Factorise completely 9a^2-1

Answer:

D. 150 metres

Step-by-step explanation:

speed = (60) times 5/18 = 50/3

lenght of the train = (speed x time)

lenght = 50/3 times (9)

   = 150 m.

ANSWER

y=-1

EXPLANATION

The given line in the graph has equation

[tex]y = 2.5[/tex]

This line is a horizontal line.

All horizontal line has a slope of 0.

Let the equation of the line that is parallel to this line be

[tex]y = mx + b[/tex]

The slope of this line must also be zero.

We substitute the slope, m=0 and the point (3,-1) into this equation to get:

[tex] - 1 = 0(3) + b[/tex]

[tex] \therefore \: b = 0[/tex]

Hence the required equation is

[tex]y = - 1[/tex]

ANSWER

y= -1

Step-by-step explanation:

The given line in the graph has equation

This line is a horizontal line.

All horizontal line has a slope of 0.

Let the equation of the line that is parallel to this line be

The slope of this line must also be zero.

We substitute the slope, m=0 and the point (3,-1) into this equation to get:

Hence the required equation is

Answer:

19% of the total variation in the y-values is not explained by the regression line

Step-by-step explanation:

The correlation coefficient, r, is a measure of the degree of association between two variables. It gives information on the direction and strength of the relationship.

On the other hand, [tex]R^{2}[/tex] is the coefficient of determination and is a measure of the percent of the total variation in the y-values explained by the regression line.

[tex]R^{2}[/tex] is simply the square of r;

[tex]R^{2}=r^{2}=(-0.9)^{2}=0.81[/tex]

This implies that 81% of the total variation in the y-values is explained by the regression line. Therefore, only 19% is not explained.

Answer:

15x + 10

Step-by-step explanation:

distribute the 3x to the 2/x and 5 inside the parentheses:

3x(2/x) + 3x(5) + 4

multiply:

6x/x + 15x +4

There is x in the numerator and the denominator of 6x/x, so the xs cancel:

6 + 15x + 4

15x + 10

Answer:

15x+10

Step-by-step explanation:

3x (2/x + 5) +4

Distribute the 3x

3x*2/x + 3x*5 +4

6x/x + 15x +4

6+15x+4

Combine like terms

15x+10

Answer:

725 grams

Step-by-step explanation:

You divide 5.8 kg by 8 (the star containers)

and the final answer is 0.725 kg or 725 grams

Answer:

w =  120 + 5*(h-30)

Step-by-step explanation:

Part A;

We are informed that Andrew is paid $4 per hour for the first 30 hours he works each week and makes $5 per hour for each hour he works over 30 hours per week. This implies that the  $4 per hour for the first 30 hours is fixed while the $5 per hour overtime depends on the number of extra hours worked.

If we let w denote the wage and h denote the hours worked per week, then;

$4 per hour for the first 30 hours; 4*30 = 120

The number of extra hours worked would be; h-30

w =  120 + 5*(h-30)

This is the function that gives Andrew’s total wages when he works more than 30 hours each week.

for a rational expression the vertical asymptotes occur when the denominator equals 0, in this case that will be when x + a = 0.

now, if there were to be a vertical asymptote of x = 1, that simply means that

x = 1 ==> x - 1 = 0.

meaning that a = -1.

horizontal asymptotes occur when the denominator has a higher degree than the numerator OR when both have the same degree.

when the degree of the denominator is higher, then the only horizontal asymptote occurring is y = 0.

when the degrees are the same, then the horizontal asymptote occurs at the leading terms' coefficient fraction.

now, if this expression were to have a horizontal asymptote of y = 2, that simply means

[tex]\bf \cfrac{2x^m}{x+a}\implies \cfrac{2x^1}{1x^1+a}\implies \stackrel{\textit{horizontal asymptote}}{\cfrac{2}{1}\implies y=2}\qquad \textit{meaning m = 1}[/tex]

ANSWER

a=-1,m=1

EXPLANATION

The given function is

[tex]f(x) = \frac{2 {x}^{m} }{x + a} [/tex]

For this rational function to have a horizontal asymptote at y=2, the degree of the numerator must equal the degree of the denominator.

This implies that, we must have m=1.

For the function to have a vertical asymptote at x=1, then,

[tex]1 + a = 0[/tex]

This implies that,

[tex]a = 0 - 1[/tex]

[tex]a = - 1[/tex]

The correct choice is the third option.

Step-by-step explanation:

l - 2 x l = 4

     2 x = 4

         x = 2

Answer:

Answer:

-2 & 2

( option C )

Answer:

The product costs $0.37 per ounce.

Step-by-step explanation:

$29.75 for 5 pounds = x for 1 pound (Cross-Multiply)

5x/5 = $29.75/5

x = $5.95 per pound

$5.95 per pound/16 ounces = $0.37

$0.37 per ounce!

Answer:

$0.371875 does it cost per ounce.

Step-by-step explanation:

Use conversion:

1 pound = 16 ounces.

As per the statement:

A product costs $29.75 for 5 pounds.

In 5 pounds = product cost $ 29.75

then;

In 1 pound = [tex]\$\frac{29.75}{5}[/tex]

Using conversion we have;

In 16 ounces = [tex]\$\frac{29.75}{5}[/tex]

then;

in 1 ounces =  [tex]\$\frac{29.75}{80} = \$0.371875[/tex]

Therefore, $0.371875 does it cost per ounce.

Final answer:

The odometer reads 2 miles for every 3 actual miles driven. To find the actual distance when the odometer shows 48 miles, a proportion is used, leading to the calculation that the automobile has driven 72 actual miles.

Explanation:

The student is dealing with a proportion problem in mathematics where the automobile's odometer is inaccurate. Given that the odometer registers 2 miles for every 3 miles driven, we can set up a proportion to find the actual distance driven. If the odometer indicates 48 miles, we can write the proportion as follows:

2 miles (odometer) / 3 miles (actual) = 48 miles (odometer) / x miles (actual)

Cross-multiply to solve for x: 2x = 48 × 3

Calculate x: 2x = 144

Divide both sides by 2 to isolate x: x = 144 / 2

Find the value of x: x = 72 miles

Therefore, the automobile has actually been driven 72 miles.

I don't have popsicle but I'm sure you will melt by this answer.

[tex]

-x^1-10x-24=0 \\

x+10x+24=0 \\

11x=-24 \\

\boxed{x=\frac{-24}{11}}

[/tex]

Hope this helps. (please don't melt)

r3t40

Answer:

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

[tex]A.\ \dfrac{7}{x^2}=7x^{-2}\qquad\bold{NOT}\\\\B.\ x-\sqrt7\qquad\bold{YES}\\\\C.\ \dfrac{7}{\sqrt{x}}=7x^{-\frac{1}{2}}\qquad\bold{NOT}\\\\D.\ \sqrt{7x}=\sqrt7\cdot\sqrt{x}=\sqrt7 x^\frac{1}{2}\qquad\bold{NOT}[/tex]

Answer:

[tex]13[/tex]

Step-by-step explanation:

As the mean is 20.2 and the standard deviation is 2.4

The range within the first standard deviation is

(17.8,22.6)

This means that we can safely use the range of (18,22) as we cannot confirm whether the other values fall within the range.

Within this range there are

[tex]2+3+4+3+1=13[/tex]

The standard deviation of the mean is 13.

As the mean is 20.2 and the standard deviation is 2.4

The range within the first standard deviation is (17.8,22.6)

This means that we can safely use the range of (18,22) as we cannot confirm whether the other values fall within the range.

Within this range there are

2 + 3 + 4 + 3 + 1 = 13

Therefore, the correct answer is option (a) 13.

To learn more about the standard deviation of the mean

https://brainly.com/question/475676

#SPJ2

Answer:

Total number of eggs in basket = 56

Step-by-step explanation:

Let z be the total number of eggs

Green eggs = [tex]\frac{2}{7}[/tex] × z   ........1

Blue eggs =  [tex]\frac{1}{4}[/tex] × z    .......2

Rest of eggs = 26  ........3

The addition of 1, 2 and 3 is equal to z  

[tex]\frac{2}{7}[/tex] × z + [tex]\frac{1}{4}[/tex] + 26 = z

[tex]\frac{8z + 7 z}{28}[/tex] + 26 = z                        ∵GCF for 4 and 7 is 28  

[tex]\frac{15z}{28}[/tex]  + 26 = z

15z + (26 × 28) = 28z                ∵ multiply both sides by 28

15z + 728 = 28z

28z - 15z = 728     .......... rearranging above equation

13z = 728  ⇒   z = [tex]\frac{728}{13}[/tex]   ⇒  z = 56

Total number of eggs = z = 56

Answer:  There are total 56 eggs in the basket.

Step-by-step explanation:  Given that an Easter basket contains eggs of three different colors, out of which [tex]\dfrac{2}{7}[/tex] are green, [tex]\dfrac{1}{4}[/tex] are blue and rest 26 eggs are red.

We are to find the total number of eggs in the basket.

Let x be the total number of eggs in the Easter basket.

Then, according to the given information, we have

[tex]\dfrac{2}{7}\times x+\dfrac{1}{4}\times x+26=x\\\\\\\Rightarrow \dfrac{8x+7x}{28}+26=x\\\\\\\Rightarrow \dfrac{15x}{28}+26=x\\\\\\\Rightarrow x-\dfrac{15x}{28}=26\\\\\\\Rightarrow \dfrac{28x-15x}{28}=26\\\\\\\Rightarrow \dfrac{13x}{28}=26\\\\\Rightarrow x=\dfrac{26\times 28}{13}\\\\\Rightarrow x=56.[/tex]

Thus, there are total 56 eggs in the basket.

$28.85 (just add it if u dont get it)

On Wednesday and Friday she spent, $9.75+$5.95=$15.70

On Monday and Tuesday she spent, $5.65+$7.50= $13.15

Its a subtraction problem so $15.70-$13.15=$2.55

The answer is $2.55

I apologize if this is not what you meant.

Calculate the volume of each shape then add them together.

4 x 32 x 10 = 1280

12 x 16 x 10 = 1920

Total volume = 1280 + 1920 = 3,200 cubic in.

Answer:

The area of the irregular figure is 140 sq. ft.

Step-by-step explanation:

Triangle:

16-12=4

6 x 4 = 24

24 x 0.5 = 12

Triangle = 12

Rectangle:

16 x 8

= 128

Rectangle = 128

Total figure:

128+12

= 140

Plzz give me brainlist!!!

I hope this helps witb you.

Final answer:

To find the nth term of the arithmetic sequence, we calculated the common difference to be 37, and deduced the first term as -301. The equation for the nth term is an = -301 + 37(n - 1). Therefore, option a is correct answer.

Explanation:

To find an equation for the nth term of the arithmetic sequence given two terms, a10 = 32 and a12 = 106, we first need to determine the common difference. The common difference d in an arithmetic sequence is the consistent interval between consecutive terms, calculated by subtracting one term from the next. In this case:

d = a12 - a10

d = 106 - 32

d = 74

Since the terms are two positions apart, this common difference corresponds to two steps, meaning the common difference per step is 74 / 2 = 37.

Now, we know that the general formula for the nth term of an arithmetic sequence is:

an = a1 + (n - 1)d

Where a1 is the first term. To find a1, we can plug in the values for a10:

32 = a1 + (10 - 1)×37

32 = a1 + 9×37

32 = a1 + 333

a1 = 32 - 333

a1 = -301

Now, the equation for the nth term of the sequence is:

an = -301 + 37(n - 1)

Therefore, option a is correct answer.

Answer:

B. 68%

Step-by-step explanation:

Any number within 1 positive or negative deviation of the mean represents 68% of normally distributed data.

Math explanation:

52.4+11.8=64.2

52.4-11.8=40.6

Your answer is b, 68%

Answer:

Option A, π(4.5)²

Step-by-step explanation:

Volume of a cylinder is-

V = πr²h

Substitute the value of the radius. (9 is the diameter of the base, so it needs to be half of it)

V = π(4.5)²h

Bring the "h" inside with 4.5

V = π(4.5h)²

Hope this helps

The volume of the cylinder is [tex]\pi (4.5)^{2} h[/tex] and thus option c) [tex]\pi (4.5)^{2} h[/tex] is the correct option

Given: a cylinder of diameter 9 cm and height h cm

To find: equation to find the volume of the cylinder

We know that the volume of a cylinder can be calculate by using the formula:

[tex]\text{volume} = \pi r^{2} h[/tex]

where r is the radius of the cylinder and h is the height

It is given that the diameter of cylinder is 9 cm so radius of the cylinder will be half of the diameter:

[tex]\text{radius} = \frac{9}{2} = 4.5[/tex] cm

Now putting the values in the formula of volume:

[tex]\text{volume} = \pi (4.5)^{2} h[/tex]

Therefore, the volume of the cylinder is [tex]\pi (4.5)^{2} h[/tex] and the option that is same as our answer is option C. So, option C) [tex]\pi (4.5)^{2} h[/tex] is the correct answer

ANSWER

[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]

EXPLANATION

The complex number shown has coordinates (2,-2)

or

[tex]z = 2 - 2i[/tex]

The modulus is

[tex] |z| = \sqrt{ {2}^{2} + {( - 2)}^{2} } [/tex]

[tex]|z| = \sqrt{ 8} = 2 \sqrt{2} [/tex]

The argument is

[tex] \theta= \tan^{ - 1} ( \frac{ - 2}{2} )[/tex]

[tex] \theta= \tan^{ - 1} ( -1) = \frac{7\pi}{4} [/tex]

The polar form is

[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]

The first option is correct.

Answer:

The first option (the one all the way at the top)

Step-by-step explanation:

a.pex

Answer:

The median. Since there are some values in the data set that are arger than most, if you used the mean, the mean would not be a very accurate representation of the data set. When using median, the large numbers do not greatly effect the data set.

Step-by-step explanation:

ANSWER

B.

[tex]{f}^{ - 1} (x) = {x}^{2} - 3[/tex]

EXPLANATION

Given

[tex]f(x) = \sqrt{x + 3} [/tex]

Let

[tex]y= \sqrt{x + 3} [/tex]

Interchange x and y.

[tex]x= \sqrt{y + 3} [/tex]

Square both sides

[tex] {x}^{2} = y + 3[/tex]

Solve for y

[tex]y = {x}^{2} - 3[/tex]

Therefore the inverse of f(x) is

[tex] {f}^{ - 1} (x) = {x}^{2} - 3[/tex]

Answer:

[tex]\large\boxed{36\pi}[/tex]

Step-by-step explanation:

The formula of a volume of a sphere:

[tex]V=\dfrac{4}{3}\pi R^3[/tex]

R - radius

We have R = 3 ?. Substitute

[tex]V=\dfrac{4}{3}\pi(3^3)=\dfrac{4}{3}\pi(27)=(4)\pi(9)=36\pi[/tex]

If the radius is 30, then the volume is:

[tex]V=\dfrac{4}{3}\pi(30^3)=\dfrac{4}{3}\pi(27,000)=(4)\pi(9,000)=36,000\pi[/tex]

If 30 is the length of diameter, then the radius R = 30 : 2 = 15.

Therefore the volume:

[tex]V=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3,375)=(4)\pi(1,125)=4,500\pi[/tex]

Answer:

D) 14%

Step-by-step explanation:

Let the percent of the real fruit in the first brand = x

Given that number of gallons of  real fruit in the first brand = 9 gallons

Given that percent of the real fruit in the second brand = 48%

Given that number of gallons of  real fruit in the second brand = 8 gallons

Given that  percent of the real fruit in the mixture = 30%

then number of gallons of  real fruit in the mixture = (9+8) = 17 gallons

Then we get equation:

[x% of 9 gallons] + [48% of 8 gallons] = [30% of 17 gallons]

9x+48(8)=30(17)

9x+384=510

9x=510-384

9x=126

x=126/9

x=14

Hence final answer is D) 14%

Answer:D

Step-by-step explanation:jus took test

18 $20 Dollar Bills

5 Bills In 100

10 Bills In 200

15 Bills In 300

18 Bills In 360

Answer:

7.

rolling two number cubes

8.

2/25

Step-by-step explanation:

7.

Events A and B are said to be statistically independent if the probability of A happening, P(A), in no way affects the probability of event B occurring, P(B);

P(A∩B) = P(A) P(B)

If A and B are independent the above equation is always true.

From the list given, rolling two number cubes is an example of independent events since the outcome from the first cube does not affect the outcome of the second cube.

8.

We are informed the bag contains 4 apples, 1 plum, 2 apricots, and 3 oranges. We are required to determine the following probability;

P(Apple then Apricot) given that the fruits are drawn with replacement.

The probability of drawing an apple from the bag is;

(number of apples)/(total number of fruits)

= 4/10 = 2/5

The probability of drawing an apricot from the bag given that the apple drawn is replaced is;

(number of apricots)/(total number of fruits)

= 2/10 = 1/5

Now,  P(Apple then Apricot) = 2/5 * 1/5 = 2/25

Answer:

[tex]5\frac{1}{2}\ mi[/tex]

Step-by-step explanation:

we know that

[tex]1\frac{3}{8}\ mi=\frac{1*8+3}{8}=\frac{11}{8}\ mi[/tex]

She drove from her house to the airport and back 2 times

so

Multiply the distance from her house to the airport by 4

[tex](4)*\frac{11}{8}=\frac{11}{2}=5\frac{1}{2}\ mi[/tex]

Answer:

25 ounces of water

Step-by-step explanation:

3/5 = 15

Cross multiplying this:

1 = x

3/5 = 15

3/5x=15

x=25

Answer:

The bottle hold 25 ounces of water

Step-by-step explanation:

To find the amount of water the bottle hold, we will follow the steps below;

let x be the number of ounces of water the bottle holds

3/5  of x  = 15 ounces

3/5  ×  x   = 15

[tex]\frac{3X}{5}[/tex]   = 15

Multiply both-side of the equation by 5

[tex]\frac{3X}{5}[/tex]  ×  5   =  15×5

At the left-hand side of the equation 5 will cancel-out 5 leaving us with 3x

3x = 75

Divide both-side of the equation by 3

[tex]\frac{3X}{3}[/tex]  =  [tex]\frac{75}{3}[/tex]

(On the left-hand side of the equation 3 at the numerator will cancel-out 3 at the denominator leaving us with x while on the right-hand side of the equation 75 will be divided by 3)

x = 25 ounce

Answer:

Data Set A has less variability Data Set B because the range of Data Set A has less range of Data Set B

Step-by-step explanation:

Data Set A: 18, 24, 29, 30, 39

Data Set B: 26, 29, 39, 40, 52

Variability means you have more range so....