diana ran a race of 700 meters in two laps of equal distance. her average speeds for the first and second laps were 7 meters per second and 5 meters per second, respectively. what was her average speed for the entire race, in meters per second?

I would suggest finding k first.

If [tex]k^2-3k+5=0\\[/tex],

[tex]k=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(5)}}{2(1)}[/tex] by the quadratic formula.

[tex]k=\emptyset[/tex] by the discriminant being negative.

So the expression in terms of k that you need to find cannot be determined.

Hence, the predicted mean weight of progeny is 77.6 g (rounded off to three significant figures).

As given that the mean fruit weight of a population of tomato plants is 60 g and the heritability coefficient (h_p) is 0.12, it is required to predict the mean weight of the progeny if tomato plants whose fruit averaged 80 g were selected from the original population and interbred .

The formula for the predicted mean weight of progeny (MP) is given as: MP =  mean weight of selected individuals + (h_p) × (mean weight of original population - mean weight of selected individuals)

Using the above formula, we have ,mean weight of selected individuals = 80 g mean weight of original population = 60 gh_p = 0.12Substituting the given values in the above formula, we get :[tex]MP =  80 + 0.12 × (60 - 80)MP =  80 + 0.12 × (-20)MP =  80 - 2.4MP =  77.6 g[/tex]

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The theοrem that verifies that WXY=PME is AA, which stands fοr "Angle-Angle" similarity theοrem.

Accοrding tο the AA similarity theοrem, if twο angles οf οne triangle are cοngruent tο twο angles οf anοther triangle, the triangles are similar.

In this case, we have twο cοrrespοnding angles in triangle WXY and triangle PME that are cοngruent: angle WXY is cοngruent tο angle PME because they are vertical angles, and angle XYW is cοngruent tο angle MEP because they are alternate interiοr angles fοrmed by parallel lines.

Therefοre, by the AA similarity theοrem, we can cοnclude that triangle WXY and triangle PME are similar.

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x + 3 / 0 = y / 6 = z - 2 / 3 is the required set of parametric equation and symmetric equation of line.

Given the point (-3, 0, 2) and the vector v = 6j + 3k, we need to find the set of parametric equation and symmetric equation of the line through the point and parallel to the given vector.

Let the line be L and a point on the line be P(x, y, z).

Then, the vector from (-3, 0, 2) to P is given by

r = OP = i(x + 3) + jy + k(z - 2)

Since L is parallel to the vector v = 6j + 3k, the direction ratios of L are proportional to the components of v. Thus, the direction ratios of L are 0, 6, and 3.

Therefore, the parametric equations of L are:

x + 3 = 0 ⇒ x = -3y = tz - 2 = 3t + 2

where t is a parameter, and the symmetric equations are x + 3 / 0 = y / 6 = z - 2 / 3. This is the required answer.

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0 is a 100% decrease of 98.7. Hope this helped!

The vertices of image L′M′N′ are L′(−5, −1), M′(0, −1), and N′(−5, −2).  

Rotating a figure 90° clockwise about the origin means that each point of the figure will be moved to a new position that is located 90° clockwise from its original position, with respect to the origin of the coordinate plane.

To rotate a figure 90° clockwise about the origin follow the steps:

1. Swap the x- and y-coordinates of each point.

2. Negate the new x-coordinates.

3. Leave the new y-coordinates as they are.  

Here we have

Triangle LMN has vertices at L(−1, 5), M(−1, 0), N(−2, 5)

Triangle LMN is rotated 90° clockwise about the origin.  

Using the above condition

L(−1, 5) => (−(5), −1) => (−5, −1)

M(−1, 0) => (−0, −1) => (0, −1)  

N(−2, 5) => (−(5), −2) => (−5, −2)    

Therefore,

The vertices of image L′M′N′ are L′(−5, −1), M′(0, −1), and N′(−5, −2).  

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Answer:

The sequence 100, 50, 10, 5, 1, ... is NOT a geometric sequence because there is no single constant ratio that multiplies each term to get the next one.

Answer:

the integer solutions to the inequality -2 < x < 2 are x = -1, 0, and 1.

Step-by-step explanation:

The inequality is written as:

-2 < x < 2

This inequality can be read as "x is greater than -2 and less than 2". In other words, x is between -2 and 2, but not including -2 or 2.

The integer solutions that satisfy this inequality are -1, 0, and 1.

