Answers
Given:
a) 3 × 3 × 3 × 3 × 3
b) 4 × 4 × 4 × 5 × 5
c) 9 × 7 × 9 × 9 × 7 × 9
To find:
The index notation.
Solution:
a) Using multiplication rule of indices:
[tex]a^{n} \times a^{m}=a^{n+m}[/tex]
[tex]3\times3\times3\times3\times3=3^{1+1+1+1+1}[/tex]
[tex]=3^5[/tex]
Therefore, [tex]3\times3\times3\times3\times3=3^{5}[/tex]
b) Using multiplication rule of indices:
[tex]4\times4\times4\times5\times5=4^{1+1+1}5^{1+1}[/tex]
[tex]=4^35^2[/tex]
Therefore, [tex]4\times4\times4\times5\times5=4^{3}5^{2}[/tex]
c) Using multiplication rule of indices:
[tex]9\times7\times9\times 9\times7\times9=9^{1+1+1+1}7^{1+1}[/tex]
[tex]=9^47^2[/tex]
Therefore, [tex]9\times7\times9\times 9\times7\times9=9^{4}7^{2}[/tex]
Related Questions
Which of the following is equivalent to the complex number i^80
Answers
The equivalent to the complex number i^80 is 1
How to determine the equivalent?The complex number is given as:
i^80
In complex numbers:
i^4 = 1
So, we have:
i^80 = (i^4)^20
Substitute i^4 = 1
i^80 = (1)^20
Evaluate
i^80 = 1
Hence, the equivalent to the complex number i^80 is 1
Read more about complex numbers at:
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If you have 8 quarters and 9 dimes, what is the value of the
total amount in dollars?
Answers
Answer: $2.90
Step-by-step explanation:
Each quarter is worth 25 cents so we do 8x25 which is 200 and we do 9x10 which is 90 and when we add them up we get 290 cents which is 2.90 dollars
Answer:
$2.90
Step-by-step explanation:
8 times 25 equals 200 ($2)
9 times 10 equals 90 ($0.90)
Suppose you received $10 from your grandmother for your birthday. You spent $4 on snacks. Using addition how would you write an equation to represent this situation?
Answers
Answer:+10-4
Step-by-step explanation:
This would be the equation to represent this situation because you first got $10, then you spent $4 on snacks.
5. A salesman makes a salary of $350 per week. In addition, he makes 49
commission on his total sales. If he sells $1500, what was his total income
for the week? Remember...it's money.please write it that way. *
Answers
[tex]\text{We have to find the salesman's total salary for the week}\\\\\text{We know that he makes a base price of \$350 a week}\\\\\text{We also know he makes 4\% in commission from SALES}\\\\\text{From the given information, it says that he sold \$1500 worth of stuff}\\\\\text{Lets find his commission. To find this, we would multiply 1500 by 0.04:}\\\\1500*0.04=60\\\\\text{He makes \$60 in commission}\\\\[/tex]
[tex]\text{Now we need to find his total income for the week. To do this, add his}\\\text{salary and commission. Don't add how much he sells, he doesn't make}\\\text{money from that.}\\\\350+60=410\\\\\text{His income for the week was \$410}\\\\\boxed{\$410}[/tex]
Find the GCF for the following list.
60, 14, 21
The GCF is
. (Simplify your answer.)
Answers
Answer:
The GCF if 60, 14, 21 is 1
Omar and Caleb each had a repair made on their cars. The initial cost of each repair is $1,000. Omar and Caleb each have two coupons. Each of them uses both of his coupons toward the cost of the repair. One coupon is for $80 off the repair cost. The other coupon is for 15% off the repair cost. Omar and Caleb use their coupons in a different order, as shown below. •Omar uses the $80 off the repair cost coupon first. He then uses the 15% off the repair cost coupon on the remaining balance. •Caleb uses the 15% off the repair cost coupon first. He then uses the $80 off the repair cost coupon on the remaining balance. Who paid the least amount of money for his car repair and how much less did he pay? Show all work HELP PLEASE SO I WON'T FAIL THEN I won't GET A CARRR
Answers
Answer:
Caleb paid $12 less
Step-by-step explanation:
Omar1. $80 off
$1000 - $80 = $9202. 15% off
$920- 15% = $920 * 0.85 = $782Omar paid for repair: $782
Caleb1. 15% off
$1000 - 15% = $1000*0.85 = $8502. $80 off
$850 - $80 = $770Caleb paid for repair: $770
As per above:
$782 - 770 = $12Caleb paid $12 less than Omar for his car repair.
