2. In how many ways can the 18 members of a Boy Scout troop elect a president, a vice-president, and a secretary, assuming that no member can hold more than one office?
3. If a family has three children, find the probability that the two of the children are girls?
4. In how many ways can we seat 7 people at a round table with a certain 3 people side by side?
5. In testing an HP printer, the Quality Inspector found that 25% of the printers fail to pass the test
print. Of the next 15 printers tested, find the probability that fewer than 4 fail to pass the test print.

Answer:

they both are right triangle

Step-by-step explanation:

The range for the usual number of correct answers is given as follows:

[7, 16]

The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

p = 0.5, n = 23.

The mean and the standard deviation are given as follows:

The usual range of correct answers is within 2.5 standard deviations of the mean, hence:

More can be learned about the binomial distribution at https://brainly.com/question/24756209

#SPJ1

We know that sum of all angles of a triangle is 180°,

So,

[tex] \sf2x + 1 + 5x + 5 + 90 = 180 \\ \sf7x + 96 = 180 \\ \sf7x = 180 - 96 \\ \sf7x = 82 \\ \tt \: x = 12[/tex]

Now,

[tex] \tt∠1 = 2x + 1 \\ \tt = 2(12) + 1 \\ \tt = 24 + 1 \\ \tt= 25 \degree[/tex]

&

[tex] \tt∠ 2 = 5x + 5 \\ \tt = 5(12) + 5 \\ \tt = 60 + 5 \\ \tt = 65 \degree[/tex]

The required measure of the angles ∠A and ∠C is 25° and 65° respectively.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Consider the given triangle ABC,

Since we know that the sum of the interior angle of a triangle is equal to 180°.

∠A + ∠B + ∠C = 180,
2x + 1 + 90 + 5x + 5 = 180

7x + 6 = 90
7x = 84
x = 12

Now,
∠A = 2(12) + 1 = 25°
∠C = 5(12) + 5 = 65°

Thus, the required measure of the ∠A and ∠C is 25° and 65° respectively.

Learn more about triangles here:
https://brainly.com/question/2773823

#SPJ1

U is a subspace of R3.  A basis for U is  {(1, -2, 3)}  and dim(U) = 1.

a) To show that U is a subspace of R3, we must verify the three conditions:

1. U is non-empty, since the vector (0,0,0) ∈ U, since 0 + 2(0) - 3(0) = 0.
2. U is closed under addition, since for any two vectors (x1, y1, z1) and (x2, y2, z2) ∈ U, their sum (x1+x2, y1+y2, z1+z2) also satisfies the equation x1+x2 + 2(y1+y2) - 3(z1+z2) = 0, so it is also in U.
3. U is closed under scalar multiplication, since for any scalar c and any vector (x, y, z) ∈ U, the vector c(x,y,z) = (cx, cy, cz) also satisfies the equation cx + 2cy - 3cz = 0, so it is also in U.

Therefore, U is a subspace of R3.

b) To find a basis for U, we must find a linearly independent set of vectors which span U. One such set is the vector (1, -2, 3), since it satisfies the equation x + 2y - 3z = 0. Therefore, {(1, -2, 3)} is a basis for U.

c) The dimension of U is the number of vectors in its basis, which is 1. Therefore, dim(U) = 1.

To learn more about Vector Subspaces

Visit; brainly.com/question/30031077

#SPJ11

(C) p = p , could have been the final line of her work.

What is linear equation?

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

The linear equation with an infinite number of solutions must be of the form a = a, where a is some expression involving the variable.

So, out of the options given, the only one that fits this form is C.p = p, where both sides of the equation are equivalent for any value of p. Therefore, the correct answer is (C) p = p.

To know more about linear equation visit,

https://brainly.com/question/28732353

#SPJ1

To solve this problem, we will use polynomial long division. The solution to the problem is the solution to the problem is (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2) using polynomial long division. The steps are as follows:

1. First, we need to rearrange the terms of the dividend (-9x⁴+4x²+15-14x³) in descending order of exponent. This gives us: -9x⁴-14x³+4x²+15

2. Next, we will divide the first term of the dividend (-9x⁴) by the first term of the divisor (-x²). This gives us 9x².

3. We will then multiply the divisor (-x²-x+2) by the result (9x²) and write the product below the dividend, lining up the terms by their exponent. This gives us:
-9x⁴-9x³+18x²

4. We will then subtract this product from the dividend to get the remainder:
-9x⁴-14x³+4x+15
-(-9x⁴-9x³+18x²)
= -5x³-14x²+15

5. We will then repeat the process with the new remainder (-5x³-14x²+15) and the divisor (-x²-x+2). This gives us:
-5x³-14x²+15
-(-5x³-5x²+10x)
= -9x²+10x+15

6. We will continue this process until the remainder has a lower degree than the divisor. In this case, the final remainder is -9x²+10x+15.

