Use logb2 ≈ 0.401, logb3 ≈ 0.503, and logb5 ≈ 0.842 to approximate the value of the given logarithm to 3 decimal places.
Assume that b>0 and b≠1.
logb50 ≈ ?

The equations that is true for the values x = -2 and x = 2 is x² – 4 = 0  and 4x² = 16.

Equations:

Equation is an an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

For example, 3x² − 2x + 9 is an algebraic expression.

Given,

Here we have the following equations

x² – 4 = 0

x² = –4

3x² + 12 = 0

4x² = 16

2(x – 2)² = 0

Now, we need to find which of these equations are tur for the values x = -2 and x = 2.

In order to find the true equation, we have to apply the given values on each of these to find which one is correct,

When x = 2 then,

(2)² – 4 = 0 => 4 - 4 = 0 (True)

(2)² = –4 => 4 ≠ -4 (Not true)

3(2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)

4(2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)

2(2– 2)² = 0 => 2(0) = 0 = 0 = 0 (True)

Similarly, when we apply the value of x = -1, then we get,

(-2)² – 4 = 0 => 4 - 4 = 0 (True)

(-2)² = –4 => 4 ≠ -4 (Not true)

3(-2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)

4(-2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)

2(-2– 2)² = 0 => 2(-4)² = 0 => 32 ≠ 0 = 0 (Not true)

Therefore, the resulting equations are x² – 4 = 0  and 4x² = 16.

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At confidence, how large a sample should be taken to obtain a margin of error for the estimation of a population proportion? We now assume that past data are not available for developing a planning value for

Preliminary estimate for proportion (Not Known) is equal to 0.5

Margin of error = E = 0.03

Level of significance = 1-0.99 = 0.01

Z critical value is considered as (by using Z table) = 2.576

So, the sample size formula is taken as

n = [p(1 – p)][tex]\left[Z/E]^{2}[/tex]

=[0.5*(1-0.5)] [2.576/0.03][tex]^{2}[/tex]

=1,843.03                    

Hence, the sample size is approximately will be 1,844

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The value of x is .[tex]\sqrt{170}[/tex]

What is Pythagorean Theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, the two sides of the triangle are, 7 and 11.

By Pythagorean theorem,

[tex]7^2 + 11^2 = x^2\\49 + 121 =x^2 \\170 = x^2\\x = \sqrt{170} \\[/tex]

Hence, the value of x is [tex]\sqrt{170}[/tex].

Here, the sum of two sides of triangle is not a perfect square.

Therefore, the side lengths is not a Pythagorean triple.

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Answer:

The total amount of college students enrolled part-time that year would be approximately 2 million.

Step-by-step explanation:

In order to find out the amount of college students enrolled part-time that year, we need to convert the 23% into 0.23, and then use a calculator, with this equation:

0.23 x 6,600,000 = 1,518,000

Now, it says to "round your answer to the nearest million."

1.518 million is closer to 2 million than 1 million, so our answer would be 2 million.

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The solution set of 'b' for the given compound inequality is

-2 < b < 4.

Given, a compound inequality 6b < 24 and 4b + 12 > 4.

Now, solving the first inequality,

6b < 24

On dividing both the sides by 6, we get

6b/6 < 24/6

b < 4.

Now, solving the second inequality,

4b + 12 > 4

On subtracting 12 from both the sides, we get

4b + 12 - 12 > 4 - 12

4b > -8

On dividing both the sides by 4, we get

4b/4 > -8/4

b > -2.

So, the solution set of b to satisfy the compound inequality be,

greater than -2 and less than 4 i.e.

-2 < b < 4.

Hence, the solution set of 'b' is -2 < b < 4.

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Answer:

Problem: 0.5(5-7x)=8-(4x+6)

Answer: x= -1

Answer:

314

Step-by-step explanation:

1. Divide 63 by pi (equals 20)

2. Divide 20 by 2 which equals 10.

3. Multiply 10 by itself to get the square. which would be 100

4. Multiply 100 by pi

3. Finally A=314

For the given inequality –3(2x – 5) < 5(2 – x) the correct way of representation is x > 5 which means an open circle is at 5 and bold line starts at 5 and is pointing to the right.

As given in the question,

Given inequality is given by:

–3(2x – 5) < 5(2 – x)

Simplify the given inequality to get the correct way of representation,

Open the parenthesis we get,

-3(2x) + 3(5) < 5(2) -5(x)

⇒-6x +15 < 10 -5x

Take like terms on the same side we get,

⇒15-10< 6x -5x

⇒ x > 5

This means value of x starts from 5 move towards right direction excluding 5.

Therefore, for the given inequality –3(2x – 5) < 5(2 – x) the correct way of representation is x > 5 which means an open circle is at 5 and bold line starts at 5 and is pointing to the right.

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Answer:

b < 8

Step-by-step explanation:

Given inequality:

[tex]\dfrac{3}{2}b+5 < 17[/tex]

Subtract 5 from both sides:

[tex]\implies \dfrac{3}{2}b+5-5 < 17-5[/tex]

[tex]\implies \dfrac{3}{2}b < 12[/tex]

Multiply both sides by 2:

[tex]\implies 2 \cdot \dfrac{3}{2}b < 2 \cdot 12[/tex]

[tex]\implies3b < 24[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3b}{3} < \dfrac{24}{3}[/tex]

[tex]\implies b < 8[/tex]

The number line that satisfies the inequality is option (B).

What are number lines?
Number lines are horizontal straight lines in mathematics where numbers are arranged in equal intervals. A numeric line can be used to represent every number in a sequence. The endpoints of this line go on infinitely. In other terms, it is an image of numbers on a straight line. It functions as a guide for distinguishing and organizing numbers. It can be used to represent any real number, including all whole numbers and natural numbers.

Solution Explained:
- (a+5) < 4/-2 <= -3-a

[tex]\left \{ {{- (a+5) < 4/-2} \atop { 4/-2 < -3-a}} \right.[/tex]

[tex]\left \{ {{-a - 5 < -2} \atop {-2 < = -a -3}} \right.[/tex]

[tex]\left \{ {{-a-5) +5 < -2+5} \atop {-2+3 < = (-a-3)+3}} \right.[/tex]

[tex]\left \{ {{-a- 5 +5 < 3} \atop {1 < = -a-3+3}} \right.[/tex]

[tex]\left \{ {{-a < 3} \atop {1 < = -a}} \right.[/tex]

[tex]\left \{ {a > -3} \atop {-a > = 1}} \right.[/tex]

[tex]\left \{ {{a > -3} \atop {a < = -1}} \right.[/tex]

[tex]-3 < a < = -1[/tex]

a ∈ (-3, -1]

Hence, the number line that satisfies the inequality -(a+5) < b/-2 <= -3-a is in option (B).

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Answer:

7/5

Step-by-step explanation:

12x - 15 = 6 - 3x

15x = 21

x = 7/5

Answer:

Step-by-step explanation:

it is 2

Answer:

120

Egg.    Egg tarts

2.75 = 1

330  = 1 x 330 divided by 2.75 = 120

The volume of a drill bit with a radius of 3 centimeters is of:

16.32 cm³.

To obtain the numeric value of a function or of an expression, each instance of the input variable of the function has to be replaced by the value at which we want to find the numeric value.

The volume of a drill bit with a radius of r centimeters is given by the equation presented as follows:

[tex]V = \frac{\sqrt{3}}{9}\pi r^3[/tex]

Hence, for a radius of 3 centimeters, as is the case in this problem, the lone instance of r is replaced by 3, and the volume is obtained as follows:

[tex]V = \frac{\sqrt{3}}{9}\pi (3)^3 = 16.32[/tex]

The unit of the volume is in cubic centimeters, as the radius is measures in centimeters and then it is cubed.

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The value of 200 US dollars into canadian dollars is 259.74

What is an example of a unitary method?

