which inequality is graphed on the coordinate plane?​

Answer:

The probability that 100 or fewer will have 3 ​girls is 0.00734.

Step-by-step explanation:

The complete question is:

In a family with ​3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with ​3 children, what is the approximate probability that 100 or fewer will have 3 ​girls? Approximate a binomial distribution with a normal distribution.

Solution:

Let X represent the number of families who has 3 girls.

The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.

But the sample selected is too large.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

 [tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]

Thus, a Normal approximation to binomial can be applied.

So,  [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]

The mean and standard deviation are:

[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]

Compute the probability that 100 or fewer will have 3 ​girls as follows:

Apply Continuity correction:

[tex]P(X\leq 100)=P(X<100-0.50)[/tex]

                  [tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]

*Use a z-table.

Thus, the probability that 100 or fewer will have 3 ​girls is 0.00734.

Answer:

see explanation

Step-by-step explanation:

tan x = -1

[tex]x = tan^{-1}(-1)[/tex]

x = -45

tan x = 5

[tex]x = tan^{-1}(5)[/tex]

x = 78.69

Answer:

See below.

Step-by-step explanation:

So we want to find the solutions to the two equations:

[tex]\tan(x)=-1 \text{ and } \tan(x)=5[/tex]

I)

[tex]\tan(x)=-1\\x=\tan^{-1}(-1)[/tex]

Recall the unit circle. First, note that the number inside tangent is negative. Because of this, we can be certain that the x (in radians) must be in Quadrant II and/or IV (This is because of All Students Take Calculus, where All is positive in QI, only Sine is positive in Q2, only Tangent is positive in Q3, and only Cosine is positive in QIV. Tangent is negative so the only possible choice are QII and QIV).

From the unit circle, we can see that x=3π/4 is a possible candidate since tan(3π/4)=-1.

Since tangent repeats every π, 7π/4 must also be an answer (because 3π/4 + π = 7π/4). And, as expected, 7π/4 is indeed in QIV.

Therefore, for the first equation, the solutions are:

[tex]x=3\pi/4 \text{ and } 7\pi/4[/tex]

II)

For the second equation, there is no exact value for which tangent of an angle would be equal to 5. Thus, we need to approximate.

So:

[tex]\tan(x)=5\\x=\tan^{-1}(5)\\x=\tan^{-1}(5) \text{ and } \tan^{-1}(5)+\pi[/tex]

We got the second answer because, like previously, tangent repeats every π, so we only need to add π to get the second answer.

In approximations, this is:

[tex]x\approx1.3734 \text{ and } x\approx4.5150[/tex]

Note: All the answers are in radians.

Segment AB was added to segment BC to get segment AC

representing it as an equation,

AC = AB + BC.

Substitute the values in the equation which means you are going to find the value of x.

77 = x + 16 + 4x +11

77 = 5x + 27

(group like terms)

77 - 27 = 5x

50 = 5x

( divide both sides by 5 to make x stand alone)

50/5=5x/5

10 = x

therefore ,x = 10.

To prove that segment AB =26, place x in the statement

AB = x+16

AB=10+16

AB=26/

Answer:

AandB=80miles

Total=240miles

Step-by-step explanation:

Draw the figure first indicating the figures then find the distance each degrees then find the total

The distance ship travels from A to B is 273.2 miles and total distance covered by ship is  707.82 miles.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given distance from C to A = 100 miles north

From B to A ship travels 60° east of north,

and From B to C 45° west of south,

the figure for problem is attached,

from figure we can  calculate the angles of A, B and C

so ∠A makes supplementary with 60°

∠A + 60° = 180°

∠A = 120°

for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get

∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)

∠B = 90 - 75 = 15°

and ∠C can be found by,

∠A + ∠B + ∠C = 180°

∠C = 180 - 15 - 120

∠C = 45°

now use sine formula for triangles,

sinA/a = sinB/b = sinC/c

where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.

a = BC, b = AC, and c = AB

so

sinA/BC = sinB/AC = sinC/AB

we have AC = 100 miles

substitute the values

sinC/AB = sinB/AC

sin(45)/AB = sin(15)/100

AB = 100/(√2sin(15))

AB = 100/0.3659

AB = 273.298 miles

and sinA/BC = sinB/AC

BC = AC sinA/sinB

BC = 100(sin 120/sin15)

BC = 100(0.866/0.2588)

BC = 100 x 3.3462

BC = 334.62 miles

total distance = AB + BC + AC

total distance = 334.62 + 273.2 + 100

total distance =  707.82 miles

Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.

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Answer:A terminating decimal between -3.14 and -3.15.

Step-by-step explanation:

A natural number includes non-negative numbers like 5, 203, and 18476.

It is encapsulated by integers, which include negative numbers like -29, -4, and -198.

Integers are further encapsulated by rational numbers, which includes terminating decimals like 3.14, 1.495, and 9.47283.

By showing a terminating decimal between -3.14 and -3.15, you are showing that rational numbers include integers (because integers include negative numbers.

Answer:

1) What does it mean when a polynomial equation is in standard​ form?

All terms are on one side of the equation, and zero is on the other side.

2) When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?

It should be written as 8x−15x.

3) Is the given equation a quadratic equation? Explain.

x(x−6)=−5

The equation is a quadratic equation because there is an x2-term.

4) Which of the following factored forms given below represent the correct factorization of the trinomial x2+10x+16?

