Mary and her sister mona decide to rent a paddleboat for 2 hours at a total cost of $25 which statement describes the relationship

Answer:

18

Step-by-step explanation:

The hypotenuse is BC.

According to the Pythagorean Theorem;

[tex]BC^2=AC^2+AB^2[/tex]

Since the base angles are equal:

[tex]AC=BC=9\sqrt{2}[/tex]

We substitute the given values into the formula to obtain:

[tex]BC^2=AC^2+AB^2[/tex]

[tex]BC^2=(9\sqrt{2})^2+(9\sqrt{2})^2[/tex]

[tex]BC^2=81(2)+81(2)[/tex]

[tex]BC^2=162+162[/tex]

[tex]BC^2=324[/tex]

Take positive square root.

[tex]BC=\sqrt{324}[/tex]

[tex]BC=18[/tex]

Hence the hypotenuse is 18 units

[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( \frac{1}{2} \right)^{\frac{20}{20}}\implies A=100\left( \frac{1}{2} \right)^1\implies A=50[/tex]

50 grams of that sample will be left after 20 years since it’s only gone through one half-life exactly.

Answer: True

Step-by-step explanation:

By definition for a function of the form:

[tex]ax ^ n + ... + bx + c[/tex]

It is true that if [tex]a <0[/tex] and n is odd then:

[tex]\lim_{n \to -\infty}ax^n + ...+bx+c = \infty[/tex]

In this case

[tex]f(x)=-2x^3-2x^2+7x-25[/tex]

Therefore

[tex]a=-2<0[/tex] and [tex]n =3[/tex] → odd number

Then

[tex]\lim_{n \to -\infty}-2x^3-2x^2+7x-25= \infty[/tex]

This means that when [tex]x \to -\infty,\ f(x) \to \infty[/tex]

The statement  x -> -∞, f(x) -> ∞  is True

Answer: Its is True

Answer:

2 1/2

Step-by-step explanation:

you have 2 whole pizzas and 1 half (1/2)

Answer:

A

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

add the 1 to the other 1 and it equals 2

Answer:

2

Step-by-step explanation:

1 and 1 is 2

Answer:

The surface area of the rectangular prism is 700 units² ⇒ answer A

Step-by-step explanation:

* Lets revise how to find the surface are of the rectangular prism

- The rectangular prism has 6 rectangular faces

- Each two opposite faces are equal

- It has 4 side faces and 2 bases

* We can find the surface area of it by adding the area of

 the 6 faces

- In the problem

# The dimensions of the bases are 12 units and 14 units

# The dimensions of the side faces are 12 units and 7 units,

   14 units and 7 units

* Now lets find the area of each 2 equal faces

- In the bases

∵ Area of the rectangle = length × width

∴ The area of one base =  12 × 14 = 168 units²

∴ The area of the two bases = 2 × 168 = 336 units² ⇒ (1)

- In the two opposite faces with dimensions 12 units and 7 units

∵ The area of one face = 12 × 7 = 84 units²

∴ The area of the two faces = 2 × 84 = 168 unit² ⇒ (2)

- In the two opposite faces with dimensions 14 units and 7 units

∵ The area of one face = 14 × 7 = 98 units²

∴ The area of the two faces = 2 × 98 = 196 unit² ⇒ (3)

* To find the surface area of the prism add (1) , (2) , (3)

∴ The surface area of the prism = 336 + 168 + 196 = 700 units²

* The surface area of the rectangular prism is 700 units²

Answer:

1/6

Step-by-step explanation:

The probability of tossing 6 tails in a row with a fair coin is 1/64, as each toss's outcome is independent and the probability of tail on a single toss is 1/2.

To compute the probability of tossing 6 tails in a row with a fair coin, you recognize that for each individual toss, the probability of getting a tail is ½. Since each toss is independent, you simply multiply the probabilities of each event occurring consecutively. Therefore, the probability of tossing 6 tails in a row is:

(½) × (½) × (½) × (½) × (½) × (½) = ½6

½6 = 1/64

So, the probability of tossing 6 tails in a row is 1/64.

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In the village of 3500 people, 63 individuals are both left-handed and have blonde hair.

To find out how many people in the village are both left-handed and have blonde hair, we first need to calculate the number of left-handed people, and then find 15% of that number to determine those who are also blonde.

Therefore, 63 people in the village are both left-handed and blonde-haired.

The solution involves using the distance formula to calculate the lengths of the sides of triangles ABC and ABD, and the Pythagorean theorem to identify the type of triangles they are by their side lengths.

To determine the characteristics of triangle ABC with vertices A(1, 7), B(-2, 2), and C(4, 2), we use the distance formula which is relevant because the length of the side of the triangle labeled a is the difference in the x-coordinates of points A and B. The same applies for side b, being the difference in the y-coordinates of points B and C. The length of side c is derived from the Pythagorean theorem, understanding that c represents the longest side of a right triangle, which is the hypotenuse.

Considering triangle ABD with an additional point D(1, 2), we first need to determine the lengths of the sides by using the formula for distance between two points in a coordinate plane for sides AB, BD, and AD. This will help to ascertain the type of triangle ABD is, based on the lengths of its sides. The length of side AD can be directly obtained since points A and D have the same x-coordinate.

The longest side of triangle ABC, which we determine by comparing the calculated lengths of AB, BC, and AC, will help us state whether the triangle is isosceles, scalene, or equilateral. For triangle ABD, once we have the lengths of AB, BD, and AD, we can determine its type similarly. This understanding stems from the standard geometric principles and the properties of triangles in a Euclidean space.

The answer is:

The second option,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Discarding each given option in order to find the correct one, we have:

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}[/tex]

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

The statement is true, we can prove it by using the following properties of exponents:

[tex](a^{b})^{c}=a^{bc}[/tex]

[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]

We are given the expression:

[tex](\sqrt[m]{x^{a} } )^{b}[/tex]

So, applying the properties, we have:

[tex](\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }[/tex]

Hence,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}[/tex]

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }[/tex]

Hence, the answer is, the statement that is true is the second statement:

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Have a nice day!

The sequence that shows geometric progression are options A), B), C), and E) and this can be determined by finding the geometric ratio.

Check all the options in order to determine which sequence is the geometric sequence.

A) 10, 7.5, 5.625, 4.21875,...

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{7.5}{10}[/tex]

r = 0.75

Ratio between second and third term:

[tex]\rm r =\dfrac{5.625}{7.5}[/tex]

r = 0.75

So, yes this sequence is in geometric progression.

B) 160, 40, 10, 2.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{40}{160}[/tex]

r = 0.25

Ratio between second and third term:

[tex]\rm r =\dfrac{10}{40}[/tex]

r = 0.25

So, yes this sequence is in geometric progression.

C) 20, 70, 245, 857.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{70}{20}[/tex]

r = 3.5

Ratio between third and fourth term:

[tex]\rm r =\dfrac{857.5}{245}[/tex]

r = 3.5

So, yes this sequence is in geometric progression.

D) 13, 16.5, 20, 23.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{16.5}{13}[/tex]

r = 1.27

Ratio between third and fourth term:

[tex]\rm r =\dfrac{23.5}{20}[/tex]

r = 1.175

So, no this sequence is not in geometric progression.

E) 5, 5.5, 6.05, 6.655, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{5.5}{5}[/tex]

r = 1.1

Ratio between third and fourth term:

[tex]\rm r =\dfrac{6.655}{6.05}[/tex]

r = 1.1

So, yes this sequence is in geometric progression.

F) 16, 17.1, 18.2, 19.3, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{17.1}{16}[/tex]

r = 1.07

Ratio between third and fourth term:

[tex]\rm r =\dfrac{19.3}{18.2}[/tex]

r = 1.06

So, no this sequence is not in geometric progression.

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Answer:

1, 2, 3, 5

Step-by-step explanation:

Answer:

The correct option is letter D.

Step-by-step explanation:

We have the following expression:

sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)

We now that sqrt(a*b) = sqrt(a)sqrt(b)

Applying this rule, we have:

sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)

sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y)

Also we know that a*sqrt(b) = sqrt(b*a^2)

Applying this we have:

sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y) = sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3)

Then the result is:

sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3) = sqrt(y^3) = y*sqrt(y)

The correct option is letter D.

Answer:

The carpet needed is [tex]288\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of the master bedroom is the area of a rectangle

so

The area is equal to

[tex]A=bh[/tex]

we have

[tex]b=16\ units[/tex]

[tex]h=18\ units[/tex]

substitute

[tex]A=(16)(18)=288\ units^{2}[/tex]

therefore

The carpet needed is [tex]288\ units^{2}[/tex]

Answer:

A

Step-by-step explanation:

The arc length formula is:

Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]

Where

[tex]\theta[/tex] is the angle measure of the arc, and

2πr is the circumference

Putting 84 in place of circumference and 14 in place of arc length, we can solve for [tex]\theta[/tex]:

Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]

14 = [tex]\frac{\theta}{360}*(84)[/tex]

14 = [tex]\frac{84\theta}{360}[/tex]

[tex]14*360=84\theta\\5040=84\theta\\\theta=\frac{5040}{84}=60[/tex]

answer choice A is right.

Answer:

2 hours,  142 miles

Step-by-step explanation:

Write a distance formula for both cars and then equate these formulas:

Car A:  y = 55x + 32  =  y = 42x + 58:  Car B

Then 55x + 32  =  y = 42x + 58  →  13x = 26, and so x = 2

That distance will be 55(2) + 32, or 142 miles.

The cars will reach the same point after 2 hours (first possible answer)

An equation is formed when two equal expressions. The correct option is A, 2hours, and 142 miles.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation for the distance covered by car A in x hours is y = 55x + 32, similarly, the equation for the distance covered by Car B in x hours is y=42x+58.

Now, to know at what time and at what distance the two cars will meet we need to solve the two equations. Since the car will cover the same distance we can write,

y = y

55x + 32 = 42x + 58

55x - 42x = 58 - 32

13x = 26

x = 2

Substitute the value of x in any one of the equations,

y = 55x + 32

y = 55(2) + 32

y = 110 + 32

y = 142

Thus, the car will meet after 2 hours, and the distance will be 142 miles.

Hence, the correct option is A, 2hours, and 142 miles.

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Answer: Y=2 !! ;) XD ;P

Answer:

1. We already have the measure of the hypotenuse and one out of two acute angle, therefore:

sin53° = x/45 => x = sin53° · 45 ≈35.94

2. We already have one out of two legs of the triangle and one acute angle so we know that:

tan27° = 48/x => x = 48/tan27° ≈ 94.21

The value of x in the first right angle triangle is 27.08.

The value of x in the second right angle triangle is 24.46.

In order to determine the value of x in the first triangle, cos would be used.

Cos 53 = opposite / hypotenuse

Cos 53 = x / 45

0.7071 = x /45

x = 45 x 0.6018

x = 27.08

In order to determine the value of x in the second triangle, tan would be used.

Tan 27 = opposite / adjacent

Tan 27 = x / 48

x = 0.5095 x 48  

x = 24.46

i dunno man, B looks about right.

Answer: c. The class median is lower than the exam median.

Step-by-step explanation:

the median is at a lower point on the number line, its to the left of the exam, so that means its lower

1/2 of the cake was eaten

1+2=3. 3/6=1/2

All the slices are the same size

Answer:

5,000 meters * 1 kilometer / 1,000 meters = 5 kilometers answer is B

Step-by-step explanation:

Answer:

the answer is 5k

Step-by-step explanation:

Answer:

The domain is all real values

Step-by-step explanation:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

In this case, we can observe from the graph that the function is defined for all x-values. So the domain is all real values.

Four litres of pure water should be mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.

To find the litres of pure water mixed:

Given:

Pure water is mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.

Amount of pure water mixed =?

Now,

As given in the question, we have

18 litres of 12% saline solution

= 18 × (12/100)

= 2.16 litres

To make a saline solution containing 3% salt

Hence, four litres should be mixed to obtain a saline solution having 3% salt.

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ANSWER

D. [tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]

EXPLANATION

The given explicit formula is

[tex]a_1= - 7[/tex]

and

[tex]a_n=\frac{1}{3} a_{n-1}[/tex]

This implies that,

[tex]r = \frac{1}{3} [/tex]

The explicit formula is given by:

[tex]a_n=a_{1}( \frac{1}{3} )^{n - 1} [/tex]

We substitute the known values to get;

[tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]

Answer:

D

Step-by-step explanation: A P E X

Answer:

6 per minute

Because you divide by 8 minutes

Answer:

5

Step-by-step explanation:

Let's rewrite this a bit.

[tex]-11-(-7-9)=-11+7+9[/tex]

This is because there is a -1 before the expression inside the parentheses, so every sign is reversed.

Now we can add.

[tex]-11+7+9=5[/tex]

Answer:

C. (-1, 0)

Step-by-step explanation:

(You don't need a picture to figure this out...it's simple algebraic manipulation.)

We could start off by rewriting the equation for the parabola with the negative on the other side, which tells us then that the parabola opens downward:

[tex]-(x+1)^2=8(y-2)[/tex]

Dividing both sides by -1 doesn't change anything.  Because this parabola opens downward, the focus is p units below the vertex at the same x-coordinate.  The vertex can be found from the equation to be (-1, 2).  The standard form of a parabola of this type is

[tex]-(x-h)^2=4p(y-k)[/tex]

where is the number of units between the vertex and the focus.  Our equation to find p is:

4p = 8 so p = 2.

That means that the focus is 2 units below the vertex at the x coordinate of -1.  Moving 2 units down from the y coordinate of 2 leaves us at a y coordinate of 0.  Therefore, the coordinates of the focus have to be (-1, 0)

Answer:

109 kg total

57 3/4 after

Step-by-step explanation:

31/4 orange

302/4 pineapples

103/4 bananas

436/4 total=109

436/4-205/4=231/4=57 3/4

The dress is originally 160$, but we take 30% off which is that same as .3 .

To find 30% or .3 of 160 we multiply 160 by .3 which gets us 48.

48 is 30% of 160 so to find the new price of the dress we need to subtract

160 - 48 = 112. The new price of the dress is 112$.

Since Claire's aunt works at the store Claire will get an additional 10% off from the "new" price which is 112$.  10% is also .1, so we will multiply 112 by .1 which equals 11.20.

As 10% of 112 is 11.20 so we will subtract 11 dollars and 20 cents from the price. 112 - 11.20 = 100.80$.

For sales tax we will do the same thing, multiply 100.80 by .075 which equals 7.56. This time since we are ADDING sales tax, we will add 100.80 and 7.56 rather than subtract. 100.80 + 7.56 = 108.36.

Claire will be paying 108.36$ for the prom dress.

Answer:

c

Step-by-step explanation: