Answer: unit rate is $0.16
1 bottle cost $0.16
Step-by-step explanation:
I got the rest of the answers just stuck on these two
The slope for the first table will be;
⇒ m = - 4/3
The slope for the second table will be;
⇒ m = 1 / 4
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
There are two table is shown in figure.
Now,
For first table;
Two points are,
⇒ (x, y) = (3, -6) (0, - 2)
Since, The slope of the line passing through the points (x₁ , y₁) and
(x₂, y₂) will be;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Hence, Slope for first table;
⇒ m = (- 2 - (-6)) / (0 - 3)
⇒ m = (- 2 + 6) / (-3)
⇒ m = - 4/3
And, For second table;
Two points are,
⇒ (x, y) = (0, -3) (4, - 2)
Since, The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) will be;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Hence, Slope for second table;
⇒ m = (- 2 - (-3)) / (4 - 0)
⇒ m = (- 2 + 3) / (4)
⇒ m = 1 / 4
Thus, The slope for the first table will be;
⇒ m = - 4/3
The slope for the second table will be;
⇒ m = 1 / 4
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x, 3, 1, 12, 8 if x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers? (1) x > 6 (2) x is greater than the median of the 5 numbers.
if x is an integer it does not show the median of the 5 numbers to be greater than the average of the 5 numbers
What is a median in math?The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
How do you find the median?Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the center, making it the median of 4, 1 and 7.
(1) x must be higher than one or three. It will be the median if it is 8 or fewer.
Consequently, if x = 7, then the list is 1, 3, 7, 8, 12, and median is 7, while the average is 31/5, which equals 6.2, and the answer is YES.
The list is 1, 3, 8, 8, 12, and the median is 8 if x = 8. Average = 32/5 = 6.4; if x = REALLY BIG, the list is 1, 3, 8, 12, and x; and the median is 8; the answer is YES. The answer to the question is NO since the average is REALLY BIG.
insufficient
(2) According to the aforementioned findings, x must be at least 9.
Depending on the amount of x, the list is either 1, 3, 8, x, 12, or 1, 3, 8, x.
The median and mean expressions are the same, regardless of whether order is appropriate:
Mean (average): 8 median = (1 + 3 + 8 + 12 + x)/5 = (24 + x)/5 mean (average):
The mean is at least (24 + 9)/5 = 33/5 = 6.6 since x is at least 9.
This is not convincing because the mean might be either millions or 6.6 (if x = 9) (if x is huge).
insufficient
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A
Given:
O HA
ZC, ZF are rt. Z's; AC= DF, BC= EF
O LA
OLL
B D.
OHL
F
E
Answer: your question is not very clear
Step-by-step explanation:
1. A local zoo had 750 visitors on Saturday. If
20% of the guests traveled from out of town,
how many local guests visited the zoo on
Saturday?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The number of local guests who visited the zoo is 600.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total number of visitors = 750
The percentage that visited the zoo.
= 100% - 20%
= 80%
Now,
The number of local guests who visited the zoo.
= 80% of 750
= 80/100 x 750
= 600
Thus,
The number of local guests who visited the zoo is 600.
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An arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 60 students?
1. The students that the academy have per teacher is 18.
2. The students per tutor will be 10.
3. The tutors that the academy need if it has 60 students is 6 tutors.
How to calculate the number of students?Given that the arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students.
The students that the academy have per teacher will be:
= Number if students / Teacher
= 72/4
= 18 students per teacher.
The students per tutor will be:
= 30/3
= 10 students per tutor
The number of tutors for 60 students will be:
= 60 / 10
= 6 tutors.
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The sum of 4 times a number and 2 is two times the number minus 8. What is the number?
Answer:
Step-by-step explanation:
The word "Sum" = addition.
"A number" = the unknown, aka 'x'.
"Is equal to" is =.
Go piece by piece. I will set your equation exactly as it is worded as you read it. Follow along:
4x + (-2) = 5x + (-2)
Imagine there is a "1" infront of the parenthesis around the -2. A positive * a negative always = negative. So.
Identify each of the following as rational or
irrational.
√23
104.42
√64
49.396
10.97846727460
Answer:
Irrational, rational, rational, rational, rational.
Step-by-step explanation:
√23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q.
104.42 this is a rational number! An irrational number has repeating values or just random numbers after the decimal point.
Here's an example...
Tell, does this number look rational?
4.2359712309458730495870192354870394587234098657293085412364781236409584790853467923456790324785098234570923845702398547 (and it goes on forever...and ever...and ever......)
√64 is a rational number. As we know that √64 = 8, a rational number.
49.396 with the 6 repeating is rational because we can express 49.39 as:
49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with
49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.
10.97846727460 is rational because the decimal places stop, it is rational. Remember, an Irrational number is non-repeating and non-terminating. Since the number terminates, it is rational
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
In triangle LMN, the measure of angle L is 50° and the measure of angle M 70°. What is the measure of the exterior angle to angle N?
Answer:
120°
Step-by-step explanation:
The 3 angle measures of a triangle will always equal 180.
Since we've already got two angles, all we need to do is a simple equation to get our missing angle:
180-(50+70)=60
Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:
180-60=120
And there's your answer, 120°
There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!
suppose a department store wants to estimate the average age of the customers of its contemporary apparel department, correct to within 2 years, with level of confidence equal to 0.95. management believes that the standard deviation is 8 years. the sample size they should take is .
By using the formula for sample size, it can be calculated that the sample size is 62
What is sample?
At first it is important to know about population.
Population is the group of items from where samples are taken for study and research and for statistical purpose
A subset of population is called sample.
Here, margin of error E = 2
Value of z for 95 % confidence interval = 1.96
Standard deviation = 8
Sample size = [tex](\frac{1.96 \times 8}{2})^2[/tex] [tex]\sim[/tex] 62
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Please answer! Question is below! Thanks!
Answer:
y=4x+4
Step-by-step explanation:
slope intercept form is y=mx+b
m is slope
B is y intercept
To find slope we use y2-y1/x2-x1
16-(-4)/3-(-2)
20/5
4 is the slope
We can fill this in
y=4x+b
To find b we fill in any coordinates
-4=4(-2)+b
-4=-8+b
+8. +8
4=b
Now we can fill it in
y=4x+4
Hopes this helps please mark brainliest
Find the Base & Height of the triangle
Area =42 in^2
Answer:
Height: 6
Base: 14
Step-by-step explanation:
Area=42 in^2
height=x-1
base=2x
bh/2=42
Substitute in the values:
2x(x-1)/2=42
The 2s cancel out each other.
x(x-1)=42
x^2 - x =42
x^2 - x - 42=0
When we factor that, we get:
(x-7)(x+6)=0
x=7 or x=-6
We will take the positive answer.
height= x-1 = 7-1 = 6
base= 2x = 2(7) = 14
Now let's double check if we are correct.
6(14)/2
=84/2
=42
We are correct!
Answer:
Base: 14 and height: 6 OR Base: -12 and height -7
Step-by-step explanation:
First, set up a proportion. (base x height) divided by 2 on one side and 42 over 1 on the other.
[tex]\frac{2x(x-1)}{2}=\frac{42}{1}[/tex] Next, cross multiply. This involves taking the numerator of
one side (top) and multiplying it by the denominator
(bottom) of the other side.
84=2x(x-1) 42*2=84 and anything multiplied by 1 equals itself. Next,
distribute (multiply) the 2x by each term in the
parentheses.
84=2[tex]x^2[/tex]-2x 2x*x=2[tex]x^2[/tex]. 2x*-1=-2x. Next, subtract 84 from both sides.
0=2[tex]x^2[/tex]-2x-84 Now, you can simplify this by dividing by 2 on both sides.
0=[tex]x^2[/tex]-x-42 This is a quadratic equation, which means you have to
factor or use the quadratic formula. In this case, you can
factor by using product and sum. You have to find what
multiplies to -42 and adds to -1. Those numbers would be
-7 and 6. -7*6=-42 and -7+6=-1 Therefore, you will have
x-7 and x+6
0=(x-7)(x+6) Next, solve each equation with each binomial set equal
to 0. For x-7=0, x=7 because you add 7 to both sides. For
x+6=0, x=-6 because you subtract 6 from both sides.
x=7 x=-6
You can check if these values work by plugging them into the formula.
[tex]\frac{2x(x-1)}{2}- > \frac{2*7(7-1)}{2}- > \frac{14(6)}{2}- > \frac{84}{2}- > 42[/tex]. x can be 7.
[tex]\frac{2x(x-1)}{2}- > \frac{2*-6(-6-1)}{2}- > \frac{-12(-7)}{2}- > \frac{84}{2}- > 42[/tex] x can be -6
The base and height are the numbers in the numerator of the equation after the 3rd arrow for both processes.
(9 * 6) * 1 = 3 operations
Answer:
53
Step-by-step explanation:
PEMDAS
Parenthesis
multiply the numbers
Divide
Add
Subtract
In a city with an 8.5% tax rate, what would be the total cost for a $66.00
What is the equation of a line that has a
3/4
slope of and an x-intercept of 0?
A y=0
B y=3/4
C y=3/4x
D y=x+3/4
Answer: C
Step-by-step explanation: This is because there is no y - intercept. But since there is still a slope an x but be next to the 3/4. Which represents the rate of change.
let m be the number of five-element subsets that can be chosen from the set of the first 14 natural numbers so that at least two of the five numbers are consecutive. find the remainder when m is divided by 1000.
