Gerald ordered a small pizza, asked for it to be divided into 8 equal slices and ate 3 of them. Sarah also ordered a small pizza asked it to be divided into 24 slices, and ate 6 of them. Who ate more pizza? ( My sister's 6th grade question, please help her)
The Gerald ordered and ate more pizza than Sarah .
What is fraction?
A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
Gerald ordered a small pizza, divided into 8 equal slices and ate 3 of them.
Sarah also ordered a small pizza ,divided into 24 slices, and ate 6 of them.
According to given question we have
Gerald divided into 8 equal slices and ate 3 of them.
=3/8
Sarah divided into 24 slices, and ate 6 of them.
=6/24
=1/4
Multiply with 2 in both numerator and denominator we get,
=1*2/4*2
=2/8
∴3/8>2/8
So, Gerald ate more pizza.
Therefore, the Gerald ordered and ate more pizza than Sarah .
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What is the domain of the exponential function shown in the graph?
-8
-6
9
-4
-2
y
8+
6+
4-
2+
2+
9
-6-
-8
ස
No
2
4
to
too!
8
44
X
Answer:
Hey there, your domain is all real numbers!! the graph is staying above the x-axis, but it's crossed from the negative x-values to the positive x-values. that means choice D is incorrect, because some of the function does cross through negative values.
if the domain was either of the inequality choices, the function wouldn't extend all over the graph--it would be ONLY between 0 and 5, or 5 and -5. this graph would be all real numbers because it isn't restricted like that.
Hope this helps!!!
How do I factorise this Quadratic Equation to find x?[tex]2x^2-x-120=0[/tex]
The factors of the given Quadratic Equation 2x² - x - 120 = 0 is 8 and -15/2.
What are zeros ?
zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.
Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.
Now, considering the given Quadratic Equation to find x :
2x² - x - 120 = 0
writing the above equation into two linear factors as :
2x² - 16x + 15x - 120 = 0
2x(x-8) + 15(x-8) = 0
(x-8)(2x+15) = 0
Now, equating each linear equation to zero to find the factors:
(x-8) = 0 and (2x+15) = 0
x = 8 and x = -15/2.
Therefore, the factors of the given Quadratic Equation is 8 and -15/2.
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can someone check if I did this question right, ?.
Answer:
Yes, you did it correctly. Note that shape B is 3 bigger than shape A, so it has much larger dimensions and properties.
A bubble gum machine in a grocery store is filled with 500 candies. Each time a person puts in money, 10 candies come out. This function is a model for the number of candies left in the machine after a person buys some candy.
The required function will be
y= 500-10x
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
let amount of money = x and
number of remaining candy =y
total 500 remaining candies= total 10x amount of money
y= 500-10x
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Mckenzie and Cara both tried to find the missing side of the right triangle. HURRY PLEASE DUE TODAY. I WILL MARK BRANLIEST IF MULTIPLE PEOPLE ANSWER.
Mckenzie's Work: Cara's Work:
a2 + b2 = c2 a2 + b2 = c2
52 + 132 = c2 52 + b2 = 132
25 + 169 = c2 25 + b2 = 169
194 = c2 b2 = 144
Square root 194 equals square root c squared. Square root b squared equals square root 144.
13.93 ≈ c b ≈ 12
McKenzie is right and Cara is wrong.
Step-by-step explanation:a² + b² = c²
[The Pythagoras theorem a , b are the square edge)
5² + 13² = c²25 + 169 = c²194 = c²[tex]\sqrt{194}[/tex] = c13.93 = cSo, McKenzie is right and Cara is wrong.Answer:
the correct answer is McKenzie's
Step-by-step explanation:
the problem looks for the measure of the hypotenuse, which is the longest side of a right triangle, so it cannot be 12 in because we have a cathetus of 13 in, therefore, without making calculations but following a simple reasoning, the correct answer is McKenzie's , about 13.93, the only possible option
if a1=5 and an=-3an-1 then find the value of a5
Recursive expressions are ways of expressing sequence using functions. The fifth term of the recursive sequence is 405.
Recursive functionsRecursive functions are ways of expressing sequence using functions.
