If f(x) = 1 - 2x^3, find the inverse of f.

Answer:

B

Step-by-step explanation:

√((-20)²+21²)=√(400+441)=√841=29

cos θ=-20/29

sec θ=-29/20

Answer:

x=ln 24

Step-by-step explanation:

e^x=24

If we take the ln of both sides

ln e ^x= ln 24

x=ln 24

Answer:

60

Step-by-step explanation:

[tex]\frac{300}{5}[/tex]

60

Hence, 60 is the answer

Answer:

60 mph

Step-by-step explanation:

For this problem, we are looking at the rate, miles per hour. We know that Andrea traveled 300 miles in 5 hours, but how many miles did she travel in one hour? Let's do the math:

[tex]300[/tex]÷[tex]5=60[/tex] miles.

So, in one hours, Andrea travels 60 miles. We get the rate, 60mph.

Andrea was driving at 60 mph.

I hope this helps! Please let me know if you have any questions :)

[tex]5[/tex] ✅

Step-by-step explanation:

[tex]14 + {6}^{2} \div ( - 4) \\ \\ \: = 14 + \frac{6 \times 6}{ - 4} \\ \\ \: = 14 - \frac{36}{4} \: \\ \\ = 14 - 9 \\\\ \: = 5[/tex]

Note:-

[tex]\sf\purple{BODMAS\: rule.}[/tex]

B = Brackets

O = Orders

D = Division

M = Multiplication

A = Addition

S = Subtraction

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]

Answer:

12.5

Step-by-step explanation:

14+6²÷(-4)

=14+6×6÷(-4)

=14+36÷(-4)

=50÷-4

=12.5

Answer:

113.081 mm²

Step-by-step explanation:

A semicircle is the half part of a circle. And we know that the semicircle have 24 mm of diameter, and the radius is 24/2 = 12 mm. The small circle is inside the semicircle, so its diameter is equal to the radius of the semicircle, and its radius is 12/2 = 6mm

Now, consider π = 3.141, the area of the small circle is:

π•6² = 3.141 • 36 = 113.076 mm²

The area of the semicircle is (π•12²)/2 = (3.141•144)/2 = 226.151 mm²

Now, you just subtract the areas:

226.151 - 113.076 = 113.081 mm²

Answer:

[tex]P(New\ House) = \frac{1}{6}[/tex]

Step-by-step explanation:

Given

See attachment

Required

[tex]P(New\ House)[/tex]

This is calculated as:

[tex]P(New\ House) = \frac{New\ House}{Total}[/tex]

From the attachment, we have:

[tex]New\ House = 60^o[/tex]

[tex]{Total}= 360^o[/tex] --- total angle in a pie chart

Note that the measurements must be converted to degrees (if not already in degrees).

So, we have:

[tex]P(New\ House) = \frac{60}{360}[/tex]

Simplify

[tex]P(New\ House) = \frac{1}{6}[/tex]

Step-by-step explanation:

diamonds and hearts are red cards

spades and clubs are black cards

15+11=26

26/52 is the probability of selecting a black card, 50%

Answer:

The expanded form of 6,398 is 6000 + 300 + 90 + 8

Answer:I hope this could help !ut the answer is 4

Step-by-step explanation:

2 of them left so there are 4 left

As both the angles are linear, their sum is equal to 180°

i.e m<EFG+m<GFH = 180

=>( 2n+17 )+(4n+37) = 180

=> 6n + 54 = 180

=> 6n = 180-54

=>6n =126

=> n= 21

m<EFG = 2(21)+17 = 59°

m<GFH =4(21)+37 =121°

Given: ∠EFG and ∠GFH are a linear pair

We know that: Sum of the angles which make a linear pair should be equal to 180°

⇒  ∠EFG + ∠GFH = 180°

Given :

∠EFG = 2n + 17

∠GFH = 4n + 37

⇒  2n + 17 + 4n + 37 = 180°

⇒  6n + 54 = 180°

⇒  6n = 180 - 54

⇒  6n = 126

⇒  n = 21°

Substituting the value of n in ∠EFG and ∠GFH, We get:

⇒  ∠EFG = 2(21) + 17 = (42 + 17) = 59°

⇒  ∠GFH = 4(21) + 37 = (84 + 37) = 121°

Answer:

Step-by-step explanation:

Two similar triangles have a scale factor of 2 : 3.

7a. The ratio of their perimeters is 2 : 3.

As the sides are 2 : 3, the perimeters which are sums of all sides will also be 2 : 3

True

7b. The ratio of their areas is 4 : 6. True or False

As the sides are 2 : 3, the areas which are the products of two sides will be in the ratio of 2*2 : 3*3 = 4 : 9

False

7c. Their perimeters could be 14 cm and 21 cm. True or False

As the perimeter ratio for 14cm and 21 cm is 14 : 21 = 2 : 3 which complies with 7a. So they could be the perimeters.

True

7d. Two corresponding sides could be 6 in and 7 in. True or False

As the corresponding sides of 6in and 7in, the ratio is 6 : 7 and is different from 2 : 3.  So they cannot be corresponding sides.

False

Answer:

Step-by-step explanation:

7a. perimeter=3 sides added so the ratio is the same

The ratio of their perimeters is 2 : 3.

True

7b. area= sidexside so the ratio is 2x2:3x3 = 4:9

The ratio of their areas is 4 : 6.

False

7c. 14:21 =2:3

Their perimeters could be 14 cm and 21 cm.

True

7d. 6:7 <> 2:3

Two corresponding sides could be 6 in and 7 in.

False

Answer:

A = $ 4188.38

Step-by-step explanation:

A= $2500

r = 3.5% = 0.035

t = 15years

n = 1

     [tex]A = P(1 + r)^t[/tex]

        [tex]= 2500 ( 1 + 0.035)^{15}\\\\= 2500 (1.67535)\\\\= \$ 4188.38[/tex]

Answer:

Al cabo de una semana, 2187 personas han participado en la cadena, y al cabo del quinto día se habrán donado $1215000.

Step-by-step explanation:

Dado que tres hermanas deciden comenzar una cadena, donando cada una a tres personas $5.000 en un mismo día; con la condición que a quienes ellas ayuden también deberán hacer lo mismo con tres personas al día siguiente, para determinar, al cabo de una semana, cuántas personas han participado en la cadena, y finalizado el quinto día cuánto dinero se ha donado, se deben realizar los siguientes cálculos:

3^7 = X

2,187 = X

(3^5) x 5000 = X

243 x 5000 = X

1,215,000 = X

Por lo tanto, al cabo de una semana, 2187 personas han participado en la cadena, y al cabo del quinto día se habrán donado $1215000.

Answer: B. 4.11

Step-by-step explanation:

Using Binomial distribution  ( as the arrival times of workers are independent).

Formula for standard deviation: [tex]\sqrt{{p(1-p)}{n}}[/tex], where p= population proportion, n= sample size.

As per given ,

p= 0.06, n=300

Required standard deviation= [tex]\sqrt{0.06\left(1-0.06\right)300}[/tex]

[tex]=\sqrt{(0.06)(0.94)(300)}\\\\=\sqrt{16.92}\approx4.11[/tex]

Hence, the correct option is B.

SOH = Sine Opposite Hypotenus

CAH = Cosine Adjacent Hypotenus

TOA = Tangent Opposite Adjacent

Based on the key I wrote above, TOA is what you will use. Starting from angle Z look at the opposite side and adjacent side. (Opposite = 21 and Adjacent = 20) Make sure you're not looking at the hypotenus which is the side that is always across from the 90° angle.

Going by opposite over adjacent, that would be 21/20

The answer is the first choice 21/20

Answer:

B

Step-by-step explanation:

To find f(- 2) substitute x = - 2 into f(x)

f(- 2) = - 2(- 2)³ + (- 2)² + 4(- 2) - 3

        = - 2(- 8) + 4 - 8 - 3

        = 16 + 4 - 8 - 3

        = 9 → B

Answer:

x = 72.09555249

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan x = opp / adj

tan x = 65/21

Taking the inverse tan of each side

tan ^-1 ( tan x) = tan ^-1 ( 65/21)

x = 72.09555249

Answer:

18.9 km²

Step-by-step explanation:

Formula for area of a triangle: [tex]\frac{1}{2}bh[/tex]

0.5(7 × 5.4) = 18.9 km²

Answer:

A = 1/2 bh

1/2 x 7 x 5.4

= 18.9km2

Answer:

0.58823529411

Answer:0.8

Step-by-step explanation:

Answer:

$10,667.66

Step-by-step explanation:

The formula for calculating the compound interest is expressed as:

A = P(1+r/n)^nt

P is the principal = $9000

r is the rate = 3%

time t = 6years

n = 1/4

Substitute

A = 9000(1+0.03/(1/4))^6/4

A = 9000(1+0.03(4))^1.5

A = 9000(1+0.12)^1.5

A = 9000(1.12)^1.5

A = 9000(1.1853)

A = 10,667.67

Hence the amount after 6 years is $10,667.66

Answer:

-14-2= -16

I hope it helps :)

Answer:

Step-by-step explanation:

The center of the circle is the midpoint of the two end points of the diameter.

