Exponential properties

Answer:

Option C is the correct option

Step-by-step explanation:

g = 8 ( given )

Now,

[tex] \frac{g}{2} + 3[/tex]

Plugging the value of g

[tex] \frac{8}{2} + 3[/tex]

[tex] \frac{8 + 3 \times 2}{2} [/tex]

[tex] \frac{8 + 6}{2} [/tex]

[tex] \frac{14}{2} [/tex]

[tex]7[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Step-by-step explanation:

Let's organise our information :

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

Now let's solve this equation :

Δ=1²-4*(1/2)*(-4)

 = 9

So we have two solutions :

So the solutions are -4 and 2

Answer:

53/28

Step-by-step explanation:

100 g jam

Blackberry / sugar= 53/28

Answer:

Solution,

Amount of sugar=100-(19+53)

=100-72

=28 gram

Ratio of blackberries to sugar=53/28

=53:28

Hope this helps..

Good luck on your assignment..

Answer:

352 cm/s

Step-by-step explanation:

circ = 44pi

speed = distance * time

distance = circ * 4 = 176pi

speed = 176pi/0.5

Answer:

≈ 1106 cm/s

Step-by-step explanation:

linear speed = angular speed x radius of the rotation

v = ωr

v = linear speed (m/s)

ω = angular speed (radians/s)

r = radius of the rotation (m)

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

Given:

Linear speed is:

Answer:

(3,2)

(-9,-6)

Step-by-step explanation:

Given that the graph is a direct variation.

The equation of variation is:

[tex]x=ky[/tex]

Since point (6, 4) is on the graph

[tex]6=4k\\\\k=\dfrac64[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac64y[/tex]

[tex]\text{When y=2},x=\dfrac64 \times 2 =3\\\\\text{When y =}-6,x=\dfrac64 \times -6 =-9\\\\\text{When y =}8,x=\dfrac64 \times 8 =12\\\\\text{When y =}-3,x=\dfrac64 \times -3 =-4.5[/tex]

Therefore, the points that are also on the graph are:

(3,2) and  (-9,-6)

Answer:

(-9, -6) and (3, 2)

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

3y=5x

Put x as 3 and y as 5.

3(5) = 5(3)

15 = 15

Hence, true.

Answer:

X=3

y=15

[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]

Proved.

Hope it helps..

Answer:

$200

I hope this helps!

Answer:

200rupees

Step-by-step explanation:

according to the question ,kajol has 75 rupees

amount earned=3/8* amount earned

                        =75/3*8

                         =200 rupees

Answer:

The individually paid $1.5 for the tip and $8.5 for the food

Step-by-step explanation:

Total money spent =  $40

Food bill =  $34

if the situation is represented by the equation [tex]\frac{1}{4}(t+34) = \frac{40}{4}[/tex] where t is the amount of the tip, the amount for the tip can be calculated as shown;

[tex]\frac{1}{4}(t+34) = \frac{40}{4}\\ t+34 = 40\\t = 40-34\\t = 6[/tex]

Amount of the tip = $6

If they decided to split the bill and tip evenly among themselves, amount paid by each friend for the food and the tip can be gotten using the equation representing the situation where t = $6 as shown;

[tex]= \frac{1}{4}(t+34) \\= \frac{1}{4}(6+34)\\= \frac{1}{4}(6)+\frac{1}{4}(34)\\= 1.5+8.5\\[/tex]

From the result above, it can be seen that each friend paid $1.5 for their tip and $8.5 for their food

Answer:

A) Each friend paid $8.50 for the food and $1.50 for the tip.

Answer:

25%

Step-by-step explanation:

The probability of having a boy is 50%

To calculate the probability of him having 2 boys, multiply the probabilities together

0.5(0.5) = 0.25

Answer:

6.85

Step-by-step explanation:

6 17/20

Convert to improper fraction.

137/20

Divide.

= 6.85

Answer:

6.85

Step-by-step explanation:

17/20 = 85/100

17 x 5 = 85

20 x 5 = 100

so,

6 + 85/100 = 6.85

Answer:

solution,

Highest score=9

lowest score=1

now,

range= highest score-lowest score

=9-1

=8

Hope this helps...

Answer:

8

Step-by-step explanation:

The range of the sequence is the largest number - the smallest number.

The largest number is 9.

The smallest number is 1.

9 - 1

= 8

The range of the sequence is 8.

[You've posted your question under the wrong subject. Please try your best to post your questions under the right subject so that you get the required answer to your question.]

Answer:

11,340 cents

Step-by-step explanation:

• Step I)

Power of the air conditioning = 3500 W

Our first step to calculating energy consumption is:

Converting it into kilowatts:

1000 W = 1 kW

3500 W = 3.5 kW

• Step II)

Take the time the appliance was used, in hours:

Time is taken = 6 hours per day

For 30 days,

Time = 6 × 30

= 180 h

• Step III)

Calculate the energy consumption by multiplying the power rating of the appliance with the time it was used (in hours).

E = 3.5 kW × 180 h

= 630 kWh

• Step IV)

For billing the amount:

Multiply the energy consumed by the cost per kWh (often written as "unit")

Cost = 18 cents per kWh

Total cost = 18 × 630

= 11, 340 cents

Thus, his AC costs him 11, 340 cents.

Complete Question

In a study of the accuracy of fast food? drive-through orders, Restaurant A had  249 accurate orders and 80 that were not accurate.  

a. Construct a 90?% confidence interval estimate of the percentage of orders that are not accurate.  

b.  Compare the results from part? (a) to this 90?% confidence interval for the percentage of orders that are not accurate at Restaurant? B: 0.164< p <0.239. What do you? conclude?

 Choose the correct answer below.  

A. Since the two confidence intervals  overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.  

B. The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A. Therefore, Restaurant B has a significantly higher percentage of orders that are not accurate.  

C. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.  

D. Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant? A, this indicates that Restaurant B has a significantly higher percentage of orders that are not accurate.

Answer:

a

The  90?% confidence interval  is  [tex]0.2041 < p < 0.282[/tex]

b

Option A is the correct option

Step-by-step explanation:

From the question we are told that  

      The sample size is  n  =  249+80  = 329

        The number that are not accurate is  k  = 80

Generally the sample proportion of orders  that are not accurate is  mathematically evaluated as

                   [tex]\r p = \frac{ 80 }{329}[/tex]

                    [tex]\r p = 0.243[/tex]

Given that the confidence level is 90% then the level of significance is mathematically evaluated as

              [tex]\alpha = 100 -90[/tex]

              [tex]\alpha = 10\%[/tex]

               [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is  

               [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

              [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]

=>            [tex]E = 1.645* \sqrt{ \frac{0.243 (1- 0.243 )}{329} }[/tex]

=>              [tex]E = 0.0389[/tex]

Generally the 90% confidence interval is  mathematically represented as

         [tex]\r p -E < p < \r p +E[/tex]

=>       [tex]0.2041 < p < 0.282[/tex]

Comparing the two 90% confidence of restaurant A and B we see that they overlap and  Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.  

Answer:

0.04.

Step-by-step explanation:

The first significant number is and since the second is 3 we do not change the 4.

Answer:0.04

Step-by-step explanation:numbers from 0-4 can't be rounded up they are rounded off but numbers from 5-9 are rounded up by adding 1 to the number before. Therefore 0.043118 to 1 significant number will be 0.04

Answer:  c) rotation of 180° & shift right 1 unit and down 2 units

Step-by-step explanation:

Rotation of 180° changes the signs of x and y

(x, y)   →   (-x, -y)

Shift right one unit adds 1 to x, Shift two down subtracts 2 from y

(-x, -y)   →   (-x + 1, -y - 2)

  (x, y)          (-x + 1, -y - 2)  

(-1, -2)    →       (2, 0)

(-4, -1)    →       (5, -1)

(-4, -3)   →       (5, 1)

Answer:

8

Step-by-step explanation:

the value of x is 8 because the sides are the same

Answer:

2

Step-by-step explanation:

I would have to say it is two bc Everitt had 30% where Desery had 20%.

Answer:

x = 270 gallons

270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze

Step-by-step explanation:

Let x represent the number of gallons of the 50% antifreeze solution.

The volume of the 10% antifreeze is = 90 gallons

The volume of the mixture that is 40% antifreeze = 90+x

The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;

50% of x + 10% of 90 = 40% of (90+x)

0.50(x) + 0.10(90) = 0.40(90+x)

0.50x + 9 = 36 + 0.40x

Collecting the like terms;

0.50x - 0.40x = 36-9

0.10x = 27

x = 27/0.10

x = 270 gallons

270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze

Answer:

-12+28i+3i-7i-65i+28

14 -41i

Answer:

Hope it helps you :)

And i hope you understand  

For store 1, it can be placed on 16 sites. Store 2 can be placed on 15 sites( since store 1 is already on site 1). Store 3 can be placed on 14 sites and so on until store 5 which has 12 sites.

Therefore the number of way is

C= 16*15*14*13*12

c=524,160 possibilities

Answer:

She is saving 10 cents per pound

Step-by-step explanation:

First, we need to find how much she would pay without the sale:

12.5(1.8) = 22.5

Now, we can calculate how much she saved:

22.5 - 21.25 = 1.25

To find how much she's saving per pound, we divide the difference by the number of pounds:

1.25/12.5 = 0.1

She is saving 10 cents per pound

Answer:

A

Step-by-step explanation:

I took the test and got it right

Answer:

a)0.654

b)-0.34

Step-by-step explanation:

a)2 3 4 5 6 7

[tex]\mu = 4[/tex]

[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{2+3+4+5+6+7}{6}\\Mean =4.5[/tex]

Standard deviation [tex]=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]

Standard deviation [tex]=\sqrt{\frac{(2-4.5)^2+(3-4.5)^2+(4-4.5)^2+(5-4.5)^2+(6-4.5)^2+(7-4.5)^2}{6-1}}=1.87[/tex]

[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\t=\frac{4.5-4}{\frac{1.87}{\sqrt{6}}}\\t=0.654[/tex]

Df = n-1 = 6-1 = 5

Assume α=0.05

So[tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]

So, t critical = 2.57

So, t calculated < t critical

b)1 2 2 5 5 7

[tex]\mu = 4 \\Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{1+2+2+5+5+7}{6}\\Mean =3.67[/tex]

Standard deviation =[tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]

Standard deviation =[tex]\sqrt{\frac{(1-3.67)^2+(2-3.67)^2+(2-3.67)^2+(5-3.67)^2+(5-3.67)^2+(7-3.67)^2}{6-1}}=2.338[/tex]

[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}t=\frac{3.67-4}{\frac{2.338}{\sqrt{6}}}t=-0.34[/tex]

Df = n-1 = 6-1 = 5

Assume α=0.05

So, [tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]

So, t critical = 2.57

So, t calculated < t critical

Answer:

fg t f h 10

Step-by-step explanation:

Step-by-step explanation:

a. 3.14 * 4² = 50.24 cm²

b. 16 cm

c. V = B * h = 50.24 * 16 = 803.84 cm²

Answer:

75435912

Step-by-step explanation:

1495486+73940426

= 75435912

Answer:

75,435,912

Step-by-step explanation:

=> 1495486 + 73940426

Using Calculator

=> 75,435,912

Answer:c

Step-by-step explanation:

hyp=6[tex]\sqrt{2}[/tex]

adj=6

hyp:adj=6[tex]\sqrt{2}[/tex]  :2

hyp:adj=[tex]\frac{6\sqrt{2} }{6} \\[/tex]

[tex]=\frac{\sqrt{2} }{1} \\hyp:adj=\sqrt{2} :1[/tex]

Answer:

Step-by-step explanation:

a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.

__

b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.

Answer:

Step-by-step explanation:

Answer:

The answer is 1/27

Step-by-step explanation:

According to the rules of indices

a^-b can be written as 1/a^b

So 3^- 3 can be written as 1/3³

And

1/3³ = 1/27

Hope this helps you

Answer:

Step-by-step explanation:

Let the five courses with their corresponding credit hours be represented as shown;

FST 201 = 4

FST 203 = 5

FST 112 = 1

FST 219 = 5

FST 223 = 4

If a student earned grades of​ B, B,​ A, C, and D respectively in those courses with the following grading system  A =​4, B =​3, C =​2, D =​1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.

Credit point for each course = Number of credit hour * point for each grade

FST 201 = 4 * 4 = 16points (A)

FST 203 = 5 * 4 = 20points (A)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 4 = 20points (A)

FST 223 = 4 * 4 = 16points (A)

Total credit point = 16+20+4+20+16 = 76points

Total credit point gotten by the student is calculated as thus;

FST 201 = 4 * 3 = 12points (B)

FST 203 = 5 * 3 = 15points (B)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 2 = 10points (C)

FST 223 = 4 * 1 = 4points (D)

Total credit point gotten by the student = 45points.

student's Grade Point Average​ (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)

Answer:

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X¿ 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s¿4.2 represent the sample standard deviation

n¿65 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]