Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, how long will it take them to mow the lawn?
a.15.0 minutes
b.22.5 minutes
c.30.0 minutes
d.120.0 minutes

Answer:

Step-by-step explanation:

Question One

Multiply through by 2

2*1/2 * (2x + y ) = 21/2 * 2

Combine

2x + y = 21

Subtract 2x from both sides

y = 21 - 2x

Now equate the two given equations

y = 21 - 2x

y = 2x

Add 2x to both sides

2x = 21 - 2x

2x + 2x = 21

4x = 21

x = 21/4

x = 5 1/4

or

x = 5.25

Question 2

[tex]\dfrac{2x + 6}{(x + 2)^2} - \dfrac{2}{(x + 2)}[/tex]

multiply numerator and denominator of the second fraction by (x + 2)

[tex]\dfrac{2x + 6}{(x + 2)^2} - \dfrac{2(x + 2)}{(x + 2)*(x + 2)}[/tex]

Remove the numerator brackets in the right hand fraction. Look out for the minus sign.

[tex]\dfrac{2x + 6}{(x + 2)^2} - \dfrac{2(x + 2)}{(x + 2)^2}\\\\\dfrac{2x + 6- 2x - 4}{(x + 2)^2}}\\\\\dfrac{2}{(x + 2)^2}[/tex]

Answer:  [tex]\bold{x=\dfrac{21}{4}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{2}(2x+y)=\dfrac{21}{2}\\\\\text{Multiply both sides by 2 to clear the denominator:}\\2x + y = 21\\\\\text{Now, the system is:}\bigg\{{2x+y=21\atop{y=2x}}\\\\\text{Substitute y in the first equation with 2x to solve for x:}\\2x + y = 21\\2x + 2x = 21\\.\qquad 4x=21\\\\.\qquad \large\boxed{x=\dfrac{21}{4}}[/tex]

Answer:  a = 2

Step-by-step explanation:

[tex].\quad \dfrac{2x+6}{(x+2)^2}-\dfrac{2}{x+2}\bigg(\dfrac{x+2}{x+2}\bigg)\\\\\\=\dfrac{2x+6}{(x+2)^2}+\dfrac{-2(x+2)}{(x+2)^2}\bigg\\\\\\\\=\dfrac{2x+6-2x-4}{(x+2)^2}\\\\\\=\dfrac{2}{(x+2)^2}\implies \large\boxed{a=2}[/tex]

Compute the surface element:

[tex]\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv[/tex]

[tex]\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}[/tex]

[tex]\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}[/tex]

So the integral is

[tex]\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)[/tex]

[tex]=\dfrac23(37^{3/2}-1)[/tex]

Answer:

  5

Step-by-step explanation:

Among the 20 digits shown, each digit appears in the list twice except 0 and 1 appear 3 times and 6 and 9 appear once. That means ...

So, if 1 and 2 represent red candies, there are 3+2 = 5 red candies in the simulated random sample of 20 candies.

_____

Comment on the question

The simulation makes sense only if it represents taking a single candy from each of 20 packages (of unknown quantity of candies). That is, it seems we cannot answer the question, "how many red candies will be in the packages?" We can only answer the question, "how many of the simulated candies are red?"

1.25 meters im pretty sure. i hope i helped

Answer: 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]3x^{2} + 5x-12=0[/tex]

[tex]-12=-5x-3x^{2}[/tex]

[tex](-12=-5x-3x^{2} ) * -1[/tex]

[tex]\sqrt{12=5x+3x^{2}[/tex]

Theoretical probably is what you would expect to happen.

Example, flipping a coin has a 50% chance of landing on heads, so if you flipped a coin 100 times, theoretically the coin would land on heads 50 times ( 50%).

Experimental probablity is what actually happens. Using the coin example, flipping the coin 100 times, it could actually land on heads 100 times or any number of times from 0 to 100.

Hello There! Theoretical probability deals with events happening in theory. It is what is expected t happen.

Experimental probability is a little different. This is based on the number of repeated trials during an experiment.

