A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 7.6 reproductions and the population standard deviation is known to be 2.2. If a sample of 707 was used for the study, construct the 90% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.

Step-by-step explanation:

The radians is just the length of the arc, so if you had a unit circle where the radius was 1, the length of that entire circle would be [tex]2\pi[/tex] since the circumference of any circle is [tex]2\pi r[/tex] except r is 1 so the length is just [tex]2\pi[/tex]. So if you take 1/4 of this you get [tex]\frac{2\pi}{4}[/tex] which can be simplified to  [tex]\frac{\pi}{2}[/tex]

Answer:

Step-by-step explanation:

Comments

You need to get the radian measure of the circle.

The radian measure of the entire circle is 2 * pi

To get the radian measure of 1/4 of the circle, just divide by 4.

2 pi / 4 = pi/2

The central angle is = to 1/4 of the circumference of the circle.

So the central angle is also pi/2

Answer: pi/2

Answer: 55°

Step-by-step explanation:

Hi!

since an angle bisector splits it in half,

110°, being the entire angle divided by 2 = 110/2 = 55°

Answer: Mustafa is incorrect. He made a mistake in step 2.

Step-by-step explanation: Mustafa was certainly correct in step 1 that x(9x+3) + 3(x+3) is 9x^2 + 6x + 9. However when he was factoring, he made a mistake.

(3x + 3)^2 is NOT equal to 9x^2 + 6x + 9. Rather, (3x + 3)^2 is equal to 9x^2 + 18x + 9. If you want to double check this, use FOIL.

The correct factoring of 9x^2 + 6x + 9 is actually 3(3x^2 + 2x + 3). So, Mustafa made a mistake in step 2.

Answer:

Just look at the other answer

Step-by-step explanation:

Answer:

f is always positive on the interval.

Step-by-step explanation:

Answer:

7x-13y=-117

Step-by-step explanation:

I don't know how this question wants me to solve it, but I just used the slope intercept form. So first, start off with y = mx+b. Plug in the slope for m, so 7/13. Then plug in your points for x,y which is 0,9. You'll get 9 = b. So then you have y = 7/13x+9. So now you need to change into standard form. So, multiply by the denominator (13) and you'll get 13y = 7x+117. Then move the variable over and you'll get 13y - 7x = 117. But it doesn't fit any, so then just multiply by -1 and you'll get -13y + 7x = -117.  

Answer:

Ista is 11 years old. Her father is 46 years old.

Step-by-step explanation:

Let ista's age be x.

Fathers age=4x+2.

Fathers age + Ista's age = 57.

4x+2+x=57.

Combine like terms:

5x+2 -2 =57 -2

5x=55

x=11

Fathers age: 4(11)+2

= 46

If ista father has an age that is 2 years greater than four times her age. The sum of their ages is 57 years. Then ista age is 11 and her father age is 46.  

Two or more expressions with an equal sign is called as equation.

Given that,

ista father has an age that is 2 years greater than four times her age.The sum of their ages is 57 yeasrs

Let the age of ista be x.

ista father has an age that is 2 years greater than four times her age.

it means father age = 2+4x

The sum of ista age and her father age is 57.

So x+(2+4x)=57

Add the common terms

5x+2=57

Subtract 2 from both sides

5x=55

Divide both sides by 5

x=11

Hence ista age is 11 and her father age is 46.

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If line J is perpendicular of line K, they should cross to make an X. If the slope of line K is -5, Line J would be 5.

The first four terms of the sequence are 8,12,16 and 20.

Given the function is f(n) = (2n+2)2

Now, we want first four terms, therefore, putting 1, 2, 3, 4 in the sequence we get:

f(1) = (2*1+2)2 = 8

f(2) = (2*2+2)2 = 12

f(3) = (2*3+2)2 = 16

f(4) = (2*4+2)2 = 20

Hence, The first four terms of the sequence are 8,12,16 and 20.

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Answer:

A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school? and "how old are you?" are statistical questions.

Step-by-step explanation:

Answer:

22.25

Step-by-step explanation:

take the two values away

the sector is the full address , the triangle is in it. the segment is the bit left near the circumference

The value of y for the system of equation is -1/2 .

A system of equation is a set of equation that have common solution

The set of equation given is

3x+4y=4

2x−4y=6

To solve the system , Elimination method will be used

Add equation 1 and 2 to eliminate y

5x  = 10

x = 2

Substitute the value of x in equation 1 to determine y

3x +4y = 4

6 + 4y = 4

4y = -2

y = -1/2

Therefore the value of y for the system of equation is -1/2 .

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Answer:

62 and 64

Step-by-step explanation:

Let x be the first number

Let y be the 2nd number

Given,

x + 2 = y (Consecutive even numbers)

x - y = -2 (rearranged) - Equation 1

x + y = 126 - Equation 2

Now we can solve for x and y to find the 2 numbers by using substitution method in solving simultaneous equations.

x = y-2 (rearranged equation 1)

Now we substitute equation 1 into equation 2.

y - 2 + y = 126

2y - 2 = 126

2y = 126 + 2

2y = 128

y = 128 / 2

= 64

Now we will substitute y into equation 1.

x - 64 = -2

x = -2 + 64

= 62

Therefore the 2 numbers are 62 and 64.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find two consecutive even numbers whose sum is 126.

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

For now, let the first number be x.

Let the second number be x+2. (consecutive even numbers are right next to each other, like 2 and 4)

These two integers add up to 126. This gives us an equation that we can solve in terms of x.

[tex]\bf{x+x+2=126}[/tex] | arrange the like terms

[tex]\bf{2x+2=126}[/tex] | subtract 2

[tex]\bf{2x=124}[/tex] | 2 was subtracted from BOTH sides

[tex]\bf{x=62}[/tex]

[tex]\cline{1-2}[/tex]

Now, the second integer is [tex]\bf{x+2}[/tex].

[tex]\bf{So\;let's\;put\;the\;first\;number\;into\;the\;formula\;x+2}[/tex].

[tex]\bf{62+2}[/tex] | add (mental arithmetic)

[tex]\bf{64}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                  [tex]\bf{=Number\;1=62}\\\\=Number\;2=64[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

[tex]p(c) = 0.6 \\ p(ch) = 0.59 \\ p(any)= 0.77[/tex]

[tex]p(both) = p(c) + p(ch) - p(any) \\ p(both) = 0.6 + 0.59 - 0.77 \\ p(both) = 0.42[/tex]

Answer:

x = 0

Step-by-step explanation:

if 2y + x = 4

we can assume that y = 2
if y - 3x = 2

it means 2 - 0 = 2

therefore x = 0

The conclusion is that there is sufficient evidence to support the claim that the percentage of vacant housing units in their district differs from the percentage of vacant housing units in the country.

Given that the total number of a housing units in her country is 550 and the number of vacant housing units in her country is 130.

The Null hypothesis is p₀=13%=0.13, n=550 and x=130

Significance level α=0.05

Claims given: percentage other than 13%

The claim is anyone of the null hypothesis or the alternative hypothesis. The null hypothesis shows that the proportion of the population is equal to the value stated in the claim. If the null hypothesis is a claim, then the alternative hypothesis states the opposite of the null hypothesis.

H₀:p=13%=0.13

Hₐ:p/0.13

I'm interested in testing population proportion claims, so I'll use z-text with proportions.

Conditions: Random sample, 10% condition, pass / fail condition

Sample: I'm happy because the housing units were randomly selected.  10% Condition: We are happy because the sample of 550 homes in your county is less than 10% of the population.

Pass/ fail condition: Satisfied because both np₀ and n(1-p₀) are both at least 10.

np₀=550(0.13)=71.5≥10

n(1-p₀)=550(1-0.13)=478.5≥10

Therefore, we conclude that all the conditions are met.

The sample percentage is the number of successes divided by the sample size.

[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{130}{550}\\ &\approx 0.2364\end[/tex]

Determines the value of the test statistic:

[tex]\begin{aligned}z&=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \\ &=\frac{0.2364-0.13}{\sqrt{\frac{0.13(1-0.13)}{550}}}\\ &=\frac{0.1064}{0.0143}\\&\approx 7.41 \end[/tex]

The P-value is the probability of getting a test statistic value  or a  more extreme value if the null hypothesis is true. Use the normal probability table in the appendix to determine the P-value.

P=P(Z<−7.41 or Z>7.41)

P=2P(Z>7.41)

P=2(0)

P=0

If the P-value is less than the significance level α,  the null hypothesis is rejected.

P<0.05⇒ Reject H₀

Therefore, there is ample evidence to support the claim that the proportion of vacant homes in the area is different from the proportion of vacant homes in the country.

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Answer:

See below.  I assume that (x) = 8x2 - 7x + 3 is really (x) = 8x^2 - 7x + 3

Step-by-step explanation:

Substitute the value of x given in f(x) into the equation f(x) = 8x^2 - 7x + 3

For example, f(0) would be f(0) = 8(0)^2 - 7(0) + 3.  f(0) = 3

f(-2) would be f(-2) = 8(-2)^2 - 7(-2) + 3.  

                                =   8*4  + 14 +3

                                = 32 + 17        therefore      f(-2) = 49

x f(x)

-2 49

-1 18

0 3

1 4

2 21

Answer:

.5

Step-by-step explanation:

Point = P (1, 0, -2)

Origin= 0 (0, 0, 0)

The distance formula in 3D = √(n2 - n1)² + (y2 - y1)² + (Z2 - Z1)²

                                             = √(1 - 0)² + (0 - 0)² + (-2 - 0)²

                                             = √1 + 4

                                             = √5

As a special case of the distance formulation, think we need to recognize the distance of a point (x,y) to the beginning. in step with the gap formula, this is √(x−0)2+(y−0)2=√x2+y2. A point (x,y) is at a distance r from the starting place if and simplest if √x2+y2=r, or, if we square each aspect: x2+y2=r2.

Conclusion: The method to find the distance among the two factors is commonly given with the aid of d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the gap among any two factors on a coordinate aircraft or x-y plane.

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The compound periods and Interest rates for compound interest have been explained below.

1) Compound Periods (n); If we want to calculate the compound interest, the number of compounding periods makes a significant difference due to the fact that the higher the number of compounding periods, the greater the amount of compound interest.

2) Interest rate per compounding periods (I); This affects the interest rate compounded annually due to the fact that the interest rate will be compounded once a year.

Complete question is;

In your own words and using visuals, explain the following. Regarding compound interest, how does the number of times interest is compounded per year affect the:

a) number of compounding periods (n)

b) interest rate per compounding period (i)

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The computation of the decimals are illustrated below.

1. 7/4 + √5

= 1.75 + 2.24

= 3.99

2. -✓2 + 9

= -1.41 + 9

= 7.59

3. 2 - 5/4

= 2 - 1.25

= 0.75

4. 7.93 + 1/7

= 7.93 + 0.14

= 8.07

5. π + ✓5

= 3.14 + 2.24

= 5.38

6. ✓2 + 13/4 - 3

= 1.41 + 3.25 - 3

= 1.66

7. 8.5 - 12.65

= -4.15

8. 4 + ✓3 - 11/3

= 4 + 1.73 - 3.67

= 2.06

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Length = 7 + 2x [L]

Breadth = 6 + x [B]

So, Area = L × B

=> Area = (7 + 2x) (6 + x)

=> Area = 7 × 6 + 7x + 2x × 6 + 2x²

=> Area = 42 + 7x + 12x + 2x²

=> Area = 2x² + 19x + 42

Option B is correct.

Any questions, you may ask.

Answer: b.) 2x² + 19x + 42

Area of rectangle:

⇒ Length × Width

⇒ (6 + x) × (7 + 2x)

⇒ 6(7) + 6(2x) + x(7) + x(2x)

simplify

⇒ 42 + 12x + 7x + 2x²

arrange

⇒ 2x² + 19x + 42

Answer:

A

Step-by-step explanation:

1) given

2) definition of an angle bisector

3) reflexive

4) [tex]\triangle ABD \cong \triangle CBD[/tex] (ASA)

5) [tex]\angle A \cong \angle C[/tex] (CPCTC)

The statements that are true are B, C, and F.

Here we have the exponential function:

[tex]f(x) = 4*5^x[/tex]

We can see that the initial value is 4, and the base is 5. Because the base is larger than 1, this is an exponential growth function.

The statements that are true are:

B: The domain of an exponential function is always the set of all real numbers.

C: Is an exponential growth, so yes, it is increasing.

F: The y-intercept is given by evaluating the function in x = 0, when you do that, you get the initial value, which is 4. So the y-intercept is (0, 4).

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Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the increase or decrease in the size of a figure.

Figure A maps to figure B with a scale factor of 4/9, hence:

4/9 * x = 16

x = 54

Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

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The height of 70 inches, and location of the wristband as well as the period of 15 seconds gives the function for the height of the wristband as the equation;

The model for the height can be derived from the general form of the sine function as follows;

Maximum point = 70 - 4 = 66 at t = 0

Minimum point = 4

Amplitude, A = (66 - 4) ÷ 2 = 31

D = 4 + 31 = 35

At t = 0, we have;

66 = 31 × sin(B × 0 - C) + 35

31 = 31 × sin(- C)

sin(- C) = 1

C = -π/2

1 minute = 60 seconds

1 second= 1 minute/60

15 seconds = (15/60) minutes

Period = 15 seconds = 15/60 minutes

Period = 2•π/B

Therefore;

15/60 = 2•π/B

1/4 = 2•π/B

B = 2•π/(1/4) = 8•π

y = Height of the function

Let h represent the height of the wristband.

The equation for the height is therefore;

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50

---- ×700=350

100

700-350=350

Therefore 350 grams is left in a person's system after 5 hours

Answer: $12.63

Step-by-step explanation:

$14.87 + $7.76 = $22.63

2pizzas x $5 = $10

$22.63 - $10 = $12.63

The procedure to rewrite the standard form in slope intercept form is as shown below.

The standard form of the equation of a line is;

ax + by + c  = 0

Slope intercept form is;

y = mx + c

Intercept form is;

x/p  + y/q = 1    

To Convert ax + by + c  = 0  into  y = mx + c

1) Move ax and c to the right hand side to get;

by = -ax  - c

Divide both sides by b to get;

y = - ax/b  - c/b

Comparing to slope intercept form, we can say that;

Slope = -a/b

y-intercept = -c/b

If we are using y = mx + b as slope intercept form, this will also be accurate because we will just switch c with b in the standard form to arrive at same answer.

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At least 832 teenagers must be interviewed.

It is given that the standard deviation is of 1.24 liters.

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2}[/tex] = 0.005

Now, we have to find z in the Ztable as such z has a p-value of [tex]1-\alpha[/tex].

So it is z with a p-value of [tex]1-0.005 = 0.995[/tex], so [tex]z= 2.575[/tex]

Now, find the margin of error M as such

[tex]M = Z * \frac{SD}{\sqrt{n} }[/tex]

In which SD is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liters when constructing a 99% confidence interval?

At least n teenager must be interviewed.

n is found when M = 0.1.

We have that SD = 1.12

So

[tex]0.1 = 2.575*\frac{1.12}{\sqrt{N} }[/tex]

[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]

[tex]n = 831.7[/tex]

So rounding up to at least 832 teenagers must be interviewed.

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