Therefore, the integer solutions to the inequality -2 < x < 2 are x = -1, 0, and 1.

Answer:

Step-by-step explanation:

Let's simplify the expression step by step:

(5-3i)(-7-31) - (6-2i)

= (5)(-7) + (5)(-31i) - (3i)(-7) - (3i)(-31) - 6 + 2i

= -35 - 155i + 21i + 93 - 6 + 2i

= -35 + 87 - 63i + 2i - 155i

= 52 - 216i

Therefore, the simplified expression is 52 - 216i.

Answer: 36

Step-by-step explanation: Since the sum of the angles in a triangle is 180 degrees, we can set up an equation:

x + 2x + 2x = 180

Simplifying the equation, we get:

5x = 180

Dividing both sides by 5, we get:

x = 36

Therefore, the value of x is 36 degrees.

Answer:

look at the photo.........................

The third term of a sequence is 14. Term to term rule is square, then subtract 11. The first term of the sequence is 6.

The given information is about the third term of a sequence which is 14, and the term to term rule is square, then subtract 11.

We have to find the first term of the sequence. The sequence can be calculated using the following formula:

An = A1 + (n-1)d

Where, An is the nth term of the sequence A1 is the first term of the sequence d is the common difference between the terms of the sequence. Let's solve the problem by finding the value of the common difference between the terms of the sequence.

Using the given information, we can write: A3 = 14=> A1 + (3 - 1)d = 14=> A1 + 2d = 14 ----- (i)

Also, the term to term rule is square, then subtract 11.So, we can write, A2 = A1 + d = (A1)² - 11 ---- (ii)

Substituting the value of d from equation (ii) in equation (i),

we get: A1 + 2 [(A1)² - 11] = 14 Simplifying this equation, we get: A1² - 2A1 - 12 = 0 On solving this quadratic equation

we get: A1 = -2 or A1 = 6 Ignoring the negative value of A1, we get the first term of the sequence to be 6.

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Answer:

Step-by-step explanation:

In this expression, the number 3 represents the initial group of friends to whom Carol told the joke.

The base number 4 represents the number of people each friend told the joke to on the following day.

The exponent x represents the number of days that have passed since Carol first told the joke, and as a result, the number of "generations" of people who have heard the joke.

Therefore, 4 raised to the power of x represents the total number of people who have heard the joke after x days, including Carol's initial group of friends and all subsequent generations of people who have been told the joke by those who heard it before.

Finally, multiplying 3 and 4 raised to the power of x gives the total number of unique people who have heard the joke after x days, since the initial group of friends is not included in the later generations.

Using division operation, the length it will take the three hoses to fill the pool is 8.33 hours.

The division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.

The division operation involves the dividend, the divisor, and the result called the product.

In this situation, it will take Hose A 10 hours to fill the pool and Hose B 5 hours.  If the two hoses are in use, it will 7.5hours (10 + 5)/2.

When the third hose is added, it will take 8.33 hours (10 + 5 + 10)/3.

The first hose's filling rate for the pool = 10 hours

The second hose's filling rate for the pool = 5 hours

The third hose's filling rate for the pool = 10 hours (the slower rate)

The total number of hours used by the three hoses = 25 hours (10 + 5 + 10)

The number of hoses used = 3

The length of time it will take the 3 hoses to fill the pool = 8.33 hours (25/3)

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The distance from point AA to BB is 577 ft.

An angle of depression is a measure of an angle formed when an observer views an object below the horizontal plane.

In the given question, let the distance from lighthouse to point AA be represented by x. So that;

Tan θ = opposite/ adjacent

Tan 11 = 137/ x

x = 137/ 0.1944

x = 704.733 ft

Let the distance from the lighthouse to point BB be represented by y, so that;

Tan 47 = 137/ y

y = 137/ 1.0724

y = 127.751 ft

Thus,

x - y = 704.733 - 127.751

                                            = 576.982

The distance between point AA and point BB is 577 ft.

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Answer:

Step-by-step explanation: DEFINITIONS vvvvv

Transformations

Refers to the movement of objects in the coordinate plane. There are 4 types: Translation, Reflection, Rotation, and Dilation

Reflection

transformation that flips a figure across a line to form its mirror image on the opposite side of the line

Translation

Transformation that slides a figure.

Rotation

A transformation in which a figure is turned around a point

Dilation

A transformation that changes the size of an object, but not the shape.

Congruence

correspondence of parts.

center of dilation

in a dilation, the fixed point about which the figure is enlarged or reduced

similar

Figures that have the same shape but not necessarily the same size

scale factor

The ratio of any two corresponding lengths in two similar geometric figures.

enlargement

a dilation with a scale factor greater than 1. Image will be greater than the pre-image

reduction

a dilation with a scale factor less than 1. Image will be smaller than the pre-image.

remote interior angles

the angles of a triangle that are not adjacent to a given exterior angle

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Transversal

a line that intersects two or more lines at different points

SAS Theorem (Side-Angle-Side)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Angle-Angle-Side (AAS) Theorem

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Side-side-side (SSS) Theorem

If the sides of two triangles are in proportion, then the triangles are similar.

Angle-Side-Angle (ASA) Theorem

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Angle-Angle-Angle (AAA)

does NOT prove triangles congruent because the sides could be different lengths.

Parallel lines

lines in the same plane that never intersect

From the given information provided, the number you are thinking of can be approximately 20.375.

Since the number you are thinking of is between 5 and 203, we can use the following steps to find it:

Take the average of the two endpoints: (5 + 203) / 2 = 104

Check if 104 is greater than or less than 71. Since 104 is greater than 71, we know that the number is between 5 and 104.

Take the average of 5 and 104: (5 + 104) / 2 = 54.5

Check if 54.5 is greater than or less than 17. Since 54.5 is greater than 17, we know that the number is between 17 and 54.5.

Take the average of 17 and 54.5: (17 + 54.5) / 2 = 35.75

Check if 35.75 is greater than or less than 5. Since 35.75 is greater than 5, we know that the number is between 5 and 35.75.

Take the average of 5 and 35.75: (5 + 35.75) / 2 = 20.375

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Alexis has 12 quarters and 8 dimes.

Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.

We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:

10d + 25q = 380

To make things easier, let's divide both sides of the equation by 5:

2d + 5q = 76

Now we can use the first equation to solve for d in terms of q:

d + q = 20

d = 20 - q

Substituting this into the second equation gives:

2(20 - q) + 5q = 76

Expanding the parentheses and simplifying, we get:

40 - 2q + 5q = 76

3q = 36

q = 12

Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:

d + q = 20

d + 12 = 20

d = 8

The total value of 12 quarters and 8 dimes is:

12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80


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The standard error of the mean represents a sample, while the standard deviation represents a population. The correct option is (c) sample; population

The standard error of the mean is a measure of the variability of sample means from multiple samples, while the standard deviation is a measure of the variability of individual data points from the mean of a single sample or population.

The standard error of the mean helps us estimate the accuracy of the sample mean as an estimate of the true population mean, while the standard deviation gives us an idea of how much the data points deviate from the mean. In statistics, it is important to distinguish between these two measures to properly interpret data and draw meaningful conclusions.

Therefore, the correct option is (c) sample; population

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The given question is incomplete, the complete question is:

The standard error of the mean represents a ___, while the standard deviation represents a _______.

a. law of large numbers; central limit theorem

b. population; sample

c. sample; population

d. central limit theorem; law of large numbers

Using RFID (radio frequency identification) technology, a supplier can use RFID tags on each crate, case, or shipping unit to create a digital shipping list.

Radio frequency identification (RFID) technology is a wireless communication technology that enables the automatic identification and tracking of objects. RFID tags contain a microchip and an antenna, and are typically attached to or embedded within objects such as crates, cases, or shipping units.

These tags can store information such as a unique identification number or product details, which can be read wirelessly by RFID readers or scanners.

When used in shipping and logistics, suppliers can attach RFID tags to each crate, case, or shipping unit to create a digital shipping list. As the products move through the supply chain, the RFID tags can be read at various checkpoints, providing real-time information on the location and status of the products.

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Answer: 90

Step-by-step explanation: I've done this before

The other diagonal of the rhombus is 4 cm.

The other diagonal of the rhombus can be found using the formula for the area of a rhombus, which is A = (d₁ × d₂)/2, where d₁ and d₂ are the lengths of the diagonals.

We're given that the area of the rhombus is 20 cm² and that one diagonal (d1) is 10 cm. Plugging these values into the formula, we get:

20 = (10 × d₂)/2

Simplifying, we get:

20 = 5 d₂

Dividing both sides by 5, we get:

d₂ = 4

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The unit rate at which the bakery makes donuts is 2 donuts per minute.

