A compound inequality is graphed, and its graph consists of all real numbers.

Which open sentence could have resulted in this solution set?


A. r < 3 or r > –2


B. r > 3 or r > –2


C. r < 3 or r < –2


D. r > 3 or r < –2

Answer:

It simply is the product between 8 and 1.8 so 14.4, as anything added to himself n times is equal to the product between the number and n.

In fractions:

1.8 = 18/10 = 9/5

8·(9/5) = 72/5

If we add 1.8 for 8 times we will get the resulted value in decimal form as 14.4.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that we have to add 1.8 for 8 times. We know that if a number is added n number of times that meant we to multiply that number by n.

Here , addition of 1.8 for 8 times will be equal to product of 8 and 1.8.

As required we have to express the result in decimal form. So,

Addition of 1.8 for 8 times is :

1.8 + 1.8 + 1.8 + 1.8 + 1.8 + 1.8 + 1.8 + 1.8

= 14.4

Let's check if this is equal to product of 8 and 1.8 which is :

= 1.8 × 8

= 14.4

So , the result is 14.4.

Therefore , if we add 1.8 for 8 times we will get the resulted value in decimal form as 14.4.

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a) The Ferris wheel has an angular speed is 12.222 radians per minute.

b) The Ferris wheel makes 116.712 revolutions in an hour.

Kinematics is a branch of mechanical physics that studies the motion of objects without considering its causes. In other words, kinematics studies displacements, velocities and accelerations in translation, rotation and combined motion. In this case we find a Ferris wheel rotating around its axis at constant rate.

a) Then, the angular speed (ω), in radians per minute, is determined by the following product:

ω = v / R

Where:

Please notice that the length of the radius is the half of the length of the diameter.  

If we know that v = 5 mi / h and R = 36 feet, then the angular speed of the wheel is:

ω = [(5 mi / h) · (1 h / 60 min) · (5280 ft / 1 mi)] / [(0.5) · (72 ft)]

ω = 12.222 rad / min

The angular speed is 12.222 radians per minute.

b) A revolution is equal to an angular displacement of 2π radians and an hour is equal to 60 minutes. Then, we can derive the number of revolutions in an hour by dimensional analysis:

n = (12.222 rad / min) · (1 rev / 2π rad) · (60 min / h)

n = 116.712 rev / h

There are 116.712 revolutions in an hour.

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Answer:

C

Step-by-step explanation:

7.55 x 35 =

264.25

Hope this helped

The 1995 processor when compared to the processor in today's phones is 12 .5 times larger .

To find how much larger the 1995 processor is , you first need to find the area of the processors.

Area of 1995 processor:

= 3. 8 x 2 . 9

= 11. 02 cm ²

Area of 2005 processor :

= 1. 1 x 0. 8

= 0. 88 cm ²

In comparison to the 2009 processor, the 1995 processor is :

= 11. 02 / 0.88

= 12 .5 times larger

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Answer:

2 times 12 is 24

Step-by-step explanation:

Answer:

B. 2 • 2 • . . . • 2 • 2 } 12 times

D. 2¹²

Why are both of the answers to the last question correct?  An exponent is a short way to write repeated multiplication. So 212 means the same as 2 • 2 • . . . • 2 • 2.

Step-by-step explanation:

Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?

Answer:

The value of x is 19.

Step-by-step explanation:

Given:

m∠1 = (4x + 9)°

m∠2 = (x - 14)°

Since m∠1 and m∠2 are complementary angles, we have:

m∠1 + m∠2 = 90°

Substituting the given expressions for m∠1 and m∠2:

(4x + 9)° + (x - 14)° = 90°

Combining like terms:

4x + 9 + x - 14 = 90

Combining the x terms and the constant terms:

5x - 5 = 90

Adding 5 to both sides:

5x = 90 + 5

Simplifying:

5x = 95

Dividing both sides by 5:

x = 95 / 5

Simplifying further:

x = 19

Solution:

Given:

The table can be completed as shown.

From the table, the number of students that do not play football or basketball is marked below;

Therefore, 5 students do not play football or basketball.

