When Jace runs the 400 meter dash, his finishing times are normally distributed with a mean of 87 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 95% of his finishing times in the 400 meter race.

The solution of the equation is [tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]

Given is an equation, [tex]\frac{1}{z+9} -\frac{1}{z} = \frac{1}{9}[/tex], we need to solve it,

[tex]\frac{1}{z+9} -\frac{1}{z} = \frac{1}{9}[/tex]

[tex]\frac{z-(z+9)}{z(z+9)} = \frac{1}{9}[/tex]

[tex]\frac{-9}{z^2+9z} =\frac{1}{9}[/tex]

[tex]z^2+9z = -81\\\\z^2+9z+81 = 0[/tex]

Using the quadratic formula,

[tex]x = \frac{[-b \±\sqrt{(b^2-4ac)}]}{2a}[/tex]

here, a = 1, b = 9 and c = 81.

So,

[tex]z = \frac{[-9 \±\sqrt{(81-4(81))}]}{2}\\\\z = \frac{[-9 \±\sqrt{(-243)}]}{2}\\\\\\\\\z[/tex]

[tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]

Hence, the solution of the equation is [tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]

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The solution to the system of linear equations graphed below is (3, -1).

Given are two graphs of linear equations.

The solution of a system of linear equations can be solved either numerically or graphically.

In the graphical method, the solution of a system of linear equations is the point where all the lines intersect.

Here the lines of both the equations intersect at (3, -1).

This means that the intersecting point is (3, -1).

Solution is (3, -1).

Hence the required solution is (3, -1).

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Answer:

The single transformation that maps triangle P onto triangle R is a reflection about the origin followed by a translation of 5 units to the right and 2 units down.

Answer:

Slope-Intercept Form: y=2x+1

Standard Form: 2x-y=6

1. [tex]y=\frac{1}{3}x-1[/tex]

2. [tex]y=-\frac{2}{5}x[/tex]

3. [tex]y=x+8[/tex]

4. [tex]y=-\frac{1}{2}x+3[/tex]

5. [tex]y=2x+1[/tex]

6. [tex]y=-4x-5[/tex]

7. [tex]y=-x+2[/tex]

8. [tex]y=\frac{2}{3}x-4[/tex]

9. [tex]y=x\\[/tex]

Answer:

Step-by-step explanation:

Set up a simple system.

Price = 4x where x = price of donut

For the sale, the price = 3.78, but the x value is 0.5x as it is half off.

$3.78 = 4(0.5x)

Solve for x =$1.89

Therefore, the original price of the donuts were $1.89.

Check by doing 4 x 50%(.5) of 1.89 which equals 3.78!

Answer:

SP = 19

Step-by-step explanation:

the diagonals of a parallelogram bisect each other, then

SP = RS = 19

Answer:

4

Step-by-step explanation:

1p:80°-140。＝40°，40°

S-62 degrees

T-76 degrees

Step-by-step explanation:

IJ and KJ are congruent, so s would have the same measurement as I.

You would simply subtract from both s and i to get t.

Comparing the two probabilities option d: The theoretical probability of landing on an A is less than the experimental probability of landing on an A. is correct.

The chance of an event based solely on mathematical precepts or hypotheses, without any actual experiments or observations, is known as theoretical probability. Probability theory frequently uses theoretical probability to create predictions about the chance of events occurring based on presumptions or models.

On the other hand, experimental probability is the likelihood of an event based on real observations or experiments. A set of trials or experiments are conducted to determine the experimental probability, and the number of times the event occurs during those trials is counted.

For the given spinner the theoretical probability of landing on any one letter is:

P(one letter) = 1/4

Now, experimental probability is given as:

Experimental probability of A = 36/180 = 0.2

Experimental probability of B = 48/180 = 0.2667

Experimental probability of C = 51/180 = 0.2833

Experimental probability of D = 45/180 = 0.25

Thus, comparing the two probabilities option d: The theoretical probability of landing on an A is less than the experimental probability of landing on an A. is correct.

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The total surface area of the cuboid with 7cm,5cm, and 10cm as dimensions is 310 square. cm and the volume is 350 cubic. cm.

Given dimensions of the figure are 7cm,5cm, and 10cm.

Length = 7cm.

Width = 5cm.

Height = 10cm.

The surface area of the cuboid = 2(lw+wh+lh).

Now, let us substitute the given values in the above formula.

2(7*5+5*10+7*10)

2(35+50+70)

2(155) = 310.

Therefore, the surface area of the figure is 310 square. cm.

Now, we have to find the volume of the figure.

Volume = Length x Width x Height.

Volume = 7*5*10

Volume = 350.

Therefore, the volume of the figure is 350 cubic. cm.

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Answer:

40%

Step-by-step explanation:

To transform the left-hand side of the given identity "1 + cos(2x)" into the right-hand side "[tex]2cos^2(x)[/tex]", the expression "1" should be changed to "[tex]2sin^2(x)[/tex]" and the left-hand side should be simplified.

Trigonometric identities are mathematical equations that may be used to express trigonometric functions. These identities, which are also used to solve trigonometric equations, can be utilised to simplify and manage trigonometric expressions.

Trigonometric identities, which are derived from the geometric properties of triangles and the unit circle, provide a way to describe trigonometric functions in terms of other trigonometric functions or constants. In many areas of mathematics, physics, engineering, and other fields where trigonometry is used, they are commonly used.

Replacing  "1" with "[tex]2sin^2(x)[/tex]".

[tex]1 + cos(2x) -- > 2sin^2(x) + cos(2x)[/tex]

Using the double angle formula for cosine

The double angle formula for cosine is: cos(2x) = [tex]2cos^2(x) - 1[/tex]

Substitute the double angle formula into the expression for cos(2x) on the left-hand side.

[tex]2sin^2(x) + cos(2x) -- > 2sin^2(x) + (2cos^2(x) - 1)[/tex]  [Substitute cos(2x) with [tex]2cos^2(x) - 1[/tex]]

Simplify the expression on the left-hand side.

[tex]2sin^2(x) + (2cos^2(x) - 1) -- > 2sin^2(x) + 2cos^2(x) - 1[/tex] [Simplify using distributive property]

[tex]2sin^2(x) + 2cos^2(x) - 1 -- > 2(sin^2(x) + cos^2(x)) - 1[/tex] [Apply trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex]]

[tex]2(sin^2(x) + cos^2(x)) - 1 -- > 2(1) - 1[/tex] [Substitute [tex]sin^2(x) + cos^2(x)[/tex]with 1]

[tex]2(1) - 1 -- > 2 - 1\\2 - 1 -- > 1[/tex]

So, following simplification, the left-hand side equation "1 + cos(2x)" may be changed into "1." As a result, "1" in the equation needs to be altered to "2sin(x)" and the left side should be simplified to "1".

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The length of the hypotenuse is 4√2.

What is the Pythagoras theorem?

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, we have

Given: base = 4

perpendicular = 4

We have to find the length of the hypotenuse.

We apply here Pythagoras theorem and we get

b² + p² = h²

(4)² + (4)² = h²

16 + 16 =  h²

32 =  h²

h = 4√2

Hence, the length of the hypotenuse is 4√2.

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The graph of the absolute value function y = -g(x) + 1 is shown in the image attached below.

The graph of the absolute value function y = 2h(x + 4) is shown in the image attached below.

In Mathematics, the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

In this scenario, we can logically deduce that the equation of the first parent absolute value function is g(x) = |2x| and it would be reflected over the y-axis, and then translated by 1 units upward;

g(x) = |2x|

y = -g(x) + 1 = |2x| + 1

h(x) = |2x + 4| - 4

y = 2h(x + 4)

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The probability of the TPMS triggering a warning is 0.0198 or about 0.02, rounded to four decimal places.

It is used to predict and estimate the likelihood of future events and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Let's assume that the tire pressure follows a normal distribution with a mean of 32 psi and a standard deviation of 3 psi.

Let's also assume that the TPMS warning is triggered when the tire pressure falls below 25 psi or rises above 39 psi.

Using a standard normal distribution table or calculator, we can find the z-scores corresponding to 25 psi and 39 psi:

z₁ = (25 - 32) / 3 = -2.3333

z₂ = (39 - 32) / 3 = 2.3333

Then, we can find the probabilities associated with these z-scores:

P (z < -2.3333) = 0.0099

P (z > 2.3333) = 0.0099

The total probability of the TPMS triggering a warning is the sum of these two probabilities:

P(TPMS warning) = P(z < -2.3333) + P(z > 2.3333) = 0.0099 + 0.0099 = 0.0198

Therefore, the probability of the TPMS triggering a warning is 0.0198 or about 0.02, rounded to four decimal places.

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Part A:

To calculate the mean, we add up all the values and divide by the total number of values:

12 + 12 + 19 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 281

Mean = 281 / 10 = 28.1

To find the median, we need to find the middle value. Since there is an even number of values, we take the average of the two middle values:

Median = (22 + 26) / 2 = 24

The mode is the value that appears most frequently. In this case, there is no mode as no value appears more than once.

The range is the difference between the highest and lowest values:

Range = 68 - 12 = 56

Part B:

The median may be a better measure of central tendency in this scenario as there is an outlier value of 68 that can skew the mean. Since outliers can have a significant impact on the mean, reporting the median may give a better representation of the typical amount of time spent practicing for the tournament. Therefore, the tennis players should report the median value.

The number of volumes of the encyclopedia on the bottom shelf is given as follows:

H) 19.

The number of volumes of the encyclopedia on the bottom shelf obtained as the subtraction between the highest number and the lowest number identifying the numbers, adding one.

We add one as the amount of numbers between n and n + 1, inclusive, is of n + 2. For example, between 12 and 13, we have two numbers.

Then the number of volumes of the encyclopedia on the bottom shelf is given as follows:7

30 - 12 + 1 = 19.

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The identity (x² + y²)² = (x² - y²)² + (2xy)²

An identity is a mathematical equation which shows that one side of the equation is equivalent and equal to the other side of the equation.

To verify the following Pythagorean identity for all values of x and y:

(x² + y²)² = (x² - y²)² + (2xy)², we need to shows that

left-hand side L.H.S = right hand side

So, we proceed as follows

L.H.S = (x² + y²)²

Expanding the brackets, we have that

(x² + y²)² = (x² + y²)(x² + y²)

= (x²)² + 2x²y² + (y²)²

=  (x²)² + (y²)² + 2x²y²  

Now, we know that (a - b)² = a² + b² - 2ab. So,

a² + b² = (a - b)² + 2ab

Let a = x² and b = y²

So, we have that

(x²)² + (y²)² =  (x² - y²)² + 2x²y²

So, substituting this into the equation, we have that

(x²)² + (y²)² + 2x²y² = (x² - y²)² + 2x²y²  + 2x²y²

= (x² - y²)² + 4x²y²

= (x² - y²)² + 2²x²y²

= (x² - y²)² + (2xy)²

So, Since L.H.S = R.H.S

(x² + y²)² = (x² - y²)² + (2xy)²

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Examining the graph it can be deduced that

The domain is

The range is

The graph is not a function

To qualify as a function, any input (x-value) of a graph must be linked to a single output (y-value). Therefore, each x-value ought to have one and only one y-value that matches it.

A method for identifying whether or not a given graph is representative of a function is by conducting a vertical line test. To achieve this, vertically draw lines through the graph. When every vertical line hits the graph at just one point, then the illustration aptly presents a function. Conversely, if the graph forms multiple intersection points with any vertical line, it isn't classified as a functional representation.

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To subtract 47.96 from 320.041, you can align the decimal points and then subtract each digit from right to left.

First, write the numbers with the decimal points aligned:

320.041

- 47.960

Next, subtract the digits in the ones place, which is 1 minus 0, resulting in 1. Then, subtract the digits in the tenths place, which is 4 minus 6. Since 4 is less than 6, you need to borrow 1 from the digit to the left, making the 2 into a 1 and adding 10 to the 4, giving you 14. So, 14 minus 6 equals 8.

Continue subtracting each digit in the same way:

   320.041

-   47.960

= 272.081

Therefore, 320.041 minus 47.96 is equal to 272.081.

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Answer:

is the answer A????????????

to be honest I’m only here for the answers but I also need the points

Answer:

Surface Area = 2×(3.5×10 + 3.5×8 + 10×8) = 286 feet

Step-by-step explanation:
First, multiply 3.5 by 10 (35)
Secondly, multiply 3.5 by 8 (28)
Then, multiply 10 by 8 (80)
Next, add all the values together (143)
And lastly, multiply 143 by 2 (286)

Please turn this into your own work, (By making it look like it's worked out) since they can catch you for Plagiarism.

The reflection of the figure over y = -2x - 1 is attached accordingly.

A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a fixed point set; this set is known as the axis or plane of reflection.

Because the line of reflection has a slope of -1/2, each image point will be on a line with a slope of 2 that passes through the associated pre-image point.

It might be simplest to count the grid squares between the pre-image point and the line, then from the line to the image point's location. Those measurements will be the same.

The second attachment shows the mirrored image.

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Answer:

Step-by-step explanation:

A

Answer:

Step-by-step explanation:

To find the answer, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of games, r is the number of losses, and n-r-1 is the number of ties (since we already know there are 9 wins).

Substituting the values, we get:

13C3 * 10C1

= (13! / 3!10!) * (10! / 1!9!)

= (13*12*11 / 3*2*1) * 10

= 2860

Therefore, there are 2860 ways the schedule can end with 9 wins, 3 losses, and 1 tie.

Answer:

f(x) = 16*0.75^x

Step-by-step explanation:

first off let's use this coordinate (the one given) :

(0,16)

let's substitute this into the equation with x being 0 and f(x) being 16

16 = a*b^0

*anything to the power of 0 is 1*

so:

a = 16

now use the second coordinate :

(1,12)

and do the same by substituting 1 for x and 12 for f(x), we also know what 'a' is:

12 = 16*b^1

12 = 16 * b

b = 3/4

so :

f(x) = 16*0.75^x

The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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[tex]f(x) = x^2 + 6x - 7[/tex] is the equation of the function.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

To find the equation of the quadratic function, we need to use the vertex form of the equation:

[tex]f(x) = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola.

We know that the vertex is (-3, 16), so h = -3 and k = 16. We also know that the x-intercepts are at -7 and 1, which means that the factors of the quadratic function are (x + 7) and (x - 1).

To find the value of 'a', we can use either of the x-intercepts:

[tex]f(-7) = a(-7 + 3)^2 + 16 = 0\\\\16a = 16\\\\a = 1[/tex]

Therefore, the equation of the quadratic function is:

[tex]f(x) = (x + 7)(x - 1)\\\\f(x) = x^2 + 6x - 7[/tex]

So the answer is (A)[tex]f(x) = x^2 + 6x - 7[/tex].

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