A random sample of students were asked whether they prefer milk juice or water is it results are summarized in the table.

With a greater mean value , we can conclude that the sixth period class test was better than the second period .

Second period class:

Mean = (55+70+6*75+6*80+2*85+3*90+95)/20

Mean = 1590/20 = 79.5

Sixth period class:

Mean = (65+3*75+5*80+6*85+3*90+2*95)/20

Mean = 1660/20 = 83

Therefore, From the mean values , we can infer that students performed better in test for the sixth period class than the second .

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(x - 3)² + y² = 100/9  is the equation of a circle with a radius of 10/3 and a xy-plane with a center at (3, 0) and an endpoint at (1, 83).

The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. A circle is a plane figure that is bounded by a single curved line and in which all straight lines drawn from any point inside the circle to the boundary are equal. Its center is the point, and its perimeter is the bounding line.

given

Circle Formula: (x - h)² + (y - k)² = r²  ; (h, k) is the center & r is the radius

Use the distance formula for (3, 0) and (1, 1/8 )

\(r = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\\ r = \sqrt{( 3 - 1)^{2} + ( 0 - 8/3 )^{2} }\)

\(\sqrt{\frac{100}{9} }\\ r = \frac{10}{3}\)

Center (h, k) = (3, 0)   Radius (r) =  10 / 3

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 0)² = (10/3)²

(x - 3)² + y² = 100/9

So (x - 3)² + y² = 100/9  is the equation of a circle with a radius of 10/3 and a xy-plane with a center at (3, 0) and an endpoint at (1, 83).

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The matrix A that transforms the letter 'n' in regular 12-point font to the italicized 'n' in 16-point font can be determined by scaling and shearing operations.

To achieve the desired transformation, we can apply a combination of scaling and shearing operations using a 2x2 matrix. Let's denote this matrix as A.

To find the specific values of the matrix A, we need to consider the differences between the regular 'n' and the italicized 'n' in terms of scaling and shearing.

The italicized 'n' is slanted compared to the regular 'n'. This slant can be achieved by applying a shear transformation along the x-axis.

We can determine the values of A by examining the specific slant and size changes of the italicized 'n' compared to the regular 'n'.

The matrix A will consist of scaling factors and shear coefficients that capture the desired transformation. The exact values of the matrix elements will depend on the specific slant and size adjustments required for the italicized 'n'.

To obtain the matrix A, we would need to analyze the italicized 'n' in 16-point font and compare it to the regular 'n' in 12-point font to determine the necessary scaling and shearing parameters.

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The parabola opens upward, the range of the function is [6/5, ∞) in interval notation.

We can find the range of the function by finding the vertex of the parabola, which will give us the minimum value, and then noting that the function increases without bound as x approaches infinity.

First, we need to find the vertex of the parabola. We can do this by finding the x-coordinate of the vertex, which is given by:

x = -b/2a

where a = 5, b = -2. Substituting these values, we get:

x = -(-2)/(2(5)) = 2/5

To find the y-coordinate of the vertex, we can substitute this value of x into the equation for g(x):

g(2/5) = 5(2/5)^2 - 2(2/5) + 1 = 5/5 - 4/5 + 1 = 6/5

So the vertex of the parabola is (2/5, 6/5), which is the minimum value of the function.

Since the parabola opens upward, the range of the function is [6/5, ∞) in interval notation.

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The answer is (a) (30, 50). To find the 98% confidence limits,

We can use the formula:

\(98% confidence limits = sample mean ± (Z-score for 98% confidence level) * (standard error)\)

We don't know the sample mean or the standard error, but we do know the 90% confidence limits. We can use these to estimate the standard error:

Standard error = (90% confidence limits upper bound - 90% confidence limits lower bound) / (1.645 * 2)

Standard error = (47 - 33) / (1.645 * 2) = 4.73

Now we can use this to estimate the 98% confidence limits:

98% confidence limits = sample mean ± (2.33) * (4.73)

We know that the range of the 90% confidence limits is 14 (47 - 33). The range of the 98% confidence limits will be wider than this, so we can eliminate options b), c), and e).

Now we just need to check which of the remaining options gives us a range wider than 14. We can do this by subtracting the lower limit from the upper limit:

a) (30, 50) -> range = 20
d) (38, 45) -> range = 7

Therefore, the answer is (a) (30, 50).

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The probability that exactly two of the CDs are in the wrong cases is 1, or 100%.

To solve this problem, we can use the formula for permutations and combinations. The number of ways to place four CDs in four cases is 4!, which equals 24. The number of ways to place exactly two CDs in the wrong cases is the product of two combinations: the number of ways to choose two CDs out of four to be in the wrong cases, and the number of ways to place those two CDs in the wrong cases.

The number of ways to choose two CDs out of four is given by the combination formula:

C(4,2) = 4! / (2! × (4-2)!) = 6

The number of ways to place those two CDs in the wrong cases is 2, since each of the two incorrectly placed CDs can go in one of the two remaining cases.

The number of ways to place the other two CDs in their correct cases is 2, since each CD has exactly one correct case left.

Therefore, the total number of ways to place exactly two CDs in the wrong cases is:

6 × 2 × 2 = 24

So the probability of this happening is:

24 / 4! = 24 / 24 = 1

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Answer: 0.68 or 13.92

Step-by-step explanation:

If the height is 47 meters, then the height, h, is equal to 47.

\(47=73t-5t^2\\\\5t^2 - 73t+47=0\)

Using the quadratic formula,

\(t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}\)

Answer:

Graph A:  y = (1/2)x - 2

Step-by-step explanation:

2x−4y=8 in slope-intercept form is -4y = -2x + 8, or y = 1/2x - 2

The slope of this line is 1/4 and the y-intercept is -2.  This is represented by Graph A.

Answer:

x= 17

Step-by-step explanation:

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides adjacent to the right angle. The hypotenuse is the side of the triangle opposite the right angle.

Hope this helps.

The length of the side length x = 17 units, for the given right-angled triangle, was found using the Pythagoras Theorem.

In a right-angled triangle, the side opposite to the right angle is called the hypotenuse, and the other two sides are called the two legs (or, base and perpendicular respectively).

According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is the sum of the squares of the two legs. This can be written as:

Hypotenuse² = Base² + Perpendicular².

In the question, we are given a right-angled triangle with lengths of the legs as 8 and 15 units respectively, and the length of the hypotenuse is x units.

We are asked to find the value of the x.

To find the value of x, we will use the Pythagoras Theorem, by which,

Hypotenuse² = Base² + Perpendicular².

or, x² = 8² + 15²

or, x² = 64 + 225

or, x² = 289 = 17²

or, x = 17.

∴ The length of the side length x = 17 units, for the given right-angled triangle, was found using the Pythagoras Theorem.

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The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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Answer:

28.125

Step-by-step explanation:

A bar weights 3 ounces, she has a box of 150 so you multiply

150 times 3 = 450

well one pound equals 16 ounces, so you divide

450 divide by 16 = 28.125

The two theoretical quantities of ANOVA (Analysis of Variance) are:
1. Between-group variance.

2. Within-group variance:

1. Between-group variance.

This is the variance that can be attributed to differences between the group means.

It is calculated by comparing the mean of each group to the overall mean of all the data points.

The larger the between-group variance, the more likely there are significant differences between the groups.
2. Within-group variance:

This is the variance that can be attributed to differences within each group, i.e., the individual differences among the data points in each group.

It is calculated by comparing the individual data points in each group to their respective group mean.

The smaller the within-group variance, the more likely the groups are homogeneous.
In ANOVA, these two quantities are compared using an F-ratio.

If the between-group variance is significantly larger than the within-group variance, it indicates that there are significant differences between the group means, and the null hypothesis can be rejected.

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Answer:

35*x=280

Step-by-step explanation:

Answer:

x = 8

35 x 8 = 280

Step-by-step explanation:

Answer: slope: 2, y-intercept: (0,4)

Step-by-step explanation:

the equation y = 2x - 4 is written in slope intercept form: y = mx + b where m is the slope and b is the y-intercept

m = 2

b = -4

the slope is 2

and the y-intercept (if written as an ordered pair) is (0,4)

Answer:

3.47 and 3.21

Step-by-step explanation:

Let us assume the nails length be X

\(X \sim N(3.34,0.07^2)\)

Value let separated the top 3% is T and for bottom it would be B

\(P(X < T)= 0.97\)

Now converting, we get

\(P(Z < \frac{T-3.34}{0.07})= 0.97\)

Based on the normal standard tables, we get

\(P(Z < 1.881)= 0.97\)

Now compare these two above equations

\(\frac{T-3.34}{0.07} = 1.881 \\\\ T = 1.881 \times 0.07 + 3.34 \\\\ = 3.47\)

So for top 3% it is 3.47

Now for bottom we applied the same method as shown above

\(P(Z < \frac{B-3.34}{0.07})= 0.03\)

Based on the normal standard tables, we get

\(P(Z < -1.881)= 0.03\)

Now compare these two above equations

\(\frac{B-3.34}{0.07} = -1.881\)

\(= -1.881 \times 0.07 + 3.34 \\\\ = 3.21\)

hence, for bottom it would be 3.21

In the triangle ABC, i) ABC = 52.12° ii) BCA = 31.08° and iii) AB = 8.11cm.

Based on the provided information, ∠ BAC = 96.8°; AC = 12.4cm, and BC = 15.6cm

i) According to the law of sine,

Sin ∠A/a = Sin ∠B/b = Sin ∠C/c where a is the length opposite to ∠A, and so forth.

Hence, based on the information, ∠ABC = ∠B

Sin ∠B/AC = Sin ∠A/BC

Sin ∠B/12.4 = Sin 96.8/15.5

Sin ∠B = (Sin 96.8/15.5)*12.4

∠B = Sin^-1((Sin 96.8/15.5)*12.4)

∠B = 52.12°

ii) As the sum of interior angles of a triangle is 180°. ∠As BCA = ∠C

∠A + ∠B + ∠C = 180

96.8 + 52.12 + ∠C = 180

∠C = 31.08

iii) According to the law of cosine,

c^2 = a^2 + b^2 – 2ab cos C where C is the angle opposite to c.

BC^2 = AB^2 + AC^2 – 2(AB)(AC)cos98.6

15.6^2 = AB^2 + 12.4^2 – 2(AB)(12.4)cos98.6

Solving for AB,

AB = 8.11cm

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Remember that when you multiply a number by 10, the decimal point is moved one place to the right. Then:

Therefore, the answer is 275.4

Step-by-step explanation:

this is just a simplified situation. normally people have more deductions from their salary than just taxes.

but anyway,

100% = $52,000

1% = 100%/100 = 52000/100 = $520

20% = 20×1% = 20 × 520 = $10,400

so, she pays $10,400 taxes.

and that leaves her from her salary

52000 - 10400 = $41,600

as net pay.

FYI - to calculate the remaining amount, we could have also done the following :

20% get deducted, so, 80% remain.

80% = 80×1% = 80 × 52000/100 = 52000 × 80/100 =

= 52000 × 0.80 = $41,600

Answer:

A

Step-by-step explanation:

The function representing the price per video game after the store's markup can be defined as f(x) = 1.25x + 1.50, where x is the manufacturer's cost of the game.

To calculate the price per video game after the store's markup, we need to consider two factors: the store's markup percentage and the shipping charge. The store adds a 25% markup on each game, which means the price is increased by 25% of the manufacturer's cost. Mathematically, this can be represented as 1.25x, where x represents the manufacturer's cost.

In addition to the markup, the store also incurs a shipping charge of $1.50 on each game. Regardless of the manufacturer's cost, this fixed charge is added to the price. Therefore, we add $1.50 to the previously calculated markup price.

Combining both factors, the function representing the price per video game after the store's markup can be defined as f(x) = 1.25x + 1.50. This function takes the manufacturer's cost (x) as input and returns the final price per game after considering the 25% markup and the $1.50 shipping charge.

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Answer:

3.935 x 10^5.

Step-by-step explanation:

There are five digits after the first 3 so  it will be 10^5.

The answer is 3.935 x 10^5.

393500 equals 3.935×10⁵

If we write xⁿ then we mean to say that x is multiplied n times.

The exponent of a number says how many times the number is multiplied by itself.

393500=3.935×100,000=3.935×10⁵

Hence, 393500=3.935×10⁵

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Answer:

b140

Step-by-step explanation:

14*10=140 that's all

Answer:

the answer is B

Step-by-step explanation:

because 14*10 is 140

The two different expressions for the total cost will be written as:-

C = 2S x 1.065

C = 0.13S + 2S

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Benita buys 2 shirts for the same price, s. The sales tax rate is 6.5%.

The two expressions for the total cost of the two shirts will be:-

C = 2S x ( 1 + 0.065)

C = 2S x ( 1.065)

The second way of writing the expression is:-

C = 2S x  0.065 + 2S

C = 0.13S + 2S

Hence, the expressions are C = 2S x 1.065 and C = 0.13S + 2S.

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The length of the rope must be, at least, 5.9 meters.

The rope will allow the sheep to move in an almost perfect circle (except for the part where the shed is) so we will have 3/4 of a circle.

So here we just need to find the length L of the rope such that:

10 yd² = (3/4)*pi*L^2

Where (3/4)*pi*L² is the area of 3/4 of a circle of radius L.

and pi = 3.14

Solving for L we will get:

L = √( 10 yd²*(4/3*3.14)) = 6.4 yd

Writting this in meters, we will get:

1 yd = 0.9144 m

then:

L = 6.4* 0.9144 m = 5.9m

The rope must be at least 5.9 meters long.

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Answer:

51 Yards

Step-by-step explanation:

Each side is 36 yards. split the square in half(corner to corner) making two right triangle use the pythagorean theorem (\(A^{2}\) + \(B^{2}\) =\(C^{2}\) ) to solve.

\(36^{2}\)+\(36^{2}\)= \(C^{2}\)

1296+1296= 2592

√2592= 50.911

50.911 rounds up to 51

The length of each walkway would be,

⇒ 51 yards

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

We have to given that;

A school has a square courtyard and wants to create diagonal walkways.

Here, The length of each side of the courtyard is 36 yards.

Now, The length of each walkway would be,

⇒ √ 36² + 36²

⇒ √ 1296 + 1296

⇒ √ 2592

⇒ 50.91

⇒ 51 yards

Thus, The length of each walkway would be,

⇒ 51 yards

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The perpendicular height of the given oblique prism is 6 units. The answer is not one of the options given, but it is closest to option :

(d) 8 units

We can use the formula for the volume of an oblique prism, which is:

V = Bh, where B is the area of the base and h is the perpendicular height.

We are given that the volume is 144 cubic units and the area of the base is 24 square units. Substituting these values into the formula, we get:

144 = 24h

Simplifying, we can divide both sides by 24:

h = 6

Therefore, the perpendicular height of the prism is 6 units. The answer is not one of the options given, but it is closest to option d, which is 8 units.

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The time it would take Mabel to edit a 15-minute long video is 20 hours.

The first step is to determine how long it would take Mabel to edit a 1-minute long video. The time it would take is known as Mabel's unit rate.

Unit rate = number of hours it takes to edit / length of the video

4 / 3 hours per minute

The next step is to multiply the unit rate by the length of the video.

Time it would take to edit a 15-minute long video = unit rate x length of he video

4/3 x 15 = 20 hours

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Answer:

3 miles

Step-by-step explanation:

Answer:

3 miles.

Step-by-step explanation:

The radius is always half of the diameter.