Answer:

\(p = 7\)

Step-by-step explanation:

So the key is that a line has a measure of 180 degrees. Notice the square between the rays. That is a 90-degree angle. So let's add this up and see what's going on

\((5p + 2) + 90 + (7p + 4) = 180\)

\(12p + 96 = 180\)

\(12p = 84\)

\(p = 7\)

Answer:

p = 7

Step-by-step explanation:

From the diagram, we can see that all the angles given form a straight line, and therefore add up to 180°.

We can create an equation with what is given:

***The angle with the square marked is 90°.

5p° + 2° + 90° + 7p° + 4° = 180°

You can combine the like terms, getting:

12p° + 96° = 180°

Now, subtract 96° from both sides:

12p° = 84°

Now, divide by 12°, and get:

p = 7

Step-by-step explanation:

option H is the correct answer og this question

g = a -uv/h

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Answer:

thanks for the free points peace ✌✌✌ Merry Christmas

Answer:

A. Add Equation A and Equation B.

Step-by-step explanation:

When you add Equation A and Equation B, you'd get (when combining like terms)

(7y + 3y) + (-4x + 4x) = (5 + 25), which becomes 10y = 30

This show us that adding the equations allows us to cancel (eliminate) the x variable.  Then we'd solve for y and later we'd solve for x by plugging in the value for y into either equation A or equation B.

There are taller lines on the left side of the line.

This means it is skewed to the right.

Answer:

Your welcome! :)

Step-by-step explanation:

To find the inverse of a function, we use the following steps:

1. Replace f(x) with y.

2. Interchange x and y.

3. Solve for y.

4. Replace y with f -1 (x).

The number of red blood cells in the sample will be 42 × \(10^{5}\)

Here, we are given that an average person has 6 x \(10^{2}\) times as many red blood cells as white blood cells.

This means that if a person has 1 white blood cell, he/she will have 6 x \(10^{2}\) red blood cells.

Now, it is given that a sample of blood collected has 7 x \(10^{3}\) white blood cells.

Thus, the number of red blood cells present in the sample will be-

(7 x \(10^{3}\)) (6 x \(10^{2}\))

= 7 x 6 × \(10^{2}\) x \(10^{3}\)

= 42 × \(10^{5}\)

Thus, the number of red blood cells in the sample will be 42 × \(10^{5}\).

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The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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b)3

16 + 12 = 28

31 - 28 = 3

b/c 5 people play both games we wont add them

Answer:

0.0092

Step-by-step explanation:

Rewrite the denominator out of its scientific notation. The numerator will always be 1 when you are working with whole numbers turning into fractions.

\(=9.2\cdot \frac{1}{10^3}\\=\frac{1\cdot \:9.2}{10^3}\\=\frac{9.2}{10^3}\\=\frac{9.2}{1000}\\=0.0092\)

Answer:

a) \( E = \frac{49.2-17.6}{2}= 15.8\)

b) For this case we have 95% of confidence that the true mean would be between \(\pm 15.8\) units respect the true mean.

c) \(n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112\)

So the answer for this case would be n=112

d) \(36.5-2.58\frac{45}{\sqrt{112}}=25.53\)    

\(36.5+2.58\frac{45}{\sqrt{112}}=47.47\)

Step-by-step explanation:

Part a

For this case we know that the cinfidence interval for the true mean is given by:

\( \bar X \pm E\)

Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:

\( E = \frac{49.2-17.6}{2}= 15.8\)

Part b

For this case we have 95% of confidence that the true mean would be between \(\pm 15.8\) units respect the true mean.

Part c

The margin of error is given by this formula:

\( ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)    (a)

And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

\(n=(\frac{z_{\alpha/2} \sigma}{ME})^2\)   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be \(z_{\alpha/2}=2.58\), replacing into formula (b) we got:

\(n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112\)

So the answer for this case would be n=112

Part d

The confidence interval for the mean is given by the following formula:

\(\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)   (1)

Replcaing the info given we got:

\(36.5-2.58\frac{45}{\sqrt{112}}=25.53\)    

\(36.5+2.58\frac{45}{\sqrt{112}}=47.47\)

Answer:

8

Step-by-step explanation:

56 shirts were sold, and including Mandy, 7 people sold them.

