The exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
What is exponential expression?
Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.
Applying the laws of indices,
The expression 8^3 can be written as,
8 x 8 x 8 = (2^3) x (2^3) x (2^3)
= 2^(3+3+3) ...{If a^m x a^n then a^(m+n) }
8 x 8 x 8 = 2^9
Therefore, the exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
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Sandi randomly selects a single bill from an envelope containing 8 ones, 5 fives, 4 tens, and 3 twenties. Whatis the expected value of the money she selects?expected value =
the formula to get the expected value is
[tex]E(x)=\sum ^n_{i\mathop=1}x_if(x_i)[/tex]So, first we calculate teh probabilities. We have 20 bills in total. so we divide the quantity of bills of each value by the total:
we have 8 ones: 8/20= 2/5
5 fives: 5/20=1/4
4 tens: 4/20= 1/5
3 twenties = 3/20
now, we multiply each value with te probabilitiy of picking it and add all
[tex]E=\text{ 1}\cdot\frac{2}{5}+5\cdot\frac{1}{4}+10\cdot\frac{1}{5}+3\cdot\frac{3}{20}=\text{ 4.1}[/tex]the expected value is 4.1
What is a degree of a monomial and how do you find it? Like for example, how do you find the degree of the monomial x^2?
The degree of a monomial is the power of the variable in the monomial
What is a degree of a monomial?
The degree of a monomial is defined as the highest power of the variable term in the monomial
How to find the degree of a monomial?As a general rule, a monomial has only one term
An instance of a monomial is
ax^n
Using the definition above, the degree of the monomial is n
Simlarly, the degree of x^2 is 2
This is because 2 is the power of the variable term
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Why are there two possible solutions to the equation, X2 = 100?
Answer:
100 is perfect square
Step-by-step explanation:
in x² =100, we have x×x=100 and x could be ±10 since both 10² and (-10)² is equal to 100
A family buys a studio apartment for 200,000 . They pay a down payment of 50000
Answer:
A 20% B. 45%
Step-by-step explanation:
A 40,000/200000=.2 0r 20%
b. 90,000/200000=.45 or 45%
4x^2-5x-1. find the roots
Answer:
Please comment if it is wrong.
On what day does frank first get charged an overdraft fee? a. wednesday b. thursday c. friday d. saturday
Frank first get charged an overdraft fee on Wednesday
Frank has $66.50 in his account as of Sunday.
He made a debit of $60.33 on Monday (66.50 - 60.33), leaving him with a balance of $6.17. He added $80.75 to the account on that same Monday (6.17 plus 80.75). He has $86.92 left over as of Monday.
Frank had a balance of $86.92 on Tuesday when he made a $54.45 debit (86.92 - 54.45). The remaining balance is $32.47.
Frank had a balance of $32.47 at the beginning of the day on Wednesday. He subsequently made withdraw of $49.20. debit(32.47 - 49.20). Frank has overdrawn and will be assessed an overdraft fee following the debit because his balance is -$16.73. Frank still has a negative balance even after making a deposit of $15.
Therefore, Frank was therefore assessed an overdraft fee on Wednesday.
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A student simplifies 5(x+3) - 3x by distributing and combining all the terms.
1. 5(x+3)-3x This is what is given
2. 5x +15-3x After applying the Distributive Property
3. 2x+15
Adding Like Terms
4. 17x
Combining non like terms.
Which step contains the error?
O Step 4
O Step 1
O Step 2
Step 3
Answer:
Step 4
Step-by-step explanation:
You cannot combine non-like terms like 2x and 15
They have to be left as is
Steps would be:
2. 5x +15-3x → Distributive property
3. 2x+15 → Combining like terms
And that's it. You cannot go any further
In 2022, a company made a profit of $1.38 million. That amount is $2.54 million more than the profit from 2021.
What is the profit from 2021? Write & solve an Algebraic Equation.
Answer: 6x+2xz*52-35^5=
Step-by-step explanation: rs:p=4436x
Answer: The profit from 2021 = $ -1.16 Million ($1.16 Million loss)
Step-by-step explanation:
Profit for 2022 = $ 1.38 Million
Profit for 2021 = Profit for 2022 - $ 2.54 Million
Algebraic equation:
p2021 = p2022 -$ 2.54 Million
p2021 = $ 1.38 Million - $ 2.54 Million
p2021 = $ -1.16 Million
3. For the following function, evaluate 2f(-2), *
f(x) = -2x²-x+3
Answer: 26
Step-by-step explanation:
[tex]f(-2)=-2(-2)^2 -(-2)+3=13\\\\2f(-2)=2(13)=26[/tex]
Can you help me pls with the answers
The remainder when 14 is divided by 3 is 2
What is remainder?
When we divide a number by another number if at the end if we have a number less than quotient and we can not divide further we say that the remaining number is remainder.
We are given a number as 14 and we divide 14 by 3
And on dividing 14 by 3 we get the quotient as 4 and remainder as 2.
Hence the remainder we get on dividing 14 by 3 is 2.
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Please helppp as fast as possible
FIND THE DOMAIN & RANGE OF THE FUNCTION
g(x)=|x + 4|
Please helppp as fast as possible
THE DOMAIN & RANGE OF THE FUNCTION g(x)=|x + 4| is
Domain: [tex]$(-\infty, \infty),\{x \mid x \in \mathbb{R}\}$[/tex]Range: [tex]$[0, \infty),\{y \mid y \geq 0\}$[/tex]This is further explained below.
What is the domain?Generally, The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
[tex](-\infty, \infty)[/tex]
Set-Builder Notation:
[tex]$\{x \mid x \in \mathbb{R}\}$[/tex]
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
[tex]$[0, \infty)$[/tex]
Set-Builder Notation:
[tex]$\{y \mid y \geq 0\}$[/tex]
Determine the domain and range.
Domain: [tex]$(-\infty, \infty),\{x \mid x \in \mathbb{R}\}$[/tex]
Range: [tex]$[0, \infty),\{y \mid y \geq 0\}$[/tex]
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I NEED HELP WITH THIS ASAP!!!! The following diagram describes the mixture's volume of blue and red paint. What is the ratio of blue color to real paint in the mixture?
The ratio of blue color to red paint in the mixture is 5 :3.
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of one value compared to the frequency of another value. The sign that is used to measure ratio is :.
In order to determine the ratio, count the number of blue tiles and the number of red tiles.
Number of blue tiles = 10
Number of red tiles = 6
The ratio of blue to red is 10 : 6. When expressed in its simplest form, it is 5 : 3.
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a force of 4 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 1.1 feet beyond its natural length?
Using the spring's force we know that 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
What does a spring's force mean?When a spring is in its equilibrium position, it applies a force F = -kx in that direction. A spring's force works as a restoring force, bringing the spring back to its equilibrium length.So, F is the 4 lb force required to maintain the spring's stretched position.
The spring has a 0.2-foot stretch, and its spring constant is k.Applying the equation F = k x 4 = k (0.2) k = 80 lb/ft.U is the effort put in to expand the spring, where x' is equal to 1.1 feet.The labor of extending a spring is denoted by the formula:
U = (0.5) k x'2So, calculate:
U = (0.5). (80). (1.1)² U = 48.4 lb-ftTherefore, 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
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HELP ME PLEASE ANY HELP WILL BE APPRECIATED
Answer:
a) Yes, the graph is proportional. It is linear and it goes through the point (0,0)
b) No shells cost no dollars
c) 3 shells cost 1.20
Step-by-step explanation:
To graph this, you only need 2 points. You have the points (0,0). You can put a point at (0,0) and at the point ( (3, 1.20) and then draw a line through those 2 points.
in a certain school district in a large metropolitan area, the sat scores over that past five years are normally distributed with a mean of 1468. furthermore, p 20 p20 is 1216. what is the p 98 p98 score for this population?
