List the excluded values of the rational equation. Type a numerical answer in the space provided. Do not include spaces in your answer. If there is more than one excluded value, separate them with a comma. For example, if the excluded values are 10, 12 and , type 0,3. 1a+1/2a=1/a-3

Working together, they can mow the yard in 48 minutes.

Given data;

A lawn can be mowed by Wilma in 120 minutes. In 80 minutes, Vanessa can cut the same lawn. When working together, how long does it take Wilma and Vanessa to mow the lawn?

Let 't' is their time in minutes working together.

Add their rates of working to get their rate working together,

Wilma's rate: [ 1 lawn ] / [ 120 min ]

Vanessa's rate: [ 1 lawn ] / [ 80 min ]

Rate working together: [ 1 lawn ] / [ t min ]

1/120 + 1/80 = 1/t

Multiply both sides by 240t;

2t + 3t = 240

5t = 240

t = 48

It takes them 48 min to mow the lawn working together.

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Answer:

the answer is c

Step-by-step explanation:

i took the test

Answer:

The the rate of the motorboat in still water is 40 km/h;  the rate of the current is  10 km/h.

Step-by-step explanation:

Let  u  be the rate of the motorboat in still water (in kilometers per hour),

let  v  be the rate of the current.

Then the rate of the motorboat going downstream is  u+v  km/h,

while its rate going upstream is  u-v  km/h.

From the other side, the rate of the motorboat going downstream is  150/3=50km/h = 30 km/h.

Thus you have these two equations

   u + v = 50    (1)   (for the rate downstream),   and

   u - v = 30    (2)   (for the rate upstream).

To solve the system, add equations (1) and (2). You will get

   2u = 50 + 30 = 80;   hence,

    u           = 80/2 = 40 km/h.

Then from the equation (1),  v = 50 - u = 50 - 40 = 10 km/h.

ANSWER.  The the rate of the motorboat in still water is 40 km/h;  the rate of the current is  10 km/h.

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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There are 10 terms in the arithmetic series. To find the number of terms in the arithmetic series, we can use the formula for the sum of an arithmetic series:  Sum = (n/2)(2a + (n-1)d).

Where Sum is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. Given that the first term (a) is 123, the common difference (d) is 12, and the sum (Sum) is 1320, we can substitute these values into the formula: 1320 = (n/2)(2 * 123 + (n-1) * 12). Simplifying further: 1320 = (n/2)(246 + 12n - 12); 1320 = (n/2)(234 + 12n)

Dividing both sides by 6: 220 = (n/2)(39 + 2n). Now, we can check for values of n that satisfy this equation. By trial and error, we find that n = 10 satisfies the equation. Therefore, there are 10 terms in the arithmetic series.

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Since the proposed side length of the square is between 6 and 7, we can assume that it is 6.5 hence, the lengths will be d = 6.5 and c = 9.19.

Here is what we were given:

Side length of square = 6 > x <7

A convenient assumption for this is 6.5

We also know that d and c and the base of two right triangles. where their hypotheses' are equal to the side lenght of the square = 6.5

we also know that the in between the line formed by D and C is a 90 degree angle.

Hence the sum of the other angle will be 45 degrees each.

This is  based on sum of angles in a triangle.

Hence,

c = b /sin(β)

= 6.5/sin (45)

= 6.5/0.70710678118

 c = 9.19

d = √c² - b²

 = √(9.19238815542512² - 6.52²)

= √42.25

d = 6.5

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In general, the linear regression formula is shown below

Answer:

a

Step-by-step explanation:

your a could be the same.

The probability of spinning a red is 2/5

Probability is the likelihood or chance that an event will occur

Given the following information

Pr(spinning a red) = 12/30

Pr(spinning a red)  = 2/5

Hence the probability of spinning a red is 2/5

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The first term is 2, the common difference is 2 and the sum of the first ten terms is 110

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

An arithmetic term is given as:

\(a_n=a+(n-1)d\)

where a is the first term and d is the common difference.

The 5th term and 8th term of an AP are 10 and 16. Hence:

a + 4d = 10    (1)

and:

a + 7d = 16     (2)

subtract equation 1 from 2 to get d:

3d = 6

d = 2

Common difference is 2

a + 4d = 10

a + 4(2) = 10

a = 2

First term is 2

The sum of first ten terms is:

\(S_{10}=\frac{n}{2} (2a+(n-1)d)=\frac{10}{2}(2(2)+(10-1)2) = 110\)

The sum is 110

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Answer:

80%

Step-by-step explanation:

using equivalent fractions:

40/50 = 80/100 = 80%

also since 50 is half of 100 (in other words 100%), you can just multiply 40 by 2 to get a number out of 100 which is your percentage

hope this helped :)

Answer:

\( \sf \: x=34\)

Step-by-step explanation:

Let's solve your equation step-by-step.

x/2 = 17/1

Step 1: Cross-multiply.

x/2 = 17/1

x*(1)=(17)*(2)

x=34

The answer is \(k(t) = 408 / (209\sqrt{209})\) for the given vector function \(r(t)=2cos(4t)i+2sin(4t)j+9tk\) by using formula .

The formula  \(k(t) = || r'(t) * r''(t)||/||r'(t)||^3\)can be used to find κ(t) for the given vector function \(r(t)=2cos(4t)i+2sin(4t)j+9tk\).

To calculate κ(t), we need to find r'(t) and r''(t) first. Taking the derivative of r(t), we get:

\(r'(t) = -8sin(4t)i + 8cos(4t)j + 9k\)

Taking the derivative of r'(t), we get:

\(r''(t) = -32cos(4t)i - 32sin(4t)j\)

Now, we can substitute r'(t) and r''(t) into the formula  \(k(t) = || r'(t) * r''(t)||/||r'(t)||^3\).

Let's calculate it step by step.

Step 1: Calculate the cross product of r'(t) and r''(t):

\(r'(t) × r''(t) = (-8sin(4t)i + 8cos(4t)j + 9k) × (-32cos(4t)i - 32sin(4t)j)\\= (288sin(4t) - 288cos(4t))i + (288cos(4t) + 288sin(4t))j + 0k\\\)

Step 2: Calculate the magnitudes of r'(t) and r''(t):

\(||r'(t)|| = \sqrt{((-8sin(4t))^2 + (8cos(4t))^2 + 9^2) }= \sqrt{(64 + 64 + 81) }= \sqrt{209}\\||r'(t)|| = \sqrt{((-32cos(4t))^2 + (-32sin(4t))^2)} = \sqrt{(1024 + 1024)} = \sqrt{2048} = 32 \sqrt2\)

Step 3: Calculate the magnitude of the cross product:

\(||r'(t) * r''(t)|| = \sqrt{((288sin(4t) - 288cos(4t))^2 + (288cos(4t) + 288sin(4t))^2)}\\= \sqrt{(82944 + 82944)} = \sqrt{165888} = 408 \sqrt{2\)

Step 4: Substitute the values into the formula \(k(t) = || r'(t) * r''(t)||/||r'(t)||^3\):

\(k(t) = (408\sqrt2) / (\sqrt{209})^3\\= (408\sqrt2) / (209\sqrt{209})\\= 408 / (209\sqrt{209})\)

Therefore,\(k(t) = 408 / (209\sqrt{209})\) for the given vector function \(r(t)=2cos(4t)i+2sin(4t)j+9tk\) by using formula \(k(t) = || r'(t) * r''(t)||/||r'(t)||^3\).

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The equation of circle centered at the origin and has a radius of 7 is,

⇒ x² + y² = 49

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

Radius of circle = 7

Centre of circle = (0, 0)

Now, The equation of circle centered at the origin and has a radius of 7 is,

⇒ (x - 0)² + (y - 0)² = 7²

⇒ x² + y² = 49

Thus, The equation of circle centered at the origin and has a radius of 7 is,

⇒ x² + y² = 49

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Answer:

x²¹ /64

Step-by-step explanation:

To know the mistake made by Javier, let us simplify the given expression. This can be obtained as follow:

(20x / 5x⁸)¯³ = (20x)¯³ / (5x⁸)¯³

= (5x⁸)³ / (20x)³

= 5³x²⁴ / 20³x³

= 125x²⁴ /8000x³

= 125x²⁴ ÷ 8000x³

Recall

Mᵃ ÷ Mᵇ = Mᵃ¯ᵇ

Therefore,

125x²⁴ ÷ 8000x³ = (125/8000)x²⁴¯³

= (1/64) x²¹ = x²¹/64

Thus,

(20x / 5x⁸)¯³ = x²¹/64

Answer:

nhbh

In the last step, Javier divided the exponents. He should have used the quotient of powers property and subtracted them.

Step-by-step explanation:

Step-by-step explanation:

-3p+6p is 3p

-3 + 6 = 3

So when you simplify the equation you get 3p

Using translation concepts, it is found that the table of values for function g(x) is given as follows:

x      0  1  2 3

g(x) -7  0 5 8

When a function is reflected across the x-axis, all it's values are multiplied by -1.

Hence, considering the values of f(x) given in the problem, the table of values for function g(x) is given as follows:

x      0  1  2 3

g(x) -7  0 5 8

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The invoice date is December 23, so the payment is due on January 7 (3/15 ROG) of the following year. However, the shipment arrives on May 18 of the following year, which means the payment is overdue by 132 days (May 18 minus January 7). Since there are 360 days in a year, this is equivalent to 132/360 or 11/30 of a year.

Let x be the selling price per basket of apples. Therefore, the selling price per basket of apples is $0.12.3. The item was marked down by 40%, which means the cost is: 60%($491.80) = $295.08 The operating expenses are 38% of the cost, which means the operating expenses are: 38%($295.08) = $112.12 Therefore, the operating loss is: $362.40 - $295.08 - $112.12 = -$45.80The absolute loss is the absolute value of the operating loss, which is: $45.80.4. The simple discount note is a promissory note that is discounted before it is issued.

The discount rate is 6%, which means that the bank will subtract 6% of the face value of the note as interest. The proceeds are the amount that Sundaram receives after the bank takes its interest.

The proceeds are:

$54,800 = Face value - 6%(Face value)0.94(Face value)

= $54,800

Face value = $58,297.87

Therefore, the face value of the simple discount note is $58,297.87.5. The interest rate is 4.5% compounded daily, which means that the effective annual interest rate is:(1 + 0.045/365)365 - 1 = 0.0463The balance on June 30 is the sum of the balance on April 1 and the balance on May 7 plus the interest earned between April 1 and June 30. Let x be the balance on April 1. Then:(1 + 0.0463)90 = (1 + 0.045/365) x + $4,500x = $29,216.17

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Answer:

Its B. 4

Step-by-step explanation:

Answer:

x>9/5

Step-by-step explanation:

2/3x-1/5(+1/5)>1(+1/5)

[add 1/5 on both sides]

2/3x (÷3/2)>6/5 (÷3/2)

[flip 2/3 to 3/2 so that they cancel out]

x>9/5

8/12 is your answer hope i could help

No, because intergers don't include fractions.

Answer:

No

Step-by-step explanation:

Integers cannot have any fractions.

If you simplify this to get 8/1 and then 8, 8 is an integer

(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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The correct option is a) $5161.24

To evaluate the expression P(1+rt) with the given values:

P = 1575

r = 0.055

t = 168/365

First, let's calculate rt:

rt = 0.055 * (168/365)

= 0.0252836 (rounded to 7 decimal places)

Now, substitute the values into the expression P(1+rt):

P(1+rt) = 1575 * (1 + 0.0252836)

= 1575 * 1.0252836

= 1615.85846 (rounded to 5 decimal places)

The result is approximately $1615.86.

Therefore, the correct option is a) $5161.24

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Answer:

8000

Step-by-step explanation:

Because when you will add it (8000+800+80+9)

then you will get 8889

The value of x in the expression -2/9=8/(-3x) will be 12.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given

-2/9 = 8/(-3x)

By cross multiplication

-2 = 8 × 9/(-3x)

-2 = -8 × 3/x

Again cross multiplication

x = 24/2

x = 12

Hence the value of x will be 12.

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Answer: Graphing a Quadratic Function

y=−10x2−31x

Step-by-step explanation:

Graphing a Quadratic Function

f(x) ÷ x - k.

9) f(x) = x' - 8x? - 10x² – 24x