Answer:
Let x be the amount (in liters) of the 5% acetic acid solution to be added.
Let y be the amount (in liters) of the 10% acetic acid solution to be added.
The system of equations is:
x + y = 2 (the total amount of solution is 2 liters)
0.05x + 0.10y = 0.07(2) (the amount of pure acetic acid in the final solution is 7% of 2 liters)
Simplifying the second equation:
0.05x + 0.10y = 0.14
5x + 10y = 14 (multiplying both sides by 100)
We now have a system of two equations with two variables. We can solve it by substitution or elimination. Here, we'll use substitution:
x + y = 2 => x = 2 - y (subtracting y from both sides)
Substituting x in the second equation:
5(2 - y) + 10y = 14 (replacing x by 2 - y)
10 - 5y + 10y = 14
5y = 4
y = 0.8
So the photographer should add 0.8 liters of the 10% acetic acid solution and 2 - 0.8 = 1.2 liters of the 5% acetic acid solution. We can check that this solution satisfies both equations:
0.05(1.2) + 0.10(0.8) = 0.06 + 0.08 = 0.14
1.2 + 0.8 = 2
Therefore, the answer is:
The photographer should add 0.8 liters of the 10% acetic acid solution and 1.2 liters of the 5% acetic acid solution.
Find the real zeros (if any ) of the rational function. Use a gra g(x)=(x^(2)-13x+42)/(x^(2)+9) x= NONE Submit Answer
The real zeros of the rational function [tex]g(x)=(x^2-13x+42)/(x^2+9)[/tex] are x=7 and x=6, and there are no vertical asymptotes
The real zeros of a rational function are the values of x that make the numerator equal to zero. In this case, we need to
find the values of x that satisfy the equation [tex]x^2-13x+42[/tex]=0.
We can use the quadratic formula to find the real zeros:
x = (-b ± √(b^(2)-4ac))/(2a)
where a=1, b=-13, and c=42.
Plugging these values into the formula,
we get: [tex]x = (-(-13) ± √((-13)^2-4(1)(42)))/(2(1))[/tex]
Simplifying the expression, we get:
x = (13 ± √(169-168))/2
x = (13 ± √1)/2
x = (13 ± 1)/2
The two real zeros are:
x = (13 + 1)/2 = 14/2 = 7
x = (13 - 1)/2 = 12/2 = 6
Therefore, the real zeros of the rational function are x=7 and x=6.
As for the denominator, since [tex]x^2+9[/tex]=0 has no real solutions, there are no values of x that make the denominator equal to zero. Therefore, the rational function has no vertical asymptotes.
In conclusion, the real zeros of the rational function [tex]g(x)=(x^2-13x+42)/(x^2+9)[/tex] are x=7 and x=6, and there are no vertical asymptotes.
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tes of the vertex for the parabola y=-x^(2)-14x-49. If there is more than one x-intercept, separate them
The vertex of the parabola y=-x^(2)-14x-49 is located at (-7,0). And there is only one x-intercept, which is (-7,0)
The vertex of a parabola is the point where the parabola changes direction. The vertex is found by completing the square for the quadratic equation. The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. The y-coordinate of the vertex is found by substituting the x-coordinate of the vertex into the equation for y.
For the given parabola, y=-x^(2)-14x-49, the coefficients are a=-1 and b=-14.
The x-coordinate of the vertex is:
x = -b/2a = -(-14)/(2*(-1)) = -7
The y-coordinate of the vertex is:
y = -(-7)^(2)-14(-7)-49 = -49+98-49 = 0
Therefore, the vertex of the parabola is (-7,0).
To find the x-intercepts, we need to solve the equation for when y=0:
0 = -x^(2)-14x-49
0 = (x+7)(x+7)
x = -7
Since the equation has only one solution, there is only one x-intercept, which is (-7,0). This is also the vertex of the parabola.
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The equation 4x+5y=35 represents the total cost, in dollars, of a customer’s purchase at a home improvement store, where x is the price of an extension cord, and y is the price of a lightbulb. Which represents the equation when solved for the price of a lightbulb, y?
The equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]
What is linear equation?A statement that shows the equality of the two expressions is known as an equation. Mathematical operations including addition, subtraction, multiplication, division, and exponentiation are included, along with one or more variables, constants, and other operations.
