») Noah finds 14 caterpillars and puts them in 2 cages.
There are the same number of caterpillars in each cage.
How many caterpillars are in each cage?
Complete the division equation to represent the problem.

Answer:

397.61m

Step-by-step explanation:

A = 1

4πd^2 = 1

4 x π x 22.52 = 397.60782

Answer: 13.6 or 9.2

Step-by-step explanation:

Answer:

x=2/7

Step-by-step explanation:

The most important thing to note is that angle A and angle B are vertical angles. Vertical angles are always equal. So, you can set 4x+2=11x and solve.

To get x by itself, subtract 4x from both sides to get 2=7x. Then divide 7 from both sides which gets x equal to 2/7.

The test statistic for this test is -0.213.

To test the hypothesis that two populations have the same mean, we can use a two-sample t-test. The test statistic for this test is calculated by taking the difference between the sample means and dividing it by the standard error of the difference.

In this case, the sample averages are 6 and 7, and the standard deviations for the two samples are 16 and 15, respectively. Both samples have 32 observations.

To calculate the test statistic, we first need to calculate the standard error of the difference. This is given by:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

where s1 and s2 are the standard deviations for the two samples, and n1 and n2 are the sample sizes. Plugging in the values we have, we get:

SE = sqrt[(16^2/32) + (15^2/32)]
  = 4.698

Next, we calculate the t-statistic:

t = (x1 - x2) / SE

where x1 and x2 are the sample means. Plugging in the values we have, we get:

t = (6 - 7) / 4.698
 = -0.213

The test statistic for this test is -0.213.

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\(3 - \frac{1}{2}x > x \\ \)

Add sides ½ x

\(3 - \frac{1}{2}x + \frac{1}{2} x > x + \frac{1}{2}x \\ \)

\(3 > \frac{2}{2}x + \frac{1}{2}x \\ \)

\(3 > \frac{3}{2}x \\ \)

Multiply sides by 2

\(3 \times 2 > 2 \times \frac{3}{2}x \\ \)

\(6 > 3x\)

Divided sides by 3

\( \frac{6}{3} > \frac{3}{3}x \\ \)

\(2 > x\)

\(x < 2\)

_________________________________

Done♥️♥️♥️♥️♥️

Answer:

hmmmmmmmmmmmmmmmmmmmm

\(Hello\) \(There!\)

Quite easy...

It's -20.

Hopefully, this helps you!!

P.S I love late points.

:>

\(AnimeVines\)

Answer:

Mary increased both assets and liabilities.

Step-by-step explanation:

Answer:

Negative 0.2 (x minus 4) = negative 1.7.

Negative 0.2 x + 0.8 = negative 1.7.

Negative 0.2 x = negative 2.5. x = 12.5.

Step-by-step explanation:

i believe thats the correct anwser

Answer:

its c

Step-by-step explanation:

on egde

Using the perimeter of the rectangle, it is found that she should buy at most 16 plants.

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

The perimeter of a rectangle of length l and width w is given by:

\(P = 2(l + w)\)

In this question, the perimeter is of 1 ft by 4.5, thus, \(l = 1, w = 4.5\), and the perimeter is:

\(P = 2(1 + 4.5) = 2(5.5) = 11\)

1 plant - 2/3 ft

x plants - 11 ft

Applying cross multiplication:

\(\frac{2x}{3} = 11\)

\(2x = 33\)

\(x = \frac{33}{2}\)

\(x = 16.5\)

At least 8 inches apart(can be more), thus she should buy at most 16 plants.

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The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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Answer:

k=1 or k=-15

Step-by-step explanation:

The first step is simplifying:

\(k^{2}+18k-15=4k\)

\(k^{2}+14k=15\)

Now, take half the k term and square it ( \((\frac{14}{2})^{2}=7^{2}=49\)), and add the result to both sides.

\(k^{2}+14k+49=64\)

Now, we know  \(k^{2}+14k+49=(k+7)^{2}\), so let's rewrite our equation as:

\((k+7)^{2}=64\)

Now we solve:

\((k+7)^{2}=64\)

\(k+7=\sqrt{64}\)

So k+7=8 or k+7=-8

Therefore k=1 or k=-15

The property that justifies the statement "OP = RS, RS = OP" with "Sym" is symmetry. Symmetry refers to the property of an object or equation where it remains unchanged under certain transformations or operations.

In this case, if we reflect the circuit across the line of symmetry, the circuit will be exactly the same as the original circuit, except that the voltage source will be flipped over.

Therefore, if we take the voltage across the resistor (RS) and multiply it by the resistance of the voltage source (R), we will get the same result as if we take the voltage across the resistor (OP) and multiply it by the resistance of the resistor (R). This property is symmetric, and thus the statement "OP = RS, RS = OP" is true

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Answer:

Sym. Prop. of ≅ is the correct answer

The distinct prime factors of 9999 are 3, 11, and 101. So the sum of each distinct prime factor of 9999 is 115.

To find the sum of the distinct prime factors of 9999, we first need to factorize 9999 into its prime factors.

9999 can be factorized as follows:

9999 = 3 * 3333

= 3 * 3 * 1111

= 3 * 3 * 11 * 101

So, the distinct prime factors of 9999 are 3, 11, and 101.

The sum of these distinct prime factors is:

3 + 11 + 101 = 115

Therefore, the sum of each distinct prime factor of 9999 is 115.

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Answer:

5

Step-by-step explanation:

Answer:

m<K = 51°

m<L = 78°

m<M = 51°

Step-by-step explanation:

Base angles of an isosceles ∆ are equal to each other, therefore,

m<M = m<K

Substitute

3x + 36 = 4x + 31

Collect like terms and solve for x

3x - 4x = -36 + 31

-x = -5

Divide both sides by -1

x = 5

Let's find each degree measure using the value of x

m<K = 4x + 31

Plug in the value of x

m<K = 4(5) + 31

m<K = 20 + 31

m<K = 51°

m<M = 3x + 36

= 3(5) + 36

= 15 + 36

m<M = 51°

m<L = 180° - (m<M + m<K) (sum of triangle theorem)

Substitute

m<L = 180 - (51 + 51)

m<L = 78°

Answer:

1) The equation of the line in slope-intercept form is \(y = 5\cdot x +9\). The equation of the line in standard form is \(-5\cdot x + y = 9\).

2) The equation of the line in slope-intercept form is \(y = \frac{2}{5}\cdot x +\frac{14}{5}\). The equation of the line in standard form is \(-2\cdot x +5\cdot y = 14\).

3) The equation of the line in slope-intercept form is \(y = 3\cdot x +4\). The equation of the line in standard form is \(-3\cdot x +y = 4\).

4) The equation of the line in slope-intercept form is \(y = 2\cdot x + 6\). The equation of the line in standard form is \(-2\cdot x +y = 6\).

5) The equation of the line in slope-intercept form is \(y = \frac{5}{6}\cdot x -\frac{7}{6}\). The equation of the line in standard from is \(-5\cdot x + 6\cdot y = -7\).

Step-by-step explanation:

1) We begin with the slope-intercept form and substitute all known values and calculate the y-intercept: (\(m = 5\), \(x = -1\), \(y = 4\))

\(4 = (5)\cdot (-1)+b\)

\(4 = -5 +b\)

\(b = 9\)

The equation of the line in slope-intercept form is \(y = 5\cdot x +9\).

Then, we obtain the standard form by algebraic handling:

\(-5\cdot x + y = 9\)

The equation of the line in standard form is \(-5\cdot x + y = 9\).

2) We begin with a system of linear equations based on the slope-intercept form: (\(x_{1} = 3\), \(y_{1} = 4\), \(x_{2} = -2\), \(y_{2} = 2\))

\(3\cdot m + b = 4\) (Eq. 1)

\(-2\cdot m + b = 2\) (Eq. 2)

From (Eq. 1), we find that:

\(b = 4-3\cdot m\)

And by substituting on (Eq. 2), we conclude that slope of the equation of the line is:

\(-2\cdot m +4-3\cdot m = 2\)

\(-5\cdot m = -2\)

\(m = \frac{2}{5}\)

And from (Eq. 1) we find that the y-Intercept is:

\(b=4-3\cdot \left(\frac{2}{5} \right)\)

\(b = 4-\frac{6}{5}\)

\(b = \frac{14}{5}\)

The equation of the line in slope-intercept form is \(y = \frac{2}{5}\cdot x +\frac{14}{5}\).

Then, we obtain the standard form by algebraic handling:

\(-\frac{2}{5}\cdot x +y = \frac{14}{5}\)

\(-2\cdot x +5\cdot y = 14\)

The equation of the line in standard form is \(-2\cdot x +5\cdot y = 14\).

3) By using the slope-intercept form, we obtain the equation of the line by direct substitution: (\(m = 3\), \(b = 4\))

\(y = 3\cdot x +4\)

The equation of the line in slope-intercept form is \(y = 3\cdot x +4\).

Then, we obtain the standard form by algebraic handling:

\(-3\cdot x +y = 4\)

The equation of the line in standard form is \(-3\cdot x +y = 4\).

4) We begin with a system of linear equations based on the slope-intercept form: (\(x_{1} = -3\), \(y_{1} = 0\), \(x_{2} = 0\), \(y_{2} = 6\))

\(-3\cdot m + b = 0\) (Eq. 3)

\(b = 6\) (Eq. 4)

By applying (Eq. 4) on (Eq. 3), we find that the slope of the equation of the line is:

\(-3\cdot m+6 = 0\)

\(3\cdot m = 6\)

\(m = 2\)

The equation of the line in slope-intercept form is \(y = 2\cdot x + 6\).

Then, we obtain the standard form by algebraic handling:

\(-2\cdot x +y = 6\)

The equation of the line in standard form is \(-2\cdot x +y = 6\).

5) We begin with a system of linear equations based on the slope-intercept form: (\(x_{1} = -1\), \(y_{1} = -2\), \(x_{2} = 5\), \(y_{2} = 3\))

\(-m+b = -2\) (Eq. 5)

\(5\cdot m +b = 3\) (Eq. 6)

From (Eq. 5), we find that:

\(b = -2+m\)

And by substituting on (Eq. 6), we conclude that slope of the equation of the line is:

\(5\cdot m -2+m = 3\)

\(6\cdot m = 5\)

\(m = \frac{5}{6}\)

And from (Eq. 5) we find that the y-Intercept is:

\(b = -2+\frac{5}{6}\)

\(b = -\frac{7}{6}\)

The equation of the line in slope-intercept form is \(y = \frac{5}{6}\cdot x -\frac{7}{6}\).

Then, we obtain the standard form by algebraic handling:

\(-\frac{5}{6}\cdot x +y =-\frac{7}{6}\)

\(-5\cdot x + 6\cdot y = -7\)

The equation of the line in standard from is \(-5\cdot x + 6\cdot y = -7\).

A linear equation can be written in slope intercept and in standard form.

(1) Slope = 5, Point = (-1,4)

The equation is calculated as:

\(\mathbf{y = m(x - x_1) + y_1}\)

So, we have:

\(\mathbf{y = 5(x + 1) + 4}\)

\(\mathbf{y = 5x + 5 + 4}\)

\(\mathbf{y = 5x + 9}\)

Subtract 5x from both sides

\(\mathbf{-5x + y = 9}\)

So, the equations are:

(2) Points = (3,4) and (-2,2)

First, we calculate the slope (m)

\(\mathbf{m =\frac{y_2 - y_1}{x_2 - x_1}}\)

So, we have:

\(\mathbf{m =\frac{2-4}{-2-3} = \frac{2}{5}}\)

The equation is calculated as:

\(\mathbf{y = m(x - x_1) + y_1}\)

So, we have:

\(\mathbf{y = \frac 25(x - 3) + 4}\)

\(\mathbf{y = \frac 25x - \frac{6}{5} + 4}\)

\(\mathbf{y = \frac 25x + \frac{-6 + 20}{5}}\)

\(\mathbf{y = \frac 25x - \frac{14}{5}}\)

Multiply through by 5

\(\mathbf{5y = 2x - 14}\)

Rewrite as:

\(\mathbf{2x - 5y = 14}\)

So, the equations are:

(3) Slope = 3, y-intercept = 4

The m and b in y = mx + b represent slope and y-intercept, respectively.

So, we have:

\(\mathbf{y = 3x + 4}\)

Rewrite as:

\(\mathbf{3x - y = -4}\)

So, the equations are:

(4) x-intercept = -3, y-intercept = 6

Calculate the slope using:

\(\mathbf{m = -\frac{y-intercept}{x-intercept}}\)

\(\mathbf{m = -\frac{6}{-3}}\)

\(\mathbf{m = 2}\)

The m and b in y = mx + b represent slope and y-intercept, respectively.

So, we have:

\(\mathbf{y = 2x + 6}\)

Rewrite as:

\(\mathbf{2x - y =-6}\)

So, the equations are:

(5) Points = (-1,-2) and (5,3)

First, we calculate the slope (m)

\(\mathbf{m =\frac{y_2 - y_1}{x_2 - x_1}}\)

So, we have:

\(\mathbf{m =\frac{3--2}{5--1} = \frac{5}{6}}\)

The equation is calculated as:

\(\mathbf{y = m(x - x_1) + y_1}\)

So, we have:

\(\mathbf{y = \frac 56(x + 1) - 2}\)

\(\mathbf{y = \frac 56x + \frac 56 - 2}\)

\(\mathbf{y = \frac 56x + \frac{5 - 12}{6}}\)

\(\mathbf{y = \frac 56x - \frac{ 7}{6}}\)

Multiply through by 6

\(\mathbf{6y = 5x - 7}\)

Rewrite as:

\(\mathbf{5x - 6y =7}\)

So, the equations are:

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So, the first mechanic charged $30 per hour, and the second mechanic charged $10 per hour using given equation.

Let's assume the first mechanic's rate per hour is x, and the second mechanic's rate per hour is y.

According to the given information, the first mechanic worked for 10 hours, so the amount charged by the first mechanic would be 10x. Similarly, the second mechanic worked for 5 hours, so the amount charged by the second mechanic would be 5y.

The total amount charged is given as $200.

Therefore, we have the equation:

10x + 5y = 200

We are also given that the sum of the two rates is $40 per hour:

x + y = 40

We have a system of two equations with two unknowns. We can solve this system using the Aleks graphing calculator or other methods.

Solving the system, we find that x = 30 and y = 10.

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The rate at which the angle between the ladder and the wall changes is 30√75 ft/sec and the rate at which the base of the ladder slides away from the wall at this instant is 13.2 ft/sec.

When a 10-foot ladder slides down a wall at a rate of 3 ft/sec, the rate at which the (acute) angle between the ladder and the wall changes when the foot of the ladder is 5 feet from the wall and the rate at which the base of the ladder slides away from the wall are required to be calculated.

Let's mark the length of the ladder as ‘l’ and the distance of the ladder from the wall as ‘x’.If the ladder has slid x feet down the wall at time t, the triangle formed by the ladder, the wall, and the ground is such that l² = x² + y². The angle is θ, then sin θ = y/l, cos θ = x/l, and tan θ = y/x.

Thus, we have the following equation:(l)² = (x)² + (y)²Differentiate with respect to t.2(l)(dl/dt) = 2(x)(dx/dt) + 2(y)(dy/dt)

Solve for dy/dt when x = 5ft and dx/dt = 3 ft/sec.dy/dt = (l/x)(dx/dt)√[l² - x²]dy/dt = (10/5)(3)√[10² - 5²]dy/dt = 30√75 ft/sec

Now, let's differentiate the equation l² = x² + y² with respect to time:2l(dl/dt) = 2x(dx/dt) + 2y(dy/dt)

We have already calculated the value of dy/dt from the previous step. Substituting, l = 10, x = 5 and dx/dt = 3, we get: 20(dl/dt) = 10(3) + 2(5)(30√75)dl/dt = 13.2 ft/sec

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Answer:

48.852

Step-by-step explanation:

\(5.31=\dfrac{p}{9.2}\)

Multiply both sides by 9.2:

\((5.31)\times9.2=(\dfrac{p}{9.2} )\times9.2\)

\(48.852=p\)

\(\boxed{p=48.852}\)

Answer:

£12000

Step-by-step explanation:

1 year = 1.5%

4 years = 6%

6% = 0.06

200000 times 0.06 = £12000

So, Katy will get £12000 interest rate at the end of 4 years.