We have (123) different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.
The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .
According to our question-
Let n be the maximum number of subsets of five elements that can be selected from the first 14 natural numbers,
with at least two of the five numbers being consecutive.
I have made a block of two consecutive numbers (like (1,2),(2,3),(13,14) etc.).
Now we can choose this block in 13 ways. Now we have to choose 3 numbers from the rest 12 numbers.
Hence, multiplication principle we come to know that there are 13×(123).
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Can someone help? Solve for a given that the height of the triangle is 3 centimeters and each of the legs are 6 centimeters. I also need the centimeters please !!
Answer:
6√3 centimeters
Step-by-step explanation:
This is an isosceles triangle because two of the sides are the same. We can divide this into two triangles to make two right triangles, and use the Pythagorean theorem. The base (a) will be divided by 2.
Pythagorean theorem: a^2 + b^2 = c^2
a and b are the legs of the triangle. c is the hypotenuse.
Let's replace the variables with the given information we know.
The hypotenuse is 6. One of the legs is 3. the other leg is a/2.
3^2 + b^2 = 6^2
9 + b^2 = 36
b^2 = 27
b = √27 = 3√3
Since this was for half of the base, we will multiply it by 2.
3√3 x 2 = 6√3
That is our answer.
I hope this helps.
It is -4 in Iceland at 7 am. The temperature then
increases by 6 Degrees. What is the new temperature?
Answer:
Step-by-step explanation:
kakaka
Answer: 2 degrees.
Step-by-step explanation: If it is -4 degrees in Iceland at 7 am and the temperature increases by 6 degrees, the new temperature would be -4 + 6 = 2 degrees.
Determine which integer in the solution set will make the equation true. 8x − 4 = 2(2x + 4)
S: {−4, 0, 3, 12}
Solving the equation 8x − 4 = 2(2x + 4) the required integer to make the equation true is 3
How to find the integerThe integer required to be found is solved as follows
The given equation is 8x − 4 = 2(2x + 4)
solving for x
8x − 4 = 2(2x + 4)
8x - 4 = 4x + 8
collecting like terms
8x - 4x = 8 + 4
4x = 12
dividing through by 4
x = 3
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please help me due in 10 min
Answer: A = 2(x+3y)+2z=2z+4x+2y
B=2(x+3y)=4x+2y
c=x+3y=2x+y
d=2y=x
Step-by-step explanation:
Answer:
2y=x:D
x+3y=2x+y:C
2(x+3y)=4x+2y:B
2(x+3y)+2z=2z+4x+2y
Step-by-step explanation:
D is the only possibility for 2y=x because it has 3 total. Similarly for C. B only has two different types, so it must be 2(x+3y)=4x+2y.
an english reading list has 9 american novels and 7 english novels. a student must read 4 from the list, and at least 2 must be american novels. in how many different ways can the 4 books be selected?
The total ways in which the student can readd the books are 1512 ways.
What is Combination?
A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant (unlike permutations).
Solution:
Since reading 2 american novels is compulsory
The student therefore needs to read only two more novels
It can be either American Novels or English Novels
Ways to read American Novel = 7C2
Ways to read English Novel = 7C2
Total Ways = 9C2 * (7C2 + 7C2)
Total Ways = 36 * (42)
Total Ways = 1512 ways
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A car is sold for $80, 000. Every year it loses 1/4 of its value.
a. Write an equation to represent the value of the car after 1 year.
b. Write an equation to represent the value of the car after t years.
A=P(1+ r/n)^n•t
An equation to represent the value of the car after 1 year is P(t) = 80,000(1 - 0.25)¹.
An equation to represent the value of the car after t years is P(t) = 80,000(1 - 0.25)^t.
How to write this equation?Generally speaking, a physical asset that loses its value at specific period of time represent an exponential decay. Therefore, a mathematical model for any physical asset (car) that decreases by r percent per unit of time is an exponential equation of this form:
P(t) = I(1 - r)^t
Where:
P(t ) represents the value of car in dollars.t represents the time or number of years.I represents the initial value of car.r represents the decay rate.Note: 1/4 is equal to 0.25.
For a car that loses 1/4 of its value annually, after 1 year its value is given by;
P(t) = 80,000(1 - 1/4)^1
P(t) = 80,000(1 - 0.25)¹
For a car that loses 1/4 of its value annually, after t year its value is given by;
P(t) = 80,000(1 - 0.25)^t
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A particle of mass mm moves in the plane with coordinates ( x ( t ) , y ( t ) )(x(t),y(t)) under the influence of a force that is directed toward the origin and has magnitude k / \left( x ^ { 2 } + y ^ { 2 } \right)k/(x 2 +y 2 )—an inverse-square central force field.
An inverse-square central force field is [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].
From Newton's second law of motion,
mass × acceleration = Force acting on the mass
Resolving the force F along x and y directions and applying Newton's second law of motion,
Using,
[tex]r = \sqrt{x^2+y^2}[/tex]
Therefore,
[tex]m\frac{d^2x}{dt^2} =-|F|cos \theta[/tex]
[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]
Where [tex]r = \sqrt{x^2+y^2}[/tex]
and cosθ = [tex]\frac{x}{\sqrt{x^2+y^2} }[/tex]
Similarly using,
[tex]r = \sqrt{x^2+y^2}[/tex]
we get,
[tex]m\frac{d^2y}{dt^2} = -|F|sin\theta[/tex]
[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]
Where [tex]r = \sqrt{x^2+y^2}[/tex]
and sinθ = [tex]\frac{y}{\sqrt{x^2+y^2} }[/tex]
Therefore we showed that holds
[tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex]
Hence the answer is an inverse-square central force field is [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].
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What is the color red?
Answer:
red im pretty sure
Fill in the table using this function rule.
y=3x+1
X
2
3
6
7
X
y
0
0
0
S
Answer:
y={7,10,19,22}
Step-by-step explanation:
3(2)+1 = 6+1 = 7
3(3)+1 = 9+1 = 10
3(6) + 1 = 18+1 = 19
3(7) + 1 = 21+1 = 22
What is the distance between the points (11,19) and (11,-6) in the coordinate plane?
Answer: 25 units
Step-by-step explanation:
distance with negatives is still an addition but you have to turn the negative into a positive to get the answer.
Elouise and Marcus are 20km apart.
There is a lake due west of Elouise that is also 10√3 km due north of Marcus.
Work out the bearing of Marcus from Elouise
Elouise and Marcus are 20 km apart. There is a lake due west of Elouise that is also 10√3 km due north of Marcus, so 22.36 km distance the bearing of Marcus from Elouise.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two legs. Pythagoras theory triangles are another name for these triangles.
At first assume a triangle, In the triangle, assume Elouise at the point A and Marcus at the point B, and the lake at the C point.
Given that,
Elouise and Marcus are 20 km apart (AB)
There is a lake due west of Elouise that is also 10√3 km due north of Marcus (BC)
Now, according to a Pythagoras theorem,
(AC)² + (AB)² = (BC)²
or, (AC)² = (BC)²- (AB)²
or, (AC)² = (10√3)² - (20)²
or, AC = [tex]\sqrt{500}[/tex]
or, AC = 22.36 km
So, distance bearing of Marcus from Elouise is 22.36 km.
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Ernesto guesses there are 69 marbles in a jar, but there are actually 60.
What is the percent error in Ernesto's guess?
Answer:
15%
Step-by-step explanation:
Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:
60 = 100%
68 = x
x = 69x100/60
x = 115
That means 69 is 115% of 60, which means that the error is of:
115 - 100 = 15%
Hope this helps, have a great day! :D
what is the sum of the infinite geometric series?25 minus 10 plus 4 minus eight fifths plus continuing the series diverges.
Answer:
Geometric Sequence
Finding the sum
The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.
Solution:
Geometric Series Sum Formula: S = a₁/1 - r
Given: a₁ = 3/4
a₂ = -9/16
a₃ = 27/64
a₄ = -81/256
1. Find the common ratio.
a_n = a₁r ⁿ ⁻ ¹
a₂ = a₁r ⁿ ⁻ ¹
-9/16 = 3/4 r ² ⁻ ¹
-9/16 = 3/4 r
2. Divide both sides of the equation by 3/4 to find r.
-9/16/3/4 = 3/4 r/3/4
(-9/16)(4/3) = r
-36/48 = r
-3/4 = r
3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...
S = a₁/1 – r
S = 3/4/1 – (-3/4)
S = 3/4/1 + ¾
S = 3/4/4/4 + 3/4
S = 3/4/7/4
S = (3/4)(4/7)
S = 12/28
S = 3/7
4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.
Definition:
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.
Code: 10.3.1.1
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Step-by-step explanation:
Which equation could generate the curve in the graph below?
Answer:
(Not accurate because I'm estimating amounts) y = ((x-2)/2)^2 + 4
Step-by-step explanation:
Scales horizontally by 2, Shifts up 4, right 2
5pts and who ever get this right gets brainliest
Answer:D is incorrect
Step-by-step explanation:
D is the only one that is incorrect because D is 9x-81
Answer:
(d) 9(x -9)
Step-by-step explanation:
You want the expression that is not equivalent to the other three.
Simplified expressionsThe simplified versions of the expressions are ...
9(x -1) = 9x -99x -92x -4 +7x -5 = (2+7)x +(-4 -5) = 9x -99(x -9) = 9x -81 . . . . . . . not equivalent to the othersThe expression not equivalent to the other three is 9(x -9).
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