Final answer:
Omar and Caleb had car repairs costing $1,000. By utilizing coupons differently, Caleb paid $12 less than Omar for the repair.
Explanation:
Omar and Caleb each had a repair made on their cars costing $1,000 initially. Omar used the $80 coupon first and then the 15% coupon. Caleb used the 15% coupon first and then the $80 coupon.
Omar: $1,000 - $80 = $920 remaining, then 15% off: $920 - 0.15*$920 = $782
Caleb: $1,000 - 0.15*$1,000 = $850 remaining, then $80 off: $850 - $80 = $770
Caleb paid less by $12 compared to Omar for his car repair.
Recall that the scores in Mr. Young’s class had a mean of 78 and a standard deviation of 8. About what percent of students scored between 78% and 94%?
A. 47.5%
B. 34%
C. 13.5%
D. 68%
Answers
Answer:
B. 34%.
Step-by-step explanation:
94 - 78 = 16 which is 2 times the standard deviation from the mean.
For a normal distribution this is 34% of the total students.
In the diagram, angle abc is a right angle. Find the value of x
Show full working out pls ty
Answers
Answer:
x = 3.75
Step-by-step explanation:
ABC is a right angled triangle.
Therefore, by Pythagoras theorem:
[tex] {(10 - x)}^{2} = {x}^{2} + {5}^{2} \\ 100 - 20x + {x}^{2} = {x}^{2} + 25 \\ 100 - 20x = 25 \\ - 20x = 25 - 100 \\ - 20x = - 75 \\ x = \frac{ - 75}{ - 20} \\ \: \: \huge \red { \boxed{x = 3.75}}[/tex]
please help I mark brainliest
Answers
Answer:
graph a
Step-by-step explanation:
y has to be less than the line
postive slope
the only graph that has both is graph a
Given that a randomly chosen student participates in
band, what is the probability that the student also
participates in track?
Answers
Answer:
9/33
Step-by-step explanation:
Answer:
9/33
Step-by-step explanation:
Solve these problems:
A) 4y + 3 = 19
B) (1/2)n-3=5
Answers
Step-by-step explanation:
a 4y=19-3
4y=16
y=16/4
y=4
b. 1/2n=5+3
1/2n=8
n=8×2 as 1/2 become on right so it become 2
n=16
Step-by-step explanation:
[tex]4y + 3 = 19 \\ 4y = 19 - 3 \\ 4y = 16 \\ \frac{4y}{4} = \frac{16}{4} \\ y = 4[/tex]
[tex]( \frac{1}{2} )n - 3 = 5 \\ \frac{n}{2 } - 3 = 5 \\ \frac{n}{2} = 5 + 3 \\ 2 \times \frac{n}{2} = 8 \times 2 \\ n = 16[/tex]
Find the area of the figure.
Answers
Answer:
98 ft ^2
Step-by-step explanation:
big triangle: (find the area of the space between)
bh/2
(14 x 14) /2 = 98
square: 14 x 14 = 196
196 - 98 = 98.
can someone please help? will give brainlest!
Answers
Answer:
Step-by-step explanation:
Rounding to nearest tenth:
i) if number in 100th place is 5,6,7,8 or 9, then add 1 to number in the tenth place and after adding remove all the digits right to it.
EG: 4.567 = 4.6
ii) if number in 100th place is 0,1,2,3 or 4, then write down number in the tenth place as it is and then remove all the digits right to it.
Eg: 4.523 = 4.5
a) 0.32 = 0.3 (b) 3.87 = 3.9 (c)0.709 = 0.7
d) 12.75 = 12.8 (d)12.745 = 12.8 e) 645.059 = 645.1
Using ur knowledge of fractions and the second power law, explain
Answers
Answer:
1
Step-by-step explanation:
according to the law of exponents a0 = 1. Similarly b0=1
Any number with an exponent 0 will be a 1.
ASAP!!!!! !!
I need help, it’s urgent please!!!
