Matt and his siblings bought their mom her favorite perfume for her birthday. They gave the cashier $80. The cashier gave them back 1 ten-dollar bill, 1 five-dollar bill, 8 dimes, and 1 nickel as change. How much did the perfume cost?

Answer:

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Step-by-step explanation:

9514 1404 393

Answer:

  73 ft²

Step-by-step explanation:

The ratio of areas is the square of the ratio of linear dimensions.

  smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)

  smaller area = 73 1/3 ft² ≈ 73 ft²

Answer:

Area of the smaller triangle = 73 square feet

Step-by-step explanation:

Area of the larger triangle = 165 square feet

Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]

[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]

Height = 22 ft

Since, both the triangles are similar.

By the property of similar triangles,

Corresponding sides of the similar triangles are proportional.

Let the height of smaller triangle = h ft

Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]

h = [tex]\frac{22\times 10}{15}[/tex]

h = 14.67 ft

Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]

                                              = 73.33

                                              ≈ 73 square feet

The length of arc APD is: [tex]\frac{\pi r}{2}[/tex]

A square when inscribed in a circle will fit the circle such that, the 4 edges of the square touches the sides of the circle. The radius of the circle can be drawn from any of the 4 edges.

Given that ABCD is a square:

This means that:

[tex]AB = BC = CD = DA[/tex] --- equal side lengths

To calculate the length of arc APD, we make use of the following arc length formula

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

Where

[tex]\theta = \angle ADO[/tex] and O is circle center

Since ABCD is a square, then:

[tex]\theta = \angle ADO = 90^o[/tex]

So, we have:

[tex]APD = \frac{90}{360} * 2\pi r[/tex]

[tex]APD = \frac{1}{4} * 2\pi r[/tex]

[tex]APD = \frac{\pi r}{2}[/tex]

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Answer:

2) Add 21 to both sides

Step-by-step explanation:

When solving [tex]16x-21=52[/tex] for [tex]x[/tex], our goal to isolate [tex]x[/tex] such that we have [tex]x[/tex] set equal to something.

Therefore, we want to start by adding 21 to both sides. This leaves us with [tex]16x=73[/tex] and we are one step closer to isolating [tex]x[/tex].

Answer:

The correct answer is "17.414 years".

Step-by-step explanation:

Given:

Doubling time,

= 7.5 years

As we know,

[tex]P(t) = P_oe^{rt}[/tex]

now,

⇒ [tex]2P_o=P_o e^{r\times 7.5}[/tex]

       [tex]2 = e^{r\times 7.5}[/tex]

       [tex]r = \frac{ln2}{7.5}[/tex]

          [tex]=0.092[/tex]

          [tex]=9.2[/tex]%

then,

⇒ [tex]P(t) = P_o e^{0.092 t}[/tex]

here,

[tex]P(t) = 5P_o[/tex]

hence,

⇒ [tex]5P_o = P_o e^{0.092 t}[/tex]

[tex]e^{0.092t}=5[/tex]

        [tex]t = \frac{ln5}{0.092}[/tex]

          [tex]=17.414 \ years[/tex]        

Answer:

The correct answer is "17.414 years".

Step-by-step explanation:

Answer:

Step-by-step explanation:

16x-8y = 16 ⇒ 8x - 4y = 8, which is identical to the second equation.

The equations are equivalent, so there are an infinite number of solutions.

Answer:

The interval 52% to 58% is based on a procedure that includes the true population value 95% of the time.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

95% confidence

We are 95% sure that the interval contains the true mean/proportion, and thus, the correct option is:

The interval 52% to 58% is based on a procedure that includes the true population value 95% of the time.

Answer:

0.5555 = 55.55% probability that Max will get the job.

Step-by-step explanation:

What is the probability that Max will get the job?

The sum of all probabilities is 100% = 1, so, considering Max's probability as x:

[tex]x + \frac{1}{3} + \frac{1}{9} = 1[/tex]

[tex]\frac{9x + 3 + 1}{9} = 1[/tex]

[tex]9x + 4 = 9[/tex]

[tex]9x = 5[/tex]

[tex]x = \frac{5}{9}[/tex]

[tex]x = 0.5555[/tex]

0.5555 = 55.55% probability that Max will get the job.

