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Angie jarred 28 liters of jam after 4 days. How much jam did Angie jar if she spent 7 days making jam? Assume the relationship is directly proportional.

Answer:

\(x=\dfrac{\ln \left(\frac{21}{25}\right)}{\ln 6125}\)

Step-by-step explanation:

Given equation:

\(2 \cdot 5^{3x+2} = 6 \cdot 7^{1-2x}\)

Divide both sides of the equation by 2:

\(\implies 5^{3x+2} = 3 \cdot 7^{1-2x}\)

Take natural logs of both sides:

\(\implies \ln \left(5^{3x+2}\right) = \ln \left(3 \cdot 7^{1-2x}\right)\)

\(\textsf{Apply the product law:} \quad \ln xy=\ln x + \ln y\)

\(\implies \ln 5^{3x+2} = \ln 3 + \ln 7^{1-2x}\)

\(\textsf{Apply the power law:} \quad \ln x^n=n \ln x\)

\(\implies (3x+2)\ln 5 = \ln 3 + (1-2x)\ln7\)

Expand:

\(\implies 3x\ln 5+2\ln 5=\ln 3+\ln7-2x\ln7\)

Collect the terms in x on the left side and the constants on the right side of the equation:

\(\implies 3x\ln 5+2x\ln7=\ln 3+\ln7-2\ln 5\)

Factor out the common term x on the left side:

\(\implies x(3\ln 5+2\ln7)=\ln 3+\ln7-2\ln 5\)

\(\textsf{Apply the power law:} \quad n \ln x=\ln x^n\)

\(\implies x(\ln 5^3+\ln7^2)=\ln 3+\ln7-\ln 5^2\)

Simplify:

\(\implies x(\ln 125+\ln 49)=\ln 3+\ln7-\ln 25\)

\(\textsf{Apply the product law:} \quad \ln x + \ln y=\ln xy\)

\(\implies x(\ln (125 \cdot 49))=\ln (3\cdot 7)-\ln 25\)

\(\implies x(\ln 6125)=\ln 21-\ln 25\)

\(\textsf{Apply the quotient law:} \quad \ln x - \ln y=\ln \left(\dfrac{x}{y}\right)\)

\(\implies x(\ln 6125)=\ln \left(\dfrac{21}{25}\right)\)

Divide both sides of the equation by ln 6125:

\(\implies x=\dfrac{\ln \left(\frac{21}{25}\right)}{\ln 6125}\)

To solve this question

We will follow the steps below:

Let

Check the picture below.

so hmmm let's find the length of the slanted side, namely the hypotenuse of the triangle with sides of 9 and 7(half of 14).

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{9}\\ o=\stackrel{opposite}{7} \end{cases} \\\\\\ c=\sqrt{ 9^2 + 7^2}\implies c=\sqrt{ 81 + 49 } \implies c=\sqrt{ 130 }\)

so now let's get the areas of those triangles and those rectangles.

\(\stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(14)(9) \right]}~~ + ~~\stackrel{\textit{left and right rectangles}}{2(\sqrt{130})(20)}~~ + ~~\stackrel{\textit{bottom rectangle}}{(20)(14)} \\\\\\ 126+40\sqrt{130}+280\implies 406+40\sqrt{130} ~~ \approx ~~ \text{\LARGE 862.07}~cm^2\)

The interest amount is $622.85

The given parameters are:

The interest amount is calculated as:

I = P(1 + r/n)^(nt) - P

This gives

I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000

Evaluate the products and the quotient

I = 1000 * (1 + 0.045)^(11) - 1000

Evaluate the sum

I = 1000 * (1.045)^(11) - 1000

Solve

I = 622.85

Hence, the interest amount is $622.85

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Answer:

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

3(15.9 - 3.9)

3 · (15.9 - 3.9)

3(15.9) - 3(3.9)

47.7 - 3(3.9)

47.7 - 11.7

36

Answer:

I believe the answer is 15

Step-by-step explanation:

15.9 - 3.9 (line up the decimals correctly)

then subtract it and you get 12.0

add 12.0 + 3 (under the 2)

12.0

+3

and you get 15 as your answer :)

Answer:

138

Step-by-step explanation:

f(x)= 18x + 12

Let x = 7

f(7) = 18*7 +12

     = 126+12

     = 138

Answer:

f(7) = 138

Step-by-step explanation:

\(f(x)= 18x + 12\\f(7) = ?\\\\f(7) = 18(7) +12\\f(7) = 126+12\\f(7)=138\)

Answer:

R = ∞

I = (-∞, ∞)

Step-by-step explanation:

Use the ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] / [xⁿ⁺⁵ / (2n!]│

lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] × (2n! / xⁿ⁺⁵)│

lim(n→∞)│x 2n! / (2(n+1)!)│

lim(n→∞)│n! / (n+1)!││x│

lim(n→∞) (1 / (n+1))│x│

0

The series converges if the limit is less than 1.

The limit is always less than 1, so the radius of convergence is infinite.

So the interval of convergence is (-∞, ∞).

Answer:

This equation is false.

Step-by-step explanation:

27x15=405

You're doing the distributive property here so you're supposed to add but they subtract. Since you're doing 20x15 you have to add because 27-20=7.

The equation 27 × 15 = (20 × 15) – (7 × 15) is false.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The distributive property is the distributed law of multiplication over operations in fundamental algebra, such as adding and subtracting.

The expression is given below.

⇒ 27 × 15

The expression can be written as,

⇒ 27 × 15

⇒ (20 + 7) × 15

⇒ 20 × 15 + 7 × 15

The equation 27 × 15 = (20 × 15) – (7 × 15) is false.

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Answer:

speak English I don't understand your letter?and what your question?

Answer:

Step-by-step explanation:

-72/80 = -36/40 = -18/20 = -9/10

Answer:  -7x3 + 13x2 + 9x - 12

Answer:

3(5x2+2x-4)-x7x2+2x-3)

15 x 6 + 6x -12 - x7 + x2 + 2x -3

90 + 6x - 12 - x7 + x2 + 2x -3

(6x + 2x) (+90 - 12 - 3) (-x7 + x2)

8x + 75 - x5

Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Step-by-step explanation:

The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.

The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.

To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:

For y = sin(x):

x = 0, y = 0

x = π/2, y = 1

x = π, y = 0

x = 3π/2, y = -1

x = 2π, y = 0

For y = sin(2x):

x = 0, y = 0

x = π/2, y = 0

x = π, y = 0

x = 3π/2, y = 0

x = 2π, y = 0

As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).

Therefore, the correct statement is: It is compressed horizontally.

Answer:

see below

Step-by-step explanation:

10(9-1)

Distribute

10 * 9  - 10 *1

90 - 10

80

Answer: 80

Step-by-step explanation:

10(9-1) = 90 - 10 = 80

(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment

Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.

The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:

D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63

Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)

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Answer: It’s -1,-3

Step-by-step explanation:

got 100 on the test

Answer:

1 hour and 15 min

Step-by-step explanation:

I think this is right but look it up just to be sure

Step-by-step explanation:48miles in 60 min. 1/4 of 60 is 1so 60 +15 = 1hr 15 min.

Answer:

Step-by-step explanation:

blah blah blah

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

9:16

Step-by-step explanation:

If there are 9 dogs and 7 cats and you need to know the total number of cats and dogs add the numbers together (16) and put the number of dogs in front of it (9). So the answer is 9:16

Answer:

9:16

Step-by-step explanation:

because he ratio of cats to dogs is 9:7, so that means the 9 is how many dogs their are, 9 + 7= 16, making 9:16 (i'm wrong i'm positive i might be right)

Answer:

We can use the slope formula

y2-y1/x2-x1

Now we can use this with any 2 known points to determine slope

9-5=4

4-1=3

4/3 slope

Answer:

M = 1.333333....

Step-by-step explanation:

Slope = y2 - y1 / x2 - x1

5 - 9 / 4 - 1

-4 / 3

M = -1 1/3

The volume of the rectangular prism is 4.84 cm cube.

A rectangular prism is filled exactly with 605 cubes. Each cube has edge

length 1 / 5 cm. Therefore, the volume of the rectangular prism can be

calculated as follows:

volume of each cube = l³

volume of each cube = (1 / 5)³

volume of each cube = 1 / 125 cm³

Therefore,

volume of the rectangular prism = 605 × 1 / 125

volume of the rectangular prism = 605 / 125

volume of the rectangular prism = 4.84 cm³

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Answer: $355.39

Step-by-step explanation: subtract 174.25,180.96,184.24 from 8194.84 =

The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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Answer:

- When all side faces are the same:

Surface Area = (Area of the Base) + 1/2 × Perimeter × (Slant Length)

- When side faces are different :

Surface Area = (Area of base) + (Lateral Area).

Step-by-step explanation:

A pyramid is formed by connecting a base to a top. There are no curves in a pyramid, the base is a polygon and all other faces are triangles.

There are many types of Pyramids, and they are named after the shape of their base.

We have Triangular Pyramid, Square Pyramid, Pentagonal Pyramid, and so on.

The Surface Area of a Pyramid.

We need to consider the two cases:

- When all side faces are the same:

Surface Area = (Area of the base) + 1/2 × Perimeter × (Slant Length)

- When side faces are different :

Surface Area = (Area of base) + (Lateral Area).

We consider the Area of Base because a pyramid's base varies, as I have explained earlier. It can be a square, a triangle, a pentagon, and so on.

Answer:

\( I = \frac{1}{8} e^{4x^2} + C \)

Step-by-step explanation:

This can be solved using substitution method. Let us work it out.

\( Let \: I = \int xe^{4x^2} dx\)

\( \implies \: I = \int e^{4x^2} xdx\)

\( Put \:4x^2 = t \)

\( \implies 8x dx = dt \)

\( \implies x dx = \frac{1}{8}dt \)

\( \implies \: I = \int e^{t} \frac{1}{8}dt \)

\( \implies \: I = \frac{1}{8} \int e^{t}dt \)

\( \implies \: I = \frac{1}{8} e^{t} + C \)

\( \implies \: I = \frac{1}{8} e^{4x^2} + C \)

\( \implies \: \int xe^{4x^2} dx = \frac{1}{8} e^{4x^2} + C \)

Answer:

y = -5x - 11

Step-by-step explanation:

We are given that a line passes through the point (-3,4) and also has a slope of -5.

We want to write an equation of this line.

The equation of the line can be written in 3 different ways:

Since the question did not specify, any of these 3 options will be valid, however, the most common way to write the equation of the line is in slope-intercept form, so let's do it that way.

Because we are already given the value of the slope, we can immediately plug that into the equation.

Replace m with -5.

y = -5x + b

Now we need to find b.

As the equation passes through the point (-3, 4), we can use its values to help solve for b.

Substitute -3 as x and 4 as y.

4 = -5(-3) + b

Multiply

4 = 15 + b

Subtract 15 from both sides.

-11 = b

Substitute -11 as b in the equation.

y = -5x - 11

Topic: finding the equation of the line

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The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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