The unit rate is 22.5 cents per oz .
The unit rate of any quantity is calculated by dividing (total cost) with (total units purchased).
For Example : If 12 bananas cost $120 then 1 banana will cost 120/12=$10.
In the given question
16oz bottle costs $3.59.
As we have to find the unit rate in cents per oz , we first convert $3.59 to cents.
We know that
$1=100cents
$3.59=100*3.59
=359cents
So the price of 16 oz bottle = 359 cents
Unit rate = (total price ) / (units purchased)
Substituting the total price as 359 cents and units purchased as 16oz.
Unit rate = 359/16
=22.4375
≅22.5
Therefore , the unit rate is 22.5 cents per oz.
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assuming I = E(R + r), prove that I/I = R/E + r/E
If we assume that I = E(R + r), then I/I = R/E + r/E.
The inverse of a value of a number is known as the reciprocal of the number. The reciprocal can be found out by replacing the numerator with the denominator and vice versa. For example, reciprocal of a number x will be 1/x and vice versa.
Here, we are given that I = E/(R + r)
Taking reciprocals of both sides we get-
Reciprocal of I will be- 1/I
Reciprocal of E/(R + r) will be- (R + r)/ E
Thus,
1/I = (R + r)/ E
Simplifying the equation further, we get-
1/I = R/E + r/E
Hence, proved
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write the product using an exponet
(5.6)(5.6)(5.6)
Answer: [tex](5.6)^3[/tex]
This is the same as saying (5.6)^3
===============================================
Explanation:
The base is 5.6 and it is multiplied a total of 3 times. We use an exponent of 3 to condense things down. So [tex]5.6 * 5.6 * 5.6 = (5.6)^3[/tex]
Another example: [tex]2^4 = 2*2*2*2 = \text{four copies of '2' multiplied}[/tex]
An observation deck extends 456 feet out above a valley. The deck sits 406 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by h=-161 +406. How long will it take for the object to be 6 feet above the valley floor?
We need to know the relation between height, time to solve this problem. The time taken by the object to be 6 feet above the valley floor is 25 seconds.
The distance an object falls is proportional to the time it took to fall because of gravitational force. Here we have been given an equation that shows us the relation between height of the object and the time taken to reach that height. We know that the initial height of the object is 406 feet, if we substitute the initial height in the equation we get time to be zero which shows us that this is the initial height. We need to find out the time taken by the object to be 6 feet above the valley floor.
h= -16t+406
6=-16t+406
-400=-16t
t=400/16=25 seconds
Therefore the time taken by the object to be at a height 6 feet above the valley floor is 25 seconds.
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5. The average monthly salary among a firm's twelve employees is 3500 € There are two part-time workers in the firm who both earn 2500 €/month. If the salaries of these two part-time workers are excluded from the average, what will the new average salary be? a) 3700 € b) 4300 € c) 4000 € d) other
Answer:
Choice a) 3700 €
Step-by-step explanation:
Total salary among 12 workers = Avg Salary x 12 = 3500 x 12 = 42,000 €
Total salary of 2 part-timers = part-time avg x 2 = 2500 x 2 = 5000
Total salary without part-timers salary= 42,000 - 5000 = 37,000 €
If we exclude the 2 part-timers, there are 10 full-timers who earn 37,000 €
So new Average Salary = 37000/10 = 3,700 €
answer: Choice a) 3700 €
The picture is uploaded above. I will give brainliest
The question is question 2
4,12
represents that jorge takes 4 steps to walk 12 feet
or represents number of steps that it takes to walk 12 feet either is right
Perform the following metric-metric conversion.
1.68 g/L_____ g/mL
Answer: 1680ml
Step-by-step explanation:
1000 mL are in 1 L, so with that logic
1=1000
.68=680
1000+680=1680
Annie runs in the park every 3 days. Ron runs in the park every 5 days. They both ran on 1 January. How many more times will they run in the park on the same day up to the end of February?
Answer:
Step-by-step explanation:
annie runs in park = every 3 days
ron runs in park = every 5 days
lets find LCM of 3 and 5 = 3*5 = 15
if they ran on 1st of January then they will meet again on on 15th January , will again meet on 30th of January and will again meet on 14 February . if is was a leap year they would again meet at 29th February .
6. Answer the following questions given the following infinite geometric series:
8 + 12 + 18 + 27 + ...
For the given geometric sequence, we have that:
The first term is: [tex]a_1 = 8[/tex]The common ratio is: [tex]r = \frac{3}{2}[/tex]Since it is an infinite sequence with r > 1, the sequence diverges.What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For the series given by:
8, 12, 18, 27, ...
We have that:
The first term is: [tex]a_1 = 8[/tex]The common ratio is: [tex]r = \frac{12}{8} = \frac{3}{2}[/tex] (simplifying by 4).When a geometric series is infinite and has a common ratio greater than 1, it diverges.
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Solve for the unknown value using the equation for the constant of proportionality,
1) When k = 1.5 and x = 50, the value of y is; y = 75
2) When k = 14 and y = 334, the value of x is; x = 23.84
3) When k = 12 and x = 245, the value of y is; y = 2940
4) When k = 16 and y = 38, the value of x is; x = 2.375
We are given the equation for the constant of proportionality, as y/x = k
1) When k = 1.5 and x = 50, we want to find the value of y = ?
y/50 = 1.5
y = 50 * 1.5
y = 75
2) k = 14 and y = 334, x = ?. We want to find the value of x. Thus;
334/x = 14
x = 334/14
x = 23.84
3) k = 12 and x = 245, y = ?
y/245 = 12
y = 245 * 12
y = 2940
4) k = 16 and y = 38; x = ?
38/x = 16
x = 38/16
x = 2.375
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Complete question is;
Solve for the unknown value using the equation for the constant of proportionality, y/x = k .Known Values Unknown Value
k = 1.5 and x = 50
y = ?
k = 14 and y = 334, x = ?
k=12 and x=245, y = ?
k = 16 and y = 38; x = ?
What is (-1, 2) reflected across the y-axis?
If the coordinate is reflected over the y-axis, the resulting coordinates will be (1, 2).
Reflection of coordinatesImages that are reflected are mirror images of each other. For instance, given the coordinate points (x, y), if it is reflected across the y-axis, then the result of the expression is (-x, y).
Given the coordinate point (-1, 2), if the coordinate is reflected over the y-axis, the resulting coordinates will be (1, 2).
Note that the x-coordinate point is negated if the coordinate is reflected over the y-axis.
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Write the ratio of pencils to
erasers in simplest form.There are 10 pencils and 2 erasers
If m is one sixth of n and p is five less than m, write a p as a function of n
p = (n - 30)/ 6 as a function of n.
Here we need to find the value of p in terms of n.
From the question, we have two equation
The first equation is:
m = 1/6n .......(1)
The second equation is:
p = m - 5.......(2)
From equations 1 and 2 we have to find the value of p in term of n.
So by putting the value of m in the second equation we have:
p = 1/6n - 5
= (n - 30)/6
Therefore we get the value of p as (n -30)/6 in terms of n.
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Someone help meee!
Solve 4(x-3)-2(x-1)>0
Answer:
{x|x>5}
Explanation:
4(x-3)-2(x-1)>0
4x-12-2x+2>0
2x-10>0
2x>10
x>5
What is the image of the point
(
1
,
−
4
)
(1,−4) after a rotation of
18
0
∘
180
∘
counterclockwise about the origin?
The image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)
How to determine the image of the point?The given parameters are
Point = (1, -4)
Transformation: 180∘ counterclockwise about the origin
The rule of 180∘ counterclockwise about the origin is
(x, y) = (-x, -y)
When this rule is applied to the given point, we have the image to be
Image = (-x, -y)
This gives
Image = (-1, 4)
Hence, the image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)
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The number 56 is an integer, but not a whole number.
Answer:
False.
Step-by-step explanation:
Whole numbers can be described as the integers greater than and including zero. 56 has no fractional or decimal part, and is positive, so it is a whole number and an integer!
Simply and show how you got the answer
[tex] \frac{3}{ \sqrt{5} - 2 } [/tex]
Rationalize the denominator by multiplying the numerator and denominator by the denominator. (Important: if the denominator has a minus sign, change to plus and vice versa)
[tex]⟹\frac{3 \times \sqrt{5 + 2} }{ (\sqrt{5} - 2 ) \times ( \sqrt{5} + 2) } [/tex]
[tex] ⟹ \frac{3 \sqrt{5} + 6 }{ \sqrt{25} + 2 \sqrt{5} - 2 \sqrt{5} - 4 } ⟹\frac{3 \sqrt{5} + 6 }{5 - 4} [/tex]
[tex] ⟹\frac{3 \sqrt{5} + 6}{1} ⟹3 \sqrt{5} + 6[/tex]
Problem 2.[tex] \frac{6 - \sqrt{12} }{ \sqrt{3} + \sqrt{10} } [/tex]
Rationalize the denominator.
[tex] ⟹\frac{(6 - \sqrt{12} ) \times ( \sqrt{3} - \sqrt{10} )}{ (\sqrt{3} + \sqrt{10} ) \times ( \sqrt{3} - \sqrt{10} } [/tex]
[tex]⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ \sqrt{9} - \sqrt{30} + \sqrt{30} - \sqrt{100} } [/tex]
[tex]⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{3 - 10} ⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ - 7} [/tex]
[tex] ⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + \sqrt{12 \times 10} }{ - 7}⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 4 \sqrt{3 \times 10} }{ - 7} [/tex]
[tex] ⟹ - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]
Therefore:
1. [tex]3 \sqrt{5} + 6[/tex]
2. [tex] - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]
I hope these helpWhich point is part of the intersection of planes ACD and MHG?
A point that is part of the intersection of planes ACD and MHG is: Point B.
How to Find the Points of Intersection of Planes?A plane has at least three points that lie on it. When two planes intersect, they do so at some certain points. This means that two intersecting planes share some points in common alone the line of their intersection.
In the diagram given, plane ACD and plane MHG intersect along line BA. This means that both planes share points A and B in common.
Therefore, we can state that a point that is part of the intersection of planes ACD and MHG is: Point B.
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Compare the steepness of the following functions. How does F3 compare to F1
Answer:
Function 3 is less steep.
Step-by-step explanation:
The steepness of a linear function is determined by its coefficient of x.
Since the coefficient of x in [tex]f_3(x)[/tex], 0.5, is smaller than that of [tex]f_1(x)[/tex], 2, function 3 is less steep than function 1.
Significance of the coefficient of x
We can think of the function as an equation of a line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.
Steepness and value of x
The larger the numerical value of m, the steeper the line is.
Significance of the sign of x
The sign (positive or negative) of m tells us the direction in which the line is sloping towards. A positive m value gives us a line sloping upwards from left to right, while a negative m value gives us a line that is sloping downwards from left to right.
Additional:
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https://brainly.com/question/13359759These questions are about calculus, I would greatly appreciate your help on both questions! ASAP PLEASE!
The slope of the line -1/6.
The value of m = -1.
what is slope?The slope of a line is a measure of its steepness. slope is calculated as "rise over run" (change in y divided by change in x).
given:
f(x) = √10-x
let f(x)=y
y = √10-x
Now,
dy/dx = -1/2(√10-x)
at x=1
dy/dx = -1/2(√10-1)
dy/dx = -1/2(3)
dy/dx = -1/6
equation of line is
y= mx + b
y= (-1/6)x + b
6y = -x + b
So, m= -1
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Given this equation for converting temperature from Fahrenheit (f) to Celsius (c) is C = [5(f – 32)]/9, what is the Celsius temp when Fahrenheit is 104 degrees?
Answer:
40 degrees
Step-by-step explanation:
Substitute f = 104:
[tex]C = \frac{5(f - 32)}9 \\\\\to C = \frac{5(104 - 32)}9 \\\\\to C = \frac{5 \times 72}9 \\\\\to C = 5 \times 8 = 40 \text{ degrees}[/tex]
Which statement correctly describes the expression (-18)(-3)?
Answer:
Both factors are negative,so that the product will be positive
Step-by-step explanation:
Hope it helps you
Hazel plans to mow her neighbors' yards to earn money. She charges a base fee of $25 and $7 for every hour she mows. The amount she earns per yard can be represented by the linear function M(t) = 7t + 25. What is the value of M(2), and what is its interpretation?
a. M(2) = 39; If Hazel mows 2 yards, she will earn $39.
b. M(2) = 14; If Hazel mows 2 yards, she will earn $14.
c. M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39.
d. M(2) = 14; If Hazel mows a yard for 2 hours, she will earn $14.
The correct option is M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39 . Option C
What is a function?A function can be defined as an expression that shows the relationship between an independent variable and a dependent variable.
Given the function;
M(t) = 7t + 25
Where;
M is the amount she earns per yardt is the time in hoursFor M(2), we substitute the value of t as 2 in the function
M(2) = 7(2) + 25
M(2) = 14 + 25
M(2) = $39
This explains that the she mows the yard for t = 2 hours, she would earn $39
Thus, the correct option is M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39. Option C
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A group of friends wants to go to the amusement park. They have no more than $605 to spend on parking and admission. Parking is $17.25, and tickets cost $37.25 per person, including tax. Which inequality can be used to determine pp, the maximum number of people who can go to the amusement park?
Considering the definition of an inequality, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is:
17.25 + 37.25×p ≤ 605
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
A group of friends have no more than $605 to spend on parking and admission. Parking is $17.25, and tickets cost $37.25 per person, including tax.Being "p" the number of people who can go to the amusement park, the inequality that expresses the previous relationship is
17.25 + 37.25×p ≤ 605
Finally, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is:
17.25 + 37.25×p ≤ 605
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Use the distance formula to determine how far apart the given points are. Given: D(-12, 10) E(-1,5) Find: DE
Answer:
it d
Step-by-step explanation:
Mr. McDowell bought a block of fudge that weighed 7/10 of a pound. He cut the fudge into 7 equal pieces. What was the weight of each piece of fudge?
Answer: 1/10 of a pound
Step-by-step explanation:
The total weight was 7/10 of a pound. Cutting the fudge into 7 pieces implies dividing the fudge by 7.
7 is the same as 7/1.
When dividing fractions, we can multiply by the reciprocal. Essentially, we just flip the second number.
[tex]\frac{7}{10}/7 =\frac{7}{10} / \frac{7}{1} =\frac{7}{10} *\frac{1}{7}[/tex]
We can multiply this out to 7/70 and then simplify to 1/10,
or we could first cross simplify by dividing the 7s out of the numerator and denominator before multiplying. Either way, your answer ends up being 1/10 of a pound.
Hope this helps!
Which angles in the picture are NOT adjacent?
A. ∠2 and ∠3
B. ∠3 and ∠4
C. ∠1 and ∠2
D. ∠1 and ∠3
Answer:
D. ∠1 and ∠3
Hope this helps!
Answer:
1 and 3 or also known as D
Step-by-step explanation:
i took the test and got it right
AB = x, BC = x + 4, AC = 40
A •--------------------•B--------------------• C
Help please
Step-by-step explanation:
A=Xb c
2+4=6
5+5=10
9+20=75
Answer:
ab=20 bc=16+4=20 ac=40
Damon has 37 inches of space on his car bumper that he wants to use for bumper stickers. How many short bumper stickers can Damon fit side by side on his car bumper?
Answer: Does it specify how long his short bumper stickers are?
Step-by-step explanation:
Which of the following is an example of the Commutative Property? 2x + 3x = 5x 5xy = 5(xy) 5z - 3x = -3x + 5z 3(a + b) = 3a + 3b
From the given examples 5z - 3x = -3x + 5z and 5(xy) = 5(xy) are following the commutative property.
According to the given question.
We have some equations
2x + 3x = 5x
5xy = 5(xy)
5z - 3x = -3x + 5z
3(a + b) = 3a + 3b
Here, we have to find which equation is following the commutative property.
As we know that, the commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
For, example 4 + 5 gives 9, and 5 + 4 also gives 9.
From the given example the equation
5z - 3x = -3x + 5z is following the commutaive property of addition.
And, 5(xy) = 5(xy) is following the commutative property of multiplication.
Hence, from the given examples 5z - 3x = -3x + 5z and 5(xy) = 5(xy) are following the commutative property.
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2) If x = y – 9, and y – 4 = 10, x = ?
A. -5
B. +5
C. 1
D. A and B
Answer:
the answer is B
Step-by-step explanation:
x = y - 9
y - 4 = 10
x = ?
y = 10 + 4
° y = 14
x = y - 9
= 14 - 9
✔️ x = +5
ANSWERS
y-4=10
y=10+4
y=14
sub y equ 1
x=14-9
x=+5