Persons younger than 18 years old are not eligible to vote. Let a be age in years. Which inequality models this situation? A. a < 18 and a may be a negative number B. a < 18 and a must be a positive number C. a > 18 and a may be a negative number D. a > 18 and a must be a positive number

QUESTION POSTED AT 14/01/2020 - 03:06 PM

Related questions

All real numbers y greater than or equal to 12?

It is very important to read the question very minutely and then it would be easy to reach a logically correct solution. It is important to note that "y" is greater than or equal to 12 and y is considered as all real numbers. Then we can mathematically represent this situation as 
≥ 12

ANSWERED AT 21/01/2020 - 10:49 AM


QUESTION POSTED AT 21/01/2020 - 10:49 AM

What is the sequence technique of this number sequence17,9,?,16.5,35,90

The sequence is as follows:

(17 + 1)(1/2) = 9
(9 + 1)(2/2) = 10
(10 + 1)(3/2) = 16.5
(16.5 + 1)(4/2) = 35
(35 + 1)(5/2) = 90

Therefore, the missing value in the sequence is 10.

ANSWERED AT 21/01/2020 - 10:49 AM


QUESTION POSTED AT 21/01/2020 - 10:49 AM

Which of the following verbal expressions represents the algebraic expression 2x – 8?. A.. eight less than twice a number. B.. the difference between eight and twice a number. C.. twice eight less than a number. D.. twice a number and eight

Step-by-step explanation:

We are given an algebraic expression as (2x - 8). We have to write the verbal expression for the above expression. Here, x is a variable, 8 is a constant minus is the algebraic operations. 2 is multiplied by the variable x.    

A variable is defined as the number which changes. It stores only an integer.

Addition, subtraction, division etc are algebraic operations.

In the given verbal expression, it can be written as "the eight less than twice a number".

Hence, the correct option is (a) "eight less than twice a number".

ANSWERED AT 21/01/2020 - 10:48 AM


QUESTION POSTED AT 21/01/2020 - 10:48 AM

If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number? A. 42 B. 24 C. 64 D. 46 E. 36

The answer is A. 42

Solution:
Let x= ones digit, y=tens digit

1st condition (original number) : 7(x+y)=10y + x
2nd condition (new number by reversing the digits): 18+x+y=10x+y

simplifying:
1st condition: 6x=3y
2nd condition: x=2
substituting x=2 to 6x=3y
y=4

ANSWERED AT 21/01/2020 - 10:47 AM


QUESTION POSTED AT 21/01/2020 - 10:47 AM

The length of a rectangle is four times its width. If the perimeter is at most 130 centimeters, what is the greatest possible value for the width? Write an inequality to model the problem.. A.2w + 2 • (4w) < 130. B.2w + 2 • (4w) > 130. C. 2w + 2 • (4w) ≤ 130. D.2w + 2 • (4w) ≥ 130


Solution.

L = 4w --------The length of a rectangle is four times its width.
2w + 2L ≤ 130 ------- the perimeter is at most 130 centimeters.
Now, if substitute the first equation into the second inequality you will get
2w + 2 • (4w) ≤ 130.

Therefore, the inequality model in C is correct.

Bonus.
If you solve the inequality you will have a final answer w ≤ 13. The greatest value being 13.

Hope it helps,

ANSWERED AT 21/01/2020 - 10:46 AM


QUESTION POSTED AT 21/01/2020 - 10:46 AM

To buy concert tickets there is a service charge and a cost per ticket. Write an equation to show the cost for any number of tickets. x y Number of Tickets Cost in Dollars 1 22 2 40 3 58 4 76 A. y = 22x B. y = 18x + 4 C. y = 18x D. y = 4x + 18

Given table:

X | Y
-------
1 | 22
2 | 40
3 | 58
4 | 76

As easy way to find out which of the equations in the choices is correct, is to plug in the different values of x, and see which equation gives out the corresponding values of y. Let us try this below:

A. y = 22x

22(1) = 22 || OK
22(2) = 44 || WRONG

B. y = 18x + 4

18(1) + 4 = 22 || OK
18(2) + 4 = 40 || OK
18(3) + 4 = 58 || OK
18(4) + 4 = 76 || OK

Therefore, the correct answer is B.

ANSWERED AT 21/01/2020 - 10:44 AM


QUESTION POSTED AT 21/01/2020 - 10:44 AM

There are 8 brooms and 6 mops in a janitor's closet. What is the ratio of the number of mops to the total number of brooms and mops?. . A: 4/3 . B:3/7 . C:7/3. D:3/4

B 3:7

If there are 6 mops, and 14 mops and brooms, you get 6:14, which simplifies to 3:7.

ANSWERED AT 21/01/2020 - 10:44 AM


QUESTION POSTED AT 21/01/2020 - 10:44 AM

If 6 times a certain number is added to 8, the result is 32.. . Which of the following equations could be used to solve the problem?. . . 6x = 32. 6(x + 8) = 32. 6x = 8 + 32. 6x + 8 = 32

Let x be the certain number and that six time this number may be expressed as 6x. Based on the conditions presented above, the sum of 6x and 8 should be equal to 32. This may be mathematically expressed as,
 
                                     6x + 8 = 32

Therefore, the answer is fourth choice. 

ANSWERED AT 21/01/2020 - 10:42 AM


QUESTION POSTED AT 21/01/2020 - 10:42 AM

The number of music CDs sold weekly by a store follows a normal distribution with a mean of 455 and a standard deviation of 65. Which sentence summarizes this information?. . A.There is an 84% chance that the shop sells more than 390 CDs in a week. . B.There is a 34% chance that the shop sells more than 390 CDs in a week.. C.There is a 34% chance that the shop sells fewer than 390 CDs in a week.. D.There is a 68% chance that the shop sells fewer than 390 CDs in a week.. E.There is a 95% chance that the shop sells more than 390 CDs in a week.

Answer:

A. There is an 84% chance that the shop sells more than 390 CDs in a week.

Step-by-step explanation:

The number of music CDs sold weekly by a store follows a normal distribution with a mean of 455 and a standard deviation of 65.

Hint- First we will have to calculate the z score and then using z score table we can calculate the probability or area below that point.

Z score can be calculated by the following formula,

Z=\dfrac{X-\mu}{\sigma}

Where,

X = the raw score,

μ = mean of the sample

σ = standard deviation,

Putting the values,

Z=\dfrac{390-455}{65}=-1

From the z score table, we get

P(z<-1)=0.1586=15.86\%\approx 16\%

As from the table we get the probability less than the point which in case is 390 with z score of -1, the probability more with z score more than -1, is

=100-16=84\%


ANSWERED AT 21/01/2020 - 10:42 AM


QUESTION POSTED AT 21/01/2020 - 10:42 AM

WWhich of the following would not be a correct interpretation of a correlation of r = .90? . a) the variables are inversely related.. b) most of the data points fall very close to a distinct pattern. c) there exists a positive relationship between the variables. d) there exists a strong relationship between the variables. e) all of the above statements are correct

The answer to this question is letter A. the variables are inversely related. This means that if the number is bigger the lesser the prediction which is not the definition of correlation coefficient that has an r = .90. A correlation of r = .90 means a positive relationship between variables.

ANSWERED AT 21/01/2020 - 10:41 AM


QUESTION POSTED AT 21/01/2020 - 10:41 AM

A solid has faces that consist of 4 triangles, 3 rectangles, and 1 hexagon. The solid has 9 vertices. How many edges does the solid have?. A.. 12 edges. B.. 15 edges. C.. 18 edges. D.. 21 edges.

Drawing this solid may be hard. Basing on the given description, a solid with nine vertices and having faces consisting of four triangles, three rectangles and one hexagon (polygon with six sides) would have a number of edges around twelve edges. Hence, letter A. 

ANSWERED AT 21/01/2020 - 10:40 AM


QUESTION POSTED AT 21/01/2020 - 10:40 AM

The equation of line XY is (y−3) = negative 2 over 3(x − 4). What is the slope of a line perpendicular to XY?

