Determine whether the set {v1, v2} is a basis for R
2.

Answer:

A) Matched pairs design

Step-by-step explanation:

In experimental design, the match pairs experimental design is one that often involves only two treatment conditions; which in this case are the 'refrigerated and the room temperature battery storage types'.

Thus, these two treatment conditions form a matched pair because we are told that 10 fully charged batteries are placed into each type of storage.

Answer:

\(\frac{3}{2m}\)+8m

Answer:

the sum of quotient of 3 and 2m and the product of 8 and m is

(3/2m +8m)

Answer:

b

Step-by-step explanation:

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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The roots of the given quadratic equation are 5 and -4

Quadratics are the polynomial equation which has the highest degree of 2. Also, called quadratic equations.

Given is an equation 3x²-13x-10 = 0, we need to solve by using completing the square method,

The given equation is =

3x²-13x-10 = 0

3(x²-13x/3-10/3) = 0

3(x²-2x·13x/6-10/3) = 0

Adding and subtracting (13/6)²

3(x²-2x·13x/6+(13/6)²-(13/6)²-10/3) = 0

3[(x-13/6)²-169/36-10/3] = 0

3[(x-13/6)²-289/36] = 0

(x-13/6)²-289/36 = 0

(x-13/6)² = 289/36

Taking roots,

x-13/6 = ±17/6

x = 17/6+13/6

x = 5

Or,

x = -17/6+13/6

x = -4

Hence, the roots of the given quadratic equation are 5 and -4

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In the given proof, the phrase " There exists k = n+1 " is not a general practice to write.

option (d) is correct [ans]

An integer is a whole number that can be positive, negative, or zero, and does not include any fractional or decimal parts.

Integers are part of the set of numbers called the integers, which includes all positive numbers, negative numbers, and zero.

We write " Let k = n+1 or assume n = k+1".

And then, we say that, it is obvious that

n < k = n+1 < n+2 for any integer n.

Hence, option (d) is correct [ans]

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Answer:

0.0625

Step-by-step explanation:

hope this helps :)

Answer:

64°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 26° = 180°

x + 116° = 180° ( subtract 116° from both sides )

x = 64°

the other angle is 64°

Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

Here ya go!! Hope this helps :D

Answer:

3t+6.75b > 550

Step-by-step explanation:

Got it right on delta math but hope this helps

Answer:

2%

Step-by-step explanation:

b= 1-r

0.98=1-r

r=1-0.98

r=0.02

The Answer: 758.83 in³

Step-by-step explanation:

Volume of Solids

The volume of the solid is 758.83 in³

Step-by-step explanation:

Given that the cone and half sphere is hollow

The volume of the cone =

The Volume of the sphere  =

So the Volume of the half sphere =

The volume of solid = volume of cone + volume of the half sphere

Given

height h = 19 in

radius r = 5 in

 =

    = 1/3 × 3.14 × 5 × 5 × 19

    = 497.16 in³

  = 2/3 × 3.14 × 5 × 5 × 5

  = 261.67 in³

V =  497.16 in³ + 261.67 in³

 = 758.83 in³

Hence the volume of the solid is 758.83 in³

Volume of Solids

The volume of the solid is 2813 in³

Step-by-step explanation:

Given that the cone and half sphere is hollow

The volume of the cone  \(=1/3\pi r^2h\)

The Volume of the sphere \(=4/3\pi r^3\)

So the Volume of the half sphere \(=2/3\pi r^3\)

The volume of solid = volume of cone + volume of the half sphere

\(V=V_1+V_2\)

Given

height h = 26 in

radius r = 8 in

\(V_1=1/3\pi r^2h\)

    \(= 1/3 \times 3.14 \times 8 \times 8\times 26\)

    \(=1741.65 \ in^3\)

\(V_2=2/3\pi r^3\)

 \(= 2/3 \times 3.14 \times 8 \times 8\times 8\)

  \(= 1071.78 \ in^3\)

\(V = 1741.65 \ in^3 + 1071.78 \ in^3\)

\(2813 \ in^3\)

Hence the volume of the solid is 2813 in³

Step-by-step explanation:

Did you mean

Evaluate 3/2 + (-k) + (-2) where k = -5/2

= 3/2 - (-5/2) - 2

= 3/2 + 5/2 - 2

= 8/2 - 2

= 4 - 2

= 2

Answer:

6(x+4) hope this helps

Step-by-step explanation:

Answer:

y = 24x

Step-by-step explanation:

In a direct variation, we have

output = k * input, with k being a positive number.

Therefore, with the output being the number of water bottles and the input being the number of cases, we have y = kx. We know that the output is y and the input is x because the question states that the number of water bottles (y) is directly proportional to the number of cases (x), so x must be multiplied by something to obtain y.

We have 120 water bottles as one output and 5 cases as its corresponding input.

120 = k(5)

divide both sides by 5 to isolate k

k = 24

y = 24x

Solution,

16.87+(-98.35)

=16.87-98.35

= -81.48

Hope it helps

Good luck on your assignment

Answer:-81.48

Step-by-step explanation:

16.87 + (–98.35)

-81.48

If you stumble in other questions like there you can use a calculator or ask me. :D hope that helps

The value of k is 18.

If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.

Substituting x = -2 into f(x), we have:

f(-2) = (-2)³ + 5(-2) + k

= -8 - 10 + k

= -18 + k

Since f(-2) should equal zero, we have:

-18 + k = 0

k = 18

Therefore, the value of k is 18.

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For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Complete Question

It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 households in Iowa City is taken, would you be surprised to find that fewer than 3% of households in the sample recycle their garbage? Use the fact that p-hat has an approximately normal distribution.

Group of answer choices

A I would not be surprised because there are lots of lazy students in Iowa City.

B I would not be surprised because 3% is not that far away from 9%.

C I would be surprised because Iowa City is a very clean community which means lots of people recycle their garbage.

D I would be surprised because if the 9% average is true, the chance of a sample proportion being less than 3% is very small (only 1%). Who cares? It's only garbage!

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

    The sample size is  n  = 120

    The  mean of the proportion is  p =  0.09

Generally the standard deviation is mathematically represented as

      \(\sigma  =  \sqrt{\frac{p(1-p)}{n} }\)

=>   \(\sigma  =  \sqrt{\frac{0.09(1-0.09)}{120 } }\)

=>   \(\sigma  = 0.02612\)

Generally the chance that fewer than 3%   of households in the sample recycle their garbage is mathematically represented as

    \(P(X < 0.03) =  P( \frac{X - p}{\sigma}  <  \frac{0.03 -0.09}{0.02612} )\)

    \(P(X < 0.03) =  P( Z  < -2.297 )\)

From the z-table  

     \(P( Z  < -2.297 ) = 0.01\)

=> \(P(X < 0.03) = 0.01/tex]

=>   \(P(X < 0.03) = 1\% /tex]

Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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Answer:

Give the other guy brainliest he earns it

Step-by-step explanation:

Answer:

Step-by-step explanation:

its c.

also dont give up hope

Answer:

C = 21

Step-by-step explanation:

trust me its correct brainliest pls

Answer:

m=2

Step-by-step explanation:

that is the answer for m

Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

Answer:

The first answer is $4.97. The second answer is 1 over 16.

Step-by-step explanation:

For the first question you have to subtract the money that the total price, $26.73 from the money that she has, $21.76 and you will get the find the difference that she needs.

For the second question think about it as mulitplying one quarter 4 times. So 1 multiplied four times still remains one and 4 x 4 is 16.

Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

Answer:

\(A=\frac{\sqrt{3}}{4}a^2\)

Step-by-step explanation:

Since an equilateral has all of the sides equal, we can find the height of triangle using: \(a^2+b^2=c^2\). I attached a diagram which should explain how I got the dimensions of the three sides. Using the information from the diagram we get the equation:

\(h^2+(\frac{a}{2})^2=a^2\)

Subtract a^2 from both sides

\(h^2=a^2-(\frac{a}{2})^2\)

Take the square root of both sides

\(h = \sqrt{a^2-(\frac{a}{2})^2}\)

If you know the area of a triangle, it's: \(\frac{1}{2}bh\). In this case the base=a, and the height is what we defined above. Using this we get:

\(A = \frac{a}{2}*\sqrt{a^2-(\frac{a}{2})^2}\)

We can distribute the exponent over the division to get:
\(A = \frac{a}{2}*\sqrt{a^2-(\frac{a^2}{4})\)

Now we can rewrite a^2 as 4a^2/4

\(A = \frac{a}{2}*\sqrt{\frac{4a^2}{4}-(\frac{a^2}{4})\)

Now add the two fractions:

\(A = \frac{a}{2}*\sqrt{\frac{3a^2}{4}\)

We can distribute the square root the division just like how we distributed the exponent 2, since the square root can be expressed as an exponent (1/2)

\(A = \frac{a}{2}*\frac{\sqrt{3a^2}}{\sqrt{4}}\)

There's a radical identity that states: \(\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{a*b}\). We can use this to rewrite one radical as multiple radicals to simplify it:

\(A = \frac{a}{2}*\frac{\sqrt{a^2}*\sqrt{3}}{2}\)

Simplify:

\(A = \frac{a}{2}*\frac{a*\sqrt{3}}{2}\)

Now multiply the two fractions

\(A = \frac{a^2*\sqrt{3}}{4}\)

This is the formula for the area of an equilateral triangle, but it is also often written as:
\(A=\frac{\sqrt{3}}{4}a^2\)