7. The final answer is the quotient plus the remainder over the divisor: (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2)

Know more about polynomial long division here:

https://brainly.com/question/30989082

#SPJ11

By answering the above question, we may state that A kite has graphs perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

The measurements of the numbered angles in each kite cannot be given without a reference image or particular kite. We can, however, offer some general knowledge on kites and their angles.

With two sets of neighboring congruent sides and angles, a kite is a quadrilateral with congruent sides on all four sides. A kite has perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Let's give a generic kite's angles the labels displayed in the accompanying diagram:

  A-------B

 /         \

D-----------C

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

Likelihood that a randomly selected A Train will arrive on time is 0.44 or 44%.

What is the randomly selection?

Random selection is a process of choosing individuals, items, or samples from a population in a way that every member of the population has an equal chance of being selected.

To find the likelihood that a randomly selected A Train will arrive on time, we need to determine the number of A Trains that arrived on time and divide that by the total number of A Trains that arrived at the station.

From the table, we can see that there were a total of 50 trains that were A Trains, out of which 22 arrived on time. Therefore, the probability that a randomly selected A Train will arrive on time is:

P(A Train arrives on time) = Number of A Trains that arrived on time / Total number of A Trains

= 22 / 50

= 0.44

Therefore, likelihood that a randomly selected A Train will arrive on time is 0.44 or 44%.

To know more about probability, visit:

brainly.com/question/13604758

#SPJ9

When rounding a number to 2 decimal places, we are essentially keeping only the first two digits after the decimal point and discarding the rest. The third digit after the decimal point is the one that affects the rounding decision.

In this case, the number y is rounded to 9.68, which means that the third digit after the decimal point is either 5 or greater than 5. If it is 5 or greater, we round up the second digit after the decimal point. If it is less than 5, we simply truncate the decimal part.

To find the upper bound of y, we need to add 0.005 to 9.68, which is the smallest possible value for the third digit that would cause rounding up:

9.68 + 0.005 = 9.685

Therefore, the upper bound of y is 9.685.

To find the lower bound of y, we need to subtract 0.005 from 9.68, which is the largest possible value for the third digit that would not cause rounding up:

9.68 - 0.005 = 9.675

Therefore, the lower bound of y is 9.675.

Hence, the upper and lower bounds of y are 9.685 and 9.675, respectively.

let's keep in mind that in the II Quadrant, sine is positive and cosine is negative, so just about the same for the opposite and adjacent sides of the angle "x", so

[tex]\sin(x )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=adjacent\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ a=\pm\sqrt{ 5^2 - 3^2} \implies a=\pm\sqrt{ 16 }\implies a=\pm 4\implies \stackrel{II~Quadrant }{a=-4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cos(x )=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}}\hspace{9em} \tan\left(\cfrac{\theta}{2}\right)=\cfrac{\sin(\theta)}{1+\cos(\theta)} \\\\\\ \tan\left(\cfrac{x}{2}\right)\implies \cfrac{\frac{3}{5}}{1-\frac{4}{5}}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{\frac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{5}{1}\implies \text{\LARGE 3}[/tex]

This vector has a magnitude of 5 and points in a direction 175 degrees counterclockwise from the positive x axis.

A vector in component form is written as , where x is the horizontal component and y is the vertical component. We can use trigonometry to find the x and y components of the vector.

The x component is found by multiplying the magnitude of the vector by the cosine of the direction angle:

x = magnitude * cos(direction)

x = 5 * cos(175)

x = -4.98

The y component is found by multiplying the magnitude of the vector by the sine of the direction angle:

y = magnitude * sin(direction)

y = 5 * sin(175)

y = 0.43

So, the vector in component form is:

Vector = <-4.98, 0.43>

This vector has a magnitude of 5 and points in a direction 175 degrees counterclockwise from the positive x axis.

Learn more about Magnitude

brainly.com/question/14452091

#SPJ11

The number of balloons which will not be used by Anissa is 4 balloons.

To make all 5 hats the same, Anissa needs to use the same number of balloons for each hat.

Let us call the number of balloons she uses for each hat "x". Since she's making 5 hats, she'll use a total of 5x balloons. We know that she has 54 balloons in total, so we can set up an equation:

5x = 54

To solve for x, we can divide both sides by 5:

x = 54 / 5

x = 10.8

Since she can't use a fraction of a balloon, she'll need to use 10 balloons for each hat.

= 5 hats x 10 balloons/hat

= 50 balloons used

So Anissa will not use:

= 54 - 50

= 4 balloons.

Read more about balloons

brainly.com/question/1286703

#SPJ1

The triangles are similar by SAS rule.

Similar triangles are those triangles which have the same shape, but different size.

