The equivalent expression for the given expression is 1/2⁹⁸.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is (2⁻¹⁰/4²)⁷.
Now, (2⁻¹⁰/(2²)²)⁷
= (2⁻¹⁰/2⁴)⁷
= (1/2¹⁰×2⁴)⁷
= (1/2¹⁰⁺⁴)⁷
= (1/2¹⁴)⁷
= 1/2⁹⁸
Therefore, the equivalent expression for the given expression is 1/2⁹⁸.
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For each 70 mm of coloured fabric Alex uses to make his curtains, he also uses 20 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
20 : 7 is already the simplest term and there is no need to further simplify.
What is ratio?Ratio can be defined as the given value divided by total value.
When presenting a ratio as an answer:
1. It has to be in the form of integer, it cannot be in the form of fraction or decimals
2. There should be of the equivalent units.
3. It must be in its simplest form
Convert the units in cm
Coloured Fabric = 70 mm
Coloured Fabric = 70 ÷ 10 cm
Coloured Fabric = 7 cm
Find the ratio of the Colour Fabric to White Fabric:
Coloured Fabric = 7 cm
White Fabric = 20 cm
Ratio of White Fabric : Colour Fabric = 20 cm : 7 cm
Ratio of White Fabric : Colour Fabric = 20 : 7
Therefore, 20 : 7 is already the simplest term and there is no need to further simplify.
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what would be the number of years it would take for 1500 to earn 350 in simple intrest at a rate of 4.3%
The number of years it would take for $1500 to earn $350 will be 5.43 years.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
The amount of $1500 is invested to earn $350 in simple interest at a rate of 4.3%.
Then the number of years is given as,
350 = (1500 x 4.3 x T) / 100
350 = 15 x 4.3 x T
64.5T = 350
T = 5.43 years
The number of years it would take for $1500 to earn $350 will be 5.43 years.
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What part of an hour is 5 minutes?
Answer:
1/12
Step-by-step explanation:
An hour consists of 60 minutes and 5 minutes would be 1/12 of an hour.
5 minutes / 60 minutes
divide both sides by 5
1/12 of an hour
A game piece used in a math game is shaped like a right trapezoid. The drawing is not to scale. What is the area of the game piece? Enter your answer in the box. in² A square with sides measuring 3 inches is attached to a triangle, giving a total combined length on one side of 10 inches.
Answer: The game piece is a right trapezoid and its area can be calculated by using the formula:
Area = (b1 + b2) * h / 2
Where b1 and b2 are the lengths of the bases (the parallel sides of the trapezoid) and h is the height.
We can use the information given to find the area of the game piece:
A square with sides measuring 3 inches is attached to a triangle, giving a total combined length on one side of 10 inches.
So, the length of the base of the triangle is 7 inches (10 inches - 3 inches) and the height of the trapezoid is 3 inches.
Now we can substitute these values into the formula:
Area = (3 + 7) * 3 / 2
Area = 10 * 3 / 2
Area = 15 in²
So the area of the game piece is 15 square inches.
Step-by-step explanation:
cool beans is a locally owned coffee shop that competes with two large coffee chains, planeteuro and frothies. alicia, the owner, hired two students to count the number of customers that entered each of the coffee shops to estimate what percent of people who are interested in coffee are visiting each shop. after a week, the students found the following results: 606 visited cool beans, 810 visited planeteuro, and 1,160 visited frothies. the students were surprised that cool beans had 148 visits on monday which represented 60% of all people who visited one of the three coffee shops on mondays. how many people visited one of the three coffee shops on monday?
48.15% people visited one of the three coffee shops on monday
The scholars discovered that;
518 people went to Cool Beans, 974 to Planet Euro, and 1,160 to Frothies.
Assume that x% of Monday's customers at each of the three coffee shops were x.
One hundred thirty-five people went to Cool Beans on Monday.
Of the total number of customers who went to one of the three coffee shops on Monday, 52% went to Cool Beans.
