What is the solution, if any, to the inequality |3x|\ge0? all real numbers no solution x\ge0 x\le0

Answer:

x intercept : -1

y intercept : 3

Step-by-step explanation:

We have 3x - y = -3 ---eq(1)

The x intercept is the value of x when y = 0 in eq(1),

⇒ 3x - 0 = -3

⇒ x = -3/3

⇒ x = -1

The y intercept is the value of y when x = 0 in eq(1),

⇒ 3(0) - y = -3

⇒ -y = -3

⇒ y = 3

The function for which f(x) is equal to f⁻¹(x) is: C. [tex]f(x) = \frac{x+1}{x-1}[/tex]

In this exercise, you are required to determine the inverse of the function f(x) with an equivalent inverse function f⁻¹(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

[tex]f(x) = y = \frac{x+6}{x-6} \\\\x=\frac{y+6}{y-6}[/tex]

x(y - 6) = y + 6

y = xy - 6x - 6

f⁻¹(x) = (-6x - 6)/(x - 1) ⇒ Not equal.

Option B.

[tex]f(x) = y = \frac{x+2}{x-2} \\\\x=\frac{y+2}{y-2}[/tex]

x(y - 2) = y + 2

y = xy - 2x - 2

f⁻¹(x) = (-2x - 2)/(x - 1) ⇒ Not equal.

Option C.

[tex]f(x) = y = \frac{x+1}{x-1} \\\\x=\frac{y+1}{y-1}[/tex]

x(y - 1) = y + 1

y - xy = x + 1

f⁻¹(x) = (x + 1)/(x - 1) ⇒ equal.

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Answer:

Step-by-step explanation:

Let's calculate the expression step by step:

93 - (15 × 10) + (160 ÷ 16)

First, we perform the multiplication:

93 - 150 + (160 ÷ 16)

Next, we perform the division:

93 - 150 + 10

Finally, we perform the subtraction and addition:

-57 + 10

The result is:

-47

Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.

Answer:

she mixed up the slope and y- intercept in step 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

she correctly calculated the slope as m = - 4 and the y- intercept b = - 3

thus equation she should have is

y = - 4x - 3

Brooke's error was that she found the incorrect slope in step 1.  

The slope formula is:  m = (y₂ - y₁) / (x₂ - x₁)  

Using the given points:  m = (13 - 25) / (-4 - (-7))  m = -12 / 3  m = -4  

So, the slope is -4, not -12/3 as Brooke calculated in step 1.  

The correct equation for the line passing through the points (-7, 25) and (-4, 13) is: y = -4x - 3 (as found in step 3)

The value of cos E in the triangle is √2/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.

Some of the trigonometric functions are ;

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.

Therefore;

cos E = 5/5√2

cos E = 1/√2

rationalizing the value;

cos E = √2/2

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Answer:

Step-by-step explanation:

Converting between Fraction, Decimal, and Percent:

Fraction to Decimal: Divide the numerator by the denominator. The result is the decimal form.

Example: 1/4 = 1 ÷ 4 = 0.25

Decimal to Fraction: Write the decimal as a fraction by placing the decimal value over the appropriate power of 10.

Example: 0.75 = 75/100 = 3/4

Fraction to Percent: Divide the numerator by the denominator and multiply by 100.

Example: 1/3 = (1 ÷ 3) × 100 = 33.33...%

Percent to Fraction: Write the percent as a fraction with a denominator of 100 and simplify if necessary.

Example: 40% = 40/100 = 2/5

Decimal to Percent: Multiply the decimal by 100 and add the percent symbol (%).

Example: 0.75 = 0.75 × 100 = 75%

Percent to Decimal: Divide the percent by 100.

Example: 40% = 40 ÷ 100 = 0.4

Answer:

the radius of the cylinder is approximately 2.26 feet.

Step-by-step explanation:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given that the volume is 400 feet, the height is 25 feet, and using π ≈ 3.14, we can rearrange the formula to solve for the radius:

400 = 3.14 * radius^2 * 25

Divide both sides of the equation by (3.14 * 25):

400 / (3.14 * 25) = radius^2

Simplifying:

400 / 78.5 ≈ radius^2

5.09 ≈ radius^2

To find the radius, we take the square root of both sides:

√5.09 ≈ √(radius^2)

2.26 ≈ radius

Rounding to the nearest hundredth, the radius of the cylinder is approximately 2.26 feet.

Answer:

Step-by-step explanation:

Volume Formula for a cylinder is  V=πr²h

Substitute the following:    400 = 3.14(r²)(25)

r=[tex]\sqrt{\frac{V}{\pi h} }[/tex]

r=[tex]\sqrt{\frac{400}{\pi 25} }[/tex]

r≈2.25676ft

The solution to the given equation is x = -1/4.To solve the equation, let's break down the steps as outlined by Deepak:

Combine like terms: Starting with the left side of the equation, combine the x terms and the constant terms separately. On the left side, we have -3x and 4x, which can be combined to give x. Similarly, we have -5 and 5, which cancel each other out, leaving us with zero.

Simplify both sides: Now, the equation becomes x = -7/4 - 3x.

Move all the x terms to one side: To isolate the x term on one side, we can add 3x to both sides of the equation. This gives us 4x + 3x = -7/4.

Combine like terms: On the left side, we have 4x and 3x, which can be added to give 7x. The equation now becomes 7x = -7/4.

Solve for x: To solve for x, we divide both sides of the equation by 7. This yields x = -1/4.

Therefore, the solution to the given equation is x = -1/4.

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Answer:

Step-by-step explanation:

To solve the inequality -5 < 2x - 1 < 3, we will break it down into two separate inequalities and solve each one individually.

First, let's solve the left inequality:

-5 < 2x - 1

Add 1 to both sides:

-5 + 1 < 2x - 1 + 1

-4 < 2x

Divide both sides by 2 (remembering to reverse the inequality when dividing by a negative number):

-4/2 < 2x/2

-2 < x

Now, let's solve the right inequality:

2x - 1 < 3

Add 1 to both sides:

2x - 1 + 1 < 3 + 1

2x < 4

Divide both sides by 2:

2x/2 < 4/2

x < 2

So, the solutions to the inequalities are:

-2 < x < 2

This means that x is greater than -2 and less than 2.

Remember to use the appropriate units for measurements when calculating surface area.

To find the surface area of an object, you need to calculate the total area of all its exposed surfaces. The method for finding the surface area will vary depending on the shape of the object. Here are some common shapes and their respective formulas:

1. Cube: The surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 since a cube has six equal faces. The formula is: SA = 6s^2, where s is the length of a side.

2. Rectangular Prism: A rectangular prism has six faces, each of which is a rectangle. To find the surface area, calculate the area of each face and add them up. The formula is: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

3. Cylinder: The surface area of a cylinder includes the area of two circular bases and the area of the curved side. The formula is: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.

4. Sphere: The surface area of a sphere can be found using the formula: SA = 4πr^2, where r is the radius.

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Answer:

Step-by-step explanation:

To evaluate the expression {p - q, p - q}, which represents the inner product of the polynomial (p - q) with itself, you can follow these steps:

Given p(x) = 5x^2 - x - 3 and q(x) = 2x^2 + 4x - 3.

Subtract q(x) from p(x) to get (p - q):

(p - q)(x) = (5x^2 - x - 3) - (2x^2 + 4x - 3)

= 5x^2 - x - 3 - 2x^2 - 4x + 3

= (5x^2 - 2x^2) + (-x - 4x) + (-3 + 3)

= 3x^2 - 5x

Now, calculate the inner product of (p - q) with itself using the given inner product formula:

{p - q, p - q} = 5(a1)(a2) + 4(b1)(b2) + 3(c1)(c2)

= 5(3)(3) + 4(-5)(-5) + 3(0)(0)

= 45 + 100 + 0

= 145

Therefore, the value of {p - q, p - q} is 145.

The expression that represents the statement "Divide the difference of 27 and 3 by the difference of 16 and 4" is (27 - 3) / (16 - 4), which simplifies to 2.

The statement "Divide the difference of 27 and 3 by the difference of 16 and 4" can be represented using algebraic expressions.

To find the difference between two numbers, we subtract one from the other. So, the difference of 27 and 3 is 27 - 3, which can be expressed as (27 - 3). Similarly, the difference of 16 and 4 is 16 - 4, which can be expressed as (16 - 4).

Now, we need to divide the difference of 27 and 3 by the difference of 16 and 4. We can use the division operator (/) to represent the division operation.

Therefore, the expression that represents the given statement is:

(27 - 3) / (16 - 4)

Simplifying this expression further, we have:

24 / 12

The difference of 27 and 3 is 24, and the difference of 16 and 4 is 12. So, the expression simplifies to:

2

Hence, the expression (27 - 3) / (16 - 4) is equivalent to 2.

In summary, the expression that represents the statement "Divide the difference of 27 and 3 by the difference of 16 and 4" is (27 - 3) / (16 - 4), which simplifies to 2.

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Answer: 2,2

Step-by-step explanation:

trust me

Answer:

Step-by-step explanation:

Let's break down the given information step by step to solve the problem:

The sum of three numbers x, y, and z is 165: x + y + z = 165.

When the smallest number x is multiplied by 7, the result is n: 7x = n.

The value n is obtained by subtracting 9 from the largest number y: y - 9 = n.

The value n is also obtained by adding 9 to the third number z: z + 9 = n.

We can use this information to form a system of equations:

Equation 1: x + y + z = 165

Equation 2: 7x = n

Equation 3: y - 9 = n

Equation 4: z + 9 = n

To find the product of the three numbers, we need to determine the values of x, y, z, and n.

First, let's solve for n using Equation 2:

7x = n

Now, let's substitute the value of n into Equations 3 and 4:

Equation 3: y - 9 = 7x

Equation 4: z + 9 = 7x

We can rearrange Equation 3 to express y in terms of x:

y = 7x + 9

Now, we can substitute the value of y in Equation 1:

x + (7x + 9) + z = 165

Simplifying:

8x + z = 156

Now, we have two equations:

Equation 4: z + 9 = 7x

8x + z = 156

We can solve this system of equations to find the values of x and z:

From Equation 4, we have z = 7x - 9.

Substituting z in Equation 8x + z = 156:

8x + (7x - 9) = 156

15x - 9 = 156

15x = 165

x = 11

Substituting x = 11 in Equation 4:

z + 9 = 7(11)

z + 9 = 77

z = 68

Now, we have the values of x = 11, y = 7x + 9 = 7(11) + 9 = 86, and z = 68.

The product of the three numbers x, y, and z is:

Product = x * y * z = 11 * 86 * 68 = 64648.

Therefore, the product of the three numbers is 64648.

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-[tex]1)^2[/tex] + (-[tex]5)^2[/tex]) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

R = {(0, 8), (0, -8), (8, 0), (-8, 0), (6, ±2), (-6, ±2), (2, ±6), (-2, ±6)}

Step-by-step explanation:

Since [tex](\pm8)^2+0^2=64[/tex], [tex]0^2+(\pm 8)^2=64[/tex], [tex](\pm 6)^2+2^2=64[/tex], and [tex]6^2+(\pm 2)^2=64[/tex], then those are your integer solutions to find R.

Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.

Alonso has $21.00 to spend on eggs and avocados. He buys eggs that cost $2.50, which leaves him with $18.50. Since the store only sells avocados in bags of 3, he will need to find the cost per bag in order to calculate how many bags he can buy.

First, divide the cost of 3 avocados by 3 to find the cost per avocado. $5.00 ÷ 3 = $1.67 per avocado.

Next, divide the money Alonso has left by the cost per avocado to find how many avocados he can buy.

$18.50 ÷ $1.67 per avocado = 11.08 avocados.

Since avocados only come in bags of 3, Alonso needs to round down to the nearest whole bag. He can buy 11 avocados, which is 3.67 bags.

