A one-terabyte external hard drive is on sale at a 25% discount. If the original price was $345, what is the sale price?

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

I THINK 1

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve this, we would first need to see how many times 7 can fit into 24.

7 + 7 + 7 = 21.

We can see that is fits 3 times into 24, but what about the remaining 3? We can take that 3 and make it into a fraction of 7, making it \(\frac{3}{7}\).

Now, putting the 3 and the 3/7 together, we get  \(3\frac{3}{7}\).

From the given data of traffic circle, the center of the circular monument is covering approximately 148,000 square feet then the radius of the monument is equal to 217.10 feet.

As given in the question,

Given that traffic circle is a round intersection.

It has circular monument in the center.

Area covered by circular monument is equal to 148,000 square feet.

Let us consider radius of the circular monument be 'r'

Area of circular monument  = 148,000

⇒ πr² = 148,000

⇒r² = 148,000 / π

⇒ r² = 148,000/ 3.14

⇒ r = √148,000/ 3.14

⇒ r = 217. 103... feet

⇒ r = 217.10 feet ( nearest hundredth)

Therefore, from the given data of traffic circle, the center of the circular monument is covering approximately 148,000 square feet then the radius of the monument is equal to 217.10 feet.

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Answer:

The correct set of hypotheses is:

\(H_0: \pi=0.75\\\\H_a:\pi>0.75\)

Step-by-step explanation:

This should be researched with a hypothesis test on the proportion of tourists visiting Rock City.

The claim that want to be tested is if the proportion has increased from the past proportion (π=0.75).

Then, the alternative hypothesis will state that the proportion is significantly higher than 0.75.

On the contrary, the alternative hypothesis will state that the proportion is not significantly different than 0.75.

This can be written as:

\(H_0: \pi=0.75\\\\H_a:\pi>0.75\)

Answer:

D

Step-by-step explanation:

16 times the # of boxes = $24.

You can solve this equation by doing 24/16=$1.5 per box

answer- u have to subtract the great no. from the smaller one

Given numbers are 5429 and 5907..

To find the difference we should subtract..

5907

- 5429

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

478

_______

The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

The graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.

If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.

In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

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The amount of sandwich they eat altogether is 2/3

A fraction can be defined as the part of a whole number, a whole number, a whole element.

The different types of fractions are listed as;

From the information given, we have that;

Angie ate 1 / 3 of the sandwich

Kim ate another 1 / 3 of the sandwich

To determine the total amount, we have;

1/3 + 1/3

add the values

1 + 1/3

add the values, we get;

2/3

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The complete question:

Angie and Kim are sharing a large sub sandwich. Angie ate 1 / 3 of the sandwich, and Kim ate another 1 / 3 of the sandwich. Please work out in detail.

Answer:

83

Step-by-step explanation:

Keywords: more means + and times means x

We don't know the number of boys, so it is the variable. I will use b to represent the number of boys.

3 + 4b

It says 20 boys work at the Super Shopper, so plugin 20 for b. Multiply the 4 and 20 together.

3 + 4(20)

3 + 80

83

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer: What is this free?

Answer:

yes

Step-by-step explanation:

yes+yes(no-no)

=yes

a) sin 36° ≈ 0.5878

b) cos 14° ≈ 0.9691

c) tan 86° ≈ -9.5144

To find the values of trigonometric functions, such as sine, cosine, and tangent, for specific angles, we can use a scientific calculator or trigonometric tables. However, I can provide you with step-by-step calculations to find the values of sin 36°, cos 14°, and tan 86°.

a) sin 36°:

Step 1: Convert 36° to radians:

36° * (π/180) ≈ 0.6283 radians

Step 2: Use a scientific calculator to find the sine of 0.6283 radians:

sin 0.6283 ≈ 0.5878

Therefore, sin 36° ≈ 0.5878

b) cos 14°:

Step 1: Convert 14° to radians:

14° * (π/180) ≈ 0.2443 radians

Step 2: Use a scientific calculator to find the cosine of 0.2443 radians:

cos 0.2443 ≈ 0.9691

Therefore, cos 14° ≈ 0.9691

c) tan 86°:

Step 1: Convert 86° to radians:

86° * (π/180) ≈ 1.5009 radians

Step 2: Use a scientific calculator to find the tangent of 1.5009 radians:

tan 1.5009 ≈ -9.5144

Therefore, tan 86° ≈ -9.5144

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The probability values

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

n = 14

p = 2/14

The probability P(x =1) can be calculated as

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

In this case, we have

P(x = 1) = C(14, 1) * (2/14)^1 * (1 - (2/14))^(13

Evaluate

P(x = 1) = 0.2696

The probability P(x >= 1) can be calculated as

P(x) = 1 - P(0)

In this case, we have

P(x >= 1) = 1 - [C(14, 0) * (2/14)^0 * (1 - (2/14))^(14)]

Evaluate

P(x >= 1) = 0.8845

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Answer:

None of the following statements have the same result.

Step-by-step explanation:

1) f(2) when f(x) = 3x + 4

We just have to put x=2

\(f(x)=3x+4\\f(2)=3(2)+4\\f(2)=6+4\\f(2)=10\)

So, f(2) when f(x) = 3x + 4 is x=10

2) f⁻¹ (4)  when f(x) =3x-4/5

We need to find f⁻¹(x) first.

Put \(y=3x-\frac{4}{5}\)

Now solve for x

Add 4/5 on both sides

\(y+\frac{4}{5}=3x-\frac{4}{5}\\y+\frac{4}{5}=3x\\x=\frac{1}{3}y+\frac{4}{5*3}\\x=\frac{1}{3}y+\frac{4}{15}\\x=\frac{5y+4}{15}\)

Now put  f⁻¹(x)  instead of x and replace y with x

\(f^{-1}(x)=\frac{5x+4}{15}\)

Now finding f⁻¹(4)

\(f^{-1}(x)=\frac{5x+4}{15} \\f^{-1}(4)=\frac{5(4)+4}{15} \\f^{-1}(4)=\frac{20+4}{15} \\f^{-1}(4)=\frac{24}{15}\)

f⁻¹ (4)  when f(x) =3x-4/5 is 24/15

3) \(3y - 6 = y + 10\\\)

Solving:

\(3y - 6 = y + 10\\3y-y=10+6\\2y=16\\y=16/2\\y=8\)

Solving 3y − 6 = y + 10, we get y=8

None of the following statements have the same result.

Given equation is

Consider the order of operations PEDMAS

P-parenthesis

E-exponents

D-division

M-multiplication

A-addition

S-subtraction.

First, we need to solve it inside the bracket.

Add 5 and 5, we get 10.

Multiply 2 and 10, we get 20.

Hence the value of x is 20.

As Josh says that you can write division problems two ways such as in "72/6=12" or "72/12=6", then, from this, we will agree that there is nothing wrong with either division problem. The Option A is correct.

A number is divided in division, which is a straightforward operation. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. Basically, division works by dividing numbers into equal groups of numbers.

A division problem has three main components: the dividend, the divisor, and the quotient. The amount that will be divided is the dividend. The quantity of "people" among whom the number is divided is referred to as the divisor. The answer is the quotient.

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Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

Answer:

b/2-1 has a verbal phrase can be one minus the quotient of b and 2.

Carrie has 4 more pints of paint than Bryan.

Carrie has 3 gallons of paint, which is equivalent to 12 quarts (1 gallon = 4 quarts). On the other hand, Bryan has 10 quarts of paint.

To compare the quantities in the same unit, we note that 1 quart is equal to 2 pints.

Carrie's 12 quarts of paint is equivalent to 12 × 2 = 24 pints.

Bryan's 10 quarts is equivalent to 10 × 2 = 20 pints.

To find the difference, we subtract Bryan's pint quantity from Carrie's:

24 - 20 = 4 pints.

Therefore, Carrie has 4 more pints of paint than Bryan.

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1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.

2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.

When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.

Similar figures have the same shape, but they may have different sizes and be located in different positions.

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Answer:

1. 2x-4=10

2. 3x+3=2x-1

3. 7x+x=24

4. 5+x=-18

5. -14=10-6x

6. 2x-2=x+12

7. 3x-31=2

8. 5x-14=16

9. 2x+8=4(5-x

10. 2x-3=3(1+x)

Explanation:

I JUST TAKEN THE QUIZ!!!!!

Answer:

1936

Step-by-step

\([15 - (1 - 6 + 21 + \sqrt{9} )] ^{2}\)

use BIDMAS

(1 - 6 + 21 + \(\sqrt{9}\)) = (1 - 6 + 21 + 3) = (1 - 30) = -29

[15 - -29] = [15 + 29] because two minuses together make a plus

\(44^{2}\) = 1936

Answer:

I believe it is y=1x or y=x

Answer:

14

Step-by-step explanation:

The constant of proportionality is the y number when x is 1.  Look on the bottom of the graph.  Find 1, so up to the line and then across left to the y axis.  you will be at 14.  This means that every time the x increases by 1, the increases by 14

Answer:

A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5.

Step-by-step explanation:

The table with all y-values the same will graph as a horizontal line, a line with a slope of zero.

Apparently, the first table is like that.

Answer:

A is the answer

Step-by-step explanation:

just took the test

Answer:

C option SAS is the correct answer of this question .....plz mark my answer as brainlist plzzzz vote me also plzzzz

Answer: B 0.4

Step-by-step explanation:

50-20=30

0.4 is 40%

40% of 50 is 20

Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

Answer: c

Step-by-step explanation:

Because group B has Pharrell lines