If you can buy 4 containers of pudding for $4.20 how much can you buy for $9.45 math problem PARAMETERS
*** 7 STEPS ***

In around 6.35 years, the population will be 1 million.

The population is modeled by the exponential equation:

[tex]P(t) = 232,012*e^{0.23*t}[/tex]

Then we just need to solve the equation for t:

[tex]P(t) = 232,012*e^{0.23*t} = 1,000,000[/tex]

Let's solve that:

[tex]232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\[/tex]

If we apply the natural logarithm to both sides:

[tex]ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35[/tex]

So in around 6.35 years, the population will be 1 million.

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let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".

[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}[/tex]

When [tex]n=0[/tex], we have

[tex]5^{3^0} + 1 = 5^1 + 1 = 6[/tex]

[tex]3^{0 + 1} = 3^1 = 3[/tex]

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for [tex]n=k[/tex], that

[tex]3^{k + 1} \mid 5^{3^k} + 1[/tex]

Now for [tex]n=k+1[/tex], we have

[tex]5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)[/tex]

so we know the left side is at least divisible by [tex]3^{k+1}[/tex] by our assumption.

It remains to show that

[tex]3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1[/tex]

which is easily done with Fermat's little theorem. It says

[tex]a^p \equiv a \pmod p[/tex]

where [tex]p[/tex] is prime and [tex]a[/tex] is any integer. Then for any positive integer [tex]x[/tex],

[tex]5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3[/tex]

Furthermore,

[tex]5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3[/tex]

which goes all the way down to

[tex]5^{3^k} \equiv 5 \pmod 3[/tex]

So, we find that

[tex]\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3[/tex]

QED

The equation of the line in standard form is 6x - 7y = - 11

The standard form for linear equations in two variables is Ax + By = C.

Therefore, using (-3, -1)(1 / 2, 2)

y = mx + b

where

Hence,

m = 2 + 1 / 1  /2 + 3 = 6 / 7

Hence,

-1 = 6 / 7(-3) + b

- 1 = - 18 / 7 + b

-1 + 18 / 7 = b

b =  -7 + 18/ 7

b = 11 / 7

Therefore,

y = 6 / 7 x + 11 / 7

Using the standard form,

6 / 7 x - y = - 11 / 7

6x - 7y = - 11

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The linear equation in standard form is:

6x - 7y = -11

Which is the last option.

The line in slope-intercept form is written as:

y = a*x + b

We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:

[tex]a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}[/tex]

Then we can write:

y = (6/7)*x + b

To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:

-1 = (6/7)*-3 + b

-1 + 18/7 = b

-7/7 + 18/7 = b

11/7 = b

Then the equation is:

y = (6/7)*x + 11/7

If we multiply both sides by 7 we get:

7y = 6x + 11

Now we move the term with "x" to the left:

7y - 6x = 11

That is the line in standard form.

If we multiply both sides by -1, we get the last option:

6x - 7y = -11

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The number makes the expression a perfect square trinomial is 25.

Hence, we have v² - 10v + 25.

Given the expression; v² - 10v

To determine the number that makes the expression a perfect square trinomial, we divide the coefficient of v by 2 and square the result.

( -1 × 10/2 )²

(-1 × 5)²

( -5 )²

25

We add 25 to the expression to get a perfect square trinomial.

v² - 10v + 25.

Therefore, the number makes the expression a perfect square trinomial is 25.

Hence, we have v² - 10v + 25.

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Answer:

16[tex]n^{3}[/tex]

Step-by-step explanation:

we evaluate from left side to right side

so -2*n =-2n

-2n *8 = -16n

-16n * n =-16n^2

-16 n * -n =16 n^3

hope this helps

The rays and lines in the picture are as follows;

rays: BD, AC and AB

lines: AC

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.

A ray is named using its endpoint first, and then any other point on the ray

A line segment has two endpoints.

Therefore, the rays and lines are as follows:

rays: BD, AC and AB

lines: AC

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There are 80 students studying at least one language

The given parameters are:

Using the above parameters, we have:

German and French only = 5 - 3 = 2

Italian and French only = 10 - 3 = 7

Italian and German only = 8 - 3 = 5

French only = 42 - 7 - 2 - 3 = 30

German only = 30 - 2 - 5 - 3 = 20

Italian only = 28 - 7 - 5 - 3 = 13

See attachment for the Venn diagram

This is calculated as:

None + At least one = Total

Using the Venn diagram, we have:

None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100

This gives

None + 80 = 100

Subtract 80 from both sides

None = 20

Hence, there are 20 students studying none of the languages

This is calculated as

French only = French - French and Italian - French and German + All three

So, we have:

French only = 42 - 10 - 5 + 3

Evaluate

French only = 30

Hence, there are 30 students studying French only

In (b), we have:

None + At least one = Total ⇒ None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100

By comparing both equations, we have

At least one = 3 + 2 + 5 + 7 + 13 + 20 + 30

This gives

At least one = 80

Hence, there are 80 students studying at least one language

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In math, Exponentiation refers to the operation of raising one quantity to the power of another. See the program running the exponentiation below.

The code is given below:

number_of_days = 30

amount_after_30days = 0.01 * (2 ** number_of_days)

# print the amount

print(amount_after_30days)

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It is false that x is a function of y

The equation is given as:

x = y^2

Set y = 2

x = (2)^2

x = 4

Set y = -2

x = (-2)^2

x = 4

Different values of y give the same x value.

This means that x is not a function of y

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Answer:

1/6

Step-by-step explanation:

1/15 yellow, 1/10 green, and 1/20 white

1/15 + 1/10 is the probability for yellow or green.

2/30 + 3/30 = 5/30 = 1/6

Brainliest, please :)

The volume of the rectangular prism is of 28.6875 mm³.

The volume of rectangular prism of length l, width w and height h is given by:

V = lwh.

For this problem, the dimensions are:

Hence the volume is:

V = 2.125 x 6.75 x 2 = 28.6875 mm³.

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Answer:

best answer is c. (2,3),(4,4),(6,5),(8,6)

Step-by-step explanation:

multiply x and y components 2*3,4*4,6*5,8*6

14.11 is the price of one share in the company TYK.

Given:

Find:

Solution:

The dividend is the amount paid to the shareholders for their investment in the company.

Dividend at end of 7th year = $1 per share (given)

dividend expected growth rate = 6%  (given)

the dividend will be paid from the end of seven years.

So find the price of the share at the end of the 6th year.

price at the end of the 6th year

= Dividend at the 7th year/discount rate growth rate

= 1/(10%-6%) = 1/4% = 25

price of the share at the end of the 6th year is $25

discount price 10% (given)

current price share = 25/(1+10%)^6

                              = 25/(1.1)^6

                              = 25/1.77

                             = 14.11

The current price of the share is $ 14.11

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The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

Sequences are series of elements generated according to at least one condition, usually equations. geometric sequences are generated according to a exponential formulas, whose form and characteristics are described below:

f(n) = a · bⁿ ⁻ ¹    (1)

Where:

If we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:

f(12) = 4 · 2¹² ⁻ ¹

f(12) = 4 · 2¹¹

f(12) = 4 · 2,048

f(12) = 4,096

The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

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The cost of buying 32 shirts according to the function given is $268.

Given that the function f(x) = 8x + 12 represents the cost of ordered a shirt.

We need to find the cost to buy 32 shirts.

To find out how much it would cost to buy 32 shirts, you can use the given function f(x) = 8x + 12, where 'x' represents the number of shirts and 'f(x)' represents the cost of ordering 'x' shirts.

Let's plug in x = 32 into the function:

f(32) = 8 × 32 + 12

f(32) = 256 + 12

f(32) = 268

So, it would cost $268 to buy 32 shirts.

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Answer:

135 pi centimeters squared

Step-by-step explanation:

Hello!

where la is lateral surface area

[tex]first \: the \: formula \: for \: the \: lateral \: surface \: are \: of \: cone \: is \\ la = \pi \times r \times l \\ where \: r = radius \\ l = slant \: height \\ therefore.first \: find \: the \: radius(r) = \frac{d}{2} \\ r = \frac{18cm}{2} = 9cm \\ so \: as \: we \: have \: the \: radius \: we \: can \: solve \: for \: the \: la \\ la = \pi \times r \times l \\ la = \pi \times (9cm) \times (15cm) \\ la = 135\pi \: cm {}^{2} [/tex]

Answer:

c) 212 sq ft

Step-by-step explanation:

I don't know which ways you tried, but I will show you three different ways, and the answer will be the same using all three ways.

1) The length of the upper horizontal side is 8 ft + 12 ft = 20 ft

Think of a rectangle 20 ft by 16 ft with a rectangle 12 ft by 9 ft missing at the lower right corner.

area = 20 ft × 16 ft - 12 ft × 9 ft

area = 320 ft² - 108 ft²

area = 212 ft²

2) Break up the shape into an upper horizontal rectangle 20 ft long by (16 ft - 9 ft) = 7 ft wide and a lower left rectangle 9 ft high and 8 ft wide.

area = 20 ft × 7 ft + 9 ft × 8 ft

area = 140 ft² + 72 ft²

area = 212 ft²

3) Break up the shape into an left vertical rectangle 16 ft high by 8 ft wide and an upper right rectangle 7 ft high and 12 ft wide.

area = 16 ft × 8 ft + 7 ft × 12 ft

area = 128 ft² + 84 ft²

area = 212 ft²

Answer: c) 212 sq ft

Answer:

Step-by-step explanation:

espero ter ajudado

The function that represents the given trigonometric graph is; f(x) = cos (x)

From the given trigonometric Graph, we can see the following;

When x = 0, y = 1

When x = π/2, y = 0

When x = π, y = -1

When x = 2π, y = 1

Now, according to trigonometric functions in radians, we know that;

cos 0 = 1

cos  π/2 = 0

cos  π = -1

cos  2π = 1

These values correspond with what we have in the given trigonometric graph and as such we can say that the function that is graphed is;

f(x) = cos (x)

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The range of [tex]y =\log_8(x)[/tex] is the set of all real values

The function is given as:

[tex]y =\log_8(x)[/tex]

The above function is a parent logarithmic function.

The parent logarithmic function have a range of the set of all real values

Hence, the range of [tex]y =\log_8(x)[/tex] is the set of all real values

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Answer:

D

Step-by-step explanation:

on edg

The correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;

x^2 + 6x +8 +1  = 0 + 1

x^2 + 6x +8 +1  = 1

x^2 + 6x + 9 = 1

(x+3)² = 1

The vertex form of a quadratic equation is expressed as:

a(x-h)² + k

Given the quadratic equation

x^2 + 6x +8=0

Subtract 8 from both sides

x^2 + 6x +8 - 8 = 0 - 8

x^2 + 6x  = -8

Complete the square

(x^2+6x+3^2) = -8 + 9

(x+3)² = -8 + 9

(x+3)² = 1

Hence the correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;

x^2 + 6x +8 +1  = 0 + 1

x^2 + 6x +8 +1  = 1

x^2 + 6x + 9 = 1

(x+3)² = 1

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Answer:

200

Explanation:

126.8 x 100

126.8/63.4 = 200

The graph of function f is shifted right 3 units and up 4 units.

Let f(x) be the parent function

Now use the Rule : f(x)→f(x-b) to find the shifting of graph

The graph shifts right by b units

So, shift the graph by 3 unit

So, f(x)→f(x-3)

So, the graph shifted right by 3 units

2nd rule used is Rule : f(x)→f(x)+b to find the another shifting of graph

The graph shifts up by b units

Now shift the obtained graph up by 4 units

So,  f(x-3)→f(x-3)+4

So, the graph shifts up by 4 units

Thus, The graph of function f is shifted right 3 units and up 4 units.

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Option D, 4.1 is the correct answer. The mean baseball score is 4.1 given the table of values of baseball scores and score number of students. This can be obtained by using the formula for mean.

Mean can be obtained by the formula,

Mean = [tex]\frac{sum\ of\ observations}{total\ number\ of\ observations}[/tex]

Sum of basketball scores = 0×1 + 1×2 + 2×5 + 3×3 + 4×6 + 5×7 + 6×9

= 0 + 2 + 10 + 9 + 24 + 35 + 54

total number of basketball scores =  1 + 2 + 5 + 3 + 6 + 7 + 9 = 33

Mean = [tex]\frac{0+2+10+9+24+35+54}{33}[/tex] = 4.06 ≈ 4.1

Hence the mean baseball score is 4.1 given the table of values of baseball scores and score number of students. Option D, 4.1 is the correct answer.

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The 4 reasons for the Algebra proof are respectively;

Given; Distributive property; Addition Property; Division Property

We want to use algebra properties to find the value of x in the expression; -5(x + 4) = 90

Statement 1;  -5(x + 4) = 90

Reason 1; Given

Statement 2; -5x - 20 = 90

Reason 2; Distributive property of Algebra because we distributed -5 into the bracket terms.

Statement 3; -5x = 110

Reason 3; Addition property of equality because we added 20 to both sides to achieve that.

Statement 4; x = -22

Reason 4; Division property of equality because we divided both sides by -5 to obtain x = -22.

Thus, the 4 reasons are respectively;

Given; Distributive property; Addition Property; Division Property

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Answer:

telephone was $45, utility was $135

Step-by-step explanation:

Let the telephone bill be x, then the utility bill is 3x

3x+x = 180

4x = 180

x = 45

3x = 135

The equation y = -0.5x +45 represent the linear relationship.

According to the statement

We have given that the When she plants 30 stalks, each plant yields 30 oz of beans and When she plants 33 stalks, each plant produces 29 oz of beans.

And we have to find the linear relationship between the plants which are stalks.

So, For this purpose,

When we consider this graph as a straight line, the two points lying on the line would be

(30, 30) and (34, 28) taking n as horizontal and y vertical

Using two point equation we find that

the equation of the line is

y-y1 / y2-y1 =  x-x1 / x2-x1

Substitute the points as x =n and put the other values in it then

y-30 / 28-30 =  x-30 / 34-30

Then

y = -0.5x +45

This represent the relationship.

So, The equation y = -0.5x +45 represent the linear relationship.

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Answer: 57.59- 56.3=1.29

Step-by-step explanation:

57.59-x = 1.29

-x= 1.29-57.59

(—) -x= - 56.3

x=56.3