a represents pounds of apples and b represents pounds of bananas. guillermo and cara are finding and interpreting the solution. is either correct? explain your reasoning.
Both Guillermo's and Cara's solutions are incorrect due to the incorrect substitution of values of a variable to find the dependent one.
Guillermo's solution is incorrect because he did not substitute the value of 'b' from the first equation into the second equation. Instead, he directly added 0.49b to both sides and solved for a, which gives an incorrect result.
Cara's solution is also incorrect because she did not substitute the value of 'a' from the first equation into the second equation. Instead, she used the equation a + b = 7 to solve for the value of b, which gave her an incorrect result.
We can find the correct solution as follows -
The system of equations is,
⇒ a + b = 7 .. (i)
And 1.29a + 0.49b = 6.63 .. (ii)
Now, we will solve the system of equations as follows -
⇒ a + b = 7
⇒ a = 7 - b .. (i)
And, ⇒ 1.29a + 0.49b = 6.63 .. (ii)
Substitute the value of a from (i) in (ii), we get;
⇒ 1.29a + 0.49b = 6.63
⇒ 1.29(7 - b) + 0.49b = 6.63
⇒ 9.03 - 1.29b + 0.49b = 6.63
⇒ - 0.8b = 6.63 - 9.03
⇒ - 0.8b = - 2.4
⇒ 0.8b = 2.4
⇒ b = 2.4 / 0.8
⇒ b = 3
And, From (i);
⇒ a = 7 - b .. (i)
⇒ a = 7 - 3
⇒ a = 4
Hence, 4 pounds of apples and 3 pounds of bananas were bought.
Thus, both of their solutions are incorrect.
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The complete question is -
FIND THE ERROR In the system a + b = 7 and 1.29a + 0.49b = 6.63, a represents pounds of apples and b represents pounds of bananas a person bought. Guillermo and Cara are finding and interpreting the solution. Is either correct? Explain your reasoning.
a. Guillermo: 1.29a + 0.49b = 6.63 ⇒ 1.29a +0.49(a + 7) = 6.63 ⇒ 1.29a + 0.49a + 3.43 = 6.63 ⇒ 1.78a = 3.2 ⇒ a = 1.8
a + b = 7, so b = 5.2. The solution (1.8, 5.2) means that 1.8 pounds of apples and 5.2 pounds of bananas were bought.
b. Cara: 1.29a + 0.49b = 6.63 ⇒ 1.29(7-b) + 0.49b = 6.63 ⇒ 9.03- 1.29b + 0.49b = 6.63 ⇒ -0.8b = -2.4 ⇒ b=3
The solution b = 3 means that 3 pounds of apples and 3 pounds of bananas were bought. volunteers. The ratio of boys to girls is 7:5.
consider the equation y=100x+500 where y is the number of park visitors and x is the average daily temperature in degrees Fahrenheit.
these are the answer choices
A. 500 people will go out to the park when its 100F
B. even if its 0F, 500 people will still go to the park
C. when it is 0F, 100 people will go to the park
Answer:
A. 500 people will go out to the park when its 100F is incorrect.
of five letters (a, b, c, d, and e), three letters are to be selected at random. how many possible selections are there?
Three letters will be selected from five letters. The number of possible selections is 10.
A combination is a method of picking elements from a collection where the order of selection is irrelevant. Assume we have three numbers P, Q, and R. The number of ways we can choose two numbers from each set is determined by combination.
Suppose we want to pick k elements from a set of n elements, then the number ways it can be chosen is:
C(n,k) = n! / k! (n-k)!
Where n! is n factorial.
In this case, there are 5 letters and we want to select three letters. Hence, k = 3, and n = 5.
C(5,3) = 5! / 3! (5-3)!
C(5,3) = 5! / (3! 2!) = 10
Thus, there are 10 possible selections.
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suppose we have a bag with $10$ slips of paper in it. eight slips have a $3$ on them and the other two have a $9$ on them. how many $9$'s do we have to add before the expected value is at least $8$?
There are a total of 10 slips.
8 slip with 3 on it
2 slips with 9 on it
value = Probability of 3 x 3 + Probability of 9 x 9.
= (8 / 11) x 3 + (2/ 11) x 9
24 / 11 + 24 / 11 = 4.36
probability
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
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given four sets: a, b, c and d. each set has 15. the pair-wise intersections have 4 elements. the three-way intersections have 3 elements. there are 2 elements in the intersection of all sets. how many elements are there in total?
