The exponent form of given integer is equal to [tex]2^{5[/tex] with base 2 and exponent 5.
What is Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
An exponent refers to the number of times a number is multiplied by itself.
We know from property of Exponents
[tex]a^m a^n= a^{m+n[/tex]
We have the number 32.
Then, the prime factorization of 32
32 = 2 x 2 x 2 x 2 x 2
= [tex]2^{1+1+1+1+1[/tex]
= [tex]2^{5[/tex]
So, the base is 2 and exponent is 5.
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Please hurry Which expression is equivalent to 2^8? A) 8^2 B) 2•8 C) 2^4 • 1^4 D) 2^4 • 2^2 E) 2^4 • 2^4
Expression which is equivalent to 2⁸ is 2⁴ · 2⁴. Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. Thus, option D is correct.
What is the process for determining an equivalent expression?Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. The x-term is typically put before constants when arranging the terms in the same sequence.The two phrases are equal if each of the terms in both of them is the same. Our final solution is 2 x, minus 2, but you may also write 2 x, minus 3 or 2 x, minus 3. The only viable solution was this one. The proper response is option d, as you can see in this case.When reduced to their most basic form, two or more ratios are said to be similar if their values are the same.2⁸ = 256
and
2⁴ • 2²
= 16 · 16
= 256
2⁸ = 2⁴• 2²
Thus, Expression which is equivalent to 2⁸ is 2⁴ · 2⁴
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Geo question
Find perimeter of triangle HIJ
The value of the variable 'x' is 12.5. Then the perimeter of the ΔJHI is 50 units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔGEF and ΔJHI are similar triangles. Then the equation is given as,
5 / x = 8 / 20
5 / x = 2 / 5
x = 25/2
x = 12.5
The perimeter of the ΔJHI is given as,
P = 17.5 + 20 + 12.5
P = 50 units
The value of the variable 'x' is 12.5. Then the perimeter of the ΔJHI is 50 units.
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Computer A has a processor speed of 5 x 10^9 cycles per second. Computer B has a processor speed of 2 × 10^8 cycles per second. How many times faster is computer A than computer B?
•25
•30
•250
•300
Answer:
25
mark brainliest
Step-by-step explanation:
5/2=2.5
10^9/10&8=10
10*2.5=25
Find stations for sin A, cos A and Tan A(pic included)
The rations for sin A, cos A and Tan A are 0.86,0.5 and 1.6
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
Given
Hypotenuse=65
Base=33
Height=56
Now,
sin A= 56/65
=0.86
cos A= 33/65
=0.5
tan A=56/33
=1.6
Hence, the trigonometric rations will be sin A=0.86, cos A=0.5, tanA=1.6
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Each side of the base of a square pyramid measures 10 inches. The height of each lateral face of the pyramid is also 10 inches.
What is the surface area of the pyramid?
Enter your answer in the box.
in²
Step-by-step explanation:
The surface area of a square pyramid can be found by adding the area of the base and the sum of the areas of each of its lateral faces.
The area of the base is 10 inches * 10 inches = 100 square inches.
The lateral faces are isosceles triangles with a base of 10 inches and a height of 10 inches, so the area of each lateral face is (1/2) * 10 inches * 10 inches = 50 square inches.
Since there are 4 lateral faces, the sum of their areas is 4 * 50 = 200 square inches.
Adding the area of the base to the sum of the areas of the lateral faces:
Surface area = 100 + 200 = 300 square inches.
Answer:250
Step-by-step explanation:
Two lines intersecting at a right angle
form a line.
are parallel.
are perpendicular.
form a ray
1) Sandra bought coffee in a cup shaped like a cylinder with a radius of 10 centimeters and a height of 20 centimeters. Sandra fills the cup with coffee, but she leaves 5 centimeters of space at the top to have room for cream. What is the volume of coffee in her cup?
Given,
Radius of the cylinder 10cmHeight of the cylinder is given as 20So right now we need to find the volume of the cup i.e. like a cylinder
So she leaves 5 centimeter of gap which means the height of the cup will be
Height = 20 - 5
= 15
Applying the formula to find the volume of the cup
Volume = πr²h
= π(10)²x 15
= 1500π
Substituting π as 3.14 we get
1500 x 3.14 = 4710cm³
Hence the volume is 4710cm³
PLEASE HELP ASAP A SOON AS YOU CAN. The percentage of battery remaning y on a tablets battery after x hours can be represented by the the given graph
A.After 40 hours the tablet will have 0 percent of battery left
B. The tablet will not have any battery remaining after 4 hours
C. The tablet starts with 40 percent of battery remaining
D. The tablet loses 4 percent of battery every hour
The typical runtime of a tablet is between three and ten hours. More charge is typically needed for less expensive models than for more expensive tablets.
The number of hours a tablet's battery can last.The typical runtime of a tablet is between three and ten hours. More charge is typically needed for less expensive models than for more expensive tablets. It might go a week or longer between charges if you only use the tablet once or twice each day.Many people find that charging merely 80% is ineffective. Your phone won't function if you fully charge it and then use it in a single day. The 40-80% rule applies if, like me, your daily usage is limited to 25–50%.The typical runtime of a tablet is between three and ten hours. More charge is typically needed for less expensive models than for more expensive tablets.To learn more about tablet's battery refer to:
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I don’t get this question at all help
The required value of s is 6 for the given polygon.
What is the Exterior Angle?An exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
The polygon is given in the question, as shown,
As we know that exterior angles are always 360° in the regular polygon.
So, 25s - 5 + 8s - 5 + s + 47 + 24s - 25 = 360
Rearrange the likewise terms and apply the arithmetics operation,
25s + 8s + s + 24s - 5 - 5 + 47 - 25 = 360
58s - 5 - 5 + 47 - 25 = 360
58s + 12 = 360
58s = 348
s = 348/58
Apply the division operation, and we get
s = 6
Thus, the required value of s is 6.
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Can you solve this equation for me. I attached a picture below.
Answer:
8 is your y-intercept
and -1/2 is your slope (I think)
Step-by-step explanation:
For a given input value xxx, the function fff outputs a value yyy to satisfy the following equation.
-5x-4y=-8
Write a formula for f(x)
The formula for the function f(x) is given as -
f(x) = - (5/4)x + 2.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the function as follows -
- 5x - 4y = - 8
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
The given expression is -
- 5x - 4y = - 8
- 4y = 5x - 8
y = - (5/4)x + 2 = f(x)
Therefore, the formula for the function f(x) is given as -
f(x) = - (5/4)x + 2.
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a bowl contains 675 sweets
ratio of red to blue sweets is 3:7
ratio of blue to green sweets is 4:5
calculate the number of blue sweets
Answer:
We know that the ratio of blue to green sweets is 4:5
We can let y be the number of green sweets
the total number of sweets is 675, and we know that the ratio of blue to green sweets is 4:5, so we can set up the equation:
x + y = 675
where x is the number of blue sweets and y is the number of green sweets.
Also we know that x:y = 4:5
by cross multiplying x * 5 = y * 4
x = (5/4) y
Now we can substitute x in the first equation:
(5/4) y + y = 675
by combining like terms we get:
9/4 y = 675
multiply both sides by 4/9 to get:
y = (675 * 4) / 9
y = 300
the number of blue sweets is:
x = (5/4) y = (5/4) * 300 = 375
so the number of blue sweets is 375.
find the value of x/y if 5^x×3^y=675
The value of x/y from the given expression is 2/3.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is [tex]5^x3^y=675[/tex].
Here, the prime factorization of 675 is
675=3×3×3×5×5
= 3³5²
[tex]5^x3^y[/tex]=5²3³
When bases are same equate powers
x=2 and y=3
Now, x/y =2/3
Therefore, the value of x/y from the given expression is 2/3.
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The state of Wyoming is roughly rectangular in shape. It has an area of more than 96,000 square miles. Write some possible dimensions of the state's length and width
The possible length and width of the shape will be 309.58 miles.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
Given that the state of Wyoming is roughly rectangular in shape. It has an area of more than 96,000 square miles.
The sides will be calculated as,
Sides² = 96000
Take the square root of the number and solve,
Sides = √96000
Sides = 309. 53 miles
Hence, the length and width of the shape will be 309.53 miles.
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For a ride on a rental scooter, Abdul paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for Abdul's ride was $20.71 . For how many minutes did Abdul ride the scooter?
Answer:
6min and 39sec
Step-by-step explanation:
$3+11cents=$3.11
1min=$3.11
?min=$20.71
$20.71÷$3.11
=6min and 39secs
Susan is calculating her final grade in Statistics. The grade is broken down as follows: tests (50%), lab (30%), and final exam (20%). Susan's category averages are the following. Tests: 82 Lab: 78 Final Exam: 86
The final grade of Susan will be 81.6%
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
As per the given question, the required solution would be as:
Test grade + Lab grade + FE
Test grade = (82 × 50)/100 = 4100/100 = 41%
Lab grade = (78 × 30)/100 = 2340/100 = 23.4%
final grade = (86 × 20)/100 = 1720/100 = 17.2%
final grade = 41 + 23.4 + 17.2
Apply the addition operation, and we get
final grade = 81.6%
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The question seems to be incomplete the correct question would be:
Susan is calculating her final grade in Statistics. The grade is broken down as follows: tests (50%), lab (30%), and final exam (20%). Susan's category averages are the following. Tests: 82 Lab: 78 Final Exam: 86
What is her final grade?