Given the following recursive functions
a₁=5 and;
aₙ = -3aₙ₋₁
For the second term;
a₂ = -3a₁
a₂ = -3(5)
a₂ = -15
For the third term a₃
a₃ = -3a₂
a₃ = -3(-15)
a₃ = 45
For the fourth term
a₄ = 3a₃
a₄ = 3(45)
a₄ = 135
For the fifth term
a₅ = 3a₄
a₅ = 3(135)
a₅ = 405
Hence the fifth term of the recursive sequence is 405.
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If a gas has a volume of 1 l at a pressure of 200 kpa, what volume would it have when the pressure is increased to 400 kpa? assume the temperature and number of particles are constant.
With an inverse relationship, when the pressure is increased to 400 kPa, the volume will be 0.5L, assuming that the temperature and number of particles are constant.
Boyle's Law states the inverse relationship between volume and pressure. It states that a constant amount of gas at a constant temperature, decreasing the volume will increase its pressure, and increasing its volume will decrease its pressure.
V = k/P or P1V1 = P2V2
where V = volume
P = pressure
If a gas has a volume of 1 L at a pressure of 200 kPa, and assuming that the temperature and number of particles are constant, using the inverse relationship, solve for the volume of the gas at a pressure of 400 kPa.
P1V1 = P2V2
200 kPa(1L) = 400 kPa(V2)
V2 = 200/400
V2 = 0.5 L
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Let f(x)=3 x-2 and g(x)=x^{2}+1 . Perform each function operation.
f(x)-g(x)
Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, subtraction, multiplication, and division.
-x² + 3x +3 is the domain of all real numbers.
What is meant by function operation?Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, subtraction, multiplication, and division.
Let the two functions be f and g then f(x) = 3x - 2 and g(x) = x² + 1.
we have to calculate (f - g)(x)
Which is equivalent to:
(f - g)(x) = f(x) - g(x)
Taking the two functions and substituting them into this expression, we get,
f(x) - g(x) = (3x - 2) - (x² + 1)
simplifying the above function, we get
f(x) - g(x) = 3x - 2 - x² - 1
(f - g)(x) = -x² + 3x - 2 - 1
Therefore, (f - g)(x) = -x² + 3x +3
We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.
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the coefficients of variation for each data set are within 5 percentage points of each other. therefore, the systolic measurements vary ▼ the diastolic measurements.
The answer is 16.7 %.
What is meant by mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including the geometric mean, the harmonic mean, and the simple arithmetic mean.Why are you being so cruel, it demands to know. So, someone would ask you that if they thought you were being harsh or disrespectful.In just two easy steps, you can determine the mean, or average, of a set of data: Add up all of the values to determine the sum. By how many values there are in the data collection, divide the total.adjective Being cruel to another person, such as by denying them the opportunity to do something, is what it means to be mean.The necessary calculation is below:
observations Systolic(x) Diastolic(y) x^2 y^2
1 120 79 14400 6241
2 130 74 16900 5476
3 157 75 24649 5625
4 96 50 9216 2500
5 156 89 24336 7921
6 124 87 15376 7569
7 116 59 13456 3481
8 137 66 18769 4356
9 124 71 15376 5041
10 118 81 13924 6561
sum 1278 731 166402 54771
For Systolic (x)
mean= sum(x)/10 = 1278/10 = 127.8
stdev= s =sqrt( (sum(x^2 - 10*127.8^2)/9) = sqrt ( (166402 - 10*127.8^2)/9) =18.48
So coefficient of variation ( systolic) is = (stdev/mean )*100 = (18.48/127.8)*100 = 14.5 %
For Diastolic (x)
mean= sum(y)/10 = 731/10 = 73.1
stdev= s =sqrt( [tex](sum(x^2 - 10*73.1^2)/9) = sqrt ( (54771 - 10*73.1^2)/9)[/tex]= 12.18
so coefficient of variation ( systolic) is = (stdev/mean )*100 = (12.18/73.1)*100 = 16.7 %
Here, systolic is less varied than the diastolic.
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Find values of X and Y
Answer:
Step-by-step explanation:
Simplify each expression. x²/₇ . x³/₁₄
The result of simplifying each number x²/₇ . x³/₁₄ using the exponent rules is [tex]\sqrt{}[/tex]x
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(x²/₇) * (x³/₁₄)
Base= x
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
(x) ⁽²/₇ ⁺ ³/₁₄⁾
(x) ⁽⁴⁺³⁾/₁₄
(x) ⁽⁷/¹⁴⁾
(x) ⁽¹/²⁾
As we have a fractional exponent, you must convert the exponent to root:
[tex]\sqrt{}[/tex]x
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Select all parts from the expression above that represents a coefficient. (Just the coefficient... not the coefficient AND the variable.) Group of answer choices -4.9t2 -4.9 22 1.8 22t
The part from the expression above that represents a coefficient is -4.9
How to determine the parts from the expression above that represents a coefficient?The expression is given as
-4.9t^2
To solve this question, we make use of the following illustration.
Let an expression be represented as
ax^n
Where the variable is n
In the expression
Coefficient = a
Variable = x
Power = n
Using the above as a guide, the part from the expression above that represents a coefficient is -4.9
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Write each equation in logarithmic form.
4= (1/2)⁻²
The equation in logarithmic form is log base (1/2) of (4) = -2
Given the equation is:
4= (1/2)⁻²
The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function ay = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).
Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).
A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form.
Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.
log base (1/2) of (4) = -2
log₁/₂ (4) = ₋2
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The populations of cities A and B are 3.6*10 to the 5 and 2,060,000, respectively. The population of City C is twice the population of City B. The population of City C is how many times the population of City A?
The population of City C is 11.4 times the population of City A.
How to calculate the value?From the information, the populations of cities A and B are 3.6*10 to the 5 and 2,060,000, respectively
It was stated that the population of City C is twice the population of City B. That means the population of C will be:
= 2060000 × 2
= 4120000
Therefore, the population of City C is how many times the population of City A will be:
=4120000 / 360000
= 11.4
Therefore, the population of City C is 11.4 times the population of City A.
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A rocket is launched from the top of a platform 50 feet above the ground. The rocket will fall after exploding at its maximum height. The rocket's height above the ground is given by the function h(r) = −16r2 + 64r + 50.
The function g(r) is shown in the graph.
graph with r on the x axis and g of r on the y axis that is increasing from the left going through about negative 8 and one half comma 0 to negative 4 comma 100 and then decreasing through negative 1 comma 55 and continuing down and to the right
Which function has the greater maximum?
a
h(r)
b
g(r)
c
h(r) and g(r) have the same maximum.
d
h(r) and g(r) do not have a maximum.
Answer:
The maximum height that the rocket will reach is 271 feet.
Step-by-step explanation:
We first calculate the time, t it takes the rocket to reach maximum height from v = u - gt. Since u = initial velocity = 128 ft/s, v = velocity at maximum height = 0 ft/s and g = acceleration due to gravity = 32 ft/s².
So, v = u - gt.
t = (u - v)/g
= (128 ft/s - 0 ft/s)/32 ft/s²
= 128 ft/s ÷ 32 ft/s²
= 4 s.
We calculate the maximum height from
y - y₀ = ut - 1/2gt² where y₀ = 15 ft and all other variables are as above.
Substituting these values into the equation, we have
y - y₀ = (u - 1/2gt)t
y - 15 ft = (128 ft/s - 1/2 × 32 ft/s² × 4 s) × 4 s
y - 15 ft = (128 ft/s - 64 ft/s)4 s
y - 15 ft = 64 ft/s × 4 s
y - 15 ft = 256 ft
y = 256 ft + 15 ft
y = 271 ft
So, the maximum height that the rocket will reach is 271 feet.
Step-by-step explanation:
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
Answer: -3x+4=2 is the new equation x= 2/3
Step-by-step explanation: brainliest?
There are many different kinds of growth patterns. Patterns that increase by a constant rate are linear. Patterns that grow exponentially increase by an ever-increasing rate. If your allowance doubles each week, does that represent linear growth or exponential growth?
If the allocation doubles every week, that represents exponential growth.
Given there are many types of growth models, and models that grow at a constant rate are linear and models that grow exponentially at an increasing rate.
Linear growth is characterized by growth by the same amount per unit time.
Exponential growth is a process of increasing numbers over time. This happens when the instantaneous rate of change of a quantity over time is proportional to the quantity itself.
Exponential growth because the first week you may only get a dollar, but the next week you get 2, then 4, and so on. Your allowance doesn't grow by the same amount every week, so the number it doubles is exponential.
Therefore, if the allowance doubles every week, it represents a exponential growth multiplier because samples growing at a constant rate are linear.
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The number below is not correctly written in scientific notation.
145 × 105
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?
1.45 × 10?
Write the new exponent in the blank below. PLEAZ HELP will give brainliest
The new exponent for the power of 10 after rewriting the number correctly in scientific notation would be 1.45 × 10^7
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex]where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
The scientific notation is value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
We have been given that number below is not correctly written in scientific notation.
145 × 10⁵
Therefore, new exponent would be 1.45 × 10^7
Hence, The new exponent for the power of 10 after rewriting the number correctly in scientific notation would be 1.45 × 10^7
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The number below is not correctly written in scientific notation. Write it using correct scientific notation.
6.57*1000
Answer: 6.57x10^3
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Hope this helped :)
Ms.Shultis is driving along the road moves at a rate of 56 miles per hour driven. How long does it take for her to travel 84 miles?
Answer:
: A person driving along the road moves at a rate of 56 miles per hour driven.
Step-by-step explanation:
It cost Chloe $17.70 to send 177 text messages. How much would it cost to send 98 text messages?
Answer:
Step-by-step explanation:
17.7 -> 177
19.1 -? ?
17.7177=19.1x
cross multiply
17.7x=19.1(177)
can you solve from there?
The cost to send 98 text messages will be $9.8.
What is mean by proportion?
A proportion is a fraction of a total amount, in which two ratios are set equal to each other.
Given that;
The cost of 177 text messages = $17.70
Now,
Since, The cost of 177 text messages = $17.70
So, The cost to send 98 text messages will be;
= $17.70 x 98 / 177
= $9.8
Thus, The cost to send 98 text messages will be $9.8.
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Find each product or quotient. √5(√5)
The product of √5(√5) is 5.
To find : the product of √5(√5).
This question can be easily solved using the concept of square root. It can be solved in a few simple steps
Step 1 : Check the power of roots for each term
Both the terms are √5
Since both the numbers have the same root power they can be combined under the same sqaure root for further operation
=> √ ( 5 x 5 )
=> √ 25
It can also be written as √ 5²
square root can also be mentioned as number raised to 1/2
If we solve the powers of 5 => 1/2 x 2 = 1
=> √ 25 = √ 5² = 5
Therefore, we get the product of √5(√5) as 5.
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Julian describes an angle in the triangle using these statements.
GH is the adjacent side.
HK is the opposite side.
GK is the hypotenuse.
Triangle G H K is shown. Angle G H K is a right angle.
Which angle(s) is Julian describing?
∠G
∠H
∠K
∠H and ∠K
Step-by-step explanation:
The hypotenuse is the longest side of the right-angled triangle. The angle about which Julian is describing is ∠G.
Answer:
A. <G
Step-by-step explanation:
Took the test on edge, hope this helps
Look at the picture please
The minimum value is 20
The maximum value is 9
The range is 11.
The mean is 16.8
The median is 18.
The mode is 18.
The landmark that best describes the dot plot is the mean because it incorporates all the data in the dotplot.
What are the measures of the data in the dotplot ?A dot plot is a graph that displays the information of a dataset. A dot plot consists of a number line and dots above the numbers on the number line. The dots in the dot plot is indicate the frequency of the data in the dataset.
The minimum value is the smallest number in the dataset. The smallest number that is represented in the dot plot is 9. The maximum value is the largest number in the dataset. The largest number that is represented in the dot plot is 20.
The range is the difference between the maximum value and the minimum value.
Range = maximum value - minimum value
20 - 9 = 11
The mean is the average of he numbers in the dataset.
