range: 4
Step-by-step explanation:
got a 100%
Answer:
C,D,C in that order
Step-by-step explanation:
In the figure below, AB is a diameter of circle P.
What is the arc measure of AC on circle P in degrees?
14
C
Answer:
The arc measure of ABC is 221°
Answer:
139 degrees
Step-by-step explanation:
Subtract 41 from 180. You will get 139 degrees. Arc AC is 139 degrees.
-Briannah-
Which of the equations below represents the relationship shown in the table?
Answer:
D
Step-by-step explanation:
just check at least two
Write a rational function f(x) such that f has vertical asymptotes at x = 3 and x = -1, no horizontal asymptote, and end behavior that can be modeled by y = 2x.
Answer:
[tex]f(x)=\frac{2x^3-4x^2-6x}{x^2-2x-3}[/tex]
Step-by-step explanation:
Roots of a denominator in a rational function gives to us the vertical asymptotes. Hence we can take the denominator as
[tex](x-3)(x+1)=x^2-2x-3[/tex]
if we want that the end behavior as y=2x we can choose a polynomial whose factors cancel out with the denominator. Thus
[tex]2x(x-3)(x+1)=2x^3-4x^2-6x[/tex]
Hence, the function is
[tex]f(x)=\frac{2x^3-4x^2-6x}{x^2-2x-3}[/tex]
Hope this helps!!
What should be done to solve the following equation?
c - 7 = 0
Add 7.
Subtract 0 from both sides.
Add 7 to both sides.
Subtract 7 from both sides.
Answer:
Add 7 to both sides
Step-by-step explanation:
c - 7 + 7 = 0 + 7
c = 7
Answer: subtract 5 b
Phil is buying a sandwich. He has the following choices. Bread: wheat (W), italian (I), baguette (B) Cheese: grated (G), sliced (S) Meat: chicken (C), turkey (T), fish (F), ham (H) If each sandwich consists of one type of bread, one type of cheese, and one type of meat, which best represents four of his possible sandwich choices?
Answer: c
Step-by-step explanation:
A can of tomato soup is 4 1
4
inches tall and has a diameter of 3 inches. The company that
makes the cans uses sheets of metal that are 1,000 in2
.
Completely answer the following questions. Show all work.
1. How many whole cans can the company make out of each sheet of metal?
2. Will there be any metal left over? If so, how much
the can of soup is 3 inch wide and 4 1/4in height
Answer:
1. 17 whole cans
2. Yes, 38.65 in2 of metal
Step-by-step explanation:
First we need to find the surface area of the can.
The base and the top of the can have a area of pi*r^2.
If the radius is half the diameter, we have r = 3/2 = 1.5 inches, so:
A1 = pi * 1.5^2 = 7.069 in2
The side of the can has a area of pi*d*h. If the diameter is 3 inches and the height is 4.5 inches, we have:
A2 = pi*3*4.5 = 42.412 in2
So the total area of the can is:
2*A1 + A2 = 56.55 in2
To know how many cans we can make with 1000 in2 of metal, we just need to divide the total metal for the surface area of each can:
number of cans = 1000 / 56.55 = 17.684 cans
We can make 17 cans, and the metal left over is 1000 - 17 * 56.55 = 38.65 in2
consider the function f(x)=x^2+2x-8
1) what are the x intercepts of the graph of the function?
2) what is the y intercepts of the graph of the function?
3) what is the equation of the axis of symmetry?
4) what is the vertex of the function?
5) graph the function
1) The x-intercepts of the function [tex]\( f(x) = x^2 + 2x - 8 \)[/tex]are [tex]\( x = -4 \)[/tex]and [tex]\( x = 2 \).[/tex]
2) The y-intercept of the function [tex]\( f(x) = x^2 + 2x - 8 \) is \( y = -8 \).[/tex]
3) The equation of the axis of symmetry is [tex]\( x = -1 \).[/tex]
4) The vertex of the function [tex]\( f(x) = x^2 + 2x - 8 \) is \( (-1, -9) \).[/tex]
5) The graph of the function is a parabola opening upwards with the vertex at [tex]\( (-1, -9) \).[/tex]
Explanation:1) To find the x-intercepts, set [tex]\( f(x) = 0 \)[/tex] and solve for x. The quadratic equation [tex]\( x^2 + 2x - 8 = 0 \)[/tex] factors into [tex]\( (x - 2)(x + 4) = 0 \),[/tex] yielding x-intercepts of [tex]\( x = -4 \)[/tex] and [tex]\( x = 2 \).[/tex]
2) To find the y-intercept, set \( x = 0 \) in the function. \( f(0) = 0^2 + 2(0) - 8 = -8 \), so the y-intercept is [tex]\( y = -8 \).[/tex]
3) The axis of symmetry for a quadratic function in the form [tex]\( f(x) = ax^2 + bx + c \)[/tex] is given by [tex]\( x = \frac{-b}{2a} \).[/tex] For [tex]\( f(x) = x^2 + 2x - 8 \)[/tex], the axis of symmetry is [tex]\( x = -1 \).[/tex]
4) The vertex of a quadratic function in the form [tex]\( f(x) = ax^2 + bx + c \) is located at \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \).[/tex]Substituting [tex]\( x = -1 \)[/tex] into the function, we find that the vertex is [tex]\( (-1, -9) \).[/tex]
5) The graph of the function is a parabola that opens upwards, consistent with the positive coefficient of the [tex]\( x^2 \)[/tex] term. The vertex at (-1, -9) is the lowest point on the graph, and the parabola extends upward indefinitely from there.
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A circular plate has circumference 22 inches. What is the area of this plate? Use 3.14 for pi.
IM MARKING BRAINLIEST!!
Answer:
A≈38.52 in²
Step-by-step explanation:
Answer:
Step-by-step explanation:
The diameter of a circle is 101010 units. What is the radius of the circle?
Answer:
50505 units
Step-by-step explanation:
The radius is the fixed distance from the center of a circle to any point on its circumference. The radius of a circle always equals half of its diameter, so to find the diameter, multiply the radius by two. ( 101010/ 2=50, 505 units)
Jasmine invests $2,658 in a retirement account with a fixed annual interest rate of 9% compounded continuously. What will the account be after 15 years
Answer:
$10,253.04
Step-by-step explanation:
You are going to want to use the continuous compound interest formula, which is shown below.
[tex]A = Pe^{rt}[/tex]
P = principal amount
r = interest rate (decimal)
t = time (years)
First, change 9% into a decimal:
9% -> [tex]\frac{9}{100}[/tex] -> 0.09
Next, plug the values into the equation:
[tex]A=2,658e^{0.09(15)}[/tex]
[tex]A=10,253.04[/tex]
The account will have $10,253.04
Kristin drinks 0.5 liters of orange juice with breakfast each day for 15 days. How many milliliters of orange juice does Kristin drink during the 15 days?
Answer:
she drank 7500 milliliters of juice
Step-by-step explanation:
In this question, we are asked to calculate the amount of juice in milliliters consumed by Kristin.
From the question, she drank 0.5 liters per day for 15 days. This means that the total amount she drank for the 15 days will be 0.5 * 15 = 7.5 liters
what we now need to do is to calculate the equivalent of this in milliliters.
To get this, we need to multiply the volume in liters by 1000. This is simply because 1000 milliliters make 1 liter
so that will be 7.5 * 1000 = 7500 milliliters of juice
Final answer:
To find out how much orange juice Kristin drinks over 15 days, convert her daily intake from liters to milliliters and multiply by the number of days. She drinks 7500 milliliters in total.
Explanation:
The question asks how many milliliters of orange juice Kristin drinks during 15 days if she drinks 0.5 liters each day. First, we need to convert liters to milliliters, knowing that 1 liter equals 1000 milliliters. Then, we multiply the daily amount of orange juice by the number of days.
Convert liters to milliliters: 0.5 liters = 500 milliliters (since 0.5 × 1000 = 500).
Multiply by the number of days: 500 milliliters/day × 15 days = 7500 milliliters.
Therefore, Kristin drinks 7500 milliliters of orange juice over 15 days.
What is P(z ≥-0.82)?
Answer:
79% C on edge
Answer:
The first one on edge is 80%
Step-by-step explanation:
the second one is 79%