it would take the object approximately 11.51 seconds to reach the ground.
What is time?Generally, Time is a concept used to describe the progression of events, or the duration of those events. It is often measured in units such as seconds, minutes, hours, days, and years.
Time can also be described as a continuum, with past events on one end and future events on the other.
Time is a fundamental aspect of the universe and is closely related to concepts such as causation, change, and entropy.
The time it would take the object to reach the ground can be found by setting the distance from the ground, s, to 0 and solving for t.
0 = -16t^2 + 2120
t^2 = (2120/16)
t = [tex]\sqrt{(2120/16)}[/tex]
t = approximately 11.51 seconds
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Which best describes the offspring of protists?
always genetically identical to one parent
always genetically identical to both parents
never genetically identical to one parent
sometimes genetically different than both parents
The best description of the offspring of Protists is D. sometimes genetically different than both parents
How do Protists reproduce ?Asexual reproduction in protists includes methods such as binary fission, budding and fragmentation, in these methods the offspring are always genetically identical to one parent.
Sexual reproduction in protists can be through conjugation, meiosis, or syngamy, in this case the offspring are not always genetically identical to one or both parents. It is possible for the offspring to be genetically different from both parents due to the genetic recombination that occurs during sexual reproduction.
So, the statement that best describes the offspring of protists is "sometimes genetically different than both parents" as it depends on the type of reproduction method used.
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Maddox has 21 to spend on souverniers as gift for his friends. He wants to buy each friend a keychain and a pin. The equation 3f + 4f =21 can be used to find f, the number of friends for which he can buy souvenirs
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{3f + 4f = 21}[/tex]
[tex]\textbf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(3f + 4f) = 21}[/tex]
[tex]\mathsf{3f + 4f = 21}[/tex]
[tex]\mathsf{7f = 21}[/tex]
[tex]\textbf{DIVIDE 7 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{7f}{7} = \dfrac{21}{7}}[/tex]
[tex]\textbf{SIMPLIFY it!}[/tex]
[tex]\mathsf{f = \dfrac{21}{7}}[/tex]
[tex]\mathsf{f = 3}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{f = 3}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
The given equation had a solution r in the interval -2≤r≤-1. Approximate the solution correct to two decimal places.
8x^3+3x^2-7x+6=0
r≈ ?
The approximate solution of the polynomial in the interval -2≤ x ≤-1 is given as follows:
x = -1.5.
What is the rational zero theorem?The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant divided by the factors of the leading coefficient.
The polynomial for this problem is given as follows:
8x³ + 3x² - 7x + 6.
Hence the leading coefficient and the constant are given as follows:
Leading coefficient: 8.Constant: 6.The factors of the leading coefficient and of the constant are given as follows:
Leading coefficient: {1, 2, 4, 8}.Constant: {1, 2, 3, 6}.Hence the possible roots are given as follows:
±1, ±2, ±3, ±6, ±0.5, ±1.5, ±0.25, ±0.75, ±0.125, ± 0.375.
The only possible root between -2 and -1 is given as follows:
x = -1.5.
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Ris is a botanist who works for a garden that many tourists visit. the function f(s) = 2s + 25 represents the number of flowers that bloomed, where s is the number of seeds she planted. the function s(w) = 25w represents the number of seeds she plants per week, where w represents the number of weeks. part a: write a composite function that represents how many flowers iris can expect to bloom over a certain number of weeks. (4 points) part b: what are the units of measurement for the composite function in part a? (2 points) part c: evaluate the composite function in part a for 30 weeks. (4 points)
The hybrid factor is f(w) Equals 50w + 25 according to the preceding statement. The hybrid value is measured in units of f (flowers) and w (weeks), etc. 30 weeks of Part A's synthesis function equal 1525.
