he points ​(​12,10​) and ​(30​,25​) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.

(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

Given that,

One thousand bacteria make up a culture at the beginning. The number of bacteria is 8000 after an hour.

We have to find

(a) Track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, locate the population.

(c) How long will it take for there to be 15,000 bacteria?

(d) Draw the population function's graph.

We know that,

(a) The initial size of the culture is 1000 bacteria.    

So,  

n₀=500

The size of the culture after one hour (for t =1) is 4000 so we extract the equation:

n(1) = 8000

1000er¹=8000

e to the power of r =8

[taking logarithms both side]    

r ln e  =  ln 8                          

r=2.080

[ln e  =  1]

So, we got  

n₀=1000 and r=2.08

The function will be,

n(t)=1000[tex]e^{2.08t}[/tex]

(b) for t = 1.5

n(1.5)=1000[tex]e^{2.08(1.5)}[/tex]

22646

(c) 15000=1000[tex]e^{2.08t}[/tex]

15=[tex]e^{2.08t}[/tex]

Taking log on both sides

ln15= 2.08(t)lne

t=3.68/2.08

t=1.7

(d) Since we have have the exponential equation therefore our graph should be curve not straight line.

Also at t=1, population of bacteria is 4000

Hence the correct graph will be in picture.

Therefore,

(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

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If the base of the right triangle is 6 and the perpendicular height is 8 , then the length of the hypotnuse is  10 .

In the question ,

it is given that ,

the base of the right triangle is 6 , and

the height of the perpendicular is 8 ,

let the length of the hypotnuse of the given triangle be = h

Since the triangle is a right triangle , So , it follows Pythagoras Theorem ,

that means ,

h² = 6² + 8²

h² = 36 + 64

h² = 100

Simplifying further ,

we get ,

h = 10

Therefore , the length of the hypotnuse is = 10 .

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Answer$200+$50x

Step-by-step explanation:

Answer:

4 Months

Step-by-step explanation:

if X = total (not sure)

thats means you must do $200 / $50 = 4 Months

Answer:

50%

Step-by-step explanation:

It is a half chance, you could be lucky

There is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

In inferential statistics, the null hypothesis states that two possibilities are equal.

The observed difference is thought to be the sole product of chance, which is the underlying premise.

Statistical tests can be used to calculate the likelihood that the null hypothesis is true.

So,

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

As the population standard deviation is given when n > 30

So, we'll run the Z test.

Formula: [tex]z=\frac{x-\mu}{\frac{a}{\sqrt{n}}}[/tex]

Replace the values:

[tex]\begin{aligned}& z=\frac{7.7-7.6}{\frac{11.6}{\sqrt{160}}} \\& z=2.449\end{aligned}[/tex]

For the p-value, see the z table.

Consequently, p = 0.9927.

The two-tailed nature of the test So, p = 2(1- 0.9927) = 0.0146

α = 0.1

p value< α

Thus, we disregard the null hypothesis.

Hence, at the 0.1 level, there is enough evidence to conclude that the valve does not function as intended.

Therefore, there is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

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Answer:

t >28= the temp is warmer than 28

t >29= the table is heavier than 29 kilos

t <29= tony is you get than 29 yrs old

t <28= tia ran the race in under 28 secs

Step-by-step explanation:

hope this helps

The number of ways there for the 125 pages to be assigned to the four printers = 5^125 ways.

As per the question,

A 125-page document is being printed by four printers.

Each page will be printed exactly once.

There are no restrictions on how many pages a printer can print.

One of the possible combinations is that printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90 and printer D prints out pages 81-85 and 91-100.

Since, there are no restrictions in printing the pages any printer cannot print even a single page and any printer can print all 125 pages. To print 100 pages we have four printers.

⇒ Number of possible ways a single paper can be assigned to the four printers = 4 ways

⇒ Number of possible ways 125 pages can be assigned to the four printers

=  5 × 5 × 5 × 5 .................... 5 ( a total of 125 terms )

=     ways.

Therefore, In   ways we can assign 125 pages to four printers with no restrictions.

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The increase in the salary for Charolette will be $251.65.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since Charolette earns 3,595 per month at her job. She will receive a 7% raise. The amount of raise will be calculated by simply multiplying the percentage that she was given for the raise in the salary by the initial salary that she was earning.

