Answer: -1/2
Step-by-step explanation:
3^2x3^3 write on exponential form
The exponential form of the given information 3^2x3^3 is 3⁵.
What are exponential forms?The exponential form is a convenient way of expressing or writing repeated multiplication expressions concerning their bases and power.
From the information given, the given expression can be written in exponential form by using the law of indices.
= 3^2x3^3
[tex]\mathbf{=3^{2+3}}[/tex]
[tex]\mathbf{=3^{5}}[/tex]
Therefore, we can conclude that the exponential form of the given expression is 3⁵.
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Please Solve the equation by factoring: x2+2x−15=0
Answer:
x = 3, -5
Step-by-step explanation:
I just know
Answer:
x= -5
x=3
Step-by-step explanation:
You are factoring here. The standard form of an equation is Ax² + Bx + C.
The 2 factors must multiple together to be C, but add together to be B. The easiest way to do this is to factor C.
C is -15. Factoring this, we find the only factors of 15 that will add together to be 2 are 5 & -3.
Therefore, the factors are (x+5) and (x-3). If you set each of these factor pairs to 0 and solve, the answers are:
x+5=0
x = -5
x-3 = 0
x=3
Emily purchased a bond valued at $20,000 for highway construction for $10,460. If the bond pays 7.2%
annual interest compounded monthly, how long must she hold it until it reaches its full face value?
...
Answer:
26.556192
Step-by-step explanation:
7.2×10460÷100
20000÷(7.2×10460÷100)
What is the difference of the fractions below? 10x/3-2x/3 2x 13 3 A. 8 B. 8x C. 8x/3 D. 8/3x
The difference of the fractions is 8x/3. Option C is correct.
Given the fraction is 10x/3-2x/3.
When subtracting fractions with the same denominator, just subtract the numerators of the fractions. To find the difference between equal fractions, we subtract the smaller numerator from the larger numerator.
The given expression is 10x/3-2x/3.
Here the denominator in both the fractions are same so, we will take the LCM, we get
10x/3-2x/3=(10x-2x)/3
Now, we will simplify the numerator by subtracting the smaller term from larger, we get
10x/3-2x/3=8x/3
Hence, the difference of the fractions 10x/3-2x/3 is 8x/3 and the correct option is C.
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Which of the following best describes both the domain and range of the distance function d=55t
Answer: All real numbers
Step-by-step explanation:
The domain and range of all linear functions is the set of real numbers.
Find the surface area of the square pyramid below if the length of the sides of the base are 10 cm, and the slant height is 15 cm.
The surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
Surface areaSurface area of the square pyramid
= a² + 2a√a²/4 + h²
where,
a = sides of base = 10 cmh = slant height = 15 cmSurface area of the square pyramid
= a² + 2a√a²/4 + h²
= 10² + 2(10)√10²/4 + 15²
= 100 + 20√100/4 + 225
= 100 + 20√25 + 225
= 100 + 20√250
= 100 + 20(15.81)
= 100 + 316.2
= 416.2 cm²
Therefore, the surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
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Evaluate 2a x 3 + b, if a = 5 and b = 1.
Answer:
31
Step-by-step explanation:
replace the values of a and b in the given term
=2a x 3 + b
2(5) x 3 + (1)
2x5 x 3 + 1
10 x 3 + 1
30 + 1
31
Which is the graph of the function f(x) = 1/2x^2+2x-6?
See the graph in the attached image.
Practise the Skill
A container holds 4 yellow balls, 3 blue balls and 1 red ball.
Luke chooses a ball at random.
What is the probability that Luke will pick a blue ball?
Give your answer as a fraction in its lowest terms.
The probability that Luke will pick a blue ball is 3/8.
We have,
To find the probability of Luke picking a blue ball, we need to determine the total number of balls in the container and the number of blue balls.
Total number of balls
= 4 (yellow balls) + 3 (blue balls) + 1 (red ball)
= 8 balls
Number of blue balls = 3
Now, the probability (P) of picking a blue ball is given by:
P = Number of favorable outcomes (picking a blue ball) / Total number of possible outcomes
P = 3 (number of blue balls) / 8 (total number of balls)
Now, we can simplify the fraction to its lowest terms:
P = 3/8
Thus,
The probability that Luke will pick a blue ball is 3/8.
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There are 18 apple candies and 12 cherry candies mixed in a bag. If one candy is chosen from that bad, the odds of picking an apple candy are:
A: 1 out of 18
B: 2 out of 5
C: 3 out of 5
D: 3 out of 8
Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
The dimensions of the length and width are 25 meters and 12. 5 meters respectively.