The difference is Theoretical probability is what you expect to happen

Experimental probability is what actually ends up happening.

the answer Is B) 3c(3ab+a+4b)

Answer

B) 3c(3ab+a+4ab)

Step-by-step explanation:

First find the common factor of (9abc+3ac+12bc) (the common factor is 3c because 3 is the greatest common factor of the coeffecients given and c is in all the terms of the variables given)

then, put 3c outside the parenthesis and factor the terms.

3c(3ab+a+4ab)

when you multiply 3c(3ab+a+4ab) you should get the polynomial that the question gave you. (9abc+3ac+12bc)

Answer:

  The number generator is fair. It picked the approximate percentage of red lollipops most of the time.

Step-by-step explanation:

The other answer choices represent various misinterpretations of the nature of the experiment or the meaning of the numbers generated.

___

A number generator can be quite fair, but give wildly varying percentages of red lollipops. Attached are the results of a series of nine (9) simulations of the type described in the problem statement. You can see that the symmetrical result shown in the problem statement is quite unusual. A number generator that gives results that are too ideal may not be sufficiently random.

Option D is correct as it indicates that the number generator picked a percentage of red lollipops close to the expected 80% most of the time, reflecting fairness and random sampling variability.

Let's analyze the question regarding the fairness of the number generator. We know that 80% of the lollipops in the bag are red.

Option A: The number generator picked red lollipops 90% of the time in 3 experiments. This slight variation could be due to sampling variability, not necessarily unfairness.

Option B: States the correct percentage of red lollipops was not chosen at all, which might suggest the generator is faulty, but without more data, it's inconclusive.

Option C: Indicating the generator picked red lollipops half the time is incorrect as it would be inconsistent with the given information.

Option D: The generator picked the approximate percentage of red lollipops most of the time. This is plausible as the results can vary slightly due to random sampling.

Based on this analysis, Option D seems to be the most accurate description, assuming the observed percentages are close to the theoretical 80% on average, reflecting a fair and random selection process.

Answer:

174 cm²

Step-by-step explanation:

The figure is composed of a rectangle and a triangle, so

area of figure = area of rectangle + area of triangle

area of rectangle = 8 × 15 = 120 cm²

area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 12 and h = 15 - 6 = 9 cm

area of triangle = 0.5 × 12 × 9 = 6 × 9 = 54 cm²

Hence

area of figure = 120 + 54 = 174 cm²

Answer:

x = 1 and y = 2

Step-by-step explanation:

Let apples are represented by x

and let oranges are represented by y

You purchase 5 pounds of apples and 2 pounds of oranges for $9. This line in equation format can be written as:

5x + 2y = 9

Your friend purchases 5 pounds of apples and 6 pounds of oranges for $17.

This line in equation format can be written as:

5x + 6y = 17

Now we have two equations:

5x + 2y = 9 -> eq (i)

5x + 6y = 17 -> eq(ii)

We can solve these equations to find the value of x and y.

Subtracting eq(i) from eq(ii)

5x + 6y = 17

5x + 2y = 9

-     -         -

_________

0+4y= 8

=> 4y = 8

y= 8/4

y = 2

Now, putting value of y in eq (i)

5x + 2y = 9

5x +2(2) = 9

5x +4 = 9

5x = 9-4

5x = 5

x = 1

so, x = 1 and y = 2

Answer:

(0,5) (0,-5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The basic (parent) function here is y = |X|, the absolute value function.

This function has a v-shape that opens up and has its vertex at (0, 0).

Each leg is at a 45° angle to the x - axis.  Draw this.

Then translate the entire graph upward by 5 units.  The result will be the graph of  y = | x | + 5.

Answer:

Step-by-step explanation:

1/2log8,342 is almost correct.  Should enclose that "1/2" inside parentheses.  The "1/2" stems from our needing to find the value of the square root of 8342.