The slope of the line would also be 2 since the number of donuts made is directly proportional to the time elapsed. This means that for every minute that passes, 2 donuts are made.

To find the unit rate, we divide the total number of donuts made (30) by the time it takes to make them (15 minutes).

Unit rate = 30 donuts ÷ 15 minutes = 2 donuts per minute

To find the slope of the line, we use the formula:

slope = rise ÷ run

In this case, the "rise" is the number of donuts made and the "run" is the time elapsed. Therefore, the slope is:

slope = 30 donuts ÷ 15 minutes = 2 donuts per minute.

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The likelihood that the decision made based on the sample differs from the decision that would have been made if the entire population had been examined is called sampling risk.

Sampling error refers to the disparity between a sample's characteristics and those of the population from which it was drawn. It arises from using a sample rather than the whole population to estimate statistics such as mean, variance, and proportions.

Since a sample only represents a portion of the population, it cannot be expected to have the same characteristics as the whole population. The study of sampling error is an essential part of statistical analysis, as it is a source of uncertainty in making inferences about the population from a sample.

To reduce the sampling error in your survey, you can utilize a larger sample size. It is also beneficial to ensure that the sample is chosen randomly and without bias.

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Answer:

2/13

Step-by-step explanation:

A standard deck of cards has four suits
Therefore there are four twos, one from each suit
There are also 4 kings, one from each suit

P(two) = 4 twos/52 cards = 4/ 52 = 1/13

PKing) = 4 kings/52 cards = 1/13

P(two or king) = P(two) + P(king)
= 1/13 + 1/3

= 2/13

The company's total income, expenditure and profit is given respectively as follows:

a.) £180

b.) £146

C.) £34

To calculate the profit of the company the formula such as given below is used.

Profit = total income - total expenditure

The total income = 25+20+35+100 = £180

The total expenditure = 110+20+6+10 = £146

Profit = 180-146 = £34

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Answer:

16x + 3

Step-by-step explanation:

Simplify by combining like terms.  Add the terms with x, then add the integers.

8x + 8x + 4 - 1 = 16x + 3

All dodecagons must have eleven sides is false and and can be proven through a counter example.

What are dodecagons?

A dodecagons is a polygon which has 12 sides, 12 vertices. In this word do means "Two" and deca means "Ten".

Similar to other polygons, a dodecagon is also a two-dimensional plane figure. A regular dodecagon polygon has 12 equal sides and has 12 equal measures of angles. Irregular dodecagons have unequal sides and angles. Also, a dodecagon can be a convex polygon or concave polygon.

What is a Polygon?

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges.

So a dodecagon must have twelve sides even though it may be regular or irregular.

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When released, a yo-yo falls towards the floor due to conservation of energy.

Conservation of energy:

As it falls, its potential energy is converted into kinetic energy. When the yo-yo reaches its lowest point, it begins to spin rapidly, storing some of this kinetic energy as rotational energy. As the string wraps around the yo-yo's axle, it exerts a force which starts pulling the yo-yo back up towards your hand. This force converts the rotational energy back into potential energy as the yo-yo rises. When the yo-yo reaches your hand, it has regained all its initial potential energy, enabling it to return to your hand.

When the yo-yo reaches the end of the string, the rotational kinetic energy it has stored is used to wind the string back around the axle. This winding motion causes the yo-yo to move back up toward your hand. As the yo-yo moves back up, its potential energy increases, while its rotational kinetic energy decreases. Eventually, the yo-yo reaches your hand and comes to a stop.

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The solutions to the equation secθ = undefined from the  least to greatest is π/2 and 3π/2.

The equation secθ = undefined means that the secant of θ is undefined. Recall that the secant function is defined as 1/cosine(θ).

Therefore, secant is undefined when the cosine of θ is equal to zero, since division by zero is undefined.

In the interval [0, 2π), the cosine function equals zero at θ = π/2 and θ = 3π/2.

Therefore, the solutions to the equation secθ = undefined in the interval [0, 2π) are θ = π/2 and θ = 3π/2.

Listing the solutions from least to greatest, we have:

θ = π/2 ≈ 1.571

θ = 3π/2 ≈ 4.712

Note that these values are given in radians.

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