The slope of line XY: m = - 2/3
The slope of a line perpendicular to XY:
m1 =  \frac{-1}{ \frac{-2}{3} }=  \frac{3}{2}
m 1 = 1.5

ANSWERED AT 21/01/2020 - 10:39 AM


QUESTION POSTED AT 21/01/2020 - 10:39 AM

Which of the following best specifies the purpose of error bars on a graph?. . to show the mean of a data set. to identify the independent variable. to give a visual display of measurement precision. to indicate the total number of measurements that are made

The correct answer for this question is "to give a visual display of measurement precision." The statement that best specifies the purpose of error bars on a graph in order to give a visual display of measurement precision. In this way, it is easier to identify the error.

ANSWERED AT 21/01/2020 - 10:39 AM


QUESTION POSTED AT 21/01/2020 - 10:39 AM

Which number is between 0.6 and 7/9 ?

First number 0.6

second number 7/9 = 0.77

If we take other number as x, it would be between 0.6 and 0.77
there are infinite numbers between 0.6 and 0.77.
0.6 < x < 0.77

ANSWERED AT 21/01/2020 - 10:38 AM


QUESTION POSTED AT 21/01/2020 - 10:38 AM

A model rocket is launched vertically with an engine that is ignited at time t = 0. The engine provides an upward acceleration of 30 m/^2 for 2 seconds. Upon reaching its maximum height, the rocket deploys a parachute, and then descends vertically toward the ground. A) Determine the speed of the rocket after the 2s firing of the engine B) What maximum height will the rocket reach? C) At what time after t=0 will the maximum height be reached?

A. For the first questions, it asked for the speed of the rocket when it goes down. A stands for speed so you add the upward speed of 30 then slows down by 10 when it goes down so

a=30+10=40m/s2

B. This refer to speed of the rocket as it goes down so with the formula

V = u +at

V = 40*2 = 80m/s

Then solve for S

S = ut + ½^2

S = 1/2* 40 * 2*2 = 80m

C. At t=0, the rocket is at rest.

ANSWERED AT 21/01/2020 - 10:35 AM


QUESTION POSTED AT 21/01/2020 - 10:35 AM

The test to detect the presence of the hepatitis B virus is 97% accurate for a person who has the disease and 99% accurate for a person who does not have the disease. If 0.55% of the people in a given population are infected, what is the probability that a randomly chosen person gets an incorrect result?. . 0.98455. . 0.000165. . 0.009945. . 0.001011

The probability tests to detect the presence of hepatitis B:
P (presence)= 0.97 (true)  0.03 (false)
P (absence)= 0.99 (true)  0.01 (false)

P(infected)=0.0055
P(not infected)= 0.9945

To have an incorrect result:
P[infected and false from P(presence)] + P[not infected and false from P(absence)]

=0.0055*0.03+0.9945*0.01= 0.01011

The answer is 0.01011 

ANSWERED AT 21/01/2020 - 10:35 AM


QUESTION POSTED AT 21/01/2020 - 10:35 AM

Make a conjecture about the solution of a system of equations if the result of subtracting one equation from the other is 0 = 0. . . . . . a. . . . there are no solutions . . . c. . . . cannot determine any solution . . . . . b. . . . there are infinite number of solutions . . . d. . . . the solutions are inverses of each other . @petiteme

The correct answer for this question is "b. there are infinite number of solutions."

Following the steps: Make a conjecture about the solution of a system of equations if the result of subtracting one equation from the other is 0 = 0. This will give you an infinite number of solutions.

ANSWERED AT 21/01/2020 - 10:32 AM


QUESTION POSTED AT 21/01/2020 - 10:32 AM

1. Stacy owns a hair salon and haircuts are $10. She charges hairdressers $20 per hour to rent a chair and serve clients. What is the minimum number of haircuts a hairdresser should give per hour to earn money at Stacy's salon? . . Two . . Three . . Four . . Five .

Let us make an equation to solve :
Y=mx+b (general form of a linear equation)
y=10x-20 (x is the number of haircuts,y is the amount she earns)
the minimum amount to carry out all the expenses is $20
so,
20=10x-20
20+20=10x
40=10x
40/10=x
4=x
so she must do 4 haircuts in an hour

ANSWERED AT 21/01/2020 - 10:32 AM


QUESTION POSTED AT 21/01/2020 - 10:32 AM

A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 35 cm. To the nearest tenth, what is the area of the wheel?. . 97.5 cm2. 195.1 cm2. 27.5 cm2. 390.1 cm2.

Circumference of the wheel in question = 35 cm
As the wheel is a circle, so
Circumference of the wheel = 2 * (pi) * (radius)
35 = 2 * (pi) * (radius)
Then
Radius = 35/2(pi)
Area of the wheel = (pi) * (radius) ^2
                             = (pi) * [35/2(pi)]^2
                             = (35)^2/4(pi)
                             = 1225/(4 * 3.14159)
                             = 1225/12.56636
                             = 97.48 cm^2
                             = 97.5 cm^2
The correct option among all the options that are given in the question is the first option.

ANSWERED AT 21/01/2020 - 10:32 AM


QUESTION POSTED AT 21/01/2020 - 10:32 AM

The function C(x) = 400x – 0.2x2 represents the total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold. Which statement is true?. A. One thousand units have the minimum cost of $200,000.. B. One thousand units have the maximum cost of $200,000.. C. Two thousand units have the minimum cost of $800,000.. D. Two thousand units have the maximum cost of $800,000..

To determine the maxima and minima of the polynomial, differentiate the given based on x and equate to 0.
                                   C(x) = 400x - 0.2x²
                               dC(x) / dt = 400 - 0.4 x = 0 
The value of x is 1000. This is the value of the maxima. As the value of C(x) continously becomes lesser as the value of x is set higher, the minima is not identified. Substitute x to the original equation,
                               C(x) = (400)(1000) - 0.2(1000²) = $ 200,000
Thus, the answer is letter B. 

ANSWERED AT 21/01/2020 - 10:31 AM


QUESTION POSTED AT 21/01/2020 - 10:31 AM

The product of two consecutive positive integers is 812. What is the value of the lesser integer?

lets name the smaller integer as x

the consecutive integer is x + 1 as its the next number

the product of these 2 numbers are 812

you get the product once you multiply the 2 numbers

x * (x + 1) = 812

x² + 1x = 812

x² + x - 812 = 0

this a quadratic equation

we have to first find the factors of 812 * x² with a difference or sum of + x

the 2 factors are +29x and - 28x which have a product of 812x² and difference of +x

we substitute +x in the quadratic equation with +29x - 28x

x² + 29x -28x - 812 = 0

x(x + 29) -28(x + 29) = 0

(x+ 29)(x-28) = 0

so there are 2 possibilites for x

x + 29 = 0 or x - 28 = 0

x = -29 x = 28

since we are asked to find positive integers from the 2 possible values of x

x = 28 is the positive number

therefore smaller integer is 28

ANSWERED AT 21/01/2020 - 10:30 AM


QUESTION POSTED AT 21/01/2020 - 10:30 AM

The product of two numbers is 713. The first number is 9 more than the second number. Which equation can be used to find x, the greater number?

Guys, the answer is A. for short.

Good luck with the rest of the test, and have a nice day!

ANSWERED AT 21/01/2020 - 10:29 AM


QUESTION POSTED AT 21/01/2020 - 10:29 AM

Given the geometric sequence where a1 = 3 and the common ratio is -1, what is the domain for n? a. All integers where ≤ 0. b. All integers where n ≥ 0. c. All integers where n ≤ 1. d. All integers where n ≥ 1 . . Would the answer be A considering that the ration is a negative?

Answer:

Option: d is the correct answer.

The domain for n is all the integers where n≥1.

Step-by-step explanation:

We know that a geometric sequence also known as geometric progression in which each term is found by multiplying the preceding term by a constant factor.

That common factor is also known as a common ratio and is denoted by 'r'.

Now, the sequence is given as:

a_1=a\\\\a_2=ar\\\\a_3=ar^2\\\\a_4=ar^3\\.\\.\\.\\.\\.\\.\\.\\.\\.

Hence, the nth term of the sequence is given by:

a_n where n belongs to natural numbers.

Where a is the first term of the sequence i.e. when n=1

Hence, the domain for n is:

d. All integers where n ≥ 1

ANSWERED AT 21/01/2020 - 10:27 AM


QUESTION POSTED AT 21/01/2020 - 10:27 AM

A small child is at a candy store, eager to spend his $1 allowance on candy. His two favorite candies are priced at $0.05 and $0.10, respectively. If the child is intent on spending his entire allowance on candy, which of the following represents a standard form equation that describes this situation?.

Choices:
A.0.05x+0.10y=1.00
B.0.10x-0.05y=1.00
c.5x+10y=100.00
d.x+2y=20.00

Given:
Allowance: $1
Candy 1 priced at $0.05
Candy 2 priced at $0.10

Let x be Candy 1 and y be Candy 2. So the equation would be.

0.05x + 0.10y = 1  Choice A.



ANSWERED AT 21/01/2020 - 10:26 AM


QUESTION POSTED AT 21/01/2020 - 10:26 AM

Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols.. . 1.2x+7y=4. 2..-4x-3y=14. .

Using the given equations to solve:

2x + 7y = 4
-4x - 3y = 14

Expressing one equation in terms of x:

2x + 7y = 4
2x = 4 - 7y
x = (4 - 7y)/2

Substituting to the other equation:

-4 [(4 - 7y)/2] - 3y = 14
-8 + 14y - 3y = 14
11y = 22
y = 2

Substituting back to the first equation:

2x + 7(2) = 4
2x + 14 = 4
2x = -10
x = -5

Therefore, (x,y) = (-5 , 2)

ANSWERED AT 21/01/2020 - 10:26 AM


QUESTION POSTED AT 21/01/2020 - 10:26 AM

If you save one penny on January 1, two pennies on January 2, three pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal.

The given condition is an arithmetic sequence with the first term (a1) is 1 penny and the common difference (d) is 1 penny. A year that is not a leap year has 365 days (n). The arithmetic series (S) is calculated through formula,
 
                               S = (n/2) (2a1 + (n - 1) x d)

Substituting the known values,
 
                               S = (365/2) (2 x 1 + (365 - 1) x 1)
 
                               S = 66795 pennies

A dollar is 100 pennies. Therefore, at the end of the year, the total savings is $667.95.




ANSWERED AT 21/01/2020 - 10:25 AM


QUESTION POSTED AT 21/01/2020 - 10:25 AM

What is the additive inverse of the complex number 9 – 4i?. . A.–9 – 4i. B.–9 + 4i. C.9 – 4i. D.9 + 4i

Given the complex number 9 - 4i, the additive inverse is the number that when added to the original number, would equate to zero. Another term this may be known as is the additive identity. The additive inverse is simply:
(a + bi) = -(a + bi)

Given: 9 - 4i

-(9 - 4i) = -9 + 4i

Therefore, the answer is B.

ANSWERED AT 21/01/2020 - 10:25 AM


QUESTION POSTED AT 21/01/2020 - 10:25 AM

What are some limitations when using a line of best fit on a scatter plot to make predictions?. a.There may be too much information given on the scatter plot. b.The line may represent a negative or positive correlation.. c.It is possible to draw different lines to approximate the same data. The line of best fit is only an estimate. d.The axes of the scatter plot may be labeled incorrectly.

The limitation when using a line of best fit in a scatter plot to make predictions is that: "It is possible to draw different lines to approximate the same data". 

In making a line of best fit, you choose two points from the given scatter plot that you think are closest to the possible values of the scatter plot. From the line of best fit created from these two points, an equation to the scatter plot is then created. However, another person may choose two different points, thus making a different equation than your own, resulting in another equation which may still lead to the same result. Contrary to the name, the line of best fit is at best, an approximation.

ANSWERED AT 21/01/2020 - 10:25 AM


QUESTION POSTED AT 21/01/2020 - 10:25 AM