The exponent expression that is used to express 75 as sum of the powers of 8 is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The integer 75 is written as -
[tex]2^0+2^1+2^2+2^6[/tex]
75 is expressed as sum of the powers of 2, with whole number exponents.
To find 75 expressed as sum of the powers of 8, divide the integer by 8 -
[tex]8^0=1[/tex]
[tex]8^1=8[/tex]
[tex]8^2=64[/tex]
Only one integer 2 is left to complete the sum as 75.
To find what the power value is use the equation -
[tex]8^x=2\\x=\frac{2}{8} \\x=\frac{1}{3}[/tex]
So, the last exponent is [tex]8^{\frac{1}3} }[/tex].
So the expression is [tex]8^0+8^1+8^2+8^\frac{1}{3} =75[/tex].
Therefore, the exponent expression is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].
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Wendy's math certificate is 7 inches tall and 9 inches wide. Wendy wants to put the certificate in a fancy frame that costs $2.00 per inch. How much will it cost to frame Wendy's math certificate?
Answer:
Step-by-step explanation:
The perimeter of Wendy's math certificate is 7 inches + 7 inches + 9 inches + 9 inches = 32 inches.
So, the cost to frame Wendy's math certificate would be $2.00 per inch * 32 inches = $64.00.
5. 7 movie tickets for $56
To find out how much each ticket costs, we can use this equation:
Total cost ÷ Number of tickets = Price of each ticket
Inserting the numbers into the equation would look like this:
56 ÷ 7 = 8To check our work, we can multiply the number of tickets by the price of each ticket to see if it matches up to the correct total price.
7 × 8 = 56Therefore, each ticket costs $8.
I HAVE 10 MINUTES PLEASE HELP!!!!The density of water is 1 gram per cubic centimeter. An object floats in the water if its density is less than water's density, and it sinks if its density is great than water's.
Suppose a ball with mass 90 grams is in the shape of a sphere with radius 4 centimeters. Will the ball sink or float in the water?
ROUND YOUR ANSWERS TO THE NEAREST HUNDRETH AND USE THE
π
π
BUTTON WHEN CALCULATING
The volume of the ball is about___cubic centimeters. The density of the ball is___grams per cubic centimeter. Based on its density, the ball will___.
Answer:
Step-by-step explanation:
Basically, we want to use the formula for the area of a sphere: V = 4/3πr^3
And plug-in our radius, 4 for r.
We get an answer around 67 sooooooo
The volume of the ball is about__67__cubic centimeters. The density of the ball is__1.343__grams per cubic centimeter. Based on its density, the ball will__sink__.
Answer:
The base should be sink
Calculation of the volume, density:
Since the density of water is 1 gram per cm^3.
The volume is
Here a = base area and h = height of the pyramid
So,
Now
Density is
Since The mass of the pyramid is 1.17 g.
So, the density is
Density
Since its density is more than that of water, so it will sink.
Hence, we can conclude that The base should be sink.
Step-by-step explanation:
Hope this helped!
Which fraction of the whole circle is this sector?
Answer: 23/72
Step-by-step explanation:
180 degrees = half of circle
5 degrees = 1/72 of circle
5 degrees times 23 = 115 degrees
1/36*23 = 23/72
Answer:
23/72 of a circle
Step-by-step explanation:
4×sector=circle
90÷360=1/4
so,
115/360=23/72
A company manufactures computer memory chips as circular silicon wafers with a diameter of 10 inches. The wafers are cut into different sized sectors. Match each wafer's central angle to the area of that sector.
The area and the angle are matched as below.
Area Angle
25/8 π in² = 45°
25/18 π in² = 20°
25/36 π in² = 10°
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Diameter = 10 in
Radius = 5 in
Area of the circle in sector = 360°
πr² = 360
π x 5² = 360
25π in² = 360° _____(1)
Now,
From (1),
25π in² = 360°
Divide both sides with 8.
25/8 π in² = 45°
From (1),
25π in² = 360°
Divide both sides with 18.
25/18 π in² = 20°
From (1),
25π in² = 360°
Divide both sides with 36.
