The estimated quotient of 895 divided by 19 is what number?a. 40 b. 45 c. 55 d. 60

Answer:

32

Step-by-step explanation:

8*4=32

The answer is , the nth term of the quadratic sequence is: nth term = 2n² - 7

The quadratic sequence you provided is -5, -3, 3, 13, 27, 45, 67. To find the nth term of this sequence, we first need to determine the common second difference, which represents the quadratic coefficient.
1st differences: 2, 6, 10, 14, 18, 22
2nd differences: 4, 4, 4, 4, 4
The common second difference is 4, so the quadratic coefficient (a) is 4/2 = 2. Now, we can set up a quadratic equation in the form an² + bn + c:
nth term = 2n² + bn + c
To find b and c, we can use the first two terms of the sequence:
-5 = 2(1)² + b(1) + c
-3 = 2(2)² + b(2) + c
Solving the system of equations, we get:
b = 0 and c = -7
So, the nth term of the quadratic sequence is:
nth term = 2n² - 7

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A mathematical concept known as the distributive principle explains how to simplify multiplication, addition, and subtraction-based expressions.

A basic property of mathematics known as the distributive property is frequently used in algebraic operations and problem-solving.

For example, if you have the expression  \(2 \times(3 + 4),\) you can use the Distributive Property to simplify it as follows:

\(2 \times (3 + 4) = (2 \times 3) + (2 \times 4) = 6 + 8 = 14\)

Similarly, if you have the expression  \(5 \times (2 - 3)\) , you can use the Distributive Property to simplify it as follows:

\(5 \times (2 - 3) = (5 \times2) - (5 \times 3) = 10 - 15 = -5\)

Therefore,

a. Multiplicative Inverse \(- 4. $5 \cdot \frac{1}{5}=1$\)

b. Additive Inverse  \(- 5. $7+(-7)=0$\)

c. Commutative Property of Multiplication  \(- 1. $5 \cdot 6=6 \cdot 5$\)

d. Distributive Property  \(- 6. $5(x-4)=5 x-20$\)

e. Additive Identity Property  \(- 2. $-8+0=-8$\)

f. Associative Property of Addition \(- 3. $(3+5)+9=3+(5+9)$\)

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To determine the control limits for the fraction of defective batteries using three sigma limits, we will follow certain steps. A sample of 50 batteries was used to collect data and the data below shows how many batteries out of each sample failed the test. Sample Number of Failed Batteries 1 4 2 2 3 5 4 2 5 4 6 8 7 3 8 2.

First, we need to find the mean of the sample size of the failed batteries and use it to calculate the upper and lower control limits (UCL and LCL). Next, we will calculate the fraction of batteries that failed for each sample, which is value = (number of failed batteries)/50.

Now, let us find the mean and standard deviation of these fractions. First, we will calculate the sum of all the values and divide it by the number of values to get the mean. Mean = (4 + 2 + 5 + 2 + 4 + 8 + 3 + 2)/400 = 0.0375. Then, we will find the standard deviation of these values, which is 0.0172.

The upper and lower control limits will now be calculated. Upper control limit = 0.0375 + 3(0.0172) = 0.0891. Lower control limit = 0.0375 - 3(0.0172) = -0.0141.

However, we can see that the lower control limit is negative, which is not possible since the fraction value cannot be negative. Thus, we will set the lower control limit to zero. The final control limits for the fraction of defective batteries are: Upper control limit = 0.0891 and Lower control limit = 0.0000 (or 0).

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I would call this method incorrect.

If you're trying to solve for b, what you should do is first isolate b ² :

5 + b ² = 30

b ² = 30 - 5

b ² = 25

Then take the square root of both sides, noting that √(x ²) = |x| for all x :

√(b ²) = √25

|b| = 5

Then b = +5 or b = -5.

Given:

The equation is

\(y = 0.445x + 14.7\)

To find:

The given equation as function P.

Solution:

We have, the given equation \(y = 0.445x + 14.7\), to write it as a function P, we need to substitute y=P(x) in the given equation.

On substituting y=P(x) in equation \(y = 0.445x + 14.7\), we get

\(P(x)= 0.445x + 14.7\)

Therefore, the required function is \(P(x)= 0.445x + 14.7\).

Answer:

2/935

Step-by-step explanation:

I have attached an image of the equation to use. Assuming that this is without replacement, we'll be taking out one piece out of the bag every time that one is chosen.

Therefore, for probability, the fraction is part/whole. We first have 9 red to 36 pieces in total, but if we take one out, we'll get 8 red left in the bag, and 35 pieces in total. This continues until we fulfill the prophecy (I don't know. qualifications?) that 4 of the pieces are red.

You can try this for yourself, but once simplified, it should be 3024/1413720, which simplifies to 2/935.

Please let me know if you need more clarification or have issues! probability can be confusing :)

Answer:

2/935

Step-by-step explanation:

dito^

The number of lattice paths from (2, 1) to (24, 30) with a constraint of passing through (8, 10) but not (7, 7) or (16, 25) is a complex problem that requires a detailed mathematical calculation, that is explained below.

Lattice paths are sequences of steps in the form of up steps (U) and right steps (R) that connect two points in a grid. The number of lattice paths from one point to another can be calculated using combinatorics.

To determine the number of lattice paths from (2, 1) to (24, 30) that pass through the point (8, 10) but do not pass through either of the points (7, 7) and (16, 25), we need to calculate the total number of paths and subtract the number of paths that pass through the restricted points.

Let's call the total number of paths T, the number of paths that pass through (8, 10) P, the number of paths that pass through (7, 7) Q, and the number of paths that pass through (16, 25) R.

The number of paths from (2, 1) to (8, 10) is given by the binomial coefficient C(10 - 1, 8 - 2) = C(9, 6) = 84.

The number of paths from (8, 10) to (24, 30) is given by the binomial coefficient C(30 - 10, 24 - 8) = C(20, 16) = 18564.

The number of paths from (2, 1) to (24, 30) that pass through (8, 10) is given by T = P = 84 * 18564 = 1,547,136.

Similarly, the number of paths from (2, 1) to (7, 7) is given by the binomial coefficient C(7 - 1, 7 - 2) = C(6, 5) = 15.

The number of paths from (7, 7) to (24, 30) is given by the binomial coefficient C(30 - 7, 24 - 7) = C(23, 17) = 9,139,554.

The number of paths from (2, 1) to (24, 30) that pass through (7, 7) is given by Q = 15 * 9139554 = 137,093,310.

The number of paths from (2, 1) to (16, 25) is given by the binomial coefficient C(25 - 1, 16 - 2) = C(24, 14) = 3003.

The number of paths from (16, 25) to (24, 30) is given by the binomial coefficient C(30 - 25, 24 - 16) = C(5, 8) = 70.

The number of paths from (2, 1) to (24, 30) that pass through (16, 25) is given by R = 3003 * 70 = 210,210.

Finally, the number of paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is T - P - Q - R = 1547136 - 137,093,310 - 210,210 = -135,599,384.

The number of lattice paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is zero, as the result is negative.

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Answer:

The value of x is 138

Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

The equation that represents p, the number of seashells that Pierre collected is 3p + p = 52

From the question, we are to determine the equation which represents p

From the given information,

Nardia collected triple the number of seashells that Pierre did

If Pierre collected p number of seashells

Then,

Nardia collected 3p number of seashells

Also, from the given information,

They collected 52 seashells in total

That is,

3p + p = 52

Hence, the equation that represents p, the number of seashells that Pierre collected is 3p + p = 52.

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Check the picture below.

let's recall that on an isosceles triangle, twin sides make twin angles.

The volume of the solid of revolution generated by revolving the region under the curve y = √x from x = 0 to x = 10 about the x-axis is approximately 1046.67 cubic units.

To find the volume of the solid of revolution, we can use the method of cylindrical shells. The volume of each cylindrical shell is given by the formula V = 2πrhΔx, where r is the radius of the shell, h is the height of the shell, and Δx is the width of the shell.