There are 46 elements in total for 4 sets A, B, C, and D.
Consider 4 sets A, B, C, and D.
Each set has 15 elements.
The pair-wise intersection has 4 elements.
The three-way intersection has 3 elements.
There are 2 elements in the intersection of all sets.
So,
P(A) = P(B) = P(C) = P(D) = 15
P(A ∩ B) = P(A ∩ C) = P(A ∩ D) = P(B ∩ C) = P(B ∩ D) = P(C ∩ D) = 4
P(A ∩ B ∩ C) = P(A ∩ B ∩ D) = P(A ∩ C ∩ D) = P(B ∩ C ∩ D) = 3
P(A ∩ B ∩ C ∩ D) = 2
The total number of elements are:
P (A U B U C U D) = P(A) + P(B) + P(C) + P(D) - P(A ∩ B) - P(A ∩ C) - P(A ∩ D)- P(B ∩ C) - P(B ∩ D) - P(C ∩ D) + P(A ∩ B ∩ C) + P(A ∩ B ∩ D) + P(A ∩ C ∩ D) + P(B ∩ C ∩ D) - P(A ∩ B ∩ C ∩ D).
P (A U B U C U D) = 15 + 15 + 15 + 15 - 4 - 4 - 4 - 4 - 4 - 4 + 3 + 3 + 3 + 3 - 2
= 60 - 24 + 12 - 2
= 60 + 12 - 24 - 2
= 72 - 26
= 46
Therefore there are 46 elements.
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Line F passes through points (2, 8) and (9, 3). Line g passes through points (1, 8) and (10, 1). Are line f and line g parallel or perpendicular? Pls help I’m getting frustrated
The linear functions f(x) and g(x) are neither parallel nor perpendicular.
How to obtain if the lines are parallel or perpendicular?To obtain whether they are parallel of perpendicular, first we must obtain the slope of each line.
Given two points, the slope of a line is calculated as the change in y divided by the change in x.
Hence, the slope for each line is obtained as follows:
Line F: m = (3 - 8)/(9 - 2) = -5/7.Line G: m = (1 - 8)/(10 - 1) = -7/9.They would be:
Parallel if they have the same slope.Perpendicular if the product of the slopes was of -1.Hence they are neither.
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What is this answer for this page
Answer: 24x+ (-12y)= -36
Step-by-step explanation:
A gym charges its customers an initial membership fee, plus an hourly fee. The graph shows the cost of using the gym
The initial fee charged to customers for using the gym, given the graph showing the charges to customers is $ 20.
How to find the initial membership fee ?To find the initial membership fee, you should look at the y - intercept of the graph.
The y - intercept is the point where the x vale is 0 and this case this point shows the cost when the customers have not worked out in the gym for any hour yet.
This y - intercept is therefore $ 20 as this is the point on the graph where the value of x is 0.
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The question is:
What is the initial fee charged to customers for using the gym?
Consider a force F = 〈–1, 3〉 applied to an object that is moving from the point (3, –9) to the origin. Find the displacement vector of the object.
Answer:
d = 〈 -3 , 9 〉
W = 30 Joules
The displacement vector of the object is (-3, 9) and the work done is 30 Joules
The term called vector in math is defined as a quantity or phenomenon that has two independent properties such as magnitude and direction.
Here we know that the value of force F is (-1, 3) and the point is (3, -9)
Then the displacement from origin to (3, -9) is calculated as,
=> d = (0-3, 0-(-9))
Then the value of d is ( -3, 9)
Here the formula to Work done is written as,
=> F x d
=> (-1, 3) x (-3, 9) = 3 + 27
=> 30 joules.
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conditions for rhombuses rectangles and squares practice
Conditions which help us to differentiate the properties of rectangle, rhombus , and square are:
Rectangle : Opposite sides are congruent with measure of each of the angle 90°.
Rhombus : Parallelogram whose diagonals are perpendicular.
Square: All four sides are congruent with measure of each of the angle 90°.
