three consecutive odd integers have a sum of 51. what is the smallest integer

The equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]

The expression is given as:

[tex]\frac{(5ab)^3}{30ab^{-7}}[/tex]

Expand the numerator

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}[/tex]

Divide 125 and 30 by 5

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}[/tex]

Apply the law of indices

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}[/tex]

Evaluate the exponent

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}[/tex]

Hence, the equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]

Read more about equivalent expression at:

https://brainly.com/question/2972832

#SPJ1

Work Shown:

[tex]\displaystyle \lim_{x \to c}f(x) = -4\\\\\\\lim_{x \to c}g(x) = 1/5\\\\\\L = \lim_{x \to c}\frac{g(x)}{f(x)}\\\\\\L = \frac{\displaystyle \lim_{x \to c}(g(x))}{\displaystyle \lim_{x \to c}(f(x))}\\\\\\L = \frac{1/5}{-4}\\\\\\L = (1/5)*(-1/4)\\\\\\L = -1/20\\\\[/tex]

Put simply, we divide the two given values g(x) = 1/5 over f(x) = -4 to end up with -1/20

Answer:

1.  0.9925  (4 d.p.)

2.  17°

3.  67°

Step-by-step explanation:

Question 2

⇒ sin 83° = 0.9925461516...

⇒ sin 83° = 0.9925 (4 d.p.)

Question 3

[tex]\sf \implies \sin X=0.2923[/tex]

[tex]\sf \implies X=\sin^{-1}(0.2923)[/tex]

[tex]\implies \sf X=16.99570395...^{\circ}[/tex]

[tex]\implies \sf X=17^{\circ}\:\:(nearest\:degree)[/tex]

Question 4

Sine Ratio

[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]

where:

From inspection of the triangle:

Substitute the values into the formula and solve for W:

[tex]\implies \sf \sin(W)=\dfrac{24}{26}[/tex]

[tex]\implies \sf W= \sin^{-1}\left(\dfrac{24}{26}\right)[/tex]

[tex]\implies \sf W=67.38013505...^{\circ}[/tex]

[tex]\implies \sf W=67^{\circ}\:\:(nearest\:degree)[/tex]            

Answer:

The actual width would be 9.75 feet. (I think).

Step-by-step explanation:

If two inches represents three feet, then two inches also represents thirty-six inches. You would then have to set up the proportion [tex]\frac{2}{36} = \frac{6.5}{x}[/tex]. Solving that proportion would get you an answer of 117 inches, equal to 9.75 feet. I hope this helps! :)

Answer:

$25.10

Step-by-step explanation:

lunch=$7.52

dinner=$9.74

breakfast=$5.16

money left=$2.68

make total money he began with ‘x’

to find the total money he began with it will be

x-lunch+dinner+breakfast=money left

x-$7.52+$9.74+$5.16=$2.68

x-$22.42=$2.68

x=$2.68+$22.42

x=$25.10

The principal value of Arccsc (1.607) to the nearest minute is 38°29'

To answer the question, we need to know what arccsc is

Arccsc is the inverse of the cosec of an angle.

Let x =  arccsc(1.607)

So, taking the inverse, we have

csc(x) = 1.607

Since csc(x) = 1/sinx, we have

1/sinx = 1.607

sinx = 1/1.607

sinx = 0.6223

Taking inverse, we have

x = arcsin(0.6223)

x = 38.483°

Since 60' = 1°, we have

x = 38 + 0.483° × 60'/1°

x = 38° + 28.98'

x = 38°28.98'

x ≅ 38°29'

So, the principal value of Arccsc (1.607) to the nearest minute is 38°29'

Learn more about arccsc here:

https://brainly.com/question/14495359

#SPJ1

Answer:

y=x+4

Step-by-step explanation:

pretty sure

Answer:

24 is the length of segment XZ

After considering the given data we come to the conclusion that the two other cards are 6 and 10, under the condition that Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8.

