the official world record for the men's marathon is 2 hours and 3 minutes 59 seconds set by Haile Gebrselassie of Ethiopia. This berlin, marathon, held in September 2008, was 42.195 kilometers long. Write Gebrselassie's average speed for this marathon in meters per second. round your answer to the nearest tenth

We knοw that the y-intercept is -1 here we get -25a = -1, which means that a = 1/25.

We can write the pοlynοmial P(x) as:

[tex]P(x) = a(x-1)^2(x+5)[/tex]

where "a" is a cοnstant cοefficient that we need tο determine.

We knοw that the y-intercept is -1, which means that P(0) = -1. Plugging in x=0, we get:

[tex]P(0) = a(0-1)^2(0+5) = -25a[/tex]

Therefοre, -25a = -1, which means that a = 1/25.

Sο, the pοlynοmial P(x) is:

[tex]P(x) = (1/25)(x-1)^2(x+5)[/tex]

We can see that this pοlynοmial has a multiplicity 2 rοοt at x=1 and a multiplicity 1 rοοt at x=-5, as required.

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Answer:

3/4 of a second

Step-by-step explanation:

step by step in picture

The union and intersection operations for the sets E and F are given as follows:

The union and intersection sets of multiple sets are defined as follows:

The sets are given as follows:

Hence the union and intersection sets are given as follows:

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the baseball team needs 9 boxes for the order.

if the baseball team needs 100 new bats and can only put 12 bats in a box, we can find the number of boxes they need by dividing the total number of bats by the number of bats per box:

100 / 12 = 8.33

We must round to the nearest whole number because we cannot have a fraction of a box. Therefore, the baseball team must order 9 boxes.

If the team wants to make sure they get all the bats they ordered, the remaining 0.33, which represents the four bats that can't fit in a complete box, is important. They could either arrange an additional container to oblige the excess bats, or they could contact the provider to check whether they can buy simply 4 extra bats to finish their request.

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Step-by-step explanation:

tossing 2 coins at the same time, or one coin twice is the same scenario.

anyway, a probability is always the ratio

desired cases / all possible cases

when having 2 coin tosses, there are 2×2 = 4 total possible results (each toss has 2 possibilities, so 2 tosses have them 2×2 = 4 possibilities) :

head head

head tails

tail head

tail tails

how many of these 4 possible cases show at least one head ?

3 : head-head, head-tails, tails-head

so the probability to get at least one head is

3/4 = 0.75

formally calculated we would get this by saying either

this is NOT 2 times tail.

the probability of 2 times tails is

1/2 × 1/2 = 1/4 = 0.25

the probability for NOT 2 times tails is then

1 - 0.25 = 0.75

or by saying

this is either heads on the first coin and tails on the other, or tails on the first coin and heads on the other, or heads on both.

the probability of heads on the first and tails on the other coin is

1/2 × 1/2 = 1/4

the probability of tails on the first and heads on the other coin is

1/2 × 1/2 = 1/4

the probability of heads on both coins is

1/2 × 1/2 = 1/4

so, the total probability of all 3 cases is

1/4 + 1/4 + 1/4 = 3/4 = 0.75

you see : for an exclusive "or" condition we add the probabilities. for an exclusive "and" condition we multiply the probabilities.

There are [tex]n=11[/tex] scores given.

[tex]\text{Median}=\dfrac{11+1}{2} =6^{\text{th}} \ \text{term}=78[/tex]

[tex]\text{Lower quartile range}=\dfrac{11+1}{4} =3^{\text{rd}} \ \text{term}=74[/tex]

[tex]\text{Upper quartile range}=\dfrac{3(11+1)}{4} =9^{\text{th}} \ \text{term}=88[/tex]

Interquartile range of team [tex]\text{A}=88-74=14[/tex]

By box and whisker plots,

Median of team [tex]\text{A}=78[/tex]

Median of team [tex]\text{B}=86[/tex]

Median of team [tex]\text{C}=82[/tex]

Team B has the highest median

[tex]\bold{Interquartile \ range = upper \ quartile - lower \ quartile}[/tex]

Interquartile range of team [tex]\text{A}=14[/tex]

Interquartile range of team [tex]\text{B}=90-78=12[/tex]

Interquartile range of team [tex]\text{C}=86-70=16[/tex]

Therefore, Team B has the lowest interquartile range and the highest median.