Answers
Answer: A
Step-by-step explanation: Because if an ecosystem has a high biodiversity, then it’s most likely to survive things like an invasive species for example
What is the equation of a line with a -y-intercept of -5 and a slope of 8.
a. y=8x+5
b .y=8x-5
c. y=-5x+8
d. y=-5x-8
Answers
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 8 and c = - 5, thus
y = 8x - 5 → B
Answer:
B
Step-by-step explanation:
y = mx + b
m represents slope and b is the y intercept
so 8x is mx in this equation and -5 is b
Explain step by step how you factor:
6x^2+ 11x + 3
Answers
Answer:
6x^2+ 11x + 3
= (3x +1) (2x +3)
Step-by-step explanation:
Math Term Definition. Factor. To factor a number means to break it up into numbers that can be multiplied together to get the original number. EXAMPLES: 6 = 3 x 2 so, factors of 6 are 3 and 2 9 = 3 x 3 so, factors of 9 are 3 and 3 Sometimes, numbers can be factored into different combinations.
if a circle has the radius 50cm what is the area
Answers
Step-by-step explanation:
I found it on Google, hopefully it's right
Sales Tax in the state of Mathland is 8.5%. After buying school supplies, your total was $81.42, before tax. How much do you end up paying including tax? (SHOW WORK.)
A: $6.92
B: $74.50
C: $88.34
Answers
Answer:
A
Step-by-step explanation:
8.5% of 81.42
8.5 81.42 692.07
------- X ---------- = -------------
100 1 100
divide 692.07/100 which gives you 6.9207
if you round it to the nearest hundredth you get 6.92
A patient takes vitamin pills. Each day he must have at least 420 IU of vitamin A, 5 mg of vitamin
B1, and 60 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin A, 1
mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of
vitamin B7, and 15 mg of vitamin C. Pill 1 costs 30¢, and pill 2 costs 60¢. Complete parts a and b
below.
Answers
Final Answer:
Pill 1 is more cost-effective, meeting or exceeding daily requirements for vitamins A, B1, and C with lower cost (30¢) compared to pill 2 (60¢). It provides 480 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C with fewer pills, making it the optimal choice.
Step-by-step explanation:
The patient's daily requirements are 420 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C. Let's evaluate the contribution of each pill to these requirements.
Pill 1 provides 120 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C.
Pill 2 provides 60 IU of vitamin A, 1 mg of vitamin B7, and 15 mg of vitamin C.
To meet the vitamin A requirement, the patient can take 4 pills of type 1 (4 * 120 IU = 480 IU), while it would take 7 pills of type 2 (7 * 60 IU = 420 IU). So, pill 1 is more efficient for meeting the vitamin A requirement.
For vitamin B1, both pills contribute 1 mg each, and since the requirement is 5 mg, the patient needs to take 5 pills of either type.
For vitamin C, the patient needs 60 mg. Pill 1 provides 10 mg per pill, so 6 pills are needed (6 * 10 mg = 60 mg). Pill 2 provides 15 mg per pill, so 4 pills are needed (4 * 15 mg = 60 mg).
Considering the cost, pill 1 costs 30¢, and pill 2 costs 60¢. Since both pills are equally effective in meeting the B1 requirement and pill 1 is more efficient for vitamin A and equally efficient for vitamin C, the patient should choose pill 1 due to its lower cost.
six more than the product of four times the difference between x and 3
When x=8
Answers
Answer:
26
Step-by-step explanation:
Six more than four times the difference between x and 3
6+4(x-3)
And x is said to be 8
So let's substitute
6+4(8-3)
6+4(5)
6+20
26
So the final answer is 26
Answer: 26
Step-by-step explanation:
A cone has a volume of 75 pie and a height of 9 cm.
What is the cone's diameter?
Enter your answer in the box.
Answers
Answer:
Volume of the cone is given by
[tex]V = \frac{\pi {r}^{2}h }{3} = 75\pi[/tex]
[tex] = > \frac{\pi {r}^{2}9 }{3} = 75\pi[/tex]
[tex] = > {r}^{2} = \frac{75\pi}{\pi \times 3} = 25[/tex]
[tex] = > r = \sqrt{25} = 5[/tex]
Diameter of the cone = 2×5 cm = 10 cm
Use the Pythagorean theorem to find a whole number estimate of the length of the unknown side of the right triangle. The length of the unknown side of the triangle is approximately cm.
Answers
Answer:
12 cm
Step-by-step explanation:
Leg of one side = 5 cm
Hypotenuse = 13cm
According to the theorem,
A^2 + B^2 = C^2
5^2 + B^2 = 13^2
25 + B^2 = 169
Subtract 25 form both sides,
B^2 = 169 - 25
B^2 = 144
B = sqrt( 144 )
B = 12
Done!
11.
Paula designed a three-dimensional scale model of a department store. The volume of
the scale model was 35 cubic feet. The ratio of the dimensions of the model to the
dimensions of the store was 1:20. Determine the volume of the actual department
store that Paula planned to build.
Answers
Answer:
V = 280000 cubic meters
Step-by-step explanation: Given that the volume of the scale model was 35 cubic feet. The ratio of the dimensions of the model to the
dimensions of the store was 1:20.
Let the volume of the actual department store that Paula planned to build be V. Then
35/V = (1/20)^3
35/V = 1/8000
Cross multiply
V = 8000 × 35
V = 280000 cubic meters
Answer: The volume of the actual department store is 280,000 cubic feet
Step-by-step explanation: The question has provided the volume of the model built by Paula, and that is 35 cubic feet. The volume of a three sided solid is given as;
Volume = L x W x H
This can also be conveniently expressed as;
Volume = L³ (which implies that the solid has all sides measuring the same for simplicity's sake)
However, given that the ratio of the model to that of the actual store is 1:20, we simply use the given ratio to substitute for the value of the side of the actual store, hence we now have dimension as;
Volume = L³
35 = L³
Add the cube root to both sides of the equation
∛35 = L
The dimension of the actual store which is an enlargement by a ratio of 1:20 now becomes;
Actual store = 20 x L
Actual store = 20 x ∛35
Actual store = 20 x 3.27106631018859
Actual store = 65.42132620377179
Therefore the volume of the actual store is given as;
Volume = L³
Volume = 65.42132620377179³
Volume = 280000
Therefore the volume of the actual store is 280,000 cubic feet
what is the quotient for -20/ -10
Answers
Answer:
2
Step-by-step explanation:
To find the quotient you just divide the numerator (-20) by the denominator (-10)
-20 / -10 = 2
(The negatives cancel out!)
Find the median, lower quartile, and upper quartile for the set of data. 4, 1, 11, 8, 2, 9, 7, 6, 10, 5 Median = Lower quartile = Upper quartile =
Answers
Answer:
the answer is 6.5, 4, and 9.
Step-by-step explanation:
The median is 6.5.
The lower quartile is 4.
The upper quartile is 9.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
To find the median, we need to first put the data in order:
1, 2, 4, 5, 6, 7, 8, 9, 10, 11
There are 10 numbers in the data set, so the median is the average of the two middle numbers:
Median = (6 + 7)/2 = 6.5
To find the lower quartile, we need to find the median of the lower half of the data set: 1, 2, 4, 5, 6
There are 5 numbers in the lower half, so the median is the middle number:
Lower quartile = 4
To find the upper quartile, we need to find the median of the upper half of the data set: 7, 8, 9, 10, 11
There are 5 numbers in the upper half, so the median is the middle number:
Upper quartile = 9
Thus,
The median, lower quartile, and upper quartile are 6.5, 4, and 9.
Learn more about median here:
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How much would $300 invested at 7% interest compounded continuously be
worth after 4 years? Round your answer to the nearest cent.
A. $306.53
B. $384.00
C. $396.93
D. $347.09
Answers
Answer:
Hi there
The formula of compounded continuously is
A=pe^rt
A future value?
P present value 300
R interest rate 0.07
T time 4 years
E constant
So
A=300×e^(0.07×4)
A=396.932 round your answer to get
A=396.93
Good luck!
Step-by-step explanation:
Use pythagorean theorem to solve the questions
Answers
9^2 + b^2 = 12^2
81 +b^2 = 144
-81 (subtract 81 from both sides of the equation)
b^2 = 63
b = square root of 63
A screen door spring has a spring constant of 188 N/m, and stretches 0.292 m when the door is opened. What force does it exert?
(Unit = N)
Answers
Answer:
The answer is 54.896N
Step-by-step explanation:
From Hooke's law,
Force = spring constant x extension
i.e
F = k x e
F = 188N/m x 0.292m
F = 54.896N
Answer:
54.846N
Step-by-step explanation:
Force = ?
Spring constant (K) = 188N/m
Spring stretch (x) = 0.292m
Force acting on a spring = spring constant * spring stretch
Force = 188 * 0.292
Force = 54.896N
The force acting on the spring is 54.896N
what’s the missing angle
Answers
Answer:
86°
Step-by-step explanation:
The total of all of the angles needs to add up to 180 degrees.
45 + 49 = 94
180 - 94 = 86 degrees
Answer:
86
Step-by-step explanation: