Standard notation:
7.83 x 10^6
9 x 10^5
5.67 x 10^-7
1.36 x 10^-4
hElp-

The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

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Answer:

2√e√3√f / 3f

Step-by-step explanation:

√4√e / √3√f

2√e / √3√f  * (√3√f / √3√f)

2√e√3√f / 3f

The number of different orders of top-three finishers in the free throw contest depends on the total number of participants. The specific number of participants is not provided in the given information.

To determine the number of different orders of top-three finishers, we need to know the total number of participants in the free throw contest. The order of finishers can be calculated using the concept of permutations, where the order matters.

If there are "n" participants, the number of different orders of top-three finishers can be calculated using the formula nP3, which represents the number of permutations of "n" objects taken 3 at a time. However, since the total number of participants is not provided in the given information, we cannot determine the exact number of different orders of top-three finishers.

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Answer: \(- \frac{62}{5}\)

Convert the decimal number into a fraction

Multiply by 10

\((- \frac{12.40}{1} ) (\frac{10}{10})\)

\(- \frac{124}{10}\)

Divide the fraction by 2

\(- \frac{62}{5}\)

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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The quadratic equation that Olivia is solving is y = x² + 4x + 6

Any expression that can be changed into standard form, such as the ones below, is considered to be a quadratic equation in algebra:

y = ax² + bx +c

Now from the given step and by using the quadratic formula we can ascertain that the values of a ,b and c are 1 ,4 and 6 respectively.

hence the quadratic equation is y = x² + 4x + 6.

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Answer:

(3, - 1 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

here (x₁, y₁ ) = R (4, - 5 ) and (x₂, y₂ ) = D (2, 3 )

midpoint = ( \(\frac{4+2}{2}\) , \(\frac{-5+3}{2}\) ) = ( \(\frac{6}{2}\) , \(\frac{-2}{2}\) ) = (3, - 1 )

The minimum yield value of the key material should be determined based on the yield stress of the shaft, which is 36 kg/m², the dimensions of the key, and the safety factor of 2.

To ensure that the key smoothly transmits the torque of the shaft, it is essential to choose a key material with a minimum yield value that can withstand the applied forces without exceeding the yield stress of the shaft.

The dimensions of the key given are 20x20x120 mm. To calculate the torque transmitted by the key, we need to consider the dimensions and the applied forces. However, the specific values for the applied forces are not provided in the question.

The safety factor of 2 indicates that the material should have a yield strength at least twice the expected yield stress on the key. This ensures a sufficient margin of safety to account for potential variations in the applied forces and other factors.

To determine the minimum yield value of the key material, we would need additional information such as the expected torque or the applied forces. With that information, we could calculate the maximum stress on the key and compare it to the yield stress of the shaft, considering the safety factor.

Please note that without the specific values for the applied forces or torque, we cannot provide a precise answer regarding the minimum yield value of the key material.

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Answer:

17.5

Step-by-step explanation:

15^2+9^2=225+81=306 then sqrt 306

Answer:

I think it is 156 (sorry if the answer is incorrect)

Step-by-step explanation:

every triangle will equal to 180 degrees so 15+9 is 24, 180-24=156

Answer:

The answer to this question is x= 51/4

To find first-order linear differential equations solution, we have to derive the general form or representation of the solution.

With the help of the steps shown below, we can learn how to solve the first-order differential equation.

1. Reorder the terms in the given equation so that they have the form \($\frac{dy}{dx}+Py=Q\) where P and Q are constants or functions of the independent variable x only.

2. Integrate P (obtained in step 1) with respect to x and then put this integral as a power of e to determine the integrating factor.

\($e^{\int P d x}\) = IF

3. The linear first-order differential equation's two sides should be multiplied by the IF.

4. The L.H.S of the equation is always a derivative of \($y \times M(x)$\) i.e. L.H.S \($= \frac{d(y \times I . F)}{dx}\)

\($d(y \times I . F) d x=Q \times I . F$\)

5. In order to arrive at the solution, we simply integrate both sides with respect to x in the last step.

Therefore \(y \times I . F=\int Q \times I . F d x+C$,\)

where C is some arbitrary constant

Similarly, we can also solve the other form of linear first-order differential equation \($\frac{dy}{dx}+Py=Q\) using the same steps.

P and Q are y's functions in this manner. We determine the solution, which will be, by using the integrating factor (I.F), which is

\($(x) \times(I . F)=\int Q \times I . F d y+c$\)

Now, to get a better insight into the linear differential equation, let us try solving some questions. where C is some arbitrary constant.

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the chance that the weight of a product is between 115 LB and 118 LB is approximately 0.1207, or 12.07%.

To find the probability that the weight of a product is between 115 LB and 118 LB, we can use the properties of the normal distribution.

Given that the weight of products follows a normal distribution with a mean (µ) of 120 LB and a standard deviation (σ) of 30 LB, we can standardize the values of 115 LB and 118 LB using the z-score formula:

z = (x - µ) / σ

For 115 LB:

z1 = (115 - 120) / 30 = -0.1667

For 118 LB:

z2 = (118 - 120) / 30 = -0.0667

Next, we can use a standard normal distribution table or a calculator to find the corresponding probabilities for these z-values.

Using a standard normal distribution table, the probability of having a z-value between -0.1667 and -0.0667 is approximately 0.1207.

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Answer:

To simplify √3^15, we can use the property of exponents that says (a^m)^n = a^(m*n). Therefore, we have:

√3^15 = √(3^5)^3 = √(3^(5*3)) = √3^15 = 3^7

So the answer is option (d), 3^7√3.

Step-by-step explanation:

To find bases for row(A), col(A), and null(A), we first need to understand what each of these terms means.

- Row(A): This refers to the set of all rows in the matrix A.
- Col(A): This refers to the set of all columns in the matrix A.
- Null(A): This refers to the set of all vectors x such that Ax = 0.

Now let's find bases for each of these sets for the given matrix A:

- Row(A): To find a basis for the row space, we need to find a set of linearly independent rows that span the row space. We can use row reduction to find the row echelon form of A:

$$
\begin{pmatrix}
1 & 1 & -4 & 0 & 2 \\
1 & -1 & -5 & 0 & 0 \\
\end{pmatrix}
\sim
\begin{pmatrix}
1 & 1 & -4 & 0 & 2 \\
0 & -2 & -1 & 0 & -2 \\
\end{pmatrix}
$$

From this, we can see that the first two rows are linearly independent (since they have pivots in different columns), so they form a basis for the row space. Therefore, a basis for row(A) is:

$$
\left\{ \begin{pmatrix} 1 & 1 & -4 & 0 & 2 \end{pmatrix}, \begin{pmatrix} 1 & -1 & -5 & 0 & 0 \end{pmatrix} \right\}
$$

- Col(A): To find a basis for the column space, we need to find a set of linearly independent columns that span the column space. We can use the same row echelon form from above to do this. Any column with a pivot in it corresponds to a linearly independent column of A. Therefore, a basis for col(A) is:

$$
\left\{ \begin{pmatrix} 1 \\ 1 \end{pmatrix}, \begin{pmatrix} -4 \\ -5 \end{pmatrix}, \begin{pmatrix} 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 2 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \end{pmatrix} \right\}
$$

- Null(A): To find a basis for the null space, we need to find all solutions to the equation Ax = 0. We can use row reduction to do this:

$$
\begin{pmatrix}
1 & 1 & -4 & 0 & 2 \\
1 & -1 & -5 & 0 & 0 \\
\end{pmatrix}
\sim
\begin{pmatrix}
1 & 0 & -3 & 0 & 2 \\
0 & 1 & 2 & 0 & 1 \\
\end{pmatrix}
$$

From this, we can see that the solution set to Ax = 0 is:

$$
\left\{ \begin{pmatrix} 3s - 2t \\ -2s - t \\ s \\ t \\ 0 \end{pmatrix} \mid s,t \in \mathbb{R} \right\}
$$

Therefore, a basis for null(A) is:

$$
\left\{ \begin{pmatrix} 3 \\ -2 \\ 1 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} -2 \\ -1 \\ 0 \\ 1 \\ 0 \end{pmatrix} \right\}
$$

These two vectors are linearly independent and span the null space, so they form a basis for null(A).
It seems like the matrix A is not properly formatted. Please provide the matrix A in the following format:

A =
[row1, column1] [row1, column2] [row1, column3] ...
[row2, column1] [row2, column2] [row2, column3] ...
...
[row_n, column_n]

Once you provide the correct matrix format, I will be able to help you find the bases for row(A), col(A), and null(A).

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The value of given differential equation \(y' = y - x\) with the initial condition \(y(0) = 1.5\), on the interval \(0 \leq x \leq 1.5\), is \(y(1.5) = y_4 = 5.4296875\).

The differential equation we are given is \(y' = y - x\), with the initial condition \(y(0) = 1.5\). We are asked to approximate the solution on the interval \(0 \leq x \leq 1.5\) with a step size of \(h = 0.5\), and we want to achieve an accuracy of \(e = 0.0001\).

We start by calculating the first two values, \(y_0\) and \(y_1\), using the formula:

\(y_1 = y_0 + h \cdot f(x_0, y_0)\)

Here, \(h\) represents the step size, \(f(x, y)\) represents the derivative \(y'\) in terms of \(x\) and \(y\), and \((x_0, y_0)\) is the initial condition.

Using the given values, we can calculate \(y_1\) as:

\(y_1 = 1.5 + 0.5 \cdot (1.5 - 0) = 2.25\)

Next, we calculate \(y_2\) using the same formula:

\(y_2 = y_1 + h \cdot f(x_1, y_1)\)

Substituting the values \(x_1 = 0.5\) and \(y_1 = 2.25\), we get:

\(y_2 = 2.25 + 0.5 \cdot (2.25 - 0.5) = 3.375\)

Similarly, we can calculate \(y_3\) and \(y_4\) as:

\(y_3 = 3.375 + 0.5 \cdot (3.375 - 1) = 4.3125\)

\(y_4 = 4.3125 + 0.5 \cdot (4.3125 - 1.5) = 5.4296875\)

So, the value of \(y\) at \(x = 1.5\) is \(y(1.5) = y_4 = 5.4296875\).

Using Euler's method with a step size of \(h = 0.5\) and an accuracy of \(e = 0.0001\), the solution to the given differential equation \(y' = y - x\) with the initial condition \(y(0) = 1.5\), on the interval \(0 \leq x \leq 1.5\), is \(y(1.5) = y_4 = 5.4296875\).

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Answer:  No the banner is not square.

Step-by-step explanation:

If it were square, the diagonal would be about 35.36 inches.

Pythagorean Theorem: a² + b² + = c²

?25² + 25² = 48² ?

625 + 625 ?=? 2304

1250 ≠ 2304

√1250 ≈ 35.3553

Answer:

The second option

Step-by-step explanation:

Source: trust me bro

b

Step-by-step explanation:

because it is a function

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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Answer:

D.

πr2(2h)pi r squared left parenthesis 2 h right parenthesis

Step-by-step explanation:

Step-by-step explanation:

i guess it helps..if yuh need step by step explanation.comment i try to explain in worda

Answer:

Step-by-step explanation:

circumference is 2πr

r=d/2

r=4.46m

C=2π(4.46)=28.02

Answer:

Two causes of a shift in a PPC could be changes in market conditions or changes in the company's budget. Market conditions may cause fluctuations in prices, while changes in the company's budget can cause them to adjust their PPC spending.

Answer:

its B and D

Step-by-step explanation:

cause 1.5 times 1.5 times 1.5 is 3.375 which is (1.5)  and the explanation for D is that 2.5 times 1.25 Is 3.375 which is (1.5) Hope i helped:)

The expression is equivalent to 3.375 and 2.25 × 1.5.

We have to determine

Which expression is equal to \((1.5)^3\)?

The expression is equivalent to;

\(= (1.5)^3\\\\= 1.5 \times 1.5 \times 1.5\\\\= 3.375\)

Therefore,

The expression is equivalent to;

\(= 2.25 \times 1.5\\\\= 3.375\)

Hence, the expression is equivalent to 3.375 and 2.25 × 1.5.

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The difference between the maximum value of g(x) to the maximum value of f(x) is 11. The maximum value of g(x) is -5 and f(x) is 6.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given,

f(x) = -(x - 5)² + 4

At x = -3

f(-3) = -(-3 - 5)² + 4

f(-3) = -81 + 4 = -77

At x = 2

f(2) = -(2 - 5)² + 4

f(2) = -9 + 4 = -5 (maximum)

Now,

g(x) = 6 (maximum)

6 - (-5) = 11

Hence "The difference between the maximum value of g(x) to the maximum value of f(x) is 11. The maximum value of g(x) is -5 and f(x) is 6".

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Answer:

3/8

Step-by-step explanatio

the person shows the answer and explanation nice!

Answer:

35

Step-by-step explanation:

180-(100+45)= 35

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

----------------------------------------------------------------------------------------------------------

The pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that:

In a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3

Let the common factor be x:

7x = raising

3x = dates

7x + 3x = 7

10x = 7

x = 7/10

7x = 7(7/10)

Raisin =  49/10 pounds

Thus, the pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.

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Answer:

x = 04

Step-by-step explanation:

7x-2(x-10)=40

7x-2x+20=40

5x=20

therefore x=20/5

that is 4