Apr 23, 8:46:54 AM
What is the missing term?

Answer:

The speed of the current is 3 miles per hour

Step-by-step explanation:

The equations for rate (r), distance (d), and time (t) are ⇒ d = rt, r = d/t, = t = d/r

Let x = speed in still water

Let c = speed of the current

The main difference with these problems is rate needs to be expressed using two variables  because moving upstream the current is against you and downstream it moves with you.

Distance Rate Time

Upstream x − c

Downstream x + c

The distance column with the numbers from the problem and the value for speed in  still water for x.

Distance Rate Time

Upstream 4 5 − c

Downstream 16 5 + c

The column for time using the other two columns knowing that  rate,  distance  ⇒ time =  Distance Rate Time

Upstream 4 5 − c

5 − c

4

Downstream 16 5 + c

5 + c

16

“It takes as long …” from the problem means that the two times are equal to each other.  So, the equation can be written as:

4/5− c = 16/5 + c  ⇒ Solve by cross-multiplying ⇒ 5(4 + c) = 16 5( − c) ⇒ c = 3

Answer:

The hourly growth rate is of 4.43%.

The function showing the number of bacteria after t hours is [tex]P(t) = 80(1.0443)^t[/tex]

Step-by-step explanation:

Equation of population growth:

The equation for the population after t hours is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

The conditions are such that the number of bacteria is able to double every 16 hours.

This means that [tex]P(16) = 2P(0)[/tex]. We use this to find r.

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]2P(0) = P(0)(1+r)^{16}[/tex]

[tex](1+r)^{16} = 2[/tex]

[tex]\sqrt[16]{(1+r)^{16}} = \sqrt[16]{2}[/tex]

[tex]1 + r = 2^{\frac{1}{16}}[/tex]

[tex]1 + r = 1.0443[/tex]

[tex]r = 1.0443 - 1[/tex]

[tex]r = 0.0443[/tex]

The hourly growth rate is of 4.43%.

80 bacteria are placed in a petri dish.

This means that [tex]P(0) = 80[/tex].

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 80(1+0.0443)^t[/tex]

[tex]P(t) = 80(1.0443)^t[/tex]

The function showing the number of bacteria after t hours is [tex]P(t) = 80(1.0443)^t[/tex]

Answer:

The initial height of the leaf is 18 feet. (False)

The leaf falls at a rate of foot every 1 second. (False)

The leaf is 3 feet above the ground after 6 seconds. (True)

Answer:

C. Addition Property of Equality

Step-by-step explanation:

Given,

x - 6 = 4

To find x, the addition property of equality is applied by adding 6 to both sides.

Thus:

x - 6 + 6 = 4 + 6

x = 10

Answer:

30 cm^3

Step-by-step explanation:

for find the volume we have to multiply the three numbers:

V = 5 x 2 x 3 = 30 cm^3

Answer:

-9.25 in decimal form

-9 1/4 :) in fraction form

hope this helps here is the explanation on how I got this answer :)!

therefor it will be the last answer :)

Step-by-step explanation:

-9.25

= –  9.25 × 100

1 × 100= –925

100

= –  925 ÷ 25

100 ÷ 25

= –  374

= – 9 1/4

Answer:

its the second one

Step-by-step explanation:

see image below

Answer:

H0 : μ = 4.50

H1 : μ > 4.50

Test statistic = 1.525

we conclude that there is no sufficient evidence to conclude that the mean wait time for customers is longer than 4.50.

Step-by-step explanation:

H0 : μ = 4.50

H1 : μ > 4.50

Test statistic :

(xbar - μ) ÷ s/sqrt(n)

(4.94 - 4.50) ÷ 2.10/ sqrt(53)

0.44 / 2.10/ sqrt(53)

= 1.525

α = 1 - 98% = 0.02

Decision region :

Reject H0 ; if Pvalue < α

Pvalue = p(Z < 1.525) = 0.936

Pvalue = 0.936

Since Pvalue > α ; We fail to reject H0

Hence, we conclude that there is no sufficient evidence to conclude that the mean wait time for customers is longer than 4.50.

Answer:

The answer to your question is the letter C

Answer:

I think it is c

Step-by-step explanation:

Answer:B 1072.5 ft^3

Step-by-step explanation: The steps are in the picture

Answer:

C

Step-by-step explanation:

So you can use two points on the line to find the gradient. I used K and G. B and D could've been easily eliminated since the line goes through the origin (0,0) so there's no y - intercept or b value.

