A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. Group members took a random sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged overnight and the number of hours of use before needing to be recharged was recorded. Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours. The 90% confidence interval is (-1.93, 0.13). The correct interpretation is:__________
A. We are 90% confident that, on average, there is no difference in operating hours between toothbrushes from Company A compared to those from Company B.
B. We are 90% confident that, on average, there is a difference in operating hours between toothbrushes from Company A compared to those from Company B.
C. We are 90% confident that, on average, the toothbrushes from Company B operate longer before needing to be recharged than the toothbrushes from Company A.
D. We are 90% confident that, on average, the toothbrushes from Company A operate longer before needing to be recharged than the toothbrushes from Company B.

Answer:

combine 4m -8m to get -4m

[tex] - 4m - 2[/tex]

Answer:

− 4m-2

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

to calculate f(-1), you know that x = -1. so all you have to do is substitute:

f(-1) = (-1)2 + 1

f(-1) = -2 + 1

f(-1) = -1

Answer:

0

Step-by-step explanation:

Answer:  4.4 seconds

Step-by-step explanation:

h(t) = -16t² + 315

Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0

  0  = -16t² + 315

-315 = -16t²

[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]

Answer:

≈ 4.44 sec

Step-by-step explanation:

h= 315 ft

h= 16t²

315 = 16t²

t²=315/16

t=√315/16 ≈ 4.44 sec

Answer: 2x²-√3

Step-by-step explanation:

Another way to say the conjugate is the opposite. All you have to do is to change the sign in the binomial, which is 2x²+√3. When you change the sign, it becomes 2x²-√3.

Answer:

  Annuity C:  Deposit $72,000 one lump sum

Step-by-step explanation:

The yield is improved when the money is on deposit for a longer period.

If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.

If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.

  Annuity C will provide the largest yield.

Answer:  see table below

Step-by-step explanation:

Simply add the digit on the left to the digit on the top

1, 2 --> 1 + 2 = 3

3, 4 --> 3 + 4 = 7

4, 2 --> 4 + 2 = 6

6, 6 --> 6 + 6 = 12

[tex]\begin{array}{c|c|c|c}&\underline{\quad 2\quad }&\underline{\quad 4\quad }&\underline{\quad 6\quad }\\\underline{\quad 1 \quad}&\bold{\underline{\quad 3\quad}}&\underline{\quad 5\quad}&\underline{\quad 7\quad}\\\underline{\quad 2 \quad}&\underline{\quad 4\quad }&\underline{\quad 6\quad }&\underline{\quad 8\quad}\\\underline{\quad 3 \quad}&\underline{\quad 5\quad }&\bold{\underline{\quad 7\quad}}&\underline{\quad 9\quad}\\\end{array}[/tex]

[tex]\begin{array}{c|c|c|c}{\underline{\quad 4 \quad}&\bold{\underline{\quad 6\quad }}&\underline{\quad 8\quad }&\underline{\quad 10\quad }\\\underline{\quad 5 \quad}&\underline{\quad 7\quad}&\underline{\quad 9\quad}&\underline{\quad 11\quad}\\\underline{\quad 6 \quad}&\underline{\quad 8\quad }&\underline{\quad 10\quad }&\bold{\underline{\quad 12\quad}}\\\end{array}[/tex]

Answer:

13-n=4

Subtract both sides by 13

-n=-9

n=9

Step-by-step explanation:

13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you

Answer :

I have solved for the points.

Explanation :

Just get a protractor and plot out the angles into a circle. Starting with the largest angle.

Answer:

[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]

Step-by-step explanation:

hello,

saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]

means that 1 is a root of this expression, so it comes

1+1-1-k=0

<=> 1-k=0

<=> k = 1

Answer:

Option (2)

Step-by-step explanation:

The given table represents the relation between the velocity and the time for an object is falling under the gravity.

Change in velocity with respect to time is directly proportional so the change is linear.

Acceleration due to gravity of this object is defined by the slope of the line joining the ordered pairs given in the table.

Let the two points lying on the line are (0, 0) and (1, 9.8)

Slope of the line passing through two points = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

                                                                          = [tex]\frac{9.8-0}{1-0}[/tex]

                                                                          = 9.8 [tex]\frac{m}{s^{2} }[/tex]

Option (2) will be the answer.

Answer:

B.

Step-by-step explanation:

The correct table that shows the justified solution steps is the second table.