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer as a ratio in simplified form by filling in the boxes.
The unit rate for the graph given is 5/4.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a graph as shown in the image.
Unit rate is defined as the rate at which {y} changes per unit change in {x}. Mathematically -
{r} = Δy/Δx
{r} = (y₂ - y₁)/(x₂ - x₁)
We can write the unit rate as -
r = (1/2 - 0)/(2/5 - 0)
r = (1/2)/(2/5)
r = (1/2 x 5/2)
r = 5/4
Therefore, the unit rate for the graph given is 5/4.
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According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are
yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places
where possible)
a. Compute the probability that a randomly selected peanut M&M is not blue.
b. Compute the probability that a randomly selected peanut M&M is blue or orange.
c. Compute the probability that three randomly selected peanut M&M's are all green.
d. If you randomly select two peanut M&M's, compute that probability that neither of them are brown.
e. If you randomly select two peanut M&M's, compute that probability that at least one of them is brown.
Submit Question
If according to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown. The probability that a randomly selected peanut M&M is not blue is 0.77.
How to find the Probability?a. The probability that a randomly selected peanut M&M is not blue:
Probability= 1 - 0.23
Probability = 0.77
b. Probability that a randomly selected peanut M&M is blue or orange
Probability = 0.23 + 0.23
Probability = 0.46
c. Probability of selecting three green M&M's in a row
Probability= (0.15)^3
Probability = 0.003375
d. Probability that neither of two randomly selected peanut M&Ms are brown
Probability = (1 - 0.12)^2
Probability = 0.7396
e. Probability that at least one of two randomly selected peanut M&Ms is brown
Using complement rule:
Probability = 1 - (1 - 0.12)^2
Probability = 0.2604
Therefore the probability that a randomly selected peanut M&M is not blue is 0.77.
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URGENT PLEASE HELP
f(x) = √x + 7. Find the inverse of f(x) and its domain.
Answer: B
Step-by-step explanation: The inverse is f^-1(x)=x^2-7 and the domain is x>7
Which of the following fraction is equivalent to 0.748? 93/125, 187/250, 7 13/50, 56 5/6
Answer:gg
Step-by-step explanation:gg
Answer: 187/250
Step-by-step explanation:
187 divided by 250 = 0.748
Find the value of x
Please help this is due soon
A carpenter needs to cut a small triangular piece of wood for part of a jewelry box. He knows the height is 23 inches and the base is an unknown value a. The angle between the unknown base a and the hypotenuse is θ=29∘. What is the length of a to the nearest tenth of an inch? Do not include the units in your answer.
Answer:
83
Step-by-step explanation:
Let the base be of length a
The height h, half the base a/2 and the hypotenuse form a right triangle.
Two of the angles of this triangle are known: 90° and 29°
The third angle with is opposite the side of length a/2 = 180-(90+29) = 61°
Use the Law of Sines
f a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states:
[tex]\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]
Therefore
[tex]\dfrac{23}{\sin 29} = \dfrac{a/2}{\sin 61}\\\\\\a/2 = \dfrac{23(\sin61)}{\sin 29} = 41.493 \; inches\\[/tex]
The base length a = 2 x 41.493 = 82.986
Rounding this to the nearest tenth will make it an integer: 83
A triangle cannot have side lengths that are 3, 5, and 9.
False
True
Answer:
False
Step-by-step explanation:
Add any 2 side lengths and see if it is greater than the third.
3 + 5 = 8
8 < 9
So it is not a triangle.
Consider the equation below.
(2 + 4x)
6
(x-3)
4
=
Answer options A through D present a
series of steps for solving this equation.
Identify the first step in which an error
occurs. If there is no error, choose
answer option E.
A 6(2 + 4x) = 4(x - 3)
B
12+ 24x = 4x - 12
C
20x = -24
6
5
E No errors
The solution of the given equation is x = -6/5.
Solving an equation:An equation is a mathematical statement that is formed by variables and constant terms. By adding or subtracting the same integer on both sides or by multiplying or dividing by the same integer on both sides we can solve an equation.