To solve the equation 4x + 5y = 35 for the price of a lightbulb, y, we need to isolate y on one side of the equation. Here are the steps:
Subtract 4x from both sides of the equation:
4x + 5y - 4x = 35 - 4x
Simplifying, we get:
5y = 35 - 4x
both sides divided by 5 in the equation:
(5y)/5 = (35 - 4x)/5
Simplifying, we get:
y = (35/5) - (4/5)x
y = 7 - (4/5)x
Therefore, the equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]
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I need help on this asap!!!
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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Regular hexagon ABCDEFG in inscribed into circle O and AB=8cm. Calculate each of the following:
(a)What is the radius of circle O
(b)What is the area of circle O
(c)What is m
(d)What is m
(e)What is the measure of arc AB
(f)What is the measure of arc ACE
(g)What is the length of arc AB
(h)What is the area of sector AOB
a. The radius of the circle O is 8 cm.
c. The circle has an area of 213.66 square centimeters.
e. AB's arc length equals 60 degrees
f. ACE has arc measure of 240 degree.
g. the arc length is 8.38 cm
h. area of the sector AOB is 33.51 cm²
How to find the radius of the circlea. The radius of the circle is solved using the properties of a regular hexagon
It has equal sides and angles on all six sides.There is a 120° inside angle and a 60° outside angle.There are six equilateral triangles in it.The radius is 8 cm since the base of one of the equilateral triangles is the radius.
b. Area of circle O
= 3.142 * 8^2
= 213.66 squared cm
e. measure of arc AB
The center angle that creates the intercepted arc is what is known as the arc measure, which is measured in degrees.
= 60 degrees
f. measure of arc ACE
= arc AB + arc BC + arc CD + arc DE
= 60 + 60 + 60 + 60
= 240 degrees
g. length of arc AB
= 60/360 * 2 * 3.142 * 8
= 8.38 cm
h. area of the sector AOB
= 60/360 * 3.142 * 8²
= 33.51 cm²
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96n^3 - 84n^2 + 112n - 98
Answer:
2(8n-7)(6n^2+7)
Chandra is building a 5,280 foot fence around her property. Her property is the shape of a rectangle. The length of the property is three times the width of the property.
a. Write an equation that can be used to find the length and width of the property. Explain how you came up with your equation,
b. Find the length and width of the property. Justify your answer, using the conditions given in the problem.
Answer:
a. Let's denote the width of the property as "w". According to the problem, the length of the property is three times the width, so we can represent the length as "3w".
To find the equation that can be used to solve for the length and width, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
Since we know the perimeter (5,280 feet), and we have expressions for the length and width, we can substitute these values into the formula and solve for the variables:
2(3w + w) = 5,280
2(4w) = 5,280
8w = 5,280
w = 660
Therefore, the width of the property is 660 feet, and the length is 3 times the width, or 1,980 feet.
b. To check that these values are correct, we can substitute them back into the formula for perimeter and make sure it equals 5,280:
2(1,980 + 660) = 5,280
This is true, so we can be confident that the width of the property is 660 feet and the length is 1,980 feet.
A baseball team won of its games this season. Which percent is equivalent to ?
A. 55%
B. 55.5%
C. 55%
D. 59%
55.5% is equivalent to 5/9.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
A baseball team won of its games of 5/9 this season.
We need to find the equivalent percentage of 5/9.
To convert 5/9 to a percentage, we can multiply it by 100.
(5/9) x 100 = 55.5%
So, the percentage equivalent to 5/9 is 55.5%.
Therefore, 55.5% is equivalent to 5/9.
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CL 7-123. Without using a calculator, rewrite each expression without parentheses and using only positive exponents.
The final expressiοns fοr a, b, c and d will be 3x(3y)(1/2) / (y¹/3), 1/x, 5²/3, 8z³/2 / x².
Define the term expressiοn?An expressiοn is a mathematical phrase that cοmbines numbers, variables, and οperatοrs tο represent a value οr a quantity. It can include cοnstants, variables, cοefficients, and mathematical οperatiοns.
a. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radicals and rewrite the expοnents as fractiοns.
(9¹/2x²y) (27¹/3y-¹) = 3xy¹/2) * 3*(3/3) * y⁻¹/3 = 3x(3y)(1/2) / (y¹/3)
b. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can apply the negative expοnent rule and simplify the radical.
(x¹/2)⁻² = (1/x¹/2)² = 1/x
c. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radical and rewrite the expοnent as a fractiοn.
(25)²/3 = (5²)¹/3 = 5²/3
d. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radical and mοve the negative expοnent tο the denοminatοr.
8z³/2x⁻² = 8(z¹/2)³ / x² = 8z³/2 / x²
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5. The FBI Standard Survey of Crimes shows that for about 84% of all property crimes (burglary, larceny, car theft, etc.
the criminals are never found, and the case is never solved. Suppose
a neighborhood district in
a large city sumers
repeated property crimes, not always perpetrated by the same criminals. The police are investigating seven properti
crime cases in this district. What is the expected number (u) that will arrive on time? What is the standard deviation
of this distribution?
The expected number (μ) of property crimes that will be solved in this district can be found by multiplying the total number of property crimes by the probability that a property crime will be solved. Since the probability that a property crime will be solved is 1 - 0.84 = 0.16, the expected number of property crimes that will be solved is:
μ = 7 × 0.16 = 1.12
The standard deviation (σ) of this distribution can be found by taking the square root of the product of the total number of property crimes, the probability that a property crime will be solved, and the probability that a property crime will not be solved:
σ = √(7 × 0.16 × 0.84) = 1.01
Therefore, the expected number of property crimes that will be solved in this district is 1.12, and the standard deviation of this distribution is 1.01.
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if f(x)=2x+1 and g(x)=x^2 find g(f(3))
i need answers quick please
g(f(-1)) = g(2(-1)-1) = g(-3)
g(-3) = (-3)^2 + 3 = 9+3 = 12
So g(f(-1)) = 12
Hope this helps.
Choose a positive integer N from the infinite set of positive integers N= {1,2,3,....n-1, n, n+1,...,[infinity]} with probability PN = 1/2^n For example P(N = 1) = P1 = 1/2, P(N = 2) = P2 = 1/4, P(N = 3) = P3 = 1/8, and so on. Consider the three events A = {1,2,3,4}, B = {n ∈ N is even} and C = {n ∈ N is odd} (a) Determine P(A) (b) Determine P(B) (c) Determine P(BIA) (d) Determine P(CAB).
The probability of P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.
The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
(a) P(A) = P(1) + P(2) + P(3) + P(4) = 1/2 + 1/4 + 1/8 + 1/16 = 15/16
(b) P(B) = P(2) + P(4) + P(6) + ... = 1/4 + 1/16 + 1/64 + ... = 1/3
(c) P(BIA) = P(B ∩ A) / P(A) = (P(2) + P(4)) / P(A) = (1/4 + 1/16) / (15/16) = 5/15 = 1/3
(d) P(CAB) = P(C ∩ A ∩ B) / P(A ∩ B) = 0 / P(A ∩ B) = 0
Therefore, the probabilities of the events are: P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.
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which is bigger 5 oz or 6 oz
Answer: 6 oz
Step by step:
5 < 6
Did i miss something?
Answer: 6 oz. is greater than 5 oz.
Step-by-step explanation:
Imagine you had 6 dogs. Now let's say that one passed away due to a car accident. Now you have 5 dogs. We can say by the fundamental theorem of common sense that you indeed did have more dogs before that accident. Using that logic in the grand scheme of metrics, we can say that 6oz is larger as a value than 5oz.
A right triangle has side lengths 5, 12, and 13 as shown below. Use these lengths to find sinY, tanY, and cosY.
The value of
1 sinY = 12/13
2. cos Y = 5/13
3. tanY = 12/5
What is trigonometry?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin Y = opp/hyp
cos Y = adj/hyp
tan Y = opp/adj
if opp = 12
adj = 5
hyp = 13
then,
sinY = 12/13
cos Y = 5/13
tanY = 12/5
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Whelp the teacher said to solve them and something abt shading HELP
Shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
First, we graph the lines y = -x-2 and y = -5x+2 using their y-intercepts and slopes.
The line y = -x-2 has a y-intercept of -2 and a slope of -1, which means that for every increase of 1 in x, y decreases by 1.
The line y = -5x+2 has a y-intercept of 2 and a slope of -5, which means that for every increase of 1 in x, y decreases by 5.
The shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.
Hence, shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.
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Use the ruler provided to measure the dimensions of the parallelogram shown to the nearest 0.5 centimeter.
Which measurement is closest to the area of the parallelogram in square centimeters?
F.14 cm2
G.16.5 cm2
H. 4114
cm2
J.8.5 cm2
The closest answer choice to 26.25 cm² is G. 16.5 cm².
What is area ?
Area is a measurement of the amount of space inside a two-dimensional figure, such as a square, rectangle, triangle, parallelogram, or circle. It is expressed in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), or square feet (ft²).
Based on the given image, we can use the ruler to measure the dimensions of the parallelogram.
