Every number has only one quality: its distance from zero.
O A. True
OB. False

The length of the straw is 4.26 inches.

We have,

On the bottom face,

Applying the Pythagorean theorem,

x² = 1² + 3²

x² = 1 + 9

x² = 10

Now,

Applying the Pythagorean theorem with the diagonal side.

d² = x² + 3²

d² = 10 + 9

d² = 19

d = √19

d = 4.36 in

Thus,

The length of the straw is 4.26 inches.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ1

The acceleration of the collar at point A is 5 ft/s^2.

A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:

N - 5 = 0

where N is the normal force. Solving for N, we get:

N = 5 lb

B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:

x = L - y = 3 - 0 = 3 ft

where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:

F = kx = 10 lb/ft × 3 ft = 30 lb

The weight of the collar is:

W = mg = 5 lb

where g is the acceleration due to gravity. The net force on the collar is therefore:

Fnet = F - W = 30 - 5 = 25 lb

Using Newton's second law, we can write:

Fnet = ma

where a is the acceleration of the collar. Solving for a, we get:

a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2

Therefore, the acceleration of the collar at point A is 5 ft/s^2.

Accelerationhttps://brainly.com/question/16850867

#SPJ11

The polynomial equation of the smallest degree is f(u) = (u + 2)³(u - 1)²(u - 3)

Given that we have the graph of a polynomial

The degree of the graph is the number of times the graph intersect and/or crosses the x-axis

In this case, we have the following points at which the graph intersect and/or crosses the x-axis

When the multiplicities are added, we have

Degree = 3 + 1 + 2

Degree = 6

So, the degree is 6

In (a), we have

This means that

The zero at u = 1 has a multiplicity of 1

The equation is represented as

f(u) = (u - zero)^multiplicity

So, we have

f(u) = (u + 2)³(u - 1)²(u - 3)

Read more about polynomial at

https://brainly.com/question/7693326

#SPJ1

Answer:

m/2 -6= m/4+2 can be solved as follows:

Multiply both sides of the equation by the least common multiple of the denominators, which is 4:

4(m/2 - 6) = 4(m/4 + 2)

2m - 24 = m + 8

Subtract m from both sides:

m - 24 = 8

Add 24 to both sides:

m = 32

Therefore, the value of m is C) 32.

k/12 = 25/100 can be solved as follows:

Multiply both sides of the equation by 12:

k = 12 * (25/100)

k = 3

Therefore, the value of k is A) 3.

9/5 = 3x/100 can be solved as follows:

Multiply both sides of the equation by 100:

100 * (9/5) = 3x

Simplify:

180/5 = 3x

36 = 3x

Divide both sides by 3:

x = 12

Therefore, the value of x is not one of the options provided.

Step-by-step explanation:

Answer:

[tex] \sf \longrightarrow \: \frac{m}{2} - 6 = \frac{m}{4} + 2 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{m - 12}{2} = \frac{m + 8}{4}\\ [/tex]

[tex] \sf \longrightarrow \: 4(m - 12) =2(m + 8)\\ [/tex]

[tex] \sf \longrightarrow \: 4m \: - 48 =2m + 16\\ [/tex]

[tex] \sf \longrightarrow \: 4m \: - 2m = 16 + 48\\ [/tex]

[tex] \sf \longrightarrow \:2m = 64\\ [/tex]

[tex] \sf \longrightarrow \:m = \frac{64}{2} \: \\ [/tex]

[tex] \sf \longrightarrow \:m = 32 \: \\ [/tex]

[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: C) \: \: \: 32 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

[tex] \sf \leadsto \: \frac{k}{12} = \frac{25}{100} \\ [/tex]

[tex] \sf \leadsto \: 100(k)= 12(25) \\ [/tex]

[tex] \sf \leadsto \: 100 \times k= 12 \times 25 \\ [/tex]

[tex] \sf \leadsto \: 100 k= 300 \\ [/tex]

[tex] \sf \leadsto \: k= \frac{300}{100} \\ [/tex]

[tex] \sf \leadsto \: k= 3 \\ [/tex]

[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: a) \: \: \: 3 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

[tex] \sf \longrightarrow \: \frac{9}{5} = \frac{3x}{100} \\ [/tex]

[tex] \sf \longrightarrow \: 100(9)= 5(3x) \\ [/tex]

[tex] \sf \longrightarrow \: 100 \times 9= 5 \times 3x \\ [/tex]

[tex] \sf \longrightarrow \: 900= 15x \\ [/tex]

[tex] \sf \longrightarrow \: x= \frac{900}{15} \\ [/tex]

[tex] \sf \longrightarrow \: k= 60 \\ [/tex]

[tex]\qquad{\underline{\overline {\boxed{ \sf{ \: \: a) \: \: \: 60 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

Answer:

The length of the second train is 416.67 meters.

Step-by-step explanation:

mark brainliest

s√3 is the distance from point A to point B. Therefore, the correct option is option D among all the given options.

While distance and displacement appear to have the same meaning, they actually have very different definitions and meanings. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "the amount of ground the object has travelled over during its motion."

Distance² = s² + s² + s²

Distance² = 3 s²

Distance = s√3

Therefore, the correct option is option D among all the given options.

To know more about distance, here:

https://brainly.com/question/15172156

#SPJ1

The length of the arc GH is 13.3 cm

The length of an arc is the distance that runs through the curved line of the circle making up the arc.

The length of an arc is expressed as;

l = tetha/360 × 2πr

tetha = R

R = 360-( 170+80)

R = 360-250

R = 110°

l = 110/360 × 2 × 3.14 × 6.4

l = 4787.2/369

l = 13.3 cm (1.dp)

therefore the length of the arc GH is 13.3 cm

learn more about length of an arc from

https://brainly.com/question/2005046

#SPJ1

The horizontal distance more that Jake was able to cover, given the incline, would be A.4.1 ft.

We can find the horizontal distance that both Jake and Raphael covered .

Jake's distance was:

cos ( 7.9 ° ) = adjacent / 100

adjacent = 100 x 0.989

adjacent = 98.9 ft

Rafael's distance was :

cos ( 18. 3° ) = adjacent / 100

adjacent = 100 x 0.951

adjacent = 95.1 ft

The difference and the distance covered in addition by Jake would be:

= 98. 9 - 95. 1

= 3. 8 ft

The closest option is 4. 1 ft.

Find out more on distance at https://brainly.com/question/24283318

#SPJ1

The trigonometric expression 1/sin(2x) - cos(2x)/sin(2x) = tanx

A trigonometric expression is an equation that contains trigonometric ratios.

Given the expression 1/sin(2x) - cos(2x)/sin(2x), we need to find the expression that is equivalent to it.

So, we proceed as follows.

1/sin(2x) - cos(2x)/sin(2x) = [1 - cos(2x)]/sin(2x),

Using the trigonometric identity cos2x = cos²x - sin²x and sin2x = 2sinxcosx, we have that

[1 - cos(2x)]/sin(2x) = [1 - (cos²x - sin²x)]/2sinxcosx

=  [1 - cos²x + sin²x)]/2sinxcosx

Now, 1 - cos²x = sin²x.

So, substituting this into the equation, we have that

[1 - cos²x + sin²x)]/2sinxcosx = [sin²x + sin²x)]/2sinxcosx

=  [sin²x + sin²x)]/2sinxcosx

=  2sin²x/2sinxcosx

=  sinx/cosx

= tanx

So, 1/sin(2x) - cos(2x)/sin(2x),= tanx

Learn more about trigonometric expression here:

https://brainly.com/question/26311351

#SPJ1

Answer:

Suppose X ~ N(12,2) represents a normal distribution with mean 12 and standard deviation 2. According to the empirical rule, about 68% of the x values lie within one standard deviation of the mean .

We can calculate the endpoints of the interval that represents one standard deviation from the mean as follows:

Lower endpoint: 12 - 2 = 10

Upper endpoint: 12 + 2 = 14

Therefore, about 68% of the x values lie between 10 and 14 1.

Step-by-step explanation:

Answer:

4(x-1)=2(6-2x)

4x-4=12-4x

4x+4xd=12+4

8x=16

x=2

Answer:

x=2

Step-by-step explanation:

Step 1: Distribute

To solve this problem, the first step is distributing the four and the 2.

[tex]4(x-1)=2(6-2x)\\\\4x-4=12-4x[/tex]

So this is our simplified problem.

Step 2: Solve for x

Step 2a: Add 4x to both sides:

(This is because we do not have two variables in the equation, making it easier to solve.

[tex]4x+4x-4=12-4x+4x\\\\8x-4=12+0\\\\8x-4=12[/tex]
Step 2b: Add 4 to both sides:

(We do this to leave the variable on one side and the constant on the other. )

[tex]8x-4+4=12+4\\\\8x+0=16\\\\8x=16[/tex]

Step 2c: Divide both sides by 8:

(The reason why we do this is to isolate the variable without any coefficient in front.)