Thus, he will buy 3 bags of avocados.Let's test our answer to make sure that Alonso has spent all his money:

$2.50 for eggs3 bags of avocados for $5.00 per bag, which is 9 bags of avocados altogether. 9 bags × $5.00 per bag = $45.00 spent on avocados.

Total spent:

$2.50 + $45.00 = $47.50

Total money had:

$21.00

Remaining money:

$0.00

Since Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.

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The value of x is 5625 when √x + √y=138 and x-y=1656.

To solve for x using the given equations, we will use the method of substitution. Let's go through the steps:

Start with the equation √x + √y = 138.

We want to express y in terms of x, so solve for y in terms of x by isolating √y:

√y = 138 - √x

Square both sides of the equation to eliminate the square root:

(√y)² = (138 - √x)²

y = (138 - √x)²

Now, substitute the expression for y in the second equation x - y = 1656:

x - (138 - √x)² = 1656

Expand the squared term:

x - (138² - 2 * 138 * √x + (√x)²) = 1656

Simplify the equation further:

x - (19044 - 276 * √x + x) = 1656

Combine like terms and rearrange the equation:

-19044 + 276 * √x = 1656

Move the constant term to the other side:

276 * √x = 20700

Divide both sides of the equation by 276 to solve for √x:

√x = 20700 / 276

√x = 75

Square both sides to solve for x:

x = (√x)²

x = 75²

x = 5625

Therefore, the value of x is 5625.

By substituting this value of x back into the original equations, we can verify that √x + √y = 138 and x - y = 1656 hold true.

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The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.

To complete the given number sequence, let's analyze the pattern and identify the missing terms.

Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:

The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.

Using this pattern, we can determine the missing terms as follows:

To obtain the third term, we add 2 to the second term:

7 + 2 = 9

To find the fifth term, we add 3 to the fourth term:

16 + 3 = 19

To determine the seventh term, we add 4 to the sixth term:

__ + 4 = 23

Therefore, the missing terms in the sequence are 9, 19, and 23.

By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.

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Answer:

Step-by-step explanation:

Let's represent the number of people that Ms. Hernandez can bring to the zoo as "x". Each person will require an admission ticket, which costs $10.40 per person. Additionally, there is a parking fee of $3.

The total cost of admission tickets and parking is given as $150. We can set up the equation as follows:

10.40x + 3 = 150

To solve for x, we need to isolate the variable:

10.40x = 150 - 3

10.40x = 147

Now, divide both sides of the equation by 10.40 to solve for x:

x = 147 / 10.40

Using a calculator, we find:

x ≈ 14.13

Since we can't have a fractional number of people, we need to round down to the nearest whole number since we can't bring a fraction of a person. Therefore, Ms. Hernandez can bring 14 people to the zoo, including herself.

The average speed of a car is calculated by dividing the total distance traveled by the total time taken. In this case, the car travels 50+ miles in "of an hour".

To calculate the average speed in miles per hour, we need to determine the value of "of an hour". If the value is given as a fraction, we need to convert it to a decimal.

Assuming "of an hour" is 1/2 (0.5), the average speed can be calculated as:

Average speed = Total distance / Total time

Average speed = 50+ miles / (1/2) hour

To divide by a fraction, we can multiply by its reciprocal:

Average speed = 50+ miles * (2/1) hour

Average speed = 100+ miles per hour

Therefore, the average speed of the car is 100+ miles per hour.

Answer: D. 145°

Step-by-step explanation:

Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.

Answer:

Let's denote:

- A as the event "student is accepted at FSU"

- B as the event "student is accepted at UF"

We have the following probabilities given:

- P(A) = 0.4 (probability of being accepted at FSU)

- P(B|A) = 0.6 (probability of being accepted at UF given acceptance at FSU)

- P(B'|A') = 0.9 (probability of not being accepted at UF given non-acceptance at FSU), where B' is the complement of B (not being accepted at UF) and A' is the complement of A (not being accepted at FSU).

We want to find P(A|B'), or the probability of being accepted at FSU given non-acceptance at UF.