Let us assume that the other two cards x and y.
The given mean of all six cards is 8. Then, the sum of all six cards is 48 (8×6). We have that four of the cards are 8s.
So, the summation of these four cards is 32 (8×4).
The dedicated range of all six cards is 4. Therefore, the difference between the largest and smallest card is 4.
Furthermore, we know that four of the cards are 8s, the other two cards must be different from 8.
Hence, we can consider that x and y are the smallest and largest numbers in the set.
Here we have to apply basic algebraic expression
We can perform the setting up two equations:
x + y = 48 - 32 = 16 (the summation of x and y is equivalent to the summation of all six cards minus the summation of the four 8s)
y - x = 4 (the difference considering y and x is equal to the range of all six cards)
Evaluating these equations simultaneously gives us:
y = 10
x = 6
Therefore, the other two cards are 6 and 10.
To learn more about algebraic expression
https://brainly.com/question/4344214
#SPJ1

The sum of the cubes of first 15 natural numbers.

[tex]( \frac{(15 \times 16)}{2} {)}^{2} [/tex]

[tex] = (15 \times 8 {)}^{2} [/tex]

=14400

Hence, the sum of the cubes of first 15 natural numbers is 14400

Answer:

As x approaches infinity, f(x) approaches negative infinity

As x approaches negative infinity, f(x) approaches negative infinity

Step-by-step explanation:

Because the function goes in the downward direction on both sides, it would be negative infinity for both.

It's basically saying, as the x values go towards the positives, the y values go towards the negatives

and as the x values go towards the negatives, the y values go towards the negatives.

The information shows that:

It should be noted that the mean is the average of the numbers that are given.

The median is the number in the middle when they are arranged in ascending or descending order. The mode is the number that appears most.

Learn more about mean on:

brainly.com/question/1136789

#SPJ1

(x+a)(x+3a)= x²+bx+75

x²+4a+3a²=x²+bx+75

by comparing 3a²=75 and b= 4a

a= ±5

possible values of b= ±20

Two possible values of b are 20 and -20.

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The mathematical expression as;

(x + a)(x + 3a) = x² + bx + 75​

Now,

The mathematical expression is;

(x + a)(x + 3a) = x² + bx + 75​

Solve the expression as;

(x + a)(x + 3a) = x² + bx + 75​

x² + 3ax + ax + 3a² = x² + bx + 75

x² + 4ax + 3a² = x² + bx + 75

After comparison we get;

4a = b  ... (i)

And, 3a² = 75  .. (ii)

Solve the second equation for a as;

3a² = 75

Divide by 3;

a² = 25

Take square root both side, we get;

a = ± 5

So, By equation (i) we get;

b = 4a

Substitute a = 5;

b = 4 x 5

b = 20

And, Substitute b = -5;

b = 4 x -5

b = -20

Thus, Two possible values of b are 20 and -20.

Learn more about the quadratic equation visit:

https://brainly.com/question/24034973

#SPJ2

Answer:

Your answers are:

A, B and C

Step-by-step explanation:

So 12 over 3 is equal to 4 which is a Whole number. meaning Not a fraction, an Integer is a whole number (not a fractional number) that can be positive, negative, or zero. Rational numbers would include this example as well

Hope this helped have a wonderful day/night/afternoon

P(B|A) expressed in simplest form is  8/105.

Probability determines the chances that an event would happen. The chance of the event happening lies between 0 and 1.

P(B|A)  = (number of blue balls / total number of balls) x (number of white balls / total number of balls - 1 )

(4/15) x 4/14 = 8/105

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ1

The value of x in the triangle using the cosine rule is 22.1 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:

c² = a² + b² - 2ab cos C

Where a, b, c are the sides and C is the angle opposite side c.

Using cosine rule:

8² = 14² + 19² - 2(14)(19) * cos(x)

cos(x) = 0.9267

x = 22.1°

The value of x in the triangle using the cosine rule is 22.1 degrees.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Using the law of Cosines, the value of x to the nearest tenth is 77.8

From the question, we are to determine the value of x

Using the law of Cosines

c² = a² + b² - 2ab cos C

c is the unknown side length  

a and b are the given side lengths

and C is the included angle

From the given information,

a = 63

b = 62

C = 142°

Then,

x² = 63² + 61² -2×63×61 cos 142°

x² = 3969 + 3721 -7686(-0.788)

x² = 7690 + 6056.568

x² = 13746.569

x = √13746.569

x = 77.8

Hence, the value of x to the nearest tenth is 77.8

Learn more on Law of Cosines here: https://brainly.com/question/23282500

#SPJ1

The ordered pair that is 5 units away is (-1, -3)

What is a line?

A line is a distance between two points.

Analysis:

see attached file.

In conclusion, the ordered pair is (-1, -3)

Learn more about distance: brainly.com/question/7243416

#SPJ1

Answer:

5.3

Step-by-step explanation:

Since they are similar triangles, we assume the ratio between AM/AN is equal to the ratio between MB/NC.
AM/AN = 6/8 = 3/4
If MB is 4
3/4 = MB/NC = 4/NC
3/4 = 4/NC

3NC = 16
NC = 16/3
16/3 = 5.333333

Answer:

45 degrees

Step-by-step explanation:

A reference angle can be found by identifying its terminal side and see by what angle the terminal side is close to the x-axis.

To do this, we can subtract this given angle by the nearest 90° angle.

270° is the closest.

[tex]\textsf {Solving :}[/tex]

[tex]\implies \textsf{Reference angle = 270 - 225}[/tex]

[tex]\implies \textsf {45 degrees}[/tex]

The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

As per the given angle,

θ = 225°

It is going to the third quadrant as shown below,

The reference angle is the angle from x-axis.

The angle from the negative x-axis will be as,

180° + x = 225°

x = 225° - 180° = 45°

Hence "The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°".

For more about the angle,

brainly.com/question/13954458

#SPJ6

The number of ways for the jobs to be ordered in the queue so that job A is the first to finish or the last to finish is; 2 * 9!

We are told that;

There is a set of 10 jobs in the printer queue.

One of the jobs is job A. Thus, there are 9 other identified jobs.

Number of ways to order this nine jobs = 9!

Since the job A has to be ordered first or last, then;

Number of ways to order job A = 2 ways.

Thus;

Total number of ways to order the jobs in the given order = 2 * 9!

Read more about permutation and combination at; https://brainly.com/question/4658834

#SPJ4

The measure of central tendency that is most affected by the lowest score is; A: The mean.

The points table is missing and so I have attached it.

The 3 main measures of central tendency are called mean, median and mode.

Now, from the table attached, if we find the average which is the mean, we will get 56.6.

Now, the mode is the number that occurs the most times. In this case, there is no mode because no number appears more than the other.

For the median, if we arrange in ascending order, we have;

42, 48, 49, 53, 55, 56, 58, 66, 68, 71.

The median = (55 + 56)/2 = 55.5

Now, if we remove the lowest score, the measure that will be most affected will be the mean as the median will only change by 0.5 to 56.

Read more about Measures of Central tendency at; https://brainly.com/question/17631693

#SPJ1

Answer:

B

Step-by-step explanation:

Answer:

[tex]m=\dfrac{-n+p}{10}[/tex]

Solve for 'm'

To solve for 'm', we have to isolate 'm'.

          10m - p = -n

                  10m = -n + p

                   [tex]\sf\dfrac{10m}{m}=\dfrac{-n+p}{10}\\[/tex]

                    [tex]\sf \boxed{\bf m = \dfrac{-n+p}{10}}[/tex]

Answer:

hope you can understand

Answer:

11,676 M&M's

Step-by-step explanation:

A dozen is 12

the problem is saying that in the jar, there are 973 (12-M&M's)

973 * 12 is 11676

There are 11,676 M&M's in the jar

Answer:

they are 11,676

Step-by-step explanation:

A dozen is 12 so since there are 973 dozen, we multiply by 12.

A function assigns the values. The function will be 8cos(2x-π)+4.

A function assigns the value of each element of one set to the other specific element of another set.

Given the maximum value is 12, while the minimum value is -4, therefore,

A = (Max-Min)/2 = 12-(-4)/2 = 8

D = (Max+Min)/2 = (12-4)/2 = 4

Period=π, but since x =-4 at 0 or π, therefore,

(2π/B) = π

B = 2π/π = 2

C/B = π/2, {∴At π/2 maximum}

C=π

Hence, the function will be 8cos(2x-π)+4.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ4

The average rate of change for this function for the interval from x = 1

to x = 3 will be 8. Therefore option B is correct.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where when

[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]

The average rate of change can be calculated as;

From x=1 to x=3,

y = 2 and y = 18

Therefore, based on the table, when:

[tex]x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18[/tex]

Then:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8[/tex]

Therefore option B is correct.

Learn more about average;

https://brainly.com/question/12424098

#SPJ1