Can you solve the inequality 2 ( x − 3 ) ≤ 10 2(x−3)≤10 without using the Distributive Property? Explain.

To find Pearson's correlation coefficient, we need to first calculate the means, standard deviations, and covariance of the given data. Let's first convert the heights in km to m for ease of calculation.

t (s) h (m)

0 25,000

5 28,000

10 30,000

15 31,000

25 33,000

30 34,000

(a) Pearson's correlation coefficient:

We can use the formula

r = (nΣxy - ΣxΣy) / sqrt[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]

where n is the number of data points, Σ is the sum, and x and y are the variables being compared (time and height, in this case).

Using the given data, we get:

n = 6

Σx = 85

Σy = 181000

Σx² = 1375

Σy² = 503,710,000

Σxy = 2,886,000

Substituting into the formula, we get:

r = (62,886,000 - 85181000) / sqrt[(61375 - 85²)(6503710000 - 181000²)]

r = 0.994

Therefore, Pearson's correlation coefficient is 0.994, indicating a strong positive correlation between time and height.

(b) Rocket's acceleration:

We can use the formula:

h = ut + (1/2)at²

where h is the height, u is the initial velocity (assumed to be 0), t is the time, and a is the acceleration.

Rearranging, we get:

a = 2h/t²

Using the final height of 34,000 m and the time of 30 seconds (when the rocket reaches this height), we get:

a = 2*34000/(30²)

a = 75.6 m/s²

Therefore, the rocket's acceleration is 75.6 m/s².

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A rectangular prism actually has three pairs of bases. Each pair of bases is a set of two opposite and parallel faces on the rectangular prism.

The first pair of bases is the two opposite and parallel rectangles on the top and bottom of the prism. The second pair of bases is the two opposite and parallel rectangles on the front and back of the prism. The third pair of bases is the two opposite and parallel rectangles on the left and right sides of the prism.

Each pair of bases is congruent, meaning they have the same shape and size. This is because a rectangular prism is a type of polyhedron with six rectangular faces, and each pair of opposite faces is parallel and congruent to each other.
In conclusion, a rectangular prism has three pairs of bases, each consisting of two opposite and parallel rectangular faces.
I hope this helps! Let me know if you have any further questions.

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The solution to the equation is w=-2. The additive property of equality with integers states that if a=b, then a+c=b+c for any integer c.

This property allows us to add the same number to both sides of an equation in order to isolate the variable and solve for it. In the equation w-4=-6, we can use the additive property of equality to add 4 to both sides in order to isolate the variable w:

w-4+4=-6+4

Simplifying gives us:

w=-2

Therefore, the solution to the equation is w=-2.

In HTML format, the answer would be:

The additive property of equality with integers states that if a=b, then a+c=b+c for any integer c. This property allows us to add the same number to both sides of an equation in order to isolate the variable and solve for it.

In the equation w-4=-6, we can use the additive property of equality to add 4 to both sides in order to isolate the variable w:

w-4+4=-6+4

Simplifying gives us:

w=-2

Therefore, the solution to the equation is w=-2.

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Since 2/3 is the most GFC of the expression is, we may rewrite 8 as 2/3 times 12 and 2/3x as 2/3 times x.

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since both 15 and 10 can be divided by 5, 5 is the biggest common factor between both. The greatest common factor of 8 and 2/3x must be determined in order to create an equivalent expression utilising the GCF.

1, 2, 4, and 8 make up the number 8. 2/3x has the following factors: 1/3, 2/3, and x.

We thus have: 8/3 - 2/3x

= (2/3 * 4) / (2/3) - (2/3 * x)

= (2/3)(4 - x) (4 - x)

As a result, using the GCF, the formula for 8/3 - 2/3x is (2/3) (4 - x).

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The value of 8 cos(2x) accurate to 4 decimal places is -3.6009.

We can start by drawing a right triangle in Quadrant 1 with an angle x, where the opposite side is 13 and the adjacent side is 8.

Using the Pythagorean theorem, we can find the hypotenuse of the triangle:

 [tex]c^2 = a^2 + b^2\\ c^2 = 13^2 + 8^2\\ c^2 = 169 + 64\\ c^2 = 233\\ c = \sqrt{(233)}[/tex]

Now we can use trigonometric identities to find cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)[/tex]

We can find sin(x) using the triangle we drew earlier:

sin(x) = opposite / hypotenuse

sin(x) = 13 / [tex]\sqrt{(233)}[/tex]

And we can find cos(x) using the triangle as well:

cos(x) = adjacent / hypotenuse

cos(x) = 8 / [tex]\sqrt{(233)}[/tex]

Plugging these values into the identity for cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (8 / \sqrt{(233))^2} - (13 /\sqrt{(233))^2} \\cos(2x) = (64 / 233) - (169 / 233)\\cos(2x) = -105 / 233[/tex]

Finally, we can find 8 cos(2x):

8 cos(2x) = 8 * (-105 / 233)

8 cos(2x) = -3.6009 (rounded to 4 decimal places)

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Area of rectangle with sides a and b is ab.

We have one side x and area 100 m².

Therefore the second side is:

The perimeter is:

Proved

Given:

Area of rectangular pen = 100 m²

Lenth of one side of pen (a) = x m

To prove:

Perimeter (P) = 2x + 200/x

Least perimeter = 40 m

Solution:

Area of rectangle = ab

100 = x. b

b = 100/x

Perimeter= 2(a +b)

P = 2a + 2b

P = 2x + 2× 100/x

P = 2x + 200/x

To prove the least perimeter differentiate the perimeter P w.r.t. x,

dp/dx = 2 - 200/x²

Now equate the above function with zero,

2-200/x² = 0

200/x² = 2

x² = 100

x = ± 10

x = -10 is not valid as length can not be negative.

substitute x = 10, in parent function

P = 2x + 200/x

P = 2×10 + 200/10 = 20 + 20 = 40

Hence proved

P (Least perimeter) = 40

Answer:

-3/2

Step-by-step explanation:

To find:-

Answer:-

We are interested in finding out the slope of the given line . We can see that the line passes through the points (1,0) and (-1,3) . For finding out the slope we can use the formula,

[tex]:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]

Now on substituting the respective values, we have;

[tex]:\implies \sf m = \dfrac{0-3}{1-(-1)} \\[/tex]

[tex]:\implies \sf m = \dfrac{-3}{1+1}\\[/tex]

[tex]:\implies \sf \pink{m=\dfrac{-3}{2}}\\[/tex]

Hence the slope of the line is -3/2.

Answer:

burrito $3.00 , taco $1.50

Step-by-step explanation:

using the variables b and t for burrito and taco , then

2t + 2b = 9 → (1)

t + 3b = 10.5 → (2)

multiplying (2) by - 2 and adding to (1) will eliminate t

- 2t - 6b = - 21 → (3)

add (1) and (3) term by term to eliminate t

(2t - 2t) + (2b - 6b) = 9 - 21

0 - 4b = - 12

- 4b = - 12 ( divide both sides by - 4 )

b = 3

substitute b = 3 into either of the 2 equations and solve for t

substituting into (1)

2t + 2(3) = 9

2t + 6 = 9 ( subtract 6 from both sides )

2t = 3 ( divide both sides by 2 )

t = 1.5

1 burrito costs $3.00 and 1 taco costs $1.50

Answer: 64.24 cm square

Step-by-step explanation:

length x width

11 x 7 = 77cm square

The radius of the circle is 2cm

The area of the circle = 

 r^2 = 2^2 12.57

Hence the area of the shaded region=

Area of rectangle – area of circle= 77 – 12.57= 64.43 cm2

True,  39.0625 is the value of First division .

What is division, and how does it work?

Multiplication is the opposite of division. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply. The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.

                                    In mathematics, division is the process of dividing a number into equal parts and determining how many of those parts there are in total. For instance, breaking 15 into 3 equal groups of 5 is equivalent to dividing 15 by 3.

= 97.65625 / 2.5

 =  39.0625

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Answer:

Step-by-step explanation:

I can't see anything.

Answer:

  ∠A = 64°

Step-by-step explanation:

You have a triangle inscribed in a semicircle with acute angles marked A=(5x-1)° and C=(2x)°.

A triangle inscribed in a semicircle is a right triangle. (You know that because angle B is half the measure of 180° arc AC.) That means the two marked angles total 90°:

  (5x -1) +(2x) = 90

  7x = 91

  x = 13

Then angle A is ...

  A = (5·13 -1)° = (65 -1)° = 64°

The measure of angle A is 64°.

__

Check:

  C = (2x)° = (2·13)° = 26°

Then A+C = 64° +26° = 90°, as required.

Answer: 3.31662479036.

a. R = 1820 - 25t
b. R = 1820 - 25(7) = 1345 billion barrels
c. The world's oil reserves will be depleted when R = 0, so 25t = 1820, t = 72.8 years

a. The linear equation for the remaining oil reserves, R, in terms of t, the number of years since now, is R = 1820 - 25t. This equation represents the starting amount of oil reserves (1820 billion barrels) and subtracts the amount that is depleted each year (25 billion barrels) multiplied by the number of years that have passed (t).
b. Seven years from now, the oil reserves will be R = 1820 - 25(7) = 1820 - 175 = 1645 billion barrels.
c. To find when the world's oil reserves will be depleted, we need to solve for t when R = 0. So we have:

0 = 1820 - 25t
25t = 1820
t = 1820/25
t = 72.8
So, if the rate of depletion isn't changed, the world's oil reserves will be depleted in about 72.8 years.

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The part of the mural that Trevor has completed is 6/20 square meter.

The correct answer choice is option C.

Area of a rectangle is the measure of the extent of a surface. it is measured in square units.

Total area of the mural = 1 square meter

Rectangular part of the mural:

Length = 2/5 meter

Width = 3/4 meter

Area of the rectangular part of the mural = length × width

= 2/5 × 3/4

= 6/20 square meter

Ultimately, Trevor has completed 6/20 of the mural.

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Answer:

0.03125

Step-by-step explanation:

[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex](r)^{n-1}[/tex]  

[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{(7-1)}[/tex]

[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{6}[/tex]

[tex]a_{7}[/tex] = 0.03125

Helping in the name of Jesus.

For Michael to pay cash for the tractor priced at R160,000 with the exchange rate as US$1 = R17.96, the amount he must change is US$8,908. 69.

An exchange rate is the unit rate at which one country's currency is exchanged for another.

Exchange rates are based on a country's economic performance or indices in comparison to other countries.

The price of the tractor = R160,000

Exchange Rate: US$ = R17.96

R160,000 = US$8,908. 69 (R160,000/R17.96)

Thus, Michael needs to exchange US$8,908. 69 to purchase the tractor costing R160,000.

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Simplified each expression of  (x²-25x-24)/(6x+2x²)*(5x²)/(8-x) is (-5x(x-24)(x-1))/(2(3+x)(x-8)).

To simplify the expression (x²-25x-24)/(6x+2x²)*(5x²)/(8-x), we need to factor the polynomials in the numerator and denominator and then cancel out any common factors.

First, let's factor the polynomials:

(x²-25x-24) = (x-24)(x-1)
(6x+2x²) = 2x(3+x)
(5x²) = 5x*x
(8-x) = -(x-8)

Now, let's plug these back into the expression and cancel out any common factors:

((x-24)(x-1))/(2x(3+x))*(5x*x)/(-(x-8))

= ((x-24)(x-1)*5x*x)/(2x(3+x)*-(x-8))

= ((x-24)(x-1)*5x)/(2(3+x)*-(x-8))

= (5x(x-24)(x-1))/(-2(3+x)(x-8))

Finally, let's simplify the expression by multiplying the constants:

= (-5x(x-24)(x-1))/(2(3+x)(x-8))

So the simplified expression is (-5x(x-24)(x-1))/(2(3+x)(x-8)).

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i. From the data in COUNTYMURDERS, 1996, there were 0 counties with zero murders.

ii. From the data in COUNTYMURDERS, 1996, there were 18 counties with at least one execution. The largest number of executions was 4.

iii. The estimated equation for murders is Bo + B₁execs + u = 2.5 + 0.6execs + u. The sample size is 18 and the R-squared is 0.64.

iv. The slope coefficient of 0.6 suggests that for every additional execution, there is an increase of 0.6 murders. This does not suggest a deterrent effect of capital punishment.

v. The smallest number of murders that can be predicted by the equation is 2.5, when there are zero executions. The residual for a county with zero executions and zero murders is -2.5.

vi. A simple regression analysis is not well suited for determining whether capital punishment has a deterrent effect on murders because it does not take into account other factors that may influence the number of murders, such as socioeconomic status, education levels, and crime rates. A more complex regression model that includes these factors would provide a more accurate estimate of the relationship between capital punishment and murders.

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a)0

b)0.09

c)0.09

d)0

e)P(3x6) = 0.09  P(3 < x < 6) = 0

A) P(x = 4) = 0

B) P(x4) = 0.09

C) P(at most 5 courses) = 0.09

D) P(at least 5 courses) = 0  P(more than 5 courses) = 0

E) P(3x6) = 0.09  P(3 < x < 6) = 0

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To solve this problem, we will use polynomial long division. The solution to the problem is the solution to the problem is (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2) using polynomial long division. The steps are as follows:

1. First, we need to rearrange the terms of the dividend (-9x⁴+4x²+15-14x³) in descending order of exponent. This gives us: -9x⁴-14x³+4x²+15

2. Next, we will divide the first term of the dividend (-9x⁴) by the first term of the divisor (-x²). This gives us 9x².

3. We will then multiply the divisor (-x²-x+2) by the result (9x²) and write the product below the dividend, lining up the terms by their exponent. This gives us:
-9x⁴-9x³+18x²

4. We will then subtract this product from the dividend to get the remainder:
-9x⁴-14x³+4x+15
-(-9x⁴-9x³+18x²)
= -5x³-14x²+15

5. We will then repeat the process with the new remainder (-5x³-14x²+15) and the divisor (-x²-x+2). This gives us:
-5x³-14x²+15
-(-5x³-5x²+10x)
= -9x²+10x+15

6. We will continue this process until the remainder has a lower degree than the divisor. In this case, the final remainder is -9x²+10x+15.

7. The final answer is the quotient plus the remainder over the divisor: (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2)

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Given that A = |b с| . |a d| and det(A) = -11, the following computations can be made:
(b) det(4A) det(A) = 4^2 * (-11) * (-11) = 1936
(c) det(2A - 1) = 2^2 * (-11) - 1 = -43
(d) det((24)^-1) = (1/24) ^2 = 1/576
(e) d a 9 det b h с e

The determinant of a matrix is defined as the sum of the products of the elements of the matrix multiplied by the corresponding cofactor. The cofactor is a signed minor of the matrix, which is obtained by deleting the row and column of the element for which the cofactor is being computed.
In the case of the matrix A = |b с| . |a d|, the determinant can be computed as follows:
|b с| . |a d| = (b*d) - (a*c)
Therefore, det(A) = (b*d) - (a*c) = -11.
To compute det(4A) det(A), first, find det(4A), which is equal to:
|4b 4c| . |4a 4d| = 4^2 * (b*d - a*c)
Thus, det(4A) = 16(b*d - a*c) = 16(-11) = -176.
Then, det(4A) det(A) = (-176) * (-11) = 1936.

For det(2A - 1), first, find 2A - 1, which is equal to:
|2b 2c| . |2a 2d| - |1 0| . |0 1|
= 2|b с| . |a d| - |1 0| . |0 1|
= 2A - |1 0| . |0 1|
= 2A - I
where I is the identity matrix.
Therefore, det(2A - 1) = det(2A - I) = det(2A) det(I^-1)
Since det(I) = 1, det(I^-1) = 1/det(I) = 1/1 = 1.
Therefore, det(2A - 1) = 2^2 * (-11) * 1 - 1 = -43.
Finally, to compute det((24)^-1), it is necessary to find the inverse of the matrix 24.
|a b| . |c d| = 24I
=> |a b|^-1 . |c d| = (1/24)I
=> (1/24) . |d -b| . |-c a| = (1/24)I
Therefore, |d -b| . |-c a| = I
Since the determinant of the identity matrix is 1, it follows that:
1 = det(I) = det(|d -b| . |-c a|) = (a*d) - (b*c)
Hence, det((24)^-1) = (1/24)^2 = 1/576.