Consequently, 52/100 * x = 135
The calculation for x is (135*100)/52.
x = 260 individuals
On Monday, the following number of visitors visited either PlanetEuro or Frothies:
260-135 =125
Calculating the percentage of Monday visitors to either PlanetEuro or Frothies;
135= 52%
125=?
Cross-product as you
(125*52)/135 =48.15%
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Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded. ) The S&P 500 risk premium is estimated at 5. 6% per year, with a SD of 20. 6%. The hedge fund risk premium is estimated at 10. 6% with a SD of 35. 6%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.
Calculate Greta’s capital allocation using an annual correlation of 0. 3. (Do not round your intermediate calculations. Round your answers to 2 decimal places. )
Greta’s capital allocation is 0.37 for the S& P 500 and whereas for the hedge fund the captial allocation is 0.63. it is done using the Capital Allocation formula.
The calculation was done using the Capital Allocation formula, which is Risk Aversion multiplied by Risk Premium divided by the sum of the squared standard deviations of the two portfolios plus the correlation between the two portfolios multiplied by the standard deviation of portfolio 1 times the standard deviation of portfolio 2.
for S& P 500 : Capital Allocation = Risk Aversion x Risk Premium / (SD^2 + (Correlation x SD1 x SD2)) = 3 x 5.6% / (20.6^2 + (0.3 x 20.6 x 35.6)) = 0.37 .
whereas Hedge Fund: Capital Allocation = Risk Aversion x Risk Premium / (SD^2 + (Correlation x SD1 x SD2)) = 3 x 10.6% / (35.6^2 + (0.3 x 20.6 x 35.6)) = 0.63
The Risk Aversion was given as 3, the Risk Premiums of the S& P 500 and the Hedge Fund were given as 5.6% and 10.6% respectively, and the standard deviations of the S& P 500 and the Hedge Fund were given as 20.6% and 35.6% respectively. The correlation between the two portfolios was given as 0.3. The calculation yielded a capital allocation of 0.37 for the S& P 500 and 0.63 for the Hedge Fund.
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Give an example of each kind of Polynomial.
The correct statements to the given polynomials are x²-5, x³, x⁴+3x+6, 1,x+2
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given; To find a polynomial for each of the example.
A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients). You call an expression with a single term a monomial, an expression with two terms is a binomial, and an expression with three terms is a trinomial. An expression with more than three terms is named simply by its number of terms.
Thus we have the examples to the required polynomial accordingly:
1. A binomial of degree 2 is : x²-5
2. A monomial of degree 3 is: x³
3. A trinomial of degree 4 is: x⁴+3x+6
4. A monomial of degree 0 is: 1
5. A binomial of degree 1 is: x+2
Hence, The examples are x²-5, x³, x⁴+3x+6, 1,x+2
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Max is starting a savings account for college and puts in 2000 as his starting balance. He earbs simple interest at 5% every year and must also pay 20% income tax on the interest earned annually. What is the overall balance after 2 years on the account after taxes have been paid
The overall balance after 2 years on the account after taxes have been paid is 40.00.
The formula for simple interest is:
I=P*T*R
where P is the principal amount of money, R is the interest rate as a decimal, and T is the time.
We know the principal amount is 2000, the interest rate is 5%, and the time is 2 years.
We must convert the interest rate to a decimal.
Divide by 100 or move the decimal place to two spots to the left.
6/100=0.05 or 5.0 --> 0.5 --> 0.05
Now we know all the values.
P=2000
T=2
R=0.05
Substitute the values into the simple interest formula.
I=2000*2*0.05
Multiply.
I=2000*0.1
I=200
The simple interest is 200.00
Now, every year must also pay 20% income tax on the interest earned annually, for that we have to subtract 20% in simple interest.
overall balance =200*20/100
overall balance=40.
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One angle of an isosceles triangle measures 120°. What measures are possible for the other two angles? Choose all that apply.
80°
20°
30°
120°
Select the correct answer. Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms? A. (3 × 13^2) + (2 × 15^2) B. (2 × 13^3) + (2 × 15^2) C. (3 × 15^2) + (2 × 13^2) D. (3 × 13^2) × (2 × 15^2)
The correct answer i.e. the total area is A. (3 × 13^2) + (2 × 15^2).
What is the area formula?The edge of a shape's area is measured. You must divide the length and breadth of a rectangles or square in order to determine its area. A is x times y in size.
How do you calculate a square's area?The area of a square is composed of (Side) (Side) square units. Once the diagonally, d, is known, the surface of a square is equal to d22 square units. For instance, 8 8, or 64 sq ft is the size of a cube with sides that are each 8 feet long (ft2).
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How many different roots does the polynomial function,
y = (x − 2)(x + 3)² have?
-
A. 1
B. 3
C. 2
D. 4
The polynomial function is the product of two different linear factors, (x-2) and (x+3)^2, which means that we have two different roots, x=2 and x=-3
What are the roots the given polynomial function have?A polynomial function is a function that can be written as constants and n is the degree of the polynomial. The polynomial function y = (x − 2)(x + 3)² is a quadratic function because it has an [tex]x^{2}[/tex] term.
The roots of a polynomial function are the values of x that make the function equal to zero. In other words, they are the solutions to the equation y = 0.
The polynomial function y = (x − 2)(x + 3)² can be factored as (x-2)(x+3)(x+3), which means that we have three different linear factors, (x-2), (x+3), and (x+3) . Each linear factor corresponds to one root of the polynomial.
So the polynomial function y = (x − 2)(x + 3)² has 2 distinct roots. The correct answer is C.
Alternatively, we can also see that the polynomial function is the product of two different linear factors, (x-2) and [tex](x+3)^{2}[/tex], which means that we have two different roots, x=2 and x=-3.
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Identify the interval (–8, 3) as open, closed, half-open, or unbounded.
A.
open
B.
closed
C.
half-open
D.
unbounded
Answer:
it should be
Step-by-step explanation:
no.c half - open
Evaluate the following expressions to help the astronauts prepare for take off. These numbers will help calculate the amount of time it will take to prepare for take off. In this case x = 4, y = 5, z = ½ 7x – 5y = minutes to secure the door. 12z + 2y2 = minutes to complete the system check. 2xy + 8z = minutes to fill pantry with astronaut food
If x = 4, y = 5, z = 1/2 , then
(a) It will take 3 minutes to secure door ,
(b) It will take 56 minutes to complete system check ,
(c) It will take 44 minutes to fill pantry with astronaut food .
The values of x , y and z are x = 4, y = 5, z = 1/2 ;
Part(a) ;
The Number of minutes to secure door is calculated the by expression
⇒ 7x - 5y .
Substituting values as x = 4 and y = 5 ,
we get ;
⇒ 7(4) - 5(5) = 28 - 25 = 3 minutes .
Part(b) ;
The Number of minutes to fill pantry with astronaut food is calculated the by expression :
⇒ 12z + 2y² ,
Substituting values as z = 1/2 and y = 5 ,
we get ;
⇒ 12z + 2y² = 12(1/2) + 2(5)² = 6 + 2×25 = 6 + 50 = 56 minutes .
Part(c) ;
The Number of minutes to complete system check is calculated the by expression
⇒ 2xy + 8z ,
Substituting values as x = 4 , z = 1/2 and y = 5 ,
we get ;
⇒ 2xy + 8z = 2(4)(5) + 8(1/2) = 40 + 4 = 44 minutes .
The given question is incomplete , the complete question is
Evaluate the following expressions to help the astronauts prepare for take off. These numbers will help calculate the amount of time it will take to prepare for take off.
In this case x = 4, y = 5, z = 1/2 ;
(a) Number of minutes to secure door is found by expression ⇒ 7x - 5y .
(b) Number of minutes to complete system check is found by expression ⇒ 12z + 2y² ,
(c) Number of minutes to fill pantry with astronaut food is found by expression ⇒ 2xy + 8z .
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The length of a rectangle is 5 inches longer than it is wide. If the area is 66 square inches, what are the
dimensions of the rectangle?
According to the formula of area of rectangle, the dimensions of the rectangle is 3.6 x 18
The term called area of rectangle is calculated by using the formula
=> A = l x w
where l refers the length of rectangle and w refers the width of the rectangle.
Here we have know that the area of the rectangle is 66 square inches.
And let us consider that W refers the width of rectangle and here we know that the length is 5 inches longer than it is wide so it can be written as 5W.
Then the dimensions of the rectangle is calculated as,
=> 66 = (W x 5W)
=> 66 = 5 W²
=> W² = 13.2
=> W = 3.6
Then the value of length is calculated as,
=> L = 5 x 3.6
=> L = 18
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As part of the study described in exercise 10, the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state. (Again, D. C. Counts as a state. ) The corre- lation between these 51 pairs of averages was 0. 97. Would the correlation between the Math SAT and the Verbal SAT computed from the data on all the individuals who took the tests-be larger than 0. 97, about 0. 97, or less than 0. 97? Explain briefly
If the data for every person who took the tests were tabulated, the correlation between the Math and Verbal SATs would be less than 0.97.
Are the SAT verbal and SAT reading the same test?
The word used to designate the SAT Reading and Writing part is an older, outmoded one. The SAT Verbal section's material is still highly significant today, though. Many of the subjects and abilities from the old SAT Verbal portion are now included in the Evidence-Based Reading and Writing section.
Here we know that the correlation between these 51 pairs of averages was 0. 97.
And as we all know that the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state.
As we know that the individual people tend to have more variation when you compare them to the average person
then if we look at the individual math and rebels course then there's probably a way more variation.
Here we know that the straight line wouldn't be there.
Then the whole thing would not be the same.
And which tells that It would be less of a correlation coefficient.
So it is less that 0.97.
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3x - 4y = 6
6x - 8y = 10
The system shown has _____ solution(s).
one
infinite
no
Answer:
no solution
Step-by-step explanation:
6x - 8y = 10
Divide by 2,
6x/2 - 8y/2 = 10/2
3x - 4y = 5
3x - 4y = 6
3x - 4y = 5 = 6
But actually, 5 ≠ 6
The system shown has no solution. The answer is obtained by solving the linear equations.
What is a linear equation?
The equation with the highest degree of one is a linear equation. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. Such an equation yields a straight line on the graph.
We are given 6x - 8y = 10
On dividing both sides by 2, we get
⇒6x/2 - 8y/2 = 10/2
⇒3x - 4y = 5
But, we are given that 3x - 4y = 6
This shows that 5 must be equal to 6
But, 5 ≠ 6
Hence, the system shown has no solution.
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Part B
How does each inverse function from part A relate to its original function? Describe the relationship in terms of the context for each situation. Do this for each of the three models
The inverse function takes the output of the original function and gives the input that would produce that output.
In mathematics, the inverse function (f^-1) of a function f(x) is a function that "undoes" the action of the original function. The relationship between a function f(x) and its inverse function f^-1(y) is such that if f(x) = y, then f^-1(y) = x. In other words, the inverse function takes the output of the original function and gives the input that would produce that output.
It's important to note that not all functions have inverse functions, a function may not have an inverse if it's not one-to-one function, that is, if it's output has more than one input that produces it.
Correct Question :
How does each inverse function f^(-1)y relate to its original function? Describe the relationship in terms of the context for each situation.
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Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
The polynomial which is not equivalent to (5x – 2)(-2x + 4) is -10x + 20x + 4x – 8 and is therefore denoted as option A.
What is a Polynomial?This is referred to as a type of algebraic expression in which the exponents of all variables should be a whole number.
