Answer: The prime factorization of 216 is 2 × 2 × 2 × 3 × 3 × 3 or 23 × 33.
Step-by-step explanation:
PLEASE MARK BRAINLIEST
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60%pure antifreeze. The company wants to obtain 240 gallons of a mixture that contains 20% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?
The amount of gallons of water is 160 and gallons of the premium antifreeze solution that must be mixed is 80.
How to find the volume of water?Let y represent the volume of water
Hence,
Total volume equation :
x +y = 240 equation 1
Pure antifreeze volume:
0.60 = .20 × 240 gallons equation 2
Hence,
Equation 2
x = .20 × 240 /.60
x = 48 /.60
x = 80 (Pure antifreeze)
So,
y = 240 -80
y = 160 gallons of water
Therefore the volume of water is 160 gallons.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
x=25
Step-by-step explanation:
2x-14=36
2x=50
x=25
z varies directly as x2 and inversely as y2. If z=76 when x=5 and y=2, find z if x=9 and y=9. (Round off your answer to the nearest hundredth.)
[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \begin{array}{llll} \textit{\small "z" varies directly with }x^2\\ \textit{\small and inversely with }y^2 \end{array}}{ z=\cfrac{kx^2}{y^2}}\qquad \textit{we know that} \begin{cases} z=76\\ x=5\\ y=2 \end{cases} \implies 76=\cfrac{k(5)^2}{(2)^2} \\\\\\ 76=\cfrac{25k}{4}\implies \cfrac{4}{25}\cdot 76=k\implies \cfrac{304}{25}=k~\hfill \boxed{z=\cfrac{304x^2}{25y^2}} \\\\\\ when \begin{cases} x=9\\ y=9 \end{cases}\implies z=\cfrac{304(9)^2}{25(9)^2}\implies z=\cfrac{304}{25}\implies z= 12.16[/tex]
A client at a weight loss clinic lost 18.5 pounds (lb) in 4 weeks. If he loses the same amount of weight each day, how much weight does he lose per day? (Round your answer to 3 decimal places)
Answer:
0.007 pounds a day
Step-by-step explanation:
if he loses 18.5 pounds in 4 weeks then each week has 7 days so you divide 18.5 by 7 four times. HOPE THIS HELPS :)
find two numbers such that one number is 4 more than twice as big as the other number and the two numbers sum to 28
The first number is 8 and the second number is 20
let the first number = X
the second number = 4 + 2X
sum = 28
X + (4 + 2X) = 28
3X + 4 = 28
3X = 24
X = 8
The first number is 8
and the second number is 4 + 2X = 4 + 2(8) = 20
Addition:
When we say "the addition," we mean adding two or more numbers together. The plus sign (+) denotes addition of two numbers, therefore three is written as three plus three. You also have control over how often the plus sign (+) is used. such as 3 + 3 + 3 + 3. Mathematical addition is an essential part of children's education. Students learn basic addition sums in primary school, including one-digit facts, math addition sums, and double-digit math addition sums. Sums in addition are one of the most fundamental and fascinating Math concepts for elementary school students. Children first learn fundamental mathematical ideas like adding numbers in their early years because math is an enthralling subject.
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write the expressions as the power of 2 (4*2^5)/(2^3*1/16)
The expressions (4×2⁵) / (2³ × 1/16) written as the power of 2 is 2⁸
How to write the expressions as the power of 2?
Given: (4×2⁵) / (2³ × 1/16)
In order to write this expression as the power of 2, we need to use some in indices law:
Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base": 5⁴ x 5³ = 5⁴⁺³ = 5⁷ and P⁴ x P⁶ = P¹⁰
Division law: To divide two variables or numbers with the same base, we need to subtract their powers and raise them to that base": 5¹⁰ ÷ 5³ = 5¹⁰⁻³ = 5⁷ and P⁸ ÷ P² = P⁸⁻² = P⁶
Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:
8⁻² = 1/8² and b⁻⁶ = 1/b⁶
Let's use the laws to create the given expressions as the power of 2:
(4×2⁵) / (2³ × 1/16) = (2²×2⁵) / (2³× 1/2⁴) Note: 4 = 2² and 16 = 2⁴
= (2²⁺⁵) /(2³⁺⁽⁻⁴⁾) Note: 1/2⁴ = 2⁻⁴ (reciprocal law)
= 2⁷ / 2⁻¹
= 2⁷⁻⁽⁻¹⁾ Division law
= 2⁸
Therefore, the expressions as the power of 2 is 2⁸
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Which expression is equivalent to 4/5-1/2
Answer: 3/10
Step-by-step explanation:
4/5 is equal to 8/10 and 1/2 is equal to 5/10
then we have 8/10-5/10 which is 3/10
this is the answer since expressions can be a number
Find the slope, m of the line that passes through the points (-2/3, 3/4) and (5/6, -1/2) Enter your answer as a fraction in simplest form in the box.
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
According to question,
slope = (-1/2-3/4)/(5/6-(-2/3))
slope = (-5/4)/(9/6)
slope = -30/36
slope = -5/6
What is 5.33333333333 as a fraction?
please help!
Answer:
[tex]5\frac{1}{3} or \frac{16}{3}[/tex]
Step-by-step explanation:
endless 3’s are always 1/3
So now we just add 5 in front of it
5 1/3
Hopes this helps please mark brainliest
[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
5.333333
= [tex]\frac{16}{3}[/tex]
We see that,
3 ) 16 ( 5.333333
15
10
9
10
9
1
and so on...
Thus,
[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.
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Select the function that represents a parabola with vertex at (2,–1) and a point (5,8) on its curve.
A)
ƒ(x) = (x – 2)2 – 1
B)
ƒ(x) = 2(x – 2)2 – 1
C)
ƒ(x) = 2(x + 2)2 – 1
D)
ƒ(x) = (x + 2)2 – 1
The equation of parabola is y = (x - 2)² - 1.
What is Vertex from of Parabola?We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k.
Given:
Vertex (2, -1) and point (5, 8)
As, we know the vertex form of a parabola can be written as following
y = a(x - h)² + k ......(1)
Now, We are given that vertex is at (2,-1) and there is a point (5,8) on the curve.
i.e. h = 2 and k = -1,
x = 5 and y = 8
So, to find the value of a
y = a(x - h)² + k
8= a( 5- 2)² - 1
8= 9a - 1
9a= 9
a=1
Now, the equation of Parabola is
y = a(x - h)² + k
y = (x - 2)² - 1
Hence, the equation of parabola is y = (x - 2)² - 1.
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how to find intercepts from any given quadratic equation
Answer:
To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).
Step-by-step explanation:
Hot Chocolate Sales and Outside Temperatures
$100 $213 $830 $679 $209 $189 $1,110 $456 $422 $235 $199
Sales ($).
Temperature
(°F)
a) Make a scatterplot of the data above. (2 points)
92° 88° 54° 62° 85° 16°
+
52⁰
65° 68°
89⁰
91°
Hot Chocolate Sales and Outside Temperatures:
(A) The scatter plot is shown below.
(B) The anomaly is located at (189, 16°F).
(C) A negative correlation exists.
(D) Sales are the dependent variable, and temperature is the independent variable.
What is Temperature?
The physical concept of temperature indicates in numerical form how hot or cold something is. A thermometer is used to determine temperature. Thermometers are calibrated using a variety of temperature scales, which historically defined various reference points and thermometric substances.
The following information is provided for hot chocolate sales and outside temperatures:
(Y) Sales Temperature (X)
100 92
213 88
830 54
679 62
209 85
189 16
1110 52
456 65
422 68
235 89
199 91
(A)
Attached below is the scatter plot.
(B)
A cluster is a group of points or values gathered in one location.
A cluster of three values between the temperatures of 80°F and 100°F may be seen on the scatter plot.
A value that differs significantly from the other values in a data set is referred to as an outlier. Either it's too little or it's too big.
In the given data collection, there is an outlier.
The anomalous value is (189, 16°F).
(C)
The scatter plot's points have a decreasing slope.
This suggests that the variables temperature and sales have a bad relationship.
There is a bad association as a result.
(D)
Dependent variables are variables that are being studied, or being kept an eye on for any changes while the other variables in the model are altered.
The variables that are changed to cause the dependent variable to vary proportionately are known as independent variables.
According to the outside temperature, the data in this case shows the sales of hot chocolate.
Sales are therefore the dependent variable, and temperature is the independent variable.
This is due to an increase in hot chocolate sales as the temperature drops.
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Holly is purchasing drinks for a holiday party. She is getting a combination of soda and juice. The soda costs $2 each and the juice costs $5 each. Holly
needs to bring at most 10 drinks but doesn't want to spend more than $50. Which graph shows how many of each type of drink she can buy?
The graph that shows how many of each type of drink she can buy is as shown below.
