-3/7 x 3/8
why do i need 2o characters hello hello hello

To calculate the mean of a data set, we need to sum up all the values and then divide by the total number of values.

Sum of the data set = 33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100

Count of values = 31

Mean = (Sum of the data set) / (Count of values)

Now we can substitute the values and calculate:

Mean = (33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100) / 31

After evaluating this expression, we find that the mean of the given data set is approximately 71.29 (rounded to two decimal places).

Therefore, the mean of the data set is 71.29.

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The graph of the data has been plotted and attached below.

What is a graph?

A diagram or pictorial representation of facts or values that is ordered might be referred to as a graph in mathematics. The relationship between two or more items is commonly depicted by graph points.

In the question, we are given the data relating to the distance covered in the specific time duration.

Using this data, a graph has been obtained which has been attached below.

On the x - axis, time is shown and on the y - axis, distance has been shown.

Hence, the graph of the data has been plotted.

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Answer:

B)

Step-by-step explanation:

Answer:

B 11 1/4

Step-by-step explanation:

8 1/2 -2 + 4 3/4  convert to improper fraction

13/2 +19/4  find common denominator of 4

45/4  divide by 4 to get improper fraction

11 1/4

The most appropriate choice for domain of a  functions will be given by -

What is a domain of a function

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The set of values for which the function is defined is called domain of the function.

Here, from the graph, the set of values of x axis for which the graph is drawn is \(-6\leq x \leq 6\).

And values of x - axis represents the domain.

So domain of function is {x ∈ \(\mathbb{R}\), \(-6 \leq x \leq 6\)}

Third option is correct.

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\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 5000}}{\left( \cfrac{16}{100} \right)5000}\implies 800\)

Answer: 636,000

Step-by-step explanation:

1. 8% of 300,000 is 24,000

2. Multiply 24,000 by 14 to get 336,000

3. Add 300,000 to 336,000

If this is incorrect, I think I know what I could have done wrong so just lmk

Function transformation: Function transformation is the process of changing one function into another.

The f(x) graph will be shifted 1 unit down in the vertical direction.

Function transformation: Function transformation is the process of changing one function into another.

changing a function's form from one to another

Transformational rule

The function will move 'a' units higher when f(x)->f(x)+a is used.

f(x)-> f(x)-a The action is going to be 'a' units down.

The function will be relocated 'a' units left if f(x)->f(x+a).

The function will be relocated 'a' units right if f(x)->f(x-a).

The fundamental job is \(f(x)=\frac{1}{x}\)

F(x)-1 is used in place of f(x).

It indicates that the graph of f(x) will shift down by one unit.

A unit down will be added to the vertical translation of the f(x) graph.

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Answer:

(1,22)

(4,10)

(5,6)

(6,2)

Step-by-step explanation:

Answer:

the first two are correct

the other two boxes, in order are: 6, 2

Step-by-step explanation:

you just have to substitute x into the equation, so when it says x is 1, you substitute 1 into the equation given, in this case it's y = 26 - 4x.  After that, you just do regular math to get your y value

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

112 Degrees

Step-by-step explanation:

Since 8 is 112 degrees, and 6 is opposite of 8, that means the measure of angle 6 is also 112 degrees

Answer:

112 degrees

Step-by-step explanation:

8 and 6 are vertically opposite angles, which are equivalent

Answer:

False - The standard deviation is always positive.

A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The function f(x, y) = 2x^2 + 2y^2 corresponds to the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2."

A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The gradient vector field can be visualized by plotting vectors at different points, with the vectors pointing in the direction of the steepest ascent of the function.

In this case, the function f(x, y) = 2x^2 + 2y^2 represents a quadratic function with the coefficients 2 for both x^2 and y^2 terms. The gradient vector field plot that corresponds to this function would show vectors pointing away from the origin (0, 0) in all directions, indicating the direction of steepest ascent.

By matching the function f(x, y) = 2x^2 + 2y^2 with the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2," we can visually observe the direction and magnitude of the gradient vectors associated with the function at each point in the plane.

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Answer:

\(\dfrac{169}{32}\)

Step-by-step explanation:

First, calculate 5/8 of 2:

\(\implies \dfrac{5}{8}\;\textsf{of}\;2=\dfrac{5}{8}\times 2=\dfrac{5 \times 2}{8}=\dfrac{10}{8}=\dfrac{5}{4}\)

Therefore, to increase 2 by 5/8 of it, add 5/8 of 2 to 2:

\(\implies 2+\dfrac{5}{4}=\dfrac{8}{4}+\dfrac{5}{4}=\dfrac{8+5}{4}=\dfrac{13}{4}\)

To increase the resulting number 13/4 by 5/8 of it, first calculate 5/8 of 13/4:

\(\implies \dfrac{5}{8}\;\textsf{of}\;\dfrac{13}{4}=\dfrac{5}{8}\times \dfrac{13}{4}=\dfrac{5 \times 13}{8 \times 4}=\dfrac{65}{32}\)

Now add 65/32 to 13/4:

\(\implies \dfrac{65}{32}+\dfrac{13}{4}=\dfrac{65}{32}+\dfrac{104}{32}=\dfrac{65+104}{32}=\dfrac{169}{32}\)

Answer: Hi I'm Jimin!

English: 5(x-2)

Step-by-step explanation:

Answer:

5(x-2)

Step-by-step explanation:

5x-10 turns into 5(x-2)

Answer:

It just means that it is not equal to each other so the equation is false.

Step-by-step explanation:

The equal sign with a line through it means that they aren't the same. -12 is a different number from 12 so they can't end up being the same in the end of the equation.

Hope this helps!

The position of the particle, s(t), is given by the equation s(t) = (1/3)t^3 + (3/2)t^2 - 9t + 5. This result is obtained by integrating the acceleration function twice with respect to time and applying the initial conditions.

Given the acceleration function a(t) = 2t + 3, the initial position s(0) = 5, and the initial velocity v(0) = -9, the position function s(t) can be determined.

Part 2:

To find the position function s(t), we integrate the acceleration function twice with respect to time. The first integration gives us the velocity function v(t), and the second integration gives us the position function s(t).

Given a(t) = 2t + 3, we integrate once to find the velocity function v(t):

∫(2t + 3) dt = t^2 + 3t + C1,

where C1 is the constant of integration.

Next, we apply the initial condition v(0) = -9 to solve for C1:

v(0) = 0^2 + 3(0) + C1 = C1 = -9.

Therefore, the velocity function is v(t) = t^2 + 3t - 9.

Finally, we integrate v(t) to find the position function s(t):

∫(t^2 + 3t - 9) dt = (1/3)t^3 + (3/2)t^2 - 9t + C2,

where C2 is the constant of integration.

Using the initial condition s(0) = 5, we can solve for C2:

s(0) = (1/3)(0)^3 + (3/2)(0)^2 - 9(0) + C2 = C2 = 5.

Thus, the position function is s(t) = (1/3)t^3 + (3/2)t^2 - 9t + 5.

In summary, the position of the particle, s(t), is given by the equation s(t) = (1/3)t^3 + (3/2)t^2 - 9t + 5. This result is obtained by integrating the acceleration function twice with respect to time and applying the initial conditions.

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Answer:

The sum will be close to 1/2

Step-by-step explanation:

1/4+2/7=15/28

The common denominator of 1/4 and 2/7 is 28.

1/4 -> 7/28

2/7 -> 8/28

7/28+8/28=15/28

turn that into a decimal and it will round to 0.5257

1/2=0.5

so the answer will be closer to 1/2

Answer:The sum would be close to 1/2

Step-by-step explanation:

Answer:

The circumference is 8π yards, or about 25.13 yards. Since we need to use 3.14 for π, the circumference of the pond is about 8 × 3.14 = 25.12 yards.

The required volume of the solid which was obtained by rotating the region bounded by the curve about a line is equal to  ( π/2 ) (  e⁻⁴  + e⁴).

Graph is attached.

Volume of the solid rotating the region bounded by the curves about a line with y = eˣ with x = −2, x = 2 about x-axis.

=π \(\int_{-2}^{2}\) [( eˣ - 0)² ] dx

= π \(\int_{-2}^{2}\) e⁽²ˣ⁾ dx

= π (e²ˣ) / ( 2 \(|_{-2}^{2}\)

= ( π/2 )[  e⁻⁴  - e⁴  ]

= ( π/2 ) (  e⁻⁴  +  e⁴ )

Graph is attached.

Therefore, the volume of the solid of the rotating region bounded by curves about line is equal to  ( π/2 ) (  e⁻⁴  +  e⁴ ).

Graph is attached.

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the number of choices in each case is:

a. With no restriction: 10,000 choices.

b. No digit is repeated: 5,040 choices.

c. No digit is repeated, 2 and 5 must be present: 56 choices.

Let's calculate the number of choices in each case:

a. With no restriction:

For each digit in a 4-digit pin code, we have 10 choices (0-9). Since there are 4 digits in total, the number of choices is 10⁴ = 10,000.

b. No digit is repeated:

For the first digit, we have 10 choices (0-9).

For the second digit, we have 9 choices (any digit except the one chosen for the first digit).

For the third digit, we have 8 choices (any digit except the two chosen for the first and second digits).

For the fourth digit, we have 7 choices (any digit except the three chosen for the first, second, and third digits).

The total number of choices is 10 * 9 * 8 * 7 = 5,040.

c. No digit is repeated, and 2 and 5 must be present:

We have two fixed digits (2 and 5) that must be present in the pin code.

For the first fixed digit (2), we have only 1 choice.

For the second fixed digit (5), we have only 1 choice.

For the remaining two digits, we have 8 choices each (any digit except 2 and 5).

The total number of choices is 1 * 1 * 8 * 7 = 56

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Answer:

Area =  l × w

=  18 × 10

=  180 centimeters2

Step-by-step explanation:

Choice 3 is your answer! I have done this before.  

The wall of this type of canister is 7.984.

What is standard deviation?

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Given, mean = 8.1 mm

number of canister n = 100

standard deviation = 0.6

Standard error due to sampling:

= standard deviation/ square root of n

=0.6/10

=  0.06.

The mean wall thickness is

= 7.984

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Answer:

\(\Large \boxed{x=-2 \ \mathrm{and} \ x=3}\)

Step-by-step explanation:

The quadratic expression is given.

\(2x^2-2x-12=0\)

Factor the left side of the equation.

\(2(x+2)(x-3)=0\)

Set the factors equal to 0.

\(x+2=0\)

 \(x=-2\)

\(x-3=0\)

 \(x=3\)

The two solutions work in the original equation. The solutions make the equation true.

The quadratic expression:

\(2 {x}^{2} - 2x - 12\)

★ By split middle term,we get

\(2 {x}^{2} - 6x + 4x - 12\)

\(2x(x - 3) + 4( x - 3)\)

\((2x + 4) (x - 3)\)

\(2x + 4 = 0 \: \: and \: \: x - 3 = 0\)

\(2 x = - 4 \: \: and \: \: x = 3\)

\(x = - 2 \: \: and \: \: x = 3\)

Therefore , the two solution of given quadratic equations is -2 and 3.

Answer:

x=35

Step-by-step explanation:

simple equstion x+40+3x=180 then subtract forty combine the two X's and divide by 180

The derivatives of the frame field, analogous to the Serret-Frenet equations, are given by V₁' = κ₃V₂ - κ₂V₃, V₂' = -κ₃V₁ + κ₁V₃, and V₃' = κ₂V₁ - κ₁V₂ for some function κᵢ(s).

In this generalized Frenet frame for a unit speed curve r:[a,b]→R³, we start with the tangent vector V₁ = T, which represents the direction of the curve. We then choose V₂ as any unit vector field defined along r(s). Finally, V₃ is obtained by taking the cross product of V₁ and V₂, giving us the frame {V₁, V₂, V₃}.

To find the derivatives of this frame field, we differentiate each vector with respect to the curve parameter s. Applying the product rule and using the properties of cross products, we obtain the derivatives as follows:

V₁' = κ₃V₂ - κ₂V₃,

V₂' = -κ₃V₁ + κ₁V₃,

V₃' = κ₂V₁ - κ₁V₂.

Here, κ₁, κ₂, and κ₃ are functions of s, which represent the curvature of the curve in different directions. These functions determine how the frame vectors change along the curve.

These equations resemble the Serret-Frenet equations but have an additional term involving V₃, reflecting the choice of V₂ as a vector field along the curve. The values of κ₁, κ₂, and κ₃ depend on the specific curve and can be calculated using differential geometry techniques.

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Since these are the only two categories that contain oil, the probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil.

Given that to find

P(finding oil) = P(high-quality oil) + P(medium-quality oil)

= 0.50 + 0.20

= 0.70

Thus the probability of finding oil is 0.70, or 70%.

Probability is a measure of how likely an event is to occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of possible outcomes by the number of favourable outcomes.

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Answer:

1,184.00

Step-by-step explanation:

used a calculator

\(\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}\)

\(\Huge \textsf{Step-by-step explanation}\)

\(\LARGE \bold{\textsf{Step 1: Assign Variables}}\)

\(\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}\)

\(\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}\)

\(\large \bold{ \textsf{From the problem, we know that:}}\)

\(\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}\)

\(\large \bold{ \textsf{We can use this information to write two equations:}}\)

\(\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}\)

\(\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}\)

\(\LARGE \bold{\textsf{Step 3: Solve the system of equations}}\)

\(\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}\)

\(\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}\)

\(\large \textsf{Simplifying this expression gives us:}\)

\(\textsf{10\textit{p} + 10 = 260}\)

\(\large \textsf{Subtracting 10 from both sides:}\)

\(\textsf{10\textit{p} = 250}\)

\(\large \textsf{Dividing both sides by 10}\)

\(\textsf{\textit{p} = 25}\)

\(\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}\)

\(\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}\)

\(\large \textsf{So, 25 pizzas and 80 sodas were sold.}\)

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