Question 10 of 10
Which of the following is the solution to | x | +5 ≤1?
OA. No solution
OB. xs-4
C. All values are solutions *
OD. xs-4 and x ≥ −6

Answer:

Let the cost price be x

\(\rm{C.P. = \dfrac{S.P. \times 100}{100+ gain \% }}\)

\(\rm{C.P. = \dfrac{130 \times 100}{100+30}}\)

\(\rm{ C.P. = \dfrac{130}{30} }\)

\(\large{\boxed{\rm{ C.P. = \dfrac{13}{3}}}}\)

Answer:

1/6 or 16.67% chance

Step-by-step explanation:

Assuming its a normal six sided dice. You would have a 16.67% chance of getting a 3.

Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

Answer:

add the 11 to both sides to cancel it out.

Step-by-step explanation:

so basically

5x - 11 + 11 = 42 +11

5x = 53

The required first step of solving the given expression is to add 11 on both sides.

Given that,
The first step for the solution of the given expression 5x - 11 = 42 is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
5x - 11 = 42
Add 11 on both sides to reduce the equation as
5x = 53

Thus, the required first step of solving the given expression is to add 11 on both sides.

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a) 214 in base-five is 1324.

b) 62 in base-five is 222.

c) 8 in base-five is 13.

d) 95 in base-five is 340.

a) To determine the base five representation of 214, we need to   find the largest power of five that  is less than or equal to  214.

In this case, 125 (5³) is the largest power of five   that is less than 214.

Now, we divide 214 by 125 -  

214 ÷ 125 = 1 remainder 89

Next, we divide the remainder, 89, by the next lower power of five, which is 25 (5²) -  

89 ÷ 25 = 3 remainder 14

Finally, we divide the remaining 14 by the lowest power of five, which is 5 itself -  

14 ÷ 5 = 2 remainder 4

Therefore, the base-five representation of 214 is 1324 in base-five.

b) Following the same steps as above -  

62 ÷ 25 = 2 remainder 12

12 ÷ 5 = 2 remainder 2

Hence,  the base-five representation of 62 is 222 in base-five.

c) 8 ÷ 5 = 1 remainder 3

this menas that  the base-five representation of 8 is 13 in base-five.

d) Following the same steps as above -  

95 ÷ 125 = 0 remainder 95

95 ÷ 25 = 3 remainder 20

20 ÷ 5 = 4 remainder 0

Hence, the base-five representation of 95 is 340 in base-five.

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Answer:

13/18

Step-by-step explanation:

The two negatives cancel out.

1/6 * 4 1/3 is 13/18, first turn 4 1/3 to 13/3.

Hope this helps

Answer:

Answer in explanation

Step-by-step explanation:

The equation of a straight line can be represented in the form;

y = mx + c

where m is slope and c is y-intercept

In this particular case

y = 20x + 5

y is the weekly income, x is the number of lawns mowed

The y-intercept 5 is the amount earned in a week given they no lawn was mowed

In a case where y = 125

125 = 20x + 5

20x = 125-5

20x = 120

x = 120/20

x = 6

You need to mow 6 lawns to earn enough money in one week to buy the MP3 player

Bill enjoys collecting coins and is a member of a club for coin collectors. This club for coin collectors is an illustration of a(n) membership group.

Given that,

Bill enjoys collecting coins and is a member of a club for coin collectors, which grants him access to events and a monthly magazine. This club for coin collectors is an illustration of a(n) ________ group.

We have to fill the blank.

We know that,

Option- C is correct .

Bill enjoys collecting coins and is a member of a club for coin collectors, which grants him access to events and a monthly magazine. This club for coin collectors is an illustration of a(n) membership group.

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according to question the linearization of f(x) = x^(2/3) at a = 64 is:

l(x) = 16 + (1/6) * (x - 64)

To find the linearization of a function f(x) at a point a, we need to use the formula:

l(x) = f(a) + f'(a) * (x - a)

where f(a) is the value of the function at the point a, f'(a) is the derivative of the function evaluated at a, and (x - a) is the difference between x and a.

First, we need to find the value of f(a):

f(a) = a^(2/3) = 64^(2/3) = 16

Next, we need to find the derivative of f(x):

f'(x) = (2/3) * x^(-1/3)

Now, we evaluate f'(a):

f'(a) = (2/3) * 64^(-1/3) = (2/3) * (1/4) = 1/6

Finally, we can plug in these values into the formula for the linearization:

l(x) = 16 + (1/6) * (x - 64)

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Answer:

52.93 miles

Step-by-step explanation:

79% of 67 miles =

0.79 * 67 = 52.93

52.93 miles

-Chetan K

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Based on the provided information, there are between 9 and 10 ounces of fluid in container B.

It is given that there are 76 ounces of fluid in container A which is about 8 times the amount of fluid in container B. It means that fluid in container B is 8 times less than fluid in container A. To find the approximate amount of fluid in container B, we can divide the amount of fluid in container A by 8:

76 ounces ÷ 8 = 9.5 ounces

Therefore, there are about 9.5 ounces of fluid in container B, which falls between 9 and 10 ounces. Hence, there are between 9 and 10 ounces of fluid in container B.

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I'm not aware of any concrete information to support the assertion that New Yorkers travel less than 12,200 miles per year on average.

The average number of miles driven can vary significantly based on a number of variables, including population density, demography of urban and rural areas, transportation infrastructure, and individual preferences.

The availability of alternate modes of transportation, changes in fuel prices, and changes in the general state of the economy can all have an impact on data on average miles driven.

It's impossible to say for sure whether the typical amount of miles driven in New York is less than 12,200 without access to particular data or a research.

However, because sample data can be influenced by bias and other kinds of inaccuracy, if this statistic was obtained from a sample of data, it might not correctly reflect the general average for the entire state.

A thorough and representative study would need to be carried out to precisely establish the typical amount of miles travelled in New York.

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It is true that the slope of the horizontal tangent line to the parametric curve at a point (x(t), y(t)) is given by dy/dx = (dy/dt)/(dx/dt).

The statement is saying that if f(g(t)) has a horizontal tangent at t = 1, then the curve has a well-defined tangent line at that point, which is also a horizontal tangent. Let's break this down step by step:

f(g'(1)) = 0: This means that the derivative of f with respect to its input g(t) is equal to zero at t = 1. In other words, the slope of the tangent line of f(g(t)) at t = 1 is zero.

dx/dt is not zero at t = 1: This means that the curve g(t) has a well-defined tangent line at t = 1, because the slope of the tangent line of g(t) is not infinite (i.e., the derivative dx/dt is defined and finite).

Setting dy/dx = 0 gives dy/dt / dx/dt = 0: This is using the chain rule of differentiation to relate the derivative of f with respect to t (i.e., dy/dt) to the derivative of f with respect to x (i.e., dy/dx) and the derivative of g with respect to t (i.e., dx/dt).

dy/dt = 0 when dx/dt is not zero: Since dy/dx = 0 and dx/dt is not zero, we can conclude that dy/dt must also be zero at t = 1. This means that the slope of the tangent line of f(g(t)) is also zero at t = 1.

Therefore, the curve has a horizontal tangent at t = 1: Since both g(t) and f(g(t)) have horizontal tangents at t = 1, we can conclude that the curve f(x) also has a horizontal tangent at x = g(1). This means that the tangent line to the curve at that point is horizontal.

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1/4 of all the students in the orchestra are girls who play string instruments.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's assume there are a total of 100 students in the school orchestra. Then, according to the problem, 2/5 of them are string players.

The number of string players is:

2/5 x 100 = 40

Out of these 40 string players, 5/8 are girls.

The number of girls who play string instruments is:

5/8 x 40 = 25

Therefore, the fraction of all the students in the orchestra who are girls who play string instruments is:

25/100 = 1/4

Therefore, 1/4 of all the students in the orchestra are girls who play string instruments.

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We can find its derivative and evaluate it at x=36 to find the slope of the tangent line, and then use the point-slope formula to find the equation of the line.

To find the derivative of y = Vx, we use the power rule, which states that if y = xn, then y' = nx^(n-1). In this case, y = Vx⁽¹/²⁾, so y' = V(1/2)x(-1/2) = V/(2sqrt(x)). Evaluating this at x=36, we get y' = V/12. Therefore, the slope of the tangent line is m = V/12. Using the point-slope formula, we get the equation of the tangent line as y - 6 = (V/12)(x - 36).

In summary, to find the equation of the tangent line to the curve at the point (36,6), we first found the derivative of the function y = \(Vx^{1/2}\), which is y' = V/(2sqrt(x)). Evaluating this at x=36, we get y' = V/12, which is the slope of the tangent line. Using the point-slope formula, we then found the equation of the tangent line as y - 6 = (V/12)(x - 36).

To explain this answer in more detail, we can first note that the function

y = \(Vx^{1/2}\)  represents a square root function with a vertical stretch factor of V. This means that the graph of the function is a curve that starts at the origin and increases slowly at first, then more rapidly as x gets larger. The point (36,6) is on this curve, and we are asked to find the equation of the tangent line to the curve at this point.

To find the slope of the tangent line, we use the formula Mtan = lim f(x) - f(a)/ x-a\a, where f(x) is the function and a is the point where we want to find the tangent line. In this case, a = 36 and f(x) = Vx^(1/2), so we have \(Mtan=lim Vx^{1/2} - V(36)^{1/2}/ x-36/a\). We can simplify this expression by multiplying the numerator and denominator by the conjugate of the numerator, which is \(Vx^{1/2} +V(36)x^{1/2}\) As x approaches 36, we can use L' Hopital's rule to evaluate the limit, which gives us Mtan = V/12.

Now that we have the slope of the tangent line, we can use the point-slope formula to find the equation of the line. The point-slope formula states that if the slope of a line is m and a point on the line is (x1,y1), then the equation of the line is y - y1 = m(x - x1). In this case, the point is (36,6) and the slope is V/12, so the equation of the tangent line is y - 6

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Yes, an angle in a right-angled triangle is always present.  Without any additional information about the triangle, it is impossible to determine the value of the angle in question.

In a right-angled triangle, one of the angles is a right angle, which measures 90 degrees. The other two angles in the triangle are acute angles and their measures always add up to 90 degrees.

To find the value of the angle in question, we need to know some additional information about the triangle. If we have the lengths of two sides of the triangle, we can use trigonometric ratios to find the measure of the angle.

For example, if we know the length of the side opposite the angle and the length of the hypotenuse (the longest side of the triangle), we can use the sine ratio to find the measure of the angle.

If we know the length of the side adjacent to the angle and the length of the hypotenuse, we can use the cosine ratio.

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Answer:

13

Step-by-step explanation:

Step 1:

50 + 3x = 7x - 2      Equation

Step 2:

50 = 4x - 2      Subtract 3x on both sides

Step 3:

52 = 4x    Add 2 on both sides

Step 4:

x = 52 ÷ 4      Divide

Answer:

x = 13

Hope This Helps :)

We can write the given series as:

∑ (-1)^n / (n*2^n), n=1 to infinity

To approximate the sum of the series using the first six terms, we can simply add up the first six terms:

(-1)^1 / (12^1) - (-1)^2 / (22^2) + (-1)^3 / (32^3) - (-1)^4 / (42^4) + (-1)^5 / (52^5) - (-1)^6 / (62^6)

Simplifying this expression, we get:

1/2 - 1/8 + 1/24 - 1/64 + 1/160 - 1/384

= 0.5279 (rounded to four decimal places)

Therefore, the sum of the series, approximated by using the first six terms, is approximately 0.5279.

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In the series of a value of a(4)=216

What do the terms sequence and series mean?

Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of the elements in a sequence, which is a group of arranged elements that follow a pattern. The formulas for the nth term and the sum are typically included in the sequence and series formulas.

Given that:

a(1) = 8

a(n)= 3a(n-1)

so a(4) = 3a(3) = 72*3 = 216

a(3)= 3a(2) = 24*3 = 72

a(2)= 3a(1) = 3*8 = 24

Hence a(4) = 216

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Shawn’s science class takes 1 and half hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Shawn’s science class starts at 11:25 a. M.

It ends at 12:45 p. M.

Now, to find the How long is Shawn’s science class we have to find the time difference as

= 12: 45 pm - 11: 25 am

So, From 11:25 am to 12:25 pm it is one hour and additional of 30 minutes or half an hour.

This, the class is 1 and half hour long.

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Explanation

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair, let's check x=2

we have

2 is associated with two values from the set of second components(0 and 5), then

this is not a funcion of x

I hope this helps you

Therefore, The most general antiderivative of the function g(x) = cos(x) - 8sin(x) is F(x) = sin(x) + 8cos(x) + C. We can check the answer by differentiating F(x) which will give us g(x) = cos(x) - 8sin(x).

The most general antiderivative of the function g(x) = cos(x) - 8sin(x) is F(x) = sin(x) + 8cos(x) + C, where C is the constant of integration.
Explanation: To find the antiderivative of g(x), we use the formulae of integration of trigonometric functions. ∫cos(x) dx = sin(x) + C and ∫sin(x) dx = -cos(x) + C. Therefore, ∫cos(x) − 8sin(x) dx = ∫cos(x) dx − 8∫sin(x) dx = sin(x) + 8cos(x) + C. To check our answer, we differentiate F(x) with respect to x, we get g(x) = cos(x) - 8sin(x).

Therefore, The most general antiderivative of the function g(x) = cos(x) - 8sin(x) is F(x) = sin(x) + 8cos(x) + C. We can check the answer by differentiating F(x) which will give us g(x) = cos(x) - 8sin(x).

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The area of the irregular shape is 84 ft square.

The diagram is a trapezium. A trapezium is a quadrilateral. Therefore, the area of the trapezium can be found as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 10 ft

b = 18 ft

c = 6 ft

area of the trapezium = 1 / 2 (10 + 18)6

area of the trapezium = 1 / 2 (28)6

area of the trapezium = 168 / 2

area of the trapezium = 84 ft²

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Since each trait is inherited independently, we can multiply the probabilities together. The probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

The probability of obtaining A/a; B/b; C/c; D/d offspring can be calculated by multiplying the probabilities of each individual trait. Since each trait is inherited independently, we can multiply the probabilities together.

The probability of obtaining A/a offspring is 1/2 (A is dominant and a is recessive).

The probability of obtaining B/b offspring is 1/2 (B is dominant and b is recessive).

The probability of obtaining C/c offspring is 1/2 (C is dominant and c is recessive).

The probability of obtaining D/d offspring is 1/2 (D is dominant and d is recessive).

Therefore, the probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

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The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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