What is the remainder when the product of the 5 smallest prime numbers is divided by 42?

Answer:

64

Step-by-step explanation:

There are only pink and yellow sections of the circle, so every spin will land on pink or yellow.

Answer: 64

Answer:

Brianliest!

Step-by-step explanation:

since there are only the colors pink and yellow and the prediction for the   number of times it will land on pink or yellow, it will have a 100% probability

64

Answer:

9

Step-by-step explanation:

5≤n≤12

List all the even integers

6,8,10,12

Then find the mean

(6+8+10+12) /4

36/4

9

The mean is 9

Answer:

1/100

Step-by-step explanation:

Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?

Solution:

Probability = number of favorable outcomes/number of total outcomes

From the information given,

The probability that respondents did not provide a response, P(A) is 4/100 = 0.04

The probability that a respondent said that their experience fell short of expectations, P(B) is 26/100 = 0.26

The probability that a respondent said that their experience met expectations, P(C) is 65/100 = 0.65

A) Adding all the probabilities, it becomes 0.04 + 0.26 + 0.65 = 0.95

Therefore, the probability,P(D) that a respondent said that their experience surpassed expectations is 1 - 0.95 = 0.05

B) The event of a randomly chosen respondent saying that their experience met expectations and that their experience surpassed expectations are mutually exclusive because they cannot occur together. It means that P(C) × P(D) = 0

Therefore, the probability of P(C) or P(D) is 0.65 + 0.05 = 0.7

Answer:

Dear Yates

Answer to your query is provided below

Total Price for her vehicle will be $20600

Step-by-step explanation:

Edith's trading is worth $8000. So, without the package upgrade of the vehicle delivery charge, her cost is:

$22750 - $8000 = $14750.

Now, add the package upgrade ($5050) and the delivery charge ($800).

$14750 + $5050 + $800 = $20600.

The total cost price of the vehicle after all the expenses is given by the equation A = $ 20,500

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The initial cost of the vehicle is = $ 22,750

Now , Edith has asked for an upgrade to a premium package for which the cost is $5050

So , the new cost of the vehicle = $ 22,750 + $ 5050 = $ 27,800

Now , the delivery charge of the vehicle = $ 700

And , the updated total price = $ 27,800 + $ 700 = $ 28,500

Now , the dealer has offered her $8000

So , the final price of the vehicle = updated total price - $ 8000

On simplifying the equation , we get

The final price of the vehicle A = $ 28,500 - $ 8,000

The final price of the vehicle A = $ 20,500

Hence , the final price of the vehicle is $ 20,500

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Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Random voting:

So 50% of voting yes, 50% no, so [tex]p = 0.5[/tex]

15 members:

This means that [tex]n = 15[/tex]

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

[tex]p = P(X = 0) + P(X = 15)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003[/tex]

[tex]P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003[/tex]

So

[tex]p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006[/tex]

0.006% probability that the final vote count is unanimous.

Answer:

46

Step-by-step explanation:

Azman=35+amin

Aziz=3×amin

therefore;35+amin+2amin+amin/3=73

219=35+4amin

219-35=4amin

184=4amin

Amin's mark=184÷4

=46

Answer:

Answer choice 1

Step-by-step explanation:

[tex]5^2\cdot 5^9= \\\\5^{2+9}= \\\\5^{11}[/tex]

Therefore, the correct answer choice is choice 1. Hope this helps!

Answer:

A. 12

Step-by-step explanation:

If we split an equalateral triangle down, it will become 2 30-60-90 triangles. Remember your 30-60-90 triangle rules.

6√3 = x√3, so x = 6

2(6) (for hypotenuse) = 12

Since the hypotenuse is one side of the bigger triangle, we have our final answer of 12.

An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made so, to take the balance to $282 requires 6.4 years and this can be determined by using the simple interest formula.

Given :

SImple interest formula can be used to determine the total number of years will it take for the balance to be $282.

The formula of simple interest is given by:

[tex]\rm A = P(1+rt)[/tex]

where A is the final amount, P is the initial principal balance, r is the annual interest rate and t is the time in years.

Now, put the known values in equation (1).

[tex]\rm 282 = 250(1+0.02t)[/tex]

[tex]\rm 282=250+5t[/tex]

32 = 5t

t = 6.4 years

So, 6.4 years will it take for the balance to be $282.

So, the graph correct graph is shown by option D).

For more information, refer to the link given below:

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Answer:

D

Step-by-step explanation:

[tex]\frac{2}{3}=\frac{boys}{18}[/tex]

3*boys=2*18

3*boys=36

boys=12

12+18=30

total number of students: 30

Answer:

30 students

Step-by-step explanation:

2:3 = x:18

X = number of boys

[tex]\frac{2}{3} = \frac{x}{18}[/tex]

multiply 18 by both sides

18 × [tex]\frac{2}{3} = X[/tex]

X = 18 × [tex]\frac{2}{3} = 12[/tex]

18 + 12 = 30

[tex]solution \\ {2x}^{2} - x + ( - x - {2x}^{2} - 2) \\ = {2x}^{2} - x - x - {2x}^{2} - 2 \\ = {2x}^{2} - {2x}^{2} - x - x - 2 \\ = - 2x - 2[/tex]

Hope it helps

Good luck on your assignment

Answer:

[tex] - 2x - 2[/tex]

Step-by-step explanation:

[tex]2 {x}^{2} - x + ( - x - 2 {x}^{2} - 2) \\ 2 {x}^{2} - x - x - 2 {x}^{2} - 2 \\ 2 {x}^{2} - 2 {x}^{2} - x - x - 2 \\ - 2x - 2[/tex]

hope this helps you.

brainliest appreciated

good luck!

have a nice day!

Answer:

x=1/3 is the answer

Step-by-step explanation:

6x+15=3x+14

substracting 3x on both sides

6x-3x+15=3x-3x+14

3x+15=14

subtracting 15 on both sides

3x+15-15=14-15

3x=1

x=1/3

i hope this will help you

Answer:

[tex]solution \\ 6x + 5 = 3x + 14 \\ or \: 6x - 3x = 14 - 5 \\ or \: 3x = 9 \\ or \: x = \frac{9}{3} \\ x = 3[/tex]

hope this helps ..

Good luck on your assignment...

Answer:

Midpoint Of AB = ( 1+1/2 , -2-1/2)

= (2/2 , -3/2)

= ( 1 , -1.5)

Hope this helps

Please mark Branliest.

Answer:

-2,0

Step-by-step explanation:

Answer:

The height of the flagpole = 4.50m (3signifiant figures)

Question:

A tree and a flagpole are on the same

horizontal ground. A bird on top of the

tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, Calculate Correct to 3 significant figures the height of the flagpole.

Step-by-step explanation:

First we have to represent the above information with a diagram to enable us solve the question.

Then label them for easy identification.

To determine the distance between the tree and flagpole, we would apply tangent rule.

Let their distance = x

Tan60 = opposite/adjacent

Tan60 = 10.65/y

Tan60 × y = 10.65

y = 10.65/Tan60

y = 10.65/1.7321

y = 6.15m

See attachment for the concluding part

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

[tex] ME=0.03[/tex] the margin of error desired

[tex]Conf= 0.95[/tex] the level of confidence given

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

the critical value for 95% of confidence is [tex] z=1.96[/tex]

We can use as estimator for the population of interest [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Cos(angle) = adjacent/hypotenuse

Cos(angle) = 1.5/10

Angle = arccos(1.5/10)

Angle = 81.37 degrees

Although the angle is close, it is over the 80 degrees, so the inspector should be concerned.

Answer:

All the possible numbers she could represent using the counters are:

0.6  |  1.5  |  2.4  |  3.3  |  4.2  |  5.1  |  6

Step-by-step explanation:

Please refer to the attached diagram for this question.

We are asked to list all the possible numbers she could represent using the counters.

The possible numbers are:

When there is 0 counter in the "ones" place and 6 counters in the "tenths" place.

0.6

When there is 1 counter in the "ones" place and 5 counters in the "tenths" place.

1.5

When there are 2 counters in the "ones" place and 4 counters in the "tenths" place.

2.4

When there are 3 counters in the "ones" place and 3 counters in the "tenths" place.

3.3

When there are 4 counters in the "ones" place and 2 counters in the "tenths" place.

4.2

When there are 5 counters in the "ones" place and 1 counter in the "tenths" place.

5.1

When there are 6 counters in the "ones" place and 0 counter in the "tenths" place.

6

Therefore, all the possible numbers she could represent using the counters are:

0.6  |  1.5  |  2.4  |  3.3  |  4.2  |  5.1  |  6

Answer:

(x + 3)(x + 2)

Step-by-step explanation:

Given

x² + 5x + 6

Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)

The factors are + 3 and + 2 , since

3 × 2 = 6 and 3 + 2 = 5 , thus

x² + 5x + 6 = (x + 3)(x + 2)

Answer:

126

Step-by-step explanation:

We multiply 42 × 3= 126

The measure of the angle is 126.

The measure of angle will be 66°.

What is Complementary angle?

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

Given that;

The measure of the supplement of an angle is 42 more than 3 times the measure of the complement of an angle.

Now,

Let the measure of angle = x

So, We can formulate;

⇒ (180 - x) = 42 + 3 (90 - x)

Solve for x as;

⇒ 180 - x = 42 + 270 - 3x

⇒ 180 - x + 3x = 312

⇒ 2x = 312 - 180

⇒ 2x = 132

⇒ x = 66

Thus, The measure of angle will be 66°.

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The length of wire used for the square in order to minimize the total area is 9.42m.

We are given that;

Length of wire= 30m

Now

Let the length of the wire used for the square x. The length of the wire used for the circle is 30-x.

The perimeter of the square is 4x and the perimeter of the circle is 2πr=2π(30-x)/(2π)=15-x/π.

The area of the square is [tex]x^2/16[/tex] and

the area of the circle is π(15-x/π)2/4π=225/π-(15x)/π2+[tex]x^2[/tex]/4π.

The total area is A=x2/16+225/π-(15x)/π2+[tex]x^2[/tex]/4π.

To maximize A, we take its derivative with respect to x and set it equal to zero: d[tex]A/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]

Solving for x, we get x=120/(8+4π).

Therefore, 30-x=120/(8+4π)(3-π).

To minimize A, we take its derivative with respect to x and set it equal to zero:

[tex]dA/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]

Solving for x, we get x=120/(8+4π)(3+π).

So, 30-x=120/(8+4π)(3-π).

Therefore, by area the answer will be approximately 9.42 m.

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Answer:

4a²

Step-by-step explanation:

(2a)²

Distribute the square to all the terms in the bracket.

2²a²

Solve the powers if possible.

4a²

Answer:

4a²

Step-by-step explanation:

=> [tex](2a)^2[/tex]

=> [tex](2^2*a^2)[/tex]

=> 4 * a²

=> 4a²

Answer:

b) 0.0608

Step-by-step explanation:

As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed

Therefore the rain probability is

[tex]= \frac{T}{24}[/tex]

where,

T = Length of the time interval

Plus, as we know that rain is independent

So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes

i.e

= 5.91666 hours long.

So, P1 should be

[tex]= \frac{5.91666}{24}[/tex]

= 0.2465

Now we assume the probability of rain on day 2 is P2

So it would be same  i.e 0.2465

Since these events are independent

So, the total probability is

[tex]= 0.2465 \times 0.2465[/tex]

= 0.0608

Hence, the b option is correct

9514 1404 393

Answer:

  B)  35/111

Step-by-step explanation:

  [tex]0.\overline{315}=\dfrac{315}{999}=\boxed{\dfrac{35}{111}}[/tex]

The denominator of the fraction has as many 9s as the decimal has repeating digits. Here, the numerator and denominator both have factors of 9 that can be cancelled.

Answer:

15 cm

Step-by-step explanation:

Median means middle number

10,15,15,18,20

Answer:

15 cm

Step-by-step explanation:

The median is the number in the middle of a data set.

First, arrange the data from least to greatest.

10 cm, 15 cm, 15 cm, 18 cm, 20 cm

Now, take one number off each end of the data set until the middle number is reached.

10 cm, 15 cm, 15 cm, 18 cm, 20 cm

15 cm, 15 cm, 18 cm

15 cm

Therefore the median of the set of measurements is 15 cm.

Answer:

  see below

Step-by-step explanation:

The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.

Answer:

The numbers are 2 and 8.

Solution,

Let the numbers be X and 4x

[tex] \frac{1}{x} + \frac{1}{4x} = \frac{5}{8} \\ or \: \frac{1 \times 4 + 1}{4x} = \frac{5}{8} \\ or \: \frac{4 + 1}{4x} = \frac{5}{8} \\ or \: \frac{5}{4x} = \frac{5}{8} \\ or \: 5 \times 4x = 5 \times 8(cross \: multiplication) \\ or \: 20x = 40 \\ or \: x = \frac{40}{20} \\ x = 2 \\ again \\ 4x \\ = 4 \times x \\ = 4 \times 2 \\ = 8[/tex]

hope this helps...

Good luck on your assignment..

Answer:

60°

Step-by-step explanation:

∠ABC-∠CBD=∠1

[tex]135-75[/tex]

[tex]=60[/tex]

Answer:

Brainliest goes to me!

Step-by-step explanation:

angle abc = 135 degrees

part of it is angle 1 and the other part is angle cbd

<abc (135) = cbd (75) + <1

angle 1 = 60 degrees

Answer:

£29.37

Step-by-step explanation:

→ First step is to find the amount of hours it takes for 5 builders

[tex]\frac{3*\frac{11}{2} }{5} =\frac{33}{2} /5=\frac{33}{2} *\frac{1}{5} =\frac{33}{10} =3\frac{3}{10}[/tex]

→ Now we know how long 5 builder takes we need to multiply the hourly rate by their time worked

[tex]3\frac{3}{10} *8.90=\frac{33}{10} *8.90=3.3*8.90 = 29.37[/tex]

Answer:

Step-by-step explanation:

When the number of builders is increased, the hours worked will be reduced.

So, this is inverse proportion.

Number of hours worked by  5 builders = [tex]\frac{3*\frac{11}{2}}{5}\\\\[/tex]

                                                                  [tex]=3*\frac{11}{2}*\frac{1}{5}\\\\=\frac{33}{10}\\\\=3\frac{1}{10}[/tex]

Amount received by each builder= 33/10 * 8.90

                                                       =    £ 29.37