Help quick, State if the two triangles are congruent. If they are state how you know.

The required minimum sample size is 2875

Given that,

A government organization wanted to determine how many drivers between the ages of 16 and 24 had recently engaged in an accident. The agency wanted to make the estimate with a 90% confidence level and within one percentage point.

From the standard normal table, the z-critical value at 90% confidence is 1.65.

The information represent E = 0.01, p = 0.12 and z. =1.65 for finding sample size.

n = (Zc / E )² x P(1-P)

  = (1.65 2x0.12(1 - 0.12)0.01

  = 2874.96 ~ 2875

Hence, 2875 is the necessary number of samples, minimum.

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The statement which could be true for the function, g as required in the task content is; Choice C; g(0) = 2.

It follows from the task content that the statement which could be true about the function g is to be identified.

Since the given function instances are; g(0) = -2 and g(-9) = 6.

Since the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

Hence, the statement which could be true about the function, g is; Choice C; g(0) = 2.

This is so because, 0 is in the domain of the function and 2 is in the range of the function.

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The equation to show the total no. of minutes Carlos spends routing calls is y = 2x

To find the required equation, use the following given data:

Time taken by Carols for routing each call = 2 minutes

Total number of calls = x

Total number of minutes Carol spends routing calls = y

The one-dimensional function takes up a single input value (x) and outputs a single evaluation of the given input (y).

So, by practical application of one-dimensional function,

Total number of minutes Carols spends routing calls (y) = Time taken by Carols for routing each call * Total number of calls (x)

∴ The equation will be y = 2*x

Thus, y = 2x shows the total number of minutes Carlos spends routing the calls.

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[tex]\fbox{1.333333}[/tex]

[tex]4\frac{2}{15} \div3.1[/tex]

Simplify:

[tex]4\frac{2}{15} \div3.1[/tex]

[tex]=1.333333[/tex]

let's firstly convert the  mixed fraction to improper fraction and the decimal one to a fraction.

[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]

Answer:

2x-y=18

Step-by-step explanation:

y + 4 = 2(x - 7)     (open brackets)

y + 4 = 2x - 14      (re arrange)

4 + 14 = 2x - y

2x - y = 18

Answer:

x = -2 ; x = 6/5

Step-by-step explanation:

5x + 2 >=0

5x >= -2

5/5 x >= -2/5

x >= -2/5

if x >= -2/5

5x +2 = 8

5x = 8 -2

5x = 6

5/5 x = 6/5

x = 6/5

if x < -2/5

-5x -2 = 8

-5x = 8+2

-5x = 10

-5/-5 x = 10/-5

x = -2

The word problem including the given equation is mentioned below.

Given, a system of equations

x + y = 0

2x - y = 6

We have to make a word problem using the given system of equations.

Ram and Rahul are two friends and both attempt a test of 10 marks. Now, Ram prepared for the test whereas Rahul didn't prepared for the test and marked the wrong answers in the test. If negative marking is allowed in the test and it is given that, sum of the marks of both the students is zero. Also, twice the marks of Ram is 6 less than the marks of Rahul.

Find the marks of both the students.

Hence, the word problem including the given equation is mentioned above.

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Answer:

a. its a prime number cuz as far as ik 67 has one factor 67x1

Answer:

Number 67 is prime because it doesn't have proper factors. In other words, the only factors of 67 are 1 and itself

The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

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The equation which passes through (3,2) and slope 1/3 is:

y - 2 = 1/3 (x - 3)

Given, we have:

slope (m) = 1/3

Point = (3,2) = (x₁,y₁)

we are asked to determine the point slope form :

we know that:

point slope form:

y-y₁ = m(x-x₁)

substitute the above values in the formula:

y - 2 = 1/3 (x - 3)

Hence the correct option is B.

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Answer: $2738.02

Step-by-step explanation:

1) (3000x0.97) = 2910  } Year 1

2) (2910x0.97) = 2822.7  } Year 2

3) (2822.7x0.97) = 2738.019  } Year 3

The difference in average speed between two cars is  4 kilometers per hour . Average speed of cars are 32 kilometers per hour and 28 kilometers per hour. The average speed is the total distance traveled by the object in a particular time interval.

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path.

Both can be measured and quantified since they are physical quantities. Both phrases refer to moving bodies alone; they do not refer to static bodies.

Average speed of first car = total distance / total time

                                            =  160/ 5 = 32

Average speed of second car = total distance / total time  

                                                   = 140/ 5 = 28

The difference in average speed between two cars = 32 -28= 4

4 kilometers per hour is the  difference

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The money left with Dan is £30  .