Formula

Center = (x2 + x1)/2 , (y2 + y1)/2

Givens

x2 = 4

x1 = - 10

y2 = 6

y1 = - 2

Solution

Center = (4 - 10)/2, (6 - 2)/2

Center = -6/2 , 4/2

Center = - 3 , 2

So far what you have is

(x+3)^2 + (y - 2)^2 = r^2

Now you have to find the radius.

You can use either of the endpoints to find the radius.

find the distance from (4,6) to (-3,2)

r^2 = ( (x2 - x1)^2 + (y2 - y1)^2 )

x2 = 4

x1 = -3

y2 = 6

y1 = 2

r^2 = ( (4 - -3)^2 + (6 - 2)^2 )

r^2 = ( (7)^2 + 4^2)

r^2 = ( 49 + 16)

r^2 = 65

Ultimate formula is

(x+3)^2 + (y - 2)^2 = 65

The radius is √65 = 8.06

Given:

Toilet rolls com in packs of 4 and 9.

4-pack is priced at £2.04.

9-pack is priced at £4.68.

To find:

The pack that has better value by calculating the price per roll.

Solution:

We have, the 4-pack is priced at £2.04.

So, the price per roll for this pack is:

[tex]\dfrac{2.04}{4}=0.51[/tex]

In the pack of 4 rolls the price per roll is £0.51.

It is given that, the 9-pack is priced at £4.68.

So, the price per roll for this pack is:

[tex]\dfrac{4.68}{9}=0.52[/tex]

In the pack of 9 rolls the price per roll is £0.52.

Since the price per roll in the pack of 4 rolls is less that the price per roll in the pack of 9 rolls because 0.51 < 0.52, therefore the pack of 4 rolls has better value.

Answer: -7

Step-by-step explanation:

Well since where going below degrees the answer would be -7 because it is closer to 1

Answer:

$1,650

Step-by-step explanation:

First, we need to find how much she paid the whole year. 27,700-x=7900. If we subtract 7900 from each side and add x to each side, we get 19,800=x. Therefore, she paid $19,800 in rent the whole year. Since there are 12 months in a year, and each month she paid the same, she paid $1,650 in rent each year, for 19800/12=1650

Answer:

The family of possible values for [tex]p[/tex] are:

[tex](-\infty, -4) \,\cup \,(7, +\infty)[/tex]

Step-by-step explanation:

By Linear Algebra, we can calculate the angle by definition of dot product:

[tex]\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|}[/tex] (1)

Where:

[tex]\theta[/tex] - Angle between vectors, in sexagesimal degrees.

[tex]\|\vec a\|, \|\vec b \|[/tex] - Norms of vectors [tex]\vec {a}[/tex] and [tex]\vec{b}[/tex]

If [tex]\theta[/tex] is acute, then the cosine function is bounded between 0 a 1 and if we know that [tex]\vec {a} = (p, 3, -7)[/tex] and [tex]\vec {b} = (p, -p, 4)[/tex], then the possible values for [tex]p[/tex] are:

Minimum ([tex]\cos \theta = 0[/tex])

[tex]\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0[/tex]

Maximum ([tex]\cos \theta = 1[/tex])

[tex]\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1[/tex]

With the help of a graphing tool we get the family of possible values for [tex]p[/tex] are:

[tex](-\infty, -4) \,\cup \,(7, +\infty)[/tex]

The dot product between the two vectors is the product of the magnitude between them times cosine angle.

The possible values for [tex]p[/tex] is (7,-4), when the angle is acute between [tex]a[/tex] and [tex]b[/tex].

To find the value of [tex]p[/tex] we need to perform the dot product of two equation.

The dot product between the two vectors is the product of the magnitude between them times cosine angle

Given information-

The vector equation given in the problem is,

[tex]a = p\hat i +3\hat j - 7\hat k[/tex]

[tex]b = p\hat i - p\hat j +4\hat k[/tex]

For acute angle, the dot product of [tex]a,b[/tex] less than equal to zero.

Thus,

[tex]a .b<0[/tex]

Put the values,

[tex](p\hat i +3\hat j - 7\hat k)(p\hat i - p\hat j +4\hat k)<0[/tex]

In the dot product the multiplication of different unit vector is zero. Thus,

[tex]p^2-3p-28<0[/tex]

Factorize above equation using the split the middle term method as,

[tex]p^2-7p+4p-28<0\\(p-7)(p+4)<0[/tex]

As the factor of the above equation is 7 and -4.

Thus the possible values for [tex]p[/tex] is (7,-4), when the angle is acute between [tex]a[/tex] and [tex]b[/tex].

Learn more about the dot product here;

https://brainly.com/question/9956772

Step-by-step explanation:

answer is in picture see

hope it helpful