Here we have
(2 + 4x)6 = 4(x - 3)
We can solve the given expression as follows
=> (2 + 4x)6 = 4(x - 3)
=> 12 + 24x = 4x - 12
Add - 12 on both sides
=> 12 + 24x - 12 = 4x - 12 - 12
=> 24x = 4x - 24
Subtract - 4x from both sides
=> 24x - 4x = 4x - 4x - 24
=> 20x = - 24
Divided by 20 into both sides
=> 20x/20 = -24/20
=> x = - 6/5
Therefore,
The solution of the given equation is x = -6/5.
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please help with this.. thankyou
When a system of equations has no solutions, it is referred to as an inconsistent system.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two expressions, one on each side of an equal sign. Equations are used to solve problems in mathematics, chemistry, physics, engineering, and other sciences. They can also be used to define relationships between different variables or constants. Equations are an important tool for understanding the world around us.
This means that there is no solution that can satisfy all of the equations at the same time. This can happen when the equations are contradictory, or when one equation is an exact multiple of the other equation. In some cases, a system of equations may have infinitely many solutions, meaning that there are an infinite number of solutions that satisfy the equations. However, in the case of an inconsistent system, no solutions exist.
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Answer:
there is no solution
Step-by-step explanation:
what is a trinomial with a constant term
A trinomial is a polynomial in which it consists of three terms and it represented as ax^2+bx+c where c is a constant.
What is Quadratic Equation ?
Quadratic Equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0
where c is a constant .
Trinomial with a constant term are defined as the
A trinomial is an algebraic expression that has 3 non-0 terms and has multiple variable within the expression. A trinomial is a form of polynomial however with 3 phrases. A polynomial is an algebraic expression that has one or extra phrases
A trinomial is a polynomial in which it consists of three terms and it represented as ax^2+bx+c where c is a constant and
examples are x^2+5x+9 , xy+y^2 + 69 and etc.
Hence, A trinomial is a polynomial in which it consists of three terms and it represented as ax^2+bx+c where c is a constant.
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Kristy found a z test statistic of -1.66.
Given the data provided, what is the p-value of the z-test statistic? Answer choices are rounded to the thousandths place.
The P value of the Z statistic is given as : 0.049. Option D
How to find the p value from the test statisticThe p value is what tells you how likely that you value has occurred under the null or H0. To find the p value, you would have to make use of the z table. This would be gotten from the z value of the data set.
From the table given that the z test is found to be equal to -1.66, the p value that would correspond to this is 0.049
Hence the given the data provided here, the p value is 0.049.
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Complete question
Kristy randomly samples the out-of-state tuition and fees for 25 public universities and found a mean of $20,876 with a standard deviation of $2,494. Using the alternative hypothesis that µ < $21,706, Kristy found a z test statistic of -1.66.
Given the data provided, what is the p-value of the z-test statistic? Answer choices are rounded to the thousandths place.
a.)
0.097
b.)
0.903
c.)
0.952
d.)
0.049
In the given figures l||m find tha value of x in each of the following
X+50
Answer: In the given figures, if l and m are parallel, it means that they are always equal. Therefore, if l = m, then the value of x in each of the following X+50 is x = 50.
This is because, if l and m are parallel, that means that the measure of the angle between them is always equal to zero. Therefore, the angle between l and m is 0, and that's why the lines are parallel. So, since l = m, the value of x in each of the following X+50 is x = 50.
Step-by-step explanation:
Please give me an answerrrr
please help answer, thanks
The substitution property and the angle addition postulate indicates that m∠1 + m∠2 = m∠3 + m∠4, m∠EXG = m∠1 + m∠2, and m∠HYK = m∠3 + m∠4, therefore;
m∠EXG = m∠HYK
What is the measure of an angle?The measure of an angle is the circular distance between the two rays of the angle measured in degrees or radians.
The specified information are;
m∠1 = m∠3
m∠2 = m∠4
Required;
Prove that m∠EXG = m∠HYK
The two column method to prove m∠EXG = m∠HYK, can be presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]{}[/tex] m∠1 = m∠3 [tex]{}[/tex] Given
m∠2 = m∠4
2. m∠EXG = m∠1 + m∠2 [tex]{}[/tex] Angle addition postulate
m∠HYK = m∠3 + m∠4
3. m∠1 + m∠2 = m∠3 + m∠4 [tex]{}[/tex] Substitution property of equality
4. m∠EXG = m∠HYK [tex]{}[/tex] Substitution property
The details of the reasons used to prove m∠EXG = m∠HYK are as follows;
Angle addition postulate
The angle addition postulate states that an angle formed by two adjacent angles that share a common ray is the sum of the measures of the two angles.
Substitution property
The substitution property of equality states that if a = b then b can be substituted for a in any expression or equation and the expression or equation will remain the same or valid.
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