To calculate this, we can use Bayes' Theorem, which states that:

P(A|B') = P(B'|A) * P(A) / P(B')

We can calculate P(B'|A), the probability of non-acceptance at UF given acceptance at FSU, by using the fact that the sum of probabilities of complementary events equals 1:

P(B'|A) = 1 - P(B|A) = 1 - 0.6 = 0.4

Next, we need to find P(B'), the total probability of non-acceptance at UF. We can use the law of total probability to calculate this:

P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')

P(B') = 0.4 * 0.4 + 0.9 * 0.6 = 0.16 + 0.54 = 0.7

Finally, we can substitute these values into Bayes' theorem:

P(A|B') = P(B'|A) * P(A) / P(B') = 0.4 * 0.4 / 0.7 ≈ 0.229

Therefore, the probability that a student is accepted at FSU given that they are not accepted at UF is approximately 22.9%.

Answer:

  19 or 26

Step-by-step explanation:

You want the value of 3n² -8n -9, given that n(n -3) = 10.

We recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.

The value of 3n² -8n -9 will be one of ...

  (3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2

or

  (3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5

The expression 3n² -8n -9 will be either 19 or 26.

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(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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The number line inequality that represents x > -7 is: Option D

In number line inequalities we know that:

A closed circle indicates "greater than or equal to" or "less than or equal to" .

Meanwhile an open circle indicates "greater than" or "less than".

A closed circle pointing to the right indicates  "greater than or equal to" while a closed circle pointing to the left indicates "less than or equal to,"

Similarly:

An open circle pointing to the right indicates "greater than" while An open circle pointing to the left indicates  "less than".

Thus , the correct number line that shows x > -7 is: Option D

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Answer:

When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).

So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.

Answer:

the effective tax rate for a taxable income of $175,000 is approximately 21.02%.

Step-by-step explanation:

Let's break down the income into the corresponding tax brackets:

The first $10,275 is taxed at a rate of 10%.

Tax on this portion: $10,275 * 0.10 = $1,027.50

The income between $10,276 and $41,175 is taxed at a rate of 12%.

Tax on this portion: ($41,175 - $10,276) * 0.12 = $3,710.88

The income between $41,176 and $89,075 is taxed at a rate of 22%.

Tax on this portion: ($89,075 - $41,176) * 0.22 = $10,656.98

The income between $89,076 and $170,050 is taxed at a rate of 24%.

Tax on this portion: ($170,050 - $89,076) * 0.24 = $19,862.88

The income between $170,051 and $175,000 is taxed at a rate of 32%.

Tax on this portion: ($175,000 - $170,051) * 0.32 = $1,577.44

Now, sum up all the taxes paid:

$1,027.50 + $3,710.88 + $10,656.98 + $19,862.88 + $1,577.44 = $36,836.68

The effective tax rate is calculated by dividing the total tax paid by the taxable income:

Effective tax rate = Total tax paid / Taxable income

Effective tax rate = $36,836.68 / $175,000 = 0.21024 (rounded to the nearest hundredth)

Answer: 74

Step-by-step explanation:

The volume of the pyramid can be found using the formula:

Volume = (1/3) x Base Area x Height

To find the base area, we need to find the area of the triangular base. The area of a triangle can be found using the formula:

Area = (1/2) x Base x Height

Substituting the given values, we have:

Area = (1/2) x 8 x 6 = 24 square inches

To find the height of the pyramid, we can use the Pythagorean theorem. The slant height and one-half of the base form a right triangle, so we have:

Height^2 = (Slant Height)^2 - (1/2 x Base)^2

Height^2 = 10^2 - 4^2

Height^2 = 84

Height = √84 ≈ 9.165 inches

Now we can substitute the values into the formula for the volume:

Volume = (1/3) x Base Area x Height

Volume = (1/3) x 24 x 9.165

Volume ≈ 73.96 cubic inches

Therefore, the volume of the pyramid is approximately 73.96 cubic inches.Step-by-step explanation:

Answer:

64 and 65

Step-by-step explanation:

Let the two lockers be x and (x+1) since they are consecutive

The sum is 129 so,

x + (x+1) = 129

2x + 1 = 129

2x = 128

x = 64

x + 1 = 65

The locker numbers are 64 and 65