confused on question in screenshot.

Step-by-step explanation:

Rate of growth equals 420/100 = 4.2 times per hour

So after t=three hours,

size of culture = 100*(4.2)^t = 100*4.2^3=7408.8 bacteria,

round to nearest unit 7409 bacteria after three hours (after initial size of 100).

Answer:

a) 100•4.2^t

b) P(3)= about 7409 bacteria

c) P’(3)= about 10,632 bacteria per hour

d) t= about 3.2 hours

Step-by-step explanation:

Answer:    x1=1   x2=-2  and x3=2

Step-by-step explanation:

1st   x1=1 is 1 of the roots , so

F(1)=1-1-4+4=0 - true

So lets divide x^3-x^2-4x+4 by (x-x1), i.e  (x^3-x^2-4x+4) /(x-1)=(x^2-4)

x^2-4 can be factorized as (x-2)*(x+2)

So x^3-x^2-4x+4=(x-1)*(x^2-4)=(x-1)(x-2)*(x+2)

So there are 3 dofferent roots:

x1=1   x2=-2  and x3=2

Answer:

The value of x is x = 6

Step-by-step explanation:

[tex]\frac{1}{3}(12x - 24) = 16\\ 12x - 24 = 48\\12x = 48+ 24\\12x = 72\\12/12 = x\\72/12 = 6\\x=6[/tex]

Hope this helped! :)

Answer: a= 3x and b= 7

Step-by-step explanation:

^^

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Given that μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems, the hypothesis are

For null,

H0: μ1 − μ2 = - 10

For alternative,

Ha: μ1 − μ2 < - 10

This is a left tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 115.6

x2 = 129.3

s1 = 5.04

s2 = 5.32

n1 = 8

n2 = 8

t = (115.6 - 129.3)/√(5.04²/8 + 5.32²/8)

t = - 2.041

Test statistic = - 2.04

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [5.04²/8 + 5.32²/8]²/[(1/8 - 1)(5.04²/8)² + (1/8 - 1)(5.32²/8)²] = 45.064369/3.22827484

df = 14

We would determine the probability value from the t test calculator. It becomes

p value = 0.030

Since alpha, 0.01 < the p value, 0.03, then we would fail to reject the null hypothesis.

Answer:

Sum of 2 digit = 48

Sum of 3 digit = 317

Sum of 4 digit = 3009

Total = 3374

Step-by-step explanation:

Given:

9, 8 and 7

Required

Sum of Multiples

The first step is to list out the multiples of each number

9:- 9,18,....,99,108,117,................,999

,1008

,1017....

8:- 8,16........,96,104,...............,992,1000,1008....

7:- 7,14,........,98,105,.............,994,1001,1008.....

Calculating the sum of smallest 2 digit multiple of 9, 8 and 7

The smallest positive 2 digit multiple of:

- 9 is 18

- 8 is 16

- 7 is 14

Sum = 18 + 16 + 14

Sum = 48

Calculating the sum of smallest 3 digit multiple of 9, 8 and 7

The smallest positive 3 digit multiple of:

- 9 is 108

- 8 is 104

- 7 is 105

Sum = 108 + 104 + 105

Sum = 317

Calculating the sum of smallest 4 digit multiple of 9, 8 and 7

The smallest positive 4 digit multiple of:

- 9 is 1008

- 8 is 1000

- 7 is 1001

Sum = 1008 + 1000 + 1001

Sum = 3009

Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit

Sum of All = 48 + 317 + 3009

Sum of All = 3374

Answer:

Left tailed test

Step-by-step explanation:

A two tailed test usually determined by the alternative hypothesis involves both the less than and the greater than option.

A left tailed test corresponds to an alternative hypothesis having just one of either options (less than and the greater than option) usually the less than option.

A right tailed test corresponds to an alternative hypothesis having just one of either options (less than and the greater than option) usually the greatest than option.

In this experiment, the null hypothesis is the average amount of time that spend watching television each week is ---

He introduces a campaign to encourage the students to watch less television and then performs a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. The alternative hypothesis would be: u < ---. This means that this test is a left tailed test.

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

First let's find how much Susan earns per hour.

She earns $0.004 per word, and she does 90 words per minute, so she will earn per minute:

0.004 * 90 = $0.36

Then, per hour, she will earn:

0.36 * 60 = $21.6

Now, to find how many hours she needs to work to earn $1000, we just need to divide this value by the amount she earns per hour:

1000 / 21.6 = 46.3 hours.

She works 4 hours a day and 3 days a week, so she works 4*3 = 12 hours a week.

If a month has 4 weeks, she will work 12*4 = 48 hours a month, so she will earn:

48 * 21.6 = $1036.8

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

Answer:

[tex]50-1.64\frac{15}{\sqrt{30}}=45.509[/tex]    

[tex]50+1.64\frac{15}{\sqrt{30}}=54.491[/tex]    

The 90% confidence inverval for the mean will be 45.509 and 54.491

Step-by-step explanation:

Information given

[tex]\bar X= 50[/tex] represent the sample mean

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

[tex]\sigma= 15[/tex] represent the sample standard deviation

n= 30 represent the sample size  

Confidence interval

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

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

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be [tex]z_{\alpha/2}=1.64[/tex]

Now we have everything in order to replace into formula (1):

[tex]50-1.64\frac{15}{\sqrt{30}}=45.509[/tex]    

[tex]50+1.64\frac{15}{\sqrt{30}}=54.491[/tex]    

The 90% confidence inverval for the mean will be 45.509 and 54.491

Answer:

Solution,

Circumference of circle = 615.44 units

Radius = ?

Now,

Circumference of circle = 615.44

[tex]2\pi \: r = 615.44[/tex]

[tex]2 \times 3.14 \times r = 615.44[/tex]

[tex]6.28r = 615.44[/tex]

[tex]r = \frac{615.44}{6.28} [/tex]

[tex]r = 98 \: units[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

924 cm²

Step-by-step explanation:

The surface area is equal to the area of the two triangles + area of the three rectangles.

Area of two triangles:

12 × (9+5) × 1/2

= 84

84(2) = 168

Area of the three rectangles:

15 × 20 + 13 × 20 + 14 × 20

= 840

840 + 84

The surface area of the triangular prism is 924 cm².

Answer:

Hello!

______________________

x4 – 6x2 + 5

= ( x^2 - 5) ( x + 1 ) ( x - 1 )

Step-by-step explanation: Factor.

Hope this helped you!

Answer:

For this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:

[tex] z_{\alpha}= 1.64[/tex]

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:  

[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]  

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

Step-by-step explanation:

We have the following dataset given:

[tex] X= 43[/tex] represent the households consisted of one person

[tex]n= 125[/tex] represent the sample size

[tex] \hat p= \frac{43}{125}= 0.344[/tex] estimated proportion of  households consisted of one person

We want to test the following hypothesis:

Null hypothesis: [tex]p \leq 0.27[/tex]

Alternative hypothesis: [tex]p>0.27[/tex]

And for this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:

[tex] z_{\alpha}= 1.64[/tex]

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:  

[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]  

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

Answer:

Step-by-step explanation:

hello,

so we know y in terms of t and x in terms of t and we need to find y in terms of x

[tex]x=21t^2<=>\sqrt{x}=\sqrt{21}*t \ \ as \ \ t>=0 \ \ So\\t=\sqrt{\dfrac{x}{21}}[/tex]

and then

[tex]y=f(x)=3\sqrt{\dfrac{x}{21}}+5=\sqrt{\dfrac{9x}{21}}+5=\sqrt{\dfrac{3x}{7}}+5[/tex]

hope this helps

Answer:

Step-by-step explanation:

[tex] \frac{8 {x}^{4} }{16 {x}^{7} } [/tex]

Reduce the fraction with 8

[tex] \frac{ {x}^{4} }{2 {x}^{7} } [/tex]

Simplify the expression

[tex] \frac{1}{2 {x}^{3} } [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Step-by-step explanation:

Regular price  = $ 83

Discount  = 95% of 83

               = 0.95 * 83

              = $ 78.85

Price after discount = 83 - 78.85

                                = $ 4.15

Answer:

$4.15

Step-by-step explanation:

Multiply 83 by .05 to get the new price of $4.15. Additionally, multiply 83 by .95 to get the amount taken off ($78.85).

Answer: 79% probability

Step-by-step explanation:

.17 + .13 + .33 + .16 = .79

.79 x 100 = 79%

Answer:

.79

Step-by-step explanation:

Answer:

x+4=0,x=−4x−7=0,x=7

Answer:

[tex] X= 189[/tex] represent the number of non-fatal accidents involved the use of a cell phone

[tex] n=400[/tex] represent the sample size

And we want to find a  point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone and we can use the following formula:

[tex]\hat p=\frac{X}{n}[/tex]

And replacing we got:

[tex] \hat p=\frac{189}{400}=0.4725[/tex]

Step-by-step explanation:

For this problem we have the following info given:

[tex] X= 189[/tex] represent the number of non-fatal accidents involved the use of a cell phone

[tex] n=400[/tex] represent the sample size

And we want to find a  point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone and we can use the following formula:

[tex]\hat p=\frac{X}{n}[/tex]

And replacing we got:

[tex] \hat p=\frac{189}{400}=0.4725[/tex]

Answer:

49

Step-by-step explanation:

When Karen was born, the dad is 22 so Karen is now 27 which means the dad is 22+27= 49

Answer:

Their father is 49.

Step-by-step explanation:

Her father had her when he was 22, meaning that he is 22 years older than Karen. Karen is 27 right now, so her fathers age is (27+22) 49 years old.

Hope this helps!

Answer:

This is proved using Proof by induction method. There are two steps in this method

Let P(n) represent the given statement  ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

1. Basis Step: This step proves the given statement for n = 1

2. Induction step: The step proves that if the given statement holds for any given case n = k  then it should also be true for n = k + 1.

If the above two steps are true this means that given statement P(n) holds true for all positive n and the mathematical induction P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true.

Step-by-step explanation:

Basis Step:

For n = 1

∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] = ∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

We show that

∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]  for n = 1

Hence P(1) is true

Induction Step:

Let P(k) be true which means that we assume that:

for all k with k≥1, P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true

This is our induction hypothesis and we have to prove that P(k + 1) is also true

This means if ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] holds for n = k  then this should also hold for n = k + 1.

In simple words if P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true then ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is also true

∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex]

           ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex]                 As ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

           ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex]                 As  [tex]A_{k+1}[/tex] ⊆ [tex]B_{k+1}[/tex]

           =  ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

The whole step:

∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex] =  ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

shows that the P(k+1) also holds for ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

hence P(k+1) is true

So proof by induction method proves that P(n) is true. This means

P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true

Answer:

Approximately standard deviation= 108

Step-by-step explanation:

Let's calculate the mean of the data first.

Mean =( 330+ 274+ 492 +371 +160+ 283+ 164)/7

Mean= 2074/7

Mean= 296.3

Calculating the variance.

Variance = ((330-296.3)²+( 274-296.3)²+ (492-296.3)²+( 371-296.3)²+ (160-296.3)² (283-296.3)²+(164-296.3)²)/7

Variance= (1135.69+497.29+38298.49+5580.09+18577.69+176.89+17503.29)/7

Variance= 81769.43/7

Variance= 11681.347

Standard deviation= √variance

Standard deviation= √11681.347

Standard deviation= 108.080

Approximately 108

Answer:

that's cool . . .

\is ok everyone makes mistakes

Answer:

Step-by-step explanation:

5/2 is 2.5

Answer: E and

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \frac{x + 5}{ {x}^{2} } - \frac{2}{5x} [/tex]

Write all the numbers above the least common denominator [tex] {5x}^{2} [/tex]

[tex] \frac{5(x + 5) - 2x}{5 {x}^{2} } [/tex]

Distribute 5 through the parentheses

[tex] \frac{5x + 25 - 2x}{5 {x}^{2} } [/tex]

Collect like terms

[tex] \frac{3x + 25}{5 {x}^{2} } [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

third option

Step-by-step explanation:

Given

[tex]\frac{x+5}{x^2}[/tex] - [tex]\frac{2}{5x}[/tex]

We require the denominators to be common before subtracting.

Multiply numerator/ denominator of first fraction by 5

Multiply numerator/ denominator of second fraction by x

[tex]\frac{5(x+5)}{5x^2}[/tex] - [tex]\frac{2x}{5x^2}[/tex]

Simplify numerator leaving common denominator

= [tex]\frac{5x+25-2x}{5x^2}[/tex]

= [tex]\frac{3x+25}{5x^2}[/tex]

Answer:

Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.

y= -3x+b

Now, we can substitute in the point given to find the intercept.

2= -3(4)+b

2= -12+b

b=14

Finally, put in everything we've found to finish the equation.

y= -3x+14

Answer:

y = -3x + 14

Step-by-step explanation:

First find the reciprocal slope since it is perpendicular.  Slope of the other line is 1/3 so the slope for our new equation is -3.  

Plug information into point-slope equation

(y - y1) = m (x-x1)

y - 2 = -3 (x-4)

Simplify if needed

y - 2 = -3x + 12

y = -3x + 14

Answer:

Vertex: (-1, 0)

Axis of Symmetry: x = -1

Step-by-step explanation:

Use a graphing calc.

Answer:

the answer is C. y=[x-4]-2

Answer:

Step-by-step explanation:

Y=(x+4)-2

Answer:

Option 4

Step-by-step explanation:

=> [tex]-3x^2+2x-4 + 4x^2+5x+9[/tex]

Combining like terms

=> [tex]-3x^2+4x^2+2x+5x-4+9[/tex]

=> [tex]x^2+7x+5[/tex]

Answer:

The interval is constructed at 93% confidence.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between these two bounds, divided by 2.

Confidence interval of proportions concepts:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have that:

2050 people, so n = 2050.

Lower bound: 0.878

Upper bound: 0.903

[tex]\pi = \frac{0.878 + 0.903}{2} = 0.8905[/tex]

[tex]M = \frac{0.903 - 0.878}{2} = 0.0125[/tex]

Confidence level:

We have to find z.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.0125 = z\sqrt{\frac{0.8905*0.1095}{2050}}[/tex]

[tex]0.0069z = 0.0125[/tex]

[tex]z = \frac{0.0125}{0.0069}[/tex]

[tex]z = 1.81[/tex]

[tex]z = 1.81[/tex] has a pvalue of 0.965.

That is:

[tex]]1 - \frac{\alpha}{2} = 0.965[/tex]

[tex]\frac{\alpha}{2} = 0.035[/tex]

[tex]\alpha = 2*0.035[/tex]

[tex]\alpha = 0.07[/tex]

Finally

[tex]1 - \alpha = 1 - 0.07 = 0.93[/tex]

The interval is constructed at 93% confidence.