7 * x = 56

(7x)/7=56/7 (canceling out the 7 to get x alone)

x=8

So basically just 56 divided by 7

The 0.2 mm spacers will be utilized in order to achieve the correct valve clearance.

On motorcycle and automobile engines, valve clearances essentially refer to the gap or distance between the top of the valve stem and the camshaft that controls it.

The exhaust valves in an automobile engine release the burned gases, while the intake valves permit air and fuel into the cylinder.

Given that:

The difference in between the current and clearance range is:

However, for clearance to be positioned within 0.18 mm - 0.22 mm. The required spacers to be used are 0.04 mm, and 0.08 mm in conjunction with:

The mean value = 3.04

Therefore, for us to approach and get to the value of 3.02, the required spacers to be that must be added are:

Therefore, we can conclude that the 0.2 mm spacers will be utilized in order to achieve the correct valve clearance.

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Answer:

There are several ways to find this. For example:

√

6.25

=

√

6

+

1

4

=

√

25

4

=

√

25

√

4

=

5

2

=

2.5

√

6.25

=

√

625

100

=

√

625

√

100

=

25

10

=

2.5

The ratios are;

Sin θ =  5/6

Cos θ = √11/6

Tan θ =  5√11/11

Sec  θ =  6√11/11

Cosec  θ = 6/5

Cot θ =  √11/5

These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides

We can see that the hypotenuse is obtained from;

x =√\((10)^2 + (2\sqrt{} 11)^2\)

x = √100 + 44

x = 12

Then;

Sin θ = 10/12 = 5/6

Cos θ =  2√11/12

= √11/6

Tan θ = 10/2√11

= 20√11/44

= 5√11/11

Sec  θ =  1/Cos  θ

=  6/√11

= 6√11/11

Cosec  θ = 1/Sin

 θ = 6/5

Cot θ = 1/tan θ

= 11/ 5√11

= 55√11/275

= √11/5

Sinβ = 2√11/12

= √11/6

Cos β = 10/12

= 5/6

Tan β = 2√11/10

= √11/5

Sec β = 6/5

Cosec β = 6√11/11

Cot β = 5√11/11

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Answer:

The circle equation is  x2+y2=9

Step-by-step explanation:

∴ The equation is x2 + y2=9

the parallel linear equation to y = (4/3)*x + 8 that passes through (-6, -6) is:

y = (4/3)*x + 2

A general line equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two linear equations are parallel if the slope is the same, but the y-intercept is different.

Then, an equation parallel to y = (4/3)*x  + 8

Will be of the form:

y = (4/3)*x + c

Where c ≠ 8.

Now, we also want our line to pass through the point (-6, -6), then we must have:

-6 = (4/3)*(-6) + c

With that, we can find the value of c.

-6 + 6*(4/3) = c

6*(-1 + 4/3) = c

6*(1/3) = c = 2

Then the parallel linear equation to y = (4/3)*x + 8 that passes through (-6, -6) is:

y = (4/3)*x + 2

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Answer:

  4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

  2^4 = 16

  2^5 = 32

A logarithm can be considered to be an exponent of the base.

  \(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)

The ordering of powers of 2 relative to the number of interest (17) is ...

  16 < 17 < 32

  2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

  log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

  4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

__

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

  log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

Answer:

Step-by-step explanation:

The length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

To determine the angles and length of sides, we use the sine rule

The sine rule is thus:

\(\frac{sin A}{a}= \frac{sin B}{b} = \frac{sin C}{c}\)

Given;

Let's find angle C

\(\frac{sin 43}{2. 5} = \frac{sin C}{3. 6}\)

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = \(sin^-^1 (0. 982)\)

C = 79°

To find length of b

\(b = \sqrt{c^2 - a^2}\)

substitute the values

\(b = \sqrt{3. 6^2 - 2. 5^2}\)

b = 2. 59 cm

b = 3cm

To find angle B, we have

\(\frac{sin 43}{2. 5} =\frac{sin B}{3}\)

cross multiply

0. 682 × 3 = sin B × 2. 5

sin B = 0. 7065

\(B = sin ^-^1 (0. 7065)\)

B = 45°

Hence, the length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

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