The correct option is B.

The correct table that shows the justified solution steps is:

A 2-column table with 4 rows.

Column 1: Solution step

3x - 15 + 7x = 65

10x - 15 = 65

10x = 80

x = 8

Column 2: Method to Justify

Distributive property

Combine like terms

Addition property of equality

Division property of equality

In this table, the solution steps are correctly listed in the first column, showing the step-by-step process of solving the equation. The methods to justify each step are accurately provided in the second column, demonstrating the mathematical properties used at each stage.

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Answer:

each bag of candy is $6.00

Step-by-step explanation:

1 bag would cost $6.00

1×$6.00=$6.00

6 bags × $6.00 = $36.00

Answer:

the constant of proportionally is 6

the prices of 6 bags of candy is 36

Step-by-step explanation:

to find the constant u divide 6 by 1 to find how they multiplying it by

the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36

hope this helps

Answer:

12/40=0.3

0.3 car parts per minute

9 / 0.3 = 30 minutes

30 minutes for 9 parts

Hope this helps

Step-by-step explanation:

Jose required 30 minutes to assemble 9 parts.

Jose assemble 12 car parts in 40 minutes. Time consumed by jose to assemble 9 parts to be calculated.

In mathematics it deals with numbers of operations according to the statements.

Here,
40 minute = 12 parts
40/12 = 1 part

Time to assemble 9 parts: = 40/12 x 9
                                             = 10/3 x 9
                                             =  30

Thus, Jose required 30 minutes to assemble 9 parts.

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Answer:

  x = -5

Step-by-step explanation:

You are often told to start a problem like this by clearing fractions. Multiply the equation by the least common denominator of the fractions. Here, that value is 6.

  4x -3 = 2 +5x . . . . multiply the equation by 6

  -5 = x . . . . . . . . . . . add -2-4x to both sides

The solution is x = -5.

_____

If you're comfortable with arithmetic using fractions, you can "cut to the chase." Subtract 2/3x+1/3 from both sides:

  (2/3x -1/2) -(2/3x +1/3) = (1/3 +5/6x) -(2/3x +1/3)

  -1/2 -1/3 = 5/6x -2/3x . . . . simplify a little

  -5/6 = 1/6x . . . . . . . . . . . . .simplify more

  -5 = x . . . . . . multiply by 6

Answer:

Step-by-step explanation:

Let the number of children's tickets sold =c

Let the number of adult's tickets sold =a

Let the number of student's tickets sold =s

A total of 204 tickets were sold, therefore: c+a+s=204

Child tickets are $6, adult tickets are $12, and student tickets are $8.

Total revenue =$2,008

Therefore:

6c+12a+8s-2008

We are also told that 4 more adult tickets were sold than the total number of student and child tickets combined.

c+s=a+4

We then solve the resulting system of equation.

Substituting c+s=a+4 into the first equation

c+a+s=204

a+4+a=204

2a=204-4

2a=200

a=100

Substitute a=100 into the second and third equation

6c+12(100)+8s=2008

6c+8s=2008-1200

6c+8s=808

From the third equation

c+s=100+4

c=104-s

Substitute c=104-s into 6c+8s=808

6(104-s)+8s=808

624-6s+8s=808

2s=808-624

2s=184

s=92

Since c=104-s

c=104-92

c=12

Therefore:

Answer:

4y = -3x +18

Step-by-step explanation:

Let's get the gradient from this line equation first.

4x-3y=10

4x-10=3y

Y= 4/3x -10/3

The gradient is 4/3.

For a line perpendicular to another line.

M*M'= -1

M= -/(4/3)

M = -3/4

So the gradient to be used is -3/4

Formula for solving is

(Y-y1)/(x-x1)= M

X1= 2

Y1= 3

M = -3/4

(Y-y1)/(x-x1)= M

(Y-3)/(x-2)= -3/4

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

4y -12 = -3x +6

4y = -3x +18

Answer:

7

Step-by-step explanation:

hh

ht

th

tt

so it's a 1/4 chance

1/4 * 28 = 7

Answer:

7

Step-by-step explanation:

The probability of both coins landing on heads is:

1/2 × 1/2 = 1/4

Multiply by 28.

1/4 × 28

= 7

Answer:  55.6 days

Step-by-step explanation:

[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]

Answer:

(a)f(4) square cm.

(b)f(10.91)-f(10.9) Square centimeter.

Step-by-step explanation:

f(r)=the area of a circle (in square cm) that has a radius of r cm.

(a)Area (in square cm) of a circle whose radius is 4 cm.

Since r=4cm

Area of the circle = f(4) square cm.

(b) When the radius of the increases from 10.9 to 10.91 cm.

Change in the Area = f(10.91)-f(10.9) Square centimeter.

Answer:

It  was gained 4 1/4 points.

Step-by-step explanation:

- 7 1/8 - 1 5/8 + 13 = - 8 6/8 + 13 = - 8 3/4 + 13 = - 8 - 3/4 + 12 + 4/4 =  4 1/4

Answer:

[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=21-1=20[/tex]  

the p value for this case would be given by:

[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]  

For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm

Step-by-step explanation:

Information given

[tex]\bar X=2567[/tex] represent the mean height for the sample  

[tex]s=\sqrt{121}= 11[/tex] represent the sample standard deviation

[tex]n=21[/tex] sample size  

[tex]\mu_o =2564[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to check if the true mean is equal to 2564 mm, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 2564[/tex]  

Alternative hypothesis:[tex]\mu \neq 2564[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing we got:

[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=21-1=20[/tex]  

the p value for this case would be given by:

[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]  

For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm

Answer:

d) E = 8h + 0.05s

Her total sales in computers for the week is $2800.

Step-by-step explanation:

Let Rhea's hourly pay =h

She makes $8/hour, therefore sales for h hours =$8h

Let the volume of sales = s

She also earns 5% commission on sales = 5% of s = 0.05s

Therefore, the expression which best describes Rhea's total earnings:

(D) E=8h+0.05s

Rhea worked 15 hours last week and made $260 in total.

h=$15

From the formula

260=8(15)+0.05s

0.05s=260-8(15)

0.05s=140

s=2800

Her total sales in computers for the week is $2800.

Employers offer commissions to their employees to motivate them to seek to make sales rather than just passing time.

In so far as the sales commission do not eat up the profit of the business,  there are no potential problems with this form of earnings  

Work Shown:

log(200) = log(2^3*5^2)

log(200) = log(2^3) + log(5^2)

log(200) = 3*log(2) + 2*log(5)

log(200) = 3*q + 2*p

log(200) = 2p + 3q

The log rules I used were

log(A*B) = log(A)+log(B)

log(A^B) = B*log(A)

The equivalent expression of log(200) is 2p + 3q

The logarithmic expression is given as:

[tex]\mathbf{log 200}[/tex]

Rewrite as:

[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]

Express as exponents

[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]

Split

[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]

Apply law of logarithms

[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]

From the question;

log(5) = p and log(2) = q

So, we have:

[tex]\mathbf{log(200) = 2p +3q}[/tex]

Hence, the equivalent expression of log(200) is 2p + 3q

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Answer

value of x is 34 degrees  

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is in complete. Here is the complete question.

"The dimensions of a triangular pyramid are shown below. The height of

the pyramid is 6 inches. What is the volume in cubic inches?

Base of triangle = 1in

height of triangle = 5in"

Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\

B = Base area

H = Height of the pyramid

Base area  B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]

b = base of the triangle

h = height of the triangle

B = [tex]\frac{1}{2} * 5 * 1\\[/tex]

[tex]B = 2.5in^{2}[/tex]

Since H = 6inches

Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]

[tex]V = 2.5*2\\V =5in^{3}[/tex]

Answer:

$23161.10

Step-by-step explanation:

Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t

Step 1: Convert months to years

60 months/12 month/year = 5 years

Step 2: Plug in known variables

A = 18400(1 + 0.0471)^5

Step 3: Solve

When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.

Answer:

[tex]x=2$\pm$\sqrt{42}[/tex]

Step-by-step explanation:

The given equation is:

[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]

Formula:

A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:

[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]

Where [tex]D= b^{2} -4ac[/tex]

Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]

a = 1

b = -4

c= -38

Calculating D,

[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]

Now, finding the roots:

[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]

So, the solution is:

[tex]x=2$\pm$\sqrt{42}[/tex]

Answer is A or the first one

Answer:

576 for the week

Step-by-step explanation:

First determine how many hours she worked

4/5 * 40 = 32 hours

32 hours times the hourly rate of 18

32*18 =576