Using the normal distribution, the 98th percentile of the distribution of scores is of 2084.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean of the scores is given as follows:
[tex]\mu = 1468´[/tex]
The 20th percentile is of 1216, meaning that when X = 1216, Z = -0.84, hence the standard deviation is calculated as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{1216 - 1468}{\sigma}[/tex]
[tex]0.84\sigma = 252[/tex]
[tex]\sigma = \frac{252}{0.84}[/tex]
[tex]\sigma = 300[/tex]
The 98th percentile is X when Z = 2.054, hence it is calculated as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
2.054 = (X - 1468)/300
X - 1468 = 300 x 2.054
X = 2084.
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find M angle one and M angle to justify your answers
Answer:
Step-by-step explanation:
13.
m1 is 120 because angle 120 and angle 1 are tranversal angle
So now we know that angles m1 and m2 are vertically opposite angle
Then m2 = 120
m1 = 120
m2 = 120
14.
angle 1 and 105 have the sum of 180 because they are Interior angles on the same side of the transversal
So angle 1 equals 180-105=75
angle 2 and angle 1 are on a line so the sum of the 2 angles are 180
So: 180 - 75 = 105
m1 = 105
m2 = 75
46 x 2 in standard algorithm
Answer:
92
Step-by-step explanation:
1
46
x 2
92
Suppose we are buying beans and rice to feed a large gathering of people, and we plan to spend $120 on the two ingredients. Beans cost $2 a pound and rice costs $0.50 a pound.
If x represents pounds of beans and y pounds of rice, the equation 22 + 0.50y = 120 can represent the constraints in this situation.
The line below shows the graph of this equation (ignore the points not on the line).
Please help me I would appreciate it so much
The true statements about the constraints in this situation are:
If we buy 30 pounds of beans we can buy with 120 pounds of rice.If we buy no beans we can buy 240 pounds of rice.If we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.How to determine the true statements?In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:
2x + 0.50y = 120
Where:
x represents pounds of beans.y represents pounds of rice.When x = 40 and y = 60, we have:
2x + 0.50y = 120
2(40) + 0.50(60) = 120
80 + 30 = 120
110 ≠ 120 (Not a solution).
When x = 30 and y = 120, we have:
2x + 0.50y = 120
2(30) + 0.50(120) = 120
60 + 60 = 120
120 = 120 (True solution).
Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.
When x = 0 and y = 240, we have:
2x + 0.50y = 120
2(0) + 0.50(240) = 120
0 + 120 = 120
120 = 120 (True solution).
Therefore, if we buy no beans we can buy 240 pounds of rice.
When x = 0 - 5 and y = 240 + 20, we have:
2x + 0.50y = 120
2(0 - 5) + 0.50(240 + 20) = 120
-10 + 130 = 120
120 = 120 (True solution).
Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.
When x = 0 + 10 and y = 240 - 60, we have:
2x + 0.50y = 120
2(0 + 10) + 0.50(240 - 60) = 120
20 + 90 = 120
110 = 120 (Not a solution).
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Multiply: -6 x 1 II don't get it!!!
The multiplication we need to make is:
[tex]-6\times1[/tex]To answer this question we need to use the following rules for multiplications with signs:
[tex]\begin{gathered} (+)\times(+)=+ \\ (-)\times(-)=+ \\ (+)\times(-)=- \\ (-)\times(+)=- \end{gathered}[/tex]We can see that in our expression we have the last case: a negative number multiplied by a positive number. In this case, the negative number is -6 and the positive number is 1.
So, we know from the rule that the result will be negative.
And finally, we multiply just the numbers: 6 by 1 is 6.
In summary, the result is:
[tex]-6\times1=-6[/tex]Answer: -6
Answer:
-6
Step-by-step explanation:
hope this helps
PLEASE help thank you!
Answer:
70
Step-by-step explanation:
So 175% of 40 is the amount in april so we can split it up into 2 problems
100% of 40? 40
75% of 40? 30
Then you add the 2 to get 175% of 40 which will be 70!
the snowy tree cricket is sometimes called the temperature cricket because the frequency of it chirps varies based on the temperature. the number of chirps per minute is 148 less than 4 times the outside temperature in degrees fahrenheit. write an equation that relates the number of chirps per minute, x, and the outside temperature in degrees fahrenheit, f. whatiis the outside temperature if a snowy tree cricket chirps 100 times a day?
The equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.
The number of chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.
The number of chirps per minute = x
The outside temperature in degrees Fahrenheit = f
Then the linear equation will be
x = 4f - 148
Given that x = 100 chirps per minutes
Substitute the values in the equation
100 = 4f -148
4f = 100+148
4f = 248
f = 248/4
f = 62 degrees Fahrenheit.
Hence, the equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.
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At the start of a trip, a car's gas tank contains 12 gallons of gasoline. During the trip, the car consumes 10 gallons of gasoline. How much gasoline is left in the tank? Should you represent this amount with a positive or negative value? Why?
If the tank contains 12 gallons and then the car consumes 10, we can know how much gasoline is left by substracting 12 with 10:
12 - 10 = 2
Then, 2 gallons of gasoline is left in the tank
Since there is still gasoline because 12 is higher than 10, then we represent this amount with a positive value.
WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZYX has a measure of 34 degrees. Find the measure of angle ZWY.
Angle ZWY has a measure of what
degrees.
Angle ZWY has a measure of 13 degrees.
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.
Given,
Angle WXY has a measure of 133 degrees
Angle ZYX has a measure of 34 degrees
Angle ZWY:
= 180 - 133 -34
= 13
Angle ZWY has a measure of 13 degrees.
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the length of a rectangle is 5 meters less twice it’s width. if the perimeter of the rectangular is 38 meters, then what is the value of the length
The length has a value of 9 meters
How to determine the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 5 meters less twice it’s width
This means that
Length = 2Width - 5
The perimeter is given as
Perimeter = 38 meters
The perimeter is calculated as
Perimeter = 2 x (Length + Width)
So, we have
2 x (2Width - 5 + Width) = 38
Divide by 2
2Width - 5 + Width = 19
This gives
3Width= 21
Divide
Width - 7
Recall that Length = 2Width - 5
So, we have
Length = 2 * 7 - 5
Evaluate
Length = 9
Hence, the length is 9 meters
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apesville is a utopian island of 5000 square kilometers. there are currently 250,000 inhabitants of the island. last year, there were 12,000 new children born and 10,000 people were recorded as deceased. in how many years will the population of apesville double?
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If you love codes answer this question!
Answer:
Your answer would be
(a) FPUGT.
(-25)^(/3) =?-125 1 O A. -25 B. 5 or -5 C. -15 D. -5
We will have that the expression has the solution of:
[tex]\sqrt[3]{-125}=-5[/tex]Therefore the solution is D. -5.
When we elevate to the power of 3 -5 will be equal to -125.
The first three terms of an arithmetic sequence are as follows.17, 25, 33Find the next two terms of this sequence.17, 25, 33,
The sequence is given by the following formula:
[tex]y_{i+1}=y_{i-1}+8[/tex][tex]\begin{gathered} y_0=17 \\ y_1=17+8=25 \\ y_2=25+8=33 \\ y_3=33+8=41 \\ y_4=41+8=49 \end{gathered}[/tex]Finally, the answers are 41 and 49.
Amira is younger than Marques. Their ages are consecutive integers. Find Amira's age if the sum of Amira's age and 2 times Marques's age is 38.
Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.
According to the question,
We have the following information:
Amira is younger than Marques.
Their ages are consecutive integers.
The sum of Amira's age and 2 times Marques's age is 38.
Now, let's take Amira's age to be x years.
Then, Marques's age will be (x+1) years.
So, we have:
x + 2(x+1) = 38
x + 2x + 2 = 38
3x+2 = 38
3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)
3x = 36
x = 36/3
x = 12 years
Hence, Amira's age is 12 years.
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I need help figuring out the answer, I’m very much confused
My first step is to draw a picture
We know that the length is 2 times the width
L = 2w
We are given a width of 4.6 yards
L = 2(4.6) = 9.2 yards
We can find the area by using the formula
A = l*w
A = 9.2 * 4.6
A =42.32 yd^2
