Answer: Alex Paid $175 for 40 months
Step-by-step explanation:
$4000 = y-int or b
$11000 = y
40 months = x
Slope - intercept form : Y=mx+b
We are solving for m which is the slope (How much Alex Paid per month)
11000=m(40)+4000
11000=40m+4000
7000=40m
7000/40
m=175
answer please have no idea how to start or do it just please show the workings aswell.
The evaluation of P10–Focus 1 indicates that we get by using the equation for the volume of a cuboid and by calculus;
(a) [tex]L = 4\times x + 4\times 2\cdot x + 4\times \frac{81}{2\cdot x} =12\cdot x + \frac{162}{x^2}[/tex]
(b) [tex]L_{min}[/tex] = 54 cm
(c) L'' at x = 3, (where [tex]L_{min}[/tex] = 54 cm) is positive, therefore, x = 3 is a minimum point
P10-Focus2
The area = [tex]2\times x \times y+\frac{\pi\cdot x^2}{4} =4[/tex], therefore, [tex]y = \frac{16- \pi \cdot x^2}{8 \cdot x}[/tex]
The minimum point, which is an extremum point is a point where the derivative of the function is 0.
(a) The length of the cuboid = 2·x
The width of the cuboid = x
The volume of the cuboid = 81 cubic centimeters
The thickness of the cuboid is therefore;
Thickness = 81/(2·x × x) = 81/(2·x²)
The sum of the length of the twelve edges, L, is therefore;
[tex]L=x + x + x + x + x + 2\cdot x + 2 \cdot x + 2 \cdot x + 2\cdot x + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2}[/tex]
Therefore;
[tex]L=4\times x + 4\times 2\cdot x + 4\times \frac{81}{2 \cdot x^2} =12\cdot x + \frac{162}{x^2}[/tex]
The sum of the lengths of the twelve edges, L, is [tex]L = 12\cdot x + \frac{162}{x^2}[/tex]
(b) The minimum value of L can be found using calculus by finding the point at which dL/dx = 0 as follows;
[tex]\frac{dL}{dx} = 12 - \frac{324}{x^3} =0[/tex]
Therefore;
[tex]12-\frac{324}{x^3}=0[/tex]
[tex]12 = \frac{324}{x^3}[/tex]
x³ = 324 ÷ 12 = 27
x = ∛(27) = 3
x = 3
The minimum value of L can be obtained when x = 3 as follows;
[tex]L = 12\cdot x + \frac{162}{x^2}[/tex]
[tex]L_{min} = 12\times 3 + \frac{162}{3^2} = 54[/tex]
The [tex]L_{min}[/tex] = 54
The minimum value of L is 54 centimeters
(c) The value of the minimum value of L can be confirmed by further differentiation using the second derivative, L'' as follows;
At the x-value of a minimum point of a function, the value of the further derivative is larger than zero
The further derivative of the specified function is found as follows;
[tex]L'' = \frac{dL'}{dx} =\frac{972}{x^4}[/tex]
At the critical number, x = 3, from the first derivative, we get;
[tex]L'' = \frac{972}{3^4} = 12 > 0[/tex]
The value of the further derivative of the function at the point x = 3, is L'' = 12 > 0, therefore the point x = 3 is a relative minimum.
(b) The radius of the quarter circle = x
The area of the figure = 4 m²
The sum of the area of the composite figures are;
[tex]A = 2 \times x \times y + \frac{\pi \cdot x^2}{4} = 4[/tex]
Therefore;
[tex]y =\frac{\left(4 - \pi \cdot \frac{x^2}{4}\right)}{2\cdot x} = 16 - \frac{\pi \cdot x^2}{8\cdot x}[/tex]
Rearranging the right hand side expression as a fraction, we get;
[tex]y = \frac{16-\pi \cdot x^2}{8\cdot x}[/tex]
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you have paint with a voc content of 0.45 pounds per gallon. the density of the paint is 9 pounds per gallon. what is the weight percentage of voc in the paint?
the weight percentage of VOC content in the paint would be 4.05 pounds / 9 pounds x 100 = 45%.
What is percentage?A percent of a whole is referred to as a percentage. By dividing the portion by the entire and multiplying the result by 100, it is computed and denoted by the sign "%". For instance, if a book contains 100 pages and you have read 50 of them, you have read 50% of the book. In several disciplines, including finance, statistics, and mathematics, percentage is often utilized. To figure out interest rates, taxes, and discounts in finance, we employ percentages. In statistics, percentages are used to represent data that takes the form of proportions or ratios. In mathematics, questions involving proportions and ratios are solved using percentage.
How to solve?
the total weight of VOC in the paint would be 0.45 pounds x 9 pounds per gallon = 4.05 pounds.
the weight percentage of VOC in the paint would be 4.05 pounds / 9 pounds x 100 = 45%.
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3. Park rangers have been recording the number of black bear cubs born in a national preserve over (1 point)
the past 100 years. According to the following table, what is the estimated probability that there
will be more than 100 black bear cubs born in any given year?
Number of Cubs Born in a Year
0-25
26-50
51-75
76-100
101-125
126-150
151-175
Frequency
3
6
18
32
24
10
7
A 59%
B 34%
C 24%
D 41%
The estimated probability that there will be more than 100 black bear cubs born in any given year is 41%. Option D. is the answer
How to determine the probability of more than 100 black bear cubs born in any given year?
Probability is the likelihood of a desired event happening.
Experimental probability is a probability that relies mainly on a series of experiments or past events
Given: from the table, the sum of the frequency for more than 100 cubs (i.e. 101-125, 126-150 and 151-175) is:
Sum of frequency of more than 100 = 24 + 10 + 7 = 41
Total frequency (for everything) = 100
Probability of more than 100 = 41/100 = 41%
Thus, the probability of more than 100 black bear cubs is 41%
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The function g(x) = f(x – 7) + 3. Which of the following is true about the graph of g(x)
the graph of g(x) is shifted 7 units to the right and 3 units below the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units below the graph of f(x).
The graph of g(x) is shifted 7 units to the right and 3 units above the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units above the graph of f(x).
Answer:
Step-by-step explanation:
the graph of g(x) is shifted 7 units to the right and 3 units below the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units below the graph of f(x).
The graph of g(x) is shifted
7 units to the right and 3 units above the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units above the graph of f(x)
please help meeeee!!!!
Answer:
(-8(-4) + 3) - 7 = 32
Step-by-step explanation:
-8 * -4 = 8 * 4 = 36
36 + 3 = 39
39 - 7 = 32
A shop increased the price of a shirt by 10% , then decided to decrease the price of the shirt by 10%. What was the percent change in price of the shirt. Explain your answer using words
Answer:
Step-by-step explanation:
1. Increase of 10% in price of shirt.
2. Decrease of 10% in price of shirt.
Hence- both amounts cancel out, therefore there is 0% change in price of shirt as both percentages cancelled out, or we can say nullified each other. Because they added the same amount to the item and then subtracted the same percent leading to no change.
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2y + 5x = 13
2y-3x = 5
Answer:
Step-by-step explanation:
To solve the system of equations 2y + 5x = 13 and 2y-3x = 5 using the substitution method, you can follow these steps:
Begin by solving one of the equations for one of the variables. For example, you could solve the first equation for y:
2y + 5x = 13
2y = 13 - 5x
y = (13 - 5x) / 2
Substitute the expression for y into the second equation and solve for x:
2((13 - 5x) / 2) - 3x = 5
13 - 5x - 3x = 5
-8x = -8
x = 1
Substitute the value of x into the expression for y to find the value of y:
y = (13 - 5(1)) / 2
y = (13 - 5) / 2
y = 8 / 2
y = 4
The solution to the system of equations is (1,4).