This will be illustrated thus:

= Percentage × Salary

= 7% × $3595

= $251.65

The value of $251.65 will the increase in the salary.

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Answer: [tex]512x^3+960x^2+600x+125[/tex]

Step-by-step explanation: Start by spreading the expression out so it turns into (8x + 5)*(8x + 5)*(8x + 5). (* means multiply). Then, foil (multiply the first numbers, outside numbers, inside numbers, and last numbers to form a new expression) the first two expressions to get 64x^2+80x+25*(8x + 5). Foil that again, going through and multiplying each number from both expressions by every number in the other expression to get 512x^3+960x^2+600x+125. Hope that helps.

Answer:

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Perfect Cube Formula}\\\\$\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$\\\end{minipage}}[/tex]

To find the product of the given expression, use the perfect cube formula.

Given expression:

[tex](8x + 5)^3[/tex]

Therefore:

Apply the perfect cube method:

[tex]\begin{aligned}(8x+5)^3&=(8x)^3+3(8x)^2(5)+3(8x)(5)^2+5^3\\&=8^3 \cdot x^3+3 \cdot 64x^2\cdot5+3\cdot 8x\cdot 25+125\\&=512x^3+960x^2+600x+125\end{aligned}[/tex]

Answer:

just telling you but we need to see the image which we cannot but I'm not entirely sure but I think it's 2 although I cannot see the image and the other one is 4 I thinke

Using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

So, we have -9 - 9√3i:

This quantity has a modulus.

|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18

And argument θ to the effect:

tan(θ) = (-9√3) / (-9) = √3

We anticipate that will be between -π and -π/2 radians since -9-9√3i lies in the third quadrant of the complex plane, so that:

θ = arctan(√3) - π = π/3 - π = -2π/3

The polar form is then:

18 (cos(-2π/3) + i sin(-2π/3))

And since -2π/3 is the same angle as 2π - 2π/3 = 4π/3, the right answer is: 18 (cos(4π/3) + i sin(4π/3))

Therefore, using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

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Complete question:
What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot?

a. 9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

b. 9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

c. 18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

d. 18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Answer:

18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Step-by-step explanation:

D

Answer:

Step-by-step explanation:

Answer:

<XWZ ≅ < XZW  by alternate interior angles & WZ = WZ by reflexive property

Step-by-step explanation:

Because they're parallel lines cut by a transversal. So, <W is where one angle is, and <Z is where another angle is. They both share a side as well. Always look out for those types of triangles because those are types of hidden information

Answer: x = 6

Step-by-step explanation:

2x + 7 = 9x - 35

-7x + 7 = -35

-7x = -42

x=6

The box's dimensions that reduce the overall cost of the materials are as follows:

L = W = 16 cm

H = 32 cm

Given,

What is the dimensions of the rectangle?

A rectangle has two dimensions: a length and a width that are both perpendicular to it. The interior of an oval or a triangle also has two dimensions.

Here,

We've got

Volume = 512 cm3 L* W * H

Sides of the box cost = 1 cent/cm²

Top and bottom cost 2 cent/cm²

Then,

Box dimensions that reduce the overall cost of materials used

We are aware of

L× W × H = 512 cm³

Where,

L stands for length, W for width, and H for height.

So, when we reduce the cost function

C(L, W, H) = (1) 1 H + (2) 1 (L + W)

Thus insert H.

Replacing H with 512/LW yields,

C(L, W) = 512(1/L, 1/W), plus 2LW

So

When both partial derivatives are 0, there will be a minimum cost.

512/L2 - 2W = dC/dL = 0

So

512/W2 - 2L = 0 for dC/dW.

L = 256/W²

Now

The answer to the aforementioned equation is

L = W = (256)⁻³ = 16cm

And

H = 512/16 = 32

H = 32 cm

Consequently, the box's measurements that reduce the overall cost of the materials utilized are:

L = W = 16 cm

H = 32 cm

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Answer:

557

Step-by-step explanation:

7,241 divided by 13 = 557

The angle between the two vectors (4,1) and (-8,3) will be 145.4°.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is possible to calculate the angle () between two vectors using the formula

[tex]\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

Calculate dot product:

=a · b

= ax · bx + ay · by

= 4 · (-8) + 1 · 3

= - 32 + 3

= -29

=|a|

= √ax² + ay²

= √4² + 1²

= √16 + 1

= √17

=|b|

=√ bx² + by²

= √(-8)² + 3²

= √64 + 9

= √73

[tex]\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

α = 145.40771131249005°

Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.