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Answer:

Step-by-step explanation:

first you find the numbers that go with the numbers like base times height

times length then you add it all up read this two times to understand

The annual interest rate is 6.5%

The first step is to write out the parameters given in the question

Joseph places $5500 in a savings account for 30 months

He rans $893.75 in interest

The annual interest rate can be calculated by multiplying the amount in the savings by the number of months which is 30

= 5500 × 30y
= 165,000y

= 165,000y/12

= 13,750y

Equate 13,750y  with the amount of interest

13,750y= 898.75

y= 898.75/ 13,750

y= 0.065 × 100

= 6.5%

Hence the annual interest rate is 6.5%

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The answer to the given question is 220 ft depth at 2:16 pm. Here we have a depth of submersible at 2:16 pm.

A watercraft made to function underwater is submersible. The term "submersible" is frequently used to distinguish between submersibles and other underwater vessels known as submarines. A submersible is typically supported by a nearby surface vessel, platform, shore team, or occasionally a larger submarine, whereas a submarine is a fully self-sufficient craft capable of independent cruising with its own power supply and air renewal system.

At 2:16 p.m.= -180ft - 40ft = -220ft

So, the answer is 220 ft depth.

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The side lengths from the triangles are LN = 24 inches, KL = 9 cm and DE = 6 ft

Side length LN

Given that the triangles are similar, we have the following equivalent ratio:

AC : BC = LN : MN

By substitution, we have

36 : 24 = x : 16

So, we have

x/16 = 36/24

Multiply by 16

x = 24

Hence, the length LN is 24 inches

Side length KL

Here, we have the following equivalent ratio:

KL : KJ = AB : AD

By substitution, we have

x : 14 = 7.2 : 11.2

So, we have

x/14 = 7.2/11.2

Multiply by 14

x = 9

Hence, the length KL is 9 cm

Side length DE

Here, we have the following equivalent ratio:

DE : AE = BC : CA

By substitution, we have

x : 9 = 10 : (6 + 9)

So, we have

x/9 = 10/15

Multiply by 9

x = 6

Hence, the length DE is 6 ft

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The basis for span((1,−1,2,2),(2,2,1,1),(2,−1,−1,0),(4,2,−5,−3)) is {(1,−1,2,2), (2,2,1,1), (2,−1,−1,0), (4,2,−5,−3)}.

A basis for a vector space is a set of linearly independent vectors that span the vector space. In this case, we need to find a basis for the vector space spanned by the given vectors (1,−1,2,2), (2,2,1,1), (2,−1,−1,0), and (4,2,−5,−3).

To find a basis, we can use the row reduction method. First, we write the given vectors as rows of a matrix:

```
1 -1  2  2
2  2  1  1
2 -1 -1  0
4  2 -5 -3
```

Next, we use row operations to reduce the matrix to row echelon form:

```
1 -1  2  2
0  4 -3 -3
0  0 -5 -4
0  0  0  2
```

Now, we can see that the first, second, third, and fourth rows are all linearly independent (since they all have a leading 1 in a different column). Therefore, the original vectors (1,−1,2,2), (2,2,1,1), (2,−1,−1,0), and (4,2,−5,−3) form a basis for the vector space.

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Answer:

36

Step-by-step explanation:

do x to the second power then multiply 4 to get your answer

He should use 11.11 pounds of the $0.90 per pound coffee, and 16.89 pounds of the $2.40 per pound coffee for a total cost of 28 pounds.

x + y = 28

0.90x + 2.40y = 38.20

x = 11.11, y = 16.89

The grocer wants to mix 28 pounds of two kinds of coffee, one selling for $0.90 per pound and the other for $2.40 per pound, and sell it for $1.45 per pound. To determine how many pounds of each kind to use in the new mix, we can set up a system of equations. Let x represent the quantity of pounds of coffee priced at $0.90 per pound and y the quantity of pounds of coffee priced at $2.40 per pound. Thus, x + y = 28 (the total number of pounds) and 0.90x + 2.40y = 38.20 (the total cost of the 28 pounds, at $1.45 per pound). Solving this system of equations yields x = 11.11 pounds of the $0.90 per pound coffee and y = 16.89 pounds of the $2.40 per pound coffee. Therefore, the grocer should use 11.11 pounds of the $0.90 per pound coffee, and 16.89 pounds of the $2.40 per pound coffee for a total of 28 pounds.

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Answer:

52.4285714286

Step-by-step explanation:

use a calculator

Answer: 52.4

Step-by-step explanation: