p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right ) P is the product, indicated above, of all the numbers of the form 1 – \frac{1}{k}, where k is an integer from 2 to 50, inclusive. What is the value of P

Tan(Angle) = Opposite leg / Adjacent leg

Tan(B) = 4/5

B = arctan(4/5)

B = 51.34 degrees.

Answer:

Alternate Hypothesis: The true weight of the piglets is greater than or equal to 39 lbs.

Step-by-step explanation:

Hypothesis testing is more like a binary process in which only one (Either Null or Alternate Hypothesis can be true) and we have to infer that whether our Null hypothesis is true or false.

The hypothesis testing involves following 4 general steps:

As in the given question, if a number (X) is less than another number (Y) then it can't be less, equal or greater simultaneously.

Answer:

  v = 2

Step-by-step explanation:

Eliminate parentheses by using the distributive property.

  -18v +6 = -10v -10

  6 = 8v -10 . . . . . . . . . add 18v

  16 = 8v . . . . . . . . . . .  add 10

  2 = v . . . . . . . . . . . . . divide by the coefficient of v

The answer is v = 2.

Answer:

v = 2

Step-by-step explanation:

6 (-3v + 1) = 5 (-2v - 2)

- 18v + 6 = - 10v - 10

- 18v + 10v = - 10 - 6

- 8v = - 16

- v = - 16/8

- v = - 2

v = 2

Answer:

Step-by-step explanation:

160+112n=180k

112n=180k-160

for k=1

180-160=20(not divisible by 112)

k=2

180*2-160=360-160=200(not divisible by 112)

k=3

180*3-160=540-160=380(not divisible by 112)

180*4-160=720-160=560(divisible by 112)

so number of sides=560/112 +1=5+1=6

or (n-2)180=720

n-2=720/180=4

n=4+2=6

Answer:

6

Step-by-step explanation:

The sum of interior angle of a polygon is (n - 2)180.

But in the convex polygon given in the question, we know that the sum of the interior angles is as follows: : 160 + 112(n - 1)

Equating both will yield the following:

180n -360 = 112n - 112 + 160

180n - 360 = 112n + 48

180n - 112n = 360 + 48

68n = 408

n = 408/68 = 6

Hence , the convex polygon has 6 sides

Answer:

The decimal value is 99.

Step-by-step explanation:

We want to convert 01100011 to decimal.

We start counting the digit from the rightmost digit using zero-index system:

0 = 7

1 = 6

1 = 5

0 = 4

0 = 3

0 = 2

1 = 1

1 = 0

We multiply each digit by 2 having the index as power:

[tex]= (0 * 2^{7} ) + (1 * 2^{6} ) + (1 * 2^{5} ) + (0 * 2^{4} ) + (0 * 2^{3} ) + (0 * 2^{2} ) + (1 * 2^{1} ) + (1 * 2^{0} )\\= (0 * 128) + (1 * 64) + (1 * 32) + (0 * 16) + (0 * 8) + (0 * 4) (1 * 2) + (1 * 1)\\= 0 + 64 + 32 + 0 + 0 + 0 + 2 + 1\\= 99[/tex]

Therefore, the decimal value of "c" is 99.

The decimal value of the given binary value 0110 0011 is 99.

Given information:

The binary value of the ASCII letter "c" is 0110 0011.

It is required to convert the given binary value into a decimal number.

So, to convert a binary code to a decimal code, it is required to multiply the binary numbers with indices of 2.

The code can be converted to decimal number as,

[tex]d=2^0\times 1+2^1\times1+2^2\times0+2^3\times0+2^4\times0+2^5\times1+2^6\times1+2^7\times0\\d=1+2+0+0+0+32+64+0\\d=99[/tex]

Therefore, the decimal value of the given binary value 0110 0011 is 99.

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Answer: I agree with 6/5 and with 1 1/5

Step-by-step explanation: okay, to find the value of the amount of 5/6 in 1, we simply just divide 1 by 5/6

Taking a similar problem with different numbers. Let's the the amount of 2s in 10, we do 10/2 which equals 5, so we have 5 2s in 10, you get? 2,4,6,8,10

So dividing 1 by 5/6

I / (5/6)

Change since to multiplication

1 * 6/5

= 6/5

Changing this to a mixed fraction, we get 1 whole number, 1 over 5 = 1 1/5

Answer:Answer: I agree with 6/5 and with 1 1/5

Step-by-step explanation:

Step-by-step explanation: okay, to find the value of the amount of 5/6 in 1, we simply just divide 1 by 5/6

Taking a similar problem with different numbers. Let's the the amount of 2s in 10, we do 10/2 which equals 5, so we have 5 2s in 10, you get? 2,4,6,8,10

So dividing 1 by 5/6

I / (5/6)

Change since to multiplication

1 * 6/5

= 6/5

Changing this to a mixed fraction, we get 1 whole number, 1 over 5 = 1 1/5

(copied from another user) so credit to her

Answer:

  It has a single solution x=-3 y=26

Step-by-step explanation:

The ratios of coefficients of x and y are different, so the pair of equations has one solution. It is easy to tell the first offered solution (15, 17) does not satisfy the first equation, so that choice is eliminated.

Fortunately, the second offered solution, (x, y) = (-3, 26), satisfies both equations.

The equations have a single solution: (x, y) = (-3, 26).

Answer: The equation has a single solution x = -3 , y = 26.

( -3, 26 )

Step-by-step explanation:

3x + y =17 ---------------------(1)

x + 2y = 49 -------------------(2)

Using substitution approach

From (2)

x = 49 - 2y --------------------(3)

Now put (3) in equation (1) and solve.

3(49 - 2y) + y = 17

Open the bracket and solve

3 x 48 - 3 x 2y + y = 17

147 - 6y + y = 17

Gather like terms

-5y = 17 - 147

-5y = -130

Multiple through by (-1)

5y = 130

Divide by 5

y = 130/5

y = 26.

Substitute for y now in equation (3) to get the value of x

3x + y = 17

3x + 26 = 17

3x = 17 - 26

3x = -9

Now , divide by 3

x = -3

The equation had a single solution of x = -3 , y = 26

Chech.

3 x -3 + 26

-9 + 26

= 17

Good evening

Answer:

f(-3) = -4

Step-by-step explanation:

just using the calculator replace x by -3

f(-3) = 4(-4-(-3)) = 4(-4+3) = 4×(-1) = -4.

:)

Answer:

-4

Step-by-step explanation:

How you start the equation is by plugging  -3 into both of the x's in the problem to make it:

f(-3) =  4(-4 - (-3))

f(-3) = 4(-4 + 3)

f(-3) = 4(-1)

f(-3) = -4

The answer would be written as:

f(-3) = -4

I hope this helps!

Answer:

7.23%.

Step-by-step explanation:

We are asked to find APY (Annual Percentage Yield) to the nominal rate of 7% compounded semiannually.

We will use annual percentage yield formula to solve our given problem.

[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

Let us convert 7% into decimal form.

[tex]7\%=\frac{7}{100}=0.07[/tex]

Semiannually means two times per year.

[tex]APY=(1+\frac{0.07}{2})^{2}-1[/tex]

[tex]APY=(1+0.00583333)^{12}-1[/tex]

[tex]APY=(1.00583333)^{12}-1[/tex]

[tex]APY=1.0722900804298071-1[/tex]

[tex]APY=0.0722900804298071[/tex]

[tex]APY\approx 0.0723[/tex]

Let us convert 0.0723 into percentage by multiplying with 100.

[tex]0.0723\times 100=7.23\%[/tex]

Therefore, annual percentage yield would be 7.23%.

The APY for a 7% nominal rate compounded quarterly is approximately 7.19%.

To find the APY (Annual Percentage Yield) for a nominal rate of 7% compounded quarterly, we use the following formula:

APY = (1 + r/n)ⁿ - 1

where r is the nominal interest rate and n is the number of compounding periods per year.

Convert the nominal rate from a percentage to a decimal: 7% = 0.07.

Identify the number of compounding periods per year: quarterly means n = 4.

Plug the values into the formula:

APY = (1 + 0.07/4)⁴ - 1

Calculate inside the parenthesis first: 0.07/4 = 0.0175.

Add 1: 1 + 0.0175 = 1.0175.

Raise to the fourth power: (1.0175)⁴ ≈ 1.071889

Subtract 1: 1.071889 - 1 ≈ 0.071889

Convert the decimal back to a percentage to get the APY: 0.071889 × 100 ≈ 7.19%.

Therefore, the APY corresponding to a 7% nominal interest rate compounded quarterly is approximately 7.19%.

Complete Question :

Find the APY corresponding to the following nominal rate 7% compounded quarterly The APY is %. (Type an integer or a decimal. Round to the nearest hundredth as needed. Do not round until the final answer)

Answer:

And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex[ or 98%

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]p_1[/tex] represent the real population proportion for 1

[tex]\hat p_1 =0.768[/tex] represent the estimated proportion for 1

[tex]n_1=92[/tex] is the sample size required for 1

[tex]p_2[/tex] represent the real population proportion for 2

[tex]\hat p_2 =0.646[/tex] represent the estimated proportion for 2

[tex]n_2=95[/tex] is the sample size required for 2

[tex]z[/tex] represent the critical value for the margin of error  

The population proportion have the following distribution  

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]  

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]  

For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:

[tex]ME= \frac{0.2753-(-0.0313)}{2}=0.1533[/tex]

And we know that the margin of erro is given by:

[tex]ME=z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]

We have all the values except the value for [tex]z_{\alpha/2}[/tex]

So we can find it like this:

[tex]0.1533=z_{\alpha/2} \sqrt{\frac{0.768(1-0.768)}{92} +\frac{0.646 (1-0.646)}{95}}[/tex]

And solving for [tex]z_{\alpha/2}[/tex] we got:

[tex]z_{\alpha/2}=2.326[/tex]

And we can find the value for [tex]\alpha/2[/tex] with the following excel code:

"=1-NORM.DIST(2.326,0,1,TRUE)"

And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex] or 98%

The confidence level is 95%. This conclusion is reached by converting the upper bound of the confidence interval into a standard z-score and comparing it to the z-scores for common confidence levels.

To determine the confidence level of interval, we need to look at the proportion of the total area under the standard normal curve that falls within the interval when converted into a standard z-score. For instance, a 90% confidence interval corresponds to an area of 0.90 under the curve, with 0.05 in each tail, and a Z score of ±1.645. A 95% confidence interval corresponds to an area of 0.95 under the curve, with 0.025 in each tail, and a Z score of ±1.96. A 99% confidence level corresponds to an area 0.99 under the curve, with 0.005 in each tail, and a Z score of ±2.575.

In this case, with a confidence interval of (-0.0313, 0.2753) and the estimated proportions of p1=0.768 and p2=0.646, we find the estimated difference is 0.122 and its standard deviation is 0.0782.

Converting the upper bound of the confidence interval into a standard z-score: (0.2753 - 0.122) / 0.0782 = 1.959, which corresponds to a 95% confidence level. Thus, the inference can be that if we were to sample from these populations many times, in 95% of the cases, the true difference between p1 and p2 would lie within the interval (-0.0313, 0.2753).

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A driver can be jailed up to one year and fined up to $5,000 if he or she refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.

Answer: Option B

Step-by-step explanation:

This Vehicle codes 2800.1 state a violation or avoidance of police. The rules as follows: "Any person who, while driving a motor vehicle and intentionally avoiding it, intentionally escapes or attempts to escape from a peace officer " Any driver who "intentionally fails or refuses to stop the vehicle or otherwise, an attempt to escape or prosecute the pursuing police officer when he receives a visual and audible signal to stop the vehicle.

"Visual and audible" signals include sirens, lights, hand signals and voice commands. You must have been able to hear and / or see these signals to be accused of escaping and attempting to escape from the police. This is a level II or level 3 crime, and any penalties for those fleeing or trying to avoid a police officer will depend on the scale of the crime they are suspected of.

A driver can be jailed up to one year and fined up to $5,000 if he or she refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.

The correct answer is B. refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.

Under Georgia law, a driver can be jailed up to one year and fined up to $5,000 if they refuse to stop their vehicle when signaled by a police officer. This is considered a serious offense because it puts both the driver and other people's safety at risk.

Examples of situations where a driver may refuse to stop include fleeing from law enforcement, attempting to evade arrest, or engaging in dangerous driving behaviors that necessitate a traffic stop.

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Answer:

Translated in numerical form: x - 2 ≤ 33.

The solution graph on a numbered line is shown in figure a.

The solution in a set notation: {x|x ≤ 35}

The solution in interval notation: (-∞, 35]

Step-by-step explanation:

"two less than a number is less than or equal to thirty three".

let's say the number is  x.

Translated in numerical form: x - 2 ≤ 33.

Lets solve it:              

                       x - 2 ≤ 33

                       x  ≤ 33 + 2

                       x  ≤ 35

The solution graph on a numbered line is shown in figure a.

The solution in a set notation: {x|x ≤ 35}

The solution in interval notation: (-∞, 35]

Keywords: inequality, graph

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Answer:

[tex]\displaystyle a_n=8+9(n-1)[/tex]

Correct option: C]

Step-by-step explanation:

Arithmetic Sequences

Each term in an arithmetic sequence is obtained as the previous term plus a constant number called the common difference. The general term is

[tex]\displaystyle a_n=a_1+(n-1).r[/tex]

We are given this information

[tex]\displaystyle a_1=8\ ,\ a_7=62[/tex]

Replacing those values in the formula

[tex]\displaystyle 62=8+(7-1).r[/tex]

Solving for r

[tex]\displaystyle r=\frac{62-8}{6}=\frac{54}{6}=9[/tex]

[tex]\displaystyle r=9[/tex]

The general term is, then

[tex]\displaystyle a_n=8+(n-1)9[/tex]

Or equivalently

[tex]\displaystyle a_n=8+9(n-1)[/tex]

Correct option: C]

Answer:

Is below

Step-by-step explanation:

1.

b. x </= -7 OR x > 4

d. x >/= -7 AND x < 4

e. x >/= -7 OR x < 4

c. x </= -7 AND x < 4

a. x </= -7 OR x < 4

2.

( - the absolute sign

(d - 3.5) </= 1.5

d - 3.5 </= 1.5 (positive case)

d </= 5

(d - 3.5) >/= 1.5

d - 3.5 >/= -1.5 (negative case)

d >/= 2  

D. Is the number line graph of the inequality.

Answer:

Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.

Step-by-step explanation:

Given;

Total Trees = 31

Let the number of trees Flame has be 'x'.

Now given:

Sally has 7 fewer trees than Flame.

framing in equation form we get;

Number of trees Sally has  = [tex]x-7[/tex]

Also Given:

Frazer has 3 more trees than Sally.

framing on equation form we get;

Number of trees Frazer has = [tex]x-7+3 = x-4[/tex]

Now We know that Captain salamander total trees in 3 friends.

Hence we can say that;

Total Number of trees is equal to sum of number of trees Flame has and Number of trees Sally has and Number of trees Frazer has.

framing in equation form we get;

[tex]x+(x-7)+(x-4)=31\\\\x+x-7+x-4=31\\\\3x-11=31\\\\3x=31+11\\\\3x = 42\\\\x = \frac{42}{3} = 14[/tex]

Hence Number of trees Flame has = 14 trees

Number of trees Sally has = [tex]x-7 = 14-7 =7 \ trees[/tex]

Number of trees Frazer has = [tex]x-4 = 14-4 = 10 \ trees[/tex]

Hence Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.

Answer:

[tex]f(x)=3*cosine(x)[/tex]

Step-by-step explanation:

We are looking for a trigonometric function which contains the point (0, 3), and has an amplitude of 3.

We know that for a sine function [tex]f(x)=sin(x)[/tex], [tex]f(0)= 0[/tex]; therefore the function we a looking for cannot be a sine function because it is zero at [tex]x=0[/tex].

However, the cosine function [tex]f(x)=cos(x)[/tex] gives non-zero value at [tex]x=0:[/tex]

[tex]f(0)=cos(0)=1[/tex]

therefore, a cosine function can be our function.

Now, cosine function with amplitude [tex]a[/tex] has the form

[tex]f(x)=a*cos(x)[/tex]

this is because the cosine function is maximum at [tex]x= 0[/tex] and therefore, has the property that

[tex]f(0)=a*cos(0)= a[/tex]

in other words it contains the point [tex](0, a)[/tex].

The function we are looking for contains the point [tex](0, 3)[/tex]; therefore, its amplitude must be 3, or

[tex]f(x)=3cos(x)[/tex]

we see that this function satisfies our conditions: [tex]f(x)[/tex] has amplitude of 3, and it passes through the point (0, 3) because [tex]f(0)=3[/tex]

Answer:

D

Step-by-step explanation:

edge

Answer:the number of children that swam at the public pool is 259

the number of adult that swam at the public pool is 280

Step-by-step explanation:

Let x represent the number of children that swam at the public pool that​ day.

Let y represent the number of adult that swam at the public pool that​ day.

On a certain hot​ summer's day,539 people used the public swimming pool. This means that

x+ y = 539

The daily prices are $ 1.25 for children and $ 2.50 for adults. The receipts for admission totaled $ 1023.75. This means that

1.25x + 2.5y = 1023.75 - - - - - - - - - -1

Substituting x = 539 - y into equation 1, it becomes

1.25(539 - y) + 2.5y = 1023.75

683.75 - 1.25y + 2.5y = 1023.75

- 1.25y + 2.5y = 1023.75 - 683.75

1.25y = 350

y = 350/1.25 = 280

Substituting y = 280 into x = 539 - y , it becomes

x = 539 - 280 = 259

Answer:

B. x=-6, y=2

Step-by-step explanation:

Answer:

33 ft

Step-by-step explanation:

sin( angle ) = opposite / hypotenuse

Cos(Angle) = Adjacent leg / Hypotenuse

Cos(X) = 3.5/4.6

X = arccos(3.5/4.6)

X = 40.46 degrees.

Answer:

p(0) = 35

Step-by-step explanation:

-3, √7 and 1-√6 are all roots, hence, we can factorize (x-(-3)) = (x+3), (x-√7) and (x- (1-√6)) = (x-1+√6) from p. Since p has rational coefficients, then we need to cancel out both √7 and √6. To do so we should multiply by the rational conjugate, of the expressions (x-1+√6) and (x-√7), that means, where a square root of a non square positive number appears, place the opposing sign there.

The rational conjugate of (x-√7) is (x+√7), and

(x-√7)*(x+√7) = x²-7

On the other hand, the rational conjugate of (x-1+√6) is (x-1-√6), and

(x-1+√6) * (x-1-√6) = ( (x-1) + √6) * ((x-1) -√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5.

Thus, both x²-7 and x²-2x-5 are factors of p. The polynomial has the form

[tex]P(x) = c(x+3)(x^2-7)(x^2-2x-5)[/tex]

Where c is a constant. To determine c, we need to use the other piece of information given: p(-1) = 8

When we evaluate in -1, we get

[tex]p(-1) = c*(-1+3)((-1)^2-7)((-1)^2-2(-1)-5) = c* 2*(-6)*(-2) = c*24 = 8[/tex]

Thus, c = 8/24 = 1/3.

Therefore,

[tex]p(0) = \frac{1}{3} * (0+3)(0^2-7)(0^2-2*0-5) = \frac{1}{3}*3*(-7)*(-5) = 35[/tex]

I hope that works for you!

Answer:

it would be A if you choose 100 random people then they would give you some explanation of why you should or shouldn't change the dress code.

Answer:

$120

Step-by-step explanation:

Suppose the  woman had x dollars in her purse at the beginning of the shopping.

First, she spent 4/5 of all the money she had, therefore she had 1-4/5=1/5 left

1/5 of x = (1/5)x or 0.2x

Then she lost 2/3 of what was remaining, which is 2/3 * (1/5)x= (2/15)x

What will be left will be (1-2/3) or 1/3 of that 1/5x left after shopping.

This will be 1/3*(1/5)x=(1/15)x

It is given from the problem statement that this is $10 left.

Therefore, (1/15)x= 10

Multiplying through by 15 and simplifying,

x= $150.

Now she spent 4/5 of this $150, which is

(4/5)*150=$120

To find out how much money the woman spent, we need to determine the amount she had in her purse and then calculate the difference after spending and losing some. We can solve this using a step-by-step approach.

To calculate how much money the woman spent, we need to follow these steps:

Let's solve this step-by-step:

Step 1: X = Amount she had in her purse

Step 2: Y = (4/5) * X * (1/3)

Step 3: Y = $10

Step 4: Calculate X - Y to find how much money she spent.

To find the approximate probability that the total amount paid for the second movies will exceed $15.00 is (a) 0.91, we need to use the expected value and standard deviation to calculate a z-score and then find the corresponding probability.

To find the approximate probability that the total amount paid for the second movies will exceed $15.00, we need to use the expected value and standard deviation to calculate a z-score and then find the corresponding probability. First, we calculate the standard deviation using the formula: standard deviation = 0.15 * sqrt(30) = 0.2598.

Then, we calculate the z-score using the formula: z = (15 - 0.47) / 0.2598 = 57.05. Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score greater than 57.05 is extremely close to 1.

Therefore, the approximate probability that the total amount paid for these second movies will exceed $15.00 is 0.91, option (a).

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Answer:

b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up

Option b is right.

Step-by-step explanation:

Given that linear function f(x)=x is graphed on a coordinate plane.

The graph of a new line is formed by changing the slope of the original line to 2/3 and the y-intercept to 4.

The original slope was 1. Now changed to 2/3 i.e. slope is reduced. Hence the new line will be less steeper.

Also original line y =x has y intercept at the origin.

By changing y intercept to 4, we changed y intercept to upwards by 4 units.

Thus there is a vertical shift of 4 units.

b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up

Option b is right.

A linear function is represented by a straight line.

The true statement is: (b) the graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up.

The function f(x) is given as:

[tex]\mathbf{f(x) = x}[/tex]

The attributes of the new function are:

So, the new function is:

[tex]\mathbf{f'(x) = \frac23x + 4}[/tex]

The slope of [tex]\mathbf{f(x) = x}[/tex] is 1.

2/3 is less than 1.

So, the new line is less steep

The y-intercept (4) means that:

The new line is shifted up by 4 units

Hence, the correct statement is: (b)

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The angular speed of the wheel at its point of contact on the surface is 8 radians per second.

Given that:

A wheel is rolling on a horizontal surface.

The radius of the wheel, r = 0.5 m

The velocity of the axle of the wheel is constant.

Here, the linear velocity can be found by taking the ratio of the distance to the time taken to cover that distance.

So, the linear speed is:

[tex]\text{v}=\frac{20}{5}[/tex]

  [tex]=4 \text{ m/s}[/tex]

Now, the relationship between the angular speed and the linear speed is:

[tex]\omega=\frac{v}{r}[/tex]

  [tex]=\frac{4}{0.5}[/tex]

  [tex]=8[/tex] rad/s

Hence, the angular speed is 8 radians per second.

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The angular speed of the wheel about its point of contact on the surface is 8 rad/s.

To find the angular speed of the wheel about its point of contact on the surface, we can use the relationship between linear and angular velocity.

The linear velocity of a point on the wheel is given by:

v = ω * r

Where:

v is the linear velocity

ω is the angular velocity (angular speed)

r is the radius of the wheel

In this case, we know that the wheel rolls without slipping, which means the linear velocity of the point of contact with the surface is equal to the velocity of the axle. Since the axle moves a distance of 20 m in 5 s, the linear velocity can be calculated as:

v = 20 m / 5 s = 4 m/s

Given that the radius of the wheel is 0.5 m, we can rearrange the equation to solve for ω:

ω = v / r

ω = 4 m/s / 0.5 m

ω = 8 rad/s

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Answer:

15 books

Step-by-step explanation:

Given that Victor read a total of 12 books over 4 months which means for 1 month he reads 12/4 = 3 books

Also given that he belongs to the book club for 5 months

We know that he reads 3 books in 1 month

So in 5 months he reads [tex]5\times3=15books[/tex]

Answer:

   6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

  (2x -12)/2 = arcsin(16/22×sin(24°))

  x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

  2x -12 = 0

  x -6 = 0 . . . . . divide by 2

  x = 6 . . . . . . . add 6

Then the range of values of x will be ...

  6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

  22² = AB² + AC² -2·AB·AC·cos(48°)

  16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

  22² = 2·AB²·(1-cos(48°))

  16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

Answer 6<x<30:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is a combination question.

In the first instance, we select 5 from 20 and in the second case , we select 4 from 20.

The total number of ways to solve the first instance is 20C5 = 15504 ways

The total number of ways to solve the second instance is 20C4 = 4,845

The ratio of the first to the second scenario is 15,504/4,845 = 3.2 = 16 to 5