From the ruler, we can see that the base of the parallelogram is approximately 7.5 cm, and the height is approximately 3.5 cm. Therefore, the area of the parallelogram is:
Area = base x height
Area = 7.5 cm x 3.5 cm
Area = 26.25 cm² (rounded to the nearest 0.5 cm)
Among the answer choices provided, the closest one to the calculated area of the parallelogram is 26.5 cm², which is not provided in the answer choices.
Therefore, The closest answer choice to 26.25 cm² is G. 16.5 cm².
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A digital delay device echoes an input signal by repeating it a fixed length of time after it is received. If such a device receives the pure note
f1(t) = 3 sin(t) and echoes the pure note f2(t) = 3 cos(t), then the combined sound is f(t) = f1(t) + f2(t).
(a) Graph y = f(t) and observe that the graph has the form of a sine curve y = k sin(t + ϕ).
(b) Find k and ϕ.
The graph of this function is a sine curve with amplitude 3√2 and phase shift π/4.
The k cos(ϕ) would be 3 and k sin(ϕ) would be 3.
The combined sound is given by:
f(t) = f1(t) + f2(t)
f(t) = 3 sin(t) + 3 cos(t)
To find k and ϕ, we can use the following trigonometric identity:
k sin(t + ϕ) = k sin(t) cos(ϕ) + k cos(t) sin(ϕ)
Comparing this with the equation for f(t), we can see that:
k cos(ϕ) = 3
k sin(ϕ) = 3
Squaring both equations and adding them gives:
k^2 = 3^2 + 3^2 = 18
k = √18 = 3√2
Dividing the two equations gives:
tan(ϕ) = 3/3 = 1
ϕ = π/4
Therefore, the combined sound has the form:
f(t) = 3√2 sin(t + π/4)
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6 ft – 9 inches to decimal feet.
The unit conversion the value is 6.75 ft.
What is unit conversion?The same feature is expressed in a different unit of measurement through a unit conversion. Time can be stated in minutes rather than hours, and distance can be expressed in kilometres rather than miles, or in feet rather than any other unit of length.
Here the given unit measurement is ,
=> 6ft 9 inches.
We know that, to convert inches into feet we need to divide by 100. Then,
=> 9 inches = 9/12 = 0.75 ft.
Now total measurement = 6+0.75 = 6.75 ft.
Hence the after unit conversion the answer is 6.75 ft.
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how to work out surds
In an upper tail test about the population mean, where the population standard deviation is known, a sample of size 30 was taken. Use 5% significance. Find the critical value(s).
Select one:
a. Both -1.96 and 1.96
b. Only 1.699
c. Only -1.699
d. Only -1.645
e. Both -2.045 and 2.045
f. Only 1.645
In an upper tail test about the population mean, where the population standard deviation is known, a sample of size 30 was taken. Use 5% significance the critical value is 1.645. The correct answer is option f. Only 1.645.
In an upper tail test about the population mean, where the population standard deviation is known, we need to find the critical value(s) for a 5% significance level.
To find the critical value(s), we need to use the z-table. The z-table shows the probability of a z-score being less than or equal to a certain value.
Since this is an upper tail test, we need to find the z-score that corresponds to a probability of 0.95 (1 - 0.05).
Looking at the z-table, we can see that the z-score that corresponds to a probability of 0.95 is 1.645.
Therefore, the critical value for this upper tail test is 1.645. The correct answer is f. Only 1.645
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25)
Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation h = −16t + 160t + 120 models the h height at t seconds of the flare. How long will it take for the flare to hit the ground? (to the nearest tenth of a second
The flare takes 10.7 seconds to hit the ground if a flare is shot from the top of a 120-foot building at a speed of 160 feet per second.
The given data is as follows:
Height of building = 120 feets
Speed = 160 feet per second
The given equation is h = −16t + 160t + 120
Time required to hit the ground =?
The flare hits the ground when h=0.
Substitute in the given equation we get,
-16t^2 + 160t + 120 = 0
By applying the Quadratic equation formula to find out the value of t,
Quadratic equation formula = ( -b± [tex]\sqrt{b^{2} - 4ac }[/tex] ) / 2a
x = (-160 ± [tex]\sqrt{160^{2} - 4(-16)(120) }[/tex] ) / 2(-16)
x = (-160 ± [tex]\sqrt{33280}[/tex] ) / -32
x = (-160 +[tex]\sqrt{33280}[/tex] ) / -32, (-160 -[tex]\sqrt{33280}[/tex] ) / -32
x = -10.70, 10.70
Neglecting the time in Negative values, x = 10.70 seconds
Therefore, we can conclude that the flare takes 10.7 seconds to hit the ground.
