The volume of premium antifreeze to be used is 60 gallons.
The volume of water to be used is 120 gallons
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
Let the volume of 60% pure antifreeze be used to make 20% pure antifreeze.
= x gallons
The volume of 20% pure antifreeze = 180 gallons
For 60% pure antifreeze:
C₁ = 60% , V₁ = x gallons
For 20% pure antifreeze :
C₂ = 20% , V₂ = 180 gallons
Applying,
C₁V₁ = C₂V₂
60 × x = 20 × 180
x = 60 gallons
The volume of 60% pure antifreeze used = 60 gallons.
The volume of water to be used.
= 180 - 60 gallons
= 120 gallons
Thus,
The volume of premium antifreeze to be used is 60 gallons.
The volume of water to be used is 120 gallons
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77, 49, 36, 18, _
what is the next number?
what is the rule?
Answer:9
Step-by-step explanation:um
Select the equation that is true. 12 ÷ 2 = 15 ÷ 5 12 ÷ 3 = 24 ÷ 6 32 ÷ 8 = 21 ÷ 7 30 ÷ 5 = 28 ÷ 4
Answer:
12 ÷ 3 = 24 ÷ 6
Step-by-step explanation:
12/3 = 4 and 24/6 = 4
So 4 = 4
(1 po
3. Your cell phone plan is $35.98/month plus a utilities tax of 6.5% APR. During the year, you go
40 minutes over your plan at a rate of $0.35/minute. How much do you pay for the overages?
The amount that the cell phone owner will pay for the overages is $14.91.
What is the overage?The overage is the difference between the actual usage in minutes and the estimated usage.
For instance, if the plan estimates that the phone usage per year would be 4,000 minutes, but the plan holder uses 4,010 minutes, the extra 10 minutes are regarded as overages.
The opposite of overages is underages. If underages are part of the phone plan, the plan holder will be refunded accordingly.
Usually, overages attract a variable plan rate per minute.
Fixed charge per month = $35.98
Utilities tax APR = 6.5%
Overages = 40 minutes
Rate per overage minute = $0.35
The total charge for overage = $14 ($0.35 x 40)
Interest on the overages = $0.91 ($14 x 6.5%)
Total payment for the overages = $14.91 ($14 + $0.91)
Thus, for going over the plan by 40 minutes at $0.35 plus an APR of 6.5%, you will pay $14.91 for the overages.
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Find the LCM of 45 and 270 using prime factorizations
Example:
120 and 45
10 and 12 can go into 120. 10 can go into 5 and 2, while 12 can go into 3 and 4. 4 can be still divisible, so it would be 2 and 2.
45 is 9x5. 9 can be divisible, so you would turn them into 3 and 3.
The LCM will be the product of the largest multiple of each prime that appears on at least one list. For example, we have a 2, 3, and 5, so I’ll choose the largest multiples of each and find their product. There are three 2's, three 3's, and 5, or 8 x 9 x 5. That would get you 360.
See how you could get that with your problem?
P.S. I don't answer questions directly, instead, I use examples. Feel free to use other suggestions if this one doesn't appeal to you.
Calculate the distance between the points M=(-4, 9) and L= (-1, 1) in the coordinate plane.
Give an exact answer (not a decimal approximation).
The distance between the points M=(-4, 9 ) and L=(-1. 1) in the coordinate plane is [tex]\sqrt{73}[/tex].
Explain Coordinate Plane.
In a plane, a Cartesian coordinate system is a system of a coordinate that designates each point uniquely by a pair of numerical coordinate in a plane, which are the signed distances from two fixed perpendicular oriented lines to the point on the same plane, measured in the same unit of length.
Solution Explained:
Using the distance formula, we have
[tex]\sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2} }[/tex]
Substituting the values using the values of the points
[tex]\sqrt{(-1 + 4) ^{2} + (1 - 9) ^{2} }[/tex]
[tex]\sqrt{(3) ^{2} + (-8) ^{2} }[/tex]
[tex]\sqrt{9 + 64}[/tex]
[tex]\sqrt{73}[/tex]
Hence, the distance between the two points is [tex]\sqrt{73}[/tex]
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Shanice's car is traveling 10 miles per hour slower than twice the speed of Brandon's car. She covers 93 miles in 1 hour 30 minutes. How fast is Brandon driving?
The speed of a body is the distance it travels per unit of time. That means that we can also find out how far an
object moves in a certain amount of time if we know its speed: we use the equation "distance = speed time."
Here, we don't know either Brandon's speed or Shanice's, but since the question asks for Brandon's speed, that's what we'll use as our variable x.
The distance Shanice covers in miles is 93, and the time in hours is 1.5. Her speed is 10 less than twice Brandon's speed.
Shanice's speed is:
x - 10 miles per hour.
Substituting into the equation distance = speed × time gives us
93 = ( x - 10)1.5
First we distribute, to get
93 = 3x -
Then we add 15 to both sides to get
108 = 3x.
Finally we divide by 3 to get
= x.
Brandon is driving at miles per hour.
Check: We can check this answer by considering the situation another way: we can solve for Shanice's speed instead of Brandon's and then check that against Brandon's speed.
The equation for Shanice's speed is simply 2x - 10 = 2(
-10
72 - 10 = 62
So, Shanice is traveling at
miles per hour.
The problem tells us that Shanice is traveling 10 mph slower than twice Brandon's speed;
that would mean that 62 is equal to 2 times 36 minus 10. Is that true? Well, 2 times 36 is 72, minus 10 is 62.
Answer:
Step-by-step explanation: use your brain please you will get it ahhh
1/3= round to the nearest hundredth
please help ill mark brainlyest
Step-by-step explanation:
1 have to make number cross the top number n sce
You apply the rule for a pair of parallel angles cut by a line. So that means that 59 degrees equals 2x-15.
59=2x-15
59+15 = 2x
74=2x
x= 37
Find the sum:
1
6
+ √6 =
A gym floor has a perimeter of
216 feet. What is the perimeter of
the floor in yards?
Answer:
Step-by-step explanation:
216÷3=72
72 is your answer
What is the length of the garden?
The length of the garden is 63ft, in the rectangle
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,
Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.
The given perimeter is 210ft
let l be the length and 2/3 of l is the breadth.
We know that 2(a+b) = 210
2(l + 2/3l) = 210
5/3 l = 105
l = 105* 3/5 = 63ft
Hence the length of the garden is 63ft.
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Mai picked a mystery number that is less than 30. she says she can show 3 different rectangles on this grid whose area is the same as her mystery number
what could be Mai's mystery number?
Answer:The answer is 4
Step-by-step explanation:BEcause of the mail´s mystery number
murray mixes 2 quarts of liquid A and 8 pints of liquid B to make a compound. How many gallons of compound are produced?
Answer:
1 1/2 gallons
Step-by-step explanation:
there are two pints in one quart so 2 quarts plus 8 pints equals
2 quarts plus 4 quarts, or 6 quarts
there are 4 quarts in one gallon so 6 quarts is the same as 1 gallon and 2 quarts
2 quarts is half of one gallon
The average daily high temperature in June, in LA is 80°F with a standard deviation of 8°F. Suppose that the temperatures in June
closely follow a normal distribution.
(a) What is the probability of observing a 85°F temperature or higher in LA during a randomly chosen day in June?
The probability of observing an 85°F temperature or higher in Los Angeles during a randomly chosen day in June is 0.266.
We are given information about the temperatures in Los Angeles for the month of June. The average daily high temperature in June in LA is 80°F. The standard deviation in the temperature values is 8°F. The temperatures in June closely followed a normal distribution. We need to find the probability of observing an 85°F temperature or higher in Los Angeles during a randomly chosen day in June. Let the mean, standard deviation, value, z-score, and probability be represented by the variables M, S, X, Z, and P. First of all, we will find the z-score for the given temperature value.
Z = (X - M)/S = (85 - 80)/8 = 5/8 = 0.625
We want to find the probability for Z-values greater than or equal to the calculated z-score. We need to use the z-score table to find the corresponding probability.
P(z ≥ 0.625) = 0.26599
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the highest amount that can be charged to your credit account is called?
A. credit limit
B. free period limit
C. minimum payment limit
D. APR limit
The highest amount that can be charged to your credit account is called credit limit and is therefore denoted as option A.
What is a Credit account?This is referred to as a type of banking arrangement which involves a customer receiving goods from a store and paying for them over a period of time.
The credit card which is linked to the account is used for such type of transactions and the highest amount that can be charged to it is known as credit limit which is therefore the reason why option A was chosen as the correct choice.
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Mina a wrote messages to her friends on a sidewalk she used 1/3 of piece of truck that was originally 2 5/6 inches long how many inches of child did she use?
Mina uses 17/18 inches of chalk.
What is algebra?
The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.
Here, we have
she used 1/3 of a piece of chalk that was originally 2 5/6 inches long.
Now, we have to find how many inches of chalk did she use?
= 1/3 × 2 5/6
= 1/3 × 17/6
= 17/18 inches.
Hence, Mina uses 17/18 inches of chalk.
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Answer:
17/18
Step-by-step explanation:
If Nancy is two years older than Mark and the sum of their ages is 28, Mark will be 13 years old.
False
True
Answer:
I think its false
Step-by-step explanation:
Answer: True i think
Step-by-step explanation: If Nancy is two years older than Mark who is 13, then Nancy would be 15, 15 + 13 equals 28.
Horold stores 10,656 pounds of grain for his 24 cattle. Each cow eats about 12 pounds of grain each day. How many days would the food supply last?
The total number of days for which the food supply will last is 37 days.
Given,
The number of days that the food supply would last is = ?
The number of pounds of grain = 10656 pounds
The number of cattle is = 24 cattle
The number of pounds eaten by each cow each day = 12 pounds.
Therefore if one cow eat 12 pounds a day then 24 cows=
12 × 24 = 288 pounds a day
Therefore if,
288 pounds = 1 day
10656 pounds = 10656/288
= 37 days
Therefore, the number of days that the food supply would last is 37 days.
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a) Write down the conditions under which the binomial
distribution may be a suitable model to use in statistical work.
b) A six-sided die is biased. When the die is thrown the number 5 is
twice as likely to appear as any other number. All the other faces are
equally likely to appear. The die is thrown repeatedly.
Find the probability that
(i) the first 5 will occur on the sixth throw.
(ii) in the first eight throws there will be exactly three 5s.
a) The binomial distribution is suitable to use when:
Trials are independent.There is a fixed number of trials.Each trial has only two outcomes.b) The probabilities are given as follows:
i) First 5 on the sixth throw: 0.0531 = 5.31%.ii) Three fives on the first eight throws: 0.2428 = 24.28%.What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The binomial distribution is used when there is a fixed number n of trials, with each trial having only two possible outcomes, success or failure, and trials are independent, that is, the probability of success on any trial is the same.
For item b, the parameter p is obtained as follows:
Probability of a 5: p.Probability of any of the other five numbers: 0.5p.The sum of all the probabilities is of one, hence:
5 x 0.5p + p = 1
3.5p = 1.
p = 1/3.5
p = 0.2857.
For item i, the probability is obtained as follows:
Hence:
p = (1 - 0.2857)^5 x 0.2857 = 0.0531 = 5.31%.
For item ii, the probability is P(X = 3) when n = 8, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{8,3}.(0.2857)^{3}.(0.7143))^{5} = 0.2428[/tex]
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For the vertical motion model h(t)=-16t^2+54t+3, identify the maximum height reached by an object and the amount of time the object is in the air before it hits the ground. Round to nearest tenth
The values of the vertical motion modelled by the quadratic function, h(t) = -16·t² + 54·t + 3 of the object are;
The maximum height reached is approximately 48.6 units
The time of flight is approximately 3.4 seconds
What is a quadratic function?A quadratic function is a polynomial of the form y = a·x² + b·x + c, where the value of a is larger than or lesser than 0
First part;
The function, for the vertical motion, h(t) = -16·t² + 54·t + 3, is a quadratic function;
The maximum height is found by using the equation that gives the value of x at the maximum value, which is presented as follows;
At the maximum point, [tex]x = \dfrac{-b}{2\cdot a}[/tex]
From the equation, a = -16, b = 54, c = 3, and x = t, which gives;
[tex]t = \dfrac{-54}{2\times (-16)} = 1.6875[/tex]
The maximum height is therefore;
h(1.6875) = -16 × 1.6875² + 54 × 1.6875 + 3 = 48.6
The time the object is in the air is found using the equation;
h(t) = 0 = -16·t² + 54·t + 3
Using the quadratic formula, [tex]x= \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2 \cdot a}[/tex], we have;
[tex]t= \dfrac{-54\pm \sqrt{54^2 - 4\times (-16)\times 3} }{2 \times (-16)}=\dfrac{27\pm \sqrt{777} }{16}[/tex]
The time of flight is therefore;
[tex]t=\dfrac{27+ \sqrt{777} }{16}\approx 3.4[/tex]
The time of flight is 3.4 seconds
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Find the measure of each marked angle.
The larger angle measures=
The larger angle in the straight line is 101°.
What is straight line angle?
A straight angle in mathematics is one with a sine angle of 180 degrees. Due to the fact that it resembles a straight line, it is called straight. Those angles that make a straight line are known as straight angle pairs. Each angle in this pair adds up to 180 degrees, regardless of how many angles make up the pair. A straight angle in geometry is one that is equal to 180 degrees. It looks like a straight line, hence the name "straight angle." It is an angle, then, whose sides are in the same straight line but opposite to the vertex.
We know that , In straight line angle at any point is 180°.
Here,
=> (14x+3)°+(11x+2)°=180°
=>14x+3+11x+2=180
=>25x+5=150
=>25x=180-5=175
=> x = 175/25 = 7.
Then , 14(7)+3=101° and 11(7)+2=79°.
Hence the larger angle is 101°.
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Given the coordinates, classify ∆QRT by its sides. Q(-2, -1), R(1, 5), T(-8, -4) Classify:
The given triangle ∆QRT is isosceles triangle.
What is isosceles triangle?
Triangles with two equal sides are referred to as isosceles triangles. Also equal are the two angles that face the two equal sides. To put it another way, "An isosceles triangle is a triangle with two congruent sides." Assume that the sides AB and AC of the triangle ABC are equal, in which case the triangle ABC is an isosceles triangle with B = C. According to the theorem, "if the two sides of a triangle are congruent, then the angle opposite to them is also congruent."
Here the given points are Q(-2,-1) , R(1,5) , T(-8,-4).
Using distance formula
Now , The Distance between the points can be measure as :
D=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
QR = [tex]\sqrt{(1+2)^2+(5+1)^2}[/tex]
=>QR=[tex]\sqrt{3^2+6^2} = \sqrt{9+36} =\sqrt{45}=3\sqrt{5[/tex] unit
Now RT = [tex]\sqrt{(-8-1)^2+(-4-5)^2} =\sqrt{9^2+9^2} \\[/tex]
=>RT=[tex]\sqrt{81+81}=\sqrt{162} = 9\sqrt{2}[/tex] unit
Now TQ = [tex]\sqrt{(-2+8)^2+(-1+4)^2} =\sqrt{6^2+3^2} \\[/tex]
=>TQ=[tex]\sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex] unit.
Here QR=TQ then
Hence the given triangle is isosceles triangle.
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A construction worker's starting salary is $43,000. Each year she receives a $1100 raise.
A.) Let an be the construction worker's salary in the nth year. Write an explicit formula of the form an = bn + c to model this situation.
an = 41,900 + 1100n
B.) Find a10 = $ 52,900
C.) In what year will her salary be $55,100? __________
The salary is $55100 when [tex]a_n=55100[/tex].
[tex]55100=41900+1100n\\\\13200=1100n\\\\12=n[/tex]
So, her salary will be $55,100 after 12 years.
The salary is $55100 after 12 years.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that construction worker's starting salary is $43,000. Each year she receives a $1100 raise.
Therefore, an = 41,900 + 1100n
An explicit formula of the form an = bn + c to model this situation.
When n = 10,
= 41,900 + 1100n
= 41,900 + 1100(10)
= 41,900 + 11000
= 52,900
when an = 55,100
Then an = 41,900 + 1100n
55,100 = 41,900 + 1100n
1100n = 55,100 - 41,900
1100n = 13200
n = 13200/ 1100
n = 12
So, her salary will be $55,100 after 12 years.
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The width of a rectangle is the length minus 1 units. The area of the rectangle is 72 units. What is the width, in units, of the rectangle?
Answer:
The width of the rectangle should be 8 units.
Calculation of the width:
Since The width of a rectangle is 1 units less than the length. The area of the rectangle is 72 units.
Here we know that
Area = (length) (width)
Here we assume length be x
So, width be = x - 1
So,
(x) (x - 1) = 72
(x + 8) (x - 9)
So, the width should be
= 9 - 1
= 8
hence,
√16-√-2+√16 + √-200
what is that answer please
Answer:
√(16) - √(-2) + √(16) + √(-200) =
8 + 12.7279221 i
How do you solve this problem?? 5(x+6)- 5(7)
Answer:
Step-by-step explanation:
5x+30-35
5x-5
Answer:
[tex]5x[/tex] - [tex]5[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Hannah thinks of a whole number.
Rounded to the nearest 10, her number is 350
Rounded to 1 significant figure, her number is
300.
a) What is the smallest possible number
Hannah could be thinking of?
b) What is the largest possible number
Hannah could be thinking of?
The smallest possible number Hannah could be thinking of will be 351.
And, the largest possible number Hannah could be thinking of will be 355.
What is rounding off?Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.
Given that;
Hannah thinks of a whole number.
Rounded to the nearest 10, her number is 350.
And, Rounded to 1 significant figure, her number is 300.
Now,
Since, Hannah thinks of a whole number.
Rounded to the nearest 10, her number is 350.
And, Rounded to 1 significant figure, her number is 300.
Hence, We get;
The smallest possible number Hannah could be thinking of = 351.
And, The largest possible number Hannah could be thinking of = 355.
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Determine the domain of the following graph:
The domain of given graph is [-8,8].
What is Domain of a function?The domain of a function is a set of all x values i.e. the numbers for which function is defined. All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range. When viewing a graph, the whole range of numbers from left to right comprise the domain.
As seen from the graph graph is limited from -8 to +8 that means the domain of the graph is [-8,8].
Or it can be written as [tex]-8\leq x \leq 8[/tex]
Therefore, the domain of the function is [-8,8].
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3. Three different bags of pretzels are sold at the store. Which bag of pretzels is the best buy? (1 pi
Bag A:10 ounces for $1.10
Bag B:12 ounces for $1.38
Bag C: 6 ounces for $0.84
O Bag A
© Bag B
6
© Bag C
O Bag A and Bag B are equally good values
Answer:
bag A
Step-by-step explanation:
10/1.10=9.09090909091
12/1.38=8.69565217391
6/0.84 7.14285714286
Prove that A-(B-C)=(A-B)uu(A nn C) by using Properties.
Proof:
L.H.S. = A - (B - C)
= A - (B ∩ C'), since A - B = A ∩ B'
= A ∩ (B ∩ C')'
= A ∩ {B' U (C')'}, since (A ∩ B)' = A' U B'
= A ∩ (B' U C)
= (A ∩ B') U (A ∩ C)
= (A - B) U (A ∩ C) = R.H.S.
∴ A - (B - C) = (A - B) U (A ∩ C)
Hence, This completely the proof.
Some properties of set algebra:
1. A U Φ = A, A ∩ Φ = Φ
2. A U U = U, A ∩ U = A
3. A U A = A, A ∩ A = A
4. A U (B U C) = (A U B) U C
5. A ∩ (B ∩ C) = (A ∩ B) ∩ C
6. A U (B ∩ C) = (A U B) ∩ (A U C)
7. A ∩ (B U C) = (A ∩ B) U (A ∩ C)
8. A U A' = U
9. A ∩ A' = Φ
10. (A U B)' = A' ∩ B'
11. (A ∩ B)' = A' U B'
12. A - B = A ∩ B'
13. A - (B ∩ C) = (A - B) U (A - C)
14. A - (B U C) = (A - B) ∩ (A - C)
15. A Δ B = (A - B) U (B - A)
16. A Δ B = B Δ A
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