First, he heated 6 cups of milk and 1 pint of cream in a large pot. Then, he stirred in 4 cups of melted chocolate. How many cups of hot chocolate did Jasper make?

The amount of money that would be in Carmen's account in one year as required to be determined is; 3,640.

As evident from the task content; the given formula is;

y = 3500(1.04)^t.

Hence, after one year, t = 1;

y = 3500 (1.04)¹

y = 3640.

Ultimately, the amount in the account would be; 3640.

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Answer:

What is the value of x in the product of powers 55 · 5x = 52 ?

x = –3

What is the value of y in the product of p-3 · p-6 = py

y = –9

What is the value of n in th product of 92 · 9-7 · 9n  =  9-5 = \(\frac{1}{9^5} }\)

n = 0

Hope this helps :D

The value of x in the product of powers is -3, the value of y is -9 and the value of n is 0.

Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.

Given that,

5⁵ . 5ˣ = 5²

We have to use a multiplication rule for exponent here.

xᵃ . xᵇ = xᵃ⁺ᵇ

Using this,

5⁵⁺ˣ = 5²

⇒ 5 + x = 2

⇒ x = -3

p⁻³ . p⁻⁶ = p^y

Using the same rule of exponent,

p⁻³⁺⁻⁶ = p^y

⇒ y = -3 - 6 = -9

9² . 9⁻⁷ . 9ⁿ = 9⁻⁵

9²⁻⁷⁺ⁿ = 9⁻⁵

⇒ 2 - 7 + n = -5

⇒ n = 0

Hence the values of x, y and n are -3, -9 and 0 respectively.

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Answer:

Triangle Sum Theory

Step-by-step explanation:

You add all the angles to get 180

Answer:

Pythagorean theorem

I think

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/\(\sqrt{5}\)

=1\(\sqrt{5}\) *\(\sqrt{5}\)/\(\sqrt{5}\)

=1*\(\sqrt{5}\)/\(\sqrt{5}\)*\(\sqrt{5}\)

=1\(\sqrt{5}\)/5

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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The shaded areas therefore cover a total area of 86.84 cm2.

Let's calculate the whole trapezoid's area. You multiply by the height after adding the top and bottom sides and dividing the result by two.

To get the length of the top side, we sum the values that make up that side.

6.4+5.2+9.6=21.2

The underside is 5.2.

The top and bottom sides are added.

21.2+5.2=26.4

We multiply by 2.

26.4/2=13.2

We increase by the height, which is 6.2 as we can see.

13.2×9.1=120.12

Next, we locate the rectangle's unlit portion.

6.4×5.2 = 33.28

To get the total area of the two shaded triangles, we deduct this from the trapezoid's overall area.

120.12 - 33.28 = 86.84

The shaded areas therefore cover a total area of 86.84 cm2.

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The distance from the center of dilation, Q, to the image of vertex A will be 4 units.

According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.

Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.

By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x  3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.

Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.

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Answer:

\(\frac{x-2}{4x+5}\)

Step-by-step explanation:

Given

\(\frac{4x^2+3x-1}{4x^2+9x+5}\) ÷ \(\frac{4x^2+7x-2}{x^2-4}\)

Factorise numerator / denominator of both fractions

= \(\frac{(4x-1)(x+1)}{(4x+5)(x+1)}\) ÷ \(\frac{(4x-1)(x+2)}{(x-2)(x+2)}\)

Cancel common factors on numerator/ denominator of both fractions

= \(\frac{4x-1}{4x+5}\) ÷ \(\frac{4x-1}{x-2}\)

Change ÷ to × and turn second fraction upside down

= \(\frac{4x-1}{4x+5}\) × \(\frac{x-2}{4x-1}\)

Cancel the common factor 4x - 1 on numerator/ denominator, leaving

\(\frac{x-2}{4x+5}\)

The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.

The given algebraic expression is -4x²+12x.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factorization of the given polynomial is

-4x²+12x

= 4x(-x+3)

The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.

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Answer: -7/11

Step-by-step explanation:

Answer:

\(\frac{9}{10}\) ÷ \(\frac{3}{5}\)

=3/5

=1.5

Answer:

sin(150) or 1/2

Step-by-step explanation:

Using the double angle identity of sin2x = 2sinxcosx, you can determine the value of x and rewrite the function; 2sin(75)cos(75) = sin(2(75)) = sin(150) = 1/2

Answer:

No if you see this sign means (<) that the number in like this1<2 that 2 is greater than 1 so it would be no because it would be this way 9>7 not 9<7

Step-by-step explanation:

Answer:

2.77

Step-by-step explanation:

39.50x.07=2.77

The volume of the solid is 45/2 cubic units.

To find the volume of the solid, we need to integrate the area of each cross-section perpendicular to the x-axis along the interval [1, 4]. Since the cross-sections are rectangles with height x, we need to find the width of each rectangle at each value of x.

First, let's find the intersection points of the given curves. We can solve

\(y = x^2 - 5x + 7\)and y = 3 to get:

\(x^2 - 5x + 7 = 3\\x^2 - 5x + 4 = 0\\(x - 1)(x - 4) = 0\)

So the intersection points are (1, 3) and (4, 3).

Now, at each x value between 1 and 4, the width of the rectangle is the difference between the y values of the two bounding curves, which is:

\(3 - (x^2 - 5x + 7) = -x^2 + 5x - 4\)

Thus, the volume of the solid is:

\(V = \int [1,4] (-x^3 + 5x^2 - 4x) dx\)

Integrating, we get:

\(V = [-1/4 x^4 + 5/3 x^3 - 2x^2] from x = 1 to x = 4\\V = [(-1/4 \times 4^4 + 5/3 \times 4^3 - 2 \times 4^2) - (-1/4 \times 1^4 + 5/3 \times 1^3 - 2 \times 1^2)]\\V = [(-64/4 + 80/3 - 8) - (-1/4 + 5/3 - 2)]\\V = 45/2\)

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The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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C, D,E

Step-by-step explanation:

4x=2

4+x=4 1/2

16x=8

hope it helps you tell me in the comment box

(•‿•)

Answer:

(2,7), (6,-2),

Step-by-step explanation:

After finding the points you plug them in to the distance formula:

d=√((x2-x1)²+(y2-y1)²)

d=√[(6-2)²+(-2-7)²]

Answer:

scientific notation is the answer

Step-by-step explanation:

you will use scientific notation to move you decimal point when you multiply a decimal

The function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)} is a one-to-one function. It satisfies condition where each input value maps to unique output value, ensuring no repetition or multiple inputs leading to the same output.

A one-to-one function, also known as an injective function, is a type of function where each input value is uniquely mapped to an output value. In the given function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)}, we can observe that each input value corresponds to a distinct output value. For example, the input 1 is mapped to the output 5, and no other input has the same output. Similarly, the inputs -2, -4, and 2 are associated with the outputs 3, 2, and 5 respectively, without any repetition.

This lack of repetition or duplication in the outputs demonstrates that the function is one-to-one. Each input has a unique correspondence with its output, and no two different inputs yield the same output value. Therefore, based on the provided set of mappings, we can conclude that the function f is indeed a one-to-one function.

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Answer:

JUST ADD 3$

Step-by-step explanation:

Answer:

juan needs to go ask for $3 more

Step-by-step explanation:

Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.

In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.

Here,

The following algorithm must be used to determine the mean age:

=> mean = (all years added together) / (total number of persons)

The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

According to the information provided, there are 460 people in total.

=> mean = 17745.25 / 460

=> mean = 17745.25 / 460

As a result, the average lifespan is roughly 38.552 years.

The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.

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Answer:

19

Step-by-step explanation:

We need 4/3 cups of raisins to make one whole cookie recipe.

The two ratios given are equal to one another, as demonstrated by the proportional equation. For instance, it would take five hours for a train to cover 500 kilometres when it travels at 100 km per hour.

If 1 3 cup of raisins makes 1 4 of a cookie recipe, then we need to find how many cups of raisins are needed to make one whole cookie recipe.

Let's use a proportion to solve this problem:

1 3 cup of raisins is to 1 4 of a recipe as x cups of raisins is to 1 whole recipe.

We can cross-multiply to get:

1 3 * 1 = 1 4 * x

1/3 = 1/4 * x

x = 4/3

Therefore, we need 4/3 cups of raisins to make one whole cookie recipe.

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Answer:

A

Step-by-step explanation:

Sequence A works.

With sequence B, the triangles will be next to each other.

Answer: A

Answer: The greatest number of cards you can place each packet = 3

There would be 7 packets of baseball cards and 4 packets of football cards.

Step-by-step explanation:

Given: Number of baseball cards =21

Number of  football cards = 12

Each packet will have the same number of cards.

Each packet will have the cards for only one sport.

Then, the greatest number of cards you can place each packet  = GCD (21,12) i.e. greatest common divisor of 21 and 12

Since 21 = 3 x 7 and 12 = 2 x2 x3

so, GCD(21, 12)=3

So, the greatest number of cards you can place each packet = 3

Number packets of baseball cards  = \(\dfrac{21}{3}=7\)

Number packets of football cards = \(\dfrac{12}{3}=4\)

So, there would be 7 packets of baseball cards and 4 packets of football cards.

The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.

To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.

The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.

This is equal to 22/25 * 100 = 88% as a percentage.

As a result, P(not green) = 88%

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.

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Answer:

Use an app called Cymath it tells you the answer and it shows you step by step on how to work it out. I used the app multiple times and it helps me a lot!

Step-by-step explanation:

Hope I helped! :)