Need answer of number 3,4,5

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.​

Answer:

Step-by-step explanation:Math

The linear functions f(x) and g(x) are neither parallel nor 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:

They would be:

Hence they are neither.

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The probabilities for this problem are given as follows:

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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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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Answer: 24x+ (-12y)= -36

Step-by-step explanation:

Answer:

sin-1(-1/2), 180 + sin-1(-1/2), 360 + sin-1(-1/2)

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.

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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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.

Part 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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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.

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."

Answer:

-20

Step-by-step explanation:

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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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

Answer: b to the power of 3 / 8 Have a nice day!

For the table of values gives, the equation of line is obtained as y = 1/3x.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The coordinate points for cups of flour, x and loaves of bread y is given in the table.

The slope-intercept form of an equation is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

(3 - 2)/(9 - 6)

1/3

So, the slope point is obtained as m = 1/3.

The equation becomes - y =1/3 x + b

To find the value of b substitute the values of x and y in the equation -

2 = 1/3(6) + b

2 = 2 + b

b = 2 - 2

b = 0

So, the value for b is 0.

Now, the equation becomes -

y = 1/3x + 0

y = 1/3x

The graph is plotted for the equation.

Therefore, the equation is y = 1/3x.

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Answer:

2

Step-by-step explanation:

count the grids, A is 4, B is 8, so scale =2

Answer:

VALUES (5,6,12)

Step-by-step explanation:

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:

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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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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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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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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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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We can start solving this problem by using a system of equations. Let x be the selling price of a card and y be the selling price of a photo frame.

From the information given, we know that on the first day:

3x + 9y = 75 (1)

And on the second day:

8x + 5y = 67 (2)

Now we have two equations with two variables. To find the value of x and y, we can use either substitution or elimination method.

One possible way to solve for x and y is to use substitution method:

Solve equation (1) for x in terms of y:

x = (75 - 9y) / 3

Substitute this expression into equation (2) to eliminate x:

8((75 - 9y) / 3) + 5y = 67

Solving this equation for y:

y = 3

Now we can substitute this value of y back into equation (1) or (2) to find the value of x:

3x + 9(3) = 75

3x = 48

x = 16

So the selling price of a card is $16 and the selling price of a photo frame is $3.

Answer:

Photo frame = $7

Card = $4

Step-by-step explanation:

Define the variables:

Given information:

Create a system of linear equations using the given information and defined variables:

[tex]\begin{cases}3c + 9p = 75\\ 8c + 5p = 67\end{cases}[/tex]

Rearrange the first equation to isolate c:

[tex]\implies 3c+9p=75[/tex]

[tex]\implies 3(c+3p)=75[/tex]

[tex]\implies \dfrac{3(c+3p)}{3}=\dfrac{75}{3}[/tex]

[tex]\implies c+3p=25[/tex]

[tex]\implies c+3p-3p=25-3p[/tex]

[tex]\implies c=25-3p[/tex]

Substitute the expression for c into the second equation and solve for p:

[tex]\implies 8c+5p=67[/tex]

[tex]\implies 8(25-3p)+5p=67[/tex]

[tex]\implies 200-24p+5p=67[/tex]

[tex]\implies 200-19p=67[/tex]

[tex]\implies 200-19p-200=67-200[/tex]

[tex]\implies -19p=-133[/tex]

[tex]\implies \dfrac{-19p}{-19}=\dfrac{-133}{-19}[/tex]

[tex]\implies p=7[/tex]

Therefore, the selling price of a handmade photo frame was $7.

Substitute the found value of p into the expression for c and solve for c:

[tex]\implies c=25-3p[/tex]

[tex]\implies c=25-3(7)[/tex]

[tex]\implies c=25-21[/tex]

[tex]\implies c=4[/tex]

Therefore, the selling price of a handmade card was $4.

Answer:

12 strawberries

28 honeydew

Step-by-step explanation:

[tex]\frac{strawberries}{grapes}[/tex] = [tex]\frac{3}{9}[/tex] = [tex]\frac{x}{36}[/tex]

9 x 4 = 36

so, 3 x 4 = 12

There are 12 strawberries

[tex]\frac{strawberries}{honeydew}[/tex] = [tex]\frac{6}{14}[/tex] = [tex]\frac{12}{x}[/tex]

6 x 2 = 12

so, 14 x 2 = 28

There are 28 honeydew

Answer:

87.5/100

Step-by-step explanation:

Percents are parts of a whole. So if we imagine that the whole is 100, then 87 1/2% would be 87.5/100

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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Answer:

Step-by-step explanation:

12.7% = 12.7/100 = 0.127