What is the measure of angle F?

The hypothesis test to conduct in this situation is a two-sample test for

means, specifically a paired-sample t-test.

This is because the same group of workers is being tested twice, under

two different conditions: without exercise breaks and with exercise breaks.

The two sets of data are dependent because they are coming from the

same group of individuals, and the goal is to determine if there is a

statistically significant difference in their well-being between the two

conditions.

A paired-sample t-test is appropriate because it can compare the means of

two related samples, and it takes into account the correlation between the

data points in each sample.

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Answer:

6+3

Step-by-step explanation:

The house was in the shape of an octagon, with eight separate bedrooms on each side.

The house described in the statement has an octagonal shape. An octagon is a polygon with eight sides, characterized by its eight equal angles. In this case, each side of the house corresponds to one of these angles, resulting in eight separate bedrooms on each side of the octagonal structure.

The choice of an octagon as the shape of the house can have various implications. Octagonal buildings are often admired for their unique architectural design and aesthetic appeal. The shape provides symmetry and balance, allowing for an interesting and visually pleasing structure. Additionally, an octagonal layout can offer practical advantages in terms of space utilization and room distribution. In the case of the house described, each side of the octagon accommodates a separate bedroom, providing privacy and ample living space for its occupants. The symmetrical arrangement of the bedrooms around the central area of the house could create a harmonious and well-organized living environment. Overall, the octagonal shape of the house with eight separate bedrooms on each side offers both architectural and functional benefits.

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer: 19/28

Step-by-step explanation:

3/7 + 1/4

Find the LCM for 7 and 4

12/28 + 7/28 = 19/28

(a) The set {(x1,x2)T|x1 + x2 = 0} is a subspace of R2.

To check whether the given set is a subspace of R2, we need to check whether it is closed under vector addition and scalar multiplication. Let u = (u1,u2)T and v = (v1,v2)T be two arbitrary vectors in the set, and let c be an arbitrary scalar. Then:

u + v = (u1 + v1, u2 + v2)

Since u1 + v1 + u2 + v2 = (u1 + u2) + (v1 + v2) = 0 + 0 = 0 (since u and v are in the set), we see that u + v is also in the set.

c*u = (c*u1, c*u2)

Since c*u1 + c*u2 = c*(u1 + u2) = c*0 = 0 (since u is in the set), we see that c*u is also in the set.

Therefore, the set {(x1,x2)T|x1 + x2 = 0} is a subspace of R2.

(b) It is not a subspace of R2

To check whether the given set is a subspace of R2, we need to check whether it is closed under vector addition and scalar multiplication.

Let u = (u1,u2)T and v = (v1,v2)T be two arbitrary vectors in the set, and let c be an arbitrary scalar. Then:

u + v = (u1 + v1, u2 + v2)

Since u21 = u22 and v21 = v22 (since u and v are in the set), we see that (u1 + v1)2 = (u2 + v2)2. Therefore, u + v is in the set.

c*u = (c*u1, c*u2)

Since u21 = u22 (since u is in the set), we see that (c*u1)2 = (c*u2)2. Therefore, c*u is in the set.

However, the set {(x1,x2)T|x21 = x22} is not a subspace of R2 because it does not contain the zero vector (0,0)T, which is required for any set to be a subspace.

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Answer:

Translation as Triangle A has been translated by vector (3,-1) to now being (-2,-3)

Translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

The process of changing the location of the image on the coordinate system will be known as the translation.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have merely changed their direction or directions.

Given that Translate Triangle A by a vector (3, -1) to give triangle B. Then, rotate your triangle B 180° around the origin to give triangle C.

Triangle A translation ⇒ (3,-1)

The second translation = (-2,-3).

Therefore, the translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

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This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.

If there are R125 in a box and half of the total is removed each day, it will take 10 days to reduce the total to 25 cents. This is because the total amount is being halved each day, and the amount remaining at the end of each day is the amount left at the start of the day, divided by two. This can be expressed mathematically using the formula\(R125/(2^t)\) = 25, where t is the number of days.If we solve the equation for t, we get t = log2(R125/25). This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.To calculate this process over the 10 days, we can use the formula \(R125/(2^t)\) for each day, where t is the day number. Starting at day 0, the amount remaining would be R125. At the end of day 1, the amount remaining would be R125/2 = R62.50. At the end of day 2, the amount remaining would be R62.50/2 = R31.25. This process continues until at the end of day 10, the amount remaining would be R0.25.

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In the trigonometry relation the value of θ is 45 degrees and the coterminal angle between 0° < θ < 360° is 315 degrees

To find the coterminal angle of an angle, we just add or subtract multiples of 360°. from the given angle. The number of coterminal angles of an angle is infinite because there is an infinite number of multiples of 360°. If two angles are coterminal, then their sines, cosines, and tangents are also equal.

In other words, if two angles are coterminal, they have the same trigonometric functions, despite having different degrees.

If sec θ = √2

θ = arc sec (√2)

θ = arc cos (1/√2))

θ = 45 degrees

Coterminal of angle 45 degrees between 0° < θ < 360°

360 - 45 = 315.

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The given question is incomplete, So taking a similar question:

If sec 0 = √2, find 0 and identify all angles 0° < 0 < 360° that are co-terminal with the given angle.

Answer:

12*56-56+11=12

Step-by-step explanation:

12 for 56

The equation that will be used to solve the total number of loaves will be 10 + 3h.

Based on the question, the equation to solve the question will be:

= 10 + 3(h)

= 10 + 3h

where, h = number of hours

The dependent variable is 10 and the independent variable is 3h.

The number of loaves that the baker will make if he has 4 hours left in his shift will be:

= 10 + 3h

= 10 + 3(4)

= 10 + 12

= 22 loaves.

He'll make 22 loaves

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Answer:

A=hb2

Step-by-step explanation:

A continuous function is a function where small changes in the input result in small changes in the output, with no abrupt jumps or breaks in the function's graph.

Since f(x,y) is independent of x, we can write it as f(x,y) = g(y). We are given that the integral of g(x) from 0.3 to 10 is 1, so we can write:

∫0.3^10 g(x) dx = 1

Using this information, we can find g(y) by integrating g(x) with respect to x:

g(y) = ∫0.3^10 g(x) dx / ∫0^10 dx
g(y) = 1 / 9.7

Now, we can find f(x,y) by substituting g(y) into f(x,y) = g(y):

f(x,y) = g(y) = 1 / 9.7

We need to find the integral of f(x,y) over the rectangle R, which is:

∫0^3 ∫0^10 f(x,y) dy dx
∫0^3 ∫0^10 1 / 9.7 dy dx
(1 / 9.7) ∫0^3 ∫0^10 dy dx
(1 / 9.7) * 3 * 10
= 3.0928

Therefore, the value of the integral of f(x,y) over the rectangle R is 3.0928.

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Answer:

\(\frac{39}{25}\), \(\sqrt{8}\), \(\frac{77}{20}\)

Step-by-step explanation:

with the help of algebraic calculator...

sq root of 8 ≈ 2.82842712

77/20 = 3.85

39/25 = 1.56

and ordering them from least to greatest: \(\frac{39}{25}\), \(\sqrt{8}\), \(\frac{77}{20}\)

Answer:

\(\dfrac{39}{25};\sqrt{8} ;\dfrac{77}{20}\)

Step-by-step explanation:

\(\dfrac{39}{25}= \dfrac{39\cdot4}{25\cdot4}=\dfrac{156}{100} =1.56 < 2=\sqrt{4} < \sqrt{8} < \sqrt{9} =3 < 3.85=\dfrac{385}{100}=\dfrac{77}{20}\)

The volume of cube with a side length of 5 meters is 125 cubic meters, while volume of cube with side length of 4 meters is 64 cubic meters. The difference between the volumes of two cubes is 61 cubic meters.

The volume of a cube is given by V = \(s^3\), where s is the side length of the cube. To find the difference between the volumes of two cubes, we can subtract the smaller volume from the larger volume.

So, the volume of the cube with side length 5 meters is V1 = \(5^3\) = 125 cubic meters, and the volume of the cube with side length 4 meters is V2 = \(4^3\) = 64 cubic meters.

The volume of a cube is given by \(s^3\), where s is the length of the side of the cube. The volume of a cube with a side length of 5 meters is \(5^3\) = 125 cubic meters, and the volume of a cube with a side length of 4 meters is \(4^3\) = 64 cubic meters.

The difference in volumes is V1 - V2 = 125 - 64 = 61 cubic meters. Therefore, the difference in volumes of the two cubes is 61 cubic meters.

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Answer:

The length of one leg of this right triangle is 4/√2 = 2√2 cm.

The ratio of increased seats will be 5:12:16.

Ratio is a comparison between two or more quantities expressed as a fraction or a set of relative quantities it is used to compare the size of one number to another or the compare changes overtime ratio can be expressed in word as fraction or decimal receiver in important concept in mathematics used to analyse data and solve problem.


This can be found by calculating the increase as a percentage of the current number of seats.

For Financial Management, the increase of 26% is calculated as (4 x 0.26) + 4 = 5.04, which rounds up to 5.

For Marketing, the increase of 50% is calculated as (8 x 0.5) + 8 = 12.

For Office Practice, the increase of 60% is calculated as (10 x 0.6) + 10 = 16.

Therefore, the ratio of the increased seats will be 5:12:16.

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Answer:

It Is9

Step-by-step explanation:

The required distance of Cori from where he started is 35km.

Distance is a quantitative or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimation based on other criteria in physics or everyday usage. Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is also used metaphorically to mean a measurement of the amount of difference between two similar objects or a degree of separation. The concept of a metric space is used to codify most such conceptions of distance, both physical and metaphorical.

Given,

Cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers.

The distance of Cori from starting point=9+20+6

=15+20

=35

Hence, the required distance of Cori from where he started is 35km.

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Answer:

D. y=-3x

Step-by-step explanation:

Direct Proportion

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

\(\displaystyle \frac{y}{x}=k\)

Where k is the constant of proportionality.

Solving for y:

y=kx

The only choice representing a direct proportion is:

D. y=-3x

Answer:

D

Step-by-step explanation:

Answer:

wouldn't it be 81 cause the inner triangle is just a mini version of the bigger triangle?

360-81= 279

279÷3= 93 (shorter side)

93+93= 186 (longer side)

360-279= 81

Answer: A

Step-by-step explanation:

3x² - 10x + 5 = 0

a = 3      b = -10     c = 5

Δ = b²- 4ac = 100 - 4.3.5 = 40 > 0 => have 2 solutions

=> x = \(\frac{10+\sqrt{40} }{6}\) or x = \(\frac{10-\sqrt{40} }{6}\)

\(x= \frac{10\pm \sqrt{40} }{6}\) is the solution to the given quadratic equation.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = \(ax^{2} +bx+c\) = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Quadratic formula = \(\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}\)

Given quadratic equation

\(3x^{2} -10x+5=0\)

a = 3, b = -10, c = 5

Quadratic formula = \(\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}\)

\(x= \frac{-(-10)\pm \sqrt{(-10)^{2} -4(3)(5)} }{2\times3}\)

⇒ \(x= \frac{10\pm \sqrt{100 -60} }{6}\)

⇒ \(x= \frac{10\pm \sqrt{40} }{6}\)

Hence,  \(x= \frac{10\pm \sqrt{40} }{6}\) is the solution to the given quadratic equation.

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Answer:

\(f(x) = 15x^2 -14x - 8\)

\(g(x) = 5x + 2\)

Step-by-step explanation:

Represent the two polynomials with f(x) and g(x)

The question requires that we assume values for f(x) and g(x) as long as the condition in the question is met;

Let

\(f(x) = 15x^2 -14x - 8\)

\(g(x) = 5x + 2\)

To determine if the condition is met, we need to divide f(x) by g(x)

\(\frac{f(x)}{g(x)} = \frac{15x^2 -14x - 8}{5x + 2}\)

Factorize the numerator

\(\frac{f(x)}{g(x)} = \frac{15x^2 - 20x + 6x - 8}{5x + 2}\)

\(\frac{f(x)}{g(x)} = \frac{(5x + 2)(3x - 4)}{5x + 2}\)

Cross out 5x + 2

\(\frac{f(x)}{g(x)} = 3x - 4\)

The result is referred to as quotient, Q

\(Q = 3x - 4\)

Note that Q and g(x) have the same degree of 1

The probability of getting exactly 2 dead batteries is 110 / 455 ≈ 0.241 (rounded to three decimal places). None of the given options (0.073, 0.220, None of these, 0.0001) match the calculated probability of 0.241.

To calculate the probability of getting exactly 2 dead batteries when selecting 3 batteries without replacement, we need to use the concept of combinations.

The total number of ways to select 3 batteries from a bag of 15 is given by the combination formula: C(15, 3) = 15! / (3!(15-3)!) = 455.

To get exactly 2 dead batteries, we need to consider two cases:

Selecting 2 dead batteries and 1 alive battery: There are 5 dead batteries and 10 alive batteries to choose from. The number of ways to select 2 dead batteries and 1 alive battery is given by C(5, 2) * C(10, 1) = 10 * 10 = 100.

Selecting 3 dead batteries: There are 5 dead batteries to choose from. The number of ways to select 3 dead batteries is given by C(5, 3) = 10.

So, the total number of ways to get exactly 2 dead batteries is 100 + 10 = 110.

Therefore, the probability of getting exactly 2 dead batteries is 110 / 455 ≈ 0.241 (rounded to three decimal places).

None of the given options (0.073, 0.220, None of these, 0.0001) match the calculated probability of 0.241.

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Answer: B

Step-by-step explanation:

B) Copernicus rediscovered Aristarchus's heliocentric model. The event which took place during the Copernican revolution.

Answer: HELP

Step-by-step explanation:

HELP MEEEE

Answer:

Slope is: 1/2

Y-intercept is: 4

Equation is: y=1/2x+4

*Use Desmos Graphing Calculator to graph and get the answers for #3*

You can use do 37+32.5 and subtract that from 570

Hoped this Helped

Answer:

27850

Step-by-step explanation:

5% of 29,000=1450

2900-1450=27850

Brainliest pls! Help me out

Answer:

False

Step-by-step explanation:

The answer is False

The given statement is false, as the letters are used as keys in the dictionary.

The dictionary used in counting letters examples to keep track of letter frequencies uses the letters as the key and the count as the value. This means that for each letter encountered in a string, the value corresponding to the key (letter) in the dictionary is incremented by 1.

For example, if the string is "hello", the dictionary would initially be empty, and for each letter encountered in the string, the value for the corresponding key in the dictionary would be incremented by 1, resulting in a dictionary like {"h": 1, "e": 1, "l": 2, "o": 1}.

Therefore, the correct answer is false, as the letters are used as keys in the dictionary.

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Answer:

\( \huge{ \orange{y + 3 = 2(x + 7)}}\)

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1) \\ \)

where

m is the slope

( x1 , y1) is the point

From the question we have

\(y - - 3 = 2(x - - 7) \\ y + 3 = 2(x + 7)\)

Hope this helps you