Different conditions of rectangle , rhombus, and square are:
Rectangle, rhombus, and square are all type of quadrilateral.Rectangle is a type of quadrilateral whose opposite sides are congruent to each other.All the four angles in a rectangle are of 90 degrees.Rhombus is a type of quadrilateral whose all four sides are congruent to each other.Diagonals of the rhombus are perpendicular to each other.Square is a type of quadrilateral with all four congruent sides and measure of all the four angles is 90 degrees.The given question is incomplete, I answer the question in general according to my knowledge:
What are the conditions which differentiate rhombus, rectangle, and square from each other?
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Pls help me with this I am stuck cheers thanks
Answer:
x ≥ 10
Step-by-step explanation:
A solid dot on 10 means 10 is included.
An arrow pointing to the right of 10 means all numbers greater than 10 are included.
Answer: x ≥ 10
Answer:10 =< x
Step-by-step explanation:
Shaded circle means include that number so it is a <= or >= sign
Goes to x.
Think about it a bit, not quite sure if 50 is involved in this inequality
someone help pls w this questions
Answer:
2
Step-by-step explanation:
count the grids, A is 4, B is 8, so scale =2
two numbers,thrice the first number minus the second number is 19 and twice the first number plus five times the second number is minus 10 find the product of the two numbers
Answer:
-20
Step-by-step explanation:
for the differential equation a. find all equilibrium solutions and use the first derivative test to draw the phase line for the de. b. classify each equilibrium solution as asymptotically stable , unstable or semi-stable. c. use the second derivative test for concavity and the phase line to produce a phase portrait and sketch one typical solution curves in each region determined by the equilibrium solutions.
An autonomous first order ordinary differential equation is any equation of the form: dy/dt = f(y).
1. Stable: The equilibrium solution y(t) = c is stable if all solutions with initial conditions y0 ‘near’
y = c approach c as t → ∞.
2. Unstable: The equilibrium solution y(t) = c is unstable if all solutions with initial conditions y0 ‘near’ y = c do NOT approach c as t → ∞.
3. Semi-stable: The equilibrium solution y(t) = c is semistable if initial conditions y0 on one side of c lead to solutions y(t) that approach c as t → ∞, while initial conditions y0 on the other side of c do NOT approach c.
Find the equilibrium points for the differential equation (1) and determine whether each is asymptotically stable, semistable, or unstable.
The graph of y0 as a function of y, and the phase line. (It’s important that α is positive – if it were negative, we’d have very different behavior).
We can see that there are two equilibrium solutions: y = 0, which is unstable, and y = 1, which is stable.
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if this same population size wants to start decreasing over time, the population growth rate needs to be
What does ordinal number mean.
Answer: Ordinal numbers are a designation of something's place in a series by a number, such as first or third. Ordinal numbers can function as pronouns, nouns, and adjectives.
Answer:
Step-by-step explanation:
It means what place something is in. For example the ordinal of 1 is 1st 2 is 2nd and 3 is 3rd and so on. I hope this helps.
customers are used to evaluate preliminary product designs. in the past, 96% of highly successful products received good reviews, 50% of moderately successful products received good reviews, and 12% of poor products received good reviews. in addition, 40% of products have been highly successful, 35% have been moderately successful and 25% have been poor products. round your answers to four decimal places (e.g. 0.9876). (a) what is the probability that a product attains a good review? (b) if a new design attains a good review, what is the probability that it will be a highly successful product? (c) if a product does not attain a good review, what is the probability that it will be a highly successful product? (a) enter your answer in accordance to the item a) of the question statement
The probability that a product attains a good review is 0.6125
The given information can be tabulated as follows.
Success type High Moderate Low Total
0.40 0.35 0.25 1
Good reviews 0.95 0.60 0.10
Combined prob 0.4*0.95 0.35*0.6 0.25*0.1
0.38 0.21 0.025 0.6125
A)the likelihood that a product will receive a favorable review = Prob it is successful and receives a favorable review + Prob it is moderately successful and receives a favorable review + Prob it is unsuccessful and receives a favorable review = 0.6125
B) If a new design receives positive feedback, there is a 0.62 percent chance that it will be a highly successful product.
C) Chance of not receiving a favorable review: (0.40*0.05)
+0.35(0.4) +(0.25)*0.9\s= 0.385
Prob for successful but not receiving a favorable evaluation is 0.40(0.05) = 0.02; required prob is 0.0519.
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Check all that apply
From the trigonometric function sec θ = 13/12, two more functions are derived -
Option C: cos θ = 12/13
Option D: tan θ = 5/12
What is trigonometric function?
Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.
The given trigonometric function is -
sec θ = 13/12
Sec function is written as the ratio of hypotenuse to adjacent.
sec θ = 1/cos θ
Cos function is written as the ratio of adjacent to hypotenuse.
cos θ = 12/13
To find the opposite, apply the Pythagoras theorem -
(Opposite)² = (Hypotenuse)² - (Adjacent)²
(Opposite)² = (13)² - (12)²
(Opposite)² = 169 - 144
Opposite = √25
Opposite = 5
Tan function is written as the ratio of opposite to adjacent.
tan θ = 5/12
Therefore, from sec function, cos and tan function are obtained.
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Solve this (algebra) to the simplest form
Answer: b to the power of 3 / 8 Have a nice day!
In triangle ABC, the measure of angle A is 35º and the measure of angle B is 20°. In triangle
DEF, the measure of angle D is 35º and the measure of angle F is 125. Are triangles ABC
and DEF similar? Explain or show your reasoning.
ΔABC and ΔDEF are not similar because corresponding angles are not equal.
Now, According to the question:
In triangle ABC :
The measure of angle A is 35º and
The measure of angle B is 20°.
In triangle DEF:
The measure of angle D is 35º and
The measure of angle F is 125
We know that :
Sum of interior angles of triangle is 180°
Now, In ΔABC:
∠A + ∠B + ∠C = 180°
35 + 20 + ∠C = 180°
55° + ∠C = 180°
∠C = 180° - 55°
∠C = 125°
Now, In ΔDEF:
∠D + ∠E + ∠F = 180°
35 + ∠E + 125 = 180°
160 + ∠E = 180°
∠E = 180° - 160°
∠E = 20°
So, ∠C ≠ ∠E as ∠C = 125° and ∠E =20°
Hence, No, Triangles are not similar .
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PLEASE HELP!! 100 POINTS
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] and c = [tex]\frac{5}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line
Stimultaneous elimination equations
4x + 2y = 10
X+ 2y = 7
The values of x and y on solving the two simultaneous equations are x = 1 and y = 3.
The simultaneous equations to be solved are 4x + 2y = 10 and x + 2y = 7.
Rearranging the above equations, we have,
- 4x - 2y = - 10 -----(A)
x + 2y = 7 -------(B)
Solving them, we have, -3x = -3
x = 1 ------(C)
Substituting (C) in (B), we have,
1 + 2y = 7
2y = 6
y = 3 ------(D)
Now, let us substitute the x and y values in (A) and (B) and then check.
4x + 2y = 10
4 + 2(3) = 10
A is checked.
x + 2y = 7
1 + 2(3) = 7
B is checked.
Thus, the values of x and y are checked to be correct.
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how many distinct lines represent altitudes medians interior angle bisecrots of a isosceles triangle but not equilateral
The altitudes, the medians, and the angle-bisectors are distinct for the congruent sides but coincident for the base. Hence, 7 lines.
Now, According to the question:
Altitude. A line segment joining a vertex of a triangle with the mid-point of the opposite side. An altitude is a perpendicular line segment drawn from a vertex of a triangle to the opposite side. It divides the opposite sides into two equal parts.
A Median of a triangle is a straight line segment which is drawn from the vertex of a triangle to the middle point of the opposite side. It splits the opposite side of the triangle into two equal line segments. That means we know that it's a median if we have got those equal line segments.
The altitudes, the medians, and the angle-bisectors are distinct for the congruent sides but coincident for the base. Hence, 7 lines.
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Side and angle properties of a parallelogram (level 2)
find x,y,z
473 determine the answer to the following questions using long division
There are other methods to write a division issue, such as using a / or a to denote "divided by." As a result, in the equation 473 / 2 = 1 the divisor is the quotient, the remainder is 236, and the divisor is 2.
How do you find the answer in long division?Divide the dividend's first digit, which should be on the left, by the divisor, then write the result as the quotient on top. Write the difference below after subtracting the outcome from the digit. Bring down the dividend's next digit (if present).
Long division strategy: lengthy division techniques. The same symbols are used for long division as they are for short division: dividend (the number being divided) under the "bus stop," divisor (the number the dividend is being divided by), quotient (the solution) on top, and each place value aligned with the dividend.
Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.
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The complete question is "Divide the given numbers 473 and 6 using our free online Long Division Calculator and determine the Quotient and Remainder as Q 78 R 5 instantly without any hurdles."
Find the volume of the rectangular prism . Simplify
A rectangular prism has a volume of 2x ^ 3 + 19x ^ 2 + 24x
What is volume?the volume of the rectangular prism is
The area contained by an object's limits in three-dimensional space is referred to as its volume.
Thus, a rectangular prism having the following dimensions: 2x length, (x2) width, and (x + 2) height
L x B x H = volume
= x× (x +8 )(2x + 3)
= x(x + 8)(2x + 3)
(2x + 3) * x ^ 2 + 8x(2x + 3)
2x ^ 3 + 19x ^ 2 + 24x
The area contained by an object's limits in three-dimensional space is referred to as its volume.
A rectangular prism's volume is thus 2x ^ 3 + 19x ^ 2 + 24x
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To create the flower gardens, Wendell bought six pieces of wood. Pieces A and B are 6 feet long, pieces C and D are 8 feet long, piece E is 3 feet long and piece F is 2 feet long.
Part A
Can Wendell make a triangular garden using pieces A, B, and F? Why or why not?
Part B
Can Wendell make a triangular garden using pieces D, E, and F? Why or why not?
Part C
Can Wendell make a rectangular garden with the pieces of wood he has? if yes, which pieces can he use?
Part D
Describe how Wendell can use all six pieces of wood to create either two rectangular gardens or two triangular gardens. Assume the gardens do not share a common side.
Part E
Wendell's dog. Jordan, was getting in his way as he worked in the backyard. So, Wendell chained him to a pole. If the chain is 12 feet long, about how much area does Jordan have to walk around?
Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet is 113 square feet.
Making triangular and Rectanglar garden with woods of different lengthsPart A: Wendell cannot make a triangular garden using pieces A, B, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces A, B, and F) must be greater than the length of the longest side (in this case, piece F, which is 2 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces A and B is 12 feet, which is greater than the length of piece F, it is not possible to make a triangular garden using these pieces.
Part B: Wendell cannot make a triangular garden using pieces D, E, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces D, E, and F) must be greater than the length of the longest side (in this case, piece D, which is 8 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces E and F is 5 feet, which is less than the length of piece D, it is not possible to make a triangular garden using these pieces.
Part C: Wendell can make a rectangular garden with the pieces of wood he has by using pieces A and C or pieces B and D. He cannot use pieces E and F because they are not long enough to make up one of the sides of a rectangle.
Part D: Wendell can not create two triangular gardens using all six pieces of wood as the sum of the lengths of the two shorter sides of a triangle must be greater than the length of the longest side, and he only have 3 pieces with length greater than 3 feet which is required to create one triangle.
Wendell can create two rectangular gardens using all six pieces of wood by using pieces A and C, and pieces B and D.
Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet (since the chain is 12 feet long).
The formula to calculate the area of a circle is πr^2
where π is approximately 3.14 and
r is the radius of the circle,
so the area that Jordan has to walk around is approximately
3.14 x 6² =113 square feet.
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7. At an office building, the amount of time it takes before the elevator door on the first floor opens when the button is pressed to go “up” ranges uniformly from 2 seconds to 70 seconds.
Determine the probability that the elevator door with take less than 30 seconds to open.
Determine the probability that the door will take exactly 55 seconds to open
The probabilities for this problem are given as follows:
Less than 30 seconds: 0.4118 = 41.18%.Exactly 55 seconds: 0%.What is the uniform probability distribution?It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The bounds for this problem are given as follows:
a = 2, b = 70.
Hence the probability of less than 30 seconds is given as follows:
P(X < 30) = (30 - 2)/(70 - 2)
P(X < 30) = 0.4118 = 41.18%.
The uniform distribution is a continuous distribution, meaning that the probability of an exact value is of 0.
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Express 12.7% as a decimal
Answer:
Step-by-step explanation:
12.7% = 12.7/100 = 0.127
(4,0)
(5,3)
(6,0)
Identify the values of the variables in the equation when it is written in vertex form: y = a (x - h)² + k
1. What is the value of a?
2. What is the value of h?
3. What is the value of K?
Answer:
VALUES (5,6,12)
Step-by-step explanation: