Use Pythagorean Theorem to solve for x. Show all work. Keep all answers in simplified
radical form.

Using the normal distribution, it is found that 16.43% of adults in the US qualify for stage 1.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Researching the problem on the internet, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 122, \sigma = 22[/tex].

The proportion of adults in the US qualify for stage 1 is the p-value of Z when X = 160 subtracted by the p-value of Z when X = 140, hence:

X = 160:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{160 - 122}{22}[/tex]

Z = 1.73

Z = 1.73 has a p-value of 0.9582.

X = 140:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140 - 122}{22}[/tex]

Z = 0.82

Z = 0.82 has a p-value of 0.7939.

0.9582 - 0.7939 = 0.1643.

0.1643 = 16.43% of adults in the US qualify for stage 1.

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So

a_2

a_3

a_4

a_5

Answer:

14

Step-by-step explanation: because you find a common number that both the numerator and the denominator can be divided by. In this case, it is 2 . You can't divide 14 anymore so that is the final answer.

Answer:

C) x ≥ 11 or x ≤ -3

Explanation:

Given following: |x − 4| ≥ 7

Apply absolute rule: If |u| ≥ 0 then u ≤ -a, u ≥ a

Solving stepwise:

⇒ x - 4  ≤ -7, x - 4 ≥ 7

change sides

⇒ x ≤ -7 + 4, x ≥ 7 + 4

add/subtract integers

⇒ x ≤ -3, x ≥ 11

Answer:

x ≥ 11 or x ≤ -3

Step-by-step explanation:

Hi there! Please take a look at the following explanation and let me know in comment if you have any questions!

[tex]\displaystyle \large{|x-4|\geq 7}[/tex]

To solve an absolute inequality, consider the following theorems.

For b ≥ 0:

(1) If |x-a| ≥ b then we have x-a ≥ b or x-a ≤ -b so that we end up with x ≥ b+a, x ≤ -b+a

(2) If |x-a| ≤ b then we have -b ≤ x-a ≤ b which can be simplified to -b+a ≤ x ≤ b+a

From the inequality, we use the (1) theorem.

[tex]\displaystyle \large{x-4\geq 7, x-4\leq -7}\\\\\displaystyle \large{x\geq 7+4, x\leq -7+4}\\\\\displaystyle \large{x\geq 11, x \leq -3}[/tex]

Therefore, the answer is x ≥ 11 or x ≤ -3

a. The height of the ball after four seconds is 640 ft

b. The time the ball reachs a height of 768 ft is 6 s or 8 s.

c. The time the ball reachs the ground after it is thrown is 14 seconds.

Since the height of the ball is a parabola, we need to know the equation parabola is

A parabola is an equation of the form x(t) = at² + bt + c

The height of the ball after four seconds is 640 ft

Since the height of the ball is represented by the equation h(t) = -16t² + 224t. The height of the ball after four seconds is when t = 4.

So, h(t) = -16t² + 224t.

h(4) = -16(4)² + 224(4)

h(4) = -16(16) + 224(4)

h(4) = -256 + 896

h(4) = 640 ft

The height of the ball after four seconds is 640 ft

The time it takes the ball to reach a height of 768 ft is 6 s or 8 s.

To find this time, we substituie h = 768 into the equation for the height of the ball.

So, h(t) = -16t² + 224t

768 = -16t² + 224t.

16t² - 224t + 768 = 0

t² - 14t + 48 = 0

Using the quadratic formula, we find t

[tex]t = \frac{-(-14) +/- \sqrt{(-14)^{2} - 4 X 1 X 48} }{2 X 1} \\t = \frac{14 +/- \sqrt{196 - 192} }{2}\\t = \frac{14 +/- \sqrt{4} }{2}\\t = \frac{14 +/- 2 }{2}\\t = \frac{14 + 2 }{2} or t = \frac{14 - 2 }{2}\\t = \frac{16}{2} or t = \frac{12}{2}\\t = 8 or 6[/tex]

So, the time it takes the ball to reach a height of 768 ft is 6 s or 8 s.

The time it takes the ball to reach the ground after it is thrown is 14 seconds.

To find the time it takes the ball to reach the ground, the height, h = 0.

So, h(t) = 0

-16t² + 224t = 0

-16t(t - 14) = 0

t(t - 14) = 0

t = 0 or t - 14 = 0

t = 0 or t = 14 s

So, the time it takes the ball to reach the ground after it is thrown is 14 seconds.

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Answer:

Option B

Step-by-step explanation:

[tex]A=(5.1)^{2} +4(\frac{(5.1)(5.95)}{2} )=26.01+60.69=86.7cm^{2}[/tex]

Hope this helps

Answer:

S.A = 2( L×W+W×H+ H×L)

= 2(2×4+4×1+1×2)

= 2(8+4+2)

2(14)

= 2×14= 28

Step-by-step explanation:

answer 28

There are a total of  180 seats in the theater

The theatre illustrates an arithmetic sequence, with the following parameters:

Number of rows = 18

Let the number of seats per row be n.

So, we have:

Total = 18n

When there are 3 fewer rows, the total number of seats is:

Total = (18 - 3) * (n + 6)

This gives

Total = 15* (n + 6)

Substitute Total = 18n in Total = 15* (n + 6)

18n = 15* (n + 6)

Open the bracket

18n = 15n + 90

Subtract 15n from both sides

3n = 30

Divide both sides by 3

n = 10

Substitute n = 10 in Total = 18n

Total = 18 *10

This gives

Total = 180

Hence, there are 180 seats in the theater

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Answer:

21.8 m/s

Step-by-step explanation:

Given that Tom drops a object from a height of h meters and it hits the ground with a veloc8of v m/s and it is given by function ;

[tex]\longrightarrow v =\sqrt{19.6h}[/tex]

We need to find out the velocity upon reaching the ground when it is dropped from a height of 24.3 m . On plugging in 24.3 in place of h we have ,

[tex]\longrightarrow v =\sqrt{19.6\times 24.3 }\ m/s\\\\\longrightarrow v =\sqrt{ 476.28} m/s \\\\\longrightarrow v = 21.823 \ m/s \\\\\longrightarrow \underline{\underline{ v = 21.8 \ m/s }}[/tex]

And we are done !

Answer:

21.8

Step-by-step explanation:

The formula is given :

Given that h = 24.3 m, we need to find v.

Substituting the value of h in the formula :

Answer:

The correct answer is supposed to be 3.36

Step-by-step explanation:

Add up all the numbers:

4 + 3.7 + 3.4 + 3 + 2.7  = 16.8

Divide by how many numbers there are:

16.8 ÷ 5 = 3.36

Answer:

D) 0.69

Step-by-step explanation:

Given :

5 × 2³ˣ = 21

Divide by 5 on each side :

Taking the cubic root :

Using logarithm values :

Answer:

D.  0.69

Step-by-step explanation:

Given equation:

[tex]5 \cdot 2^{3x}=21[/tex]

Divide both sides by 5:

[tex]\implies \dfrac{5 \cdot 2^{3x}}{5}=\dfrac{21}{5}[/tex]

[tex]\implies2^{3x}=4.2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies(2^3)^x=4.2[/tex]

[tex]\implies8^x=4.2[/tex]

Take natural logs of both sides:

[tex]\implies \ln 8^x=\ln 4.2[/tex]

[tex]\textsf{Apply the log Power law} \quad \ln x^n=n\ln x :[/tex]

[tex]\implies x \ln 8=\ln 4.2[/tex]

Divide both sides by ln 8:

[tex]\implies \dfrac{x \ln 8}{\ln 8}=\dfrac{\ln 4.2}{\ln 8}[/tex]

[tex]\implies x=\dfrac{\ln 4.2}{\ln 8}[/tex]

[tex]\implies x=0.690129776...[/tex]

[tex]\implies x=0.69 \: \sf (2\:dp)[/tex]

Answer:

[tex] {2t}^{3} + {20t}^{2} - 2t + 15[/tex]

Hope this helps!!

Answer:

14 meters

Step-by-step explanation:

Hey there!

7 * 8/10

= 7/1 * 8/10

= 7/1 * 8 ÷ 2 / 10 ÷ 2

= 7/1 * 4/5

= 7(4) / 1(5)

= 28/5

≈ 5.6

= 5 3/5

So, therefore the answer should be:

Anywhere BETWEEN 5 & 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

  5 and 6

Step-by-step explanation:

The product of the whole number and fraction is ...

  7×(8/10) = (7×8)/10 = 56/10 = 5.6

This lies between 5 and 6.

Answer:

the answer is 0

Step-by-step explanation:

2x-4

putting 10

2x10-4

20-4

=16

putting 45

2x45-4

90-4

=86

putting 60

60x2-4

120-4

=116

putting 2

2x2=4

4-4=0

Answer:

Step-by-step explanation:

the bars, |   |, mean absolute value

for example, if it was

| -9 |

then it would be 9

if it was

| 9 |

then it would be 9

if it was

| -550 |

it would be 550

you take the number, and if its negative, then it becomes positive

thats it

The proof of the given statements is shown below:

A line segment which touches a circle specified to only one point is called a tangent to that circle.

1. given

2. A line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

3. Since the tangent is perpendicular to radius i.e., EFC is right angle then,

    angle EFC =90

4.  Sum of interior angles of a triangle is 180°.

5. proved above: angle EFC= 90

6. FEC + ECF= 180-90=90

7. As proved above

   FEC + ECF=90, its shows that angle FEC and ECF are complementary angle.

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a) losing value is exponential decay.

b) Initial value is the price you paid = $1,200

c) decay factor is 100% - the percent lost per year = 90%

d) value = starting value x decay factor^ time

 f(x) = 1200 x 0.90^x

e) replace x with 3 then 8 and solve:

f(3) = 1200 x 0.90^3 = 874.80

after 3 years it is worth $874.80

f(8) = 1200 x 0.90^8 = 516.56

after 8 years it is worth $516.56

Step-by-step explanation:

oh, come on ! one is finding the inequality itself, the other is solving it. you don't know the difference of that ?

if so, please let me know, what you don't understand of the following explanations, so that I can add whatever is necessary.

you know, what an equality (ahem, equation) is ?

both, equations and inequalities are like a balancing scale with usual different things on the two pans left and right.

an equation is when both sides are in balance. their weight is equal.

an inequality is, when one side is heavier than the other.

and you know, what a variable is ? it is a kind of placeholder for actual values. it is like keeping some space open on the scale pan with a list of conditions for what kind of things you can put in that open space, so that the status of the scale stays unchanged.

A

twenty less than a number is at least 15

looks mathematically

x - 20 >= 15 (larger or equal = "at least")

B

x - 20 >= 15

x >= 35

so, this is true for

{x € R | x >= 35}

or

{x € R | x = 35 or x > 35}

so, this is true for all real values of x that are at least 35.

Answer:

Leading term: 8n⁵

Leading coefficient : 8

Constant: -2

Step-by-step explanation:

Leading term is the term with highest degree.

 Here the highest degree is 5. so 8n⁵ is the leading term

Leading coefficient is the coefficient of the leading term.

Constant is the term without any variable.

Answer:

See below

Step-by-step explanation:

Polynomials are sums of terms in the form of k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x²+2x-5 is a polynomial.

Answer:

Step-by-step explanation:

The formula for the area of a parallelogram is base times height

so

x = 7 (base)

y = 5

h = 3 (height)

7 * 3 =

21u²

Answer:

third angle: 50°

The interior angles of a triangle sum ups to 180°.

Here given two angles: 95°, 35°, x - Let the missing angle be x

When they sum up, they equal to 180:

x + 35 + 95 = 180

x + 130 = 180

x = 180 - 130

x = 50

Given two angles are 35° and 95°

Let the unknown angle be "x"

We know that sum of angles of a triangle is 180°

Therefore,

[tex]\sf{35°+95° + x = 180°}[/tex]

[tex]\sf{130° + x = 180°}[/tex]

[tex]\sf{x = 180°-130°}[/tex]

[tex]\sf{x = 50°}[/tex]

Hence, the missing angle is 50°.

Answer:

180cm

Step-by-step explanation:

To find the volume you do Length times Width times Height

use this it'll help when you run into this again, it's formula is just

LxWxH, in this order good luck!

Answer:

A) 70%

B) 95%

Step-by-step explanation:

A) $200 to $340

Increase = $340 - $200 = $140

Percentage of increase = $140/$200 * 100% = 70%

B) Additional $50

Increase = $140 + $50 = $190

Percentage of increase = $190/$200 * 100% = 95%