The equation represents the amount of juice that remains, y, after x students are served is y = negative one-half x + 32; option C
Equation of the unknownQuantity of juice = 2 gallon = 32 cupsQuantity given to each student = 1/2 cupNumber of juice remaining = yNumber of students served = xy = 32 - 1/2x
This can also be written as;
y = -1/2x + 32
Therefore, the correct answer is option C; y = -1/2x + 32
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PLEASE ANSWER ASAP!!!!!! WILL GIVE BRAINLIEST!!!
Answer ya so 1 is the answer
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Given expression:
[tex]\sf \left(\dfrac{3a^{-2}b^6}{2a^{-1}b^5} \right)^2[/tex]
To find the value of the expression when a = 3 and b = -2, substitute these values into the expression:
[tex]\implies \sf \left(\dfrac{3(3)^{-2}(-2)^6}{2(3)^{-1}(-2)^5} \right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{3^2}\right)(-2)^6}{2\left(\dfrac{1}{3^1} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{9}\right)(-2)^6}{2\left(\dfrac{1}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{3}{9}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (2^6)}{\left(\dfrac{2}{3} \right) (-(2^5))} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (64)}{\left(\dfrac{2}{3} \right) (-32)} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1 \times 64}{3}\right)}{\left(\dfrac{2 \times -32}{3} \right)} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\dfrac{64}{3}}{\dfrac{-64}{3}} \right)^2[/tex]
When dividing fractions, flip the second fraction and multiply it by the first:
[tex]\implies \sf \left( \dfrac{64}{3} \times \dfrac {3}{-64} \right)^2[/tex]
[tex]\implies \sf \left( \dfrac{64 \times 3}{3 \times (-64)}\right)^2[/tex]
[tex]\implies \sf \left( \dfrac{192}{-192}\right)^2[/tex]
[tex]\implies \sf \left(-1\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]
[tex]\sf \implies 1^2=1[/tex]
Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps.
Find the Percent of increase
thats all she wrote
A percentage is a way to describe a part of a whole. The percentage increase of Magikarps is 100%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps. Therefore, The percentage increase of Magikarps is,
Percentage increase = (16-8)/8 × 100% = 100%
Hence, The percentage increase of Magikarps is 100%.
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During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?
Answer:
30
Step-by-step explanation:
4 cups x 60 hours a min x 2 hours of lunch ÷ 16 cups per gallon = 30 gallons
The answer is 30 gallons.
Firstly, convert the hours to minutes so you know how many minutes you're working with. 2*60=120 minutes.
Then, multiply 120 with 4 to get the number of tea (in cups) that is poured. 120*4=480 cups.
Finally, divide 480 cups with 16 cups to find out the number of gallons poured. 480/16 equals 30 gallons.
Hope this helped.
Given: l || m; ∠1 ∠3
Prove: p || q
Horizontal and parallel lines l and m are intersected by parallel lines p and q. At the intersection of lines l and p, the uppercase left angle is angle 1. At the intersection of lines q and l, the bottom right angle is angle 2. At the intersection of lines q and m, the uppercase left angle is angle 3.
Complete the missing parts of the paragraph proof.
We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because
. We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the
.
The parts that are missing in the proof are:
It is given
∠2 ≅ ∠3
converse alternate exterior angles theorem
What is the Converse of Alternate Exterior Angles Theorem?The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.
∠1 ≅ ∠3 and l║m because we are: given
By the transitive property,
∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.
Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.
Therefore, the missing parts pf the paragraph proof are:
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Answer:
it is given
angle 2
angle 3
converse alternate exterior angles theorem
Step-by-step explanation:
(8.6x107)-(9.1x10-8)simplify
Answer:
85,999,999.999 999 909
Step-by-step explanation:
The expression represents the difference of a relatively large number and one that is relatively small. That difference is approximately the value of the large number. The exact value requires 17 digits for its proper expression. Most calculators and spreadsheets cannot display this many digits.
Standard formThe numbers in standard form are ...
86,000,000 = 8.6×10^7
0.000000091 = 9.1×10^-8
DifferenceTheir difference is ...
86,000,000 -0.000000091 = 85,999,999.999 999 909
In scientific notation, this is ...
8.599 999 999 999 990 9×10^7
The correlation in error terms that arises when the error terms at successive points in time are related is termed _____.
Answer:
auto correlation is the answer to the question
4. Write the function of a linear equation that includes the
points (1,3) and (2,9).
Answer:
y = 6x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form ( linear function ) is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )
m = [tex]\frac{9-3}{2-1}[/tex] = [tex]\frac{6}{1}[/tex] = 6 , then
y = 6x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 3 ) , then
3 = 6 + c ⇒ c = 3 - 6 = - 3
y = 6x - 3 ← equation of linear function
Please Help me!!!!!!!!!
Answer:
(2,-3) (3,-3)
Step-by-step explanation:
f(x) is y
x² - 5x + 3 = -3
x² - 5x + 6 = 0
ask yourself
which 2 numbers when multiplied give you
+6 and when added give you -5
they are -3 and -2
(x-3)(x-2)
x=3 x=2
when you put x=3 and x=2
in x² - 5x + 3 it's gives -3 which is y
(3,-3) (2,-3)
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The sin (0) = - and lies in Quadrant III. Find the exact values of the sine
6'
and cosine of 20.
Answer:
Can you give exanation
I don't understand
if x + 3y = 25 write y in terms of x and also find the two solutions of this equation
Answer:
y= 25/3 - x/3
Step-by-step explanation:
y= 25/3 - x/3
A sequence is defined by the recursive function f(n + 1) = one-half(n). If f(3) = 9 , what is f(1) ?
The value of f(1) is 81
What is Recursive function?Recursive Function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms
Given:
f(n + 1) = 1/3* f(n)
f(3) = 9
let n=0
f(0+1) = 1/3 * f(0)
f(1) = 1/3 * f(0)
Let n=1
f(1+1) = 1/3 * 1/3*f(0)
f(2) = 1/9 * f(0)
let n=2
f(2+1) = 1/3 * 1/9* f(0)
f(3) = 1/27 * f(0)
Also, f(3) =9
So,
9 = 1/27 * f(0)
f(0) = 27 * 9
f(0) = 243
Now,
f(1) = 1/3 * f(0)
f(1) = 1/3/ 243
f(1) = 81
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how do i Solve this equation
√x+5-2=0
Answer:
9
Step-by-step explanation:
√x+5-2=0
√x+3=0
√x= -3
x=9 [(-3)*(-3) = 9]
An architect is designing new housing structures for the primate section at the zoo. Her plan is shown below. Which animals will live in a building that is similar to the main primate house? A orangutans B chimpanzees C gibbons D gorillas
Answer:
A
Step-by-step explanation:
:p
Please help me out…
Polygon ____ and polygon ____ are similar to polygon 1.
Polygon 3 and 4 are similar to polygon 1.
Polygons will be called similar if they are exactly in the same shape, but can be in different sizes.
Here given, Some of the images are images of the polygon 1 from similarity transformations.
So we have to find the similar polygon from the given picture.
From picture it is clear that Polygon 2 is similar to polygon 1 as the size of polygon 2 has been decreased from polygon 1 but the shape of polygon 2 is the same as polygon 1 as we can their corresponding angles are also equal.
Also, polygon 3 is similar to polygon 1 as the size of polygon 3 has been decreased from polygon 1 but the shape of polygon 2 is the same as polygon 1 and reversed of polygon 1. So polygon 3 is of the same orientation as polygon 1 as we can their corresponding angles are also equal.
So from above, it is clear that Polygon 1 is similar to polygon 3 and 4 as they have the same shape but different sizes.
Therefore Polygon 3 and Polygon 4 are similar to polygon 1.
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f(x) = x + 6 , find the ordered pair when x = -2.
(-2,4)
(2,-4)
(-2,-4)
(2,4)
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option A, (-2, 4)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{f(x) = x + 6}[/tex]
Find: [tex]\textsf{f(-2)}[/tex]
Solution: We need to plug in the value -2 into every variable x that we have in the expression and simplify to get the solution.
Plug in the values
[tex]\textsf{f(x) = x + 6}[/tex][tex]\textsf{f(-2) = -2 + 6}[/tex]Simplify
[tex]\textsf{f(-2) = -2 + 6}[/tex][tex]\textsf{f(-2) = 4}[/tex]Therefore, the ordered pair that would match would have a x-coordinate of -2 and a y-coordinate of 4 producing (-2, 4) which matches option A.
Carolyn bought two brands of socks. She bought a total of 5 pairs. One brand cost $2 each and the other brand cost $3 each. She spent $13. Find the number of pairs each brand of socks she bought
Answer:
Step-by-step explanation:
Declaration
Let Brand A number of 2.00 socks= x
Let Brand B number of 3.00 socks = y
Equations
Number of socks : x + y = 5
Cost of socks: 2x + 3y = 13
Solution
Multiply top equation by 2
2(x+ y = 5)
2x + 2y = 10
Write the new equation under the cost of socks equation
2x + 3y = 13
2x + 2y = 10 Subtract.
y = 3
She spent 3 dollars on 1 pair of socks.
Now she needs to calculate the number of 2.00 dollar socks
2x + 3y = 13
2x + 3*3 = 13 Combine the left
2x + 9 = 13 Subtract 9 from both sides.
2x +9-9 = 13-9 Combine
2x = 4 Divide by 2
2x/2 = 4/2
x = 2
Answer
#2 dollar socks = 2
#3 dollar socks = 3
Add.
(3+x3+3x2)+(2x3−2−4x2)
Express the answer in standard form.
Enter your answer in the box.
Step-by-step explanation:
(3+3+3*2)+(2*3-2-4*2)
The value of the addition of the two polynomials is 3x³ - x² + 1.
What is addition of polynomial?The addition of polynomials involves combining like terms of two or more polynomials to create a new polynomial. A polynomial is an expression consisting of variables, coefficients, and exponents, connected by addition and subtraction operations.
To add the given polynomials:
(3 + x³ + 3x²) + (2x³ - 2 - 4x²)
First, let's group the like terms:
(x³ + 2x³) + (3x² - 4x²) + (3 - 2)
Combine the coefficients of the like terms:
3x³ + 3x² - 4x² + 3 - 2
Simplify the expression:
3x³ - x² + 1
Therefore, the sum of the given polynomials is: 3x³ - x² + 1.
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What is a 10% margin increase on 1,810.69?
Answer:
1991.759
Step-by-step explanation:
1810.69×%10=181.069
1810.69+181.069=1991.759
Give ur answer in standard form.
3 x 10^4 ÷6 x 10^-4
Answer:
5.0×10⁷
Step-by-step explanation:
(3÷6)×(10⁴÷10^-4)
(0.5)×(10⁸)
5.0×10^-1×10⁸
5.0×10⁷
[tex] \frac{3 \times {10}^{4} }{6 \times {10}^{ - 4} } \\ \\ \frac{1 \times {10}^{4 - ( - 4)} }{2 } \\ \\ \frac{ 1 \times {10}^{4 + 4} }{2} \\ \\ \frac{1 \times {10}^{8} }{2} \\ \\ 0.5 \times {10}^{8} .[/tex]
What function is shown in the graph above?
By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.
What kind of function represents the graph?
Graphically speaking, linear functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). Linear functions are characterized by slope and intercept:
y = m · x + b (1)
Slope
m = (7 - 0)/[9 - (- 6)]
m = 7/15
Intercept
b = 4
By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.
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The quadrilateral below is formed from a parallelogram and an
isosceles triangle.
Calculate the size of angle VQU.
Answer:
VQU =58°
Step-by-step explanation:
angle QUV is 61 because of F angles (I don't know what they call them in ur country)
triangle QUV is an isosceles triangles so base angles are the same
61+61=122
180-122=58
A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 millimeters and an upper specification limit of 23.1 millimeters. The standard deviation is 0.19 millimeters and the mean is 22.9 millimeters. What is the process capability index for the process? Note: Round your answer to 4 decimal places.
The process capability index for the process is 0.1754.
How to calculate the index?The first sided specification limit will be:
= (Upper specification limit - mean)/(3 × standard deviation)
= (23.1 - 22.9)/(3 × 0.19)
= 0.2/0.57
= 0.3508
The second sided specification limit will be:
= (22.9 - 22.8)/(3 × 0.19)
= 0.1/0.57
= 0.1754
The process capability index for the process is 0.1754 wine it's the lower value.
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[tex](1/8)^-^3^a=512^3^a[/tex]
The equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution
How to solve the equation?The equation is given as:
[tex](\frac18)^{-3a} = 512^{3a}[/tex]
Express the equation as a base of 2
[tex](2^{-3})^{-3a} = 2^{9*3a}[/tex]
Evaluate the products
[tex]2^{9a} = 2^{27a}[/tex]
Cancel out the common base
9a = 27a
The above equation is not true because [tex]9a \ne 27a[/tex]
Hence, the equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution
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what is the equation?