The max has probability of getting this job is x= 0.5555 and 55.55%

Suppose that ;

Max has probability of getting this job is = x

and other two companies have probability to get job is [tex]\frac{1}{3} or \frac{1}{9}[/tex].

Sum of the probability have bid a job is 100% which is equal to 1.

According to given question ;

Sum of all the companies having probability to get the job = 1

[tex]x + \frac{1}{3} + \frac{1}{9} = 1[/tex]

[tex]\frac{9.x+1.3+1.1}{9} = 1\\9x+3+1 = 9.1\\9x+4 =9\\9x = 9-4\\9x = 5\\x = \frac{5}{9}[/tex]

x = 0.5555

The Max has probability of getting this job is x= 0.5555 or 55.55%

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Answer:

Step-by-step explanation:

It's never negative.

D is indeed correct, the function's values never go below 0, meaning never below the x-axis

Answer:

12.04 cm

Step-by-step explanation:

Pythagoras in general :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90 degree angle).

a and b are the side legs.

so, in our example here

17² = 12² + b²

289 = 144 + b²

145 = b²

b = sqrt(145) = 12.04 cm

Answer:

3/2

Step-by-step explanation:

Recall that slope is y2 - y1 / x2 - x1.

Excellent. The question provides us with two points: (2,4) and (0,1). We can insert these two points into our equation.

Slope = (4 - 1) / (2 - 0) = 3 / 2.

Hope this helps!

Answer:

3/2

Step-by-step explanation:

(0,1) and (2,4)

(y2-y1)/(x2-x1)

= (4-1)/(2-0)

=3/2

Answered by GAUTHMATH

The equation of the line is.

y = (3/8)*x - 1.5

A general linear relationship can be written as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂), we can write the slope as:

a = ( y₂ - y₁)/(x₂- x₁)

We define the y-intercept and the x-intercept as the points where the graph intersects the y-axis or the x-axis correspondingly.

Here we know that the x-intercept is 4, or we can write this as (4, 0)

we also know that the y-intercept is -1.5, or we can write this as (0, -1.5)

So we know two points of the line, this means that we can find the slope of the line:

a = (-1.5 - 0)/(0 - 4) = (1.5)/(4) = (3/2)*(1/4) = 3/8

Then the line is:

y = (3/8)*x + b

And remember that b is the y-intercept, which we know is equal to -1.5, so we can just replace it:

Then the equation of the line is.

y = (3/8)*x - 1.5

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Answer:

(a) 4 sample points

(b) See attachment for tree diagram

(c) The probability that no tail is appeared is 1/4

(d) The probability that exactly 1 tail is appeared is 1/2

(e) The probability that 2 tails are appeared is 1/4

(f) The probability that at least 1 tail appeared is 3/4

Step-by-step explanation:

Given

[tex]Coins = 2[/tex]

Solving (a): Counting principle to determine the number of sample points

We have:

[tex]Coin\ 1 = \{H,T\}[/tex]

[tex]Coin\ 2 = \{H,T\}[/tex]

To determine the sample space using counting principle, we simply pick one outcome in each coin. So, the sample space (S) is:

[tex]S = \{HH,HT,TH,TT\}[/tex]

The number of sample points is:

[tex]n(S) = 4[/tex]

Solving (b): The tree diagram

See attachment for tree diagram

From the tree diagram, the sample space is:

[tex]S = \{HH,HT,TH,TT\}[/tex]

Solving (c): Probability that no tail is appeared

This implies that:

[tex]P(T = 0)[/tex]

From the sample points, we have:

[tex]n(T = 0) = 1[/tex] --- i.e. 1 occurrence where no tail is appeared

So, the probability is:

[tex]P(T = 0) = \frac{n(T = 0)}{n(S)}[/tex]

This gives:

[tex]P(T = 0) = \frac{1}{4}[/tex]

Solving (d): Probability that exactly 1 tail is appeared

This implies that:

[tex]P(T = 1)[/tex]

From the sample points, we have:

[tex]n(T = 1) = 2[/tex] --- i.e. 2 occurrences where exactly 1 tail appeared

So, the probability is:

[tex]P(T = 1) = \frac{n(T = 1)}{n(S)}[/tex]

This gives:

[tex]P(T = 1) = \frac{2}{4}[/tex]

[tex]P(T = 1) = \frac{1}{2}[/tex]

Solving (e): Probability that 2 tails appeared

This implies that:

[tex]P(T = 2)[/tex]

From the sample points, we have:

[tex]n(T = 2) = 1[/tex] --- i.e. 1 occurrences where 2 tails appeared

So, the probability is:

[tex]P(T = 2) = \frac{n(T = 2)}{n(S)}[/tex]

This gives:

[tex]P(T = 2) = \frac{1}{4}[/tex]

Solving (f): Probability that at least 1 tail appeared

This implies that:

[tex]P(T \ge 1)[/tex]

In (c), we have:

[tex]P(T = 0) = \frac{1}{4}[/tex]

Using the complement rule, we have:

[tex]P(T \ge 1) + P(T = 0) = 1[/tex]

Rewrite as:

[tex]P(T \ge 1) = 1-P(T = 0)[/tex]

Substitute known value

[tex]P(T \ge 1) = 1-\frac{1}{4}[/tex]

Take LCM

[tex]P(T \ge 1) = \frac{4-1}{4}[/tex]

[tex]P(T \ge 1) = \frac{3}{4}[/tex]

Answer:

The right response is Option c ($185,870,742).

Step-by-step explanation:

Given:

n = 30

r = 5.4%

or,

 = 0.054

Periodic payment will be:

[tex]R = \frac{360000000}{30}[/tex]

   [tex]=12000000[/tex] ($)

Now,

The present value will be:

= [tex]R+R(\frac{1-(1+r)^{-n+1}}{r} )[/tex]

By substituting the values, we get

= [tex]12000000+12000000(\frac{1-(1+0.054)^{-30 + 1}}{0.054} )[/tex]

= [tex]12000000+12000000\times 14.4892[/tex]

= [tex]185,870,742[/tex] ($)

plug-in

-2(4) - 2

-8 - 2

-10

-10^2 + 1

-100 + 1

Your answer: -99

Answer:

The expectation for an event with outcomes:

{x₁, x₂, ..., xₙ}

Each one with probability:

{p₁, p₂, ..., pₙ}

Is:

Ev = x₁*p₁ + ... + xₙ*pₙ

There are 500 tickets sold.

1 of these, wins $3,000  (this is the event x₁)

4 of these, wins $100     (this is the event x₂)

2 of these, wins $75        (this is the event x₃)

The others do not have a prize.

So the probability of winning the $3000 is equal to the quotient between the number of tickets with that prize (1) and the total number of tickets (500)

p₁ = 1/500

Similarly, the probability of winning $100 will be:

p₂ = 4/500

And for the $75 prize:

p₃ = 2/500

Then the probability of not winning is:

p₄ = 493/500

Then the expected value for a single ticket is:

Ev = $0*493/500 + $75*2/500 + $100*4/500 + $3000*1/500

Ev = $7.1

If you take in account that you pay $50 for the ticket, the actual expectation should be:

E = $7.10 - $50 = -$42.90

Answer:

use the formula y = a(x-h)^2 + k

the a stretches or flattens the parabola,

The h shifts left to right , and the k shifts up/down

Step-by-step explanation:

Answer:

Step-by-step explanation:

a). Given expression in the question is,

   [tex]\frac{13822\times 623}{14}[/tex]

   Exact value of the expression will be,

   [tex]\frac{13822\times 623}{14}=615079[/tex]

b). By using approximations to 1 significant figure,

   13822 ≈ 10000

   623 ≈ 600

   14 ≈ 10

   615079 ≈ 60000

   Now use the expression,

   [tex]\frac{13822\times 623}{14}=\frac{10000\times 600}{10}[/tex]

                  = 60000

Answer:

∠ SPQ = 75°

Step-by-step explanation:

The sum of the 4 angles in a quadrilateral = 360°

Subtract the sum of the 3 angles from 360 for ∠ SPQ

∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°

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Answer:

  B.  (2, -5)

Step-by-step explanation:

Reflection across the y-axis is the transformation ...

  (x, y) ⇒ (-x, y)

Rotation 180° about the origin is the transformation ...

  (x, y) ⇒ (-x, -y)

Applying the rotation after the reflection, we get ...

  (x, y) ⇒ (x, -y)

  (2, 5) ⇒ (2, -5)

_____

Additional comment

For these transformations, the order of application does not matter. Either way, the net result is a reflection across the x-axis.

Answer:

(2,-5)

Step-by-step explanation:

Answer:

14w -14

Step-by-step explanation:

6w + 2(4w - 7)

Distribute

6w+ 8w -14

Combine like terms

14w -14

Answer:

6w+(2×4w)-(2×7)

(6w+8w)-14=14w-14

If Both triangles are similar the ratio of sides will be same

[tex]\\ \sf\longmapsto \dfrac{AB}{AC}=\dfrac{DE}{DF}[/tex]

[tex]\\ \sf\longmapsto \dfrac{8}{10}=\dfrac{12}{DF}[/tex]

[tex]\\ \sf\longmapsto 8DF=120[/tex]

[tex]\\ \sf\longmapsto DF=\dfrac{120}{8}[/tex]

[tex]\\ \sf\longmapsto DF=15cm[/tex]

Now

[tex]\\ \sf\longmapsto Perimeter=DF+DE+EF[/tex]

[tex]\\ \sf\longmapsto Perimeter=15+11+12[/tex]

[tex]\\ \sf\longmapsto Perimeter=38cm[/tex]

Step-by-step explanation:

7 times a certain number :

Let the unknown number be x

[tex]7 \times x[/tex]

is less four times that same number -2 is 58 :

7x - 4x -2 = 58

Collect like terms

7x-4x = 58+2

3x = 60

3x/3 = 60/3

x = 20

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 7x-4x-2=58[/tex]

[tex]\\ \sf\longmapsto 3x-2=58[/tex]

[tex]\\ \sf\longmapsto 3x=58+2[/tex]

[tex]\\ \sf\longmapsto 3x=60[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{60}{3}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Answer:

4

similar right triangles

[tex]\frac{8}{x} = \frac{x}{2}[/tex]

[tex]x^{2} = 16\\x=4[/tex]

Step-by-step explanation:

Answer:

FH ≈ 6.0

Step-by-step explanation:

Using the sine ratio in the right triangle

sin49° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{FH}{8}[/tex] ( multiply both sides by 8 )

8 × sin49° = FH , then

FH ≈ 6.0 ( to the nearest tenth )

Answer:

6

Step-by-step explanation:

sin = opposite/hypotenuse

opposite = sin * hypotenuse

sin (49) = 0,75471

opposite = 0,75471 * 8 = 6,037677 = 6

Answer:

The parent cubic function has been vertically stretched by a factor of 4.

Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]

Answer: Option B

OAmalOHopeO

Observe that the x coords of the roots of a polynomial are,

[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]

Which can be put into form,

[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]

with data

[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]

Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,

[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]

and a will be "lost" in the process.

If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.

Hope this helps :)

Answer:

13.73 in^2 because the circle's area is 50.27 in^2

9514 1404 393

Answer:

  184 m

Step-by-step explanation:

The direct distance from Kayla's car (C) to the door of her office building (B) can be found using the Law of Cosines. The interior angle of the triangle at the turning point is 180° -30° = 150°, so the distance is ...

  t² = b² +c² -2bc·cos(T)

  t² = 80² +100² -2·80·100·cos(150°) = 30256.406

The direct distance from her window to the car can be found from the Pythagorean theorem. The legs of the right triangle are the distance from the car to the building (CB) and the height from the building entrance to the window (BW).

  CW = √(t² +60²) ≈ 184.001

The direct line distance from Kayla to her car is 184 meters.

_____

For the first computation, we used the usual notation for a triangle, where capital letters (CTB) are the vertices and angles, and corresponding lower-case letters are their opposite sides.