You need 5 gallon of the 45% acid solution 35 gallon of the 85% solution to get 40 gallon at 80%.
How to find the number of liters?Let x represent the number of liters
0.45x+0.85(40-x) = 0.8(40)
0.45x+34-0.85x = 32
-0.4x = -2
Divide both sides by -0.4
x = -2/-0.4
x = 5
You need 5 gallon of the 45% acid solution
Gallon of the 85% solution to get 40 gallon at 80% = 40-5 = 35 gallon
Therefore 5 gallon and 35 gallon are needed.
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The expression −290+18y represents a submarine that began at a depth of 290 feet below sea level and ascended at a rate of 18 feet per minute. What was the depth of the submarine after 6 minutes?
Answer: would be -120 + 78, or -42 feet.
Step-by-step explanation:
An amount of $ 48,000$ is borrowed lord 9 years at $6 \% 6 interest, compounded annually. If the loan is paid in full at the end of that period, thaw Mach must be paid back?
Use the calculator provided and round your answer to the rarest dollar.
By using the formula for compound interest, it can be calculated that
He must pay back $81095 after 9 years
What is Compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially, rather than linearly, then the interest earned is called compound interest
If p is the principal, r is the rate and t is the time, then the amount is calculated by the formula
[tex]A = p(1 + \frac{r}{100})^n[/tex]
The difference between the amount and the principal gives the compound interest.
Principal = $48000
Rate = 6%
Time = 9 years
Amount = [tex]48000(1+ \frac{6}{100})^9\\[/tex]
= $81095
He must pay back $81095 after 9 years
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Five subtracted from seven times a number is 86
Answer:
7x-5=86
Step-by-step explanation:
Differentiate the function with respect to x. Shot steps
The differentiated form of the function with respect to x will be e³ˣ³.9x².
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range. The exponential function is that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x where a is a constant and a>1.
It is given that the function is,
y=e³ˣ³
Differentiate the function with respect to x.
[tex]=\frac{dy}{dx} \\\\ =\frac{d}{dx}\left(\left(e^3\right)^{x^3}\right) \\\\ =e^{3x^3}\frac{d}{dx}\left(3x^3\right) \\\\ =e^{3x^3}\cdot \:9x^2[/tex]
Thus, the differentiated form of the function with respect to x will be e³ˣ³.9x².
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Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1
6 units
8 units
10 units
36 units
The distance of the line segment from ( -5,5 ) to ( 3,-1 ) is 10 units
What is the distance of a line between 2 points?
The distance of a line between 2 points is always positive and given by the formula
[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Given data ,
Let the two points be A and B
A ( x₁ , y₁ ) = A ( -5 , 5 )
B ( x₂ , y₂ ) = B ( 3 , -1 )
So , the distance between 2 points is given by the formula
[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Substituting the values of x₁ , y₁ , x₂ , y₂ in the formula , we get
[tex]D = \sqrt{(-5-3)^{2} + (5-(-1))^{2} }[/tex]
[tex]D = \sqrt{(8)^{2} + (6)^{2} }[/tex]
[tex]D=\sqrt{(64+36)}[/tex]
[tex]D = \sqrt{100}[/tex]
[tex]D= 10 units[/tex]
Hence , the distance of the line is 10 units
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WILL GIVE BRAINLIEST!! PLEASE
A car travels 12 km North and then turns left to travel 5 km West before coming to a stop. What is the car’s displacement?
The answer will be 13 km that is displacement of the car.
What is displacement?
When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.
A car travels 12 km north and turns left to travel 5km.
So the final position of car from the initial position is :
So the placement of the car is √(12²+5²) = √169 =13km
Hence the Displacement of the car is 13 km
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What is the F ratio in ANOVA?
Answer:
The F value is used in analysis of variance (ANOVA). It is calculated by dividing two mean squares. This calculation determines the ratio of explained variance to unexplained variance. The F distribution is a theoretical distribution.
Step-by-step explanation:
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The F ratio in ANOVA is the difference between two mean square values. If
In ANOVA, what is the F ratio?Analysis of variance is a collection of statistical models and the estimation procedures that go with them that are used to analyze the differences between means. Ronald Fisher, a statistician, invented ANOVA. The ANOVA test compares more than two groups at the same time to see if there is a relationship between them.
If the null hypothesis is correct, you should expect F to be close to 1.0 most of the time. A high F ratio indicates that the variation among group means is greater than would be expected by chance.
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Compute the amount in an account after 4 years if $4550 is invested at an annual interest rate of 3.5% compounded semiannually. Round to two decimals.
Answer:
$5,227.41
Step-by-step explanation:
The compound interest formula is
[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]
A is the final amount
P is the initial amount
r is the interest rate as a decimal
n is the # of times the interest is applied per time period
t is the # of time periods.
We are given
Note: semi annually is twice per year.
[tex]P=4550[/tex]
[tex]r=0.035[/tex]
[tex]n=2[/tex]
[tex]t=4[/tex]
Lets solve for A.
[tex]A=4550(1+\frac{0.035}{2} )^{2*4}[/tex]
[tex]A=4550(1.0175)^{8}[/tex]
[tex]A=4550(1.14888178)[/tex]
[tex]A=5227.41211244[/tex]
Round to two decimals.
$5,227.41
Simplify the expression. 11z +9-7=
Answer: 11z+2
Step-by-step explanation:
Question 36 of 50
When graphing systems of inequalities, the possible answers are all the points that are in the overlapped, shaded region of the two lines.
True
False
The solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
Thus, the solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.
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A car leaves Rockford, Illinois, at the rate of 70 mph, bound for Madison, Wisconsin. At the same time, a truck leaves Madison at the rate of 50 mph, bound for Rockford. If the cities are 72 miles apart, how long will it take for the car and the truck to meet?
Answer:
36 minutes
Step-by-step explanation:
The total distance covered by the two vehicles per hour: 70 + 50 = 120 miles.
Time is distance over velocity.
[tex]t=\frac{72}{120}[/tex] hours
Which simplifies to
[tex]\frac{3}{5}[/tex] hours.
Convert hours to minutes.
There is 60 minutes in 1 hour.
[tex]\frac{1}{60}=\frac{\frac{3}{5} }{x}[/tex]
[tex]x=36[/tex]
If f(x) = 2*+5, fill out the following table of values:
-1
0
x
What type of function is this?
1
2
3
Answer:
2
Step-by-step explanation:
i gotchu my boy
Factor the following expression using the common factor -3
-9z - 21y - 2.4
The expression -9z - 21y - 2.4 when -3 is factored out is -3(3z + 7y + 0.8)
How to determine the factored expression?From the question, we have the following expression that can be used in our computation:
-9z - 21y - 2.4
The common factor is given as
-3
So, we divide -9z - 21y - 2.4 by 3
The results of these divisions are
-9z/3 = -3z
- 21y/3 = -7y
- 2.4 /3 = -0.8
So, we have the following results
-9z - 21y - 2.4 = -3(3z + 7y + 0.8)
Hence, the factored expression is -3(3z + 7y + 0.8)
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Raina needs to earn at least $2200 each month to cover her living expenses. Her income comes from a 4% commission that she earns on everything she sells. What is the minimum amount she needs to sell in order to earn $2200?
The person needs to sell a minimum amount of $550000 to earn $22000.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the income of the person is 4% of the total selling value.
Let the person sells $x to earn $22000, therefore,
4% of x is $22000
Or, 4x/100 = 22000
4x = 2200000
x = 550000
Hence, the person needs to sell a minimum amount of $550000 to earn $22000.
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Question 3.13R:
Which of the following are equivalent exponential function(s) to f(x)=(4/7)^−x
The equivalent function of the exponential function is (a) f(x) = (7/4)ˣ
How to determine the equivalent function?From the question, we have the following function that can be used in our computation:
f(x) = (4/7)^-x
This function can be properly expressed as
f(x) = (4/7)⁻ˣ
Solving further, we need to apply the exponent law of indices
This is represented as
a⁻ˣ = 1/aˣ
When the above rule is applied, we have
f(x) = 1/(4/7)ˣ
Evaluate the quotient
f(x) = (7/4)ˣ
Hence, the equivalent is (a) f(x) = (7/4)ˣ
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A house has increased in value by 15% since it was purchased. If the current value is 299,000, what was the value when it was purchased?
The value of the house when it was purchased is 260,000 units
How to find the value the house was purchased?The house has increased in value by 15 percent since it was purchased. The current value is 299,000.
The value of the house when it was purchased can be calculated as follows:
let the amount purchased = x
Hence,
15% of x + x = 299000
0.15x + x = 299000
1.15x = 299000
divide both sides by 1.15
Hence,
x = 299000 / 1.15
x = 260000
Therefore, the value of the purchase is 260,000 units
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The table shows the number of each type of cookie a
bakery has left at the end of the day. The baker wants to
make the greatest number of cookie boxes to sell, using
chocolate chip and sugar cookies together. If all of the
chocolate chip and sugar cookies are distributed evenly
among the boxes and the baker charges $5 per box, how
much money will the bakery bring in if they sell all of the
boxes?
14.
Solve for x.
8/6 = 12/x
Answer:
∴ [tex]x = 9[/tex]
Step-by-step explanation:
[tex]\frac{8}{6} = \frac{12}{x}[/tex]
[tex](\frac{8}{6})(6x) = (\frac{12}{x})(6x)[/tex]
[tex]8x = 72[/tex]
∴ [tex]x = 9[/tex]
The value of x for the given question 8/6 = 12/x is 9.
In the given problem, we know that we need to perform fraction multiplication and algebra to find the value of x.
Here, on the left hand side, we have ⇒ 8/6 (i)
On the right hand side, we have ⇒ 12/x (ii)
To find the value of x, we perform cross multiplication between both sides (LHS and RHS). After performing this function, we get
⇒ 8x = 72
Solving this problem even further, we get
⇒ x = 9
Therefore, the value of x is 9 for the given problem.
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Use the arc length formula to find the length of the graph of the function y = x ^ (3/2) + 4 from x = 2 to x = 9 (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answer:
[tex]\frac{1}{27}((13)^{\frac{3}{2}}-(6)^ {\frac{3}{2}})[/tex]
Step-by-step explanation:
how much more will $28,000 earn in interest than $16,000 if both invested in savings accounts with APYs of 5.8% for a year
The $28,000 investment will earn $696 more than the $16,000 investment if both make a 5.8% (APY) annual percentage yield for a year.
What is the APY?APY means annual percental yield.
Annual Percentage Yield describes the real interest rate earned on an investment in a year.
The Annual Percentage Yield refers to the interest an investment, saving, and loan attracts for the time value of money and inflationary effects.
The Annual Percentage Yield is applied to the investment amount for a year to calculate the interest earned.
Plan A Plan B
Investments $28,000 $16,000
Interest earned $1,624 $928 ($16,000 x 5.8%)
The difference in interest earned = $696 ($1,624 - $928)
Thus, when an investor puts $28,000 in a savings account at 5.8%, they earn $696 more than investing $16,000 at the same APY.
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Order each list of numbers from least to greatest. -0.6, 0, 0.5, 0.7,-0.2
Answer:
-0.6, -0.2, 0, 0.5, 0.7
Step-by-step explanation:
To find out this answer, we know first that negatives are the least. And -0.6 is farther away from 0 than -0.2, so we can have -0.6, -0.2 as our last numbers.
Then, 0.5 and 0.7 are greater than 0, so, then we have -0.6, -0.2, 0.
Then, 0.7 is greater than 0.5, so we can arrange the final numbers:
-0.6, -0.2, 0, 0.5, 0.7
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Answer: -0.6,-0.2, 0, 0.5, 0.7
Step-by-step explanation: Use a number line
What is the first term of the quotient of the following division problem?
(x³ - 1) = (x + 2)
O -0.5
O 1
O x²
Ox^4
The solution to the algebraic problem is [tex]x^{2}[/tex]
What is an Algebraic Equation?
An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
Solution:
([tex]x^{3}[/tex] – 1) = (x+2)
On dividing ([tex]x^{3} - 1[/tex]) by (x+2)
The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height as required in the task content is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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A plane has a cruising speed of 300 miles per hour when there is no wind. At this speed, the plane flew 600 miles with the wind in the same amount of time it flew 400 miles against the wind. Find the speed of the wind.
Solving a system of equations we will see that the speed of the wind is 60mi/h.
