The US National Science Foundation collects data on the dollar amount for a grant given to a scientist in the Engineering field. A sample of this year’s grants is: (given in thousands of dollars)
22 5 26 23 27 50 100 70 90 25
Calculate and interpret the following statistics (show work to receive credit).
a. Median b. Q1 c. Q3 d. IQR e. Range

First, let's define rational and irrational numbers.

Rational numbers. Are those numbers that can be expressed as the ratio of 2 integers.

Irrational numbers. These numbers are the opposite of rational numbers, they can't be expressed at the ratio of 2 integers abd their decimal numbers are infinite.

Now, addressing the question, to order rational and irrational numbers we must take a close look th the decimal numbers given for the rational number.

For example, say that we are comparing 9.43 and \(\sqrt{89} \\\). Let's convert the numbers to their decimal form to easily compare them.

9.43 is already a decimal.

\(\sqrt{89} =9.433981132\).

Based of the obtained values, the greatest number of these 2 is, clearly, \(\sqrt{89} \\\). In case we are comparing these same 2 numbers, and we are only given the decimal form of \(\sqrt{89} \\\) as 9.43, we can still affirm that \(\sqrt{89} \\\) is the greatest number, because it's irrational, it has more decimal numbers that are greater than those on 9.43, which only has 2.

The way to compare and order rational and irrational numbers is to convert all the numbers to their decimal form and see who has the greater value. It's important to always keep in mind that irrational numbers have infinite decimal figures. If we have the exact same decimal figures for an irrational and a rational number, the irrational number will always be greater since it has infinite decimal places.

Answer:

\( \frac{.029}{100} \\ \frac{29 \times {10}^{ - 3} }{ {10}^{3} } \\ = 29 \times {10}^{ - 6} \\ thank \: you\)

Answer:

0.000029

Step-by-step explanation:

Answer:

2.  88,    3.  40,   4.  48,   5.  20

Step-by-step explanation:

first multiply&divide, then calculate from left to right

2.  5 · 4² + (2 · 3 + 2) = 5 · 16 + 6 + 2 = 88

3.  (4 + 3)² - 12 + 3 = 49 - 12 + 3 = 40

4.  64 ÷ 4 · 3 = 16 · 3 = 48

5.  3² - 4 + 5 · 3 = 9 - 4 + 15 = 20

The first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

Given is an arithmetic sequence, \(a_{k+1} = a_k-20\) and \(a_1 = 300\),

we need to find the first five terms,

a₂ = a₁-20

a₂ = 300-20

a₂ = 280

a₃ = a₂-20

a₃ = 260

a₄ = a₃ - 20

a₄ = 240

a₅ = a₄ - 20

a₅ = 220

aₙ = aₙ₊₁ - 20

d = 20

Hence, the first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20

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Step-by-step explanation:

Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90 degree angle).

x² = 12² + 9² = 144 + 81 = 225

x = 15 ft

so, the first answer option is correct.

The value of hypotenuse (x) in the right angled triangle is 15ft.

Given,

Right angled triangle .

Here,

Pythagoras theorem,

c² = a² + b²

here,

c = hypotenuse

a = perpendicular

b = base

Substitute the values in the formula,

x² = 12² + 9²

x² = 144 + 81

x² = 225

x = 15 ft

Thus the length of hypotenuse is 15ft .

So, option A is correct.

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In mathematics, a combination is a selection of items from a set that has distinct members

Formula

Where

n = 20

r =3

The final answer

1140 unique groups of volunteers are possible

Answer:

Because when your finding a point on the x line going left goes towards the negative side, like a number line. So for the y line think of it like the number line but going up is positive and going down is negative.

so if we wanted to go right 6 units and down 3 units it would written as:

(x+6,y-3) Because going right on the x line is like adding 6 units and going down on the y line is like subtracting 3 units for this example

Step-by-step explanation:

To implement the second method, the administrator should first create two separate lists, one for each class.

Then, the administrator should use a computer with a random number generator to select a simple random sample of 30 students from the combined class lists. To do this, the administrator should assign a unique number to each student in each list and generate a random set of 30 numbers that correspond to the students in the list.

For example, using the random digits 47899, 92198, 80657, 73914, and 18360, the administrator can choose student 47899 from the first class and student 92198 from the second class.

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Answer:

a = - 1.1

Step-by-step explanation:

The condition for a single variable function f(x) to be decreasing is f'(x) < 0.

f(x) = 4/x^2 - 6x + 9

Then, differentiating with respect to x on both sides we get,

f(x) = 4(-2)(1/x^3) - 6 < 0

-8/x^3  - 6 < 0

8/x^3 + 6 > 0

{Dividing both sides with - 1 and hence the inequality sign changes}

8/x^3 > -6

8 > - 6x³ {Multiplying both sides with x³}

6x³ > - 8 {Interchanging the sides}

x^3 > -8/6

⇒ x > - 1.1

So,  a = - 1.1

Answer:

  a = 3

Step-by-step explanation:

The function can be written as ...

  f(x) = 4/(x -3)^2

This has a vertical asymptote at x=3 and will be decreasing for all values of x to the right of that -- on the interval (3, ∞).

  a = 3

The correct answer or scientific notation when 3.185× 10¹⁷ is divided by 9.1×10⁸ is 3.46×10⁸ and multiplying  3.185× 10¹⁷ with 9.1×10⁸  is 2.9×10²⁶.

It is given in the question that 3.185× 10¹⁷ is divided by 9.1×10⁸

we can write 3.185×10×10¹⁶ which equals 31.5×10¹⁶.

Now dividing 31.5×10¹⁶ by 9.1×10⁸ we get 3.46×10⁸.

Now multiplying  3.185× 10¹⁷ with 9.1×10⁸ we get 28.98×10²⁵

Converting 28.98×10²⁵ in scientific notation we get 2.9×10²⁶.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation and known as standard form in the UK .

In scientific notation, a representation of a number that is a power of ten can also be written with equal ease. Additionally, you'll see that the amount of zeros in a regular decimal expression is exactly equal to the power to which 10 is raised.

Any time a number is expressed in words, it must first be written down as a regular decimal number before being converted. "Ten million" becomes "10,000,000" and vice versa.Ten million is written in powers of ten notation because there are seven zeros in all.

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Answer:

the are so many numbers but here's one of them

Step-by-step explanation:

Since the number is less than 700, it cannot begin with a 7 or an 8.

So the hundreds digit can only be a 2 or a 5.

Now the tens digit can be any digit not occupying the hudreds digit. So there would be 3 possibilities, and there remain two possibilities for the units digit.

Hence, the number of such numbers is 2x3x2 which is 12.

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 will be 150.

A sample is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The number of two-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5

⇒ 25

The number of three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5 x 3

⇒ 125

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 125 + 25

⇒ 150

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Answer:

The region where the inequality is valid is (x>-5) and (x<-9).

The graph is attached.

Step-by-step explanation:

We have a inequality and we have to determine the region in the xy-plane that inequality.

\(|x+7|-2>0\\\\|x+7|-2+2>0+2\\\\|x+7|>2\)

We divide the inequality in two regions:

1) When (x+7)>0, we have:

\(x+7>2\\\\x+7-7>2-7\\\\x>-5\)

2) When (x+7)<0, we have:

\(-(x+7)>2\\\\-x-7+7>2+7\\\\-x>9\\\\(-x)(-1)<9(-1)\\\\x<-9\)

Then, the region where the inequality is valid is (x>-5) and (x<-9).

The graph is attached.

Answer:

B

Step-by-step explanation:

edg 2020

Answer:

(8/9)^2

Step-by-step explanation:

8^2=64 and 9^2=81. Therefore, 8/9 x 8/9 = 64/81.

A) 0.0764 portion of rods have a length less than 21.9 cm.

Calculation

X ~ N

μ = 22

σ = 0.07

P (X < 21.9)

Formula:

Z = ( X - μ )/ σ

Z= (21.9 - 22)/ 0.07

Z = -1.43

P[(X- μ )/ σ < (21.9 -22/ 0.07)

P ( X < 21.9)  

P (Z < - 1.43 )

P ( X< 21.9) = 0.076 cm

Hence, 0.076 portions of the rods have a length of less than 21.9 cm

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h: The domain

-5 ≤ x ≤ 5

Answer: 17 nickels, and 8 dimes.

Step-by-step explanation:

So Miles has 25 coins in his pocket, Suppose that x is the number of nickels, and y is the number of dimes, then we have that:

x + y = 25

And we also know that the total value is $1.65

Then we have that:

x*0.05 + y*0.10 = 1.65

Then we have a system of equations:

x + y = 25

x*0.05 + y*0.10 = 1.65

The first step is isolating one of the variables in one of the equations, i will isolate x in the first one.

x = 25 - y

Now we can replace that in the second equation:

(25 - y)*0.05 + y*0.10 = 1.65

Now we solve this for y.

25*0.05 - y*0.05 + y*0.10 = 1.65

1.25 + y*(0.10 - 0.05) = 1.65

y*0.05 = 1.65 - 1.25 = 0.40

y = 0.40/0.05 = 8

So Miles has 8 dimes.

And:

x + y = 25

x + 8 = 25

x = 25 - 8 = 17

And Miles has 17 nickels.

Para calcular el volumen  de un prisma rectangular, multiplica sus 3 dimensiones: longitud x ancho x altura.

Answer:

24

Step-by-step explanation:

i dont know if its correct

Answer:

289 and 324

Step-by-step explanation:

first find the root of 300 then the number you get is 17.3205.... then look in the line and look at the points in between 17 and 18 then find the square root of 17 and you'll get your answer

Answer:

luke and han solo

Step-by-step explanation:

because han solo have the most mins and luke is one of thr 2 mins and that added is 7min

The Probability of a time from 25 seconds to 150 seconds

To determine which option can be found using the given density graph, we need to understand the concept of probability and how it relates to a density graph.

A density graph represents the probability distribution of a continuous random variable. The area under the density graph within a specific interval corresponds to the probability of the variable falling within that interval.

Let's analyze the given options one by one:

OA. The probability of a time from 150 seconds to 250 seconds.

To find this probability, we need to determine the area under the density graph between 150 seconds and 250 seconds. However, the given density graph only provides information from 50 seconds to 200 seconds, so we cannot accurately determine the probability for this interval. Therefore, option OA cannot be found using the given graph.

OB. The probability of a time from 75 seconds to 250 seconds.

Again, to find this probability, we need to calculate the area under the density graph between 75 seconds and 250 seconds. Since the given density graph only covers up to 200 seconds, we cannot accurately determine the probability for this interval. Thus, option OB cannot be found using the given graph.

OC. The probability of a time from 75 seconds to 150 seconds.

Now, we can determine the probability for this interval by calculating the area under the density graph between 75 seconds and 150 seconds. As long as this interval falls within the range covered by the graph (50 seconds to 200 seconds), we can accurately find the probability for it. Therefore, option OC can be determined using the given graph.

OD. The probability of a time from 25 seconds to 150 seconds.

Since the density graph only covers the range from 50 seconds to 200 seconds, we cannot determine the probability for an interval starting at 25 seconds. Therefore, option OD cannot be found using the given graph.

In conclusion, based on the information provided, option OC (the probability of a time from 75 seconds to 150 seconds) can be determined using the given density graph.

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Answer:

76 degrees

Step-by-step explanation:

x + 1 + 7x - 15 = 90

8x - 14 = 90

8x = 90 + 14

8x = 104

8/8 x = 104/8

x = 13

B = 7 * 13 - 15

B = 91 - 15

B = 76 degrees

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Answer:

E

Step-by-step explanation:

number divided.

Answer:

$80000

Step by step explanation:

start by adding all the ratios.

2+3+4=9

next devide $360000 by 9

that should give you $40000

then look at the smallest ratio with is 2 which means you must double the amount.

so that means $40000x2= $80000

$80000 is your answer

hope this helps!

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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