The value of x and y in the figure is solved to be

x = 6

y = 8

Similar triangles are two triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal and their corresponding sides are proportional.

The proportion resulting from the similar triangles is used as follows

4 / 8 = 3 / x

4x = 8 * 3

x = (8 * 3) / 4 = 6

4 / 8 = (4 + 3) / (x + y)

4 / 8 = 7 / (6 + y)

cross multiplying

4 * (6 + y) = 8 * 7

(6 + y) = 8 * 7 / 4

(6 + y) = 14

y = 14 - 6

y = 8

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The area of the rectangle, triangles 1, and 2, and 3 are 128, 32, 24, and 16 respectively.

The formula for calculating the area of a rectangle is A = l * w

A = l w, where l is the rectangle's length and w is its width.

Triangle Area Formula: The triangle area formula is A = 1/2 * b * h

A = 1/2 * b * h, where b is the triangle's base and h is the triangle's height.

The area of rectangle = length * width = 16 * 8 = 128

The area of triangle 1 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 16 = 32

The area of triangle 2 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 12 = 24

The area of triangle 3 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 8 = 16

Subtract the area of the triangles from the area of the rectangle.

128 - (32 + 24 + 16) =56

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After the experiment begins, there will be 32 hours' worth of 23,233 bacteria.

Yet contagious microorganisms can give you a disease. Throughout your body, they multiply rapidly. Many emit toxins—a class of chemicals that may harm tissues and make you ill. The bacteria Streptococcus, Aureus, and E are just examples of those that cause infections.

Bacteria need to identify their preferred food source and be able to properly digest it in order to support growth and division. The simple sugar glucose is one of bacteria's preferred foods, much as people like eating candy.

To solve this problem, we can use the formula for exponential growth:

[tex]N = N_0 * 2^{(t/T)[/tex]

where:

N₀ = initial population

N = final population

t = time elapsed

T = doubling time (time it takes for the population to double)

T = t/log₂(N / N₀) = 14/log₂ (7000/100) = 1.89 hours

Now we can plug in all the values and solve for N:

[tex]N = N_o * 2^{(\frac{t}{T})} = 100*2^{(\frac{18}{1.89})} = 23,233[/tex]

Rounding to the nearest whole number, we get:

N = 23,233

Therefore, there will be approximately 23,233 bacteria in 32 hours from the start of the experiment.

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After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Step-by-step explanation:

So we can start gathering all the variables. 2, 5, 7, and c. So starting from the beginning. Two more means 2+ something. Next, the quotient if a number (c) and 5. That would be c/5. Is 7 means =7. Now to combine it all. 2+ c/5 = 7

The p-value was slightly above the threshold, the study's findings still suggest that the online medium may be more effective in enhancing student satisfaction levels in a Quantitative reasoning course.

The study aimed to determine whether there was a significant difference in student satisfaction levels between traditional face-to-face classes and online classes in a quantitative reasoning course.

The samples included students from four face-to-face classes and four online classes offered at the same university. The study was exploratory in nature, and therefore, the levels of significance were relaxed to the .10 level.

The independent samples t-test showed that the p-value was slightly above the conventional threshold but was rapidly approaching significance (i.e., p=.06). The results showed that students in online classes reported higher levels of satisfaction than those in the face-to-face classes.

The study is significant because it provides evidence to educators on what medium works better in producing quantitatively knowledgeable practitioners.

Although the p-value was slightly above the threshold, the study's findings still suggest that the online medium may be more effective in enhancing student satisfaction levels in a quantitative reasoning course.

Further research could be conducted to validate these findings and determine the reasons behind the observed difference in satisfaction levels.

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Answer:

Step-by-step explanation:

You want to identify intervals where the graph is increasing and where it is decreasing.

A graph is "increasing" if it is going up as you go from left to right on the graph. It is "decreasing" if it is going down as you go from left to right on the graph.

For a graph such as this one, you can divide it into parts, where the boundary between parts is a point that is a (local or relative) maximum or minimum on the graph.

The high points on this graph are at x=-4 and x=2. The graph is increasing in the intervals leading up to the high points.

The low points on this graph are at x=0 and x=4. The graph is decreasing on the intervals leading up to the low points.

The direction (increasing, decreasing) are indicated by green and magenta arrows, respectively. The interval boundaries are marked by blue lines.

We use round parentheses ( ) to designate the intervals, because the flat spots and turning points are not included in the intervals of increase or decrease.

__

Additional comment

When we say "leading up to" the turning point, we mean as you follow the graph from left to right. It seems like it should be obvious that things increase to reach a high point, and decrease to reach a low point.

You can write the first decreasing interval as an inequality:

  -4 < x < 0

This is written in "interval notation" with the lower limit of the interval on the left: (-4, 0).

If the endpoint of an interval is included in the interval, the bracket used is a square bracket:

  -6 ≤ x < 5   ⇔   [-6, 5)

The function f(x) = x² - x - 2 has x-intercepts at points x = 2 and x = - 1

To find the x-intercepts of the function, we set f(x) equal to zero and solve for x:

x² - x - 2 = 0

Factoring the left side, we get:

(x - 2)(x + 1) = 0

This gives us two solutions:

x - 2 = 0 or x + 1 = 0

Solving for x, we get:

x = 2 or x = -1

So the two x-intercepts of the function are x = 2 and x = -1.

To find the y-intercept of the function, we set x = 0 and evaluate f(x):

f(0) = 0² - 0 - 2 = -2

So the y-intercept of the function is y = -2.

To show that there is a point between the two x-intercepts where the function takes on a negative value (i.e., dips below the x-axis), we can use the fact that the function is a parabola that opens upward (since the coefficient of the x² term is positive). This means that the function is negative to the left of the left x-intercept (x = -1), and also negative to the right of the right x-intercept (x = 2). Since the function is continuous, it must pass through the x-axis at some point between these two x-intercepts. Therefore, there must be a point between x = -1 and x = 2 where the function takes on a negative value.

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To change a decimal to a percentage, we multiply it by 100 and add a percent sign (%).

Therefore, to change 8.28 to a percentage, we multiply it by 100 and get:

8.28 x 100 = 828%

So, 8.28 expressed as a percentage is 828%.

Step-by-step explanation:

The answer is 828%

The decimal 8.28 equals 828%

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 8.28 × 100 = 828% ( Which is the answer ).

Which is the answer

Thus the answer to your problem is, 828%

Step-by-step explanation:

3.

remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides. A, B, C are the corresponding opposite angles.

and again, the sum of all angles in a triangle is always 180°.

so, the angle opposite of W = 180 - 90 - 60 = 30°.

and we get

6×sqrt(3)/sin(60) = W/sin(30) = W / 1/2 = 2W

W = 6/2 × sqrt(3)/sin(60) = 3×sqrt(3)/sin(60) =

= 3×sqrt(3) / sqrt(3)/2 = 6

X we get via Pythagoras

X² = (6×sqrt(3))² + W² = 36×3 + 6² = 108+36 = 144

X = sqrt(144) = 12

in the lower triangle the angle opposite of X = 180 - 90 - 45 = 45°

so, it is an isoceles triangle (both legs are equal).

therefore,

Y = X = 12

Z² = 12² + 12² = 144 + 144 = 288

Z = sqrt(288) = sqrt(16×18) = sqrt(16×9×2) =

= 4×3×sqrt(2) = 12×sqrt(2)

4.

x² + 2x - 1 = 2

x² + 2x + 1 = 4

(x + 1)² = 4

x + 1 = ±2

x = ±2 - 1

x1 = 2 - 1 = 1

x2 = -2 - 1 = -3

5.

in a rhombus all 4 sides are equal, and the opposite sides are parallel.

a.

so, PQ = QR

3x + 7 = -x + 17

4x = 10

x = 10/4 = 2.5

b.

the diagonals are perpendicular to each other (90°), intersect each other at their midpoints and cut their corner angles in half.

the angle RSM = angle PSM = 40°.

c.

the sum of all angles in any quadrilateral is always 360°.

in a rhombus the opposing angles are equal.

so,

the angle SPQ = angle SRQ

360 = SPQ + SRQ + PSR + PQR = 2×SPQ + 2×40 + 2×40 =

= 2×SPQ + 160

2×SPQ = 360 - 160 = 200

the angle SPQ = 200/2 = 100°.

