Answer:
The answer to the question is
Its other zero (x-intercept) will be located at x = -5
Step-by-step explanation:
To solve the question, we note that a parabolic function is of the form
ax² + bx +c = 0
Therefore we have the vertex occurring at the extremum where the slope = 0
or dy/dx =2a+b = 0 also the x intercept occurs at x = 7, therefore when
ax² + bx +c = 0, x = 7 which is one of the solution
when x = 5, y = -4
That is a*25 +5*b + c = -4 also
49*a + 7*b + c = 0
2*a + b = 0
Solving the system of equations we get
a = 0.2, b = -0.4 and c = -7
That is 0.2x² -0.4x -7 = 0 which gives
(x+5)(x-7)×0.2 = 0
Therefore the x intercepts are 7 and -5
the second intercept will be located at x = -5
Final answer:
The other zero of the parabolic function with a vertex at (5, -4), and one zero at x = 7, will be located at x = 3, since it will be symmetrically placed with respect to the vertex.
Explanation:
The vertex of a parabolic function represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. The fact that the vertex of the function is given as (5, -4) and one zero is at x = 7 leads to the conclusion that the other zero must be equidistant from the vertex on the x-axis because a parabola is symmetric about its vertex. Since the distance from the vertex (5) to the given zero (7) is 2 units to the right, the other zero must be 2 units to the left of the vertex. Therefore, the other zero will be at x = 5 - 2, which is x = 3.
If the measure of angle T is 95 degrees and the measure of angle S is 100 degrees, then the measure of angle R is ___ degrees and the measure of angle Q is ___ degrees.
In a lilac paint mixture, 40% of the mixture is white paint, 20% is blue, and the rest is he rest is red. There are 4 cups of blue paint used in a batchof lilac paint. How many cups of white paint are used
Answer:
8
Step-by-step explanation:
The ratio of white paint to blue paint in the mix is ...
40% : 20% = 2 : 1
We can multiply this ratio by 4 cups to find ...
white : blue = 8 cups : 4 cups
There are 8 cups of white paint in the mixture.
Answer: the number of cups of white paint are used is 8
Step-by-step explanation:
Let x represent the total number of cups of paint used in the mixture.
40% of the mixture is white paint, this means that the number of cups of white paint used is 0.4x
20% of the mixture is blue paint, this means that the number of cups of blue paint used is 0.2x
If the rest is red, it means that the number of red cups used is
x - (0.2x + 0.4x) = 0.4x
There are 4 cups of blue paint used in a batch of lilac paint. This means that
0.2x = 4
x = 4/0.2 = 20
Therefore, the number of cups of white paint are used is
0.4 × 20 = 8
The volume of a rectangular prism is 960 cubic inches. If the dimensions of the base are doubled and the height remains the same to create a new prism, what will be the volume of the new rectangular prism in cubic inches?
Answer:
3840 cubic inches
Step-by-step explanation:
The volume of a rectangular prism is 960 cubic inches
Let the dimensions be lXwXh,
l=length of the base
w=width of the base
h=height of the base
The volume, lwh=960 cubic inches
If the dimensions of the base are doubled and the height remains the same
Volume of the new rectangular prism=2l X 2w X h =4lwh
=4 X 960 =3840 cubic inches
The area of the dining room at Thomas Jefferson so I'm in Monticello is about 342 ft.² is the approximate length of one side is a prime number less than 25 what are the approximate dimensions of the room?
Answer:
Yes, the approximate length of one side is a prime number less than 25.
The approximate dimensions of the room are 19 ft by 18 ft.
Step-by-step explanation:
Assuming the dining room is rectangular in shape
Approximate area of the dining room = 342 ft^2
The area of a rectangle is calculated by multiplying the length of the rectangle by the width.
Assuming the approximate length is a prime number less than 25
The closest prime number to 25 is 19
Approximate length = 19 ft
Approximate width = approximate area ÷ approximate length = 342 ft^2 ÷ 19 ft = 18 ft
Approximate dimensions of the room = 19 ft by 18 ft
A jewelry designer is making a pendant. The pendant will be a circular dis (center O) with a circular hold cut out of it, as shown. The radius of the disc is 35 millimeters. Find the area of the pendant. Use 3.14 for π and round to the nearest tenth
Answer:
2884.8 millimeters squared
Step-by-step explanation:
Given:
The radius of the disc is 35 millimeters, so the area of it is:
π[tex]r^{2}[/tex] = 3.14*[tex]35^{2}[/tex] = 3846.5
Then, we find out the area of the circular hold cut out of the bigger one, its radius is a haft of the radius of the bigger circle = 35/2 = 17.5
π[tex]r^{2}[/tex] = 3.14*[tex]17.5^{2}[/tex] =961.6
=> the area of the pendant = 3846.5 - 961.6 =2884.8 millimeters squared
The final result is the area of the pendant is 2887.1 mm².
To find the area of the pendant:
Calculate the area of the circular disc: A = πr² = 3.14 x (35 mm)² = 3.14 x 1225 = 3848.5 mm²Calculate the area of the circular hole: A_hole = πr_hole². Since the hole is at the center, the radius of the hole is half the radius of the disc, so r_hole = 35/2 = 17.5 mm. A_hole = 3.14 x (17.5 mm)² = 3.14 x 306.25 = 961.4375 mm²Find the area of the pendant by subtracting the area of the hole from the area of the disc: A_pendant = A - A_hole = 3848.5 mm² - 961.4375 mm² = 2887.0625 mm²Therefore, the area of the pendant is 2887.1 mm².
A 24.6 g marble sliding to the right at 62.0 cm/s overtakes and collides elastically with a 12.3 g marble moving in the same direction at 15.5 cm/s. After the collision, the 12.3 g marble moves to the right at 77.5 cm/s. Find the velocity of the 24.6 g marble after the collision. cm/s
Answer:
Velocity of the 24.6 g marble is 31 cm/s.
Step-by-step explanation:
Given:
Marble 1:
Mass of the marble [tex](m_1)[/tex] = 12.3 gm
Velocity of [tex]m_1[/tex] before collision [tex]v_1_i[/tex] = 15.5 cm/s
Velocity of [tex]m_1[/tex] after collision [tex]v_1_f[/tex] = 77.5 cm/s
Marble 2:
Mass of the marble [tex](m_2)[/tex] = 24.6 gm
Velocity of [tex]m_2[/tex] before collision [tex]v_2_i[/tex] = 62 cm/s
Velocity of [tex]m_2[/tex] after collision [tex]v_2_f[/tex] = ?
From the law of conservation of momentum, we know that momentum before equals the momentum after :
So,
⇒ [tex]P(i)=P(f)[/tex]
⇒ [tex](m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)[/tex]
⇒ Plugging the values.
⇒ [tex](12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)[/tex]
⇒ [tex]190.65+1525.2=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85-953.25=24.6\times v_2_f[/tex] ...subtracting both sides 953.25
⇒ [tex]762.6=24.6\times v_2_f[/tex]
⇒ [tex]\frac{762.6}{24.6}\ =v_2_f[/tex] ...dividing both sides with 24.6
⇒ [tex]31=v_2_f[/tex]
⇒ [tex]v_2_f =31[/tex] cm/s
The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.
PLEASE HELP
A student says that the function f(x)=3x4+5x2+1 is an even function. Is the student's statement true or not true, and why?
1) The student's claim is not true, because for any input of x, f(x)=−f(x).
2) The student's claim is not true, because for any input of x, f(x)=f(−x).
3) The student's claim is true, because for any input of x, .f(x)=−f(x).
4) The student's claim is true, because for any input of x, f(x)=f(−x).
Answer:
It's D.
Step-by-step explanation:
Final answer:
The function f(x) = 3x⁴+5x²+1 is an even function because f(-x) equals f(x) for any value of x, confirming the student's statement as true.
Explanation:
The function f(x) = 3x4+5x2+1 is indeed an even function. This can be determined by checking if f(-x) = f(x) for any value of x. An even function is symmetrical about the y-axis and does not change when x is replaced with -x. Applying this to the given function:
f(-x) = 3(-x)4+5(-x)2+1 = 3x4+5x2+1
f(x) = 3x4+5x2+1
Since f(-x) and f(x) are indeed equal, the function is even. Therefore, the correct answer to the student's statement that the function is even is: 4) The student's claim is true, because for any input of x, f(x) = f(-x).
The random variables X and Y have the joint PMF pX,Y(x,y)={c⋅(x+y)2,0,if x∈{1,2,4} and y∈{1,3},otherwise. All answers in this problem should be numerical. Find the value of the constant c . c=
Answer:
c= 1/26
Step-by-step explanation:
The joint probability mass function for X and Y must comply that:
[tex]\[\sum\]\sum\] c(x +y) = 1[/tex] for x∈{1,2,4} and y∈{1,3}
thus, all the possible values for the pairs (x,y) are:
(1,1) (1,3) (2,1) (2,3) (4,1) (4,3)
and then
c [(1+1)+(1+3)+(2+1)+(2+3)+(4+1)+(4+3)] = 1
c[26] = 1
c= 1/26
A ship departs from Port miami with 5678 tons of cargo the ship docks at the Bahamas and the uploads some cargo the crew also loads three times the quantity of cargo that was unloaded of the ship holds 8588 tons now how many tons of cargo did the ship unload at the bahamas
Answer: the ship unloaded 1455 tons of cargo at the bahamas.
Step-by-step explanation:
Let x represent number of tons of cargo that the ship unloaded at the bahamas.
The initial number of tons of cargo in the ship is 5678 tons. If it unloads x tons of cargo, the number of tons of cargo left would be
5678 - x
The crew also loads three times the quantity of cargo that was unloaded. This means that the number of tons of cargo that it loaded is 3x. The total number of tons of cargo in the ship would be
5678 - x + 3x
= 5678 + 2x
If the ship holds 8588 tons now, it means that
5678 + 2x = 8588
2x = 8588 - 5678
2x = 2910
x = 2910/2
x = 1455 tons of cargo
PLEASE HELP ME IDK HOW TO DO THIS
The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.) *see attached table*
A sine function is written to represent the data.
What is the amplitude, period, and vertical shift of this equation?
Answer:
Amplitude is 17
Period = 12
Vertical shift of 50
Step-by-step explanation:
One complete cycle in 12 months
Mean line is at y = 50, so vertical shift of 50
Amplitude = 67-50 = 17
Or , 50 - 33 = 17
The vertical shift, amplitude, and period of the given equation would be as follows:
Amplitude [tex]= 17[/tex]
Period [tex]= 12[/tex]
Vertical Shift [tex]= 50[/tex]
What is Temperature?Given that,
Duration of the cycle [tex]= 12[/tex] months
∵ Period [tex]= 12 months[/tex]
The Mean line lies at [tex]y = 50[/tex]
So,
The vertical shift [tex]= 50[/tex]
Now,
Amplitude [tex]= 67-50[/tex]
[tex]or[/tex]
[tex]50 - 33[/tex]
[tex]= 17[/tex]
Learn more about "Amplitude" here:
brainly.com/question/9351212
- Two consecutive integers are 5 and 6. Write a quadratic equation that
could be used to determine these two integers.
Answer:
x^2 -11x +30 = 0
Step-by-step explanation:
If these two integers are solutions of the quadratic, then its factors are ...
(x -5)(x -6) = 0
Multiplying this out, we get ...
x^2 -11x +30 = 0
Ten year old Chi learned a lot of math from his older brother, Shing. One day, Shing told him that when you multiply a number by 10, you just add zero?
Answer:
This is true
Step-by-step explanation:
10x1 is 10. 10x10 is 100. but if u did 100x10 you would add the amount of zeros total. which would be 1000. so 400x10 is 4000
What is the domain of the function graphed below?
The domain is the X value ( input).
The line starts at (0,2) so 0 is the first part of the domain. The horizontal line has an arrow on it pointing to the right which means the line can continue to infinity.
The answer is the second choice, 0 to infinity
Please assist me with this problem.
Answer:
r = 1.20w +2.50$12.58$9.00Step-by-step explanation:
a) The retail price (r) is the wholesale price (w) plus 20% of that price plus $2.50:
r = w + 0.20w + 2.50
r = 1.20w + 2.50
__
b) Substituting w=8.40, we have ...
r = 1.20·8.40 +2.50 = 12.58
The retail price of the chair is $12.58.
__
c) Substituting r=13.30, we have ...
13.30 = 1.20w +2.50
10.80 = 1.20w . . . . . . . subtract 2.50
9.00 = w . . . . . . . . . . . . divide by 1.20
The wholesale price of the chair is $9.00.
Find AB. (Brainly says it is too short this is why this is here)
The length of AB is 31 yd.
Solution:
Given data:
The side opposite to angle A is "a" = 22 yd
The side opposite to angle B is "b" = 26 yd
The side opposite to angle C is "c" = AB
Angle C = 80°
To find the length of AB:
Using cosine formula,
[tex]c^2=a^2+b^2-2ab \cdot \cos C[/tex]
Substitute the given values in the formula, we get
[tex]c^2=22^2+26^2-2(22)(26)\cdot \cos 80^\circ[/tex]
[tex]c^2=484+676-1144\cdot \cos 80^\circ[/tex]
[tex]c^2=1160-1144\cdot (0.1736)[/tex]
[tex]c^2=1160-198.5984[/tex]
[tex]c^2=961.4016[/tex]
Taking square root on both sides, we get
c = 31
AB = 31 yd
The length of AB is 31 yd.
My teacher is making us do online and my problems is to find 62×1000 annex Then there's a blank zeros to Then another blank to form the product So can you help
Answer:
Step-by-step explanation:
We are to find 62×1000
We can write in standard form
62×10³
6.2×10×10³
Using indices
a^m × a^n = a^(m+n)
Therefore,
6.2×10¹+³
6.2×10⁴
Using the normal multiplication
................1000
...............×. .62
...…......-------------
....., ... ..2 0 0 0
.......+.6 0 0 0
-------------------
..........6 2 0 0 0
----------------------
By selling a laptop at $1,000 for which consumers are willing to pay up to $1,200, a consumer electronics firm makes a profit of $400 per unit. In this scenario, the amount $600, that is ($1200 – $1000) + $400, is the
Answer:
600
Step-by-step explanation:
Toby and Betty Combs pay $8,719.38 in annual property taxes. Their home has a market value of $361,800.00 with a tax rate of 48.2 mills. What is the rate of assessment in their tax district?
Answer:
50% of market value
Step-by-step explanation:
The actual tax rate on the Combs home is ...
$8719.38/$361800 = 0.0241 = 24.1 mils
The rate of assessment is ...
(24.1 mils)/(48.2 mils) = 0.50 = 50%
The Combs pay tax on 50% of their home's market value.
In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.
a. We take repeated random samples of size 10 from a population of unknown shape.
b. We take repeated random samples of size 15 from a population that is normally distributed.
c. We take repeated random samples of size 50 from a population of unknown shape.
d. We take repeated random samples of size 25 from a population that of unknown shape.
Answer:
is d
Step-by-step explanation:
What is an equation of the line that passes through the points (−5,−7) and (5,1)?
Answer:
y = 4/5x -3
Step-by-step explanation:
in order to do this :
firstly , find the midpoint of the points.use the formula :
[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]
= [tex]\frac{-5 + 5}{2} , \frac{-7 + 1}{2}[/tex]
midpoint =(0 , -3)
secondly , get the gradientuse the formula :
[tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{1-(-7)}{5-(-5)}[/tex]
=[tex]\frac{8}{10}[/tex]
simplified to 4/5
gradient = 4/5
Thirdly , create the equationformula for the equation of a line
(Y-y1) = m( X-x1)
now use the values of the midpoint and the gradient(m)
y +7 = 4/5 (x + 5)
y = 4/5x + 4-7
y = 4/5x -3Answer:
y = 0.8x - 3
Step-by-step explanation:
Slope = (-7-1)/(-5-5) = -8/-10 = 0.8
When x = 5, y = 1
1 = 0.8(5) + c
1 = 4 + c
c = -3
y = 0.8x - 3
The cost for printing pages at a print shop is a $5 processing fee and $1 for each page. The rule is c=5+p, where p is the number of pages and c is the total cost
Answer:
Step-by-step explanation:
I think the photo below is your full question and my answer is presented in that too.
We create a table of values:
p c
0 5
1 6
2 7
Then draw on the graph.
Hope it will find you well
A rotating object makes 5/6 of a revolution in 7/10 second. Find the approximate speed in revolutions per second. Write your answer as a decimal to the nearest hundreth.
Answer:
1.19 revolutions per second.
Step-by-step explanation:
Given:
A rotating object makes 5/6 of a revolution in 7/10 second.
To find:
Find the approximate speed in revolutions per second ?
Solution:
As here given that a rotating object makes 5/6 of a revolution in 7/10 second,
we will have to find that in one second how many revolution does this object make:
By unitary method:
In [tex]\frac{7}{10}[/tex] second, a rotating object makes = [tex]\frac{5}{6}[/tex] revolution
In 1 second, a rotating object makes = [tex]\frac{5}{6}\div\frac{7}{10}[/tex]
[tex]=\frac{5}{6}\times\frac{10}{7} = \frac{50}{42}=1.190\ revolution[/tex]
Therefore, the approximate speed of object is 1.19 revolution per second.
We can also find by, [tex]speed = \frac{distance}{time}[/tex]
[tex]=\frac{5}{6} \div\frac{7}{10} \\=\frac{5}{6} \times\frac{10}{7} =\frac{50}{42} = 1.19[/tex]
We can use any one to solve this type of question:
Finally, the approximate speed is 1.19 revolutions per second.
If a farmer can trade four chickens for a pig, three pigs for two sheep, and five sheep for two cows, what is the minimum number of cows he needs to trade for $20$ chickens?
Answer:
The minimum of cows he needs are: 2
Step-by-step explanation:
There's a relation between each animal:
5 chickens equals 1 pig
3 pigs equals 2 sheep
5 sheep equals 2 cows
You can understand it as the following three abstractions:
5c = 1p (1)
3p = 2s (2)
5s = 2o (3)
Where:
c is for chickens
p is for pigs
s is for sheep
o is for cows
So now you have three equations with 4 variables. The next step is to obtain an equation that relates directly the variable c (chickens) with the variable o (cows). In order to do that from the equation 2 we obtain s in terms of p, as follow:
[tex]3p =2s\\s=\frac{3p}{2} \\[/tex]
Then we replace s in the equation 3 and we obtain v in terms of p:
[tex]5(\frac{3p}{2} )=2v\\\\2v=\frac{15}{2} p\\\\[/tex]
[tex]v=\frac{15}{2*2} p \\\\v=\frac{15}{4} p[/tex]
Now we replace v in the equation 1:
[tex]4c = \frac{4}{15} v[/tex]
[tex]c=\frac{1}{15} v[/tex] (4)
The equation 4 means that 1 chicken equals the fifteenth part of a cow. For this case the farmer needs 20 chikens, so we multiply per 20 each part of the equation 4:
[tex]20c = 20 * \frac{1}{15} v\\ \\\ 20c = \frac{20}{15}v = \frac{4}{3}v \\\\20c = 1.3333v[/tex]
As it is impossible to have 1.3333 cows, the answer is 2 cows approximately.
Answer:
2
Step-by-step explanation:
Let p and q be the propositions. p : I bought a lottery ticket this week. q : I won the million dollar jackpot. Express each of these propositions as an English sentence. a) ¬p b) p ∨ q c) p → q d) p ∧ q e) p ↔ q f ) ¬p → ¬q g) ¬p ∧ ¬q h) ¬p ∨ (p ∧ q)
Answer:
a) ¬p : I didn't buy a lottery ticket this week.
b) p ∨ q: I bought a lottery ticket this week or I won the million dollar jackpot.
c) p → q: If I didn't buy a lottery ticket this week, then I won the million dollar jackpot.
d) p ∧ q: I bought a lottery ticket this week and I won the million dollar jackpot.
e) p ↔ q: I bought a lottery ticket this week if and only if I won the million dollar jackpot.
f ) ¬p → ¬q: If I didn't buy a lottery ticket this week, then I didn't win the million dollar jackpot.
g) ¬p ∧ ¬q: I didn't buy a lottery ticket this week and I didn't win the million dollar jackpot.
h) ¬p ∨ (p ∧ q): I didn't buy a lottery ticket this week or I bought a lottery ticket this week and I won the million dollar jackpot.
Step-by-step explanation:
In logic, a word or group of words that joins two or more propositions together to form a connective proposition it's called connective, also called sentential connective, or propositional connective
1. Negation: the symbol is ¬, or ~. It is use for saying that the proposition is false. This connective proposition only affects one statement.
2. Disjunction ("or"): the symbol is ∨. It is use for saying that at least one of the propositions are true.
3. Conjunction ("and"): the symbol is ∧. It is use for saying that both of the propositions, at the same time are true.
4. Conditional (“if . . . then”): the symbor is →. In this structure the first proposition it's called antecedent and the second one consecuent. For this connective the only case when it's not true is when the antecendent is true and the consecuent is false.
5. Biconditional ("if and only if"): the symbol is ↔. This structure is a double conditional. And the proposition is true when antecent and consecuent are both true or both false.
Final answer:
The student's question involves translating logical propositions into English sentences. These include negation, disjunction, conjunction, conditional, and bi-conditional statements based on the scenarios presented.
Explanation:
The student wants to express each proposition as an English sentence. The propositions include notations for negation (¬), disjunction (∨), conjunction (∧), and implication (→), as well as bi-conditional (↔).
a) ¬p: 'I did not buy a lottery ticket this week.'b) p ∨ q: 'I bought a lottery ticket this week or I won the million dollar jackpot (or both).'c) p → q: 'If I bought a lottery ticket this week, then I won the million dollar jackpot.'d) p ∧ q: 'I bought a lottery ticket this week and I won the million dollar jackpot.'e) p ↔ q: 'I bought a lottery ticket this week if and only if I won the million dollar jackpot.'f) ¬p → ¬q: 'If I did not buy a lottery ticket this week, then I did not win the million dollar jackpot.'g) ¬p ∧ ¬q: 'I did not buy a lottery ticket this week and I did not win the million dollar jackpot.'h) ¬p ∨ (p ∧ q): 'I did not buy a lottery ticket this week or I both bought a ticket and won the million dollar jackpot.'Each sentence corresponds to different logical statements found in propositional logic.
What is the radius of the circle with an equation of x2 - 12x + y2 + 4y = -4?
Answer:
radius = 6
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² - 12x + y² + 4y = - 4
Using the method of completing the square on the x and y terms
add (half the coefficient of the x/y term )² to both sides
x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = - 4 + 36 + 4, that is
(x - 6)² + (y + 2)² = 36 ← in standard form
with r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6
Answer:
6
Step-by-step explanation:
h = -12/-2 = 6
k = 4/-2 = -2
h² + k² - r² = 4
6² + (-2)² - 4 = r²
r² = 36
r = sqrt(36) = 6
5/12 of the pupils in a school are left-handed and the rest are right-handed. There are 276 more pupils who are right-handed than left-handed. What is the total number of pupils in the school?
Answer:
There are a total number of 1656 students in the school.
Step-by-step explanation:
Let's set up this word problem in mathematical terms.
We can call the number of Left Handed Students as X,
and we can call the number of Right Handed Students as Y.
Since there are 276 more right handed pupils than left handed, we have the following equation:
X + 276 = Y -Equation 1
Also, since there are 5/12 ratio of left handed students and 7/12 right handed students, we get:
Total Students = T
(5/12) T = X -Equation 2
(7/12) T = Y -Equation 3
Substituting equations 2 and 3 into equation 1 we get:
[tex]\frac{5}{12} T+276=\frac{7}{12} T[/tex]
Solving for Total number of students (T) we get:
T = 1656
Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches
Carl has [tex]\( \frac{163}{36} \)[/tex] inches of string left out of the 20 inches he started with after tying the parcel and the box.
To find out how much string Carl has left after tying the parcel and the box, we'll subtract the lengths of string used from the total length he started with.
1. Convert the mixed numbers to improper fractions:
-[tex]\(10 \frac{2}{9}\) inches = \(10 + \frac{2}{9} = \frac{90}{9} + \frac{2}{9} = \frac{92}{9}\)[/tex] inches
- [tex]\(5 \frac{1}{4}\) inches = \(5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}\)[/tex] inches
2. Add the lengths of string used:
[tex]\[\text{Total length used} = \frac{92}{9} + \frac{21}{4}\][/tex]
3. Find a common denominator to add the fractions:
The common denominator for 9 and 4 is 36.
[tex]\[\frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36}\] \[\frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36}\][/tex]
4. Add the fractions:
[tex]\[\frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36}\][/tex] inches
5. Subtract the total length used from the total length Carl started with:
[tex]\[20 - \frac{557}{36}\][/tex]
6. Convert the mixed number result to an improper fraction:
\[20 = \frac{720}{36}\]
7. Subtract the fractions:
[tex]\[\frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36}\][/tex] inches
Now, Carl has [tex]\(\frac{163}{36}\)[/tex] inches of string left.
We can convert this to a mixed number if necessary.
The correct question is:
Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?
Ans:
Carl has [tex]\( {4 \frac{19}{36}} \)[/tex] inches of string left after tying both the parcel and the box.
1. Convert the mixed numbers to improper fractions:
- 10 2/9 inches = [tex]\( \frac{92}{9} \) inches[/tex]
- 5 1/4 inches = [tex]\( \frac{21}{4} \) inches[/tex]
2. Add the lengths of string used:
[tex]\( \frac{92}{9} \) inches (parcel) + \( \frac{21}{4} \) inches (box)[/tex]
To add these fractions, find a common denominator:
The least common multiple of 9 and 4 is 36.
[tex]\( \frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36} \)\\ \( \frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36} \)\\ \( \frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36} \) inches[/tex]
3. Subtract the total used from the initial length of string:
Initial length of string = 20 inches
Total used = [tex]\( \frac{557}{36} \) inches[/tex]
To subtract, convert 20 inches to a fraction with the common denominator of 36:
[tex]\( 20 = \frac{720}{36} \)[/tex]
Now, subtract:
[tex]\( \frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36} \) inches[/tex]
4. Convert the fraction to a mixed number (if necessary):
[tex]\( \frac{163}{36} \)[/tex] inches is already in its simplest form. To convert to a mixed number:
[tex]\( 163 \div 36 = 4 \) remainder \( 19 \)[/tex]
So, [tex]\( \frac{163}{36} = 4 \frac{19}{36} \) inches[/tex]
The correct question is:
Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?
Ans:_______
An 18-slice pizza was made with only pepperoni and mushroom toppings, and every slice has at least one topping. Exactly ten slices have pepperoni, and exactly ten slices have mushrooms. How many slices have both pepperoni and mushrooms
Answer:
2
Step-by-step explanation:do it on a piese of parer them it will make more sence
The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle
Answer: the area of the original rectangle is 300 square meters.
Step-by-step explanation:
Let L represent the original length of the rectangle.
Let W represent the original width of the rectangle.
The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. This means that the length of the new rectangle is 2L and the width of the new rectangle is 3W
If the area of the new rectangle is equal to 1800 square meters, it means that
2L × 3W = 1800
6LW = 1800
LW = 1800/6
LW = 300 square meters
Jane must select three different items for each dinner she will serve. The items are to be chosen from among five different vegetarian and four different meat selections. If at least one of the selections must be vegetarian, how many different dinners could Jane create?
A. 30
B. 40
C. 60
D. 70
E. 80
Answer:
Therefore, Jane can create 80 different dinners.
Step-by-step explanation:
We know that Jane must select three different items for each dinner she will serve. If at least one of the selections must be vegetarian.
The items are to be chosen from among five different vegetarian and four different meat selections.
First we count the number of combinations for one vegetarian dinner and 2 meat dinners.
[tex]C_1^5\cdot C_2^4=5\cdot \frac{4!}{2!(4-2)!}=5\cdot 6=30[/tex]
Now we count the number of combinations for 2 vegetarian dinner and 1 meat dinners.
[tex]C_2^5\cdot C_1^4=10\cdot 4=40\\[/tex]
Now we count the number of combinations for 3 vegetarian dinner.
[tex]C_3^5=\frac{5!}{3!(5-3)!}=10\\[/tex]
We get 30+40+10=80.
Therefore, Jane can create 80 different dinners.