A single or unique unit is referenced to using the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

Given That:

1 Canadian dollar is = 0.77 US dollar

So 1 US dollar is = 1/0.77 canadian dollar

So 200 US dollar is = 1/0.77 * 200 = 259.74 canadian dollar

Hence the answer is 259.74 dollar

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The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive exponents is (7)²⁰  .

In the question ,

it is given that ,

the expression is 7⁻⁴/(7⁻⁴)⁶ .

we need to find the simplified value of the expression .

So ,

= 7⁻⁴/(7⁻⁴)⁶

we know that (xᵃ)ᵇ = (x)ᵃˣᵇ

By using the above property , we get

= 7⁻⁴/(7)⁻⁴ˣ⁶

= 7⁻⁴/(7)⁻²⁴

we know that xᵃ/xᵇ = xᵃ⁻ᵇ

By using the above property , we get

= (7)⁻⁴×(7)²⁴

= (7)²⁴⁻⁴    ... by using the property xᵃ.xᵇ = xᵃ⁺ᵇ

= (7)²⁰

Therefore , The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive

exponents is (7)²⁰  .

The given question is incomplete , the complete question is

Simplify the following expression. Write your answer using positive exponents.

7⁻⁴/(7⁻⁴)⁶

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The required rate of annual decay rate is given as 11.70%.

Given that,
The half-life of Radium-228 is 5.75 years. What is the annual decay rate is to be determined.

The half-life of the element is defined as the time span in which the element grows or decays half of its whole composition of growth and decay.

Here,
According to the question,
[tex]1/2 = (1 - r)^{5.57}\\(1/2)^{1/5.57} = (1 -r)\\r = 0.1170\\r = 11.70%[/tex]

Thus, the required rate of annual decay rate is given as 11.70%.

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The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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The expression using distributive property becomes 7n - 35

The distributive property is also known as the distributive law of multiplication over addition and subtraction.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.

Using this distributive law, A × (B + C) = AB + AC. to re-write the expression -7(5 - n), A = -7, B = 5 and C = -n

we have -7(5 - n) = (-7 x 5) + (-7 x -n)

which is further simplified as (-35) + (7n) = 7n - 35

In conclusion, the re-written form of -7(5 - n) in distributive form is 7n - 35

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The probability that the random variable has a value greater than 7 is undetermined.

The formula to calculate the probability of occurrence of an event 'A' can be written as -  

P(A) = n(A)/n(S)

where -

n(A) = Number of outcomes favorable to event A.

n(S) = Total number of outcomes

We have a random variable having a value greater than 7

Now -

Number of outcomes favorable to event A = (-∞, + ∞) - (- ∞, 7)

Total number of outcomes for event A = (-∞, + ∞)

P(A) = (-∞, + ∞) - (- ∞, 7) /  (-∞, + ∞)

P(A) = ∞/∞

P(A) = undetermined

Therefore, the probability that the random variable has a value greater than 7 is undetermined.

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Answer:

the answer is 99 because the difference between the numbers is 11 and if you do 9 ×11 you get 99

Answer: The nth term of this sequence is a n= 11n-2

Step-by-step explanation:

Sequence : 9, 20, 31, 42

Difference : +11, +11, +11

The formula for nth term of an arithmetic progression is a n= d.n+a1-d

The formula for nth term of an arithmetic progression is d= 11 and a1=9

so.

a n=d.n+a 1-d

a n=11.n+9-11

a n=11n-2

Hope it helps :)

3 is an adjacent interior angle which is both adjacent and interior angle, this angle lie inside a triangle.

The two angles are said to be adjacent angles when they share the common vertex and side.

An interior angle is an angle inside a triangle.

The angle between the extended side and the side next to it is called an exterior angle.

Since we know that any two interior angles that share a common side are called the "adjacent interior angles" of the polygon, or just "adjacent angles".

Therefore,

In the diagram the adjacent angles are 3 and 4.

The interior angles from the diagram are 1, 2, and 3.

and the exterior angle is 4.

Hence , 3 is the only angle which is both adjacent and interior angle .

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Using the distance, 5/4 far distance that they ride in all.

In the given question,

Carlos and his mom went out on a bike ride.

They rode 5/8 of a mile to the park and then rode 5/8 of a mile back home.

We have to check how far did they ride in all.

We have to find the total distance that he ride to park and from the park.

We can find the total distance by adding the whole distance that he ride.

Total distance = Distance to the park + Distance back home

Total distance = 5/8+5/8

Since the denominator is same. So

Total distance = (5+5)/8

Total distance = 10/8

Now simplifying.

Total distance = 5/4

Hence, 5/4 far distance that they ride in all.

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An equation of the line that began with a y-intercept of (0, 4), shifted up 3 units, and is perpendicular to y = 3/4(x) - 2 is: A. y = -4/3(x) + 7.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

In Mathematics, the condition for perpendicularity of two lines is given by m₁ × m₂ = -1. Next, we would determine the slope of this equation that began with a y-intercept of (0, 4):

3/4 × m₂ = -1

3m₂/4 = -1

3m₂ = -4

m₂ = -4/3

In order to determine the new y-intercept, we would translate the equation by shifting it 3 units up:

Translation = y + 3 = 4 + 3 = 7.

Now, we can write this equation in slope-intercept form as follows:

y = mx + c

y = -4x/3 + 7 or y = -4/3(x) + 7.

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Complete Question:

What is the equation of the line that began with a y-intercept of (0,4), was shifted up 3 units, and is perpendicular to y = 3/4x-2?

answer choices:

A. y = -4/3(x) + 7

B. y=-3/4(x)+7

C. y=-3/4(x)+4

D. y =-4/3(x)+4

Answer:

The lines through the given points are parallel

Step-by-step explanation:

The given lines can be evaluated as follows

The first step is to calculate the slope [tex]m_{1}[/tex] of the first line using the slope formula as follows

[tex]m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Take two coordinates on the first line

[tex](10,5)~\text{and}~(-8,9)[/tex]

Substitute [tex]9[/tex] for [tex]y_{2}[/tex], [tex]-8[/tex] for [tex]x_{2}[/tex] , [tex]5[/tex] for [tex]y_{1}[/tex] , [tex]10[/tex] for [tex]x_{1}[/tex]  in the slope formula

[tex]m_{1}=\frac{9-5}{-8-10}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m_{1}=\frac{4}{-18}[/tex]

Simplify the fraction at the right side of the equation

[tex]m_{1}=-\frac{2}{9}[/tex]

The slope of the first line is [tex]-\frac{2}{9}[/tex]

Take two coordinates on the second line

[tex](2,-4)~\text{and}~(11,-6)[/tex]

Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]11[/tex] for [tex]x_{2}[/tex] , [tex]-4[/tex] for [tex]y_{1}[/tex] , [tex]2[/tex] for [tex]x_{1}[/tex]  in the slope formula

[tex]m_{2}=\frac{-6-(-4)}{11-2}[/tex]

Take out the brackets in the numerator at the right side of the equation

[tex]m_{2}=\frac{-6+4}{11-2}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m_{2}=\frac{-2}{9}[/tex]

The slope of the second line is [tex]-\frac{2}{9}[/tex]

Since the slope of both lines are equal, then the lines through the given points are parallel

Hence the lines through the given points are parallel

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Denise got $30 for her birthday, spending $6 on lunch, and having $24 left.

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

Let y represent the money that Denise get for her birthday.

Denise split her birthday money with her two sisters. the spent 6$ on lunch, so he has $24 left. Hence:

Amount gotten for birthday = $6 + $24

y = $6 + $24 = $30

Denise had $30

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Answer:

um well fierst da answer is proberly yes and no

Step-by-step explanation:

i tried to do da work

Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p.

Given, the expression 6(4 - 2p) + 9p

On simplifying, we get

24 - 12p + 9p

24 - 3p

So, on simplifying the given expression, we get

24 - 3p

Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p

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Answer:

120 minutes

Step-by-step explanation:

d=rt

D-distance

r-unit rate

T- time

14=7t

/7. /7

2=t

2 hours

2 x60=120

120 minutes

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