A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing
equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the
two pieces of equipment?

The e vertex of the decagon will be in the top position after rotating it counterclockwise by 3 times the smallest angle of rotation.

Which vertex will be in the top position of the regular decagon?

A regular decagon has 10 sides of equal lengths with points labeled 'a' through 'j' clockwise. It is given that the point a is the top-left point. Hence, the the vertex which is in the the top position currently is 'b'.

Now, the smallest angle of rotation will be the angle between the two sides of the decagon.

In the first rotation by the smallest angle in counterclockwise direction, point 'c' will come to the top position. In the second rotation by the smallest angle in counterclockwise direction,  point 'd' point will become the top most vertex. Finally, after the third similar rotation, 'e' vertex will be in the top position of the decagon. (Refer the attached diagram)

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The probability that exactly 6 of 8 adult use their smartphones in meetings or classes is 0.147 or 14.7% .

The complete question is

Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

Probability is the measure of likeliness of an event to happen.

The probability given is

p = 54% = 0.54

n =8

r = 6

The binomial Probability is given by

[tex]\rm P(x) = ^n C_r p^r q^{n-r}[/tex]

The probability that exactly 6 people use smartphones in a class of 8 student is given by

[tex]P(x) = \dfrac{n!}{r! (n-r)!} p^r q^{n-r}[/tex]

Here q represents the complement

q = 1 -p

q = 1-0.54 = 0.46

[tex]P(6) = \dfrac{8!}{6! (2)!} 0.54^6 0.46^{2}\\\\\P(6) = \dfrac{8 * 7}{ 2} 0.54^6 0.46^{2}\\\P(6) = 0.147[/tex]

Therefore The probability that exactly 6 of 8 adult use their smartphones  in meetings or classes is 0.147 or 14.7% .

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Answer:

Symmetric property

    Sin and cos are trigonometry functions used to find measurements in a right triangle.

         [tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]

         [tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]

Answer: $0.24

Step-by-step explanation:

9.5 inches --> $2.28
1 inch--->X
now cross multiply it and get,

9.5X = 2.28*1
X = 2.28/9.5

so its $0.24 per inch

Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

           b represents the y-intercept

where the format of a point is (x, y)

Given: y = 1/4x + 5, (−1, 6)

we can plug in the point (−1, 6)

6 = 1/4(-1) + 5

6 = -1/4 + 5

6 = 4.75

6 does not equal 4.75 so this point is not on the line

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Answer:

a

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (6, 4 ) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = [tex]\frac{1}{3}[/tex] x + 2 ← equation of line

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex] \tt{sin(\Theta) = \cfrac{3}{8}} [/tex]

[tex]\qquad \tt \rightarrow \: x = 6\:\: cm[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \sin( Theta) = \cfrac{Opposite \:\: side}{Hypotenuse}[/tex]

[tex]\qquad \tt \rightarrow \: \sin( \Theta) = \cfrac{3}{8} [/tex]

since the Triangles are similar, ratio of their corresponding sides are equal :

[tex]\qquad \tt \rightarrow \: \sin( \Theta) = \cfrac{3}{8} = \dfrac{x}{16} [/tex]

[tex]\qquad \tt \rightarrow \:x = 16 \sdot \cfrac{3}{8}[/tex]

[tex]\qquad \tt \rightarrow \: x = 2 \sdot3[/tex]

[tex]\qquad \tt \rightarrow \: x = 6 \: \: cm[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Since  the two right-angled triangles have the same angles, the values are; ai. sin θ= 3/8ii. sin θ= x/16b. x = 6cm

Using the sine trigonometric identity expressed as;

sin θ = opposite/hypotenuse

Then, we have that for the first triangle;

sin θ= 3/8

For the bigger triangle;

sin θ= x/16b.

Then, since we have that the sine identity is;

sin θ= x/16

But sin θ= 3/8

Divide the values and find the sine inverse in

θ= 0. 375θ = 22. 0 degrees

x = 0. 375 (16)

Multiply

x = 6 cm

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The value of the element in row 1, column 1 of matrix x is; y.

According to the task content, it follows that matrix x is defined as; x= [y 4].

