Two figures have a similarity ratio of 3 : 7. If the area of the larger figure is 294 cm2, which is the area of the smaller figure?

Answer:

The equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is [tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex].

Step-by-step explanation:

A sphere is described by its radius and center, the radius of the largest sphere contained in the first octant are determined by the least distance of the center with respect to an orthogonal axis, that is:

Distance regarding x-axis:

[tex]d_{x} = 10 - 0[/tex]

[tex]d_{x} = 10[/tex]

Distance regarding y-axis:

[tex]d_{y} = 8 - 0[/tex]

[tex]d_{y} = 8[/tex]

Distance regarding z-axis:

[tex]d_{z} = 7 - 0[/tex]

[tex]d_{z} = 7[/tex]

Hence, the radius of the sphere must have a measure of 7. The equation of the sphere is represented by the following geometric locus:

[tex](x-h)^{2} + (y-k)^{2} + (z - j)^{2} = r^{2}[/tex] (1)

Where:

[tex]h, k, j[/tex] - Coordinates of the center.

[tex]r[/tex] - Radius of the sphere.

If we know that [tex](h,k,j) = (10, 8, 7)[/tex] and [tex]r = 7[/tex], then the equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is:

[tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex]

Answer:

the answer is b

Step-by-step explanation:

Answer:

b: 78.5cm²

Step-by-step explanation:

answer is b my friend

Answer:

2f+3g+2h

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

According to pythagoras theorem;

(sinx)²+(cosx)² = 1

Given that sinФ = √3/2

Substitute into the formula

(√3/2)²+(cosx)² = 1

3/4+(cosx)² = 1

(cosx)² = 1 - 3/4

(cosx)²  = 1/4

cos x = √1/4

cos x = 1/2

Hence the value of cosФ is 1/2

Answer:

Plot B

Step-by-step explanation:

Plot B has a negative slope.

Answer:

11/20 cups left

Step-by-step explanation:

first, we need to convert 3/4 and 1/5 into fractions with common denominators

so we would have:

15/20 and 4/20

now we need to subtract the fractions to get the difference

so we would do:

15/20 - 4/20 = 11/20

and that's the answer

hope that helped

Answer:

11/20 cup

Step-by-step explanation:

3/4 - 1/5

use common denominator of 20

15/20 - 4/20

11/20 cup

Answer:

<5, <1

Step-by-step explanation:

.............

........

Total number of plants,

= 13 + 2 = 15

Number of plants in a row = 3

Hence, Total Number of rows,

Therefore, he will have five rows.

Answer:

(c) No; There is an exponent on a variable x that is not a whole number

Step-by-step explanation:

Given

[tex]f(x) = x^2 - \sqrt[5]{x}[/tex]

Required

Determine if the function is a polynomial function of not

A polynomial function is represented as:

[tex]f(x) =ax^n + bx^{n-1} + cx^{n-2}+........+z[/tex]

Where n is an integer and the least power is 0

So, we have:

[tex]f(x) = x^2 - \sqrt[5]{x}[/tex]

The degree of x is [tex]\frac{1}{5}[/tex] ----- i.e. not an integer

Hence, the function is not a polynomial

Answer:

a = 8 * (2)^(2x)

Step-by-step explanation:

There are 2 12hours periods in a day

a = 8 * (2)^(2x)

Answer:

Identify the assumptions and goals of the theorem. Understand the implications of each of the assumptions made. Translate them into mathematical definitions if you can. Make an assumption about what you are trying to prove and show that it leads to a proof or a contradiction.

Step-by-step explanation:

Answer:

There are many different ways to go about proving something, discuss 3 methods: direct proof, proof by contradiction, proof by induction. Identify the assumptions and goals of the theorem. Understand the implications of each of the assumptions made. Translate them into mathematical definitions if you can. Make an assumption about what you are trying to prove and show that it leads to a proof or a contradiction

hope this helps

have a good day :)

Step-by-step explanation:

give the other person brainliest pls

Answer:

The probability that the month starts with the letter J or the letter M is 41.66%.

Step-by-step explanation:

Given that a month of the year is chosen at random, to determine what is the probability that the month starts with the letter J or the letter M, the following calculation must be performed:

January - March - May - June - July = 5 months

(5/12) x 100 = X

0.4166 x 100 = X

41.66 = X

Therefore, the probability that the month starts with the letter J or the letter M is 41.66%.

Answer:

5/12

Step-by-step explanation:

Months that start with the letter M are March and May

Months that start with J are January, June, July

So, in total the months that start with J and M are 5 in number.

Total number of months = 12

Therefore the probability = 5/12 or 0.416 (bar on 6)

Hope u understood

Please mark as brainliest

Thank You

Answer:

diameter = 18.8 ft

circumference = 56.1 ft

Step-by-step explanation:

diameter = 2 x radius = 2 x 9.4 = 18.8 ft

circumference = 2[tex]\pi[/tex]r = 2[tex]\pi[/tex](9.4) = 56.061 rounded to the nearest tenth is 56.1

Answer:

=  -24x^5 -60x^4 - 20x^3 + 8x^2+36

Step-by-step explanation:

Given the expression

(4x + 6)(- 6x^4 - 4x - 6x ^ 3 + 6 + 4x ^ 2)

Expand

4x(- 6x^4 - 4x - 6x ^ 3 + 6 + 4x ^ 2)+6(- 6x^4 - 4x - 6x ^ 3 + 6 + 4x ^ 2)

= -24x^5 -16x^2-24x^4+24x+16x^3 - 36x^4 -24x-36x^3+36+24x^2

= -24x^5 -24x^4 - 36x^4+16x^3-36x^3 -16x^2+24x^2+24x-24x+36

=  -24x^5 -60x^4 - 20x^3 + 8x^2+36

This gives the required expression

Answer:

341.6

Step-by-step explanation:

This problem asks one to subtract (58.4) from (400).

400 - 58.4 = 341.6

Less than is subtraction.

Subtract 58.4 from 400

400 - 58.4 = 341.6

The answer is 341.6

Answer: The shorter side = 11.83 cm

Step-by-step explanation:

The diagonal of a rectangle creates a right triangle with its adjacent sides.

Given: The diagonal and the longer side of a rectangle make an angle of 43.2°. If the longer  side is 12.6cm.

According to trigonometry,

[tex]\tan x=\frac{\text{Side opposite to x}}{\text{Side adjacent to x}}[/tex]

[tex]\tan 43.2^{\circ}=\frac{\text{Shorter side}}{12.6 }\\\\0.93906251=\frac{\text{Shorter side}}{12.6}\\\\ \text{Shorter side}=12.6\times 0.93906251\\\\=11.832187626\approx11.83\ cm[/tex]

Hence, the shorter side = 11.83 cm

Answer:-5

Step-by-step explanation:

Hello!

-6-4/2 = -10/2=-5

Hope this helps, have a great day!

Answer:

[tex]\frac{37}{28}[/tex] miles

Step-by-step explanation:

Use the area formula, A = lw, where l is the length and w is the width.

Plug in the area and length into the formula, and solve for w:

A = lw

37 = 28w

37/28 = w

So, as a fraction, the width of the garden is [tex]\frac{37}{28}[/tex] miles

Answer:

37/28 =w

Step-by-step explanation:

Area for a rectangle is given by

A = l*w

Substitute in what we know

37 = 28*w

Divide each side by 28

37/28 = 28w/28

37/28 =w

9514 1404 393

Answer:

  1/2 + 1/6

Step-by-step explanation:

  2/3 = 1/2 + 1/6

__

The sum of unit fractions is called an Egyptian Fraction. There are several different algorithms for finding such a sum. Here, we are starting with the form ...

  2/p

where p is a small prime. Then the sum can be written as ...

  1/((p+1)/2) +1/(p(p+1)/2) = 1/(4/2) +1/(3(4/2)) = 1/2 + 1/6

A different algorithm is used when p is a composite number.

__

Using the "greedy" algorithm, we can find the largest unit fraction less than 2/3 to be ...

  1/ceil(3/2) = 1/2

Then the largest unit fraction in the remainder is similarly found. The remainder is ...

  2/3 -1/2 = 1/6 . . . . already a unit fraction

So, the sum is ...

  2/3 = 1/2 + 1/6

Answer: x = 28

Step-by-step explanation:

Let's solve your equation step by step!