How to determine the valuesArea of a rectangle
area of rectangle = l × w
where
l = length
w = width
Note that,
Perimeter = 2w+ l
50 = 2w + l
l = 50 - 2w
Hence,
area = w(50 - 2w)
288 = 50w - 2w²
-2w² + 50w - 288 = 0
-w² + 25w - 144 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1
b = 25
w = - 25 / 2 × -1
w = 12.5 meters
Then, we have that
l = 50 - 2w
Substitute the value of w
l = 50 - 2(12.5)
l = 50 - 25
I = 25 meters
Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.
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The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard deviation () of 0.5 hours.
What is the probability that a randomly selected cyclist will take at least 2.45 hours to complete the race?
Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 2.5, \sigma = 0.5[/tex]
The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is one subtracted by the p-value of Z when X = 2.45, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]
Z = -0.1
Z = -0.1 has a p-value of 0.4602.
1 - 0.4602 = 0.5398.
0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
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Planes A and B intersect.
n
772
W
k
Mark this and return
V
19
Z
X
2
Which describes the intersection of line m and line nº
O point W
point X
point Y
O point Z
The point that describes the intersection of line m and line n is; Point W
How to interpret Intersection of Planes?
Intersection of the two lines is defined as the point where the two lines cross or meet each other.
It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.
From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.
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The tomato plants in Ms. Lang's
garden grow 2 inches every 3 days. How much will they grow in 15 days?
Answer:
10 inches
Step-by-step explanation:
15 days/3 days =5
5 x 2 =10
What is the following product 3 root 24 • 3 root 45
Answer:
54sqrt(30)
Step-by-step explanation:
3sqrt(24) can be simplified to 6sqrt(6) as 24 can be written as 4 * 6 and 4 is a perfect square
3sqrt(45) can also be written as 9sqrt(5) as 45 can be written as 5 * 9 and 6 is a perfect square
you can multiply 6sqrt(6) * 9sqrt(5) as though the square roots were variables
so
54sqrt(30)
this is your final answer
the rounded answer is 295.770181
If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually. This can be obtained by using formulas for simple interest and compound interest.
What is the formulas of simple interest and compound interest?Simple interestA = P(1 +Rt/100) , P = principle amount ,R = rate of interest, t = time(in years)
Compound interest (annually)A = P(1 + R/100)^t , P = principal amount, R = rate of interest, t = time(in years)
What is the value of investment?
Given that,
P = $11,000 , R = 8%, t = 25 years
8% simple interestA = P(1 +Rt/100) = [tex]11000(1+\frac{(8)(25)}{100} )[/tex] = $33,000
8% compounded annuallyA = P(1 + R/100)^t = [tex]11000(1+\frac{8}{100} )^{25}[/tex] = [tex]11000(1.08 )^{25}[/tex] = $75,333.23
Hence If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
(a) 8% simple interest
(b) 8% compounded annually
In ΔOPQ, m∠O = 107° and m∠P = 28°. Which statement about the sides of ΔOPQ must be true?
QO > OP > PQ.
QO > PQ > OP.
PQ > OP > QO.
OP > QO > PQ.
PQ > QO > OP.
OP > PQ > QO.
Answer:
QO < OP < QP
Step-by-step explanation:
The third angle, angle Q, must measure 45° since angles in a triangle add to 180°.
So, OQ < OP < QP.
Answer:
PQ>OP>QO
Greater than symbol goes from largest to smallest
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Please help
Answer: (-2,2)
Step-by-step explanation:
The solution to a system of equations represented graphically is the point where the graphs intersect.
I am odd I am less than 40 both of my digits are perfect squares t-u=0
Answer:
19 or 14
Step-by-step explanation:
Since the number is odd you can disqualify all even numbers up to 40 including 0.
Next since this number has 2 digits you can take out all 1 digit numbers.
After that, find perfect squares that also are 1 digit each.
Lastly merge the combination of the numbers as each digit on each sides in such a way that the result is less than 40.
(2^x+y , 3^x-y )= (16,9) find the value of x and y
Answer:
x=3,y=1
Step-by-step explanation:
2^x+y=16,3^x-y=9
16=2^4,9=3^2
x+y=4,x-y=2 add both
2x=6,x=3
3-y=2,y=1
(07.06) There are currently 4 people signed up to play on a baseball team. The team must have at least 9 players.
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Number line with closed circle on 5 and shading to the left
Number line with closed circle on 5 and shading to the right.
Number line with open circle on 5 and shading to the left.
Number line with open circle on 5 and shading to the right.
A graph which includes the possible values for number of people who can still sign up for the team is: B. number line with closed circle on 5 and shading to the right.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.
Let the number of people who can still sign up for the team be represented by x. Thus, the inequality is given by:
x + 4 ≥ 9
x ≥ 9 - 4
x ≥ 5.
This ultimately implies that, there could be five (5) or more people that can still sign up for the team and a graph which includes these possible values is a number line with closed circle on five (5) and shading to the right because it can get larger.
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15) Mr. and Mrs. Rupe and their 4 sons are taking a 2500 mile camping trip across country. They plan to spend $120 for campsites per
day. The camper rental fee is $65 a day. While pulling the camper their car has a fuel economy of 8 miles per gallon. They estimate $85
per day for food for the 5-day trip. If gasoline is $1.92 per gallon how much will their trip cost?
O a.) $1950
Ob.) $1850
Oc.) $2950
Od.) $1750
Answer:
A $1950
Step-by-step explanation:
Food, camper rental and camp site will cost 1350
(120 + 65 + 85)5 = 1350
The trip is 2500 and the car gets 8 miles per gallon 2500/8 = 31.5. The will need to buy 31.5 gallons of gas at 1.92 a gallon or $600 (31.5 x 1.92).
When we add the cost of gas to the other costs, we get a total of 1950 (1350 + 600)
14) Write the scientific notation.
12 million
Answer:
1.2 × 107 this is the sciencetific notation for 12 million
..
Explain the difference between using area and volume with 2-D and 3-D figures.
The difference between Area and Volume lies in the fact that the former relates to plane shapes while the latter takes the concept of solid shapes into account.
What is the difference between Area and Volume?The distinctive characteristic of area is the space occupied by a two-dimensional, 2D flat object in a plane while Volume on the other hand is defined as the space covered by a three-dimensional, solid object. The area is quantised in square units while the volume is quantised in cubic units.
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Which list below shows the fractions in order from greatest to least?
A. 3/6, 4/9, 3/7, 3/10
B. 3/10, 3/7, 4/9, 3/6
C. 3/10, 4/9, 3/7, 3/6
D. 3/6, 4/7, 4/9, 3/10
Answer:
Step-by-step explanation:
Pamela is 9 years younger than Jiri and the sum of their ages is 41 what is jiri's age
Answer:
Jiri is 25 years old.
Step-by-step explanation:
1)Pamela =Jiri-9 ( Pamela is 9 years younger than Jiri)
2)Pamela +Jiri=41
Substitute equation 1 into equation 2
(J-9)+J= 41
2J-9=41
Add 9 to both sides:
2J=41+9
Divide by 2:
2J=50
J=25
the required Jiri's age is 25 years.
Pamela is 9 years younger than Jiri and the sum of their ages is 41. What is Jiri's age is to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Pamela and Jiri is x and y respectively
Pamela is 9 years younger than Jiri. so,
y = x + 9 - - - - (1)
the sum of their ages is 41
x + y = 41 - - - - (2)
From equation 1 put y in equation 2
x + x + 9 = 41
2x + 9 = 41
2x = 41 - 9
2x = 32
x = 32/2
x = 16
Now put this x =16 in equation 1
y = 16 + 9
y = 25
Thus, the required Jiri age is 25 years
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This is so confusing please help asap !
An ice chest contains 9 cans of apple juice6 cans of grape juice5 cans of orange juiceand 4 cans of pineapple juice Suppose that you reach the container and randomly select three cans in successionFind the probability of selecting no grape juice Select one 243 506 6 17/45; c * 5/506; d * 102/253
Answer:
243/506
Step-by-step explanation:
There are 24 total juice boxes.
18 of them are not grape
You have an 18/24 chance of picking not grape juice
The second time, 1 is removed, then another is removed. This creates:
(18/24)*(18/23)*(18/22) = 243/506
Write the equation of the line.
(Check image)
Options:
a. y = -2/3x + 4
b. y = 2/3x + 4
c. y = 3/2x + 4
d. y = -3/2x + 4
please show step by step
A farmer harvests 70 apples and 98 peaches. They want to make baskets that have both apples and peaches to sell at the market. Each basket should contain the same combinations of fruit. They want to sell all the apples and peaches and as many baskets as possible. they can use the greatest common factor to help them divide up the fruit.
This means the farm can make x baskets of apples and y peaches.
Farmer will made 14 basket each of 5 apple and 7 peaches.
what is greatest common factor?
Greatest common factor (GCF) is largest common factor in the given number.
first find common factor of numbers 70 and 98
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
farmer will made 14 basket each of 5 apple and 7 peaches.
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The farmer will make 14 baskets containing each of 5 apples and 7 peaches.
How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?Given:
A farmer harvests 70 apples and 98 peaches.They want to make baskets that have both apples and peaches to sell at the market.Each basket should contain the same combinations of fruit. They want to sell all the apples and peaches and as many baskets as possible.Find:
How many baskets can the farm make having x apples and y peaches in the baskets?Solution:
So, for solving this kind of question first we have to find the greatest common factor, we get;
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
So, the farmer will make 14 baskets each of 5 apples and 7 peaches.
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