[tex]\frac{8x}{8} =\frac{16}{8} \\\\x=2[/tex]

Answer:

First, we need to calculate the absolute error, which is the difference between the predicted value and the actual value:

Absolute error = |predicted value - actual value| = |87 - 107| = 20

Then, we can calculate the percent error using the formula:

Percent error = (absolute error / actual value) x 100%

Plugging in the values, we get:

Percent error = (20 / 107) x 100% ≈ 18.69%

Therefore, the percent error of the baker's prediction is approximately 18.69%.

Answer:

180

Step-by-step explanation:

To find the lowest common multiple (LCM) of 36 and 30, we can use the prime factorization method:First, we can find the prime factorization of each number:36 = 2^2 * 3^230 = 2 * 3 * 5Next, we can take the highest power of each prime factor that appears in either number and multiply them together.The highest power of 2 is 2^2 = 4.The highest power of 3 is 3^2 = 9.The highest power of 5 is 5^1 = 5.Multiplying these together, we get:LCM(36, 30) = 2^2 * 3^2 * 5 = 180Therefore, the lowest common multiple of 36 and 30 is 180.

Answer: 180

Step-by-step explanation:

To find the lowest common multiple (LCM) of two numbers, we need to find the smallest number that is a multiple of both of them.

One way to do this is to find the prime factorization of each number and then take the product of all the prime factors, with each factor occurring as many times as it appears in the factorization of either number.

The prime factorization of 36 is 2^2 × 3^2, and the prime factorization of 30 is 2 × 3 × 5. Therefore, the LCM of 36 and 30 can be found by taking the product of the highest power of each prime factor that appears in either factorization:

LCM(36, 30) = 2^2 × 3^2 × 5 = 180

Therefore, the lowest common multiple of 36 and 30 is 180.

The answers are 1) 360,000, 2) 217,060, 3) 37,140 and 4) 180,080.

1) To calculate the amount of premium paid by the employee and the employer =

Consider employee medical insurance payable, and employee life insurance payable.

The journal entries for accrual payroll, including employee deductions, consider sales salaries expense office salaries expense, social sec taxes payable Medicare tax payable, employee income taxes, life insurance payable, union dues, salaries payable.

2) Journal entry for cash payment of net payroll for month of July consider salaries payable and cash.

3) Calculate the unemployment tax amount, consider state unemployment taxes and federal unemployment taxes,

Journey Entries for accrued employer payroll taxes,

Payroll taxes expenses, social taxes, Medicare taxes, state unemployment taxes, federal unemployment taxes, employee medical and life insurance.

4) Journal entries for cash payment of all libraries, consider, social medical taxes, employee fed, medical, life and state income taxes payable.  

Learn more about journal entries, click;

https://brainly.com/question/20421012

#SPJ1

The expected values are 60 blues, 30 reds and 30 greens

From the question, we have the following parameters that can be used in our computation:

6 blue cubes, 3 red cubes, and 3 green cubes

This means that we have the following proportions

Blue = 6/(6 + 3 + 3) = 1/2

Red = 3/(6 + 3 + 3) = 1/4

Green = 3/(6 + 3 + 3) = 1/4

If you draw a cube and replace it in the bag 120 times, we have

Blue = 1/2 * 120 = 60

Red = 1/4 * 120 = 30

Green = 1/4 * 120 = 30

Hence, the expected values are 60 blues, 30 reds and 30 greens

Read more about proportions at

https://brainly.com/question/12024093

#SPJ1

Answer: 1) 66 2)

Step-by-step explanation:

1) 22x3=66

2) C

Hope this helps! :)

Answer:

The given pattern does not form an arithmetic sequence as there is no common difference between each term. An arithmetic sequence is a sequence in which there is a fixed difference between each consecutive term. For example, 1, 3, 5, 7 is an arithmetic sequence with a common difference of 2 (adding 2 to each term gives the next term). However, the given pattern of 1/2, 1, 2/3, 2 does not follow this pattern as the difference between each term varies. Therefore, this pattern does not fit the definition of an arithmetic sequence.

Step-by-step explanation:

We can see here that the measure of variability using the range will be: 1.

A statistical metric known as a measure of variability tells us how widely spaced or dispersed a group of data points are. Measures of variability are used to quantify how significantly different a dataset's individual data points are from one another.

The measure of variability using range will:

Mean (Peak season) - Mean (Off Peak Season) = 6 - 5 = 1.

We see here that the mean of the peak season population is increased compared to that of the off-peak season. The mean of the off-peak season is seen to be lower.

Learn more about measure of variability on https://brainly.com/question/14544205

#SPJ1

Answer: x = -5

Step-by-step explanation:

Answer:

x=-5

7 - 4 * (-5)

Negative times a negative equals a positive

-4*-5=20

7+20=27

Answer:

Step-by-step explanation:

Select the smaller fraction. 1/10 or 1/2

1/10 = 1 : 10 = 0.1

1/2 = 1 : 2 = 0.5

so your answer is 1/10

Two ten thousandths are 0.0002.

The number 2 will be in ten thousand place

TENS   ONES    .       TENTHS       HUNDREDTHS        THOUSANDTHS    

                          .               0                       0                                 0              

TEN THOUSANDTHS

            2

Answer:

The equation that describes a vertical translation of the square root parent function is A. y = x − 4−−√ + k where k is the vertical shift.

The square root parent function is f(x) = √x. To perform a vertical translation of this function, we add or subtract a constant value to the function. In this case, the function y = x − 4−−√ represents a vertical translation of the square root parent function by 4 units downwards.

Option B, y = x−−√−6 represents a vertical translation of the square root parent function by 6 units downwards. Option C, y = x−−√, represents the square root parent function without any vertical shift. Option D, y = −x−−√, represents a reflection of the square root parent function about the y-axis.

The zeros of g(x)= -(x+2) (x-3) (x-3) are -2 and 3.

We are given that;

g (x) = -(x+2) (x-3) (x-3)

Now,

To determine the zeros of g(x) = -(x+2)(x-3)(x-3), we need to find the values of x that make g(x) equal to zero. This means that we need to solve the equation:

−(x+2)(x−3)(x−3)=0

To solve this equation, we can use the zero product property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x:

x+2=0orx−3=0

Subtracting 2 from both sides of the first equation, we get:

x=−2

Adding 3 to both sides of the second equation, we get:

x=3

Therefore, by the given equation the answer will be -2 and 3.

To learn more about equations :

brainly.com/question/16763389

#SPJ1

Answer:

Step-by-step explanation:

Because we're told the amount doubles on each successive day, we know we're dealing with an exponential function.

The general form for an exponential function is

[tex]f(x)=ab^x[/tex], where a is the initial value, b is the base, and x is the exponent.

We know that Julia saved $0.01 on the first day so our a value is 0.01.

Because the amount doubles each time, our base is 2.

Furthermore, since we're want to find when Julia's savings exceed $1.00, we can turn the general exponential formula into an inequality where the formula is greater than 1 and solve for x (time in days):

[tex]1.00 < 0.01(2)^x\\100 < 2^x\\log(100) < log(2)^x\\log(100) < x*log(2)\\log(100)/log(2) < x\\6.64 < x\\7 < x[/tex]

We had to round the 6 to the nearest whole number (7) to get the answer.

We can check our work by plugging in both 6.64 for x and 7 for x to see how at 7 days, Julia's savings exceed 1.00

Plugging in 6.64 for x:

[tex]f(6.64)=0.01(2)^6^.^6^4\\f(6.64)=0.01*99.7\\f(6.64)=0.997\\f(6.64)=1.00[/tex]

Using 6.64 for x makes Julia's savings equal 1, but they don't exceed 1

Plugging in 7 for x:

[tex]f(7)=0.01(2)^7\\f(7)=0.01*128\\f(7)=1.28[/tex]

The 30th percentile in the uniform distribution is 2.4 min.

The correct option is (b)

The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), :

P(E)= Number of favorable outcomes/ Number of total outcomes

[tex]\mu=\frac{a +b}{2}[/tex]

[tex]\sigma=\sqrt{\frac{(b-a)^2}{12} }[/tex]

P(x) = 1/ b - a if a < x < b

P(X < a) = 0

and

P(X > b) = 0

In this case, a = 0 and b = 8

The 30th percentile in the uniform distribution, this means that the probability is 0.30. Therefore:

0.3 = [tex]\frac{1}{8-0}.x[/tex]

0.3 (8 -0) = x

2.4 = x

Learn more about Uniform distribution at:

https://brainly.com/question/13233983

#SPJ1

The given question is incomplete, complete question is :

The Sky Train from the terminal to the rental-car and long-term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. Find the 30th percentile for the waiting times (in minutes).

a. 2

b. 2.4

c. 2.75

d. 3

The given equation in exponential form will be [tex]20 = x^e[/tex]

Given is an equation, x = ㏑ 20,

So, we know that,

㏑(x) = [tex]log_e(x)[/tex]

And,

logₐ (x) = b

x = bᵃ

Therefore,

x = ㏑ 20

will be converted into,

[tex]20 = x^e[/tex]

Hence, the given equation in exponential form will be [tex]20 = x^e[/tex]

Learn more about logarithmic equations, click;

https://brainly.com/question/29197804

#SPJ1