In this case, the radius of the shell is given by r = √x, and the height of the shell is h = y = √x. Since we are revolving the region about the x-axis, the width of each shell is Δx.

To find the volume, we integrate the formula V = 2π∫(√x)(√x)dx over the interval [0, 10].

Evaluating the integral, we get V = 2π∫(x)dx from 0 to 10.

Integrating, we have V = 2π[(x^2)/2] from 0 to 10.

Simplifying, V = π(10^2 - 0^2) = 100π.

Approximating π as 3.14159, we find V ≈ 314.159 cubic units.

Therefore, the volume of the solid of revolution generated by revolving the region under the curve y = √x from x = 0 to x = 10 about the x-axis is approximately 1046.67 cubic units.

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In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

Answer:

140

Step-by-step explanation:

Sum of angles around a point = 360

So, if one angle 8 reflex and measures 220, it’s adjacent side measures.

360-220 = 140.

Hope this helps.

Good Luck

Answer:

A

Step-by-step explanation:

what is even going on at A

Hence,

The equivalent value of the function \(\rm f(x) = -2x^2 -3x + 5\) if x = -3 is -4.

Function; \(\rm f(x) = -2x^2 -3x + 5\) for the input value –3.

What are the x-intercepts of the function f(x)?

To determine the value of the function following all the steps given below.

For x = -3, we will have to substitute x = -3 into the expression to have:

Then,

The value of f(x) when x is -3 is,

\(\rm f(-3) = -2(-3)^2 -3(-3) + 5\\\\ f(-3) = -2(9) + 9 + 5 \\\\f(-3) = -18 + 14 \\\\\f(-3) = -4 \)

Hence, The equivalent value of the function \(\rm f(x) = -2x^2 -3x + 5\) if x = -3 is -4.

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If the intended margin of error equals 4 less than with a 0.95 probability, the sample size is 126.

The \(\alpha\) level is calculated by subtracting 1 from the confidence interval and dividing by 2.

\(\alpha\) = (1 - 0.95) ÷ 2

\(\alpha\) = 0.025

Find z inside the Z-table because it has a p-value of 1 - \(\alpha\).

So, z = 1.96 with a p-value = 1 - 0.025 = 0.975.

Now, consider that margin of error M.

M = z × (σ ÷ √n)

The standard deviation is determined as the square root of variance.

σ = √522 = 22.84

With a 0.95 probability, the sample size that requires to be accepted if the expected margin of error is 4 or less is,

The sample size of at least n, in which n is encountered when M = 4. So,

M = z × (σ ÷ √n)

4 = 1.96 × (22.84 ÷ √n)

4√n = 1.96 × 22.84

√n = (1.96 × 22.84) ÷ 4

√n = 11.1916

n = (11.1916)²

n = 125.25 ≈ 126

A sample size of at minimum 126 people is required.

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Work Shown:

Your teacher gave you the wrong formula. You should use the nPr formula instead of nCr. This is because order matters when forming passcodes.

For instance, the password 3CJ5 is different from J5C3

For this problem, we have n = 6 different characters and we're selecting r = 4 of them.

\(_n P _r = \frac{n!}{(n-r)!}\\\\_6 P _4 = \frac{6!}{(6-4)!}\\\\_6 P _4 = \frac{6!}{2!}\\\\_6 P _4 = \frac{6*5*4*3*2*1}{2*1}\\\\_6 P _4 = \frac{720}{2}\\\\_6 P _4 = 360\\\\\)

A slightly alternative method is to notice there are 4 slots to fill. Each slot being a digit in the passcode.

For the first slot we have 6 choices. The second has 5 choices since we can't reuse whatever goes in the first slot. We count our way down until all four slots are filled. We then multiply out the values to get

6*5*4*3 = 30*12 = 360

which is the number of permutations where we pick four items from a pool of six total.

Answer:)0.3 I Think

Step-by-step explanation:

1.8/6

The answer is:

10.8 cm

Explanation:

6 × 1.8 = 10.8

- firstly, remove the decimal point

- Secondly, multiply regularly 6 by 18

- You'll get 108 as an answer

- Take back the decimal point one to the left because you took it one to the right before, so you will have to do the inverse of the previous action

Good luck

Answer:

x = 18

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 15 when x = 9 , then

15 = 9x ( divide both sides by 9 )

\(\frac{15}{9}\) = x , that is

x = \(\frac{5}{3}\)

y = \(\frac{5}{3}\) x ← equation of variation

when y = 30 , then

30 = \(\frac{5}{3}\) x ( multiply both sides by 3 to clear the fraction )

90 = 5x ( divide both sides by 5 )

18 = x

Answer:

The twelve can be rewritten as: n = 3 5 × 12 1. Now, we can multiply the numerators and denominators: n = 3 ×12 5 × 1. n = 36 5.

Step-by-step explanation:

Answer:

There are 100³ = 1000000 cubic cm in one cubic meter so the answer is 0.1 / 1000000 = 1 / 10000000 = 0.0000001 cubic meters.

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

25

Step-by-step explanation:

brainliest please!

Answer: -16

Step-by-step explanation:

First, we need to solve the parentheses by performing the operation inside them. (-7 + 3) equals -4, so we can substitute that in the expression to get:

(-7 + 3)4 = -4 × 4

Next, we can perform the multiplication operation:

-4 × 4 = -16

Therefore, (-7 + 3)4 = -16.

Answer:

-16

Step-by-step explanation:

First, you distribute 4 into the equation, basically multiplying, so 4 * 3 is 12, then 4 * -7 is -28. Add them together so -28 + 12 is -16

Hope this helps <3

The equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.

To find the equation of the tangent line to the curve at the given point, we will differentiate the equation implicitly with respect to x.

Differentiating both sides of the equation x^(2/3) + y^(2/3) = 4 with respect to x, we get:

(2/3)x^(-1/3) + (2/3)y^(-1/3) * (dy/dx) = 0

Now we need to find the value of dy/dx at the point (-3sqrt3, 1).

Substituting x = -3sqrt3 and y = 1 into the equation, we have:

(2/3)(-3sqrt3)^(-1/3) + (2/3)(1)^(-1/3) * (dy/dx) = 0

Simplifying, we get:

(2/3)(-1/sqrt(3)) + (2/3) * (dy/dx) = 0

Simplifying further, we have:

-2/(3sqrt3) + (2/3) * (dy/dx) = 0

Now we can solve for (dy/dx):

(dy/dx) = 2/(2sqrt3) = 1/sqrt3

So the slope of the tangent line at the point (-3sqrt3, 1) is 1/sqrt3.

Now we have the slope of the tangent line and the point (-3sqrt3, 1), we can use the point-slope form to find the equation of the tangent line. The equation is given by:

y - y1 = m(x - x1)

Substituting the values, we have:

y - 1 = (1/sqrt3)(x - (-3sqrt3))

Simplifying, we get:

y - 1 = (1/sqrt3)(x + 3sqrt3)

y - 1 = (1/sqrt3)x + 3

Finally, rearranging the equation, we have:

y = (1/sqrt3)x + 4

So the equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.

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Answer:

The first and second angles are 27° and the third angle is 126°.

Step-by-step explanation:

We have that the third angle (β) is 45° more than three times the measure of either of the other two​ angles (θ):

\( \beta = 45 + 3\theta \)     (1)

Also, the sum of the measures of the 3 angles is 180°:

\( \beta + \theta + \theta = 180 ^{\circ} \)   (2)

By entering equation (1) into equation (2) we have:

\( 45 + 3\theta + \theta + \theta = 180 \)  

\( 5\theta = 180 - 45 \)

\( \theta = 27 \)

Hence, the third angle is:

\( \beta = 45 + 3\theta = 45 + 3*27 = 126 \)                                  

Therefore, the first and second angles are 27° and the third angle is 126°.

I hope it helps you!