The correct answer is an option (D)
In this question, we have been given Holly is getting a combination of soda and juice. The soda costs $2 each and the juice costs $5 each. Holly
needs to bring at most 10 drinks but doesn't want to spend more than $50.
Let x be the number of soda cans and y be the number of soda cans(or bottles)
Holly needs to bring at most 10 drinks
So, we get an inequality,
x + y ≤ 10
She doesn't want to spend more than $50.
So, we get an inequality,
2x + 5y ≤ 50
In following graph, an inequality x + y ≤ 10 is represented by blue shaded region and the inequality 2x + 5y ≤ 50 is represented by red shaded region.
The solution set for the given inequalities is represented by a purple region (common region for both the inequalities)
Therefore, the graph that shows how many of each type of drink she can buy is as shown below.
The correct answer is an option (D)
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Between which two numbers will you find |-2.65|?
A. -2.6 and -2.5
B. -2.7 and -2.6
C. 2.5 and 2.6
D. 2.6 and 2.7
|-2.65| can be found between numbers 2.6 and 2.7
|-2.65| is between which two numbers?
Absolute value means to remove any negative sign in front of a number and to think of the number as positive. This is what the vertical lines | | surrounding -2.65 means.
Thus, |-2.65| = 2.65
If we examine the options, then we can say 2.65 is between 2.6 and 2.7 i.e. 2.6, 2.65, 2.7
Therefore, |-2.65| can be found between the numbers 2.6 and 2.7. So option D is the answer
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Andrew took the midterm exam a second time this week. Andrew earned a score of 72% last week, and calculated the absolute change in the scores to be an increase of 23 percentage points. Calculate Andrew’s score on the midterm this week.
Andrew's score on the midterms this week, based on his scores last week and the absolute change, is 95%.
How to find the midterm score?The Midterm score for this week increased by 23 percentage points over the midterm score for the last week. This increase in the midterm score was an absolute change and not a relative change.
As a result of this being an absolute change, the midterm score for Andrew this week would then be:
= Midterm score last week + absolute change in the score
= 72% + 23 percentage points
= 95%
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HELP PLEASE If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’, what will be the coordinate of D’?
According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)
Quadrilateral
Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given,
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.
Here we need to find the coordinate of D'.
In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.
While we looking into the graph, we have identify the point of
A (0,0), B(-4, 3), C(1,5) and D(2,3)
Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).
According to this rule, the new coordinates are written as,
A(0,0) = A'(0,0)
B'(-4,3) = B'(-3,-4)
C(1,5) = C'(5, -1)
D(2,3) = D' (3, -2)
Therefore, the new coordinate of D' is (3, -2).
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find (f o f) x f(x) = 6x+9 and g(x)= x^2
Step-by-step explanation:
given
f(x)=6x+9
solve
6(6x+9)+9=0
36x+54+9=0
36x+63=0
36x=_63
36x/36 = _63/36
x=_63/36
Benito earns an annual salary of $36,000. He is paid twice a month with paychecks being of equal amounts. What is the gross income that Benito will earn on his paycheck? Benito must pay 1% in Medicare taxes. How much money will be withheld from each paycheck? Social security taxes are 6% of your gross income. How much money will be withheld from each paycheck for social security taxes? Benito will also have to pay $287.95 in federal income tax. How much will Benito's paycheck be?
Step-by-step explanation:
annual salary (that means the income for a whole year) is
$36,000
1 year = 12 months.
twice a month = 2 times in a month
so, he gets 12×2 = 24 paychecks in a year.
so, the gross income per paycheck is
36,000 / 24 = $1,500
100% = $1,500
1% = 100%/100 = 1500/100 = $15
so, $15 will be withheld from each paycheck for Medicare taxes.
6% = 1%×6 = 15×6 = $90
so, $90 will be withheld from each paycheck for social security taxes.
and then there is the federal income tax of $287.95
so, he will actually get for each paycheck
1500 - 15 - 90 - 287.95 = $1,107.05
How are the entries of the matrix named by position?
You can ask where you don't understand.
Question
1
Graph the line passing through (-2, 4) whose slope is m =—1/4
Answer:
Step-by-step explanation:
these seem complicated, but just think about what they are asking. they are giving you a point and a slope to a line.
That gives you the hint to use the "point-slope" formula
if you don't have it memorized you might as well start trying to now. You'll need this over and over and over...
y-y1=m(x-x1)
so plug in the given info
y-4= (-1/4)(x-(-2))
y-4 = -1/4 (x +2)
y-4 = (-1/4)x -1/2
y = (-1/4)x + 7/2 this is the slope intercept formula. y = mx +b
we can now graph this line with the slope intercept formula.
note the graph does pass through (-2,4) and has a -1/4 slope :)
The ratio of T-shirts to jumpers in Jacob's wardrobe is 8 : 7.
There are 24 T-shirts in his wardrobe. How many jumpers are there?
Answer:
24:23
Step-by-step explanation:
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling
a number less than 12.
The probability of rolling a number less than 12 is 91.6%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.
We can have the number 12, the probality will be 1/12
So the probability of rolling a number less than 12 is = (1 - probability of 12)
=1-1/12
=11/12
=0.916
Hence the probability of rolling a number less than 12 is 91.6%.
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Please help I was sick and missed out on class.Thank you
Answer:
The slope is -1.
Step-by-step explanation:
When given two points, the formula for slope is [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
4 - 7 / -2 - (-5) = -3 / 3
-3 / 3 = -1, so the slope is -1.
someone help tyyyyyy
The length of a room is two times it breadth and breadth is three times it's height. If
the area of it's four walls is 288 m², then find the area of it's floor.
Step-by-step explanation:
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The length of a room is
3
4
times its breadth. The total area of the four walls of this room is
15
28
times the area of the floor of the room. What is the ratio of the height of the room to the length of the room?
Medium
Solution
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Correct option is D)
Let breadth =x units
Then length =
3
4
x units
⇒ Area of floor = x×
3
4
x=
3
4
x
2
square units
Let the height of the room =y units. Then
Area of four walls = 2[xy+
3
4
xy]=
3
14
xy
Now,
3
14
xy=
15
28
(
3
4
x
2
)⇒xy=
15
2
×4x
2
y=
15
8
x ⇒
x
y
=
15
8
⇒ y:x=8:15
What is the domain of the function shown on the graph?
Y
4
-8 -6 -4
N
8
6
4
2+
2
4
-6
8-
N
OA. ≤ 2
OB.
x ≤ 1
O C. -10 < x < 2
O D. -8AA ∞
4
6 8
X
The domain of the given graph is x≤ 2, option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
We have to find the domain of the given graph.
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.
As we observe the graph the value of x are less than 2
Hence, the domain of the given graph is x≤ 2
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geometry lesson!! please help, i’ll make brainliest!
Answer:
GH = 42 ftStep-by-step explanation:
GivenCongruent isosceles trapezoids ABCD and EFGH.SolutionWe know that corresponding parts of congruent figures are congruent.
It means:
AB = CD = EF = GH = 42 ftA card is drawn from a 52-card deck, the result is written down, and then the deck is shuffled. A card is drawn. What is the probability that the first card was a heart and the second card was not heart? Write your answer as a fraction.
The probability that the first card is a heart and the second one is not a heart is P = 0.19
How to get the probability?
A standard deck has 52 cards divided in 4 sets, such that each set has 13 cards.
The probability of randomly drawing a heart is equal to the quotient between the number of cards of the set heart (13) and the total number of cards (52), so we get:
p = 13/52
Now, the probability of not getting a heart is equal to the number of cards that are not hearts (3*13 = 39) and the total number of cards (now is 51 because we already took one).
q = 39/51
The joint probability is equal to the product between the two individual probabilities:
P = q*p = (13/52)*(39/51) = 0.19
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worksheet- triangle sum and exterior angle theorem, help pls!
The value of x in the given triangle is 110°.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given triangle,
∠A=65°, ∠B=90°, ∠C=80°, and ∠D=50°
To find the value of ∠E,
Use triangle ∠ABC, in which eqaute the sum of the angle of a triangle to 180°.
65+90+y=180
y=25
The remaining ∠C =80-25 = 55°
Use exterior angle theorem,
According to this, the sum of two interior angles is equal to an exterior angle.
x=50+55
x=105°
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First place pays $4800 to the winner, second place $3300 and third place $1300. Is it worthwhile to enter the race if it costs $1000?
It is worthwhile to enter the race if it costs $1000.
What is total cost?Total cost is an economic measure that includes not only the initial cash outlay but also the opportunity cost of their choices when producing a product, purchasing an investment, or acquiring a piece of equipment. TVC + TFC = TC
The sum of fixed and variable costs is the total cost. For example, if a company has a fixed cost of $30 per unit and a variable cost of $5 per unit as output increases, the total cost is $35.
In this case, first place pays $4800 to the winner, second place $3300 and third place $1300. It is therefore worthwhile since the amounts are more than $1000.
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