The corresponding angles of similar triangles are equal and the corresponding sides are proportional.

Given are two triangles ΔGNH and ΔLNM.

∠N is common to both triangles are thus equal.

So ∠N ≅ ∠N

GN / LN = 40 / (12.5 + 40) = 40/52.5 = (16×2.5) / (21×2.5) = 16/21

HN / MN = 32 / (10 + 32) = 32/42 = (16×2) / (21×2) = 16/21

Two corresponding sides are proportional.

So, we have, two corresponding sides are proportional and the corresponding included angles are equal.

This is SAS Similarity rule.

Hence the triangles are similar by SAS similarity rule.

Learn more about Similar Triangles here :

https://brainly.com/question/29191745

#SPJ1

Answer:

2 hours

Step-by-step explanation:

shhsjdnd

dididjd

djdjdjdj

Answer:

the minimum value is -2

the axis of symmetry is then line x=-1

Answer:

C.

Step-by-step explanation:

C. show the undulating forms of fabric.

Answer:

Is Wendy was going faster at 10.5 mph.

To find mph, you divide the distance by the time. 63 divided by 6 is 10.5, which is faster than 10.1

By answering the above question, we may infer that Hence, during the equation blizzard, snowfall totaled about 100.43 inches.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

To begin, let's calculate the amount of snow that evaporated. If 77% of the snow melted, the quantity of snow that is left is 100% - 77%, or 23%, of what was originally there.

This can be represented as:

Snow remaining equals 0.23x.

Assume that x inches of snow were present at the start. Thus, we may construct the equation shown below:

0.23y = 30

By finding y, we obtain:

y = 30 / 0.23 ≈ 130.43

Hence, the initial snowfall measured about 130.43 inches.

We may use the difference between the present depth of snow and the original depth of snow to calculate how much snow fell during the blizzard:

130.43 - 30 = 100.43

Hence, during the blizzard, snowfall totaled about 100.43 inches.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

sql

Copy code

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

The quotient is the number above the division line, which is 10 with a remainder of 23/100. Therefore:

9 / 0.85 = 10 with a remainder of 23/100, or 10.5882 (rounded to four decimal places)

So, 9 divided by 0.85 is approximately 10.5882.

The treatment for as usual group (M = 24.32, SD = 5.19).

Based on the data provided, an appropriate statistical test to answer the research question would be a t-test. Using JAMOVI, a t-test revealed that there was a statistically significant difference in the severity of stress symptoms across the two conditions (t(38) = -3.5, p < 0.001). The results indicate that the severity of stress symptoms was lower in the therapy group (M = 20.65, SD = 5.05) than in the treatment-as-usual group (M = 24.32, SD = 5.19). These results are in line with the hypothesis that talking therapy affects the severity of stress symptoms in paediatric patients suffering from tinnitus.

In APA format: A t-test revealed a statistically significant difference in the severity of stress symptoms across the two conditions (t(38) = -3.5, p < 0.001). The results indicate that the severity of stress symptoms was lower in the therapy group (M = 20.65, SD = 5.05) than in the treatment-as-usual group (M = 24.32, SD = 5.19).

Learn more about hypothesis

brainly.com/question/29519577

#SPJ11

We can observe that Denver and Chicago are separated by 1,114 miles by changing the units.

Changing the unit is the process of converting a given quantity from one unit of measurement to another. This is done to ensure accuracy and consistency in measurement. This process is used in many different areas of life, from converting between metric and imperial measurements in cooking to converting between Fahrenheit and Celsius in temperature measurement.

We now employ the conversion in the left-hand corner. We can simplify this as: since each unit equals 557 miles,
2 units equal 1,114 miles (2 * 557 miles).
The distance between Denver and Chicago is 1,114 miles.

To learn more about changing the unit
https://brainly.com/question/30759896
#SPJ1

The product of the inverse of these elementary matrices gives us the original matrix A:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1) =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]

Consider the given Gauss-Jordan reduction:
A =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]

We need to find the elementary matrices E1, E2, E3, and E4 such that:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1)

First, we can use an elementary matrix E1 to subtract 4 times the first row from the second row:
E1 =
[ 1 0 0 ]
[ -4 1 0 ]
[ 0 0 1 ]

Next, we can use an elementary matrix E2 to add -2 times the second row to the first row:
E2 =
[ 1 -2 0 ]
[ 0 1 0 ]
[ 0 0 1 ]

Then, we can use an elementary matrix E3 to subtract the third row from the second row:
E3 =
[ 1 0 0 ]
[ 0 1 -1 ]
[ 0 0 1 ]

Finally, we can use an elementary matrix E4 to divide the second row by 8:
E4 =
[ 1 0 0 ]
[ 0 1/8 0 ]
[ 0 0 1 ]

