1 how fast must a ball be rolled along a 70-cm-high table so that when it rolls off the edge it will strike the floor at this same distance (70 cm) from the point directly below the table edge?

Check the picture below.

[tex]tan(x)=\cfrac{\stackrel{opposite}{50}}{\underset{adjacent}{42}}\implies tan(x)=\cfrac{25}{21}\implies x=tan^{-1}\left( \cfrac{25}{21} \right)\implies x\approx 50^o[/tex]

Make sure your calculator is in Degree mode.

The angle measures in this problem are given as follows:

The sides of the mountains are parallel, which means that the angles of these sides have the same measures, as follows:

Then the measure of x is obtained considering that angles x, y and z form a ray, that is, the sum of their measures is of 180º, hence:

x + y + z = 180

x + 55 + 37 = 180

x = 180 - (55 + 37)

x = 88º.

More can be learned about angle measures at https://brainly.com/question/25716982

#SPJ1

Answer:

Step-by-step explanation:

y varies directly as x.

y = 18 , x = 5

y =36 then x also double,

x = 10

We will use certain constraints to imitate the repetition of the process as mentioned below

To simulate one repetition of the procedure using random digits, we shall perform as follows:

from a line of the random digits table, ten one and two-digit numbers could be selected with the following conditions;

1. skipping repeated numbers

2. skipping numbers from 77    to 99  

here the numbers 01   to 12   i.e. first-class passengers in the group of selected random numbers are to be counted.

As we know, numbers represent first-class passengers while numbers to represent coach-class people.

Hence, using this we can use random digits

Learn more about variables:

https://brainly.com/question/17344045

#SPJ4

Answer:130.09

Step-by-step explanation:

Using the formulas

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving forA

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·7.2+8·7.2+3.5·7.2+1

2·﹣54+2·(5·8)2+2·(5·3.5)2﹣84+2·(8·3.5)2﹣3.54≈130.08536

Answer:

Below

Step-by-step explanation:

s = small box number         volume =  6s

L = large box number         volume   = 15L

6s + 15 L =243    

  AND      s = L +2  

Answer:

30 I think but I'm not positive

Step-by-step explanation:

z = -2.51 is the required test statistic.

A statistic employed in statistical hypothesis testing is known as a test statistic.

A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

The probability value, or p-value, indicates the likelihood that your data could have been true under the null hypothesis.

This is accomplished by estimating the probability of your test statistic, which is the figure obtained from a statistical analysis of your data.

So, we have to use: Ha: pB < pNY

This implies that the alternative thesis is revised as follows:

Ha: pB - pNY < 0

In contrast to the null hypothesis:

H₀: pB - pNY = 0

This is the test statistic:

z = X - μ/a

Now, pB = 0.581, pNY = 0.832.

It follows that: X = 0.581 - 0.832 = -0.251

The test for the null hypothesis is 0.

This follows to: μ = 0

Standard deviation: 0.1

This follows to: s = 0.1

Test statistic:

z = X - μ/a

z = -0.251-0/0.1

z = -2.51

Therefore, z = -2.51 is the required test statistic.

Know more about the test statistic here:

https://brainly.com/question/15110538

#SPJ4

Complete question:
A study was conducted to compare the proportion of drivers in Boston and New York who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in Boston was 0.581 and the proportion wearing seat belts in New York was 0.832. Due to local laws at the time the study was conducted, it was suspected that a smaller proportion of drivers wear seat belts in Boston than New York.

Find the test statistic for this test using Ha: pB < pNY. (Use standard error = 0.1.)

Answer:

-76

each term is being subtracted from the preceding the next odd number

The minimum value of the function occurs between 4 and 5.

A function is a relation where every input is connected to only one possible output from a set of available inputs.

Given the table of values.

Note that the value of the function is a minimum of between 4 and 5.

Hence, the minimum value of the function occurs between 4 and 5.

Learn more about functions:

https://brainly.com/question/28193995

#SPJ1

Answer:

-8 + 3 + x =  x - 5

Step-by-step explanation:

This is because X does not have a value & both 8 & 3 are constants making them computable

Step-by-step explanation:

4x+12=0

4x= -12

x = -3

.........

The balanced equation is Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄).

An equation is a combination of different variables, in which two expressions are equal to each other.

The given equation is,

Ba(C₂O₄) + K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)

Since, there are 2 atom of potassium on right side and also (IO₃) is two times.

To balance the equation, Coefficient of K(IO₃) should be 2.

The equation can be represented as,

Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)

To know more about Equation on:

https://brainly.com/question/187506

#SPJ1

The probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.

Given that.

The percentage of customers who will disclose a food allergy is 0.08

At Ying Ying's bakery, 121 people place orders on a single day.

We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.

Formula for Binomial probability distribution:

P(X=x)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ

Where P(x)= probability of getting success in x trials,

n= sample size ,

p represents the probability that each event will succeed.

As stated, we have n=12

p=0.08

Let x signify that the client will disclose a food allergy.

Following that, the probability that at least one client will disclose a food allergy will be:

P(x≥1)=1-P(x<1)

=1-P(x=0)

=1-¹²C₀(0.08)⁰(1-0.08)¹²⁻⁰

=1-(1)(0.12)¹²

=1-0.3677

=0.6323

Therefore, the probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ4

2. 2x-7=3 Addition Property

3. 2x=10  Division Property

4. x = 5

Answer:

I hope I helped

I have not been taught on this topic yet but I manage to answer the question if the answer is wrong it isn't my fault I haven't been taught yet.

I wish you a happy day

Step-by-step explanation:

1.)4x – 7 = 2x + 3

4x – 2x – 7 = 2x – 2x + 3 (subtraction property)

2x – 7 = 3

2x – 7 +7 = 3 + 7(addition property)

2x = 10(division property)

x = 5(reflexive property)

Answer:

If 6a = 5b then the ratio of 2a : 7b is 5 : 21

Explanation:

Given that 6a = 5b

We have to find the ratio of 2a : 7b

Let us first solve the given expression and find values of a and b

6a = 5b

So we have found that a = 5 and b = 6

Finding ratio of 2a : 7b

2a : 7b = 2(5) : 7(6)

2a : 7b = 10 : 42

On simplifying to lowest terms,

2a : 7b = 5 : 21

Thus the ratio of 2a : 7b is 5 : 21

Answer:This is not a proportional relationship.

Step-by-step explanation:

Answer:

60 degrees

Step-by-step explanation:

The arc length is 1/6th of the total ....the angle will be 1/6th of the total 360° of the circle

1/6th  X 360 = 60 °

Answer:

60 degrees

Step-by-step explanation:

1.) Figure out which portion of the circle that the arc is. Since the total circumference is 6, and the arc is 1, that means that the arc is 1/6 of the circle.

2.) Now, figure out the measure of the angle. Since the total angle measure in a circle is 360 degrees, we multiply 1/6*360 to figure out the measure. This is equal to 60 degrees.

The father is with the son's mother.

Given that,

a mother is 21 years older than her son.

Let us consider M be the age of the mother and S be the age of the son

which implies that,

M = S + 21 ---------------(1)

and in 6 years, mother will be 5 times as old as her son

i.e. M + 6 = 5(S + 6)

M = 5S + 24 ------------- (2)

so equation (1) and (2) implies that,

S + 21 = 5S + 24

     21 = 4S + 24

       S = - 3/4

That means son is - 3/4 years old or - 9 months.

The time at which we know the father will be with son's mother.  

To know more about age here

https://brainly.com/question/13493228

#SPJ4

Relation is an association between two sets of objects which are paired according to certain rule.

As given in the question,

Given statement is:

Association between the two given sets of objects that are paired according to the certain rule.

Explanation of each option for the given statement:

A. Domain : Domain represents all the input values of any relation.

It is not correct option.

B. Range : It represents all the output values of any relation.

It is not correct option.

C. Relation : It represents the association between two sets which are collection of ordered pairs ( x, y ) where each input value is associated with output value.

It is the correct option.

D. Function : It represents each input is uniquely related to output value.

Not a correct option.

Therefore, relation is an association between two sets of paired objects with certain rule.

Learn more about sets here

brainly.com/question/8053622

#SPJ4

The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.

Here,

All the calculations attached in image.

z= 1.96

p = 0.5

q = 1-p = 0.5

E = 0.05

sample size =

(z^2).(pq)=(1.96^2).(0.5)(.0.5)

384.16,

round up

n for study =385

Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.

To know more about confidence interval,

https://brainly.com/question/24131141

#SPJ4

Answer:

$21.6

Step-by-step explanation:

[tex]720*\frac{3}{100} =720*0.03=21.6[/tex]

Answer:

Step-by-step explanation:

1. is .4444444 or 4/9

All you do for this is enter -2 as x for 4(3)^x

2.  is x^24 or answer (4)

this is because you will multiply the exponents starting with -4 till you get 24.  

-4 x -1 = 4

4 x 6 = 24

3. sorry I have to go for this one, plug in any number into x and experiment with the 4 answers till one of them gives you the same solution

The value of x=11 and the value of an angle ∠RDB=45°.

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to the measurement of an angle or a rotation. This measurement is the ratio of the length of a circular arc to its radius.

By using the secant-secant theorem,

(13x+7-60)/2=5x-10

13x-53=10x-20

3x-53=-20

3x=33

x=11

m ∠RDB=5(11)-10

=45°

Hence, the value of x=11 and the value of an angle ∠RDB=45°.

To know more about angle, visit:

https://brainly.com/question/28451077

#SPJ1

At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, the value of a margin of error of x is 1.534%.

In the given question, at a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, then we have to explain how should we interpret that.

The given confidence interval = 95%.

We can write it as CI = 0.95.

An approval rating is 55%.

We can write it as(p) = 0.55

A margin of error is x.

Let the value of sample size n = 1000.

So the margin of error;

ME = z× {p(1-p)}/√n

The value of z for confidence interval of 95% is 1.96.

Now putting the value

x = 1.96× {0.55(1-0.55)}/√1000

x = 1.96× {0.55×0.45}/31.623

x = 1.96× 0.2475/31.623

x = 1.96×0.00783

x = 0.01534

x = 1.534%

So the margin of error should be 1.534%.

To learn more about confidence interval link is here

brainly.com/question/29657444

#SPJ4

The right question is:

At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?

A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

Given,

We must determine the kind of variable needed in the given problem to build a confidence interval for a population proportion.

Considering that;

The percentage of the entire population that possesses a specific quality is known as the population proportion (which is qualitative in nature). Therefore, a qualitative variable with two alternative outcomes must be used to generate the confidence interval for the population proportion.

Therefore, the nature of the various types of variables is used to choose the correct option. A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

Learn more about confidence interval here;

https://brainly.com/question/15871700

#SPJ4

Question is incomplete. Completed question is given below;

What type of variable is required to construct a confidence interval for a population proportion?

A. Quantitative

B. Qualitative with any number of possible outcomes

C. Continuous

D. Qualitative with 2 possible outcomes

E. Discrete

F. Qualitative with 3 or more possible outcomes

The laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].

Given,

[tex]f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}[/tex]

applying laplace transform on both sides,

[tex]L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex]

The range for values of s for which F(s) exists is when F(s)≥0

[tex]\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0[/tex]

using formula to find roots,

[tex]s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi[/tex]

Thus,  the laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].

To learn more about laplace transform refer here

https://brainly.com/question/13077895

#SPJ4

The slope of the two points passing through points  (​12,10​) and ​(30​,25​) will be 5 / 6.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. the slope is defined as the ratio of the rise to the run.

Given that points ​(​12,10​) and ​(30​,25​) form a proportional relationship.

The slope of the line passing through the two points will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 25-10 ) / ( 30-12 )

Slope = 15 / 18

Slope = 5 / 6

Therefore, the slope of the two points passing through points  (​12,10​) and ​(30​,25​) will be 5 / 6.

Learn more about slopes here

brainly.com/question/3605446

#SPJ1

Answer:

21%

Step-by-step explanation:

Approximate number = 75 

exact number = 95error

approximate number - exact number| ÷ exact number error = |(75-95)| / 95 = |20| / 95 = 0.21percentage of error = 0.21 x 100% = 21%

The answer should be correct! Hope it helps!!! Mark as Brainliest. It would make my day! Thank you :)