3 + 5(2 + 7n) = 258
Answer:
n = 7
Explanation:
[tex]\rightarrow \sf 3 + 5(2 + 7n) = 258[/tex]
apply distributive method: a(b + c) = ab + ac
[tex]\rightarrow \sf 3 + 10 + 35n = 258[/tex]
simply add the numbers
[tex]\rightarrow \sf 13 + 35n = 258[/tex]
subtract both sides by 13
[tex]\rightarrow \sf 13-13 + 35n = 258-13[/tex]
simplify the following
[tex]\rightarrow \sf 35n = 245[/tex]
divide both sides by 35
[tex]\rightarrow \sf n = 7[/tex]
Answer:
n = 7
Step-by-step explanation:
1) Subtract 3 from both sides.
5(2 + 7n) = 258 - 3
2) Simplify 258 - 3 to 255.
5(2 + 7n) = 255
3) Divide both sides by 5.
2 + 7n = 255/5
4) Simplify 255/5 to 51.
2 + 7n = 51
5) Subtract 2 from both sides.
7n = 51 - 2
6) Simplify 51 - 2 to 49.
7n = 49
7) Divide both sides by 7.
n = 49/7
8) Simplify 49/7 yo 7.
n = 7
8.
(05.04 LC)
The amount of money in tips earned by four restaurant servers waiting on 10 tables is represented by the following data sets.
Alyssa {3, 6, 2, 8, 12, 14, 5, 7, 7, 8}
Bryant {9, 2, 7, 50, 0, 5, 2, 8, 6, 8}
Camila {1, 9, 10, 3, 0, 12, 10, 9, 8, 2}
Devon {4, 2, 8, 15, 20, 7, 5, 0, 6, 2}
Which data set has the greatest interquartile range? (1 point)
Alyssa
Bryant
Camila
Devon
Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.
What is the range?It is defined as the difference between the maximum value in the data set to the minimum value in the data set.
We have:
The amount of money in tips earned by four restaurant servers waiting on 10 tables is represented by the following data sets:
Alyssa {3, 6, 2, 8, 12, 14, 5, 7, 7, 8}
Bryant {9, 2, 7, 50, 0, 5, 2, 8, 6, 8}
Camila {1, 9, 10, 3, 0, 12, 10, 9, 8, 2}
Devon {4, 2, 8, 15, 20, 7, 5, 0, 6, 2}
The IQR for Alyssa:
IQR = Q3 - Q1
IQR = 8 - 5 = 3
The IQR for Bryant:
IQR = Q3 - Q1
IQR = 8 - 2 = 6
The IQR for Camila:
IQR = Q3 - Q1
IQR = 10 - 2 = 8
The IQR for Devon:
IQR = Q3 - Q1
IQR = 8 - 2 = 6
Thus, Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.
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Someone help me with this math word questions
2) The three ways of naming an angle are by the letter at the vertex, by placing a number or variable inside the angle, or by two letters with the vertex letter placed in the middle.
3) [tex]\angle WXY, \angle YXZ, \angle WXZ[/tex]
4) [tex]X[/tex]
A basketball coach recorded how many shots each of the 30 players at tryouts made in a set of 6 attempts.
Answer:
Step-by-step explanation:
what is the question?
Answer:
Median = A
Mean = B
Step-by-step explanation:
Khan Academy
Find the HCF of
x^4 y^2 and x^3 y^3
Here's your answer down here↓:
Step-by-step explanation:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2) = (x - y)(x + y)(x^2 + y^2)
Ok. So the factor (x-y) appears once in the top line and once in the second line. So we are going to take it the least amount of times.
So, the factor (x + y) appears in the top line zero times and in the second line one time so we will take it where it appears the least which is zero times so we are still at (x - y)
And it Same goes for the factors of (x^2 + y^2) and (x^2 + xy + y^2)
f(x)=x^2. which of these is g(x) ?
a. g(x)=(1/5x)^2
b. g(x)=5x^2
c.g(x)=(1/4x)^2
d.g(x)=1/5x^2
Answer:
a
Step-by-step explanation:
we know that g(x) means y therefore in this case let's suppose we have the coordinate (5;y) so we must find the corresponding y value
*DO THE TRIAL AND ERROR METHOD*
take any equation above and substitute the value of x of which is 5 and the corresponding value should be 1.
[tex]g(x) = (\frac{1}{5} x) {}^{2} [/tex]
The vertex of this parabola is at (3-2). When the value is 4 the
y-value is 3. What is the coefficient of the squared expression in the
parabola's equation?
A. 7
B. 1
C. -1
D. 5
Answer:
D
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (3, - 2 ) , then
y = a(x - 3)² - 2
to find a substitute the point (4, 3 ) into the equation
3 = a(4 - 3)² - 2 ( add 2 to both sides )
5 = a × 1² = a
the coefficient of the squared expression is 5