3/8x + 15/2 = 18

Step 1: Subtract 15/2 from both sides.

3/8x + 15/2 - 15/2 = 18 - 15/2

3/8x = 21/2

Step 2: Multiply both sides by 8/3

(8/3) * (3/8x) = (8/3) * (21/2)

Step 3. Calculate

x = 28

Answer:

x-6+6(6+6+6)X I am a pro boiiiiii

Answer:

0.3874 = 38.74% probability that exactly 9 of the 10 consumers recognize her brand name.

0.6126 = 61.26% probability that the number who recognize her brand name is not nine.

Step-by-step explanation:

For each consumer, there are only two possible outcomes. Either they recognize the name, or they do not. The probability of a customer recognizing the name is independent of anu other customer. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The brand name of Mrs. Fields (cookies) has a 90% recognition rate.

This means that [tex]p = 0.9[/tex].

Sample of 10

This means that [tex]n = 10[/tex]

Find the probability that exactly 9 of the 10 consumers recognize her brand name.

This is P(X = 9). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874[/tex]

0.3874 = 38.74% probability that exactly 9 of the 10 consumers recognize her brand name.

Also, find the probability that the number who recognize her brand name is not nine.

1(100%) subtracted by those who recognize. So

1 - 0.3874 = 0.6126

0.6126 = 61.26% probability that the number who recognize her brand name is not nine.

Answer:

B. 500

Hope this helps!! :D

Answer:

The answer is B

explanation:

78.8 is nearly 80 and 6.8 is nearly 7

so an estimate would be 80 × 7

= 560

Answer:

87.79

Step-by-step explanation:

Given :

Number of skiers in the village = Inventory = 1562.664

Stay time in LaVilla = 17.8 days

The number of new skiers arriving on average per day is :

According to Little's theorem :

Inventory / flow time

1562.664 / 17.8

= 87.79

Hence, 87.79 arrive LaVilla per day on average

Find common denominators, note that what you multiply (or divide) to the denominator, you must also do the same to the numerator.

1)

[tex]\frac{2}{3} , \frac{3}{4} \\\frac{2}{3} * \frac{4}{4} = \frac{8}{12} \\\frac{3}{4} * \frac{3}{3} = \frac{9}{12}[/tex]

Answers: [tex]\frac{8}{12} ; \frac{9}{12}[/tex]

2)

[tex]\frac{1}{4} , \frac{2}{3} \\\frac{1}{4} * \frac{3}{3} = \frac{3}{12}\\\frac{2}{3} * \frac{4}{4} = \frac{8}{12}[/tex]

Answers: [tex]\frac{3}{12} ; \frac{8}{12}[/tex]

3)

[tex]\frac{3}{10} , \frac{1}{2} \\\frac{3}{10} * \frac{1}{1} = \frac{3}{10}\\\frac{1}{2} * \frac{5}{5} = \frac{5}{10}[/tex]

Answers: [tex]\frac{3}{10} ; \frac{5}{10}[/tex]

4)

[tex]\frac{3}{5} , \frac{3}{4}\\\frac{3}{5} * \frac{4}{4} = \frac{12}{20}\\\frac{3}{4} * \frac{5}{5} = \frac{15}{20}[/tex]

Answers: [tex]\frac{12}{20} ; \frac{15}{20}[/tex]

5)

[tex]\frac{2}{4} , \frac{7}{8} \\\frac{2}{4} * \frac{8}{8} = \frac{16}{32}\\\frac{7}{8} * \frac{4}{4} = \frac{28}{32}[/tex]

Answers: [tex]\frac{16}{32} ; \frac{28}{32}[/tex]

6)

[tex]\frac{2}{3} , \frac{5}{12}[/tex]

[tex]\frac{2}{3} * \frac{12}{12} = \frac{24}{36} \\\frac{5}{12} * \frac{3}{3} = \frac{15}{36}[/tex]

Answers: [tex]\frac{24}{36} ; \frac{15}{36}[/tex]

7)

[tex]\frac{1}{4} , \frac{1}{6} \\\\\frac{1}{4} * \frac{6}{6} = \frac{6}{24} \\\frac{1}{6} * \frac{4}{4} = \frac{4}{24}[/tex]

Answers: [tex]\frac{6}{24} ; \frac{4}{24}[/tex]

Find common denominators, note that what you do to the denominator, you do to the numerator:

8.

