Julia ate 1/8
Ellen and Jenny ate 3/8
1/8 + 3/8 = 4/8
No they didn't eat the whole pizza, they only ate half of the pizza.
Julie, Ellen, and Jenny together ate [tex]\frac{1}{8}[/tex]+ [tex]\frac{3}{8}[/tex] = [tex]\frac{4}{8}[/tex] or [tex]\frac{1}{2}[/tex]of the pizza, which means they ate only half of it, not the entire pizza.
The question involves the mathematical concept of fractions and their addition. Julie ate [tex]\frac{1}{8}[/tex] of the pizza, while Ellen and Jenny together ate [tex]\frac{3}{8}[/tex]of the pizza. To determine if they ate the whole pizza, we need to add these fractions.
[tex]\frac{1}{8}[/tex] (Julie's portion) + [tex]\frac{3}{8}[/tex] (Ellen and Jenny's portion) = [tex]\frac{4}{8}[/tex]or [tex]\frac{1}{2}[/tex] after simplifying.
Since [tex]\frac{1}{2}[/tex] is less than a whole, Julie, Ellen, and Jenny did not eat the entire pizza. They ate only half of it.
The volume v of a gas kept at constant temperature varies inversely with the pressure p. If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What will the volume be when the pressure is 30 pounds per square inch?
Answer:
[tex]V=12\ ft^{3}[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
In this problem
[tex]P*V=k[/tex]
step 1
Find the value of K
For [tex]P=24\ psi ,V=15\ ft^{3}[/tex]
substitute
[tex]24*15=k[/tex]
[tex]k=360[/tex]
the equation is [tex]P*V=360[/tex]
step 2
For [tex]P=30\ psi ,V=\ ft^{3}[/tex]
substitute in the equation
[tex](30)*V=360[/tex]
[tex]V=360/30=12\ ft^{3}[/tex]
Using Boyle's law, which states volume and pressure of a gas at constant temperature are inversely proportional, we find that at a pressure of 30 pounds per square inch, the volume will be 12 cubic feet.
Explanation:The concept behind your question involves Boyle's law, which states the volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured. This means as pressure increases, volume decreases and vice versa while maintaining the same temperature.
To solve this, we can use the mathematical expression for Boyle's law: P₁V₁ = P₂V₂.
Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. Applying these values: 24 pounds per square inch * 15 cubic feet = 30 pounds per square inch * V₂. By rearranging the equation and solving for V₂, we get: V₂ = (24 pounds per square inch * 15 cubic feet) / 30 pounds per square inch = 12 cubic feet.
Therefore, when the pressure is 30 pounds per square inch, the volume will be 12 cubic feet.
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What is the value of x?
x =
(Secants, Tangents, and Angles)
Answer:
The value of x is [tex]58\°[/tex]
Step-by-step explanation:
we know that
The measurement of the external angle is the semi-difference of the arcs which comprises
so
In this problem
[tex]51\°=\frac{1}{2}(160\°-x\°)[/tex]
solve for x
[tex]102\°=(160\°-x\°)[/tex]
[tex]x=160\°-102\°=58\°[/tex]
Linear recurrence relation
True
A linear recurrence relation involving a sequence of numbers [tex]a_n[/tex] is one of the form
[tex]\displaystyle\sum_{k=0}^nc_{n-k}a_{n-k}=c_na_n+c_{n-1}a_{n-1}+\cdots+c_2a_2+c_1a_1=c[/tex]
where [tex]c_1,c_2,\ldots,c_n[/tex] and [tex]c[/tex] are any fixed numbers.
The given recurrence can be rearranged as
[tex]a_n=a_{n-1}+2\implies 1\cdot a_n+(-1)\cdot a_{n-1}=2[/tex]
A nonlinear recurrence would have a more "exotic" form that cannot be written in the form above. Some example:
[tex]a_n+\dfrac1{a_{n-1}}=1[/tex]
[tex]a_na_{n-1}=\pi[/tex]
[tex]{a_n}^2+\sqrt{a_{n-1}}-\left(\dfrac{a_{n-2}}{\sqrt{a_n}}\right)^{a_{n-3}}=0[/tex]
The query pertains to 'linear recurrence relations' in Mathematics, particularly concerning high school algebra and series expansions, such as the binomial theorem, and plotting data on a logarithmic scale.
Explanation:The term linear recurrence relation refers to a sequence of numbers where each term is a linear combination of previous terms. The relationship is defined by two aspects: the number of terms that go into the combination (order of the relation), and the coefficients of each of those terms. A classic example of a linear recurrence relation is the Fibonacci sequence, where each term is the sum of the two preceding terms.
When addressing series expansions like the binomial theorem, it is an expression that allows us to expand polynomials raised to a power in a series format. The theorem is a key concept in algebra and is particularly useful for calculating powers of binomials and deriving coefficients of individual terms within expanded polynomials.
To plot data like the recurrence interval on a logarithmic scale, it is essential to understand that each increment on the axis represents a multiplication by a certain factor, rather than a linear addition. This type of representation is particularly useful when dealing with data that varies by orders of magnitude.
What is 71 X 9? WITH work.
Answer:
639
Step-by-step explanation:
put the 71 on the top then the 9 on the bottom then 9x1=9 then 9x7=63
639!
the revenue from selling x shirts is r(x)=12. the cost of buying x shirts is c(x)=5x+20. the profit from selling x shirts is p(x)=r(x) - c(x). what is p(x)?
Answer:
The profit function would be p(x) = 7x - 20
Step-by-step explanation:
In order to find this, start by listing just as asked.
p(x) = r(x) - c(x)
Now input the functions where indicated
p(x) = 12x - (5x + 20)
p(x) = 12x - 5x - 20
p(x) = 7x - 20
Answer:
The value of [tex]p(x)=-5x-8[/tex]
Step-by-step explanation:
Given : The revenue from selling x shirts is [tex]r(x)=12[/tex]. The cost of buying x shirts is [tex]c(x)=5x+20[/tex]. The profit from selling x shirts is [tex]p(x)=r(x) - c(x)[/tex].
To find : What is p(x)?
Solution :
The revenue from selling x shirts is [tex]r(x)=12[/tex].
The cost of buying x shirts is [tex]c(x)=5x+20[/tex].
The profit from selling x shirts is [tex]p(x)=r(x) -c(x)[/tex]
Substitute the values in the formula,
[tex]p(x)=12 -(5x+20)[/tex]
[tex]p(x)=12 -5x-20[/tex]
[tex]p(x)=-5x-8[/tex]
Therefore, The value of [tex]p(x)=-5x-8[/tex]
Find the surface area and volume of a cube with sides that are 3 inches
Answer:
A=54in²
Step-by-step explanation:
MARKING BRAINLIEST
On Thursday night, Betsy received $34.50 in tips working as a coat checker. This is $1.75 more than the amount in tips she received on Wednesday night. How much did she receive on Wednesday night?
You and a friend join a gym The registration fee is $30 and the monthly Membership is $20 if the total bill for you and your friend is $420 how many months did you pay for?
Plz help!!!!!!!!!!!!
Answer:
rational
Step-by-step explanation:
any number that can be written as a fraction is rational, it is also a termintating decimal.
Answer: rational
Step-by-step explanation:
[tex]\dfrac{1}{4}=0.25\\\\\text{Since the decimal terminates (ends), it is a rational number.}[/tex]
Pls help with this
Just do you ones you know
Answer:
Number 7 is 40
Step-by-step explanation:
set up a proportion 5/1 = x/8 cross multiply a divide and you get 40
A 10-mile bike race is divide into 4 equal sections
Answer:
each section will equal 2.5 miles
Step-by-step explanation:
if you divide 10 from 4 you get 2.5
To divide a 10-mile bike race into four equal sections, we calculate the length of one section by dividing 10 miles by 4, resulting in each section being 2.5 miles long.
The question pertains to the division of a 10-mile bike race into four equal sections. To find the length of each section, we divide the total distance of the race (10 miles) by the number of sections (4). This calculation will give us the length of one section.
10 miles \ 4 sections = 2.5 miles per section.
Thus, each section of the bike race would be 2.5 miles long. This application of division in real-world situations like races and marathons is a fundamental concept in mathematics, allowing participants and organizers to understand and manage distances more effectively.
show that 1/12 of the carpet is covered by the rug (photo provided)
the carpet is rectangular, thus its area is simply the product of its two dimensions, namely 8*6 = 48 m².
how much is the shaded area? well, since it's also rectangular, its area is also that product of 2*2 = 4, recal is a square so length = width = 2.
[tex]\bf \stackrel{\textit{how many times does 48 go into 4?}}{\cfrac{shaded}{total~area}\qquad \cfrac{4}{48}\implies \stackrel{simplified}{\cfrac{1}{12}}}[/tex]
PLEASE HELP ME!!! THIS IS DUE IN LIKE 10 MINS!!!! PLEASE DO IT FAST!!
Answer:
false
Step-by-step explanation:
because it doesn’t have the three complete angles
Answer:
False
Step-by-step explanation:
How many yards are in 1 mile?
1,760
2,640
52.8
15,840
Answer:
1,760
Step-by-step explanation:
A mile is 5280 feet
3 feet in a yard
so 5280/3=1760
your answer is A) 1,760 yards
A cube labeled 1 to 6, is tossed 6 times
and lands on the number 5 twice.
Find the probability of the cube landing on the number 5.
Answer:
1/6
Step-by-step explanation:
If we're assuming that this is a six-sided die, then we can find that the results can be 1,2,3,4,5,6. Only 1 of those 6 numbers are 5, so the probability of the cube landing on 5 would be 1/6.
To calculate the unit price of an item, divide the total number of units by the total price.
Please select the best answer from the choices provided
T
F
Answer:
F
Step-by-step explanation:
Find the probability of not rolling factors of 6 on both dice
To find the probability of not rolling factors of 6 on both six-sided dice, multiply the individual probabilities of rolling a 4 or 5 on each die. The probability is 1/9.
Explanation:The factors of 6 are 1, 2, 3, and 6. Therefore, the outcomes that are not factors of 6 are 4 and 5.
Since each die has six faces, the total number of possible outcomes when rolling two dice is 6 x 6 = 36.
Of these 36 possible outcomes, we need to count how many do not involve factors of 6. For each die rolled independently, we have 2 outcomes that are not factors of 6: {4, 5}.
So, we need to calculate the product of these individual probabilities to find the probability of both dice showing a non-factor of 6.
For a single die, the probability of rolling a non-factor of 6 (either a 4 or a 5) is 2/6 or 1/3, since we have 2 favorable outcomes out of 6 possible ones.
To find the probability for both dice, we multiply these individual probabilities:
Probability of not rolling a factor of 6 on both dice = (1/3) x (1/3) = 1/9.
This is the product rule in probability, which tells us that the probability of two independent events both happening is the product of their individual probabilities.
Therefore, the probability of not rolling a factor of 6 on both dice is 1/9.
A fisherman travels 8 miles downstream with the current in the same time that he travels 3 miles upstream against the current. If the speed of the current was 5 mph what is the speed at which the fisherman travels in still water?
I also need help with this too so I'm just here to wait and see the answer
The speed is the distance covered by an object at a particular time. The speed at which the fisherman travels in still water is 11 mph.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Let the speed of the boat be represented by x mph.
A fisherman travels 8 miles downstream with the current at the same time that he travels 3 miles upstream against the current. Also, the speed of the current was 5 mph. Therefore,
8 miles/ (x + 5)mph = 3 miles/(x - 5) mph
8x - 40 = 3x + 15
5x = 55
x = 11 mph
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Which phrase BEST describes the expression below? 15.4 − 2 n
A.twice a number n minus fifteen and four-tenths
B.twice a number n subtracted from fifteen and four-tenths
C.a number n minus the product of fifteen and four-tenths and two
D.a number n times the difference between fifteen and four-tenths and two
B is the answer hope this helps!
B) is the answer, my reasoning is that A) is 2n - 15 and four tenths which is the wrong way around , C) is just nonsense and D) is n multiplied by 15 and four tenths take away 2 which is also wrong , as that would be n x 13 and four tenths , hope this helps :)
Choose the solution to this inequality. 7/2≥b+9/5
The solution to the given inequality is [tex]b\leq 1.7[/tex]
InequalitiesFrom the question, we to determine the solution to the inequality.
To determine the solution of the inequality, we will determine the value of the variable. The variable in the given question is b.
The inequality can be solved as shown below.
[tex]\frac{7}{2} \geq b + \frac{9}{5}[/tex]
Multiply through by 10
That is,
[tex]10 \times \frac{7}{2} \geq 10\times b + 10\times \frac{9}{5}[/tex]
This becomes
[tex]5 \times 7 \geq 10b + 2 \times 9[/tex]
[tex]35 \geq 10b + 18[/tex]
Now, subtract 18 from both sides
[tex]35 - 18\geq 10b + 18-18[/tex]
[tex]17 \geq 10b[/tex]
This becomes,
[tex]10b \leq 17[/tex]
Divide both sides by 10
[tex]\frac{10b}{10} \leq \frac{17}{10}[/tex]
[tex]b\leq 1\frac{7}{10}[/tex]
OR
[tex]b\leq 1.7[/tex]
Hence, the solution to the given inequality is [tex]b\leq 1.7[/tex]
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Select the figure obtained when rotating the figure about an axis along its largest side, and find the exact surface area of the resulting figure.
A rectangle with length 22 and width 18.
The figure obtained is a (square/cylinder/sphere)
The exact surface area is ______π.
Answer:
The figure obtained is a cylinder
The exact surface area is 1440π.
Step-by-step explanation:
* Lets study the rotation of a rectangle around one of its sides
- If the dimensions of the rectangle are length (L) and width (W)
- If we rotate the rectangle around its length (L), we will construct
a cylinder with radius = W and height = L
- If we rotate the rectangle around its width (w), we will construct
a cylinder with radius = L and height = W
∵ The surface area of any cylinder =
perimeter of base × height + 2 base area
∵ The base is a circle
∴ perimeter base = 2πr and base area = πr²
∴ The surface area = 2πrh + 2πr²
* In first case:
- Surface area = 2π(W)L + 2π(w)² = 2πWL + 2πW²
* In second case:
- Surface area = 2π(L)W + 2π(L)² = 2πLW + 2πL²
* Now lats check our question:
∵ L = 22 and W = 18
- It will rotate around the largest side
∴ It will rotate around L
∴ The figure obtained is a cylinder
* From the explanation above this is the first case
∵ L = 22 and W = 18
∵ The surface area = 2πWL + 2πW²
∴ The surface area = 2 × 18 × 22 × π + 2 × (18)² × π
= 792π + 648π = 1440π
* The exact surface area is 1440π.
How do show 4/6 and 5/7 on a number line
Answer:
|-----|-----|-----|-----0-----|-----| |------|------|------|------|------0------|-----|
0 1/6 2/6 3/6 4/6 5/6 1 0 1/7 2/7 3/7 4/7 5/7 6/7 1
Step-by-step explanation:
since 4/6 means the fourth one of the 6 spots, we can just make a number line that is split into 6 parts and find the fourth line. we do the same thing with seven to get the answers above
Final answer:
To show 4/6 and 5/7 on a number line, mark 42 equal sections between 0 and 1, and place 4/6 at the 28th mark and 5/7 at the 30th mark, as they equate to 28/42 and 30/42 respectively.
Explanation:
To show 4/6 and 5/7 on a number line, you would follow these steps:
Determine a number line with a section that includes both fractions. This might typically be between 0 and 1 if you are only dealing with fractions less than a whole.Divide this section into parts that can accommodate both denominators. For example, a common denominator for 6 and 7 is 42, since 6 * 7 = 42.Mark off 42 equal sections between 0 and 1 on your number line.Count and mark the position that corresponds to 4/6 and 5/7. To find the position of 4/6, you would count 28 sections from 0 (since 4/6 = 28/42). For 5/7, you would count 30 sections from 0 (since 5/7 = 30/42).Place a point or tick mark at these positions and label them accordingly.Both 4/6 and 5/7 will be placed between 0 and 1 on the number line, with 4/6 slightly to the left of 5/7.
need help asap!!! plzz
Use mental math to find 31% of $200.
(A)$52.00
(B)$42.00
(C)$62.00
(D)$72.00
Answer:
(C)$62.00
Step-by-step explanation:
$200 x .31 = $62.00
the answer is C it is $62.00
You roll a fair 6 sided die what is p (roll greater than 4)
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Probability is measured as
[tex]\frac{favourableoutcome}{count}[/tex]
The favourable outcome is obtaining roll > 4, that is a 5 or 6
P( > 4 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Which factorization can be used to identify the real zeros of the function f(x)=-20x^2+23x-6?
Answer:
see explanation
Step-by-step explanation:
Given f(x) = - 20x² + 23x - 6
To find the zeros set f(x) = 0, that is
- 20x² + 23x - 6 = 0 ( multiply through by - 1 )
20x² - 23x + 6 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 20 × 6 = 120 and sum = - 23
The factors are - 15 and - 8
Use these factors to split the x- term
20x² - 15x - 8x + 6 = 0 ( factor the first/second and third/fourth terms )
5x(4x - 3) - 2(4x - 3) = 0 ← factor out (4x - 3)
(4x - 3)(5x - 2) = 0
Equate each factor to zero and solve for x
4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]
5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]
Answer:
-(4x - 3)(5x - 2) = 0
Step-by-step explanation:
Find the equation of a circle with a center at (7,2) and a point on the circle at (-2,-5).
( x - 7 )^2 + ( y - 2 )^2 = sqrt 130
( x + 7 )^2 - ( y + 2 )^2 = sqrt 130
( x - 7 )^2 + ( y - 2 )^2 = 130
( x + 7 )^2 - ( y + 2 )^2 = 130
Answer:
(x - 7)² + (y - 2)² = 130
Step-by-step explanation:
The first step is finding the length of the radius.
r² = (2 - -5)² + (7 - -2)²
= 7² + 9²
= 49 + 81
= 130
The general equation of a circle is:
(x - a)² + (y - b)² = r²
Where (a, b) is the coordinate of the center and r is the radius.
∴ The equation of the required circle is;
(x - 7)² + (y - 2)² = 130
Find the measures of the interior angles of the triangle
Answer:
A = 75°
B = 90°
C = 15°
Step-by-step explanation:
The diagram tells us that C = 15°.
The diagram places a square in the angle of B, showing you the angle is a 90° right angle.
You can solve for A because all angles of a triangle must equal 180°. 180° - 90° (B) = 90°. 90° - 15° (C) = 75°, the measure of A.
ASAP!!!!!
The sanitation department calculated that last year each city resident produced approximately 1.643 × 10^3 pounds of garbage. There are 2.61 × 10^5 people living in the city. How much garbage did the city sanitation department collect last year?
4.2882 pounds
428.820 pounds
428,820 pounds
428,820,000 pounds
Answer:
428,820,000 pounds
Step-by-step explanation:
The amount of garbage is number of person times the amount produced by each person. Thus, we have:
Amount of Garbage (in pounds) = 2.61 × 10^5 * 1.643 × 10^3
Note: We multiply 2.61 and 1.643, which is 4.28823 & multiplying 10^5 and 10^3 is 10^(5+3) = 10^8
Thus, we have 4.28823 * 10^8 = 428,823,000 pounds
This is approximately 428,820,000 pounds, last answer choice.
Answer:
Other answer is correct, confirmed on E2020
Step-by-step explanation:
If 30 people claimed that they get an average of seven hours of sleep, how many people claimed that they get at least eight hours of sleep each night? [Type your answer as a number.]
60 people claimed they they got at least eight hours of sleep.
Answer:
78 people claimed that they get at least eight hours of sleep each night.Step-by-step explanation:
We know that 30 people claimed that they get an average of seven hours of sleep. Using the circular diagram, we find that these 30 people represent 25% of the total number of people.
According to the graph, people that get at least eight hours of sleep each night represent 65%, that is, 50% of the people sleep eight hours and 15% sleep nine or more.
Then, we use the rule of three, if 30 people represent 25% of the total, how many people would represents 65%?
[tex]x=65\%\frac{30 \ people}{25 \%} = 78 \ people[/tex]
Therefore, 78 people claimed that they get at least eight hours of sleep each night.
Could I help some help on numbers 2,6,10,30, and 38 please
Answer:
#6. 36 #30. 24
Step-by-step explanation:
6. You add 7+29=36 so 36 is the missing number