Answer:  The required answer is [tex]\dfrac{1}{2}\log 8342.[/tex]

Step-by-step explanation:  We are given to use the logarithmic equation to find [tex]\sqrt{8342}.[/tex]

We will be using the following logarithmic property :

[tex]\log a^b=b\log a.[/tex]

Let us consider that

[tex]x=\sqrt{8342}~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Applying logarithm on both sides of equation (i), we have

[tex]\log x=\log{\sqrt{8342}\\\\\Rightarrow \log x=\log(8342)^\frac{1}{2}\\\\\Rightarrow \log x=\dfrac{1}{2}\log 8342.[/tex]

Thus, the required answer is [tex]\dfrac{1}{2}\log 8342.[/tex]

Answer:

it is A

Step-by-step explanation:

i’m petty sure you add them all up

Answer:

$2,500

Step-by-step explanation:

The situation states that the employees earn vacation pay at the rate of one day per month and their daily wage is $100. Also, it states that in july 25 employees qualify for one vacation day. So, in order to determine the amount of vacation benefit expense for july, you need to multiply the daily wage for the number of employees that got the benefit:

$100*25= $2,500

Answer:

c

Step-by-step explanation:

Answer:

1/12.

Step-by-step explanation:

The numbers divisible by 6 are 6, 12, 18, 24, 30 and 36.

Of these  12, 24 and 36 are also divisible by 4.

So the required probability is 3/36

= 1/12.

Let [tex]z=-\sqrt3+i[/tex]. Then

[tex]|z|=\sqrt{(-\sqrt3)^2+1^2}=2[/tex]

[tex]z[/tex] lies in the second quadrant, so

[tex]\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6[/tex]

So we have

[tex]z=2e^{i5\pi/6}[/tex]

and the fourth roots of [tex]z[/tex] are

[tex]2^{1/4}e^{i(5\pi/6+k\pi)/4}[/tex]

where [tex]k\in\{0,1,2,3\}[/tex]. In particular, they are

[tex]2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}[/tex]

[tex]2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}[/tex]

[tex]2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}[/tex]

[tex]2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}[/tex]

The answer is:

The lowest term will be:

[tex]\frac{7}{8}[/tex]

Reducing a fraction to its lowest term means writing it its simplified form, so, performing the operation and simplifying we have:

[tex]\frac{1}{4}+\frac{5}{8}=\frac{(1*8)+(4*5)}{4*8}\\\\\frac{(1*8)+(4*5)}{4*8}=\frac{8+20}{32}=\frac{28}{32}[/tex]

Now, to reduce the fraction to its lowest term, we need to divide both numerator and denominator by a common number, for this case, it will be "4" since is the biggest whole number that both numerator and denominator can be divided by, so, we have:

[tex]\frac{\frac{28}{4} }{\frac{32}{4}}=\frac{7}{8}[/tex]

Hence, we have that the lowest term will be:

[tex]\frac{7}{8}[/tex]

Have a nice day!

Answer:

  4/r

Step-by-step explanation:

The side lengths s of an equilateral triangle inscribed in a circle of radius r will be ...

  s = r√3

The perimeter of the triangle will be 3s.

The area of the triangle will be s^2·(√3)/4.

Then the ratio P/A is ...

  P/A = (3s)/(s^2·(√3)/4) = (4√3)/s

Substituting the above expression for s, we have ...

  P/A = 4√3/(r√3)

  P/A = 4/r

The expression for the ratio of the perimeter to the area of an equilateral triangle, whose vertices lie on a circle with radius r, is 2√3/r.

The ratio of the perimeter to the area of an equilateral triangle is derived using the formulae related to the triangle and the circle on which it lies. Let's start with the formulas for the circumference of a circle C = 2πr, and the area of an equilateral triangle A = (√3/4)*s², where s is the side length of the triangle.

As the vertices of the triangle are on the circle, the side length s is equal to the diameter of the circle. Therefore, s = 2r. Also, the perimeter P = 3*s = 6r. Substituting the terms for A and P, we find that P/A = 6r/((√3/4)*(2r)²) = (24/√3)/4r = 6/√3r. This simplifies to 2√3/r after rationalizing the denominator.

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ANSWER

See explanation

EXPLANATION

The given triangle is a right angle triangle.

We use the mnemonics SOH CAH TOA.