[tex]\frac{1}{2} [] \frac{2}{5} \\(\frac{5}{5}) \frac{1}{2} [] \frac{2}{5} (\frac{2}{2})\\\frac{5}{10} \neq \frac{4}{10}[/tex]

Answer: Does not equal.

9.

[tex]\frac{1}{2} [] \frac{3}{6} \\\frac{1}{2} (* \frac{3}{3}) [] \frac{3}{6}\\\frac{1 * 3}{2 * 3} [] \frac{3}{6} \\\frac{3}{6} = \frac{3}{6} \\\\\frac{1}{2} = \frac{3}{6}[/tex]

Answer: Does equal.

10.

[tex]\frac{3}{4} [] \frac{5}{6}\\(\frac{6}{6})\frac{3}{4} [] \frac{5}{6}(\frac{4}{4})\\\frac{18}{24} \neq \frac{20}{24}[/tex]

Answer: Does not equal.

11.

[tex]\frac{6}{10} [] \frac{3}{5} \\\frac{6}{10} [] (\frac{3}{5} )(\frac{2}{2})\\\frac{6}{10} [] (\frac{3 * 2}{5 * 2})\\\frac{6}{10} = \frac{6}{10}[/tex]

Answer: Does equal.

12. You are simply only looking for the least number of parts that both rectangles can be divided too. Find the least common multiple of both 3 and 4:

Multiples of 3: 3, 6, 9, 12

Multiples of 4: 4, 8, 12

12 is your answer.

13. Find common denominators. Note that what you do to denominator, you do to the numerator:

[tex]\frac{2}{5} * \frac{2}{2} = \frac{4}{10}\\\frac{1}{2} * \frac{5}{5} = \frac{5}{10}[/tex]

Answers: [tex]\frac{4}{10}[/tex] , [tex]\frac{5}{10}[/tex]

~

Answer:

(a) [tex]Area = 14.7824cm^2[/tex]

(b) [tex]Area = 118.2592cm^2[/tex]

(c) [tex]Area = 4nh[/tex]

Step-by-step explanation:

Given

[tex]\theta = 67.5[/tex]

[tex]b= 8cm[/tex] --- base

[tex]n = 8[/tex] --- triangles

Solving (a) The area of each triangle

First, calculate the height (h) of each triangle using:

[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle

[tex]\sin(67.5) = \frac{h}{8/2}[/tex]

[tex]\sin(67.5) = \frac{h}{4}[/tex]

Solve for h

[tex]h =4*\sin(67.5)[/tex]

[tex]h =4*0.9239[/tex]

[tex]h =3.6956[/tex]

The area of each triangle is:

[tex]Area = \frac{1}{2} *b * h[/tex]

[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]

[tex]Area = 14.7824cm^2[/tex]

Solving (b): Area of the octagon

This is calculated as:

Area = 8 * area of 1 triangle

[tex]Area = 8 * 14.7824cm^2[/tex]

[tex]Area = 118.2592cm^2[/tex]

Solving (c): Area of octagon of side length n

In (a), we have:

[tex]Area = \frac{1}{2} *b * h[/tex]

Replace b with n

[tex]Area = \frac{1}{2} *n * h[/tex]

Multiply by 8 (the sides) to get the area of the octagon

[tex]Area = 8 * \frac{1}{2} *n * h[/tex]

[tex]Area = 4nh[/tex]

Answer: b= - -log10(7)+3/2

Step-by-step explanation: log 10 (7) -2b-9=-6 : b= - -log10(7)+3/2 (Decimal : b = -1.07745...)

so these are the steps how I got it I did log 10 (7)-2b-9=-6 subtract log 10 (7) -9 from both sides log 10 (7)-2b-9-(log10(7)-9)=-6-(log 10 (7) -9)

Simplify -2b= -log10(7)+3

Divide both sides by -2  -2b/2= - log 10(7)/-2+ 3/-2 if you simplify it should give you b= - -log10(7)+3/2 that should be your answer but i'm not sure those I think that's how you do it let me know if you got it right bye!

Answer:

3`⁴ = 1/81

Step-by-step explanation:

________________