How is the space between consecutive whole numbers divided on the number line?
O into halves
O into fifths
O into sixths
O into sevenths

Step-by-step explanation:

We need to prove that,

[tex]\cot^2 a-\cos^2 a=\cot^2 a\times \cos^2 a[/tex]

Taking LHS,

[tex]\cot^2 a-\cos^2 a[/tex]

We know that,

[tex]\cot a=\dfrac{\cos a}{\sin a}[/tex]

​[tex]=(\dfrac{\cos a}{\sin a})^2 -\cos^2 a\\\\=\cos^2 a(\dfrac{1}{\sin^2 a}-1)\\\\=\cos^2 a(\dfrac{1-\sin^2a}{\sin^2 a})\\\\=\cos^2 a\times \dfrac{\cos^2 a}{\sin^2 a}\\\\=\dfrac{\cos ^2 a}{\sin^2 a}\times \cos^2a\\\\\because \ \dfrac{\cos ^2 a}{\sin^2 a}=\cot^2 a\\\\=\cot^2 a \times \cos^2a\\\\=RHS[/tex]

So, LHS = RHS

Hence, proved.

Answer: D

Step-by-step explanation:

The best use of the associative and commutative properties to simplify the expression 2.4 + 13 - 5 + 3.6 + 7 would be:

D. (2.4 + 3.6) + [13 + 7 + (-5)]

By applying the associative property, we can group the numbers in a way that allows for easier computation.

Here, we group 2.4 and 3.6 together and 13, 7, and -5 together. This allows us to simplify each group separately and then add the results together.

Calculating the groups:

(2.4 + 3.6) = 6

[13 + 7 + (-5)] = 15

Now, we add the results together:

6 + 15 = 21

So, the simplified expression is 21. Therefore, option D provides the best use of the associative and commutative properties to simplify the given expression.

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9514 1404 393

Answer:

  B.  G(x) = (x -0.5)³ -(x -0.5)

Step-by-step explanation:

The desired equation can be found by translating the function left one unit. That is accomplished by replacing x with x+1. Then you have ...

  G(x) = ((x +1) -1.5)³ -((x +1) -1.5)

  G(x) = (x -0.5)³ -(x -0.5) . . . . . . . . matches choice B

Answer:

The value of 'a' will be:

[tex]a\:=\:-\frac{f}{2}+-\frac{1}{2}m[/tex]

Step-by-step explanation:

Given the formula

[tex]-F = m+2a[/tex]

Let us solve the equation for 'a'

[tex]-F = m+2a[/tex]

Flip the equation

[tex]2a+m=-f[/tex]

Add -m to both sides

[tex]2a+m+(-m)=-f+(-m)[/tex]

[tex]2a = -f - m[/tex]

Divide both sides by 2

[tex]\frac{2a}{2}=\:\:\frac{-f\:-\:m}{2}[/tex]

[tex]a\:=\:-\frac{f}{2}+-\frac{1}{2}m[/tex]

Therefore, the value of 'a' will be:

[tex]a\:=\:-\frac{f}{2}+-\frac{1}{2}m[/tex]

Answer:

a,c,d

Step-by-step explanation:

Answer:

the answer is F, C, A

Answer:

I believe the answer is '2 solutions'.

Step-by-step explanation:

Combine each equation, solve the resulting question which comes out as two seperate variables, x = -1.197-- and y = 7.3990. I believe your answer is '2 solutions' because of this.

Answer:

1 solution

Step-by-step explanation:

Answer:

the domain is that x is a set of real numbers.

the range is y ≤ -3

Step-by-step explanation:

y = -|x + 3|

y is either positive or equal to zero.

Now, x is all real numbers because any value of x used will yield a valid value of y.

Thus, we can say that the domain is that x is a set of real numbers.

Now, for the range:

The minus sign in front of the absolute value indicates that the function has a maximum value.

Thus, the range is y ≤ -3

Answer:

13

Step-by-step explanation:

180-167= 13

× = 13 degrees

Answer:

the best interest rate would be a minimum of 3.5% annual interest

Step-by-step explanation:

An inflation rate of 3.5% would mean that the buying power of Lydia's money would decrease by 3.5% every single year. Therefore, the best interest rate would be a minimum of 3.5% annual interest. That way she would at least maintain the same buying power with her money as the day that she first placed it in the account. Any interest rate higher than 3.5% would be even better as Lydia will begin to make a profit from her savings.

This question is incomplete, the complete question is;

Students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Their replies are summarized below.

credits earned        very           deg.of certainty           very          Row Total

                           uncertain     somewhat certain        certain                                                

under10                    24                         16                          6                  46

10 through 59          16                           8                          20               44

60 or more               2                           14                          22               38

col total                    42                         38                         48               128

Under the assumption of independence, the expected frequency in the upper left cell is:__________.

A. 12.47

B. 14.56

C. 2.00

D. 11.09

Answer:

Under the assumption of independence, the expected frequency in the upper left cell is 12.47

Option A) 12.47 is the correct Option

Step-by-step explanation:

Given the data in table in the question;

the expected frequency in the upper left cell will be;

Eij = (Ti × Tj) / N

Row total Ti = 38

Column total Tj = 42  

Total frequency N = 128

so we substitute

Eij = (38 × 42) / 128

= 1596 / 128

= 12.468 ≈ 12.47

Therefore Under the assumption of independence, the expected frequency in the upper left cell is 12.47

Option A) 12.47 is the correct Option

Answer:

-10, -6, 3, 4, 7

Step-by-step explanation:

Hope it helps ^^

Answer:

2388.16 in³

Step-by-step explanation:

1) find volume of cylinder

formula: πr²h

given:

π = 3.14

r = 8/2 = 4 in

h = 9 in

[tex]\pi \: r {}^{2} h[/tex]

[tex](3.14) \times (4 {}^{2} ) \times 9[/tex]

[tex]3.14 \times 16 \times 9[/tex]

[tex]452.16 \: {in}^{3} [/tex]

2) find volume of cuboid

formula: length × width × height

given:

length = 16 in

width = 11 in

height = 11 in

[tex]l \: \times w \: \times h[/tex]

[tex]16 \times 11 \times 11[/tex]

[tex]1936 \: in {}^{3} [/tex]

total volume of figure

= volume of cylinder + volume of cuboid

= 452.16 in³ + 1936 in³

= 2388.16 in³

Answer:

8 beacaus the seven increased from 4

The quotient after increased by 4 is 8.

To calculate the quotient of 28 divided by 7, we perform the division and get:

28 ÷ 7

= 28/7

= (7 x 4)/ 7

= 4

Next, we are asked to increase this quotient by 4. Adding 4 to the quotient:

= 4 + 4

= 8.

Therefore, the quotient after increased by 4 is 8.

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There is a confusion here. “Decimal” is not a number set. “Whole numbers” is.

“Decimal” has been used to mean three different things about the representation of numbers:

- Numbers written using a base 10 place value system

- The decimal point that separates the integer and fractional parts of a number written in base 10. (Some countries use a comma. Some folks refer to the point used for this purpose in other bases as a decimal too for extra confusion.)

- A number written in the above form that has some numerals, probably nonzero, written to the right of the point. In other words, a number written in decimal form with a nonzero fractional part.

I'm guessing that the usage in this question is referring to the third meaning of “decimal” and will interpret the question as being not about representation of numbers but about transformation of numbers.

To wit, “What are some popular ways real numbers with nonzero fractional parts can be mapped to integers?”

I hope this is the correct interpretation.

There are a few common ways:

- Round towards zero: Ignore the fractional part and keep only the integral part.

- Floor: Take the greatest integer less than the number in question.

- Ceiling: Take the least integer greater than the number in question.

- Round to the nearest integer: Ignore the fractional part if it's less than a half. Otherwise, round away from zero.

These are the main ways of picking integers close to the number in question, but obviously, there are infinitely many ways to map sets of real numbers to mergers, so it is unclear if any of these are what the asker was looking for.

Answer:

if the number after the decimal is 5 or more then round the number before decimal by 1

Step-by-step explanation:

for example:

1234.5

=1235

or

6974.7

=6975

or

7796.4

=7796 (No change on the last number because the number after the decimal is 4, which is under 5)

Answer:

I think the answer is D  

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

0.875

Step-by-step explanation:

i used my calculator :D

Answer:

0.875

Step-by-step explanation:

Just divide 7/8

Hope this helped, Have a Wonderful Day!!

Answer:

a..

Step-by-step explanation:

Answer:

13/42

Step-by-step explanation:

1/7 + 1/6

13/42

Answer:

angle IJA is a right angle

Recall that

cos²(x) + sin²(x) = 1

for all x, so that

sin(x) = ± √(1 - cos²(x))

Given that cos(θ) = 4/9 > 0, and

tan(θ) = sin(θ) / cos(θ) < 0

it follows that sin(θ) < 0, so

sin(θ) = - √(1 - cos²(θ)) = - √(1 - (4/9)²) = - √(65)/9

The value of sinθ is √(65)/9.

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.

Since cos(theta) = 4/9 and tan(theta) < 0, we know that theta is in the second quadrant of the unit circle, where cosine is positive and sine is positive.

We can use the Pythagorean identity to find sin(theta):

sin²(theta) + cos²(theta) = 1

Substituting in the given value of cos(theta), we get:

sin²(theta) + (4/9)² = 1

sin²(theta) + 16/81 = 1

sin²(theta) = 1 - 16/81

sin²(theta) = 65/81

Taking the square root of both sides, we get:

sin(theta) = ± sqrt(65)/9

Since theta is in the second quadrant where sine is positive, we can take the positive root:

sin(theta) = sqrt(65)/9

Therefore, sin(theta) = sqrt(65)/9.

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Answer:

Step-by-step explanation:

lets remember that 1kg=2.2 lb

if

2.2 lbs................................1 kg

120lbs...................................? kg

120/2.2=54.54 kg

Answer:

They need to sell 32 tickets

Step-by-step explanation:

256/8=32

Answer:

They need to sell 32 tickets to pay for their expenses.

Answer:

The total surface area is 782 inches

Step-by-step explanation:

I do not know the lateral answer sorry

Answer:

The answer is 2.5 or 5/2 as a fraction.

Step-by-step explanation:

P.S Can I have brainliest?

Answer:

2.5

Step-by-step explanation:

[tex]\frac{5}{8}[/tex] ÷ [tex]\frac{1}{4}[/tex]

turns into

[tex]\frac{5}{8}[/tex] ×[tex]\frac{4}{1}[/tex] = [tex]\frac{20}{8}[/tex]

and 20/8 as a decimal is 2.5 :) hope this helps!

Answer:

A.

Step-by-step explanation:

I gotchu fam. The first thing that you would want to do is find the slope. The slope is the change in y divided by the change in x. Based on the points on the line, the change in y is 2 because it goes up two, and the change in x is one because it goes over 1. This would make your slope 2/1, or just 2! Now we have our slope, so we want to find our y-intercept. There are two ways that we can do this. The first way is just eyeballing it, but sometimes that's not always accurate. We're just going to do that because its faster (lol). It looks around -2. With this information, we have our entire equation! y=mx+b. we can plug in our information. y=2x-2. And that's how your answer's A! Hope this helps.

Answer:

-5k - 10

Step-by-step explanation:

-k + 2 (-2k - 5)

-k - 4k - 10

-5k - 10

Answer:

-K+2(-2K-5)

-K-2K-10

-3K=10

K= 10÷(-3)

K=-3.333333