How to find the speed of the wind?When the plane flies with the wind, the two speeds adds up, while if the plane flies against the wind, the speeds need to be subtracted.
We know that the speed of the plane is 300 mi/h.
If the speed of the wind is W, then we can write the two equations:
(300 mi/h + W)*t = 600mi
(300mi/h - W)*t = 400mi
So we have a little system of equations, if we take the quotient between them we get:
[(300 mi/h + W)*t]/[(300mi/h - W)*t ] = 600mi/400mi
(300 mi/h + W)/(300mi/h - W) = 6/4
Now we can solve this for W.
(300 mi/h + W) = (6/4)*(300 mi/h - W)
W + (6/4)*W = (6/4)*300mi/h - 300 mi/h
W*(10/4) = 150 mi/h
W = (4/10)*150 mi/h
W = 60 mi/h
That is the speed of the wind.
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How do you calculate p-value from z-score?
The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.
How to calculate p-value from z-score?A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.
The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.
For one-tailed tests, the directionality is also a factor.
It therefore follows that;
For a Left-tailed z-test: the p-value = Φ(Zscore)
For a Right-tailed z-test: the p-value = 1 - Φ(z-score).
For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).
The procedure described above represents how to calculate p-value from z-score.
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The following formulas can be used to determine the p-value from its corresponding z-score
Left-tailed test: Φ(z-score)Right-tailed test: 1 - Φ(z-score)Two-tailed test: 2Φ(−|z-score|)How to calculate p-value from its z-score?From the question, the parameters are given as
p-valuez-scoreAlso, from the question, we understand that:
The p value depends on the z-score for its own value
There are three types of test for z-score; these test are:
Right tailed testLeft tailed testTwo tailed testThe p-value would assume different value for a z-score when the type of test is different
This means that the p value for z = 0.2 at right tail test is different at a left tailed test.
This means that there are three formulas for calculating the p-value from the z-score, and these formulas are
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Which phrase represents this expression? (6242) x 3 O 3 times the difference of 42 and 62 O the difference of the product of 3 times 42 and 62 O the difference of 62 and the product of 3 times 42 O 3 times the difference of 62 and 42.
By using the concept of mathematical expression, it is obtained that
(62−42)×3 is represented by 3 times the difference between 62 and 42
First option is correct
What is mathematical expression?
A mathematical expression consist of numbers connected with addition, subtraction, multiplication and division.
Here the given mathematical expression is (62−42)×3
Here, the signs shown are subtraction and multiplication. So the concept of difference and times will be used here
(62−42)×3 means whole of (62 - 42) is multiplied with 3
So, this is 3 times the difference between 62 and 42
First option is correct
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Correct Question
Which phrase represents this expression?
(62−42)×3
a) 3 times the difference of 62 and 42
b) 3 times the difference of 42 and 62
c) The difference of 62 and the product of 3 times 42
d) The difference of the product of 3 times 42 and 62
Solving -8 + x > -9 for x is: x > -1.
True
False
Step-by-step explanation:
Solving -8 + x > -9 for x is: x > -1.
-8 + x > -9
add 8 to both sides:
-8 + x + 8 > -9 + 8
x > -1
True
Need help with question
The required derivatives of the given hyperbolic functions are
d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.
The differentiation formulas for the hyperbolic functions are below as
d/dx(sinhx) = coshx
d/dx(coshx) = sinhx
d/dx(tanhx) = sech²x
d/dx(cothx) = −csch²x
d/dx(sechx) = −sechxtanhx
d/dx(cschx) = −cschxcothx
As per the given question,
⇒ d/dx(sinh3x)
Using formula d/dx(sinhx) = coshx,
⇒ cosh3x × (d/dx(3x))
⇒ cosh3x (3)
⇒ 3cosh3x
⇒ d/dx(tanh6x) = 6sech²6x
⇒ d/dx(coth5x) = −5csch²5x
⇒ d/dx(sech3x) = −3sech3xtanh3x
⇒ d/dx(csch7x) = −7csch7xcoth7x
Thus, the required derivatives of the given hyperbolic functions are
d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.
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How to simplify this expression: 5-2(x+5)+2
Answer:
........
Step-by-step explanation:
...
....
.....
......
.......
how to simplify (3x)³+2x³
Answer: 5x³
Step-by-step explanation: