Colton was given a box of assorted chocolates for his birthday. Each night, Colton
treated himself to some chocolates. There were originally 30 chocolates in the box
and Colton ate 2 chocolates each night. Write an equation for C, in terms oft,
representing the number of chocolates remaining in the box t days after Colton's
birthday.

Answer:

.44%

Step-by-step explanation:

just divide

Answer:

First Option

Step-by-step explanation:

6 divided by 2 = 3 per notebook

Answer:

The store charges $3 per notebook.

The store charges $15 for 5 notebooks.

Answer:

43 ¼

a mixed number consists of a whole number and a fraction. 0.25 = ¼

therefore the answer is 43¼

Answer:

43 1/4

Step-by-step explanation:

Just add 43 and the equivalent of .25 is 1/4

There is your answer! :)

The quadratic -x^2+2x-4 can be written in the form a(x+b)^2+c, where a, b, and c are constants, then the value of a + b + c is 1.

Quadratic expressions can be used to model many real-world phenomena, such as the height of a projectile over time, the path of a ball thrown in the air, or the shape of a parabolic dish. They are also used extensively in algebra and calculus to solve equations, find roots, and calculate rates of change.

To solve the problem, we need to complete the square by expressing the quadratic in the form a(x+b)^2+c.

First, we factor out -1 to make the leading coefficient positive: -x^2 + 2x - 4 = -1(x^2 - 2x + 4).

Then, we complete the square by adding and subtracting the square of half the coefficient of x:

x^2 - 2x + 1 - 1 + 4 = (x-1)^2 - 1 + 4

Simplifying, we get:

-x^2 + 2x - 4 = -1(x-1)^2 + 3

Therefore, a = -1, b = 1, and c = 3, so a+b+c = -1 - 1 + 3 = 1.

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The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

.

Step-by-step explanation:

It should be noted that experimental probability is based on past observations and might not accurately predict future events.

It has been established that experimental probability is based on past observations or on historical data.

To determine the experimental probability of the high temperature being over 75 degrees on June 23rd, one would basically gather historical data of high temperatures on June 23rd from previous years. Then, one would calculate the proportion of times the temperature was over 75 degrees.

For example, if one had data for the past 10 years and on 7 of those years the temperature was over 75 degrees on June 23rd, the experimental probability would be 7/10 or 0.7 (or 70%).

Therefore, it's always a good idea to consult meteorological sources or weather forecasts for the most up-to-date and accurate information.

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Answer:

All numbers that are in the decimal places are significant.

Step-by-step explanation:

A decimal is a digit after the decimal dot.

E.g. 1 in 2.31 is a decimal. 1 in 2.13 is also a decimal.

Answer:

9(3+2) = 45

9 * 9 = 81

Step-by-step explanation:

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Using the cosine ratio, the distance between Dimitri and Sarah is calculated as approximately 12.4 m.

The cosine ratio is a trigonometric ratio that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is calculated by dividing the length of the adjacent side by the length of the hypotenuse.

Using the cosine ratio, we have:

Reference angle (∅) = 72 degrees

Hypotenuse length = 40 m

Adjacent length = distance between Dimitri and Sarah = x

Plug in the values:

cos 72 = x/40

x = cos 72 * 40

x ≈ 12.4 [to one decimal place]

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Answer:

9

Step-by-step explanation:

3x^2 + 3x - 9

Substitute x = 2 into the equation.

3(2)^2 + 3(2) - 9

3(4) + 6 - 9

12 + 6 - 9

18 - 9 =

9

Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

Answer:

Step-by-step explanation:

839°

Answer:

obtuse angle

Step-by-step explanation:

as it is angle 1 is greater than 90

Answer:

2042.6$

Step-by-step explanation:

12853(5/100)+1400

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Part 1

\(a=\sqrt{12^2 + 21^2 -2(12)(21) \cos 35^{\circ}} \approx \boxed{13}\)

Part 2

\(\frac{\sin B}{b}=\frac{\sin A}{a}\\\\\sin B=\frac{b\sin A}{a}\\\\\sin B=\frac{12 \sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}}\\\\B=\sin^{-1} \left(\frac{12\sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}} \right)\\\\B \approx \boxed{32^{\circ}}\)

Part 3

\(\angle C=180^{\circ}-\angle A -\angle B=\boxed{113^{\circ}}\)

Answer:

C

Step-by-step explanation:

To evaluate f(- 3) substitute x = - 3 into f(x) , that is

f(- 3) = (- 3)² - 5(- 3) + 1 = 9 + 15 + 1 = 25

Step-by-step explanation:

0.000000358 written as scientific notation is

\(3.58 \times {10}^{ - 7} \)

The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.\(\)

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72

The product of the given values is 42556

Integers are also known as whole numbers.

Given the following products

2,092 x 93

This can also be expressed as;

2,092 x 93 = (2000+92) *(90 + 3)

2,092 x 93 = 2000(90) + 2000(3) + 92(90) + 92(3)

Expand to have;

2,092 x 93 = 18000+6000+8280+276

2,092 x 93 = 42556

Hence the product of the given values is 42556

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Yes,  This is established by the Rank-Nullity Theorem, A counter-example would be a transformation that is not linear.

Yes, all linear transformations have a matrix representation. The theorem that establishes this is the Matrix Representation Theorem. This theorem states that given a linear transformation T : V → W where V and W are vector spaces over a field F, then there is a unique matrix A such that T(v) = Av for any v in V. This theorem proves that any linear transformation can be represented by a matrix.

A counter-example of a linear transformation that does not have a matrix representation is a transformation that maps a vector in one vector space to a vector in a different vector space. For example, if V is a vector space over the field F, and W is a vector space over another field K, then the linear transformation T : V → W does not have a matrix representation since the size of the matrix would need to be different for each vector in the different vector spaces.

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Answer:

π/2 = 90°

Step-by-step explanation:

Given that,

Radian measure = π/2

The formula used to convert radian measure to degree measure is given by :

\(\text{Degrees}=\dfrac{180^{\circ}}{\pi}\times \text{radians}\\\\=\dfrac{180^{\circ}}{\pi}\times \dfrac{\pi}{2}\\\\=90^{\circ}\)

So, the degree matches for π/2 is 90°.

Answer:

the answer is 4/10

Step-by-step explanation:

$37,500 should be invested in B-rated bonds and $22,500 should be invested in a certificate of deposit in order to realize exactly $6,000 in interest per year.

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The required statistical parameters has been computed as follows:

Range = 15.

Standard deviation, SD = 4.4441.

Variance = 19.75.

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 36 - 21

Range = 15.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 22 + 29 + 21 + 24 + 27 + 28 + 25 + 36

F(x) = 212.

Mean = 212/8

Mean = 26.5

Next, we would calculate the standard deviation by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × ∑(22 - 26.5)² + 1/5 × ∑(29 - 26.5)² + 1/5 × ∑(21 - 26.5)² + 1/5 × ∑(24 - 26.5)² + 1/5 × ∑(27 - 26.5)² + 1/5 × ∑(28 - 26.5)² + 1/5 × ∑(25 - 26.5)² + + 1/5 × ∑(36 - 26.5)²)

Standard deviation, SD = 4.4441.

In Statistics, the standard deviation of a data sample is the square root of the variance and this is given by this mathematical expression:

Variance = δ²

Variance = 4.4441²

Variance = 19.75.

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Answer:

4:1

Step-by-step explanation:

So, although the ratio 8:2 is technically correct, it is not in its simplest form. To get it into its simplest form you need to find the largest multiplying factor that is the same for both numbers. In this case, 2 is the largest factor because it goes into both 2 and 8. Now, you need to divide the entire ratio by 2 the reach the simplest form, so 8 divided by 2 equals 4, and 2 divided by 2 equals 1. This gives us our final ratio of 4:1.

The number of bins in the histogram determines the width of the bins and

the frequency (number of members) in a bin.

Given:

The table from  Gretchen's data is presented as follows;

\(\begin{tabular}{|c|c|} \underline{ Member}& \underline{Number of Days}\\x_1&2\\x_2&4\\x_3&7\\x_4&8\\x_5&12\\x_6&15\\x_7&10\\x_8&7\\x_9&9\\x_{10}&6\\x_{11}&13\\x_{12}&3\\x_{13}&8\\x_{14}&10\\x_{15}&10\end{array}\right]\)

The required number of bins = 8 bins

The steps to create the histogram using MS Excel;

The histogram of Gretchen's data having eight bins created with MS Excel is attached.

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Answer: you should copy and paste the numbers on the table under Gretchen's data in the order that is given into the data set, then you can apply it and it will appear on your graph.