M = (Y-y)/(X-x)

M = (8-4)/(14-7)

M = 4/7

And the equation of a line is y = mx + b. There's no b so it's just y = (4/7)x

Answer:

10.8°degrees

Step-by-step explanation:

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Answer:

45

Step-by-step explanation:

100-64 is 36. 36% paid with cash 125×35%=45 or 125×.36=45

Answer:

The value of the acount after t years is of [tex]A(t) = 650(1.0072)^{12t}[/tex]

The annual growth rate is of 0.72%.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

$650 is invested in an account earning 8.6% interest (APR), compounded monthly.

This means that [tex]P = 650, r = 0.086, n = 12[/tex]. So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(t) = 650(1 + \frac{0.086}{12})^{12t}[/tex]

[tex]A(t) = 650(1.0072)^{12t}[/tex]

The value of the acount after t years is of [tex]A(t) = 650(1.0072)^{12t}[/tex]

Annual growth rate

1.0072 - 1 = 0.0072 = 0.72%

The annual growth rate is of 0.72%.

9514 1404 393

Answer:

  (x, y) = (0, 4)

Step-by-step explanation:

Since we have an expression for x, substitution works nicely.

  (8 -2y) +3y = 12 . . . . . . use the first equation to substitute for x in the 2nd

  y = 4 . . . . . . . . . . . . subtract 8, collect terms

  x = 8 -2(4) = 0 . . . . substitute for y in the first equation

The solution is (x, y) = (0, 4).

Answer:

7

Step-by-step explanation:

It adds 2 each time to the function. Y-Intercept is 1, so you add 2 three times.

2*3=6

6 plus the starting dog (1)= 7

Answer:

Plzzzz answer fast......

Answer:

Um what’s the question?

Step-by-step explanation:

Answer:

*links* hope this helped!

Step-by-step explanation:

Answer:

6,480in.3

Step-by-step explanation:

Hope this helps!

The volume of the aquarium is   6480 [tex]in. ^{3}[/tex]

A rectangular prism is a prism whose bases (the top face and the bottom face) are also rectangles. It has 6 faces in all, out of which there are 3 pairs of identical opposite faces, i.e., all the opposite faces are identical in a rectangular prism. It has three dimensions, length, width, and height.

The volume of a rectangular prism is the space that is inside it .

The volume of the rectangular prism, V = Length * Breath * Height

According to the question

Length of the aquarium = 36 in.

Breath of the aquarium = 12 in.

Height of the aquarium = 15 in.

As aquarium is a rectangular prism

volume of the aquarium,  = Length * Breath * Height

                                                            =   36 * 15 * 12

                                                            =    6480 [tex]in. ^{3}[/tex]

Hence, The volume of the aquarium is   6480 [tex]in. ^{3}[/tex]

To know more about rectangular prism here:

https://brainly.com/question/21308574

#SPJ2

Answer:

EF = 34

Step-by-step explanation:

(9x + 23)/2 = 6x + 4

9x + 23 = 12x + 8

3x = 15

x = 5

EF = 6(5) + 4 = 34

Answer:

see the answers below

Step-by-step explanation:

Given data

P=$4,250

Rate= 5.25%

Time= t years

1. The compound interest expression is

A=4250(1+0.0525)^t

A=4250(1.0525)^t

2. P=$4,250

Rate= 5.25%

Time= 5 years

1. The compound interest expression is

A=4250(1+0.0525)^5

A=4250(1.0525)^5

A=4250*1.2915

A=$5488.875

3. P=$4,250

Rate= 5.25%

Time= 10years

1. The compound interest expression is

A=4250(1+0.0525)^10

A=4250(1.0525)^10

A=4250*1.6680

A=$7089

Answer:

5 units squared

Step-by-step explanation:

To find the area of a triangle, the formula is base * height/2

the base of this triangle is 2 while the height is 5

area = (2*5)/2

area = 5 units squared

Answer:

$600

Step-by-step explanation:

Let x = og price

x - 0.29x = 426

0.71x=426

÷0.71 ÷0.71

x = 600

Answer:

.......................................................................................................................

Step-by-step explanation:

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Answer:

(b) 2 / (1/6) = 2 * (6/1) = 12

(a)There are six sixths in a whole. In terms of numbers, 6/6 = 1.

Answer:

6 sixths in one whole and 12 sixths in 2.

Answer:

calculate P(X=1) + P(X=2) +...+ P(X=12) using the binomial formula or an individual table in excel

calculate the P(X ≥ 12) using the binomial formula or a cumulative table in excel

Step-by-step explanation:

For a binomial distribution :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

n = number of trials = 12 ; x = number of successes

p = probability of success = 0.2% = 0.002

1 - p = 1 - 0.002 = 0.998

Probability that atleast 1 is broken ;

p(1) + p(2) + p(3) +... + p(12) ;

This can be calculated by summing the values obtained using the binomial formula or in excel.

Alternatively, using the binomial formular or excel, the cumulative probability could be obtained as P(x ≥ 1)