1.5 Determine the degree of the following algebraic expressions:
a. √3xyz - 5
b. y² - 3y5-y + 2y³ - 4
c. -10³

The frequency of the data sets is defined as the number of times the data is repeated in the given dataset. The frequency of the given data is calculated in the table below.

The frequency of the data sets is defined as the number of times the data is repeated in the given dataset.

Height (cm)              Frequency

146           --             2

147           --              1  

148           --              1                

149           --              1                  

150           --             2                  

151            --              1                      

152           --             6                                  

153           --             2                                      

154          --              3                                                  

155          --              1          

As we can see that the height of 146 cm is repeated two times so its frequency is 2. From this concept, all the frequencies are calculated above.

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Answer + Step By Step Explanation:

There is no single value for y as the input could differ (x)

y = -3/4x

if x = 0, y = -3/4(0) than y = 0

if x = 1, y = -3/4(1) than y = -3/4

...

if x = 5, y = -3/4(5) than y = -15/4

If the  -8 is under the square root, then...

[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2-8}\\\\L = \sqrt{(-3)^2-8}\\\\L = \sqrt{9-8}\\\\L = \sqrt{1}\\\\L = 1\\\\[/tex]

OR

If the -8 is not under the square root, then...

[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2}-8\\\\L = \sqrt{(-3)^2}-8\\\\L = \sqrt{9}-8\\\\L = 3-8\\\\L = -5[/tex]

Either way, we replace x with -3 and simplify.

For more information, refer to the direct substitution rule for limits.

The limit of   [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.

A limit is the value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity.

The given limit is [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]

Now replace x with -3 as limit value is -3

√(-3)²-8

Square root over minus three square minus eight

The three square is nine

√9-8

When eight is subtracted from nine we get one.

√1

The square root of one is always one

[tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]=1

Hence, [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.

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Answer:

Exact Area =

16pi - 32 square meters

Decimal Approx:

A = 18.3 sq m

Step-by-step explanation:

In degrees, it's 360° all the way around a circle. The 270° in the image is to show you that the small piece (the triangle and yellow segment) are in a 90° part of the circle. That is 1/4 of the circle, this helps with area two ways. We'll find 1/4 of the circle area and also, that makes the triangle base 8 and height 8. This helps us find triangle area. See image.

Answer:

80

Step-by-step explanation:

10 limits it to 50, 60, 70, 80, and 90

2 eliminates none since 50=25, 60=30, 70=35, 80=40 and 90=45

8 divided by each number only leaves one option of 80. (80/8= 10) (80/10=8) (80/2=40)

The lake whose flood level represents an outlier is Ozark.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The flood level of Ozark is way greater than the other flood levels.

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Answer:

90π in²

Step-by-step explanation:

  r = 3 in

  h = 10 in

     [tex]\sf \boxed{\text{\bf Surface area of cylinder =$\pi r^2h$}}[/tex]

                                                   [tex]= \pi 3*3*10\\\\= 90 \pi \ in^2[/tex]

In this question it is given that the radius of a cylinder is 3 inches. The height of the cylinder is 10 inches. We are asked to calculate the surface area of the cylinder in terms of π .

Radius = 3 inches

Height = 10 inches

We know,

[tex] \star \: \small \boxed{\rm{ Surface \: area \: of \: a \: cylinder = πr²h}}[/tex]

Substituting the values we get

[tex] \small\sf{ Surface \: area \: of \: a \: cylinder = π × 3² × 10}[/tex]

[tex] \small\rm{ Surface \: area \: of \: a \: cylinder = π × 3 \times 3 × 10}[/tex]

[tex] \small\rm Surface \: area \: of \: a \: cylinder = π × 90[/tex]

[tex] \small\sf{ Surface \: area \: of \: a \: cylinder = \bf{90 π \: inches²}}[/tex]

Answer:

0.1

Step-by-step explanation:

You are adding on 0.1 for each line and since G is the first line after 0, it is 0.1.

The value of x of the cubic equation e³ˣ + eˣ - 6 = 0 will be 0.49

The cubic equation is given as ax³ + bx² + cx + d = 0. Then degree of the equation will be 3. Then we have

The cubic equation will be

e³ˣ + eˣ - 6 = 0

Let eˣ = u, then the equation will be

u³ + u - 6 = 0

Then the root of the equation is calculated by the calculator, then we have

u = 1.634, -0.817, -0.817

eˣ = 1.634, -0.817, -0.817

Take log on both sides, then we have

x = ln 1.634, ln(-0.817), ln(-0.817)

x = 0.49, not defined, not defined

Then the value of x will be 0.49.

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Answer:

122.5 squared

Step-by-step explanation:

bahh have have aheve shaved she sbdnabd sjsbd akdbd

Answer:

x = -75

Step-by-step explanation:

[tex]\frac{3}{5}[/tex] x = - 45 ( multiply both sides by 5 to clear the fraction )

3x = - 225 ( divide both sides by 3 )

x = - 75

Answer:

A

Step-by-step explanation:

The surface area will be equal to option B which is 1008 square centimeters.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The surface area of the prism will be calculated as:-

SA = area of the three rectangular faces + area of the triangular faces

Area of the rectangular faces = ( 15 X 25 ) + ( 25 X 12 ) + ( 25 X 9 )

                                                 = 375 + 300 + 225

                                                 = 900 square cm

Area of the triangular  [tex]=\sqrt{(s(s-a)(s-b)(s-c)[/tex]

                                     = [tex]\sqrt{(18(18-15)(18-12)(18-9)}[/tex]

                                     = √2916

                                     = 64

Total area of the rectangular face = 2 x 54 = 108

So the total SA area of the prism will be = 900 + 108= 1008 square cm.

Therefore surface area will be equal to option B which is 1008 square centimeters.

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Answer:

[tex]a^{7} +b^{6}[/tex]

Hope this helps :)

Answer:  [tex]\frac{n!}{(n-r)!}[/tex]

The exclamation marks indicate factorial.

For instance, 4! = 4*3*2*1 = 24. You start with the given number and multiply your way down to 1.

For more information, check out the nPr permutation formula.

A percentage is a way to describe a part of a whole. The percentage decrease is 20%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

One year, the population of a city was 358,000. Several years later it was 286,400. Therefore, the percentage decrease is,

Percentage decrease = (358,000-286,400)/(358,000) × 100% = 20%

Hence, the percentage decrease is 20%.

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Answer:

see the attachment photo!

Answer:

25

Step-by-step explanation:

Since triangle DBC is isosceles, angles DBC and DCB must be congruent. Angle BDC is 40 so the sum of the measures of the aforementioned angles must be 180 - 40 = 140; divide that by two and you get that the measure of angle DBC is 70. Angles DBC and ABD are supplementary, as they lie on a straight line, so we can deduce the measure of angle DBA is 180 - 70 = 110. The measure of angle DAB is 180 minus the measures of angle DBA and ADB, we figured out angle DBA is 110 degrees and the problem tells us angle ADB is 45 degrees, so we can subtract to get the measure of angle DAB to be 180 - (110 + 45) = 25.

Answer:

25

Step-by-step explanation:

i dont know how to explain i just know thats the answer hahaha

The weeks will it take the grass to grow 12 over 7 centimeters is 3 weeks.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

St. Augustine grass can grow at the rate of 4 over 7 centimeters per week.

The weeks will it take the grass to grow 12 over 7 centimeters

4/7 x = 12/ 7

28x = 84

x = 84/28

x = 3

The weeks will it take the grass to grow 12 over 7 centimeters is 3 weeks.

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Answer:

12/7 divided by 4/7 = 3

Step-by-step explanation:

The box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

A box-and-whisker plot consists of the following values of a data set: min, max, lower quartile, median, and upper quartile.

Here, Given the data set,

30, 22, 22, 27, 28, 23, 24, 25, 26, 23

the five-number summary for the box-and-whisker plot would be:

Minimum: 22

Quartile Q1: 22.75

Median: 24.5

Quartile Q3: 27.25

Maximum: 30

Thus, the box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

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Answer:

part 1) BC is 17491 ft

part 2)  CD is 6499 ft

Step-by-step explanation:

Answer:

part 1) BC is 17491 ft

part 2)  CD is 6499 ft

The given inequality 5x - 5y > 70 when written in Slope intercept form is gotten as; y < x + (-14)

The formula for equation of a line in slope intercept form is given by;

y = mx + c

where;

m is slope

c is y-intercept

We are given the inequality as;

5x - 5y > 70

Thus;

Subtract  5x from both sides to get;

-5y > 70 - 5x

divide both sides by -5 to get

y < x + (-14)

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Answer:

25 degrees

Step-by-step explanation:

arc divided by 2 = angle

50/2=25

Answer:

Step-by-step explanation:

The median is defined as the middle value of a data set when all the data is arranged in numerical order.

If there is an even number of values, and therefore no middle value, then the median is calculated as the mean value of the two middle values.

Answer:

c and a

Step-by-step explanation:

Answer:

it's both A and C

Step-by-step explanation:

2 x 3/8 is the same as 3/8 + 3/8

Answer:

78

Step-by-step explanation:

= 12 x^2 - 30         put in ' - 3 ' for  'x'

= 12 ( -3 )^2 - 30

 = 12 (9) - 30 = 78

Answer:

78

Step-by-step explanation:

Expression:

Evaluate x = 3 according to the question:

[tex]6 \{2 (- 3) {}^{2} - 5) \}[/tex]

Solve this problem, applying PEMDAS.

Hence,the answer to the given expression is 78.

-Regards,Hannah :)

Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:

b. 0.2.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:

p = 26/130 = 0.2, which means that option b is correct.

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Answer:

[tex]5.6 \times 10^{-8}~ m[/tex]

Step-by-step explanation:

[tex]0.000000056\\\\=\dfrac{56}{1000000000}\\\\\\=\dfrac{56}{10^9}\\\\\\=56 \times 10^{-9}\\\\\\=56 \times 10^{-1} \times 10^{-8}\\\\\\=5.6 \times 10^{-8}~[/tex]

Let S be the sum,

S = 2 + 4 + 6 + ... + 2 (n - 2) + 2 (n - 1) + 2n

Reverse the order of terms:

S = 2n + 2 (n - 1) + 2 (n - 2) + ... + 6 + 4 + 2

Add up terms in the same positions, so that twice the sum is

2S = (2n + 2) + (2n + 2) + (2n + 2) + ... + (2n + 2)

or

2S = n (2n + 2)

Divide both sides by 2 to solve for S :

S = n (n + 1)