The given angle is

[tex] \alpha [/tex]

The opposite is 8 units, the adjacent is 15 units and the hypotenuse is 17 units.

[tex] \sin( \alpha ) = \frac{opposite}{hypotenuse} = \frac{8}{17} [/tex]

[tex] \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } = \frac{17}{8} [/tex]

[tex]\tan( \alpha ) = \frac{opposite}{adjacent} = \frac{8}{11} [/tex]

[tex] \cot( \alpha ) = \frac{1}{ \tan( \alpha ) } = \frac{15}{8} [/tex]

[tex]\cos( \alpha ) = \frac{adjacent}{hypotenuse} = \frac{15}{17} [/tex]

[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } = \frac{17}{15} [/tex]

In a right-angled triangle ABC, the trigonometric functions based on the given sides equate to: sin(α) = Option 3, csc(α) = Option 4, cos(α) = Option 5, sec(α) = Option 2, tan(α) = Option 1, and cot(α) = Option 6.

In a right-angled triangle, the Trigonometric Functions can be calculated based on the sides of the triangle.

For your problem, in triangle ABC, given that AB = 15 (hypotenuse), BC = 8 (opposite α) and AC = 17 (adjacent to α), we can compute the values as follows:

sin(α) = opposite/hypotenuse = BC/AB = 8/15 = (Option 3)

csc(α) = 1/sin(α) = 15/8 = (Option 4)

cos(α) = adjacent/hypotenuse = AC/AB = 17/15 = (Option 5)

sec(α) = 1/cos(α) = 15/17 = (Option 2)

tan(α) = sin(α)/cos(α) = (BC/AB) / (AC/AB) = BC/AC = 8/17 = (Option 1)

cot(α) = 1/tan(α) = 17/8 = (Option 6)

Learn more about Trigonometric Functions here:

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The probable question may be:

In Right angle triangle ABC, Angle ABC is 90 degree, Angle BAC is α , side AB= 15, side BC=8 and side AC=17.

please match the correct trigonometric function with the correct value.

sin (α) =

csc(α) =

tan(α) =

sec(α) =

cos(α)=

cot(α)=

Options:

1. 8/17

2. 15/17

3. 8/15

4. 15/8

5. 17/15

6. 17/8

Answer:

Step-by-step explanation:

what are the statements about the data?

Answer

C) The mean is greater than the median.

Step-by-step explanation:

To find the median, order the scores from LEAST to GREATEST.

400, 575, 575, 670, 720, 885, 1250.

The mean is the middle number, which is 670.

To find the mean, average the scores:  

400 + 575 + 575 + 670 + 720 + 885 + 1250

7

= 725

725 > 670; therefore, the mean is greater than the median.

For this case we have that by definition:

[tex]Secant (A) = \frac {1} {Cosine (A)}[/tex]

Then, we find the cosine of the angle H, this will be given by the leg adjacent to H on the hypotenuse of the triangle.

[tex]Cos (H) = \frac {g} {f}[/tex]

So, the secant of H is given by:[tex]Sec {H} = \frac {1} {\frac {g} {f}}\\Sec {H} = \frac {f} {g}[/tex]

Answer:

Option C

Answer:

Step-by-step explanation:

You need the 6th row of Pascal's triangle which contains the numbers 1, 5, 10, 10, 5, 1

Fill in the expansion as follows, using those numbers and the fact that a = 1 and b = 1:

[tex]1(1a)^5(1b)^0+5(1a)^4(1b)^1+10(1a)^3(1b)^2+10(1a)^2(1b)^3+5(1a)^1(1b)^4+1(1a)^0(1b)^5[/tex]

That simplifies down nicely to

[tex]a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5[/tex]

Those are fun!  Pascal's triangle is one of the coolest things ever!

To expand (a+b)^5 using Pascal's Triangle, we can use the Binomial Theorem. The expansion can be written as (a^5) + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + (b^5).

To expand the binomial (a+b)^5 using Pascal's Triangle, we will use the Binomial Theorem. According to the theorem, the expansion of (a+b)^n can be written as:

(a+b)^n = (nC0)(a^n)(b^0) + (nC1)(a^(n-1))(b^1) + (nC2)(a^(n-2))(b^2) + ... + (nCn)(a^0)(b^n)

For (a+b)^5, the expansion would be:

(a+b)^5 = (5C0)(a^5)(b^0) + (5C1)(a^4)(b^1) + (5C2)(a^3)(b^2) + (5C3)(a^2)(b^3) + (5C4)(a^1)(b^4) + (5C5)(a^0)(b^5)

Simplifying further, we get:

(a+b)^5 = (a^5) + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + (b^5)

Answer:

130.5 in²

Step-by-step explanation:

The area (A) of a regular pentagon is

A = [tex]\frac{1}{2}[/tex] × perimeter × apothem

perimeter = 8.7 × 5 ← pentagon has 5 sides

                 = 43.5 in

A= 0.5 × 43.5 × 6 = 130.5 in²

Answer:

• V = x(11 -2x)(16 -2x)

• x ≈ 2.1 in

Step-by-step explanation:

a) The volume of the box is the product of its depth (x), width (11 -2x) and length (16 -2x). The equation can be simply ...

v(x) = x(11 -2x)(16 -2x)

__

b) A graphing calculator can plot this equation directly. All that is needed is to enter it into the appropriate space provided by the calculator. The value of x that gives the greatest volume is the value that makes the function have a local maximum between x=0 and x=5.5 (where the volume is again zero).

That value of x is about 2.1 inches.

The amount Malia earns can be shown as an addition sentence by multiplying the price of the wristbands by the quantity sold. The sum of this addition is $10, which is what Malia earned on the first day of the fundraiser. This sum can be visualized on a number line with four equal jumps of $2.50 leading to a sum of $10.

a. The amount Malia earns can be represented as an addition sentence by multiplying the price of the wristbands ($2.50) by the number of wristbands sold (4). The addition sentence would look like this: $2.50 + $2.50 + $2.50 + $2.50.

b. The sum of the addition sentence above is $10. This means that Malia has earned $10 on the first day of the fundraiser by selling 4 wristbands at $2.50 each.

c. The sum on a number line can be shown by marking off four equal jumps of $2.50 starting from zero, which leads you to the total sum of $10 at the fourth jump.

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The board must be about 4.4 ft long

Answer:

Length of board should Jessica buy is 4.4 feets.

Step-by-step explanation:

Height of the ramp = [tex]2\frac{1}{2} ft=\frac{5}{2} ft[/tex]

Distance of the porch from the ground = x

Inclination of the ramp,θ = 35°

In triangle ABC,

AB = [tex]\frac{5}{2} ft[/tex]

AC = x

θ = 35°

According trigonometric ratios:

[tex]\sin \theta =\frac{Perpendicular}{hypotenuse}[/tex]

[tex]\sin 35^o =\frac{AB}{AC}[/tex]

[tex]0.573576=\frac{\frac{5}{2} ft}{x}[/tex]

[tex]x=4.3586 ft\approx 4.4 ft[/tex]

Length of board should Jessica buy is 4.4 feets.

Answer:

c. 41.1

Step-by-step explanation:

To find a, we'll use the Law of Sines that says:

[tex]\frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex]

And we'll isolate c to get:

[tex]c = \frac{sin(C) * b}{sin(B)}[/tex]

Then we will plug-in the information we already have :

[tex]c = \frac{sin(90) * 18}{sin(26)} = 41.06[/tex]

So, let's round it to 41.1 to match the answer number C.

Answer:

The correct answer is option C.   41.1

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Sin θ = opposite side/Hypotenuse

From the figure we can see a right triangle triangle FGH.

To find the value of c

It is given that, B=26° and b=18

Sin26 = opposite side/Hypotenuse  = b/c

c = 18/Sin26 = 41.1

Therefore the correct answer is option c.   41.1

Answer:

13

Step-by-step explanation:

Volume = length x width x height

2320.5 = l x 12.75 x 14

2320.5 = l x 178.5

2320.5/178.5 = l

l = 13