What exactly are function and example?A task is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is just the input value, we would state that y is a mathematical function
Given that:
f(s) = 2s + 25
s(w) = 25w
The following combination function is used to determine how many flowers will blossom over the course of w weeks: f(w)
f(s) = 2s + 25
Replace s with s(w)
f(s(w)) = 2(s(w)) + 25
Substitute s(w) = 25w
f(s(w)) = 2(25w) + 25
f(s(w)) = 50w + 25
Hence,
f(w) = 50w + 25
Flowers are used as the units of measurement for f(w).
30 weeks of flowers translates to:
w = 30
So, we have:
f(30) = 50*30+25
f(30) = 1525
Thus, there will be 1525 blossoms throughout the course of 30 weeks.
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William invested $550 in an account paying an interest rate of 2% compounded monthly. Violet invested $550 in an account paying an interest rate of 2% compounded continuously. To the nearest hundredth of a year, how much longer would it take for William's money to triple than for Violet's money to triple?
Answer:
We can use the formula A = P(1 + r/n)^(nt) to find out how long it takes for William's money to triple, where A is the final amount, P is the principal, r is the interest rate, t is the time in years and n is the number of times the interest is compounded per year.
A = P(1 + r/n)^(nt) = 550(1 + 0.02/12)^(12*t) = 3P
Solving for t we get
t = (ln(3)/ln(1+0.02/12))/12 = 49.41
For Violet's account, using the formula A=Pe^(rt) where A is the final amount, P is the principal, r is the interest rate, t is the time in years, we get:
t = ln(3) / (2 * e^-2) = 49.41
Therefore, it will take approximately 49.41 years for William's money to triple, and 49.41 years for Violet's money to triple.
So the difference in time is 0.
What are the two types of graphs?
A Graph comprise of nodes and edges. The nodes are sometimes also denoted to as vertices and the edges are lines or arcs that joins any two nodes in the graph.
1. Finite Graphs: A graph is said to be limited if it has a finite number of vertices and a finite number of edges.
2. Infinite Graphs: A graph is said to be infinite if it has an unlimited number of vertices as well as an unlimited number of edges.
3. Trivial Graph: A graph is said to be trivial if a finite graph consists of only one vertex and no edge.
4. Regular Graph: A simple graph is called to be regular if all vertices of graph G are of equal degree.
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Given the recursive formula below, find the first five terms.
Answer:
3, 5, 7, 9, 11
Step-by-step explanation:
the recursive formula allows a term to be found by adding 2 to the previous term, that is
u₁ = 3
u₂ = u₁ + 2 = 3 + 2 = 5
u₃ = u₂ + 2 = 5 + 2 = 7
u₄ = u₃ + 2 = 7 + 2 = 9
u₅ = u₄ + 2 = 9 + 2 = 11
the first 5 terms are 3, 5, 7, 9, 11
3(2x-7)= 3
What are the solutions
A company has 120 people who assemble toys. If 60% of these people assemble yoyo's, how
many more workers must transfered from other departments so that 70% of the people are assembling yo-yo's?
Answer:
12 people
Step-by-step explanation:
Total people in the company = 120
No. of People who assemble yo- yo's = 120 × (60/100
= 72
Now, we need 70% of the total people to assemble yoyo = 120 × (70/100)
= 84
We already have 72 people assembling yoyo,
No. of more people needed = 84 - 72 = 12
Hence, if we have 12 more people from other departments, 70% of the total people would be assembling yo-yo's.
a piece of wire 10m long is cut into 2 pieces. one piece is bent into a square and the other into a circle. how much of the wire should be used for the square if you want to minimize the total enclosed area? please give an exact simplified answer.
Bend 4.4 m of the wire into a circle and bend 5.6 m of the wire into a square in order to minimize the total area.
Let x = length of the portion that is bent into a circle
Then, 10-x = length bent into a square
Each side of the square has length (10-x)/4
So, area of square = (10-x)2/16
x = circumference of circle = 2πr So, r = x/(2π)
Therefore, Area of circle = πr2 = x2/(4π)
T = total area = (10-x)2/16 + x2/(4π)
= [(10-x)2π + 4x2 ]/(16π)
= [(100-20x+x2)π + 4x2]/(16π)
= [(4+π)x2 -(20π)x+100π]/(16π)
= [(4+π)/(16π)]x2 - (5/4)x + (25/4)
The graph of T is a parabola opening upward. The minimum of T occurs at the vertex of the parabola.
The x coordinate of the parabola is (5/4)/[(4+π)/(8π)] = (10π)/(4+π) ≈ 4.4
Thus, Bend 4.4 m of the wire into a circle and bend 5.6 m of the wire into a square in order to minimize the total area.
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During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed in a horizontal circle as shown. Knowing that the speed of the hammer is 2.5 m/s and θ = 60°, determine (a) the tension in wire BC, (b) the radius of the circle, rho.
(a) The value of the tension in wire BC will be = 80.4 N
(b) The value of the speed of the hammer’s head will be = 2.30 m/s
Mass of the head of the hammer = 7.1 Kg.
The speed at which it is revolving = v
value of ρ=0.93 m
The value of the angle θ=60°
Tension is described as the force transferred through a rope, string, or wire when pushed by opposing forces. The tension force is directed along the length of the wire and draws energy evenly on the bodies at the ends.
(a) Now, we will first calculate the value of the tension in wire BC,
First, we will note
[tex]$$a_A=a_n=\frac{v_A^2}{\rho}$$[/tex]
(a)
[tex]$+\Sigma F_y=0: T_{B C} \sin 60^{\circ}-W_A=0$[/tex]
or we can write it as:
[tex]$$\begin{aligned}T_{B C} & =\frac{7.1 \mathrm{~kg} \times 9.81 \mathrm{~m} / \mathrm{s}^2}{\sin 60^{\circ}} \\\end{aligned}$$[/tex]
=> =80.426 N
=>= 80.4 N (approx)
(b) Now calculate the speed of the hammer’s head.
[tex]$\quad+\Sigma F_x=m_A a_A: T_{B C} \cos 60^{\circ}=m_A \frac{v_A^2}{\rho}$[/tex]
or
[tex]$$v_A^2=\frac{(80.426 \mathrm{~N}) \cos 60^{\circ} \times 0.93 \mathrm{~m}}{7.1 \mathrm{~kg}}$$[/tex] = 2.30 m/s
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Note: The correct question may be like this:
During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed v in a horizontal circle as shown. If ρ=0.93m and ,θ=60° determine (a) the tension in wire BC, (b) the speed of the hammer’s head.
The needed diagram is attached below
Is 1.5 in the same as one and a half in?
Yes 1.5 is the same as one and a half
Answer: Yes
Step-by-step explanation:
1/2 = a half 1/2 also = 0.5 1 + 0.5 = 1.5 or 1 and 1/2
. An integer a is said to be a type 0 integer if there exists an integer n such that a3n. An integer a is said to be a type 1 integer if there exists an integer n such that a-3n 1. An integer a is said to be a type 2 integer if there exists an integer m such that a - 3m + 2. * (a) Give examples of at least four different integers that are type 1 integers (b) Give examples of at least four different integers that are type 2 integers (c) By multiplying pairs of integers from the list in Exercise (9a), does it appear that the following statement is true or false? If a and b are both type 1 integers, then a b is a type 1 integer.
When n is known to be an integer, the formula for m also produces an integer. The assumption is confirmed once the necessary integer m was located.
what is integer ?Positive, negative, and zero are all examples of integers. As a result, integers include numbers like 0, 1, 2, 3, as well as -1, -2, and 3. There are no additional parts, such as fractions or decimals, in integers. As a result, fractional values like 3 1/2 and decimal numbers like -7.5 are NOT integers. All positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity are included in the category of integers. The fundamental arithmetic operations are included in integer operations (addition, subtraction, multiplication and division). In mathematics, integers are any numbers that are either positive, negative, or zero, with the exception of fractions. As a result, operations on integers are simple.
given
Any whole number that is a multiple of 3 is a type 0 integer. Examples are 3, 6, 9, and 12.
n=1: 3(1)=3
n=2: 3(2)=6
n=3: 3(3)=9
n=4: 3(4)=12
When n is known to be an integer, the formula for m also produces an integer.
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60 POINTS BEING AWARDED!!!!!!!! PRECISION Find the values of x and y in the trapezoid. Justify your answer.
The values of x and y in the trapezoid are x = 15 and y = 3
What is a trapezoid?You should understand that a trapezoid or trapezium is a quadrilateral having two parallel sides and two non-parallel sides
If the trapezoid is isosceles, angles A and C are supplementary, so ...
(4x+4) +(7x+11) = 180
This implies that
11x +15 = 180
Collecting terms we have
11x = 165 . . . . . . . . . subtract 15
x = 15 . . . . . . . . . . . . divide by the coefficient of x
And angles C and E are congruent.
4·15 +4 = 21y +1
63 = 21y . . . . . subtract 1
3 = y . . . . . . . . divide by the coefficient of y
In conclusion x and y are 15 and 3
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Noah ordered a meal delivery from a local restaurant. the cost of his meal, before tax, was $15.20. if the sales tax is 6.5%, what was the total cost of his meal? show or explain your thinking.
The total cost of the meal was $16.189.
What is the sales tax?
A sales tax is a consumption tax that is added to the price of goods and services. It is usually a percentage of the purchase price, and the percentage varies depending on the location and type of product or service.
We are trying to find the total cost of the meal including the sales tax. To do this, we need to calculate the amount of tax and add it to the cost of the meal.
The cost of the meal before tax is $15.20 and the sales tax rate is 6.5%. To find the amount of sales tax, we can multiply the cost of the meal by the sales tax rate as a decimal.
$15.20 x 0.065 = $0.989
The amount of sales tax is $0.989.
To find the total cost of the meal, we can add the amount of sales tax to the cost of the meal before tax.
$15.20 + $0.989 = $16.189
Hence, The total cost of the meal was $16.189.
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Which of the following is equivalent to the quadratic equation below after completing the square?
x² +6x-3=12
A. (x+6)² = 12
B. (x+3)² = 24
C. (x+6)² =9
D. (x+3)² = 9
Review the table forecasting a company’s profit based on the number of units sold.
Which statement is the best interpretation of the value 29,864 in the quadratic regression equation?
The company has an initial loss of about $29,864.
The company has an initial profit of about $29,864.
The company needs to sell about 29,864 units to break even.
The company needs to sell about 29,864 units to maximize its profit.
The statement that best interprets the value 29,864 in the quadratic regression equation (y = -0.004·x² + 34.637·x - 29,864) for the data in the table forecasting the company's profit based on the number of units sold is the option;
The company has an initial loss of about $29,864What is a regression equation?A regression equation is an equation that aims at discovering the relationship between a dependent or output variable and the input or independent variable.
The possible data in the question, obtained from a similar question, posted online, is presented as follows;
Number of Units[tex]{}[/tex] Profits ($)
500 [tex]{}[/tex] -10,000
1200 [tex]{}[/tex] 3000
2500 [tex]{}[/tex] 27000
3200 [tex]{}[/tex] 40000
3600 [tex]{}[/tex] 45000
4300 [tex]{}[/tex] 47000
5000 [tex]{}[/tex] 45000
6750 [tex]{}[/tex] 20000
Based on the above data, using the Polynomial trendline option of Order 2, in MS Excel, the quadratic regression equation, obtained using the Display Equation on chart option is; y = -0.004·x² + 34.637·x -29,864
The function, f(x) = -0.004·x² + 34.637·x -29,864, indicates that at x = 0, which is the point where 0 units have produced, we get;
Initial Profits = f(0) = -0.004 × 0² + 34.637 × 0 -29,864 = -29,864
The value, -29,864 indicates a loss of $29,864, therefore;
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Answer:
Step-by-step explanation:
The company has an initial loss of about $29,864
The perimeter of a rectangle pool is 332m, if the length of the pool is 89m, what is its width?
Answer: 77m
Step-by-step explanation:
The equation for the perimeter of a rectangle is: p = 2(length) + 2(width). We are given both perimeter and the length, so we can plug in these values to solve for what is missing.
332m = 2(89) + 2(width)
332m = 178 + 2(width)
154 = 2(width)
width = 77
Just combine like terms and get the variable (width) by itself on one side of the equation to solve. Hope this helps!
Answer:
width = 77 m
Step-by-step explanation:
Perimeter = sum of all sides
As a rectangle has 2 lengths and 2 widths making a total of four sides;
P = 2 ( l + w)
332 = 2 ( 89 + w)
332/2 = 89 + w
166 = 89 + w
166 - 89 = w
77 = w
Therefore, the width of the pool is 77 m
5 + 12.5v ≥ 170 what is v
Answer:
v ≥ 13.2 or v ∈ [13.2; ∞ )--------------------------
Given:
5 + 12.5v ≥ 170Solve it in below steps:
5 + 12.5v ≥ 170 Given12.5v ≥ 170 - 5 Subtract 5 from both sides12.5v ≥ 165v ≥ 165/12.5 Divide both sides by 12.5v ≥ 13.2 AnswerAnswer:
[tex] \sf \: v \geqslant 13.2[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of v.
The equation is,
→ 5 + 12.5v ≥ 170
Then the value of v will be,
→ 5 + 12.5v ≥ 170
→ 12.5v ≥ 170 - 5
→ 12.5v ≥ 165
→ v ≥ 165 ÷ 12.5
→ [ v ≥ 13.2 ]
Hence, the value of v is 13.2.
plsss helppppppppppppppppp
Answer:
hard
Step-by-step explanation:
ybfhf
The label on a \frac{1}{3}
3
1
-pound bag of seeds states that it will cover an area of 5656 square feet. How many square feet do the seeds cover per pound?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
To enter a mixed number on the double number line, use a space and the slash key. For example: 3 1/2
Answer: The bag of seeds covers 5656 square feet and is 1/3 pound. To find how many square feet the seeds cover per pound, we can divide the total coverage by the weight of the bag.
Formula: Coverage per pound = Total coverage/weight of the bag
5656 / (1/3) = 5656*3 = 16,968 square feet per pound.
Step-by-step explanation:
The length of a rectangle is twice its width.
The perimeter of the rectangle is 42 cm.
Label the diagram with the correct length and width for the rectangle.
cm
cm
દ
Answer: W = 7, L = 14
Step-by-step explanation: L = 2W. 2L + 2W = 42. Plug in L and we get 4W + 2W = 42. 6W = 42. W = 7. L = 14
The senior class plans a school trip to washington dc. students should bring money for meals and souvenirs. they are told to bring at least $65 but no more than $135. write a compound inequality that represents the range of the amounts of money a student can bring.
The compound inequality represents the range of the amounts of money a student can brings $65 ≤ x ≤ $135
Start by setting up the inequality with the variable x, representing the amount of money a student can bring:
x
2. The inequality should be less than or equal to the maximum amount of money a student can bring, which is $135:
x ≤ 135
3. The inequality should also be greater than or equal to the minimum amount of money a student can bring, which is $65:
65 ≤ x
4. Combine the two inequalities to get the compound inequality:
65 ≤ x ≤ 135
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4. you are looking for a deep spot to take a swim in a local river. the width of the river is about the same all along its length, but there are places where the water flows quickly and places where it flows slowly. which is a better choice for a swim?
The best choice for a deep spot to take a swim is to go to a place in the river where the cross-sectional area is larger, and the water flows slower.
If you are looking for a deep spot to take a swim in a local river, the best choice is to go where the water flows slowly. The speed of the water is determined by the formula:
v=Q/A,
where v is the speed of the water, Q is the discharge rate, and A is the cross-sectional area of the river. As Q is constant for the same river, a slower water flow can be achieved by increasing A, which is the cross-sectional area of the river. Therefore, the best choice for a deep spot to take a swim is to go to a place in the river where the cross-sectional area is larger, and the water flows slower.
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Help me out pleasereeeee
Answer:
90°
Step-by-step explanation:
So we know that ∠PRM is 120° and that line m would be 180°, we would subtract 120 from 180 to get 60°.
So ∠PRQ is 60°.
All the angles of a triangle equals to 180°.
∠PQR is given as 30°. So we will need to add 60+30=90.
180-90=90. So ∠QPR is 90°.
Write the coordinates of the vertices after a reflection over the x-axis.
The coordinate of the vertices (x,y) after a reflection over the x-axis is (x, -y). It is also known as a rule.
What are coordinates?
Coordinates are two numbers (Cartesian coordinates) or a letter and a number that point to a specific point on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical).
A reflection of a point, line, or figure in the x-axis entailed mirroring the image over the x-axis. In this case, the x-axis is referred to as the axis of reflection.
The rule for reflecting over the x-axis is to negate the value of each point's y-coordinate while keeping the x-value constant.
For instance, when point P with coordinates (7,3) is reflected across the x-axis and mapped onto point P', P"s coordinates are (7,-3). The x-coordinate for both points remained unchanged, but the y-coordinate changed from 3 to -3.
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Can 8cm 5cm 10cm form the sides of a right-angled triangle?
No, the given measurement of the sides of a triangle does not forms a right angled triangle.
As given in the question,
For the given triangle,
Length of the sides of the triangle is given by :
8cm , 5 cm , and 10cm
In the given triangle longest side is equal to 10cm
Condition for a right angled triangle:
Longest side is the hypotenuse of the right angled triangle.
By Pythagoras theorem we have,
( Hypotenuse )² = ( Side1)² + ( Side 2)²
R.H.S. ( Right hand side )
= ( 8 )² + (5 )²
= 64 + 25
= 89
≠ 10²
Here given length side of a triangle does not satisfies the Pythagoras theorem .
Therefore, the given sides of a triangle is not representing a right angled triangle.
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a teacher offers gift cards as a reward for classroom participation. the teacher places the gift cards from four different stores into a bag and mixes them well. a student gets to select two gift cards at random (one at a time and without replacement). each outcome in the sample space for the random selection of two gift cards is equally likely. what is the probability of each outcome in the sample space? startfraction 1 over 16 endfraction one-sixth one-fourth one-half
The probability of each outcome is 1/12 or 0.083.
The probability of each outcome in the sample space can be calculated using the formula for permutations. The formula for permutations is nPk = n!/(n-k)!. In this case n is the number of gift cards (4) and k is the number of gift cards to be selected (2). In this example, the sample space consists of 16 possible outcomes, and each outcome is equally likely. Thus, the probability of each outcome is 1/16. To calculate this, divide 1 by the total number of outcomes (16). This results in the probability of each outcome being 1/16.Therefore, nPk = 4P2 = 4!/2! = 12. Since each outcome is equally likely, the probability of each outcome is 1/12 or 0.083. This can be written as a fraction as 1/12 or as a decimal as 0.083.
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PLEASE HELP ASAP TYSM
Answer:
77 cups
Step-by-step explanation:
88 ounces/ day = 11 cups/ day
A week = 7 days
=> 11 x 7 = 77 cups/week
(15 + y ) - (a+ u) }{3 ^ {2} -x}
After simplification, the value of expression is,
⇒ 15 + y - 9a + ax - 9u + ux
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (15 + y) - (a + u) (3² - x)
Now, Simplify the expression as;
⇒ (15 + y) - (a + u) (3² - x)
⇒ (15 + y) - (a + u) (9 - x)
⇒ (15 + y) - (9a - ax + 9u - ux)
⇒ 15 + y - 9a + ax - 9u + ux
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