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Work Shown:
(6 servings)/(4 oz of sauce) = (8 servings)/(x oz of sauce)
6/4 = 8/x
6*x = 4*8
6x = 32
x = 32/6
x = 5.333 approximately
x = 6 we round up despite 5.333 being closer to 5, than it is to 6.
If we went with 5 ounces, then we wouldn't clear the hurdle needed to serve 8 people.
The section below goes over why this is the case in more detail.
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6 servings : 4 ounces
6/4 servings : 4/4 ounces
1.5 servings : 1 ounce
So one ounce of sauce gets us 1.5 servings.
If we multiply both sides by 5, then,
1.5 servings : 1 ounce
5*1.5 servings : 5*1 ounce
7.5 servings : 5 ounces
This shows that 5 ounces of sauce will only produce 7.5 servings, which comes up short compared to 8 servings.
If we multiplied both sides by 6, then
1.5 servings : 1 ounce
6*1.5 servings : 6*1 ounce
9 servings : 6 ounces
This shows that 6 ounces of sauce yields 9 servings. We've gone overboard, but it's better to do that than come up short.
(-8)^-2 / 3^-4 simplify the expression. Write your answer using only positiv exponents.
Answer:
3^4 / 8^2 or 81/64
Step-by-step explanation:
(-8)^-2 / 3^-4 =
= 3^4 / (-8)^2
= 3^4 / 8^2
= 81/64
Today I would like for you to work one of the following problems and explain your process/reasoning clearly and thoroughly.
Answer:
Step-by-step explanation:
A line from the center of the circle to bisect a chord is perpendicular to the chord.
Therefore, OA⊥ AS
Join O & R
OR is radius of the circle
ΔOAR is right angled triangle.
Use Pythagorean theorem to find OR
OR² = OA² + RA²
= 3² + 4²
= 9 +16
OR² = 25
OR = √25
OR = 5 cm
OP is radius. Therefore, OP = OR = 5 cm
PA = OP + OA
= 5 + 3
PA = 8 cm
Which geometric figure has 120 rotational symmetry?
Answer:
Triangle
Step-by-step explanation:
Has 120° degrees of rotation and measure of the central angle and has 3-fold rotational symmetry
What type of function is graphed in this figure?
Question 20 options:
A)
Continuous non-linear
B)
Discrete linear
C)
Discrete non-linear
D)
Continuous linear
Answer:
The correct option is;
B) Discrete linear
Step-by-step explanation:
The graph shows scatter plots of the data points and therefore the plot is a discrete plot of points. Also, we have, from the graph of the function, changes in input values are proportional with changes in output, such that the progression of the points are unidirectional.
Therefore, the graph is a discrete linear function.
Explain the differences between adding and multiplying radical expressions using 2 examples you create.
Answer:
When you multiply radical expressions you multiply the numbers under the radical symbols.3–√×7–√=21−−√
When you add radical expression you CANNOT add the numbers under the radical symbols.
3–√+7–√≠10−−√
Step-by-step explanation:
find a rational number that is between 5.2 and 5.5. explain why it is rational.
Answer:
5.3
Step-by-step explanation:
A rational number is a number that can be written as the quotient of two integers.
5.2 and 5.5 are both rational since they can be written as quotients of integers as shown below.
5.2 = 52/10
5.5 = 55/10
5.3 is a number between 5.2 and 5.5, and since 5.3 can be written as 53/10, it is rational.
Answer: 5.3
Answer:
Step-by-step explanation:
rational numbers can be written in form a/b where b≠0
5.2 and 5.5
52/10 and 55/10
so some rational numbers could be
53/10, 54/10
irrational numbers most likely the square root numbers
square them
5.2^2=27.04
5.5^2=30.25
5.2<?<5.5
square everybody
27.04<?²<30.25
so pick a number between 27.04 and 30.25
29 or 30 are 2 numbers
I'll pick 29
?²= 29
square root
?=√29
the irrational number can be √29
it is 5.39 to the hundredth
Find the equation of the line:
through (5, -1) and (2, 2).
Answer:
y = -x + 4
Step-by-step explanation:
(x₁,y₁)= (5, - 1) & (x₂,y₂)= (2 , 2)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\frac{2-[-1]}{2-5}\\\\=\frac{2+1}{-3}\\\\=\frac{3}{-3}\\\\= -1[/tex]
m = -1
Equation of the line y - y₁ = m(x - x₁)
y - [-1] = (-1)*(x - 5)
y + 1 = -x + 5 {-1 is distributed}
y = -x + 5 - 1
y = -x + 4
Is the product of two irrational numbers always an irrational number?
Answer:
Step-by-step explanation:
Not always.
√3 * √27 = √81 = 9
an apartment in rome is 98 m^2, how many square feet is the apartment?
Please show work
Answer: 9,604 m Is the answer
3.3. (08.01 LC) Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi. (4 points) . 4. (08.01 MC) Given a cube with a volume of 27 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube? (4 points)
Answer:
1. C = 10π, A = 25π
2. 9 cm³
Step-by-step explanation:
Formula for circumference = πd
Formula for area of a circle = πr²
1. Set up the equation for circumference
10π
2. Set up the equation for area (radius = 1/2diameter) and solve
π(5²) = 25π
Formula for volume of a square pyramid = 1/3s² · h
The volume of a square pyramid is equal to 1/3 of the volume of a cube. The formula for a volume of a cube is s³ which is equal to s² · h because a cube has the same side length for all sides. Therefore, the volume of a square pyramid that perfectly fits within a given cube would equal 1/3 the volume of the cube.
1. Set up the equation and solve
27 ÷ 3 = 9
Answer:
3. The fourth: C= 10π, A = 25π 4. The third: 9 cm³Step-by-step explanation:
3.
diameter is equal two radiuses
D = 10 = 2R ⇒ R = 5
circumference: C = 2πR = 2R•π = 10π
area: A = πR² = π•5² = 25π
4.
If square pyramid fit perfectly inside cube then its base is the same as a face of cube, and the height (H) of pyramid is equal to the edge (S) of its base.
[tex]A_p=\frac13S^2\cdot H =\frac13S^2\cdot S=\frac13S^3=\frac13A_c=\frac13\cdot27\,cm^3=9\,cm^3[/tex]
find the value of y
a. 118
b. 65
c. 130
d. 32.5
Answer:
Option (B).
Step-by-step explanation:
Since "measure of an angle formed between the tangent and a chord measure the half of the intercepted arc."
Therefore, x = 2 × (65)°
x = 130°
Since, measure of the inscribed angle is half of the measure of the intercepted arc.
Therefore, x = 2y
y = [tex]\frac{x}{2}[/tex]
y = [tex]\frac{130}{2}[/tex]
y = 65°
Therefore, Option (B). 65° will be the correct option.
look at image below urgant 1000 points alert
A = pi x r x l
= 3.14 x 5 x 13
= 204.1
Answer:
282.7 mi^2
Step-by-step explanation:
Surface area of cone=pi*r*(r+l)=pi*5*18=282.7
The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}
This Question is incomplete
Complete Question:
The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}
What is the five number summary:
a) Minimum
b) Q₁
c) Median
d) Q₃
e) Maximum
Answer:
a) Minimum = 18
b) Q₁ = 27.5
c) Median = 39.5
d) Q₃ = 43
e) Maximum = 49
Step-by-step explanation:
From the above diagram, we were given the following set of data.
{18, 49, 38, 41, 33, 44, 42, 22}
Before answering any of the questions, we have to rearrange the data from the lowest to the highest (ascending order). Hence, we have:
{18, 22, 33, 38, 41, 42, 44, 49}
a) Minimum
{18, 22, 33, 38, 41, 42, 44, 49}
Looking at this set of arranged data, the minimum number is the least or lowest number.
This number is 18
b) Q₁
{18, 22, 33, 38, 41, 42, 44, 49}
Q₁ means First Quartile. The formula is = ¼(n + 1)th value
n = Number of terms in the data set = 8
= ¼(8 + 1)th value
= ¼(9)th value
= 2 1/4 value
= 2.25 value
In the above Question, the 2.25 value is the value between the second and third number.
Hence:
22+33/2 = 55/2 = 27.5
Therefore, Q₁ = 27.5
c) Median
{18, 22, 33, 38, 41, 42, 44, 49}
The median of the number is the number in the middle
For this data, we have 8 number, Hence the median is the sum of the 4th and 5th term divided by 2
4th term = 38
5th term = 41
= 38 + 41/ 2 = 79/2
= 39.5
Hence, the median = 39.5
d) Q₃
{18, 22, 33, 38, 41, 42, 44, 49}
Q₃ means Third Quartile. The formula is = ¾(n + 1)th value
n = Number of terms in the data set = 8
= ¾(8 + 1)th value
= ¾(9)th value
= 6 3/4 value
= 6.75 value
In the above Question, the 6.75 value is the value between the sixth and seventh number.
Hence:
42+44/2 = 86/2 = 43
Therefore, Q₃ = 43
e) Maximum
{18, 22, 33, 38, 41, 42, 44, 49}
Looking at this set of arranged data, the Maximum number is the highest number.
This number is 49
It takes Matt 3 minutes to read one page in a book. If he continues to read at the same pace, he can read 15 similar pages in minutes. If the book has 300 pages, it will take him minutes to read it.
Answer:
a)45min
b)900min
Step-by-step explanation:
We were told that it takes Matt 3 minutes to read one page in a book.
It implies that 3minutes = 1page of the book
Then he continues to read at the same pace, he can read 15 similar pages in minutes.
a)Then, he can read 15 similar pages in
15x3 minutes.which is 45minutes.
b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins
Answer: has anyone seen my dad?
Pls help
.
Z
Z
Z
Z
Z
Z
Z
Z
A
Answer:
20.2 feet
Step-by-step explanation:
Using Pythagoras theorem, we have
Height^2+13^2=24^2, height=sqrt(407)=20.2
A
2
The distance AB
rounded to the
nearest tenth = [?]
- 2
-1
0
B
-2
-3
Hint: Use the distance formula:
d= (x2 - 1)2 + (y2 - y.)2
Answer:
slope = - 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = B (1, - 2)
m = [tex]\frac{-2-2}{1-(-1)}[/tex] = [tex]\frac{-4}{1+1}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
Answer:
AB = 4.5
Brainliest, please!
Step-by-step explanation:
A (-1, 2) B (1, -2)
y = +4
x = +2
a^2 + b^2 = c^2
2^2 + 4^2 = c^2
4 + 16 = c^2
20 = c^2
c = 4.5 (rounded)
Solve for x: 3x-4=2x-10
Answer:
x = - 6
Step-by-step explanation:
3x - 4 = 2x - 10
3x -2x = 4 - 10
x = - 6
For the equation 3x-4=2x-10, the value of x is -6.
The given equation is 3x-4=2x-10.
x is the variable in the equation.
Plus and minus are operators.
To solve for x, subtract 2x from both sides:
3x-2x-4=2x-2x-10
x-4=-10
Add 4 on both sides:
x=-10+4
x=-6
Hence, the value of x is -6.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ6
Please answer this question now
Answer:
117°
Step-by-step explanation:
Arc ABC (AB + BC) is intercepted by angle D.
Therefore, Arc ABC is 2 × m<D. (Inscribed Angle Theorem)
AB = 91°
m<D = 104°
Let BC = x
Arc ABC = (91° + x)
Thus,
91° + x = 2 × 104°
Solve for x
91 + x = 208
Subtract 91 from both sides
91 + x - 91 = 208 - 91
x = 117
Measure of arc BC = 117°
Which of the following expressions has a value of 4? A. (16 – 12)² B. – | – 4 | C. (96 ÷ 8) – 2³ D. 24 – 42
A. (16 - 12)² = 4² = 4 · 4 = 16
B. -|-4| = -4
C. (96 : 8) - 2³ = 12 - 8 = 4
D. 24 - 42 = -(42 - 24) = -18
or 2⁴ - 4² = 16 - 16 = 0
The correct answer is C
PLEASE AND THANK YOUU, u dont have to draw graph btw
Answer: sqrt(x+1)+4
This is the same as writing [tex]\sqrt{x+1}+4[/tex]
The +4 is not under the square root
==========================================================
Explanation:
g(x) is the same as y, since they're both outputs of a function
So we have the starting equation y = (x-4)^2 - 1
Swap x and y and solve for y to get the inverse.
y = (x-4)^2 - 1
x = (y-4)^2 - 1
x+1 = (y-4)^2
(y-4)^2 = x+1
y-4 = sqrt(x+1) ... see note below
y = sqrt(x+1)+4
Note: Recall that [tex]x \ge 4[/tex] and we swapped x and y. This ultimately means [tex]y \ge 4[/tex] and this only occurs if we picked the positive version of the square root (ignoring the negative version).
Durning Saturday’s thunderstorms a total of 500 mm of rain fell in fell in 20 minutes.How many mm fell per minute
Answer
25mm of rain fell each second
Step-by-step explanation:
we know that 500 mm fell in 20 minutes
so, we have to divide 500 by 20 giving us the amount of rain that fell each minute:
500/20 = 25
therefore, 25mm of rain fell each minute
hope this helped:)
Answer:
25 mm per minute
Step-by-step explanation:
Take the amount of rain and divide by the number of minutes
500/20
25 mm per minute
Type the correct answer in each box. Use numerals instead of words.
Consider the quadratic equation -x^2 - 6x + 6 = 0
Completing the square leads to the equivalent equation
-(x + ___ )^2 = ___
Answer:
-(x + 3)^2 = -15
Step-by-step explanation:
:) got it right
Can someone plz tell me What is 98% of 85
Answer: 83.3
Step-by-step explanation:
0.98 x 85 =83.3
Answer: 83.3 hope this helps.
What is the next term in the sequence?
2, -4, 8, -16, ...
Answer:
32
Step-by-step explanation:
it multiplies by -2 every time
Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Ariana will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Ariana's songs were played. Define the variables that you use to write the system.
Answer:
Commercials x = 7
Movies y = 2
Step-by-step explanation:
Let commercials = x
Let's movies = y
$40 is for commercials
$110 is for movies.
Commercials plus movies for the Year = 9
She earned total of $500
X+ y = 9..... equation 1
40x + 110y = 500.... Equation 2
Multipling equation one by 40
40x + 40y = 360
Subtracting equation one from equation 2
70y = 140
Y = 2
If y = 2
X + y = 9
X + 2 = 9
X = 9-2
X = 7
find the area of a rhombus with a 120 degree angle and sides 10 cm
Answer:
A = 50√3 cm²Step-by-step explanation:
[tex]A=s^2\cdot \sin\alpha\\\\s=10\\\alpha=120^o\\\\A=10^2\cdot\sin(120^o)=100\sin(180^o-60^o)=100\sin(60^o)=100\cdot\frac{\sqrt3}2=50\sqrt3[/tex]
A.) 170
B.) 300
C.)280
D.)155
Please help me
Answer:
Step-by-step explanation:
The formula for this is
∠G = 1/2(arcEH - arcHF)
We have angle G (5x - 10) and we have arcEH (195) so we have to solve for x to find the measure of arcEHF so we can add arcEH + arcHF = arcEHF
Filling in the formula with what we have:
[tex]5x-10=\frac{1}{2}(195-(8x+17))[/tex]
which simplifies down a bit to
[tex]5x-10=\frac{1}{2}(195-8x-17)[/tex] which simplifies down a bit more to
[tex]5x-10=\frac{1}{2}(178-8x)[/tex] Multiply both sides by 2 to get rid of the fraction and get:
2(5x - 10) = 178 - 8x which of course simplifies to
10x - 20 = 178 - 8x. Now add 8x to both sides and at the same time add 20 to both sides to get:
18x = 198 so
x = 11. Now we can find the measure of arcHF:
arcHF is 8x + 17, so arcHF is 8(11) + 17 which is 105°.
arcEH + arcHF = arcEHF so
195 + 105 = arcEHF so
arcEHF = 300°
f(x)=-4+7, what is f(2)
Answer:
3
Step-by-step explanation:
7-4
How many gallons of 30% alcohol solution and how many of 60% alcohol solution must be mixed to produce 18 gallons of 50% solution?
Answer:
x = 6 gallons (of 30% alcohol)
y = 12 gallons (of 60% alcohol)
Step-by-step explanation:
Let
x = liters of 30% alcohol
y = liters of 60% alcohol
There are two unknowns, we need two equations
x + y = 18. (1)
0.30x + 0.60y = 0.50(x+y) (2)
From (1)
x + y = 18
y = 18-x
Substitute the value of y into (2) and solve for x:
0.30x + 0.60y = 0.50(x+y)
0.30x + 0.60(18-x) = 0.50(x+18-x)
0.30x + 10.8 - 0.60x = 0.50(18)
10.8 - 0.30x = 9
-0.30x = -1.8
Divide both sides by -0.30
x = 6 gallons (of 30% alcohol)
Substitute x=6 into (1) and solve for y:
x + y = 18
6 + y = 18
y = 12 gallons (of 60% alcohol)
Someone pls help . Thank you sm☄️ .
1) 3 is the Coefficient.
2) 10 is the constant.
3) 10.8 is the ans.