25/36 π in² = 10°
Thus,
Area Angle
25/8 π in² = 45°
25/18 π in² = 20°
25/36 π in² = 10°
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Please help! Need to turn it in soon
The required time duration is 0.13 s
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
[tex]h(t)=-5t^2 + v_{0}t+h_{0}[/tex]
Substitute given the values
2=-5t² + 15 t+0
=> 5t² -15t+2 =0
On solving this quadratic equation ,w e get
t= 0.13 s
The required time duration is 0.13 s
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I NEED TO KNOW
What does 1 + 1 equal?
(A) 11
(B) 1
(C) 16
(D) 1/8
I WILL MARK BRANLIEST
Value of expression 1 + 1 = 2
What is addition?Addition is the process of adding two or more items together. In math, addition is the method of calculating the sum of two or more numbers.
Given expression,
1 + 1
+ is sign of Addition, Adding the numbers,
1 + 1 = 2
Hence, 2 is the value of expression 1 + 1.
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The number of fish on a fish farm increases by approximately 10% each month. If there were originally 350 fish, calculate to the nearest 100 how many fish there would be after 12 months.
Answer:
There would be 600 fish after 12 months.
Step-by-step explanation:
The number of fish on the farm increases by 10% each month, so the formula to calculate the number of fish after n months is:
F = 350 * (1 + 0.1)^n
where,
F is the number of fish after n months
We want to find the number of fish after 12 months, so:
F = 350 * (1 + 0.1)^12
F = 350 * 1.719178
F = 603.56 to the nearest 100, which is 600.
Find the mean of these numbers:
2,6,9,56,63,68
Explanation:
First we add up those numbers
2+6+9+56+63+68 = 204
Then divide by 6 because there are 6 values in this list.
204/6 = 34
Answer:34
Step-by-step explanation:It's obtained by simply dividing the sum of all values in a data set by the number of values.
The scatter plot and line of best fit below shows the length of two peoples femur (the long leg bone in thigh) and their height in centimeters. Based on the line of best fit, what would be the predicted femur length for someone with a height of 218 cm.
The predicted femur length is 69 cm
How to determine the predicted femur lengthFrom the question, we have the following parameters that can be used in our computation:
The scatter plot
On the scatter plot, we have
x = the length of two peoples femur (the long leg bone in thigh)
y = height in centimeters
So, we have
Height = 218 cm
From the graph, we have
x = 69
Hence, the femur length is 69 cm
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Find the value of each variable on the triangle
One side x one side y one side 13 and the measurement is 45 degrees
Value of variable x = 13/√2
Value of variable y = 13/√2
What is trigonometric ratio?Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
Given,
In the right triangle ABC
AC = 13
AB = x
BC = y
∠C = 45°
Sin 45° = AB/AC
1/√2 = x/13
x = 13/√2
AB = 13/√2
Tan 45° = AB/BC
1 = (13/√2)/y
y = 13/√2
BC = 13/√2
Hence, 13/√2 is the value of both variables x and y.
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Joe bought 5 apples and 2 oranges for his family from a refreshment stand at the beach and paid $9. Ms. Sanders bought 7 apples and 3 oranges for her family at the same refreshment stand and paid $13. Define two variables, write and solve a system of equations to find the cost of an apple and the cost of an orange.
The cost of an apple is $1 and the cost of an orange is $2
How to write and solve a system of equationsFrom the question, we have the following parameters that can be used in our computation:
x = apples
y = oranges
Using the above as a guide, we have the following:
5x + 2y = 9
7x + 3y = 13
Multiply (1) by 3 and (2) by 2
15x + 6y = 27
14x + 6y = 26
Subtract
x = 1
So, we have
5(1) + 2y = 9
This gives
y = 2
Hence, the cost of orange is $2
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Pls help me on this math equation
Step-by-step explanation:
This is a trick question I think.
It says he managed to only travel 3 7/8. So wouldn't that mean the fraction of his planned trip that he travel would be... 3 7/8? Unless they want it as 31/8? Something is odd with the question
Which expression has a solution of 12, if m = 7?
Answer:
“m + 5”
internet
What is the greatest common factor between 18 and 30 and 54
Answer: 1, 2, 3, 6, 1
Step-by-step explanation:
When listing all the factors for 18, 30 ,54....
18 , 30 , 54 to find the common factors. The common factors for 18,30,54 18 , 30 , 54 are 1,2,3,6 1 , 2 , 3 , 6 . The GCF (HCF) of the numerical factors 1,2,3,6 1 , 2 , 3 , 6 is 6 .
( Hope this helps )
If a regular octahedron has a surface area of 32 square inches what is the surface area of each face?
The surface area of each face is 4 square inches.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A regular octahedron has a surface area of 32 square inches.
That means
all sides are equal.
The surface area of each face is,
= 32/8
= 4 square inches.
Therefore, the required area is 4 square inches.
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A small country emits 92,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 5% per year for the next 15 years. In the first year of the agreement, the country will keep its emissions at 92,000 kilotons and the emissions will decrease 5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 15 year period, to the nearest whole number?
Answer:
To calculate the total amount of carbon dioxide emitted over the course of 15 years, we can start with the initial amount of 92,000 kilotons and multiply by 0.95 (the reduction factor) each year.
Step-by-step explanation:
Year 1: 92,000 kilotons
Year 2: 92,000 * 0.95 = 87,400 kilotons
Year 3: 87,400 * 0.95 = 82,990 kilotons
and so on, until year 15.
To find the total amount of carbon dioxide emitted over the course of 15 years, we need to sum up the emissions for each year:
92,000 + 87,400 + 82,990 + ... + (92,000 * 0.95^14) = 92,000 * (1 + 0.95 + 0.95^2 + ... + 0.95^14)
This is a finite geometric series and can be calculated using the formula for the sum of a finite geometric series:
S = a * (1 - r^n) / (1 - r),
where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.
For this series, a = 92,000, r = 0.95, and n = 15. Plugging these values into the formula, we get:
S = 92,000 * (1 - 0.95^15) / (1 - 0.95)
S = 92,000 * (1 - 0.556774) / 0.05
S = 92,000 * 0.443226 / 0.05
S = 92,000 * 8.86452
S = 814,178.24 kilotons
Rounding to the nearest whole number, the country would emit 814,178 kilotons of carbon dioxide over the course of 15 years.
Paula's Pizza Parlor uses the following ingredients to make pizza
Number of Pizzas
2
5
Sauce
18
Cheese
12
At this Rate how many sauce and cheese will paula use to make 5 pizzas?
To make 5 pizzas, Paula will use 45 sauce and 30 cheese.
What are multiplication and division?Multiplication is used to find the product of two or more numbers. Multiplication is also known as repeated addition.
The division is the opposite operation of multiplication. It is how one tries to determine how many times a number is contained into another.
Given,
Paula uses 18 sauce and 12 cheese to make two pizzas.
Ingredients needed to make one pizza = 18/2 sauce and 12/2 cheese
= 9 sauce and 6 cheese
Ingredients needed to make 5 pizzas = 9 × 5 sauce and 6× 5 cheese
= 45 sauce and 30 cheese
Hence, 45 sauce and 30 cheese is needed to make 5 pizzas.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Which interval notation represents the set of all number greater than or equal to 1
and less than 6?
Answer:
The interval notation for the set of all numbers greater than or equal to 1 and less than 6 is [1, 6).
Step-by-step explanation:
URGENT!! ILL GIVE
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The two sequences of transformations of ΔABC that exhibit the congruence between the two triangles include the following:
A. a rotation of 180° about the origin and a translation of 1 unit left.
E. a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left.
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Point A = (-6, 2) → Point A' = (-(-6), -(2)) = (6, -2).
By translating the pre-image of triangle A'B'C' horizontally left by 1 unit, the coordinate A" of the image of triangle A'B'C' include the following:
(x, y) → (x - 1, y - 7)
Coordinate A' = (6, -2) → Coordinate A'' (6 - 1, -2) = (5, -2)
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In the diagram below, BE BC, m/A = 39° and m/EBC = 124°. Find m/FDC
∠AFB = 73° is the angles of a triangles .
What does a math angle mean?
An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.
because the angles of a triangles add up to 180 degree
m∠A = 39° , m∠ADC = 107°
so ∠c = 180 - 107 - 39
= 34°
BE ≅ BC
∠C = ∠E = 34°
SO ∠EDF = 180 - 107 = 73°
So ∠DEF = 180 - 34 - 73 = 73°
Because m∠DFE and ∠AFB are vertical angle
so ∠DFE = ∠AFB
∠AFB = 73°
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(a) in how many ways can 3 boys and 3 girls sit in a row? (b) in how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together? (c) in how many ways if only the boys must sit together? (d) in how many ways if no two people of the same sex are allowed to sit together?
a) 720 ways 3 boys and 3 girls sit in a row.
b) 48 ways boys and the girls are each to sit together.
c) 6 ways boys must sit together.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Given:
Number of girls= 3
Number of boys = 3
a) Using Permutation
⁶P₆ = 6! / (6 - 6)!