In the question ,

it is given that

the amount of money earned by Dan in a week is = £240  .

amount of money spent by Dan on rent is = 3/4 wage

amount of money spent by Dan on food is = 1/8 of wage

So ,

the total amount spent = amount spent on food + amount spent on rent

Substituting the values ,

we get ,

= 3/4 + 1/8 = 7/8 of his wage = (7/8)*240

= 210

so , total amount spent is £210 .

Amount left = amount earned - amount spent

= 240 - 210
= 30

Therefore ,The money left with Dan is £30  .

The given question is incomplete , the complete question is

Dan spends 3/4 of his wages on rent and 1/8 on food. If he makes £240 per week, how much money does he have left?

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Which is the order from least to greatest of the following

A. 4/3, 0.8, 1/5, 30%

1.33 , 0.8 , 0.2 , 0.3

B. 30%, 4/3, 0.8, 1/5

0.3 , 1.33 , 0.8 , 0.2

C. 1/5, 4/3, 30%, 0.8

0.2 , 1.33 , 0.3 , 0.8

D. 1/5, 30%, 0.8, 4/3

0.2 , 0.3 , 0.8 , 1.33 these are listed smallest to largest

The number of soda bottles the machine can make each minute = 40

In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.

Also, we have been given two points ​(​4,160​) and ​(6​,​240)

We need to find the number of soda bottles the machine can make each minute.

i.e., we need to find the slope of line passing through points  ​(​4,160​) and ​(6​,​240)

Using the formula of slope,

m = (240 - 160) / (6 - 4)

m = 80/2

m = 40

Therefore, the number of soda bottles the machine can make each minute = 40

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A and B are two sets, and the set formula is given as n(AB) = n(A) + n(B) - n(AB), where n(AB) denotes the number of elements present in either A or B, and n(AB) is the number of elements present in both A and B.

Drawing Venn diagrams, as seen below, is the simplest method for solving set issues.

The total number of elements in any set A or B is n(AB).

The total number of elements in sets A and B is n(AB).

n(AB) is equal to n(A) + n(B) - n(AB)

U={a,b,c,d,e,f}

X={a,b,c,d},

Y={c,d,e}

Z={b,d,f}

(XUY) =  (a,b,c,d,e)

(XUZ)​ =(a,b,c,d,f)

(XUY)U(XUZ)  =  (a,b,c,d,e,f)

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Line 1  4x³ + 2x² − 6x +3 is having error.

Line 1.

4x³ + 2x² − 6x +3

Line 2.

= 2x²(2x + 1) − 3(2x + 1)

= 4x³ + 2x² - 6x - 3

Line 3.

= 2x²(2x + 1) + ( − 3)(2x + 1)

= 4x³ + 2x² - 6x - 3

Line 4.

= (2x² − 3)(2x + 1)

= 4x³ + 2x² - 6x - 3

expect line 1 remaining all three are equal.

Therefore Line 1  4x³ + 2x² − 6x +3 is having error.

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Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made = 529,200

acc to our question-

hence,Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made = 529,200

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Yes, he can mow the lawn in 2 hours.

We can define the work done as, a work done in a given period of time.

Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn

In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn

Therefore, in 8/5 hours he is mowing 7/9 part of lawn

In 1 hour = 7/9*5/8 = 35/72

In 2 hours = 35/72*2 = 35/36 ≈ 1

Hence, Yes, he can mow the lawn in 2 hours.

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Step-by-step explanation:

The graph of [tex]p(x)=2x^3[/tex] is less steep than [tex]f(x)=2.5x^3[/tex] because the coefficient 2 is less than the coefficient 2.5.  That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f.  For example, if  x = 2, the point (2, 20) is on the graph of  f  but the point (2, 16) is on the graph of  p (so it lies under the point (2, 20).

The graph of [tex]p(x)=-x^3[/tex] is less steep than the graph of  f  and it is reflected over the x-axis.  The negative coefficient -1 is doing that.  The values of the function  p(x)  are opposite sign to values of  f(x).

The graph of [tex]p(x)=3x^3[/tex] is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of   p  lie farther away from the x-axis than points on the graph of  f(x).

The similar pairs of triangles are given as follows:

Similar triangles are two triangles that have the same angle measures.

For these triangles, considering the relations between angles such as sine/cosine/tangent, or the law of sines, the side lengths have to be proportional.

Considering the need for proportional side lengths, the similar triangles in this problem are given as follows:

The other triangles are not similar as there are no proportional relationships that can be established from the side lengths of these triangles.

The problem is given by the image at the end of the answer.

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Answer:

The absolute difference is 1050

The relative percentage is 32.3076%

Step-by-step explanation:

We are given

The population of a town increased from 3,250 in 2008 to 4,300 in 2010

In 2008:

In 2010:

Absolute difference:

we know that

absolute difference =

absolute difference =

absolute difference is 1050

Relative increase:

we know that

Relative percentage is

now, we can plug values

=32.3076

So, the relative percentage is 32.3076%

The ratio of 15 and square of m is 15/m².

A ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities. This ultimately implies that, a ratio can be expressed as a quotient.

In Mathematics, quotient can be defined as a mathematical expression that is simply used to represent the division of a numerical value by another numerical value or variable.

In this scenario, the numerical value 15 would be the numerator while the variable m would be the denominator, and it should be expressed as follows:

Ratio = 15/m²

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In given word problem ending time of the play is 10.50 AM.

What is word problem?

 A comprehensive list of math word problems focuses on addition, subtraction, multiplication, division and more specific operations. life scenario. This means that children must be familiar with vocabulary associated with familiar mathematical symbols in order to understand word problems.

Here starting time of play = 9:05 AM

It took 1 hour 45 minutes to end the play. Then ,

=> 9 hour  05 minutes

    1 hour   45 minutes +

=> 10 hour 50 minutes.

Hence ending time of the play is 10.50 AM.

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After one hour (60 minutes, the value of the temperature is 550 degrees.

Temperature is the degree of hotness and coldness that a body contains.

In this case, after graph, after 12 minutes the coffee is about 110 degrees. The temperature per minute will be:

= 110 / 12

= 9.167° per minute.

Therefore, the temperature after 1 hour which is 60 minutes will be:

= Time × Rate

= 60 × 9.167°

= 550°

The temperature is 550°.

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Answer:

a) 4 x -3 x 2 = -24

b) -2 x 5 x -4 = 40

c) -3 x -1 x -6 = -18

Answer:

a.4 x -3 x 2 =

use the rules for multiplication

-(4×3×2)

-(12×2)

=2

----------------------------------

b. -2 x 5 x -4 =

note:

-2×5(-4)

multiplying an even number of negative terms makes the product positive.

-2×5= 10

10×-4

=40

----------------------------------

C. -3 x -1 x -6 =

note:

multiplying an odd number of negative terms makes the product negative.

-(3×1×6)

=-18

The magnitude is approximately 186 pounds.

A mathematical object's magnitude, often known as its size, is a quality that indicates whether it is bigger or smaller than other things of the same sort. Formally speaking, an object's magnitude represents the ordered (or ranked) outcome of the class of objects it belongs to.

We have to assume that the notation starts South and then moves 76 degrees East.

The 70-pound force is going at an angle down and to the right.

The down one is negative and the right one is positive.

We have to use the vectors as the hypotenuse of a rectangle.

70 cos(76) = vertical = 16.93 down

70 sin(76) = horizontal = 67.92 right

120 cos(80) = vertical = 20.83 up

120 sin(80) = horizontal =118.17 right

We have to add up all the values vertically and horizontally, and we get

-16.93 + 20.83 =3.9 up

67.92 + 118.17= 186.09 right

Here, the magnitude is the hypotenuse.

sqrt(15.21+34629.49) =186.13 pounds.

Direction is cos⁻¹(3.9/186.13) = 88.802  

Remember this is North then 88.802 degrees East

Therefore, the magnitude is approximately 186 pounds.

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Answer:

Round to the nearest tenth.

a. 0.54 + 0.278 = 0.5 +0.3 = 0.8

b. 2.65 + 28. 17= 2.70 + 28.20 = 30.9

c. 3.09 + 2.41 + 9.86 = 3.10+ 2.40 + 9.90= 15.4

d. 15.234 + 1.37 + 0.76 = 15.20 + 1.3 + 0.8 = 17.30

e. 39.18 + 2.48+ 0.84 = 39.20 + 2.5 + 0.8 = 42.5

Round to the nearest whole number.

f. 4.112 + 3.89 = 4 + 4 = 8

g. 23.14 + 7.6 + 3.67 = 23 + 8 + 4= 35

h. 53.2 + 3.08 + 27.51 = 53 + 3+ 28 = 84

i. 11.08 + 17.28 + 92.6 = 11 + 17 + 93 = 121

j. 24.08+ 7.9 + 3.06 = 24 + 8 + 3 = 35

Step-by-step explanation:

Hopefully it's right!!!