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Answer:

  13.5, 17.5

Step-by-step explanation:

You have two numbers whose sum is 31 and whose difference is 4. The second number is larger.

Let x represent the larger number. Then the smaller is x-4, and their sum is ...

  x +(x -4) = 31

Simplifying the expression gives ...

  2x -4 = 31

  2x = 35 . . . . . add 4

  x = 17.5 . . . . . divide by 2

  x -4 = 13.5

The two numbers are 13.5 and 17.5.

__

Additional comment

As we have seen here, the larger number is half the total of the 'sum' and 'difference'. (31+4)/2 = 17.5. This is the generic solution to any "sum and difference" problem.

Answer:

94

Step-by-step explanation:

if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pig with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

Answer:

Step-by-step explanation:if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pit with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

The compound interest after 5 years is $7,081.916.

Compound interest:

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Here we have to find the interest earned after 5 years.

Data given:

Principle (P) = $11600

rate(r) = 10%

time(t) = 5 years.

Formula to find compound interest:

CI = P( 1 + r/100[tex])^{t}[/tex] - P

Now put the values in the formula.

CI = 11600 ( 1 + 10/100[tex])^{5}[/tex] - 11600

  = 18681.916 - 11600

  = 7081.916

Therefore the compound interest is $7081.916.

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Answer:

M+N is defined

All others not defined

Step-by-step explanation:

Two matrices can be added or subtracted if and only if they have the same dimensions i.e. they must have the exact same number of rows and number of columns

Only M and N with dimensions (4 x 2) each can be added or subtracted.

(4 x 2 ) means 4 rows and 2 columns

So the only defined operation is
M + N

All the others are not defined

Answer:

[tex]\textsf{De\:\!fined}: \quad \boxed{M + N}[/tex]

[tex]\textsf{Not\:de\:\!fined}: \quad \boxed{N - Q} \quad \boxed{Q + L} \quad \boxed{M - P}[/tex]

Step-by-step explanation:

Generally, a matrix is referred to as [tex]n\times m[/tex] where n is the number of rows and m is the number of columns.

Therefore:

Matrices can be added or subtracted only when they are the same size.

[tex]\boxed{N - Q}[/tex]

Matrices N and Q are different sizes. Therefore, the operation is not defined.

[tex]\boxed{M + N}[/tex]

Matrices M and N are the same size. Therefore, the operation is defined.

[tex]\boxed{Q + L}[/tex]

Matrices Q and L are different sizes. Therefore, the operation is not defined.

[tex]\boxed{M - P}[/tex]

Matrices M and P are different sizes. Therefore, the operation is not defined.

Answer:Y=1/2x+2

Step-by-step explanation:

Slope intercept form is y=mx+b

m=slope

b= y intercept

y=1/2x+2

The difference between these distances on the Earth is 3.32 × 10⁴.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression that shows the multiplication for the same number. Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. Exponents are used to show repeated multiplication of a number by itself

Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.

The difference will be:

= 4.00x10^4 km - 6.8x10^3 km.

= 3.32 × 10⁴

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w should be equal to 92° to prove that r || s.

To prove whether the two lines are parallel we should know whether

So for the given condition, the diagram is drawn. Mark the angles w, x, y, and z.

From the diagram, by the Corresponding Angles Theorem, ∠w=∠92°.

The answer is w. Therefore, option a is correct.

The complete question is -

Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?

a)w

b)x

c)y

d)z

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Answer: 14 degrees.

Step-by-step explanation: The sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, if we know the measures of two of the interior angles of a triangle, we can use this fact to find the measure of the third angle.

In this case, we are given that two of the interior angles of the triangle have measures of 54 and 112 degrees. We can use this information to find the measure of the third angle as follows:

180 degrees = 54 degrees + 112 degrees + x

180 degrees = 166 degrees + x

x = 180 degrees - 166 degrees

x = 14 degrees

Therefore, the measure of the third angle of the triangle is 14 degrees.

The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

Let the number of number of red pencils be 'x'.

Total blue pencils = 5.

Ratio = blue pencils/red pencils

5/x = 1/2

x = 5 x 2

x = 10

Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

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Answer: rate of change is 2

Step-by-step explanation: