10) Find three numbers whose product is -72. You may use integers from -10 to 10. Give two
examples

Answer:

There are 2,598,960 ways to receive 5 cards from a deck of 52.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

a. How many ways are there to receive 5 cards from a deck of 52?

[tex]C_{52,5} = \frac{52!}{5!(47)!} = 2598960[/tex]

There are 2,598,960 ways to receive 5 cards from a deck of 52.

Answer:

obtuse angle that's the answer

9514 1404 393

Answer:

  (a)  2

Step-by-step explanation:

Each inch is 2.54 cm, so 5.08 cm is ...

  x / (5.08 cm) = (1 in) / (2.54 cm)

  x = (1 in)(5.08/2.54) = (1 in)(2)

  x = 2 in

5.08 cm equals 2 inches.

Write each equation in standard form:

3x + y + 3z = 11

x + 2y + z = 7

-x + y + z = 0

In matrix form, this is

[tex]\begin{bmatrix}3&1&3\\1&2&1\\-1&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}11\\7\\0\end{bmatrix}[/tex]

and in augmented matrix form,

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\1&2&1&7\\-1&1&1&0\end{bmatrix}\right][/tex]

Now for the row operations:

• Add row 1 to -3 (row 2), and add row 1 to 3 (row 3):

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&-5&0&-10\\0&4&6&11\end{bmatrix}\right][/tex]

• Multiply row 2 by -1/5:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&4&6&11\end{bmatrix}\right][/tex]

• Add -4 (row 2) to row 3:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&6&3\end{bmatrix}\right][/tex]

• Multiply row 3 by 1/6:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

• Add -1 (row 2) and -3 (row 3) to row 1:

[tex]\left[\begin{array}{ccc|c}3&0&0&\frac{15}2\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

• Mutiply row 1 by 1/3:

[tex]\left[\begin{array}{ccc|c}1&0&0&\frac52\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

Then the solution to the system is (x, y, z) = (5/2, 2, 1/2).

Answer:

6 and 2/3

Step-by-step explanation:

you do 1 2/3 x 4 because that is the amount of flour you need to make one batch. That is the correct answer.

9514 1404 393

Answer:

  78.5 km

Step-by-step explanation:

Measured at the airport, the angle between the two planes is ...

  180° -60° -50° = 70°

The law of cosines tells us the distance between the planes is ...

  d = √(50² +80² -2·50·80·cos(70°)) ≈ √6163.84 ≈ 78.5 . . . km

The planes are about 78.5 km apart.

Answer:

edge of cube = root 13.5/6 = 1.5

volume of cube = (Edge of cube)^3= (1.5)^3 = 3.37500 m^3

Answer:

see below

Step-by-step explanation:

10 + 15k

Factor out the greatest common factor 5

5( 2+3k)

Rewriting

5(3k+2)

Rami is correct if a=2 then his expression is 5(3k+2)

Kenneth

yk+6+8k+4

Add the terms together

k(y+8) + 10

If y =7 then Kenneth is correct otherwise he is incorrect

Answer:

A) 10%

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Sam's monthly bills are normally distributed with mean 2700 and standard deviation 230.9.

This means that [tex]\mu = 2700, \sigma = 230.9[/tex]

What is the probability that his expenses will exceed his income in the following month?

Expenses above 2*1500 = $3000, which is 1 subtracted by the p-value of Z when X = 3000.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3000 - 2700}{230.9}[/tex]

[tex]Z = 1.3[/tex]

[tex]Z = 1.3[/tex] has a p-value of 0.9032.

1 - 0.9032 = 0.0968 that is, close to 10%, and thus the correct answer is given by option A.

Answer:

Step-by-step explanation:

Given functions are,

f(x) = x + 6

g(x) = 2x + 6

(f - g)(x) = (x + 6) - (2x + 6)

                   = -x

(f . g)(x) = f(x) × g(x)

            = (x + 6)(2x + 6)

            = 2x² + 6x + 12x + 36

            = 2x² + 18x + 36

(f + g)(x) = (x + 6) + (2x + 6)

             = 3x + 12

(f + g)(1) = 3(1) + 12

            = 15  

Answer:

Step-by-step explanation:

Concept:

Here, we need to know the idea of a special triangle 30-60-90.

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.

The ratio between the corresponding side of each angle is 1 : √3 : 2

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

30-60-90 ⇔ 1 : √3 : 2

Given the side corresponding to 90° is 20

30° : 90° = 1 : 2

30° : 20 = 1 : 2

30° = 10

30° : 60° = 1 : √3

10 : 60° = 1 : √3

60° = 10√3

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x = 60

Step-by-step explanation:

The sum of the angles of a triangle add to 180

x+x+x = 180

3x = 180

Divide by 3

3x/3 =180/3

x = 60

Answer:

D) 3

Step-by-step explanation:

Rise/run, rise is 3, run is 1

Answer:

3

Step-by-step explanation:

Pick two points on the line

(0,0) and ( 1,3)

The slope is found by

m = ( y2-y1)/(x2-x1)

    = ( 3-0)/(1-0)

    = 3/1

   = 3

Answer:

3y(2x-1)(x-4y)

Step-by-step explanation:

Apply exponent rule:

6x^2y-3xy-24xyy+12yy

Rewrite 12 as 4*3

Rewrite -24 as 8*3

Rewrite 6 as 2*3

2*3x^2y-3xy+8*3xyy+4*3yy

Factor out common term 3y:

3y(2x^2-x-8xy+4y)

Factor 2x^2-x-8xy+4y:

3y(2x-1)(x-4y)

Your Answer Is 3y(2x-1)(x-4y)

Answer:

v<1 23/25

Step-by-step explanation:

The inequality simplifies to 48/25, which is equivalent to 1 23/25.

Step-by-step explanation:

Amount of acid = 14.9% of 331 mL solution

= 0.149×(331 mL)

= 49.3 mL acid

so

82-(-2)

=84

then ur answer is 84

Answer:

-40

Step-by-step explanation:

-55 + 15 = x

-40 =x

Answer:

it's going to be 4n so its going to be 4...

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Assuming you meant when n=14

10(n-6)

plug in 14 for n

10(14-6)

work out parenthesis first

10(8)=

80

Answer: Yes, but only if he houses 37, 38, 39, or 40 fish

Anything larger than 40 and he'll need more room.

==========================================================

Explanation:

The tank is 30 cm by 30 cm by 100 cm. The volume is 30*30*100 = 90,000 cm^3 which is shorthand for "cubic centimeters".

We're told that 1000 cm^3 = 1 liter, which means the 90,000 cm^3 converts to (90,000)/(1000) = 90 liters.

The fish tank is 90 liters.

Since 1 gallon = 4.5 liters, this means the 90 liter tank converts to 90/(4.5) = 20 gallons

----------------------------

Your teacher mentions "He can keep 2 small fish for every 1 gallon".

Since the tank is 20 gallons, that means he can keep 20*2 = 40 fish. This value is larger than 36, so Matt is correct to a point. If Matt is thinking 37, 38, 39, or 40 fish then he would be correct. If Matt is wanting more than 40 fish, then he'll need a bigger tank.

In short, he can't have any number over 36 and can only have 4 specific values (the four values mentioned earlier).

So technically, Matt is correct, but strong clarification is needed.

Answer:

465/1178 = .395 = 39.5%

Step-by-step explanation:

        224 + 245

224+ 387 + 245 + 322

465/1178 = .395 = 39.5%

Answer:

Total Distance : 1*60 +60=120

Total time taken = 1+ 60/30= 1+2=3

Hence average speed for the trip = 120/3= 40 kmph

Hence Answer is 40

Step-by-step explanation:

The average speed is 40 km/h.

The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:

Average Speed = Total distance covered ÷ Total time taken

Example:

sing the average speed formula, find the average speed of Sam, who covers the first 200 kilometers in 4 hours and the next 160 kilometers in another 4 hours.

Solution:

To find the average speed we need the total distance and the total time.

Total distance covered by Sam = 200Km + 160 km = 360 km

Total time taken by Sam = 4 hour + 4 hour = 8 hour

Average Speed = Total distance covered ÷ Total time taken

Average Speed = 360 ÷ 8 = 45km/hr

Given:

d1= 60 km

d2= 30

d3 = 60

Total Distance : 1*60 +60=120

Total time taken = 1+ 60/30= 1+2=3

Now,

average speed = total distance/ total time taken

= 120/3

= 40 kmph

Learn more about average speed here;

https://brainly.com/question/12322912

#SPJ2

9514 1404 393

Answer:

  3x +y -13 = 0

Step-by-step explanation:

The perpendicular line will have the variable coefficients swapped and one of them negated. The new constant will be appropriate to the given point.

  3(x -4) +1(y -1) = -0

  3x +y -13 = 0

_____

Additional comment

The given equation is in "general form", so that is the form of the equation we have given as the answer. This form is convenient in that the general form equation for a line through the origin, ax+by=0, is easily translated to make it pass through a point (h, k): a(x -h) +b(y -k) = 0. Eliminating parentheses puts the equation back into general form.

Answer:

Step-by-step explanation:

Arranging the data in the ascending order:

108.6 98.3 103.7 112 117.4 120 121.5 123.2 128.4

The median is the middle value of the data set:

a)

Hence,

median = 117.4

b)

When the value of blood pressure is 117.7 instead of 117.4 then the median will be:

Median = 117.7

c)

This indicates that the median of a well sorted set of data is depends upon the middle value of the data set.

Answer:  24.33

======================================================

Explanation:

The range is

range = max - min

range = 28.17 - 12.82

range = 15.35

This is the width of this particular uniform distribution.

Apply 75% to this value

75% of 15.35 = 0.75*15.35 = 11.5125

Then finally, add that to the min

12.82 + 11.5125 = 24.3325 which rounds to 24.33

We can see that 75% of the values are below 24.33 which makes it the 3rd quartile (Q3).

Answer:

1.) Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. ;

df = 24 ;

H0 : μ = 8.5

H1 : μ ≠ 8.5 ;

1.250 ;

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

There is insufficient evidence at the 0.05 level to reject the null hypothesis.

Step-by-step explanation:

Given :

Sample size, n = 25

xbar = 9 ; Standard deviation, s = 2

α = 0.05 ;

The degree of freedom, df = n - 1 ; 25 - 1 = 24

The hypothesis (two tailed)

H0 : μ = 8.5

H1 : μ ≠ 8.5

The test statistic :

(xbar - μ) ÷ (s/√(n))

(9 - 8.5) ÷ (2/√(25))

0.5 / 0.4

Test statistic = 1.250

The Pvalue from Tscore ;

Pvalue(1.250, 24) = 0.2234

Pvalue > α ; We fail to reject H0 ;