Therefore, the correct ordered pair is (1,4).
How can you use the point-slope form of a line when only given two points?
Answer:
YEEAH bro its called a graph you should try it
Step-by-step explanation:
a researcher obtains a negative value for the chi square test. what can you conclude because the value is negative?
A researcher obtains a negative value for the chi square test.1 is the value is negative .
What is chi-square value?
The difference between the frequencies of results of a collection of events or variables that were observed and those that were expected is measured by the chi-square (2) statistic.
Such variations in categorical variables can be examined using chi-square, particularly when they are nominal in nature.
We know that the chi-square is the sum of square of difference between observed and expected frequencies divided by the expected frequency. So, it is clear that the chi-square value can never be negative because sum of squares is always positive.
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A block of ice contains 40 three-ounce portions of shaved ice. A food truck owner wants to use the block of ice to make as many spheres of ice as possible, each weighing 18 lb. How many spheres can she make?
The maximum number of spheres that can be made through ice will be 135.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
As per the given,
Number of ice portions = 40
Weight of one ice portion = 3 ounce
Since, 1 lb = 16 ounce
3 ounce = 3/16 lb
Weight of 40 portion = 120/16 lb
The weight of one sphere of ice = 18 lb
Number of possible spheres = (120/16)/18
⇒ 120/16 x 18
⇒ 135 sphere
Hence "135 spheres are the most that can be produced by ice".
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if john paints at the rate of h houses per month how many houses does he paint in m months, in terms of h and m
Answer:
h x m=hm
Step-by-step explanation:
on my test
kendra rides her bike to school each day. it takes her 10 minutes to ride 30 blocks. what unit rate expresses the speed of kendra's bike ride? 2 block
The unite rate of the kendra's bike ride is found as 3 blocks / min.
Explain the meaning of the term unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with the number one as the denominator. A particular kind of ratio is a unit rate (or called a single-unit rate). One unit of one quantity will be compared to an unique number of units of another quantity.The given question is-
Total blocks covered = 30.Total time taken = 10 minutesUnit rate = number of blocks/ total time
Unit rate = 30 / 10
Unit rate = 3 blocks / min
Thus, the unit rate of the kendra's bike ride is found as 3 blocks / min.
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a tennis player makes a successful first serve 70% of the time- what is the probability she makes at least 65
The probability she makes at least 65 is 0.0139.
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 proposition 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.
[tex]\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}[/tex]
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Triangle ABC is a right triangle, with right angle B. Side AC has a length of 10. Side CB has a length of 6. Find the length of side AB.
The length of side AB is 8 units. Option B is the correct option.
What is right angle triangle?
A triangle is a area that bounded by three sides. The length of the sides may not be equal. A right triangle is a triangle with 90 degree angle. The rest two angles are acute angle.
Given that △ABC is a right triangle with right angle at B.
The length of side AC is 10 units. The length of side CB is 6 units.
Pythagoras theorem: The square of hypotenuse is equal to the sum of square of legs.
The legs of △ABC is AB and BC. The hypotenuse of triangle ABC is AC.
Therefore,
AB² + BC² = AC²
AB² + 6² = 10²
AB² + 36 = 100
Subtract 36 from both sides:
AB² = 100 - 36
AB² = 64
Take square root on both sides:
AB = √64
AB = 8
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write y=2/5+1 in standard form
Answer: Because the standard form is y=mx+b, and you are already in that form
Step-by-step explanation: y=mx + b is the standard form!
y=2/5x+1 is already in standard form if you compare 2 equations!
Yancy rents a car for $20 per day plus 12 cents per mile. He had the car for one day and was charged $63.68.
Answer:
he drove 30 miles
Step-by-step explanation:
please help me I'm not smart !!
The correct response is option 3 i.e n = 6.
What is a Sequence?
A sequence is a list of items arranged in a stepwise order, with members coming either before or after.
We know that,
aₙ = a₁ + (n-1)×d .............................(Arithmetic sequence formulae)
here,
aₙ = -13
a₁ = 7
d = -4
Substituting the values we get,
-13 = 7 + (n-1)×(-4)
∵ (-4)×(n-1) = -20
=> n-1 = 5
=> n = 6
Thus, the final value of n is 6.
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16. Translate the phrase "Two-tenths of a number" into an algebraic expression. Let x represent the real number.
The algebraic expression of the phrase Two-tenths of a number is 2x/10. The simplest form of the expression is x/5.
What is a phrase?
A mathematical expression is an expression that contains numbers, variables, and/or operations on those numbers and variables. A mathematical phrase is a verbal phrase that contains words and/or figures that can be turned into a mathematical expression.
Given phrase is Two-tenths of a number.
The value of two tenths is 2/10.
Assume that x be the number.
Two-tenths of x is 2/10 × x = 2x/10
Divide the denominator and numerator by 2:
= x/5
The expression is x/5.
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What is the concentration of h ions at a ph = 2? mol/l what is the concentration of h ions at a ph = 6? mol/l how many more h ions are there in a solution at a ph = 2 than in a solution at a ph = 6?
The concentration of H+ ions at a pH = 2 is 10⁻² mol/L
Theconcentration of H+ ions at a pH = 6 is 10⁻⁶ mol/L
And there are 10,000 times more H⁺ ions in a solution of pH = 2 than that of pH = 6
In this question we have been given the pH of the solution.
We need to find the concentration of H+ ions in the given solution.
The H⁺ ion concentration can be calculated from pH values using the equation: pH = - log [H⁺]
at a pH = 2,
Using the above equation, 2 = - log [H⁺]
[H⁺] = 10⁻² mol/L
at a pH = 6,
Using the above equation, 6 = - log [H⁺]
[H⁺] = 10⁻⁶ mol/L
We need to find how many more h ions are there in a solution at a ph = 2 than in a solution at a ph = 6
Consider the ratio of [H⁺] for pH = 2 and pH = 6, we have
10⁻²/10⁻⁶ = 10⁴
Therefore, there are 10,000 times more H⁺ ions in a solution of pH = 2 than that of pH = 6
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Walmart has cashews that sell for $2 a pound and peanuts that sell for $1.50 a pound. Meijer sells cashews for
$2.50 a pound and peanuts for $1 a pound. Mike paid $26 at Walmart and Jim paid $29 at Meijer for the same
amount of nuts. How many pounds of cashews and peanuts did they buy?
Let "c" represent the amount of cashews they each bought.
Let "p" represent the amount of peanuts they each bought.
Mike: 2c + 1.5p = 26
Jim: 2.5c + 1 p = 29
That's the system you need to solve. We can do this with substitution.
Start with Jim:
2.5c + p = 29
p = 29 - 2.5c
Substitute that into Mike and solve for c:
2c + 1.5p = 26
2c + 1.5(29 - 2.5c) = 26
2c + 43.5 - 3.75c = 26
-1.75c + 43.5 = 26
-1.75c = - 17.5
c = 10
Now substitute that back into Jim's last equation:
p = 29 - 2.5c
p = 29 - 2.5(10)
p = 29 - 25
p = 4
So they each bought 10 pounds of cashews and 4 pounds of peanuts.
Assuming they are charging simple interest annually and the interest rate was 21.24%, what steps would I need to do in order to solve this problem??
a cup of coffee starts at temperaryre 180 in a room where the surroundings temperature is 80. after 10 minutes, the coffee has cooled to 130. find an equation for the temperature t of the coffee as a function of time. simplify your answer as much as you can and make sure there are no unknown constants
The final equation for the temperature of the coffee as a function of time is [tex]T = 80 + 100*e^{(-4t)[/tex]. There are no unknown constants in this equation.
The temperature of a substance will naturally cool down over time due to heat transfer to the surrounding environment. The rate at which the substance cools down is described by Newton's law of cooling, which states that the rate of change of the temperature of a substance is proportional to the difference in temperature between the substance and the surroundings. Mathematically, this can be expressed as:
dT/dt = k(T - Ts)
Where T is the temperature of the substance, Ts is the temperature of the surroundings, t is time, and k is the cooling coefficient, which is a constant that depends on the properties of the substance and the surroundings.
Since we know that the initial temperature of the coffee is 180 and the temperature of the surroundings is 80, and the temperature of the coffee after 10 minutes is 130, we can write the following equation:
(180 - 130)/10 = k(180 - 80)
Solving for k, we get:
k = -4
Substituting this value back into the equation for the rate of change of temperature, we get:
dT/dt = -4(T - 80)
This is the equation for the temperature of the coffee as a function of time. To find the temperature of the coffee at any time t, we can integrate this equation with respect to time. The resulting equation will be:
[tex]T = 80 + C*e^{(-4t)[/tex]
Where C is an unknown constant of integration. Since we are given that the initial temperature of the coffee is 180, we can solve for C by substituting t = 0 and T = 180 into the equation:
[tex]180 = 80 + C*e^0[/tex]
Solving for C, we get:
C = 100
Substituting this value back into the equation for T, we get the final equation for the temperature of the coffee as a function of time:
[tex]T = 80 + 100*e^{(-4t)[/tex]
This is the final, simplified equation for the temperature of the coffee as a function of time. There are no unknown constants in this equation.
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Follow the instructions for the following inequalities.
1. 4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10
2. 11>-2 Add 5 to both sides, then add 3, then add (-4)
3. -4<-2 Subtract 6 from both sides, then 8, and then 2
4. -8<8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
The value of the inequality equations are
a) 5040 < 8820
b) 15 > 2
c) -20 < -18
d) -1 < 1
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be A
a)
4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10
The inequality equation is A
The value of A is 4 < 7
Multiplying both sides by 7 , we get
28 < 49
Multiplying both sides by 6 , we get
168 < 294
Multiplying both sides by 3 , we get
504 < 882
Multiplying both sides by 10 , we get
5040 < 8820
Therefore , the inequality equation remains the same.
b)
11>-2 Add 5 to both sides, then add 3, then add (-4)
The inequality equation is A
The value of A is 11 > -2
Adding 5 on both sides , we get
16 > 3
Adding 3 on both sides , we get
19 > 6
Adding -4 on both sides , we get
15 > 2
Therefore , the inequality equation remains the same.
c)
-4<-2 Subtract 6 from both sides, then 8, and then 2
The inequality equation is A
The value of A is -4 < -2
Subtracting 6 on both sides , we get
-10 < -8
Subtracting 8 on both sides , we get
-18 < -16
Subtracting 2 on both sides , we get
-20 < -18
Therefore , the inequality equation remains the same.
d)
-8<8 Divide both sides by -4, then by -2
The inequality equation is A
The value of A is -8 < 8
Dividing both sides by -4 , we get
2 > -2
The sign of the inequality relation changes when multiplying or dividing by a negative number
Now , dividing by -2 on both sides , we get
-1 < 1
So , The sign of the inequality relation changes when multiplying or dividing by a negative number
Therefore , the inequality equation first changes and reverts back to the original relation
Hence , the value of the inequality relations are
a) 5040 < 8820
b) 15 > 2
c) -20 < -18
d) -1 < 1
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How does a number change in total when it is decreased by 60% and increased by 80%? PLEASE HELP ASAP!
The number will be decreased by a percentage of 32%.
How does the number change?
If a number N is increased by a percentage X, then the new value is:
N' = N*(1 + X/100%)
If instead the number is decreased, then the new value is:
N' = N*(1 - X/100%)
So if we apply a decrease by 60% followed by an increase of 80%, we will have:
N' = N*(1 - 60%/100%)*(1 + 80%/100%)
N' = N*(1 - 0.6)*(1 + 0.8)
N' = N*(0.4)*(1.8)
N' = N*0.72
We can rewrite that as:
N' = N*(1 - 0.32)
0.32 = 32%/100%
So that is equivalent to a decrease by 32%
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Choose the correct name for the set of numbers.
{-₁ √11, 21.6555..., 16,
The correct name for the set of numbers {-1, √11, 21.6555..., 16} include the following;
A. Real numbers
B. Integers
C. Irrational numbers
E. rational numbers
What are the types of numbers?In Mathematics, there are six (6) common types of numbers and these include the following:
Irrational numbersReal numbersRational numbersIntegersNatural (counting) numbersWhole numbersWhat is an irrational number?In Mathematics, an irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11 or √11.
In conclusion, when the square root of 11 or √11 is taken, the output is neither a terminating decimal nor a repeating decimal. Therefore, it would be classified as an irrational number.
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Complete Question:
Choose the correct name for the set of numbers. {-√11, 21.6555..., √16, 1/9}.
real numbers
integers
irrational numbers
natural numbers
rational numbers
whole numbers
Josue has $0.33 worth of pennies and nickels. He has a total of 13 pennies and nickels altogether. Write a system of equations that could be used to determine the number of pennies and the number of nickels that Josue has. Define the variables that you use to write the system.
Josue has 8 pennies and 5 Nickels and N+P=13 and 0.01P + 0.05N ≥ 0.33 are system of equations that could be used to determine the number of pennies and the number of nickels that Josue has
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Josue has $0.33 worth of pennies and nickels.
total of 13 pennies and nickels altogether.
Let N be number of Nickels and P be number of Pennies
P + N =13..(1)
Therefore
0.01P + 0.05N ≥ 0.33..(2)
From 1,
P=13-N
0.01(13-N)+0.05N ≥ 0.33
0.13-0.01N+0.05N ≥ 0.33
0.13+0.04N ≥ 0.33
0.04N≥ 0.33-0.13
0.04N≥ 0.33-0.13
0.04N≥ 0.2
Divide both sides by 0.04
N=5
From 1, N+P=13
5+P=13
Subtract 5 from both sides
P=13-5
P=8
Hence, Josue has 8 pennies and 5 Nickels and N+P=13 and 0.01P + 0.05N ≥ 0.33 are system of equations that could be used to determine the number of pennies and the number of nickels that Josue has
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Use the reciprocal property to solve for a 36/15 8/a
Applying reciprocal property the equation 36 / 5 = 8 / a is solved to find the value of a as 10/9
What is reciprocal property?The definition of reciprocal in mathematics is the inverse of a value or a number.
If n is a real number, then 1/n will be n's reciprocal.
Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9.
The result of multiplying a number by its reciprocal now equals one. multiplicative Inverse is another name for it.
Similarly, 36 / 5 = 8 / a
the reciprocal is 5 / 36 = a / 8
cross multiplying
5 * 8 = 36 * a
36a = 40
a = 40 / 36
a = 10/9
The value of a is 10/9
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A square table has a perimeter of (16x-40) feet. Write an expression that represents the side length of the table in feet
Answer:
4x -10
Step-by-step explanation:
You want the side length of a square whose perimeter is (16x -40) feet.
PerimeterThe four sides of a square are all the same length. The perimeter is the sum of those lengths, so is 4 times the side length. Conversely, the side length is 1/4 of the perimeter.
s = P/4 = (16x -40)/4
s = 4x -10
The side length of the square table is 4x -10 feet.
Triangle ABC is rotated 180° clockwise about the origin
and dilated by a scale factor of 4. What are the
coordinates of the resulting image if the preimage
coordinate of point A is (3,-2)?
1) (-12,-8)
2) (12,-8)
3) (8,12)
4) (-12,8)
Need help with this ASAP, this is my last class and I need to finish it by Today