A .Dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 m/sec, while the cat can run at a speed of 24 m/sec. How soon will the dog catch the cat if the dog starts running after the cat?

Answer:

A. 18 divided by 2/9

Step-by-step explanation:

To determine the number of boos that will fit into a box that is 18 inches long, we divide the length of the box by the length of the books

18 inches  divided by 2/9 inches per book

This tells us how many books

copy dot flip

18 * 9/2

81 books

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:

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:

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

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]

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.

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]

Answer:

it is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

65 - Acute

72 - Acute

96 - Obtuse

Answer:

(a)

Step-by-step explanation:

Given 3 sides of a triangle a, b and c where c is the longest side, then

• If a² + b² = c² ⇒ triangle is right

• If a² + b² > c² ⇒ triangle is acute

• If a² + b² < c² ⇒ triangle is obtuse

Here a = 65, b = 72 and c = 96

65² + 72² ? 96²

4225 + 5184 ? 9216

9409 > 9216 ⇒ triangle is acute

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:

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: 2

Step-by-step explanation:

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:

(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.

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

Step-by-step explanation:

I would say that the study reveals that there may be a correlation between eating blueberries and a lower cholesterol level.

The best conclusion from the study is that the consumption of blueberries might be associated with lower cholesterol levels. However, it's important to note that correlation does not mean causation and other factors could be at play.

The statement that comes closest to an appropriate conclusion from the study is that the possible consumption of blueberries might be associated with lower cholesterol levels. However, it is important to remember that correlation does not necessarily imply causation. While the organization of farmers showed a connection between eating blueberries and lower cholesterol, this does not necessarily mean eating blueberries directly causes lower cholesterol. Other factors could be involved. For instance, those who eat blueberries daily might generally lead healthier lifestyles, contributing to lower cholesterol levels.

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Answer:

F

Step-by-step explanation:

In congruent triangles, or similar triangles, the letters in the same place will also be congruent

Answer:

the answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Observe in the attached image that the final balance in your account on 9/1 is $578.30.

Then:

*On 9/6 he makes a payment of $140.30

*On 9/8, he makes a withdrawal from an ATM of $120

This means that:

$140.30 + $120 = $260.30

Then:

*On 9/18 you receive a deposit of $356.22

This means that:

$356.22

So, we have:

Beginning Balance: $578.30.

Total Withdrawals: $260.30

Total Deposits: $356.22

Final Balance = Beginning balance + Total Deposits - Total Withdrawals

Final Balance= $578.30 + $356.22 - $260.30

Final balance= $674.22

Then:

Date     Description    Debits(-) Credits(+)    Balance

9/6        Auto Pay         140.30                       438.00

9/8         ATM               120.0                         318.00

9/18       Deposit                           356.22      674.22

The balance in Arianna's register after the transactions will be $587.88. Then the correct option is C.

A monetary transfer is a record of money entering and exiting your account and is known as a bank transaction.

Arianna's register shows a deposit on 9/5 in the amount of $310.25 an ATM withdrawal on 9/8 in the amount of $60.00 and checks #149 on 9/14 in the amount of $240.67.

No other Transactions were made.

Then the balance be in Arianna's register will be

→ $ 578.37 + $ 310.25 - $ 60 - $ 240.67

→ $ 587.88

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D. -4/3

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

9x2+24x+20=4

Step 1: Subtract 4 from both sides.

9x2+24x+20−4=4−4

9x2+24x+16=0

Step 2: Factor left side of equation.

(3x+4)(3x+4)=0

Step 3: Set factors equal to 0.

3x+4=0 or 3x+4=0

x= −4 /3

Hope This helps

Answer:

D. x = [tex]-\frac{4}{3}[/tex]

Step-by-step explanation:

Step 1: Subtract 4 from both sides.

9x^2 + 24x + 20 − 4 = 4 − 4

9x^2 + 24x + 16 = 0

Step 2: Factor left side of equation.

(3x+4)(3x+4) = 0

Step 3: Set factors equal to 0.

3x+4=0 or 3x+4=0

x = [tex]-\frac{4}{3}[/tex]

I hope this helps your assignment! Anyways, have a fantastic day! :D  

[tex]f(x)[/tex] is continuous on [0, 3] and differentiable on (0, 3), so the mean value theorem applies here. It says that there is some [tex]c[/tex] in the open interval (0, 3) such that

[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]

We have

[tex]f'(x)=-2\sin2x-e^{-x}[/tex]

so

[tex]-2\sin2c-e^{-c}=\dfrac{\cos6+e^{-3}-2}3\implies c\approx1.5418[/tex]

Solution:  Second month = m

The equation is

m + 10205 = 21894

m = 11689

So the second month will be $11,894. :)

To solve for the second month's salaries, subtract the first month salary from the total for two months. The solution to the equation $21,894 - $10,205 gives this salary: $11,689.

The subject of this problem is a toy company's salary expenses over a course of two months. Let's denote the salary expenses for the second month as X. We know from the problem that the total salary expenses for the first two months (January and February) are $21,894. Furthermore, we know that the salary expenses for January are $10,205.

We can write an equation to express these facts as follows: X (which is the salary expenses for February) is equal to the total salary for the two months minus the salary for January, or in mathematical notation, X = $21,894 - $10,205.

We solve this math equation by subtracting $10,205 from $21,894, giving us X = $11,689. Therefore, the second month's salaries total $11,689.

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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.

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.

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

170^3 this is the answer just make sure you do you're work.

Answer:

Step-by-step explanation:

The formula for the area of a sector is

[tex]A_{s} =\frac{\theta }{360}*\pi r^2[/tex]

where theta is the angle given as 45 and r is the radius (7).  Plugging in we get

[tex]A_{s}=\frac{45}{360}*\pi  (7)^2[/tex]

Simplify a bit to get

[tex]A_{s}=\frac{1}{8}*49\pi[/tex]

which gives you, in terms of pi:

[tex]A_{s}=\frac{49\pi }{8}[/tex]

or if you need to use the decimal form, rounded to the hundredths position:

A = 19.24

Monthly periodic rate = 1.95%

The APR is the annual periodic rate

The annual periodic rate is the monthly rate multiplied by 12, because there are 12 months in a year

APR = monthly periodic rate X number of months in a year

= 1.95% X 12

= 23.4%

By using the concept of Annual Periodic rate and Monthly periodic rate,

Annual periodic rate of Shelby = 23.4%

What is Annual Periodic Rate and Monthly periodic rate?

At first it is important to know about Periodic rate.

Periodic rate is the rate that can be charged on loans for a certain period.

If the periodic rate is calculated over a month then it is called monthly periodic rate.

If the periodic rate is calculated over a year then it is called Annual periodic rate.

Here,

Monthly periodic rate of Shelby = 1.95%

Annual periodic rate of Shelby = [tex]1.95 \times 12[/tex]

                                                   = 23.4%

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Answer: letter a should be the correct answer

Step-by-step explanation:

D is the answer for this question

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.

Answer:

The degree of a polynomial is the highest degree of its monomials with non-zero coefficients

Step-by-step explanation:

not sure

The maximum power of the polynomial x⁶ + 4x - 3 that is degree will be 6.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

A polynomial's degree is the greatest exponent of its variable term. The variable in this example is x, and the maximum exponent of x is 6, which is the degree of the polynomial. As a result, the polynomial x⁶ + 4x - 3 has a degree of 6.

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