(5x – 2)(-2x + 4) when expanded will give:
-10x² + 20x + 4x – 8 which can be rewritten as the following below:
-8 + 24x – 10x² -10x² + 24x – 8This is therefore the reason why -10x + 20x + 4x – 8 was chosen as the correct choice.
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The options are:
A) -10x + 20x + 4x – 8
B) 4x + 20x – 10x2 – 8
C) -8 + 24x – 10x2
D) -10x2 + 24x – 8
oh my god please someone help
1) Note the line of best fit is indicated in the attached graph.
2) Based on the line, the total score (on the y-axis) for the person who didn't study for the test (that is whose hours of homework are zero) is 38.
3) The y-intercept of the line of best fit in graph two is 8
4) The slope of the line of best fit for the scatter plot in graph 2 is -1/2
5) the equation of the line of best fit is given as y = -0.5x + 8
What is a line of best fit?A straight line with the best fit is one that minimizes the distance between it and certain data. In a scatter plot of multiple data points, the line of best fit is used to express a connection.
It is a result of regression analysis and may be used to forecast indicators and price changes.
Note that most of the answers above are self-explanatory.
1) When drawing a line of best fit, you try to keep the line in such a way that it captures as many points as possible while balancing the number of points to the left and to the right of the line as much as possible.
2) Note that the person who didn't study is the person with zero hours of homework. Thus identifying the corresponding grade
3) to determine the y-intercept, just look at the point on the y-axis where the line is touching. The total score that corresponds with zero on the y-axis is 38.
4) the formula for slope is ΔY/ΔX
Since we have the two corresponding points each on the y-axis and on the x-axis, that is:
X1 = 0
X2 = 2
Y1 = 8
Y2 = 7
ΔX = 2 – 0 = 2
ΔY = 7 – 8 = -1
Thus,
Slope (m) = ΔY/ΔX
= -1/2
=-0.5
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I really need help on this question
Answer: NOT Parallel because 98 /= 82 (Alternate angles are equal)
you are talking with 3 friends and the conversation turns to birthdays what is the probability that no two peopl ein your group were born in the same month
The answer is [tex]\frac{55}{96}[/tex] .
If A, B, and C are three dependent events,
P(A∩ B∩C) =P(A). P(A|B) .P(C|A∩B)
Let us use your birthday as a starting point.
Let A be the first friend who has a different birth month than you. Let B be the second friend who has a different birth month than friend 1 and you
Let C be the third friend who has a different birth month than friend 1, friend 2, and you
there are 12 months in a year
P(A∩ B∩C) =P(A). P(A|B) .P(C|A∩B)
P(A∩ B∩C) [tex]= \frac{11}{12} .\frac{10}{12} .\frac{9}{12}[/tex]
P(A∩ B∩C) [tex]= \frac{990}{1728} =\frac{55}{96}[/tex]
So, the result is [tex]\frac{55}{96}[/tex] .
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Over which interval is this function continually increasing?
f(x) = 2/3|x - 3| + 2
A. (3, ∞)
B. (-∞, 2)
C. (-∞, 3)
D. (2, ∞)
The given function is continually increasing at an interval (3, ∞)
What is an interval of a function?An interval is a set of (real) numbers with the property that for every pair of numbers y and z that it contains, it contains also every number between y and z.
Given that, a function f(x) = 2/3|x - 3| + 2
Plot the graph for the function. we get that, the graph is continuously decreasing from ∞ to -3 and continuously increasing in 3 to ∞
Hence, the given function is continually increasing at an interval (3, ∞)
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As a town gets smaller, the population of its high school decreases by 5% each year. The senior class has 320 students now. In how many years will it have about 100 students? Write an equation. Then solve the equation without graphing.
The number of years until the town will have 100 students is given as follows:
22.68 years.
How to model the situation?A decaying exponential function is modeled as follows:
y = a(1 - r)^x.
In which:
a is the initial value.r is the decay rate.The parameter values for this problem are given as follows:
a = 320, r = 0.05.
Hence the function is given as follows:
y = 320(0.95)^x.
The time it will take for the population to have 100 students is x when y = 100, hence:
100 = 320(0.95)^x
(0.95)^x = 100/320
(0.95)^x = 0.3125
x log(0.95) = log(0.3125)
x = log(0.3125)/log(0.95)
x = 22.68 years.
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Please help with this I’ll reward you I promise
The factorized expressions are (4x - 1)(4x + 5), (2z - 7)(z + 10) and (3x - 8)(2x + 5)
The factor pairs of -80The pair factors of -80 are (-1, 80), (-2, 40), (-4, 20), (-5, 16) and (-8, 10).
The factor pairs with a sum of 16The pair factors of -80 in this category is
(-4, 20)
This is so because
-4 + 20 = 16
Factor the expressionWe have
16x^2 + 16x - 5
So, we have
16x^2 + 20x - 4x - 5
Factorize
4x(4x + 5) -1(4x + 5)
So, we have
(4x - 1)(4x + 5)
For the other expressions, we have
2z^2 + 13z - 70
2z^2 + 20z -7z - 70
So, we have
(2z - 7)(z + 10)
6x^2 - x - 40
6x^2 + 15x -16x - 40
So, we have
(3x - 8)(2x + 5)
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Help me pls it’s due tomorrow and I really need help pls hurry and have a explanation!!
Answer: I don't know
Step-by-step explanation: good luck
Answer:
A. 3/4
Step-by-step explanation:
[tex]\frac{8}{1}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{24}{4}[/tex] = 6
6 is less than 8
Someone help me do further maths ‘transformations of graphs and functions’ question
Answer:
see attached
Step-by-step explanation:
just draw a narrower one, about 1/2 of the x value.
Gabriella drank
2
3
liter of water Monday before going jogging. She drank
3
7
liter of water after her jog. How much water did Gabriella drink altogether? Write your answer as a mixed number.
[tex]1\frac{5}{12}[/tex] liter of water Gabriella drink altogether.
What is Fraction?A fraction represents a part of a whole.
Gabriella drank 2/3L water before jog
Gabriella drank 3/4L water after her jog
Altogether water she drank (2/3+3/4)
2/3+3/4
LCM of 3 and 4 is 12
8+9/12
17/12
17/12 can be written as mixed fraction [tex]1\frac{5}{12}[/tex].
Hence, [tex]1\frac{5}{12}[/tex] liter of water Gabriella drink altogether.
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Type the integer that makes the following division sentence true: 50 –250
The integer that makes the sentence true is -200
How to determine the integerFrom the question, we have the following parameters that can be used in our computation:
50 - 250
The above expression is not a division sentence
Instead, it is a subtraction sentence
using the above as a guide, we have the following:
50 - 250
Evaluate the difference in the sentence above
50 - 250 = -200
Hence, the integer is -200
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the difference between a positive number X and 3 is 21 what is a number stepsssss
Answer:
Solution:
Let another number be x.
Then positive number = 5x
According to the question,
5
�
+
21
=
2
(
�
+
21
)
5x+21=2(x+21)
⇒
5
�
+
21
=
2
�
+
42
⇒5x+21=2x+42
⇒
5
�
−
2
�
=
42
−
21
⇒5x−2x=42−21
⇒
3
�
=
21
⇒3x=21
⇒
�
=
21
3
=
7
⇒x=
3
21
=7
Hence another number = 7 and positive number = 7 x 5 = 35.
Gib alle reellen Zahlen x an, die die Gleichung lösen.
a) x2 - 16 = 0
Answer:
x = +4 , -4
Step-by-step explanation:
Solving the equation:x² - 16 = 0
x² = 16
[tex]\sf x = \sqrt{16}\\\\x = \sqrt{4*4}\\\\[/tex]
x = ±4