Answers
The leading coefficients and parabolic equations, considering the vertices, are given as follows:
1. a = 7/4, y = 7/4(x - 4)² - 1.
2. a = -2, y = -2(x + 1)² + 2.
Equation of parabola with vertex (h,k)
The equation of a parabola with vertex given by (h,k) is presented as follows:
y = a(x - h)² + k.
In which a is the leading coeffiicent.
For item 1, the coordinates of the vertex is given as follows:
(4,-1).
Hence:
h = 4, k = -1, and the equation is:
y = a(x - 4)² - 1.
When x = 6, y = 6, hence the leading coefficient is calculated as follows:
6 = a(6 - 4)² - 1
4a = 7
a = 7/4.
Thus the equation is:
y = 7/4(x - 4)² - 1.
For item 2, the vertex is:
(-1,2).
Hence:
y = a(x + 1)² + 2.
When x = 0, y = 0, hence the leading coefficient is calculated as follows:
0 = a(0 + 1)² + 2
a = -2.
Hence the equation is:
y = -2(x + 1)² + 2.
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Related Questions
an urn contains 6 blue balls and 6 orange balls. in how many ways can we select 2 blue balls and 2 orange balls from the urn?
Answers
The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545
No. of Blue balls in the urn = 6
No. of Orange balls in the urn = 6
Total no. of balls in the urn = No. of blue balls + No. of orange balls
= 6 + 6
= 12 balls
No. of blue balls to be selected = 2
No. of orange balls to be selected = 2
No. of balls to be selected = 4
The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]
The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]
The No. of ways 2 orange balls can be selected = [tex]^{6}C_{2}[/tex]
Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn
= [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]
Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls
P = (15×15)/495
= 225 / 495
P = 0.4545
Therefore, the no. of ways to select blue and orange balls is 0.4545
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I need to paint a straight face consisting of six panels he has a green red and magenta paint and each panel should be painted with only one color how many ways are there to paint the fence
Answers
There are 20 ways to paint the fence consisting of six panels each with one color out of green, red, and magenta.
There is a total of 6 panels and 3 paint colors and each panel has to be painted with only 1 color.
∴ Total number of panels = 6
Total number of colors = 3 (green, red, and magenta)
To calculate the number of ways to paint 6 panels with one of the 3 colors, the formula of combination is used. Combinations are ways of selecting objects from a group or collections, in a way that the order of the objects does not matter.
The number of ways or the combinations of 6 panels taken with each color out of 3 at a time is given by [tex]^6C_3[/tex]
[tex]^6C_3[/tex] = 6! / [3! (6-3)!]
[tex]^6C_3[/tex] = (6*5*4*3*2*1) / [3*2*1 (3)!]
[tex]^6C_3[/tex] = 720 / (6*6)
[tex]^6C_3[/tex] = 720 / 36
[tex]^6C_3[/tex] = 20
Therefore, 20 combinations are possible to paint 6 panels each with only one color out of green, red, and magenta.
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PR is a chord of a circle Center 0 and radius 20CM - POR = 120° calculate (a) length of the Chord PR (b) length of are PQR
Answers
Answer:
i have the similar question just radius is changed frm 12 to 20 cm..
hopefully this will help u ...^_^
Show all your work!
First find the k= COP x
K=18-12=1.5
X=1.5(10)
Y=1.5 =
y
४/५
es, Show all your work!
y
of
y
First find the k= COP x
Answers
Answer:
Step-by-step explanation:
COP = Constant of Proportionality. • y varies directly to x. > If 10 miles varies directly to 5 minutes,. – then 10 = y and 5 = x. • Unit Rate (1, r). > (x, y).
you're planning on making 5 meatloafs for a party. you go to the store to buy breadcrumbs, and see they are sold by the canister. how many canisters do you need to buy?
Answers
Without decimal, 4 canisters need to buy for making 5 meatloafs for party or if answer in decimal values needed then it is 3.333 canisters.
From the provided data, we have
number of meatloafs = 5
Here we have need the cup measurements the number of meatloafs made per recipe and the net weight of canister.
net weight of the contents of 1 canister = 15 ounces
1 cup = 8 ounces
1.25 cups = 10 ounces
10 ounces of breadcrumbs makes 1 meatoafs.
but we made 5 meatloafs so, for 5 meatloaf needed breadcrumbs = 5×10
= 50
If we consider 4 canisters then
15ounces × 4 canisters = 60 ounces which are 10 more than the needed ( > 50 ounces.
and if we are consider 3 canisters then
15 ounces × 3 canisters = 45 ounces which is not enough.
So, we need 4 canisters of breadcrumbs and we will have 2/3 of a canister left over.
approximately 3.333 is a value of needed canisters in decimals values. If decimal values are not need ,i.e, whole are canisters are not partial then 4 canisters is right .
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Complete question:
you're planning on making 5 meatloafs for a party. you go to the store to buy breadcrumbs, and see they are sold by the canister. how many canisters do you need to buy?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much breadcrumbs does the recipe call for? It calls for 1 1/4 cups of breadcrumbs. How many meatloafs does the recipe make? It makes 1 meatloaf.
How many servings does that recipe make? It says it serves 10.
How big is the canister? It is cylindrical, 3.5 inches across and 7 inches tall.
What is the net weight of the contents of 1 canister? 15 ounces.
How much does a canister cost? $2.39
How much does a cup of breadcrumbs weigh? I'm not sure, but maybe something from the nutritional label will help.
Can anyone write the equation this graph?
Answers
The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.
What is the Equation of the Graph of an Absolute Value Function?The equation, in vertex form, of a absolute value function is expressed as y = a|x – h| + k, where:
(h, k) = vertex of the graph a = this value determines if the graph opens up or opens down.h = horizontal translation factork = vertical translation factorFrom the graph, we know that:
Vertex (h, k) = (3, 5)
Substitute h = 3 and k = 5 into the equation, y = a|x – h| + k:
y = a|x - 3| + 5
A point on the graph is (5, 7). To find the value of a, substitute x = 5 and y = 7 into the equation y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 = 2a + 5
7 - 5 = 2a + 5 - 5 [subtraction property of equality]
2 = 2a
Divide both sides by 2
2/2 = 2a/2 [division property of equality]
Substitute a = 1 into y = a|x - 3| + 5:
y = |x - 3| + 5 [equation of the absolute value function]
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Solve the following problems using the concept of multiples. Justify your work with a table.
3. María is shopping for party supplies. She finds that paper plates come in packages of 8,
napkins come in packages of 10, and paper cups come in packages of 12. What is the
least number of packages of plates, napkins, and cups she has to buy so that she
has the same number of each item for her party?
8
10
4. For the month of November, Jaime plays basketball every other day and he goes to sc
practice every four days.
If he starts on November 2 on what days will he do both sports?
Answers
For Maia's birthday celebration, the bare minimum amount of packets of plates, napkins, and cups she needs to purchase is 15, 12, and 10, respectively.
What is a Fraction?A portion of a whole is referred to as a fraction. such as 0.25 can be used to describe the fraction 1/4.Given that paper plates, napkins, and cups are sold in quantities of eight, ten, and twelve each, respectively, Therefore, we need to take the LCM of the following in order to determine how many packets of plates, napkins, and cups Maria needs to purchase in order to have the same quantity of each item for her birthday celebration.acc to our question-
LCM of 8, 10, and 12 = 120Now, the number of packages,Hence, the least number of packages of plates, napkins, and cups Maia has to buy so that she has the same number of each Item for her birthday party is 15, 12, and 10, respectively.Learn more about Fraction:
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If m/AGD = 72°, then what is m/DGB?
177²
37. C
A
E
D
H
a
10
5
G/1
3/2
F
B
4
Please provide an explanation.
Answers
Answer:
m∠DGB = 108°
Step-by-step explanation:
Linear pair:If the non-common arms of two adjacent angles form a straight line, then the adjacent angles are called linear pair and they add up to 180°.
m∠AGD + m∠DGB = 180° {Linear pair}
72 + m∠DGB = 180
m∠DGB = 180 - 72
m∠DGB = 108°
Find the value of x and 3x
Answers
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
now let's consider the white, "cut-out" triangle on the left side.
the purple one angles at the top and bottom corner are 45°.
the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.
so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).
and that means that the third white angle is
180 - 45 - 45 = 90°.
and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.
360 = 90 + 3x
270 = 3x
x = 90°
3x = 270°
an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x? an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x?
Answers
The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.
What is an isosceles triangle?Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.
Here,
Since the adjacent sides of isosceles triangles are equal,
4x-3=2x+5
4x-2x=5+3
2x=8
x=4
The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.
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In the recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?
Answers
The number of cans that are recycled is approximately 1 billion cans in 1 week.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that 51.9 billion aluminum cans were recycled.
Therefore, the rate of recycled the can is;
51.9 billion / 1 year
We know that 1 year has 52 weeks
Then
51.9 billion / 1 year x 1 year / 52 weeks
= 51.9 (1) billion / 1 (52 ) weeks
= 51.9 billion/ 52 weeks
= 1 billion/ 1 week
Hence, the number of cans that are recycled is approximately 1 billion cans in 1 week.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3
The quadratic function is given by
f(x) = [tex]-3(x+2)^2[/tex] + 1
The vertex form of the quadratic function is
f(x) = [tex]a(x-h)^2[/tex] + k
Where (h, k) is the coordinates of the vertex
x = h is the axis of symmetry
Compare the given function and the vertex form of the quadratic function and find the value of the each term
The value of h = -2
The value of k = 1
The coordinates of the vertex = (-2, 1)
The axis of symmetry is at x = h
h = -2
Draw the graph using the details
Hence, the the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3
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8. If a population doubles every 5 years, how many years will it take for the population to increase by 10 times
its original amount?
First: If the population gets multiplied by 2 every 5 years, what does it get multiplied by each year? Use this
to help you answer the question.
Answers
After ≈16.61 years the population will increased by times it's original amount.
What do you mean by population?
A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.
Given: If a population doubles every 5 years.
Assume, 'A' is the starting population, and 't' is the passing time in years.
Given the fact that a population doubles every five years, our population is growing exponentially, as per the question.
Here, the equation can be written as follows: [tex]A(t) = A(2)^{\frac{t}{5} }[/tex] (1)
We now need to determine when the population will have multiplied by 10 by that time.
Let's substitute [tex]A(t) = 10A[/tex] in the above equation.
[tex]10A = A(2)^{\frac{t}{5} }[/tex]
[tex]10 = (2)^{\frac{t}{5} }[/tex]
Taking the natural log of both sides we get:
[tex]ln10 = \frac{t}{5} \times ln2[/tex] {[tex]ln(a)^n= nln(a)[/tex]}
2.3025 x 5 = t x 0.6931
[tex]t = \frac{2.3025}{0.6931}\\t = 16.6096[/tex]
Therefore, After ≈16.61 years the population will increased by times it's original amount.
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Which is equivalent to 3√8x?
Answers
It is equivalent to 8^x/3
What is equivalent equations?OBJECTIVES FOR EQUALITY EQUATIONSAfter finishing this section, you need to be able to:Sort an equation into a conditional or an identity category.Mentally solve simple equations.Check to see if some equations are equal.A mathematical equation is a statement that two numerical expressions are equal.Equations go into one of two categories.acc to our question-
to write a square root into fraction. To do that, you just have to apply the formula :
x^power/root
Then, here it gives . 8^x/3
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A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
PLEASE I NEED HELP!!
Answers
Each angle in a regular polygon is 180(n-2)/n
We know n = 16 so each angle is 180 x 14 / 16
5h - 29 = 180 x 14 / 16
Multiplying both sides by 16 gives
80h - 464 = 2520
80h = 2056
h = 2056 / 80 =25.7
how do i solve 1) −10+ r = 3+r-7
Answers
Answer: No Solution
Explanation: 10 + r = 3 + r - 7
Combine like terms: 10 + r = -4 + r
Subtract R to both sides: 10 = 4
There is NO SOLUTION
Write an equation (any form) for the quadratic graphed below
Answers
The equation for the quadratic graphed is [tex]2x^{2}+4x+2[/tex].
Let the quadratic equation be [tex]y =a x^{2}+bx+c[/tex]
Points given in graph,
A(-1,0), B(-2,2), C(0,2)
Put the values in quadratic equation
For C(0,2)
[tex]2 =a(0)^{2}+b(0)+c[/tex]
[tex]2 = 0+0+c[/tex]
c = 2
For A(-1,0)
[tex]0 =a(-1)^{2}+b(-1)+2[/tex]
[tex]a-b+2 = 0[/tex]
a - b = -2 ...........(i)
For B(-2,2)
[tex]2 =a(-2)^{2}+b(-2)+2[/tex]
[tex]4a-2b+2=2[/tex]
2a - b = 0 ............(ii)
Solving eq (i) and (ii)
a = 2
b = 4
Putting the value of a, b and c in quadratic equation,
[tex]y =2x^{2}+4x+2[/tex]
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how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?
Answers
There are 100 4-digit positive integers are possible between 1000 and 9999.
Our first step is to divide the four digit number into four places: tens, hundreds, and thousands.
To solve this problem, we must start from the right-hand side and find how many even numbers should be placed where the desired answer can be obtained.
There are a total of [0, 2, 4, 6, and 8] objects
There should only be one digit on one place, since it is the only digit that makes the number divisible by five
There are 1 ways to fill the one's place, so the total number is 1.
It is possible to take any number from the given sets of even numbers in the tens place,
There are five ways to fill one place, so there are five ways to fill it.
Taking a look at the hundreds place,
All numbers can be placed in the hundreds place from the given sets, so all numbers can be taken from the hundreds place.
Therefore, there are five ways to fill the hundreds place.
Taking a look at the thousands,
It is possible to fill thousands of places with 4 numbers from a given set of even numbers.
Therefore, there are four ways to fill the thousands place
The next step is to use the concept of factorial to find the number of ways to make a 4-digit number from even numbers that are divisible by 5.
To fill the respective places, we will multiply all the ways we calculated
= 4 × 5 × 5 × 1
= 100
Hence, there 100 4-digit positive integers possible.
Question
how many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?
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Evaluate b²-4ac if: a = 1 b= -3 C = -1
Answers
9--4
9+4=13
Answer:
13
Step-by-step explanation:
To evaluate meant to find its Value at the givens
At a = 1 , b = -3 , c = - 1
[tex]b^{2}-4ac=(-3)^{2} -4*1*-1=9+4=13[/tex]
Glad to Help
Help please, I can’t think of what this is plus time is running out
Answers
The measure of width of given figure is 2 units. Therefore, option B is the correct answer.
From the given figure, the length is 9 units and the width is 1 unit.
What is a length?Length is defined as the measurement or extent of something from end to end. In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects. For example, a rectangle has its dimensions as length and breadth.
From the figure, the width is 1+1=2 units
The measure of width of given figure is 2 units. Therefore, option B is the correct answer.
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750 people go on a coach trip
each coach can hold 55 people
How many coaches are needed
Answers
Step-by-step explanation:
750 people go on a coach trip each coach can hold 55 people How many coaches are needed?
750/55 = 13.636 coaches are needed.
Because you cannot have a partial coach, you round up to needing 14 coaches.
You can’t split a coach into pieces, so rounding it up makes 14
You’ll need 14 coaches
Help Please! Its a Math question. Need help asap.
Answers
The composite figure has a total area of 12 square centimeters.
How to determine the area of a composite figure
In this problem we find the area of a composite figure, which is the result of subtracting the areas of four triangles of same dimensions from the area of the entire square. Now we proceed to determine the area:
A = (6 cm)² - 4 · 0.5 · (2 cm) · (3 cm)
A = 36 cm² - 2 · (12 cm²)
A = 36 cm² - 24 cm²
A = 12 cm²
The area of the composite figure is 12 square centimeters.
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Which of the following rational functions is graphed below?
Answers
Answer:
C
Step-by-step explanation:
In the graph, you can see an asymptote is happening for x=-5, so look for an equation that divides by 0 for x=-5. That is clearly C, for x=-5 the denominator is 0.
let nn denote the smallest positive integer that is divisible by both 44 and 9,9, and whose base-1010 representation consists of only 44's and 99's, with at least one of each. what are the last four digits of nn?
Answers
The last four digits of the number nn are 4944
Given that,
Let nn stand for the lowest positive integer that can be represented in base-1010 using only the numbers 44 and 99, with at least one of each. This number must be divisible by both 44 and 9,9.
The last two digits of n must be divisible by 4 for n to be divisible by 4.
So last digits of n will be 44.
And for divisiblity by 9, sum of all digits of n has to be divisible by 9.
As two digits are fixed and their total is 8, next feasible total will be 45 so 9 can be atleast one time in n.
And as statement says n has to be smallest number n will be 4444444944
So last 4 digits of n are 4944.
Therefore, nn's last four numbers are 4944.
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length of 3 feet, a width of 2 feet, and a height of 5 feet. What is the volume of the refrigerator?
Answers
Answer:
30 feet^3
Step-by-step explanation:
length x width x height
3 x 2 x 5
=30
y≥x²+2x-8 factor the quadratic equation to find x intercepts
Answers
The factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)
What is meant by quadratic equation?A quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown value and a, b, and c represent known numbers. In general, a = 0; equations with a = 0 are considered degenerate because the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, and they can be distinguished by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.
To find x-intercept y=0
y≥x²+2x-8
x²+2x-8≥0
x²+4x-2x-8≥0
x(x+4)-2(x+4)≥0
(x-2)(x+4)≥0
∴x≥-4, x≥2
∴(-∞, -4]∪[2, ∞)
Therefore, the factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)
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Solve the system of equations by the addition method.
3x + 4y = 7
6x - 4y= 2
Answers
6x - 4y = 2
* Delete 4y together because they are the same *
=> 9x = 9 * we divide it by 9
x = 1
can someone help me really quick
Answers
Answer:
2 swimming pool lengths
Step-by-step explanation:
to answer this we divide 1/2 by 1/4
1/2/1/4
1/2x4/1=4/2
2 swimming pool lengths
hopes this helps please mark brainliest
the center for medicare services reported that there were 295,000 reported appeals for hospitalization and other medicare part a services. for this group, 40% of the first round appeals were successful. suppose ten first round appeals were just received. the results follow a binomial distribution. what is the probability exactly two of the appeals was successful? enter answer to four decimal places.
Answers
The probability exactly two of the appeals were successful is 0.9536
We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012), and suppose ten first-round appeals have just been received by a Medicare appeals office.
This situation can be represented through Binomial distribution as;
[tex]P(X=r)={}^{n}C_{r}(p)^r(1-p)^r[/tex] where [tex]x=0,1,2,3.....[/tex]
where, n = number of trials (samples) taken = 10
r = number of success
p = probability of success which in our question is % of first-round
appeals that were successful, i.e.; 40%
So, here X ~ Binom(n=10 , p=0.40
Probability that at least two of the appeals will be successful = P(X>=2)
P(X >= 2) = 1 - P(X = 0) - P(X = 1)
= 1 - [tex]^{10}C_{0}(0.40)^0(1-0.40)^{10-0}-^{10}C_{1}(0.40)^1(1-0.40)^{10-1}[/tex]
= 1 - 0.00605 - 0.0403
= 0.9536
Hence, the probability exactly two of the appeals were successful is 0.9536
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arceus x is on its way btw let's gooo ps. i need help
Answers
The number of pages read by her will be 36.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Marion read 616 pages in 14 days, The number of pages each day will be calculated as,
N = 616 / 17
Divide the number 616 by 17,
N = 36.23
N = 36
Therefore, the number of pages read by her will be 36.
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