Therefore, the product of the inverse of these elementary matrices gives us the original matrix A:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1) =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]

Learn more about Elementary matrices

brainly.com/question/30889397

#SPJ11

The probability of selecting a red pencil and a green M&M is calculated as follows:

p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The pencil and the M&M are independent events, hence we calculate the probability of each event and then multiply then, as follows:

p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

Based on the calculation, we find that:

(fog)(x) = (15Vx)¹⁵
(gof)(x) = 15V(x¹⁵)
(fog)(x) ≠ (gof)(x)

Function composition can be meant as an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

To find (fog)(x), we need to substitute g(x) into f(x). This means that we will replace every x in f(x) with 15Vx. So, (fog)(x) = f(g(x)) = f(15Vx) = (15Vx)¹⁵.

Similarly, to find (gof)(x), we need to substitute f(x) into g(x). This means that we will replace every x in g(x) with x¹⁵. So, (gof)(x) = g(f(x)) = g(x¹⁵) = 15V(x¹⁵).

Now, to determine whether (fog)(x) = (gof)(x), we need to compare the two expressions.

(fog)(x) = (15Vx)¹⁵ and (gof)(x) = 15V(x¹⁵). These two expressions are not equal, so (fog)(x) ≠ (gof)(x).

Learn more about composite functions: https://brainly.com/question/30143914

#SPJ11

Step-by-step explanation:

similar means that they have the same angles, and that there is one common scaling factor between correlating sides of the 2 triangles.

so,

38/60 = (x + 10)/36

x + 10 = 38×36/60 = 38×3/5 = 114/5

x = 114/5 - 10 = 114/5 - 50/5 = 64/5 = 12.8

The total salary received by the tanker driver if he worked the entire month would be equal to Rs. 19980 .

It is already given that the tanker driver worked for 5 and a half days for 9 hours daily, except on Saturday where they worked for half a day (which means 4.5 hours) and were paid double than the daily rate. It is also known that the month of June has 30 days. So calculating the number of working days, we get approximately 4 working weeks in which 20 days are week days and 4 days are Saturdays.

Total amount earned by the tanker driver = (No. of week days worked × Total hours worked × Rate of pay per hour) + (No. of working Saturdays × Total hours worked × Rate of pay per hour on Saturday)

Total amount earned by the tanker driver = (20 × 9 × 92.50) + (4 × 4.5 × 185)

Total amount earned by the tanker driver = 16650 + 3330 = 19980

Learn more about salary on:

brainly.com/question/1628344

#SPJ4

Refer to complete question below:

The driver of the water tanker works for 5½ days per week and 9 hours per day on week days except on Saturdays where they work for a ½ day (4.5 hours). The rate per hour was Rs. 92.50 and the rate of pay was doubled on Saturdays. Work out the June salary that was received by the tanker driver if he worked the entire month.

Using the sine rule and triangle ABC,   the height  is 14.43375ft. BAC=40° and ABC=30°

if C is 20° and  A is 50°

ABC=50°-20°=30°

BCA=20°+90°=110°

ABC+BCA+BAC=180°

30°+110°+BAC=180°

BAC=180°-140°=40°

Using the sine rule and triangle ABC,

opposite=x

adjacent =25 m.

tanθ =x/25

Multiplying both sides by 25 gives

x=25* tan 30° =25* 0.57735.=14.43375

To put it another way, there is only one plane that contains all of the triangles. All triangles are enclosed in a single plane on the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless otherwise specified, this article deals with triangles in Euclidean geometry, specifically the Euclidean plane.

Learn more about triangle from

https://brainly.com/question/17335144

#SPJ1

Answer:

(a).

Area of circle:

=πr²

=6²×π

=36π

=113.0973355292...

=113.1 cm² (1 d.p.)

(b).

Volume of cylinder = πr²×height

1700=6²π×h

1700=113.1×h

1700÷113.1=h

15.0309460654=h

h=15.0cm (1 d.p.)

Answer:

(a) a = 60

(b) a = 75

(c) a = 108

All are corresponding.

Step-by-step explanation:

These questions involve the laws of angles on parallel lines. I like to call them "C", "F" and "Z" angles.

(a) is an example of a "Z" angle. By observation you can see that a is equivalent to the 60 degree angle as they are both internal angles of the "Z" shape created by a line intersecting the pair of parallel lines.

(b) is an example of an "F" angle. a is equivalent to the 75 degree angle because the straight line intersects the pair of parallel lines at the same angle.

(c) is another example of an "F" angle. a is equivalent to the 108 degree angle for the same reason as in question (b).

All the answers are corresponding angles because they are the same as the original. An alternate angle would be where your angle and the original sum to 180, as would be the case in "C" angles (also known as "co-interior" angles).