In essence, it follows that the matrix x contains one row and 2 columns. Therefore, the element in row 1, column 1 of matrix x is; y.

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Answer: A

Step-by-step explanation:

Answer: 12.4 x 18

-------------- = 18600

0.012

Answer:

the answer you're looking for is 60 inches

The perimeter of the base is 4 s since it is a square.

The area of the base is s².

[tex]\boldsymbol{CST=\dfrac{1}{2}(64)(17)+256=544+256=800 \ inches^{2} }[/tex]

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

C- 1/5

Step-by-step explanation:

a = 2 - 9a

10a = 2

a = 2/10

a = 1/5

Hope u got it (◠‿・)—☆

The mid-point of the numbers 3.8 and 4.1 will be 3.95.

Let C be the mid-point of the A and B.

C = (A + B) / 2

The numbers are given below.

3.8 and 4.1

Then the mid-point of the numbers 3.8 and 4.1 will be

C = (3.8 + 4.1) / 2

C = 7.9 / 2

C = 3.95

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The exact value of [tex]\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}[/tex] would be root 2.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

[tex]\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}[/tex]

We know that

The inverse tan(-1) = -π/4

cos(-π/4) = 1/√2

The inverse cos(√3/2) = π//6

sin(π/6) = 1/2

Then substitute

[tex]\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}\\\\[/tex]

[tex]\dfrac{(1/\sqrt{2}) }{(1/2)} \\\\= \sqrt{2}[/tex]

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The function over the interval is an increasing exponential function.

A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".

The complete question is

An investment group compares returns on an account

against the function represented in the table, where x is the

time in years and f(x) is the total return on investment.

Which describes the function over the interval given in the

table?

х

a decreasing quadratic function

an increasing quadratic function

a decreasing exponential function

an increasing exponential function

0

5

f(x)

10,000

12,201.90

14,888.64

22,167.15

10

20

A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. So, time in years change does not give maximum total return on investment.

For increasing quadratic equation, the graph increasing at one side of the axis and decreases at other side.

For, Exponential function          

When the exponential function then it shows total return on investment is not maximum.

When the exponential function is increasing it shows time goes, total return on investment is maximum.

Hence, the exponential function is increasing.

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Answer:

  (b)  3 terms, degree 10

Step-by-step explanation:

When simplifying polynomials, the first thing you look at is the exponents of the variables in each term. (The terms are separated by + or - signs.) Only terms with the same set of exponents can be combined.

When considering the degree of the polynomial, you look at the sum of exponents of the variables in each term. That sum is the degree of the term. The degree of the polynomial is the highest of the degrees of the terms.

__

The four terms have variables s and t. If we write the exponents of those variables as an ordered pair, we will have one ordered pair for each term:

  5s⁶t²  ⇒  (exponent of s, exponent of t) ⇒ (6, 2); degree = 6+2 = 8

  6st⁹  ⇒  (1, 9); degree = 1+9 = 10

  -8s⁶t²  ⇒  (6, 2); degree 6+2 = 8 (this is a like term to the first term)

  -6t⁷  ⇒  (0, 7); degree 0+7 = 7

The degrees are 8, 10, 8, 7, so the highest degree is 10. This is the degree of the polynomial.

__

We can only combine the terms containing s⁶t². Doing that gives ...

  (5 -8)s⁶t² +6st⁹ -6t⁷ = -3s⁶t² +6st⁹ -6t⁷ . . . . . three terms

In "standard form", the terms are written in order of decreasing degree:

  6st⁹ -3s⁶t² -6t⁷ . . . . . . 3 terms, degree 10

Answer:

(x-6y)(x-4y)

Step-by-step explanation:

Step-by-step explanation:

Well the first 3 you just plug in the value of x which results in.

a. f(0) = 7(0)^2 + 3(0) - 2

   f(0) = -2

b. f(2) = 7(2)^2 + 3(2) - 2

   f(2) = 7(4) + 6 - 2

   f(2) = 28 + 4

   f(2) = 32

c. f(-2) = 7(-2)^2 + 3(-2) - 2

   f(-2) = 7(4) - 6 - 2

   f(-2) = 28 - 8

   f(-2) = 20

for the last ones it's essentially the same thing except the value a is not known

d. f(a+1) = 7(a+1)^2 + 3(a+1) - 2

   f(a+1) = 7(a^2 + 2a + 1) + 3a + 3 - 2

   f(a+1) = 7a^2 +14a + 7 + 3a + 1

   f(a+1) = 7a^2 + 17a + 8

c. f(-a) = 7(-a)^2 + 3(a) - 2

   f(-a) = 7a^2 + 3a - 2

well if its asking for an exponent then its (-5)⁴

Answer: c

Step-by-step explanation:

It has been given that the point (3,1) is on the graph.

And in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option C

Answer:

20 + 4y

Step-by-step explanation:

To have to fewest symbols possible, we must simplify the expression by multiplying 4 into the numbers within the parenthesis. Doing so we get:

[tex]4(5+y) = 4 * 5 + 4 * y = 20 + 4y[/tex]

Answer: 20+4y

Step-by-step explanation:

Hi, let me help you.

What we should do to simplify this expression is to "distribute" 4.

The parentheses around 5+y tell us to multiply 4 times both 5 and y. This is shown below.

[tex]\multimap\quad \tt 4\cdot5+4\cdot y[/tex]

[tex]\multimap\quad\tt 20+4y[/tex] is what we obtain upon multiplying

________________

Hope I helped. Best wishes.

Reach far. Aim high. Dream big.

____________________

Answer:

40 miles

Step-by-step explanation:

10X4

The answer is 40 miles

-------------------------------------------------------

If he consistently rides ten mph (miles per hour) for 4 hours (4*10) he would have ridden 40 miles.

Answer:

[tex]\dfrac{26}{3}[/tex]

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given function:  [tex]f(x)=3^{x-1}+2[/tex]

Given interval:  1 ≤ x ≤ 4

Therefore, a = 1 and b = 4

Therefore, find the value of the given function when x = 1 and x = 4:

[tex]\begin{aligned}\implies f(1) & =3^{1-1}+2\\ & = 3^0+2\\ & = 1+2\\ & = 3 \end{aligned}[/tex]

[tex]\begin{aligned} \implies f(4) & = 3^{4-1}+2 \\ & = 3^3+2\\ & = 27+2\\ & = 29 \end{aligned}[/tex]

Substitute the found values into the formula:

[tex]\begin{aligned}\implies \dfrac{f(b)-f(a)}{b-a} & =\dfrac{f(4)-f(1)}{4-1}\\\\ & =\dfrac{29-3}{4-1}\\\\ & = \dfrac{26}{3} \end{aligned}[/tex]

Answer:

The value of x is 117°  by using Alternative interior angle theorem

Step-by-step explanation:

Alternative interior angle theorem: It states that the angles made by transverse between two parallel lines are congruent.

as in figure

Angle A = 42°

Angle B = 108°

Angle C = x

Angle D = 51°

draw two parallel lines passing through B and C .

According to Alternative interior angle theorem angle B is written as 42° + 66°

and angle C is written as x1 + x2 .

Now x1 = 51° as x1 and D are alternative angles

And similarly x2 = 66°

As x = x1 + x2

Therefore x = 51° + 66° = 117°

The value of x is 117°

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Answer:

3

Step-by-step explanation:

The first difference and second difference of the equation will be given below.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The quadratic function is given below.

y = x² + 7x + 6

Let the value of the y for x = 0, 1, 2, 3, 4 will be

y(0) = 6

y(1) = 14

y(2) = 24

y(3) = 36

y(4) = 50

The first difference and second difference will be

x       y      first difference        second difference

0       6               ...                                   ...

1       14              8                                   ...

2       24            10                                   2

3       36            12                                   2

4       50            14                                   2

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Answer:

The y-intercept is 22 spaces higher.

Step-by-step explanation:

The probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1

Note that the ratios =  5:4:2:3

toffee: coffee: orange: mint chocolates = 5:4:2:3:1

Total ratio = 15

Probability of picking a hazelnut chocolate = ratio of hazelnut chocolates/ total ratio

Probability of picking a hazelnut chocolate  = [tex]\frac{1}{15}[/tex]

The number of hazelnut chocolates in the box is gotten from the ratio which is 1

Therefore, the probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1

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