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Answer:

£3,137

Step-by-step explanation:

First year: £200000 x 1.5% = £3,000

Second year: £203,000 x 1.5% = £3,045

Third year: £206,045 (because of 203,000+3,045) x 1.5% = £3,090.675

Last year: £209,135.675 x 1.5% = approximately £3,137

Answer:

x = 240

A = 30 m, B = 60 m, C= 90 m

Step-by-step explanation:

a) Nosotros debemos determinar un numero;

para cual \(\dfrac{1}{4}x = 60\)

\(0.25 x = 60\)

Divide ambos lados entre 0.25; tenemos :

\(\dfrac{0.25 x}{0.25}= \dfrac{60}{0.25}\)

x = 240

b) A 180 m se corta en tres piezas A, B y C

Entonces;

Si la pieza B y la pieza C miden el doble y el triple de esa pieza A, respectivamente. Entonces; tenemos

x + 2x + 3x = 180

6x = 180

Divide ambos lados entre 6; tenemos:

\(\dfrac{6x}{6} = \dfrac{180}{6}\)

x = 30 m

Si A = x = 30 m

B = 2x = 2×30 m = 60 m

C = 3x = 3×30 m = 90 m

Así; A = 30 m, B = 60 m, C= 90 m

Answer:

\( \boxed{ \tt{x + y}}\)

Answer:

\(1386 in^2\)

r: radius

Circumference:  \(2\pi r\)

Area: \(\pi r^2\\\)

In this case, we are using 22/7 as an estimation for pi.

Plug into the area formula.

22/7 * (21)^2

22/7 * 441

\(1386 in^2\)

Matrix A is given as follows;\($$\begin{pmatrix}1&3&5\\0&1&0\\-5&0&-1\end{pmatrix}$$\)To determine the dimensions of Nul A, Col A, and Row A for the given matrix, the following is the main answer;The dimension of Nul A is 0, whereas the dimension of Col A is 3 and the dimension of Row A is 3.

The dimension of the Null space (Nul A) is the number of dimensions of the input which is mapped to the zero vector by the linear transformation defined by the matrix. In this case, the dimension of Nul A is zero since the reduced row echelon form of matrix A has three pivot columns that contain no zero entries.This can be computed as follows;\($$\begin{pmatrix}1&3&5\\0&1&0\\-5&0&-1\end{pmatrix}\begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}=\begin{pmatrix}0\\0\\0\end{pmatrix}$$The equation above is solved as follows;$x_1=-3x_2-5x_3$$x_2=0$$$$x_3=0$\)

Thus the vector $x=\begin{pmatrix}-3\\0\\0\end{pmatrix}$ spans the Nul A. Since the span of this vector is only one-dimensional, it follows that the dimension of the null space of A is 1.The dimension of the column space (Col A) is the dimension of the linear space spanned by the columns of A. In this case, the dimension of Col A is three, since matrix A has three pivot columns that span $\mathbb{R}^3$.Thus, the dimension of the column space of A is 3.The dimension of the row space (Row A) is the dimension of the linear space spanned by the rows of A. In this case, the dimension of Row A is also three since there are three rows that span $\mathbb{R}^3$.Thus, the dimension of the row space of A is 3.

The dimension of Nul A is 0. The dimension of Col A is 3. The dimension of Row A is 3.Thus, the long answer is;The dimension of Nul A is 0, whereas the dimension of Col A is 3 and the dimension of Row A is 3.

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Answer:

Explanation:

2.25 is a decimal and 225/100 or 225% is the percentage for 9/4.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope I helped!!!

GL :)

actual cost is 950+23,500=24450

he sold them for 25000 so his profit is 25000-950-23500=550

Answer:

A cycle + A scooter

= 950 + 23,500

= 24,450

Profit = Sold - cost

= 25,000 - 24,450

= 550

So the profit is $550

Function 1 and Function 2 have y-intercepts that are equal. The solution has been obtained by using slope-intercept form.

What is slope-intercept form?

The line that represents the graph of the equation y = mx + b has a slope of m and a y-intercept of b. The m and b values are real integers, and the slope-intercept form of the linear equation is used.

We are given two functions.

Now, we will represent the functions in the slope-intercept form to find the y-intercept.

Function 1

⇒4x - 2y = -2

⇒2x - y = -1               (Dividing both sides by 2)

⇒ -y = -1 - 2x

⇒y = 2x + 1

So, the y-intercept is 1.

Function 2

We are given two points as (-1,3) and (0,1)

The slope comes out to be = -2

So, b = 3 - (-2)(-1) = 1

So, the y-intercept is 1.

Hence, function 1 and function 2 have y-intercepts that are equal.

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Answer:

I don't see anything!!!!

Answer:

85 beats per minute

Step-by-step explanation:

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