Can anyone please help me

The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Answer:

children attended= 114

adults attended= 57

students attended= 82

Step-by-step explanation:

children attended= c

adults attended=  a

students attended=  s

c+s+a = 253

5c + 7s + 12a = 1828

c=2a

2a + s + a =253

5*2a + 7s + 12a = 1828

3a + s = 253

22a + 7s = 1828

s = 253 - 3a

22a + 7(253 - 3a) = 1828

22a - 21a + 7*253 = 1828

a = 1828 - 7*253

a = 57

s = 253 - 3a = 253 - 3*57 = 82

s = 82

c=2a=2*57= 114

c=114

The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

\(H_0\) : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

\(H_1:\mu < 25\)

The test statistic is given by:

\(t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }\)

The parameters are:

the values of the parameters are:

x = 23.5 , \(\mu=25\) , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

\(t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }\)

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

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Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

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Answer:

y = -7x + 9

Step-by-step explanation:

Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,

A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).

We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:

22/6 = 3.666666...

We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.

Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.

The difference between 40 and the product of these digits and 6 is always 4.

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Answer:

Let x be the price:

x=15-5

Step-by-step explanation:

Answer:

40$ expression= 3x15-5

Step-by-step explanation:

1.) 3x15=45

2.)45-5=40

The lengths of the segments in the drawing, obtained using Thales Theorem are;

1) [AD] = 33.5 cm

2) a) OM ║ AB, therefore, OMAB is a trapezium

b) Thales Theorem indicates that point L is the midpoint of [DE]

c) Rectangle

3) JO ║ IL and IJ ║ OL, therefore, IJOL is a parallelogram

b) [JA] ≅ [AI], therefore; {OD] ≅ [DF] and point D is the midpoint of [OF]

IF = 5.25 cm

5) 1) the point C, which is the point of intersection of the medians is the center of gravity of BJD

2) The parallel sides of the parallelogram ABCD, and Thales Theorem indicates that M and N are the midpoints [BJ], and [DI]

Thales Theorem indicates that MN = DI = IB

Thales Theorem states that a line drawn parallel to one side of a triangle such that it intersects the other two sides, then the line divides the other two sides of the triangle in the same proportion.

1) The the diagonals of a rectangle bisect each other, therefore;

The length of [AD] = Length of [AB] = BE/2

The length of [AD] = 7 cm/2 = 3.5 cm

2) a) Whereby the point M is the midpoint of [AD], then according to the midsegment theorem, [OM] is parallel to [AB], therefore; OMAB is a trapezium, by the definition of a trapezium

b) Whereby [OM] is parallel to [AB], we get;

[OM] is parallel to [BE], therefore;

[OL] is parallel to [DE]

According to the triangle proportionality theorem, which is also known as Thales Theorem, the segment [OL] that divides [BD] in two also divides DE in two, therefore, point L is the midpoint of [DE].

c) Whereby the points A and L are the midpoints of [BE] and [DE], and the point O is the midpoint of [BD], we get;

[AO] is parallel to [DL], and [AL] is parallel to [OD]

[DL] is perpendicular to [BD], by definition of rectangle HBDE, therefore, [AO] is perpendicular to [BD]

Similarly, [AL] is perpendicular to [DE], and the quadrilateral ALDO is a rectangle

3) a) [OL] is parallel to [IJ]

The midsegment theorem indicates that AD is parallel to JO and segment AD is parallel to IL, therefore;

JO is parallel to IL and IJOL is a parallelogram

b) Whereby BD is extended to the point F, and IL cuts BD in F, we get;

JO, AD, and IF cut segment OAI into parts JA and AI of the same length, therefore;

JO, AD, and IF cut segment ODF into parts OD, and DF of the same lengths, therefore, point D is the midpoint of OF

AB = AD = 3.5

FA = 3.5/2 = 1.75

BF = 3.5 + 1.75 = 5.25

IF/5.25 = 3.5/3.5

Therefore, IF = 5.25 cm

5) The center of gravity of a triangle is the point of intersection of the three medians of the triangle

Whereby point J is the symmetric of A with respect to C, we get;

AC = CJ

The parallel sides BA and CD, and the midsegment theorem indicates;

BM = MJ, therefore;

Point M is the midpoint of BJ, and DM is a median of the triangle BJD

Similarly, BN is a median of the triangle BJD

The diagonals of a parallelogram bisect each other, therefore, the point of intersection of the diagonals, I is the midpoint of BD, and JI is a median of the triangle BJD, therefore, the point C is the center of gravity of the triangle BJD

2) The segments AC and CJ are congruent, and the segments CD and BA are parallel. According to the triangle proportionality theorem, segment BM is congruent to segment MJ, and the point M is the midpoint of BJ

Similarly, BC is parallel to AD, therefore, DN is congruent to NJ, and the point N is the midpoint of DJ

The Thales Theorem or midsegment theorem indicates MN = (1/2) × BD, therefore;

MN = DI = BD

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The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820  

a + s = 900

The number of adults ticket and student tickets is 380 and 520.

We have,

Adults ticket cost = $4

Student ticket cost = $2.5

Now,

Total amount earned = $2,820

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820   ______(1)

And,

The number of tickets sold = 900.

We can write as equation as:

a + s = 900 ______(2)

Now,

We have two equations.

4a + 2.5s = 2820

a + s = 900

Solving for s.

s = 900 - a

Substituting in (1)

4a + 2.5(900 - a) = 2820

Simplifying and solving for a.

4a + 2250 - 2.5a = 2820

1.5a = 570

a = 380

Now,

a + s = 900

380 + s = 900

s = 520

Therefore,

The number of adults ticket and student tickets is 380 and 520.

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The quadratic equation in standard form is:

ax^2 + bx + c = 25x^2 - 36x + 0

To factor this quadratic equation, we can first factor out the common factor of x:

25x^2 - 36x + 0 = x(25x - 36)

Now we can see that we have a quadratic expression inside the parentheses that can be factored further. To do so, we need to find two numbers whose product is 25 * (-36) = -900 and whose sum is -36. These numbers are -40 and 4:

25x^2 - 36x + 0 = x(25x - 36) = x(5x - 4)(5x - 32)

Therefore, the factored form of the quadratic equation is:

25x^2 - 36x + 0 = x(5x - 4)(5x - 32)

Answer:

Function, function

Step-by-step explanation:

Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions

Answer:

125/10 or 12.5

Step-by-step explanation:

hope this helps

Answer:

12.5 or \(\frac{25}{2}\)

Step-by-step explanation:

The Least Common Multiple (LCM) of 10 and 5 is 10. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:The Greatest Common Factor (GCF) of 15 and 10 is 5. The result can be simplified by dividing both the numerator and denominator by 5.

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

the answer would be 139000

Answer:139000

Step-by-step explanation:

Answer:

The perimeter of the shape is approximately 68.11 yards.

Step-by-step explanation:

Because it is a semicircle, we can say that its perimeter is half that of a circle, plus its diameter.

That gives us the equation:

2πr / 2 + 2r

which we can simplify:

= πr + 2r

= r(π + 2)

≈ 5.14r

So all we need to do is multiply the radius by 5.14, and that tells us the semicircle's perimeter:

5.14 × 13.25 = 68.105

If we round to the nearest hundredth, that gives us:

68.11

Answer:

a= 20.5in.

Step-by-step explanation:

Using the law of cosine to solve the problem (adjacent/hypotenuse) you set up the equation cos(35)=a/25 since a is adjacent to the angle and since 25 is the hypotenuse. You then wanna multiply both sides of the equation by 25 to  since you are dividing by 25 because opposites cancel out and you want to get the variable x alone and on one side. After doing this you get 25*cos(35)=x. You put this in a calculator and get 20.4788011072 and when you round it to the nearest tenth you get 20.5in.

Hope this helps :)

Answer:

A. 20.5 In

Step-by-step explanation:

hello there, in order to solve a trigonometry solution you must know the law of cos sin rule..

please remember this formula...

1. SOH.. Sin Ø =

\( \sin(x) = \frac{opposite}{ hypotenus} \)

2. CAH..

\( \cos(x) = \frac{adjacemt}{hypotenus} \)

3. TOA

\( \tan(x) = \frac{opposite}{adjacent} \)

Based on the question.. the value is given such as

ø=35°

hypotenus = 25 inch

find the BC which is the adjacent..

so we have the value for hypotenus and the angle.. the only relationship that suits this category is CAH .

FORMULA FOR CAH

COS Ø = ADJACENT/ HYPOTENUS

then now we substitute the value given

\( \cos(35) = \frac{bc}{25} \)

bring up the 25 to cos 35..

\(25 \cos(35) = bc\)

calculate the value of BC

\(bc = 25 \cos(35) \)

\(bc = 20.47\)

so the length of BC is equals to 20.47 or 20.5 In

Answer:

r = d/2

Step-by-step explanation:

d=2r

2r = d

r = d/2

Answer: r=d/2

Step-by-step explanation: divided by 2 on both sides and you get r by its self and d/2

A circle having radius 5 and centre at (0,0) has equation x² + y² = 25.

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

Let (x,y) be any point on the circle.

Given that centre of the circle is origin (0,0).

Now, we know that the distance from any point on the circle to the centre is equal to the radius of the circle.

So, distance between point (x,y) and centre (0,0)  is equal to radius of the circle which is given 5 units.

Now, using the distance formula -

√[(x - 0)² + (y - 0)²] = 5

Squaring on both the sides of the equation -

(x - 0)² + (y - 0)² = 25

So, the equation of the circle with radius 5, centred at the origin is x² + y² = 25.

Therefore, the equation is x² + y² = 25.

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Answer:

7y²x³

Step-by-step explanation:

when taking an exponent to an exponent multiply them

(7y²x³)² = 49y⁴x⁶

Answer:

1 1/3

Step-by-step explanation:

Answer:

12/9= 1 and 1/3

Step-by-step explanation:

Answer:

\(f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right), \quad \textsf{for}\:\{x:0 < x < 1\}\)

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{e^x}{\sqrt{e^{2x}+1}}\)

The domain of the given function is unrestricted:  {x : x ∈ R}

The range of the given function is restricted:  {f(x) : 0 < f(x) < 1}

To find the inverse of a function, swap x and y:

\(\implies x=\dfrac{e^y}{\sqrt{e^{2y}+1}}\)

Rearrange the equation to make y the subject:

\(\implies x\sqrt{e^{2y}+1}=e^y\)

\(\implies x^2(e^{2y}+1)=e^{2y}\)

\(\implies x^2e^{2y}+x^2=e^{2y}\)

\(\implies x^2e^{2y}-e^{2y}=-x^2\)

\(\implies e^{2y}(x^2-1)=-x^2\)

\(\implies e^{2y}=-\dfrac{x^2}{x^2-1}\)

\(\implies \ln e^{2y}= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies 2y \ln e= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies 2y(1)= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies 2y= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies y= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right)\)

Replace y with f⁻¹(x):

\(\implies f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right)\)

The domain of the inverse of a function is the same as the range of the original function.  Therefore, the domain of the inverse function is restricted to {x : 0 < x < 1}.

Therefore, the inverse of the given function is:

\(f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right), \quad \textsf{for}\:\{x:0 < x < 1\}\)

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Answer:

23.7 -2.5 X 8 = 23.7 - 20

= 3.7