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Identify the vertex of the following function f(x)=3(x-1)^2+5
Answer:
Step-by-step explanation:
The answer is (1,5)
write an algebraic expression for 24 more than the product of 2 and x
Answer:
24+2x
Step-by-step explanation:
Answer:
Step-by-step explanation:
x = 24+2x
HELP ME OUTTT ASAP!!!
Answer:
slope: -4
y intercept: (0,-12)
The diameter of a circle is 12 feet. What is the circle's circumference? Use 3.14 for л.
Answer:
Circumference = 37.7 feet
Step-by-step explanation:
Use these formulas, then solve for the answer
C=2πr
d=2r
C = π times d
C = π times 12
C = 37.699
29. What is the truth value of (~p V q) Arif p is true, q is false, and r is true?
Answer:
Step-by-step explanation:
~P is true
q is true
~p v q is true
the hypothesis (or antecedent) is true
the conclusion (or consequent) is false
R is false and ~q is false
the conditional says if true then false
so the conditional is false
1. Solve ARST (find all missing sides and angles). SHOW ALL WORK, Express angles to the nearest degree and side lengths to one decimal place.
ST = 7.5m
S ∟
angle RS = 32°
A = 32°, R = 9.09m, S = 6.89m, T = 7.06m, and angle ASR = 114.90°.
To solve ARST, we must first use the given information (ST = 7.5m and S ∟ angle RS = 32°). Using the law of sines, we can calculate the following:
A = 32°R = (7.5m/sin32°) = 9.09mT = (7.5m/sin180°-32°) = 7.06mThen, using the law of cosines, we can calculate the following:
S = (9.09^2 + 7.06^2 - 2(9.09)(7.06)cos32°)^0.5 = 6.89mAngle ASR = (180° - 32° - arcsin((7.06sin32°)/6.89)) = 114.90°Therefore, the missing sides and angles of ARST are A = 32°, R = 9.09m, S = 6.89m, T = 7.06m, and angle ASR = 114.90°.
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The speed of sound is approximately 1,2251, kilometers per hour. When an object travels faster than the speed of sound, it creates a sonic boom.
The speed of sound is about 343 meters per second (or approximately 1,225 kilometers per hour).
The assertion you made appears to be incorrect. At sea level, the actual speed of sound is roughly 1,225 kilometres per hour, or 767 miles per hour.
The distance that sound travels through a medium, such air, in a predetermined length of time is known as the speed of sound. It is impacted by the medium's temperature, pressure, and humidity. The speed of sound is roughly 343 metres per second in dry air at 20 degrees Celsius (or approximately 1,225 kilometres per hour).
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for what values of k both the quadratic equations 6x² -17x+12=0 and 3x²-2x+k=0 will have a common root
The value of k for which both 6x² - 17x + 12 = 0 and 3x² - 2x + k = 0 have a common root is k = 1/3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The discriminant of the first quadratic equation, 6x² - 17x + 12 = 0, is:
b² - 4ac = (-17)² - 4(6)(12) = 1
Since the discriminant is not zero, this quadratic equation does not share a common root with any other equation.
For the second quadratic equation, 3x² - 2x + k = 0, to have a common root with 6x² - 17x + 12 = 0, its discriminant must be zero.
The discriminant of the second quadratic equation is:
b² - 4ac = (-2)² - 4(3)(k) = 4 - 12k
To find the values of k that make the discriminant equal to zero, we solve the equation:
4 - 12k = 0
Simplifying, we get:
12k = 4
k = 4/12
k = 1/3
Therefore, the value of k for which both 6x² - 17x + 12 = 0 and 3x² - 2x + k = 0 have a common root is k = 1/3.
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As a salesperson, Ken is paid $55 per week, plus $4 per sale. This week Ken wants to make more than $115. Write the inequality for the number of sales Ken needs to make this week, in dollars. Use x to represent the number of sales and do not include any $ symbols in the inequality
The inequality for the number of sales Ken needs to make this week in dollars is: 4x + 55 > 115. Where x is the number of sales.
Inequalities are the mathematical term for the relationship between two values that are not equal. Not all people are created equal. We typically use the "not equal symbol ()" when two values are not equal. However, various inequalities are utilized to compare the values, whether they are less than or greater than.
To solve for x, we first need to isolate it on one side of the inequality. We can start by subtracting 55 from both sides:
4x > 60
Then, we can divide both sides by 4:
x > 15
Therefore, Ken needs to make more than 15 sales this week to earn more than $115.
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