in one study, a sample of freshmen was taught a brief course of calculus focusing on several basic learning objectives. half of the students learned by studying repeated examples of one learning objective at a time, while the other half studied mixed problem sets that included examples of all learning objectives grouped together. at the middle of the course, all the students were given a test on the material. the students in the mixed practice group had an average grade of 83 (out of 100), while the students in the one-at-a-time group had an average grade of 52. what is the best estimate for the difference in the mean grades between freshmen who study mixed problems and those who study each learning objective independently?

Answer:

(12,-8)

Step-by-step explanation:

scale factor is 4

(x,y)=(4x,4y)

(3,-2)=(12,-8)

The solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

According to the given question.

We have a linear equation in one variable.

4y - 6 = 2y + 8

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is given by

4y - 6 = 2y + 8

⇒ 4y - 2y - 6 = 8     ( subtracting 2y from both the sides)

⇒ 2y -6 -8 = 0           (subtracting 8 from both the sides)

⇒ 2y - 14 = 0

⇒ 2y = 14

⇒ y = 14/2

⇒ y = 7

Hence, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

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The set of negative integers is a commutative group under the operation of addition.

For given question,

We need to check whether the set of negative integers is a commutative group under the operation of addition.

We know that negative integers are whole numbers that have value less than zero.

We know that, for any positive integers a, b,

a + b = b + a                        .......................(1)

For any negative integers -a, -b

(-a) + (-b) = -a - b

              = -(a + b)

              = -(b + a)                  ...............(From (1))

              = -b - a

              = (-b) + (-a)

As, (-a) + (-b) = (-b) + (-a) for any negative integers -a, -b, the set of negative integers is a commutative group under the operation of addition.

Therefore, the set of negative integers is a commutative group under the operation of addition.

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Answer:To find a scale factor between two similar figures, find two corresponding sides and write the ratio of the two sides.

Step-by-step explanation:

Answer:

what shape is it? for example a triangle etc

Answer:

$51

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

4x-10=3x+2

Subtract 3x on both sides:

x-10=2

Add 10 on both sides:

x=12

Hope this helps!

The side length of this square is equal to \(\frac{4}{7}\;inches\)

Given the following data:

To determine the side length of this square:

In this exercise, you're required to solve for the length of the sides of a square that has an area of  \(\frac{16}{49}\) square inches.

Mathematically, the area of a square is calculated by using the formula;

\(A=S^2\)

Where;

Substituting the value into the formula, we have;

\(\frac{16}{49}=S^2\)

Taking the square root of both sides, we have;

\(S=\sqrt{\frac{16}{49}} \\\\S=\frac{4}{7}\;inches\)

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Answer:

Step-by-step explanation:

Answer:

31cm

Step-by-step explanation:

14 + 8 + 9 = 31

Make sure to add the cm on the end!

The perimeter of the triangle is 31cm.

The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.

In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.

In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.

For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.

In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.

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Answer:

we know that,

y-y1=m(x-x1)

or, y-1=-3(x-5)

or, y-1=15-3x

or 3x+y-16=0 is the required equation

The graph of the line with slope -3 passing through the point (5,1) is attached.

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

The equation of a line is the representation of a line on a coordinate plane (x-y plane), which shows the relation between x and y, for every point on the particular line.

The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.

The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.

The equation of a line passing through the point (x₁, y₁), having a slope m, is represented by the one-point formula: y - y₁ = m(x - x₁).

We are asked to graph a line with a slope = -3, passing through the point (5, 1).

We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (5, 1).

Substituting these values in the equation y - y₁ = m(x - x₁), we get

y - 1 = -3(x - 5)

or, y = -3x + 15 + 1

or, y = -3x + 16.

or, 3x + y = 16

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

To graph this line we plot the points (5, 1) (as it is given that it passes through this point) and (0, 16) (as the y-intercept is at 16, so the line passes through the point (0, 16)). We join these points by a line and extend this line on both sides to get the required line.

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Answer:

4:6

Step-by-step explanation:

if you multiply each of the number 2 and 3 by 2 you will get 4:6

Answer:

B: 4:6

Step-by-step explanation:

The answer is 4:6 because you can multiply 2 by 2 to get 4 and 3 by 2 to get 6.

Answer:

it would be a rectangle

Step-by-step explanation:

The perpendicular cross-section of a soup can should be considered as the rectangle.

A rectangle refer to a 2D shape that consist of 4 sides, 4 corners, and 4 right angles.

Opposite sides of a rectangle shape should contain the same length, with one pair being bigger as compared to the other pair.

Therefore, The perpendicular cross-section of a soup can should be considered as the rectangle.

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7.     4x-4y=8...(1) and -x+y=-2,,,(2)

Choose one equation from the two above to derive the third equation from.

I choose -x+y=-2 and i will derive the third equation form it

I will make y the subject of the equation y=-2+x......(3)

Substitute the third equation from the first equation YOU DID NOT USE TO DERIVE THE THIRD EQUATION

\(4x-4(-2+x)=8\\4x+8-4x=8\\4x-4x=8-8\\0=0\)

As far as I went there are No Solutions for the system of equations for question 7

8.

6x-3y=-9 ....(1)

and

x+y=9....(2)

x=9-y....(3)

\(6(9-y)-3y=-9\\54-6y-3y=-9\\-9y=-9-54\\-9y=-63\\\frac{-9y}{9} =\frac{-63}{9} \\y=-7\)

\(x=9-(-7)\\x=9+7\\x=16\)

Given sin A = -21/29 and sin B = 12/37, we can calculate the sum of sin A and sin B by adding the given values.

To find the sum of sin A and sin B, we can simply add the given values of sin A and sin B.

sin A + sin B = (-21/29) + (12/37)

To add these fractions, we need to find a common denominator. The least common multiple of 29 and 37 is 29 * 37 = 1073. Multiplying the numerators and denominators accordingly, we have:

sin A + sin B = (-21 * 37 + 12 * 29) / (29 * 37)

            = (-777 + 348) / (1073)

            = -429 / 1073

The sum of sin A and sin B is -429/1073.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 11 in this case:

sin A + sin B = (-429/11) / (1073/11)

            = -39/97

Therefore, the sum of sin A and sin B is -39/97.

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Answer:

C and D are equivalent.

Step-by-step explanation:

if you multiply 7/6 both by 2 it will =14/2 and also if you multiply 7/6 both by 10 you will get 70/60.

Answer:

18.44%

Step-by-step explanation:

Let :

Percentage who rode bus to work last year = x

Percentage who ride bus to work this year = 27.1%

Percentage who ride bus to work this year = [percentage who rode bus to work last year + 47% of percentage who rode bus to work last year]

Mathematically ;

27.1% = x + 47% of x

0.271 = x + (0.47x)

0.271 = x + 0.47x

0.271 = 1.47x

x = 0.271 / 1.47

x = 0.1843537

x = 0.1843537 * 100%

x = 18.435%

x = 18.44%

On solving the provided question, we can say that By the help of trigonometry the angle elevation is 45.

The area of mathematics known as trigonometry looks at how triangle side lengths and angles relate to one another. In the Hellenistic era, roughly in the third century BC, the region had its initial appearance due to the use of geometry in astronomical study.

Exact mathematics focuses on specific trigonometric functions and how calculations could employ them. There are six well-known trigonometric functions in trigonometry.

They go by a variety of names and abbreviations, including sine, cosine, tangent, cotangent, secant, and cosecant (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. In geometry, the characteristics of every geometric figure are explored.

Let the pole's height be denoted by AB = h.

A pole's shadow will create the base BC.

Let the elevation angle be 9,

By the help of trigonometry

tan x = AB/BC

tan x = h/h = 1

x = tan^(-1)

x = 45

Hence, the angle elevation is 45

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The sale price of the table = 115 x 0.80 = $92

The total price including the tax = 92 x 1.075 = $98.90

Answer = $98.90

Answer:

7.5h+10=6.25(h+3)

Step-by-step explanation:

...........................................................

Answer:

greater than

Step-by-step explanation:

positive is higher than negative

The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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Answer:

Step-by-step explanation:

A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero.

For this case 4/11 are

0.36 36 36 36 36 36 36 36 36

it repeating 36  36

so 4/11 are repeating decimal

Answer:

\( \frac{4}{11} = 0.3636\)

Step-by-step explanation:

The remainders repeat in a pattern and the quotient also repeats in blocks of two. So, 4/11 = 0.3636, Which

36 repeats, In this case, 36 is the repeating pattern.

The number of different packages of 4 different sweatshirts would be 70 different packages.

The number of displays possible are 336 different displays.

Utilizing the combination formula allows us to determine the quantity of distinct packages containing four sweatshirts, derived from eight high school football teams. A combination factors in items without regard to their sequence.

C ( n, k) = n ! / ( k ! ( n - k ) ! )

C ( 8 , 4 ) = 8 ! / ( 4 ! ( 8 - 4 ) ! )

C ( 8 ,  4) = 40320 / 576

C ( 8, 4 ) = 70 different packages

The permutation formula enables us to determine the possible number of displays for a sequence of three unique sweatshirts representing different high schools, with great regard to their order. Applying this is essential when the order these items are presented holds significance.

P ( n , k) = n ! / ( n - k )!

P ( 8, 3 ) = 8 ! / ( 8 - 3 ) !

P ( 8, 3 ) = 40320 / 120

P ( 8 , 3 ) = 336

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Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b