An evil supervillian has launched a satelite from his/her flying carrier. The satelite's height, in meters
above sea level, as a function of time, t, in seconds, is given by
h(t) = – 4.9t^2+ 165t + 160

Answer:

Step-by-step explanation:

Answer:

D. Infinitely many solutions

Step-by-step explanation:

Answer:

Please refer to the attachment

Have a good day Ahead

a) The frequency distribution table regarding their serum HDL cholesterol data is present in above figure 1.

b) The relative frequency distribution table regarding their serum HDL cholesterol data is present in above figure 2.

We have a patient data of a doctor who randomly select his 40 patients. The following data is regarding their serum HDL cholesterol.

34, 51, 48, 37, 41, 63, 65, 42, 53, 58, 46, 41, 66, 36, 44, 53, 52, 63, 51, 63, 42, 54, 36, 46, 41, 63, 54, 52, 43, 36, 38, 56, 46, 56, 49, 73, 45, 46,64, 45

a) A frequency distribution can show the exact number of observations or the percentage of observations falling into each interval. Here are the steps to draw a frequency distribution table:

The frequency distribution table for HDL cholesterol data of paitents is present in above figure 1.

b) A relative frequency distribution is one of type of frequency distribution. To calculate the relative frequency, divide the frequency by the total count of data values. Steps are the following:

The relative frequency distribution table is present in above figure 2.

For more information about relative frequency distribution, visit :

https://brainly.com/question/29012139

#SPJ4

Complete question :

A doctor randomly selects 40 of his patients and obtains the following data regarding their serum HDL cholesterol.

34, 51, 48, 37, 41, 63, 65, 42, 53, 58, 46, 41, 66, 36, 44, 53, 52, 63, 51, 63, 42, 54, 36, 46, 41, 63, 54, 52, 43, 36, 38, 56, 46, 56, 49, 73, 45, 46,64, 45

a) construct frequency distribution

b) construct relative frequency distribution table

Answer:

The maximum value occurs at point (-2, 8) where x = -2 represents the axis of symmetry.

Step-by-step explanation:

Quadratic functions.

Vertex form.

Standard form.

Axis of symmetry.

Maximum value.

Minimum value.

BPEMDAS Order of Operations:

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where a ≠ 0 and (h, k ) represents the coordinates of the vertex.

a: Vertical stretch or compression factor.

h: Horizontal translation.

k: Vertical translation.

The axis of symmetry is an imaginary vertical line that goes through the vertex of a parabola and divides the graph into two symmetrical halves. The axis of symmetry is also the x-coordinate of the vertex, (h, k). Hence, the axis of symmetry is: x = h.

  \(\boxed{\\\begin{minipage}{5.4cm}\\\indent\quad\sf{\large \underline{Axis\:of\:Symmetry:}}\quad\displaystyle\mathsf{x\:=\:\frac{-b}{2a} \:\:\:}\\\end{minipage}}\)

Step 1: Transform the given quadratic function into its general form, h(x) = ax² + bx + c.

Given: h(x) = - (x + 2)² + 8

\(\displaystyle\mathsf{\Rightarrow\:h(x) = - (\:x^2 + 2x + 2x + 4\: ) + 8\: \rightarrow \textsf{[\:Expand the binomial using the \textbf{FOIL method\:}\:].}}\)

\(\displaystyle\mathsf{\Rightarrow\: h(x) = - (\:x^2 + 2x + 2x + 4\: ) + 8\:\rightarrow \textsf{[\:Combine like terms\:].}}\)  

\(\displaystyle\mathsf{\Rightarrow\: h(x) = - (\:x^2 + 4x+ 4\: ) + 8\:\rightarrow \textsf{[\:Distribute the negative sign into the parenthesis\:].}}\)

\(\displaystyle\mathsf{\Rightarrow\: h(x) = - \:x^2 - 4x - 4 + 8\:\rightarrow \textsf{[\:Simplify\:].}}\)

\(\displaystyle\mathsf{\Rightarrow\: h(x) = - \:x^2 - 4x + 4\:\rightarrow \textsf{[\:\textbf{General form}, where: a = -1, b = -4, and c = 4\:].}}\)

Step 2: Solve for the axis of symmetry.

Substitute the derived values for a  = -1 and b = -4 into the following formula:

  \(\boxed{\\\begin{minipage}{6cm}\\\indent\qquad\quad\quad\sf{\large \underline{Axis\:of\:Symmetry:}}\\\\\indent\quad\displaystyle\mathsf{x\:=\:\frac{-b}{2a}\:=\:\frac{-(-4)}{2(-1)}\:=\:\frac{4}{-2}\:=\:-2. }\\\end{minipage}}\)

Step 3: Find the maximum value.

Substitute the derived value for the axis of symmetry, x = -2, into h(x) = -x² - 4x + 4.

h(x) = -x² - 4x + 4 ⇒  General form.

\(\displaystyle\mathsf{\Rightarrow\:h(-2) = - \:(-2)^2 - 4(-2) + 4\: \rightarrow \textsf{[\:BPEMDAS: Exponent\:].}}\)  

\(\displaystyle\mathsf{\Rightarrow h(-2) = - \:4 - 4(-2) + 4\:\rightarrow \textsf{[\:BPEMDAS: Multiplication\:].}}\)

\(\displaystyle\mathsf{\Rightarrow\:h(-2) = - 4 + 8 + 4\:\rightarrow \textsf{[\:BPEMDAS: Addition\:].}}\)

\(\displaystyle\mathsf{\Rightarrow h(-2) = 8\:\rightarrow \: \textsf{[\:\textbf{Maximum value}\:].}}\)

Hence, the maximum value (vertex) occurs at point (-2, 8).

In order to find other points to plot on the graph, we can substitute different x-values into the vertex form. A good starting point is to solve for the y-intercept, which is the point on the graph where it intersects the y-axis.

Solve for the y-intercept by setting x = 0:

Vertex form: h(x) = - (x + 2)² + 8

  ⇒ h(0) = -(0 + 2)² + 8 →  [Let x = 0 in h(x) = - (x + 2)² + 8].

  ⇒ h(0) = -(2)² + 8 →  [PEMDAS: Parenthesis].

  ⇒ h(0) = -4 + 8 → [PEMDAS rule: Exponent].

  ⇒ h(0) = 4  → [PEMDAS: Addition].

Hence, the y-intercept is (0, 4).

We can graph the axis of symmetry by drawing a vertical line from x = -2, and use it as a reference point in finding other points to plot on the graph.  

Since the y-intercept, (0, 4) is 2 units to the right of the axis of symmetry, then it means that going 2 units to the left will give us (-4, 4).

We have the following points to plot on the graph:

The maximum value occurs at point (-2, 8), where x = -2 represents the axis of symmetry.

________________________

Learn more about quadratic functions here:

https://brainly.com/question/27796555

Answer:

Step-by-step explanation:

Use the given functions to set up and simplify

2%.8000=a⋅(5yearcd)= 5ea2yrcd2%=0.02

Answer:

100

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

your maximum "point" of the polynomial is the highest point that the curve makes which in this case is around x=-3.6 and y=17

The point of maxima for the given function is (-3.6, 17).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

As per the graph of the function following conclusion are as below,

It has a maxima in second quadrant.

After the point of maxima, its value starts to decrease.

Then, it reaches it lowest value in fourth quadrant after which it increases again.

By examining the given options, the correct point of maxima can be found as (-3.6, 17).

Hence, the point of relative maxima for the graph can be evaluated as (-3.6, 17).

To know more about function click on,

https://brainly.com/question/21145944

#SPJ2

Answer:

B ( -1, -8)

Step-by-step explanation:

A ( -7, -6)

midpt (-4, -7)

Equation:

(x + 3, y - 1)

Solve for B:

(-4, -7)

(x + 3, y - 1)

( -1, -8)

There are a total of 5040 different ways in which 7 files can be arranged in a file cabinet. This can be calculated by using the formula for permutation, which is n! / (n-r)!, where n is the total number of objects and r is the number of objects being arranged. In this case, n=7 and r=7, so the formula would be 7! / (7-7)!, which simplifies to 7! / 0!. Since 0! is equal to 1, the equation becomes 7!, which is equal to 5040.

To determine the number of different ways to arrange 7 files in a file cabinet, we need to consider the concept of permutations. A permutation is an arrangement of objects in a specific order.

Since there are 7 files, each file has a unique position in the cabinet. When you place the first file, you have 7 options. Once the first file is placed, you have 6 remaining options for the second file, 5 options for the third, and so on.

To calculate the total number of arrangements, we multiply the number of options for each position together:

7 (options for 1st file) × 6 (options for 2nd file) × 5 (options for 3rd file) × 4 (options for 4th file) × 3 (options for 5th file) × 2 (options for 6th file) × 1 (option for 7th file)

This is equal to 7! (7 factorial) which equals:

7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

So, there are 5,040 different ways to arrange the 7 files in the file cabinet.

To learn more about permutation, click here:

brainly.com/question/30649574

#SPJ11

The mathematical procedure for decomposing a complex waveform into simpler waveforms is known as Fourier analysis. It allows for the identification of the individual frequency components that contribute to the overall pattern.

Fourier analysis, named after the French mathematician Jean-Baptiste Joseph Fourier, is a fundamental technique used in many fields, including signal processing, physics, and engineering. It is based on the concept that any complex waveform can be represented as a combination of simpler sinusoidal waveforms. These simpler waveforms are characterized by their frequency, amplitude, and phase.

The procedure involves decomposing a complex waveform into its constituent frequencies by applying the Fourier transform. The Fourier transform converts the waveform from the time domain to the frequency domain, revealing the underlying frequency components. By analyzing the resulting spectrum, which shows the amplitude and phase of each frequency component, one can determine the simpler waveforms that make up the original complex pattern.

Fourier analysis has numerous applications, such as analyzing sound waves, image processing, and data compression. It enables us to better understand and manipulate complex signals by breaking them down into their fundamental building blocks.

Learn more about fourier analysis here:

https://brainly.com/question/28385206

#SPJ11

Answer:

Hello, I just took the test today. I will attach a screenshot. I hope I am not too late answering your question.

This question stumped me too at first. I hope this helps!

The missing parts that correctly complete the proof are;

2) Definition of a bisector

4) ∠BXP ≅ ∠BYP.

5) Reflexive property of congruence.

6) AAS congruence theorem.

7) Corresponding sides of congruent triangles are congruent.

We are given;

Point P is on the bisector of ∠ABC.

Read more at; https://brainly.com/question/11357763

If the mean number of people who attended three basketball games was 8,242, that means the sum of the number of people who attended all three games is equal to 8,242 multiplied by the number of games, which is 3.

What does math mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Total attendance = mean attendance * number of games

Total attendance = 8,242 * 3

Total attendance = 24,726

So the total attendance at the three games is 24,726 people.

Learn more about mean

https://brainly.com/question/1136789

#SPJ1

From the given equation we get that the optimal time is represented by the following inequality:

Now, recall that:

Therefore:

adding 1200 to the above inequality, we get:

Finally, dividing by 100 we get:

Answer: The time interval is between 10 and 14 days.

The distance between the two skew lines that measure along the line Perpendicular to the two lines is \(\frac{13}{\sqrt{70}}\).

To find the distance between the skew lines and measure the distance along the line perpendicular to the two lines, it is necessary to find a vector n perpendicular to both lines. Then project rAC onto that vector.

Here's the step-by-step explanation:

Step 1 Finding vector AB and vector CD

Step 2 Finding the vector n perpendicular to both lines.

The vector that is perpendicular to both lines is the cross-product of the vectors AB and CD.

Step 3 Finding the projection of rAC onto the vector n.

Therefore, the distance between the two skew lines is \(\frac{13}{\sqrt{70}}\).

Learn more about Perpendicular lines https://brainly.com/question/18271653

#SPJ11

The value of 10x + 3, when x satisfies the equation 5x + 6 = 10, is 11.

To find the value of 10x + 3, we first need to solve the equation 5x + 6 = 10 for x. Then, we can substitute the obtained value of x into 10x + 3 to find its value.

Let's solve the equation 5x + 6 = 10:

5x = 10 - 6

5x = 4

x = 4/5

Now, substitute the value of x into 10x + 3:

10(4/5) + 3

(40/5) + 3

8 + 3 = 11

Therefore, the value of 10x + 3, when x satisfies the equation 5x + 6 = 10, is 11.

Complete Question:

If 5x+6=10, what is the value of 10x+3?

To know more about equation, refer here:

https://brainly.com/question/29278673

#SPJ4

In a parallelogram, opppsite angles are equal. and the sum of the adjascent angles is 180

The volume of the Illustrated cone used as an example is 51.3cm³.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

A cone is a recognizable three-dimensional geometric shape with a flat and curved surface that is pointed upward. The formula for the volume of a cone is V=1/3hπr²

Let's say the radius is 7cm. The volume will be:

= 1/3 × 3.14 × 7²

= 51.3cm³

Learn more about volume on:

https://brainly.com/question/28790396

#SPJ1

Answer:

the answer is 7

Step-by-step explanation:

7 plus 7 add 11 equals twenty five

The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.

This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.

The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.

The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.

Learn more about the alternative hypothesis at

https://brainly.com/question/27335001

#SPJ4

Answer:

Box 1: 5

Box 2: 5

Box 3: 5

Box 4: 15

Step-by-step explanation:

the three boxes have the same number of boxes, it has 5 because 5+ 5 + 5 = 15.

so the fourth box will have 15 because that's the sum of the three boxes, 15 + 15 = 30.

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

He sold it for Rs 15 each. What is his profit percent? CP of 1 pen = 120/12= 10 SP of 1 pen = 15 Profit = 5 P % = (p/CP)*100=(5/10) x 100 = 50%.

Answer:the radius of a cone is the radius of its circular base. You can find a radius through its volume and height. Multiply the volume by 3. For example, the volume is 20.

Answer:

Either use the formula given below or , Use the formula for volume of a cone .

\(h = 36 \\Volume = 588pi\\r = \\588pi = \frac{1}{3}pir^{2} 36\\Cross-multiply\\1764pi=36pir^{2} \\Divide-both-sides-of-the-equation-by-36pi\\r^{2} =\frac{1764pi}{36pi} \\r^{2} = 49\\Square -root-both-sides-of-the-equation.\\\sqrt{r^{2} } =\sqrt{49} \\r = 7\)

Step-by-step explanation:

\(Volume -of -a- cone = \frac{1}{3} pir^{2} h\\Method 1 : Make- r- the -subject -of-the-formula.\\V = \frac{1}{3} pir^{2} h \\Cross-multiply\\3V = pir^{2} h \\Divide- both- sides -of- the -equation -by - pih\\\frac{3V}{pih} =r^{2} \\Square-root-both-sides-of-the-equation\\r = \sqrt{\frac{3V}{pih} }\)

a. We can estimate 290 as \(2.90 \times  10^2.\)

B. We can estimate 460 as 4.60 x 10^2.

To estimate each quantity in terms of powers of ten, we can express each number in scientific notation.

a) 290 can be written as\(2.90 \times  10^2\).

The first digit is 2, which is between 1 and 10.

The decimal point is after the first digit, so we have one non-zero digit to the left of the decimal point.

We need to move the decimal point two places to the left to get a number between 1 and 10, which gives us 2.90.

The exponent is 2, which means we need to multiply our number by \(10^2\) to get the original value of 290.

Therefore, we can estimate 290 as \(2.90 \times  10^2.\)

b) 460 can be written as\(4.60 \times  10^2\)

The first digit is 4, which is between 1 and 10.

The decimal point is after the first digit, so we have one non-zero digit to the left of the decimal point.

We need to move the decimal point two places to the left to get a number between 1 and 10, which gives us 4.60.

The exponent is 2, which means we need to multiply our number by \(10^2\) to get the original value of 460.

Therefore, we can estimate 460 as \(4.60 \times  10^2.\).

For similar question on estimate.

https://brainly.com/question/28416295

#SPJ11

When we estimate a quantity in terms of powers of ten, we're essentially trying to express that quantity as a multiple of 10 raised to some power. For example, we could estimate 290 as 3 x 10^2, since 3 is the first digit and there are two other digits after it.


(a) For 290, we can estimate it to the nearest power of ten as follows:
Step 1: Identify the nearest powers of ten: 100 (10^2) and 1000 (10^3)
Step 2: Determine which power of ten is closer to 290: Since 290 is closer to 100 than 1000, we'll choose 100 (10^2).

(b) For 460, we can estimate it to the nearest power of ten as follows:
Step 1: Identify the nearest powers of ten: 100 (10^2) and 1000 (10^3)
Step 2: Determine which power of ten is closer to 460: Since 460 is closer to 1000 than 100, we'll choose 1000 (10^3).

Learn more about powers of ten here: brainly.com/question/31961237

#SPJ11

Answer:

C. 5.8

Step-by-step explanation:

We use the Pythagoras theorem here. which is a²+b²=c².

a and b are the replacements for the 5miles and  3miles here.

They are a and b because a  and b are always on the right angle side.

The longest side of this triangle is called a hypotenuse which is the c in this case.

the other sides (a and b) are called the adjacent and the opposite.

it doesn't matter if you use adjacent or opposite for a and b in this case.

the only important thing is the hypotenuse here.

So it's a²+b²=c², which is 5²+3²=c².

5² is 25 and 3² is 9, so we add them and we get 34.

so c²=34, we don't want the square on c  so we send it to 34 which becomes √34.

√34 gives us 5.8 miles which is up to just only one decimal place.

You might need to use calculators for square roots because they take long to calculate.

Answer: 4/3 pounds or 1 and 1/3 pound of beans in each bag.

Step-by-step explanation: 20/15 then you divide by 5 you get 4/3

The standardized test statistic t is approximately -0.429 rounded to three decimal places

To determine the standardized test statistic t for testing the claim ρ = 0, use the formula:

t = r × √((n - 2) / (1 - r²))

Given:

r = -0.541 (correlation coefficient)

n = 20 (sample size)

α = 0.01 (significance level)

Let's plug in the values and calculate t:

t = (-0.541) × √((20 - 2) / (1 - (-0.541)²))

Calculating the expression inside the square root:

(20 - 2) / (1 - (-0.541)²) = 0.629

Now substituting this value into the formula:

t =(-0.541) × √(0.629) = -0.541 ×0.793 = -0.429

To know more about  statistic here

https://brainly.com/question/31538429

#SPJ4

The a = 0.01 critical value for the chi - square statistic with 13 degrees of freedom is given by 27.688.

Hence the correct option is (A).

Here given distribution is Chi - squared distribution.

two parameters of chi - squared distribution are given by ' a ' and ' d ' where d is degree of freedom.

The critical value against chi squared distribution changes according to the change of the values of a and d.

The table chi squared distribution is given by,

Here we have to find the critical value for the chi - squared statistic with 13 degrees of freedom when a = 0.01.

Therefore, a = 0.01 and d = 13

From the given table we can see that when a = 0.01 and d = 13 the critical value is given by 27.688.

Hence the correct option is (A).

To know more about Chi - squared distribution here

https://brainly.com/question/4543358

#SPJ4

Answer:

4 toppings

Step-by-step explanation:

22-12=10

2.50*?=10

2.50*4=10

4 toppings

Answer:

12+(2.50x)

12+(2.50*4)

12+(10)

22

Step-by-step explanation:

x stands for number of toppings