Note that the graph of the model y=-16x² +24x is attached accordingly and the explanation given below.

The vertex is located at (0.75, 4.5). The vertex means that after 0.75 seconds, the egg reaches its highest point, 4.5 feet above the ground.

The y-intercept is located at (0,0), so the y-intercept is 0. This means that the initial height of the egg is 0 feet above the ground.

The zeros of the graph are 0 and 1.5. This means that the height of the egg is 0 feet after 0 seconds and after 1.5 seconds.

The egg is in the air for approximately 1.5 seconds.

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The equation -6 = 0 is not true, which means that there is no solution to the equation 9t+6 in standard form. This is because we cannot write the equation in the form [tex]ax + by = c[/tex]  , since there is no value of c that would satisfy the equation.

To write 9t+6 in standard form, we need to rearrange the expression to have the variables first, followed by the constant term. The standard form of a linear equation is:

[tex]ax + by = c[/tex]

where a, b, and c are constants, and x and y are variables.

To rearrange 9t+6, we first need to group the t term and the constant term together. We can do this by adding 0t to the expression:

[tex]9t + 0t + 6[/tex]

Now, we can rearrange the terms so that the variable term comes first:

[tex]9t + 0t = 9t[/tex]

Finally, we can write the expression in the standard form:

[tex]9t + 0t = 9t + 6[/tex]

This can be simplified further by removing the 0t term:

[tex]9t = 9t + 6[/tex]

We can now move the constant term to the other side of the equation by subtracting 6 from both sides:

[tex]9t - 6 = 9t + 6 - 6[/tex]

[tex]9t - 6 = 9t[/tex]

[tex]-6 = 0[/tex]

Therefore, The equation  [tex]-6 = 0[/tex] is not true, which means that there is no solution to the equation   [tex]9t+6[/tex] in standard form. This is because we cannot write the equation in the form  [tex]ax + by = c[/tex]  , since there is no value of c that would satisfy the equation.

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Answer:

1) Elisa's puppy weighed 4 pounds when it was born. It gained 5 pounds per month until it was 9 months old. 5m + 4.

2) f(x) = -6.2x + 2.9

3) g(x) = 8.1x + 45.64

4) Michele has $125. She plans to spend $10 per week until she has a total of $75.

125 - 10n, or -10n + 125.

Answer: Move 5 to the left of a.5a−day, 12.4 lb, day, 4 day, 8.39 lb, day, lb

A graph of the coordinates of the vertices of the image after a dilation by the given scale factor and center of dilation is shown in the image below.

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 0.5 centered at the origin as follows:

Ordered pair J (-8, 0) → J' (-8 × 0.5, 0 × 0.5) = J' (-4, 0).

Ordered pair K (-4, 4) → K' (-4 × 0.5, 4 × 0.5) = K' (-2, 2).

Ordered pair L (-2, 0) → L' (-2 × 0.5, 0 × 0.5) = L' (-1, 0).

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/3 centered at the point B (3, 3) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, B, and C, we have;

Coordinate A = (9, 9)  →  (1/3(9 - 3) + 3, 1/3(9 - 3) + 3) = (5, 5).

Coordinate B = (3, 3)  →  (1/3(3 - 3) + 3, 1/3(3 - 3) + 3) = (3, 3).

Coordinate C = (6, 0)  →  (1/3(6 - 3) + 3, 1/3(0 - 3) + 3) = (4, 2).

For coordinate D, E, and F, we have;

Coordinate D = (2, -2)  →  (1.5(2 - 4) + 3, 1.5(-2 + 2) + 3) = (0, 3).

Coordinate E = (4, -2)  →  (1.5(4 - 4) + 3, 1.5(-2 + 2) + 3) = (3, 3).

Coordinate F = (1, -4)  →  (1.5(1 - 4) + 3, 1.5(-4 + 2) + 3) = (-1.5, 0).

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Using the k from above find x given that y = 9.  Therefore, when y = 9, x is equal to 1.

We can use the formula for direct variation to find the constant of proportionality k:

Proportionality refers to the relationship between two variables where their ratio remains constant. In other words, as one variable changes, the other changes in proportion to it. This relationship is often expressed as a direct variation or an inverse variation.

Direct variation is a type of proportionality where the two variables increase or decrease at the same rate

y = kx

We are given that y = 27 when x = 3:

27 = k * 3

We can solve for k by dividing both sides by 3:

k = 27 / 3 = 9

So the constant of proportionality is 9.

Now, we can use this value of k to find x when y = 9:

y = kx

9 = 9x

Dividing both sides by 9, we get:

x = 1

Therefore, when y = 9, x is equal to 1.

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The transformations to the parent function f(x) = x² to generate g(x) = 2x² - 4 are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The transformations to the parent function in this problem are given as follows:

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Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees.

Any two angles that sum up to 180 degrees are referred to as supplementary angles.

For the given question:

m∠PQT = m∠SQR (vertically opposite)

101 - 4b = 109 - 6b

on simplifying:

109 - 101 = 6b - 4b

2b = 8

b = 4

m∠PQT = 101 - 4(4) = 93

Now,

m∠PQT +  m∠SQP = 180 (linear pair)

93 +  m∠SQP = 180

m∠SQP = 180 - 93

m∠SQP = 87°

Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

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The estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.

From the given dot plot, we can see that the number of dots for each value up to 10 shots are:

0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33

Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 33/40

This can also be written as a decimal:

P(10 or fewer shots) ≈ 0.825

Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

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Answer:

The distance between the points (0, 4) and (0, 6) can be found using the distance formula: d = sqrt[(x2 - x1)^2 + (y2 - y1)^2] In this case, x1 = 0, y1 = 4, x2 = 0, and y2 = 6. Plugging in the values, we get: d = sqrt[(0 - 0)^2 + (6 - 4)^2] d = sqrt[0 + 4] d = sqrt(4) d = 2 Therefore, the distance between the points (0, 4) and (0, 6) is 2 units.

The formula you will need in order to solve this question is [tex]\sqrt(x_{2} -x_{1})^{2} +(y_{2}-y_{1})^{2}[/tex]

Please remember that you must substitute the order pairs into the question exactly as it is shown in the formula. By failing to do so, you may end up with the wrong answer.

(1) Consider the following:

[tex]x_{1} = 0[/tex] [tex]y_{1} = 4[/tex]

[tex]x_{2} = 0[/tex] [tex]y_{2} = 6[/tex]

(2) Substitute the ordered pairs into the formula accordingly

[tex]\sqrt (0 -0)^{2} +(6-4)^{2}[/tex]

(3) Solve

[tex]\sqrt (0 -0)^{2} +(6-4)^{2} = 2[/tex]

With that being said, the distance is 2.

Answer:

x-axis

Step-by-step explanation:

I'm 99.9% it's right

I'm really sorry if not!

hope this helps!

have a good day/night!

The final cost of 4 pounds is $28.25 and the final cost of p pounds is $4.

Expression for the cost to buy is, Cost(x) = $7.50x - $1.75

The cost price is the price from which the seller buys the product. An expression simply consists of one or more numbers that are along the operation that is given.

In this case, the price per pound of the apples is $7.50 per pound and he has a coupon for $1.75 off the final amount.

The amount to amount that Khajida has to pay to buy 4 pounds of apples will be:

7.50p - 1.75 =

where P = number of pounds

p = 4

This will be:

5.50p - 2.5

7.5(4) - 1.75

27.5 - 1.75

28.25

The amount paid is $28.25.

Therefore, the final cost of 4 pounds: $28.25.

The final cost of p pounds: 4  dollars

To write an expression for the cost to buy x pounds of apples with the coupon, we can use the formula:

Cost = price per pound * number of pounds - coupon amount

Using this formula, we can write:

Cost(x) = $7.50x - $1.75

Where x represents the number of pounds of apples Khadija wants to buy. 

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