I would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture.
(a) What is the system that models this situation?
(b) Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture; 2.5 lb peanuts and 2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work.
a)
The system of equations that models the situation is:
p + m = 5
3p + m = 15
b)
None of the given options is a solution to the system of equations.
We have,
(a)
System of equations that models the situation:
Total weight equation
p + m = 5
Proportion equation:
0.6p + 0.2m = 0.6(5)
Simplifying the second equation:
0.6p + 0.2m = 3
3p + m = 15 (dividing both sides by 0.2)
The system of equations is:
p + m = 5
3p + m = 15
(b)
To check which of the given options is a solution to the system, we substitute the values of p and m from each option into the system of equations and check if both equations are true.
Option 1:
2 lb peanuts and 3 lb mixture
p = 2, m = 3
p + m = 5 (true)
3p + m = 15 (6 + 3 = 9 ≠ 15, not true)
Option 2:
2.5 lb peanuts and 2.5 lb mixture
p = 2.5, m = 2.5
p + m = 5 (true)
3p + m = 15 (7.5 + 2.5 = 10, not true)
Option 3:
4 lb peanuts and 1 lb mixture
p = 4, m = 1
p + m = 5 (true)
3p + m = 15 (12 + 1 = 13, not true)
We see that,
None of the given options is a solution to the system of equations,
This means that the exact values of p and m that satisfy the system are different from all the given options.
Thus,
The system of equations that models the situation is:
p + m = 5
3p + m = 15
None of the given options is a solution to the system of equations.
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F.² + z² = m²
3. The lengths of the three sides are given for several right triangles. For each, write an
equation that expresses the relationship between the lengths of the three sides.
a. 10, 6, 8
b. √5, √√3, √8
c.
5, √5, √30
d. 1, √37,6
e. 3, √2, √7
With regard to the right triangles, the equations that expresses the relationship are:
a) 6² + 8² = 10²
b) (√5)² + (√3)² = (√8)²
c) √5)² + (√30)² = 5²
d) does not form a right triangle
e) (√2)² + (√7)² = 3²
In all the cases but the 4th, the sum of two sides are less than the square of the hypotenuse.
The square of the hypotenuse of a right-angled triangle is always equal to the sum of the squares of the other two sides, according to the Pythagorean property.
This theorem is written as c2 = a2 + b2, where 'c' is the hypotenuse and 'a' and 'b' are the two triangle legs.
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Solve the following linear programming problem.
z = 5x + 4y
2x + 4y ≤8
5x + y ≤8
x ≥ 0, y ²0
Maximize:
subject to:
The maximum value of the objective function z = 5x + 4y is 12
Solving the linear programmingFrom the question, we have the following parameters that can be used in our computation:
z = 5x + 4y
2x + 4y ≤8
5x + y ≤8
x ≥ 0, y ²0
This means that the objective function is
Max z = 5x + 4y
And the constraints are
2x + 4y ≤8
5x + y ≤8
x, y ≥ 0
When solved graphically, we have
(x, y) = (4/3, 4/3)
Substitute (x, y) = (4/3, 4/3) in the objective function
So, we have
z = 5 * 4/3 + 4 * 4/3
Evaluate
z = 12
Hence, the maximum value of the objective function is 12
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.
What is the graphical solution to a systems of equationsThe graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.
If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.
In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.
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write the following using rational exponents
3√10²
√3 to the -3
A formula for calculating A, the area of trapezoid, is A = 1/2 h ( b + b ), where h is height of the trapezoid, and b1 and b2 are the lengths of the parallel sides. What is A when h=4 centimeters, b1 = 10 centimeters, and b2 = 5 centimeters ? A. 35 cm 2 B. 30 cm 2 C. 25 cm 2 D. 45 cm 2 ?
The area of the trapezium is 30 square centimeters at the values of h = 4 cm, b = 10 cm, and b' = 5 cm.
We can use the formula for the area of a trapezoid:
A = 1/2 * h * (b + b')
Substituting the given values, we get:
A = 1/2 * 4 cm * (10 cm + 5 cm)
Simplifying the expression inside the parentheses:
A = 1/2 * 4 cm * 15 cm
Multiplying:
A = 30 cm²
Therefore, when h = 4 cm, b = 10 cm, and b' = 5 cm, the area of the trapezoid is 30 square centimeters.
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Which of the following statements with respect to political risk is true?
Oa. Political risk premiums are added to the required rate of return to adjust for political risks.
b. Companies cannot take any steps to reduce the potential from loss from expropriation since a foreign
government is involved.
Oc. The risk of expropriation of U.S. assets abroad is high even in traditionally friendly and stable countries.
Od. A company can reduce political risk by structuring operations so that the subsidiary has value only as a part of the
integrated corporate system.
solve the inequality and graph the solution.
4 |3x + 5| ≤ 16
The solution to the inequality is -3 ≤ x ≤ -1/3
Solving inequality with modulusGiven the inequality:
4|3x+5| ≤ 16
Let us simplify it by dividing both sides by 4 to get:
|3x+5| ≤ 4
Next, we can break the inequality into two cases, depending on whether 3x+5 is positive or negative:
First: 3x+5 ≥ 0
In this case, the inequality simplifies to:
3x+5 ≤ 4
Subtracting 5 from both sides, we get:
3x ≤ -1
Dividing by 3 (which is positive) gives:
x ≤ -1/3
Second: 3x+5 < 0
In this case, the inequality simplifies to:
-3x-5 ≤ 4
Adding 5 to both sides, we get:
-3x ≤ 9
Dividing by -3 (which is negative and requires us to flip the inequality), gives:
x ≥ -3
Therefore, the solution to the inequality is:
-3 ≤ x ≤ -1/3
The interval [-3,-1/3] is the solution set, and it includes all values of x between -3 and -1/3, including the endpoints.
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i need help ASAP! 10 pts.
The new quantity of firewood that is supplied at the price, would be A. 400 cords.
How to find quantity ?Use the formula for the slope of the supply curve to find the new quantity:
slope = ( Q2 - Q1 ) / ( P2 - P1 )
0.75 = ( Q2 - 300 ) / ( 348 - 255 )
0.75 = ( Q2 - 300 ) / 93
0.75 x 93 = Q2 - 300
69.75 = Q2 - 300
Q2 = 69.75 + 300
Q2 = 369. 75
Given that there are no options for 370 cords, we will pick the closest alternative of 400 cords.
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What is the value of x?
The value of x is 22.5
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. For two triangles to be similar , the corresponding angles of the triangle must be congruent.
Also, the ratio of corresponding sides of Similar triangles are equal.
Therefore;
6/9 = 15/x
6x = 15×9
6x = 135
divide both sides by 6
x = 135/6
x = 22.5
Therefore the value of x in the triangle is 22.5
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The slope is:
So, m = /
Now that we have both the y-intercept and slope, we can write the equation of the line
y=mx+b
8
y =
Check
C
An equation of the line in slope-intercept form is y = 1/2(x) - 2.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about the graph of this line, it can be modeled by this linear equation:
y = mx + c
y = 1/2(x) + (-2)
y = 1/2(x) - 2
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equation will solve the following word problem? Gina's income is $28,000, which is $2,000 less than twice what Frank makes. What is Frank's income?
Answer:
2x - 2,000 = 28,000
Step-by-step explanation:
1. Define Variables
Frank's Income = x
2. Write Equation
2x - 2,000 = 28,000
3. Solve (if necessary)
2x - 2,000 = 28,000
2x = 30,000
x = 15,000
Tuesday Math Problem
Two identical trains, each with 31 cars, are traveling in opposite directions. When
car Number 19 of one train is opposite car Number 19 of the other, which car is
opposite car Number 12?
門口口
—————
3
Show your work.
3 4 5 ..
The car that is opposite car Number 12 is given as follows:
Car of Number 26.
How to obtain the car pairs?The trains are travelling in opposite directions, hence, if car Number 19 of one train is opposite car Number 19 of the other, we have that the pattern is given as follows:
Car 18 is opposite to Car 20.Car 17 is opposite to Car 21.Car 16 is opposite to Car 22.An so on...
The difference between 19 and 12 is given as follows:
19 - 12 = 7.
Hence the number of the car opposite the car 12 is given as follows:
19 + 7 = 26.
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What are the characteristics of section lines?
If the object’s main edges itself are at _________ then you can use lines drawn at 30 or 60 degree. The spacing should be uniform __________ ranging from depending on the size of the drawing.
First onee
A. 90 degrees
B. 40 degrees
C. 180 degrees
Second onee
A. 1.5mm to 6mm
B. 2.5mm to 3mm
C. 0.5 mm to 1.5mm
The perimeter of parallelogram ABCD is cm. AD is cm more than twice AB. Find the lengths of all four sides of ABCD.
So the lengths of all four sides of ABCD are:
AB = BC = 15 cm
CD = DA = 31 cm
Let AB = x. Then AD = 2x + 1, since AD is 1 cm more than twice AB.
Since ABCD is a parallelogram, opposite sides are equal in length. So, BC = AB = x, and DC = AD = 2x + 1.
The perimeter of the parallelogram is the sum of the lengths of all four sides:
AB + BC + CD + DA = x + x + (2x + 1) + (2x + 1) = 6x + 2
We are given that the perimeter is 92 cm, so we can set this expression equal to 92 and solve for x:
6x + 2 = 92
6x = 90
x = 15
Therefore, AB = BC = 15 cm and AD = DC = 2(15) + 1 = 31 cm.
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Complete question:
The perimeter of parallelogram ABCD is 92 cm. AD is 1 cm more than twice AB. Find the lengths of all four sides of ABCD
10.8.8 Check Your Understanding
Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to
park her car. Each night, the hotel charged d dollars and $17.20 for parking. Which equation represents the total
amount, in dollars, Allison paid for the three nights?
A) d+3(17.20) = 782.07
(B) 3d+17.20 = 782.07
C) 3(d-17.20) = 782.07
D) 3(d+17.20) = 782.07
We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D
Which equation shows the total charge?We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.
If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.
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The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?
The complex numbers have equal imaginary coefficients.
The complex numbers have equal real numbers.
The complex numbers have opposite imaginary coefficients.
The complex numbers have opposite real numbers.
Answer:
D).The complex numbers have opposite real numbers.
Step-by-step explanation:
I just test and kid above got it wrong eng2023
I’m so confused I can’t figure out which answer would be correct
The value of S₁₀ in the given geometric series is 699050.
Given that,
The formula to find the sum of a geometric series is,
Sₙ = (a - a rⁿ) / (1 - r)
Here a is the first term and r is the common ratio.
Given is a geometric series,
2 + 8 + 32 + 128 + ....
a = 2
r = 8/2 = 4
We have to find the sum of these terms up to 10 terms.
S₁₀ = (2 - 2 . 4¹⁰) / (1 - 4)
= (2 - 2097152) / -3
= -2097150 / -3
= 699050
Hence the required value is 699050.
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What is the equation of the line graphed below
Answer:
The correct equation is A. y = (2/3)x - 2
Express the radical using the imaginary unit, i ii. Express your answer in simplified form. ± − 49 = ±
The given radical in imaginary form as ±7i.
The given number is √-49.
Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.
Here, √-49 =±7i
Therefore, the given radical in imaginary form as ±7i.
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A 2-gallon container of laundry detergent costs $27.76. What is the price per quart?
The price of the cost per quart of laundry detergent is A = $ 3.47
Given data ,
Let the unit cost rate be A
Now , There are 4 quarts in a gallon, so a 2-gallon container contains 8 quarts.
To find the price per quart, we can divide the total cost by the number of quarts:
Price per quart = Total cost / Number of quarts
Price per quart = $27.76 / 8 = $3.47
Hence , the price per quart of laundry detergent is $ 3.47
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7/8 X c for c = 8. What is the value of c?
Answer: The value of c is 8
Step-by-step explanation:
On the thing it says the c=8
which graph most likely shows a system of equations with one solution
The given graph shows a system of equations with two solutions
Which graph most likely shows a system of equations with one solutionFrom the question, we have the following parameters that can be used in our computation:
The graph
The solution to the system of equations is the point of intersection between the lines on the graph
Using the above as a guide, we have the following:
Intersection points = (-2, - 4) and (2, 3) (approximately)
This means that the solution to the system of equations are approximately (-2, - 4) and (2, 3)
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Use the given zero to find the remaining zeros of the function.
h(x)=3x^4+10x³+19x^2+90x-72; zero: -3i
The remaining zeros of h are ___
(Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.)
Answer:
Since the coefficients of the polynomial function h(x) have real values, if -3i is a zero of h(x), then its complex conjugate 3i must also be a zero of h(x). This is known as the Complex Conjugate Root Theorem.
Therefore, the remaining zeros of h(x) can be found by dividing the polynomial by the factors (x - (-3i)) and (x - 3i), using either polynomial long division or synthetic division. Here, we'll use synthetic division:
3i | 3 10 19 90 -72
| 9i -63 -216 -294
+-----------------------
3 10+9i -44 -126 -366
Step-by-step explanation:
The quotient is 3x^3 + (10+9i)x^2 - 44x - 126, and the remainder is -366. This tells us that:
h(x) = (x - (-3i))(x - 3i)(3x^3 + (10+9i)x^2 - 44x - 126)
The remaining zeros of h(x) can now be found by solving the cubic polynomial 3x^3 + (10+9i)x^2 - 44x - 126. This can be done using various methods such as the Rational Root Theorem, factoring by grouping, or numerical methods. However, these methods can be quite involved and may not always lead to exact answers.
According to a survey conducted by the Association for Dressings and Sauces, 80% of American adults eat
salad once a week. A nutritionist suspects that this percentage is not accurate. She conducts a survey of
445 American adults and finds that 374 of them eat salad once a week. Use a 0.005 significance level to
test the claim that the proportion of American adults who eat salad once a week is equal to 80%.
Claim: Select an answer which corresponds to [Select an answer
Opposite: Select an answer which corresponds to [Select an answer
The test is: Select an answers
The test statistic is: z-
(to 2 decimals)
The Critical Value is: z-
Based on this we: [Select an answer
Conclusion: There Select an answer appear to be enough evidence to support the claim that the
proportion of American adults who eat salad once a week is equal to 80%.
Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.
How to solveTo test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.
Claim: p = 0.80
Opposite: p ≠ 0.80
The test is a two-tailed z-test.
Sample proportion (p) = 374/445 = 0.8404
Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)
z = 2.53 (rounded to 2 decimals)
Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.
Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.
Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.
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Frankie solved the following inequality -2x-7>17 and stated that -5, 1, and 2 are in the solution set. what possible mistakes did frankie make? justify your response by explaining the steps you took in solving the inequality.
Simplify Simplify: (h^(1/3))/(h^(1/4))
Answer: b
Step-by-step explanation:
[tex]\frac{h^{\frac{1}{3} } }{h^{\frac{1}{4} } }[/tex] I started to subtract exponents than shortly realized that form is not an answer. The want you to covert the top and bottom to roots and that is your anser.
When you have a number to a fractional exponent that is your root
[tex]=\frac{\sqrt[3]{h} }{\sqrt[4]{h} }[/tex]
which is b
1. The diagram shows a graph y = 6x + 5. Which number should be subtracted from the right side of the equation to make it a proportional equation?
The number 5 should be subtracted from the right side of the equation to make it a proportional equation.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The function in this problem is given as follows:
y = 6x + 5.
A proportional relationship is a special case of a linear function with an intercept of zero, hence we must subtract by 5 as follows:
y = 6x + 5 - y
y = 6x.
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Ali made $144 for 9 hours of work. At the same rate, how much would he make for 7 hours of work
Answer: 112
Step-by-step explanation:
Take 144/9 to find how much he makes in a single hour. 144/9 is 16, 16*7=112. Which is how much he will make working 7 hours at the same rate.
Watermelons needed to be loaded up from the farm to go to the local market.
The mass of the load on the truck is 56 kilograms. If the mass of each watermelon is 7 kilograms, how many watermelons are on this load?
Show your work.
If the mass of each watermelon is 7 kilograms, there are 8 watermelons on the load.
To find the number of watermelons on the load, we need to divide the total mass of the load by the mass of each watermelon. We can set up an equation to represent this:
Number of watermelons = Total mass of load / Mass of each watermelon
Plugging in the given values, we get:
Number of watermelons = 56 kg / 7 kg per watermelon
Simplifying, we get:
Number of watermelons = 8
Therefore, there are 8 watermelons on the load.
It's important to note that this calculation assumes that all the watermelons have the same mass of 7 kg. In reality, there may be some variation in the mass of the individual watermelons, which could affect the total number of watermelons on the load. Additionally, other factors such as the size and shape of the watermelons may also affect how many can fit on the truck.
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