Mean = [(9 x 1) + (12 x 1) + (14 x 1) + (15 x 5) + (16 x 2) + (17 x 3) + (18 x 6) + (19 x 3) + (20 x 4)] / 26
438 /26 = 16.8
The mode is the number that occurs most in the dataset. The number that occurs most frequently is 18 with a dot of 6.
The median is the number at the center of the dataset. The median is 18.
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Solve. Check for extraneous solutions. √4 x-23 -3=2
The solution for given equation is 196 and there are no extraneous solutions.
Extraneous solutions refer to the solution, which on being placed in the equation, does not make Left Hand Side and Right Hand Side equal.
Rewriting the equation and solving it by addition or subtraction of values on both sides as per the requirement -
✓4x - 23 - 3 = 2
Adding 3 on both sides of the equation
✓4x - 23 - 3 + 3 = 2 + 3
✓4x - 23 = 5
Adding 23 on both sides of the Equation
✓4x - 23 + 23 = 5 + 23
✓4x = 28
Taking square on both sides
(√4x)² = 28²
4x = 784
Shifting 4 to Right Hand Side
x = 784 ÷ 4
Performing division
x = 196
Keep the value of x in equation to find it it is extraneous or not -
✓(4 × 196) - 23 - 3 = 2
✓784 - 23 - 3 = 2
28 - 23 - 3 = 2
25 - 3 = 2
2 = 2
Since RHS and LHS are equal, there is no extraneous solution for the given equation.
Hence, the solution for given equation is 196 and there are no extraneous solutions.
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Find the inverse of each function.
y=log (x+1)
The inverse of the function y = log(x₊1) is f ⁻¹(x) = 10ˣ ₋ 1.
Given the function is :
y = log(x₊1)
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now interchange the positions of x and y in the function.
x = log₁₀ (y ₊ 1)
the next step is to isolate the dependent variables.
f ⁻¹(x) = ₋1 ₊ 10ˣ
f ⁻¹(x) = 10ˣ ₋ 1
hence, we get the inverse of the given function as f ⁻¹(x) = 10ˣ ₋ 1.
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Compute $2^{10}\cdot 2^8\cdot 2^6\cdot 2^4\cdot 2^2\cdot 2^{-1}\cdot 2^{-3}\cdot 2^{-5}\cdot 2^{-7}\cdot 2^{-9}$.
[tex]2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}[/tex] = 32
We need to compute [tex]\bold{2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}}[/tex] .
This is the product of exponential numbers with same bases.
We use rules of exponents:
[tex]a^b.a^c=a^{b+c}[/tex][tex]a^{-b}=\frac{1}{a^b}[/tex]Using the first rule we can rewrite
[tex]2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}[/tex]
as,
[tex]2^{10+8+6+4+2}.2^{-1-3-5-7-9} = 2^{10+8+6+4+2}.2^{-(1+3+5+7+9)}[/tex]
Using the second rule,
[tex]2^{10+8+6+4+2}.2^{-(1+3+5+7+9)} = \frac{2^{10+8+6+4+2}}{2^{1+3+5+7+9} }[/tex]
[tex]=\frac{2^{30}}{2^{25}}[/tex]
[tex]\bold{= 2^5 = 32}[/tex]
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Multiply. (5√3 -2)²
Using multiplication to solve the square roots, (5√3 -2)², we get the answer as 79 - 20√3
How do we multiply square roots?To multiply a square root, multiple its radicands first—that is, the values that appear after the radical sign. If the radical sign is preceded by any coefficients, multiply those coefficients as well.
Using (a-b)² = a² + b² - 2ab
We have,
(5√3 -2)²
On expanding,
we have , (5√3)² + 2² - 2(5√3)(2)
⇒ 75 + 4 - 20√3
⇒ 79 - 20√3
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Which line from section 1 reveals Hawthorne's informal, fatherly tone for this story?
A. A boy used to be seen in the streets of Boston.
B. Ben was born in 1706; so that he was now about 10 years old.
C. His father, who had come over from england.
Answer if you're 100 percent sure, this is for a test.