⁶P₆ = 6! / (0!)
⁶P₆ = 6!
= 6 × 5 × 4 × 3 × 2 × 1
= 30 × 24
= 720
b) 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together
= 3! x 2³
= 3 x 2 x 2 x 2 x 2
= 48 ways
c) the number of ways boys can sit together
= 3!
= 6 ways
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need help with this question
Write the following as a composition of two or more non-identity functions.
(2x^3 + 2)/(x^3 - 2)
The given expression (2x^3 + 2)/(x^3 - 2) can be written as a composition of two non-identity functions as follows:
Let f(x) = 2x^3 + 2 and g(x) = x^3 - 2.
Then, the expression can be written as:
f(x)/g(x) = (2x^3 + 2)/(x^3 - 2)
So, the expression is a composition of the two non-identity functions f and g, written as:
h(x) = f(g(x)) = (2x^3 + 2)/(x^3 - 2)
8
Helen thinks of two numbers.
The Highest Common Factor (HCF) of her two numbers is 5
The Lowest Common Multiple (LCM) of her two numbers is a multiple of 12
Write down two possible numbers that Helen could be thinking of.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
what is HCF ?The biggest integer that is able to divide two or more quantities is known as the highest common factor (HCF) or greatest common factor. Highest refers to the biggest or greatest number. The sharing a common meaning of two or more integers. Feature is an integer that can be used to divide a whole number (a divisor). Write each integer as the sum of one's main characteristics in step one. Step 3: The HCF of said given integers is the greatest number that can be found among the common factors.
given
1. It is assumed that when Helen thinks of two numbers, they have corresponding HCF and LCM values of 5 and 12.
2. The smallest common multiple shared by two numbers is referred to as the least common number.
LCM of 4 and 6 is 12, for instance.
3. The highest number that divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.
HCF of 6 and 8 is 2, for instance.
4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.
5.The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values other than 5. 60 and 120 have an HCF of 60, but not 5.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
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Find the cosine of ∠U.
28
45
53
U
V
T
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.
The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.
cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53
So, the cosine of ∠U is 28/53, written as a proper fraction.
Now let's convert cosine of ∠U is 28/53 in improper fraction:
The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.
gcd(28, 53) = 1, so the fraction cannot be further simplified.
Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.
Now let's convert cosine of ∠U is 28/53 in whole number:
The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.
28 ÷ 53 = 0.526087
So, the cosine of ∠U expressed as a whole number is approximately 0.52609
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_____ The given question is not correct, so correct Question is:
Find the cosine of ∠U in Triangle UTV with side:
UV=28
VT=45
TU=53
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
(PLEASE HEEEEEEEEELP!!!!!)
a mean computed in such a way that each data value is given a weight reflecting its importance is referred to as a(
A mean computed in such a way that each data value is given a weight reflecting its importance is referred to as A weighted mean.
The weighted mean is defined as a type of mean that is calculated by multiplying the weight associated with a particular event or outcome and the associated with the quantitative outcome and then summarizing all the products together.
For each data point to contribute equally to the final mean, some data points contribute more weight than others.
The weighted mean is calculated by multiplying the weight with the quantitative outcome and adding all the products.
weighted average= The sum of variables/sum of all weights.
if the variables are denoted by x and their weights are denoted by y, then we have:
Weighted average = Σ(xy)/Σy
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it is believed that 85% of all individuals love bts. we took a sample of 30 individuals and found the 95% of all people love bts. what is the z score associated with our observation (round answers to two decimal places)?
The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.
2.45
Z score = (Observed value - Expected value) / Standard Deviation
Z score = (95 - 85) / √(85*(1-85)/30)
Z score = 2.45
We can calculate the Z score associated with our observation by taking the observed value, 95%, and subtracting the expected value, 85%, and dividing this by the standard deviation. To calculate the standard deviation, we use the formula: √(expected value*(1-expected value)/sample size). In this case, 85*(1-85)/30. The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.
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