(2+x)(8+x)

5) Which of the following is an example of the difference of two​ squares?

x2−9

Step-by-step explanation:

I hope this helps you out ☺

A binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:

A. [tex]x^2 - 9[/tex]

Recall:

Thus, from the options given, option A: [tex]x^2 - 9[/tex] is an example of a binomial that is the difference of two squares.

9 can be expressed as [tex]3^2[/tex].

In summary, a binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:

A. [tex]x^2 - 9[/tex]

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Answer:

Hey there!

The overlapping part is the product.

Thus, the product is 1/8.

Hope this helps :)

Answer:

Step-by-step explanation:

1)First convert mixed fraction to improper fraction and them prime factorize

[tex]6\frac{1}{4} = \frac{25}{4}\\[/tex]

[tex]\sqrt{\frac{25}{4}}= \sqrt{\frac{5*5}{2*2}}= \frac{5}{2} = 2 \frac{1}{2} \\\\[/tex]

2)

[tex](2 \frac{1}{2}- 1 \frac{1}{2})*1 \frac{1}{7}=( \frac{5}{2}- \frac{3}{2})* \frac{8}{7}\\\\\\= \frac{2}{2}* \frac{8}{7}\\\\=1* \frac{8}{7}= \frac{8}{7}\\\\\\=1 \frac{1}{7}[/tex]

3) 0.00706 = 7.06 * [tex]10^{-3}[/tex]

4) 144 = 12 * 12

12 = 6*2

6 = 2*3

Prime factorization of 144 = 2 * 3 * 2 * 2 * 3 *2

                                          = 2⁴ * 3²

5) To find LCM, prime factorize 96 & 144

96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3

144 = 2⁴ * 3²

LCM = 2⁵ * 3² = 32 * 9 = 288

6) HCF

105 = 7 * 5 * 3

135 = 5 * 3* 3 * 3

180 = 5 * 3 * 3 * 2 * 2

HCF = 5 * 3 = 15

7) 24 = 3 * 2 * 2 * 2 = 3 * 2³

   36 = 3 * 3 * 2 * 2 = 3² * 2²

   40 = 5 * 2 * 2 * 2 = 5 * 2³

LCM = 5 * 2³ * 3² = 5 * 8 * 9  = 360

HCF = 2² = 4

Difference = 360 - 4 = 356

8) Multiply each digit of the binary number by the corresponding power of 2, solve the powers and add them all

1111 = 1 *2³ + 1*2² + 1*2¹ + 1*2° = 8 + 4 + 2 + 1 = 15

Ans: 15

9) 36₇ = 102₅

10) 6.9163 = 6.916

I knew only this much

hope it's helpful

:)

Answer:

The Answer would be ∠W ≅ ∠C

Step-by-step explanation:

Only one that is congruent

The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

A triangle is a three-sided polygon with three edges and three vertices in geometry.

Given that the triangle ∆MTW is congruent to the triangle ∆CAD.

So, we have

∠MTW ≅ ∠CAD

∠WMT ≅ ∠DCA

∠TWM ≅ ∠ADC

If two triangles are equivalent, the ratio of matching sides will stay constant.

The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.

Therefore, at that point, the right choice is B.

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Answer:

-15÷35 is different from 4÷-6

Step-by-step explanation:

-15÷35=-3/7

4÷-6=-2/3

-3/7 is different from -2/3

Answer:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The lower quartile range is shown by the bottom of the box which is at 10.

The median is shown in the middle line, which is closer to 18 than 18.5.

The upper quartile range in the end of the box, which is at 22!

(You can also look at the picture attached if that helps.)

Answer:

The two integers are greater than or equal to 17 and 19

Step-by-step explanation:

Consecutive odd integers means 1, 3, 5, 7, 9 and so on

That means there is a always a gap of 2 in between each of them. Knowing this, we can set up an equation. Let x represent the first of the consecutive integers.

x+(x+2)=36

x+2 represents the second consecutive interger

x+x=34

2x=34

x=17

The two integers are 17 and 19

Answer:

no solution

Step-by-step explanation:

1/3(12-6x)=4-2x

4-1.3x=4-2x

4=4-0.7x

0=0.7x

ns

Hello, because of the geometric sequence we can say that:

[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]

So there is no real root, so the function does not cut the x axis.

Thank you

For the given quadratic function, the x-axis is not cut by the function because there is no true root.

To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.

As per provided data in question,

α = b/a = c/b

c/a = (c × b)/(a × b) = (c/b) (b/a) = α²

For the equation,

ax² + bx + c = 0

x² + b/a(x) + c/a = 0

⇒ x² + ax + α² =0

Δ = b² - 4 ac = α² - 4α²

Δ = -3α² < 0, which means that no real root is there.

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Answer:

Step-by-step explanation:

For the m it would just be -3 because the equation for slope intercept form is y=mx+b

Answer:

19

Step-by-step explanation:

The pattern is that it +6 every number.

-5 + 6 = 1

1 + 6 = 7

7 + 6 = 13

So the next number is 13 + 6 = 19.

EDIT - I can't add sorry.

Answer:

Step-by-step explanation:

This is an arithmetic sequence.

-5, 1 , 7 , 13 ,.....

First term = a = -5

Common difference =  d = second term - first term

                                   = 1 - [-5] = 1 + 5

                                  = 6

Next term = previous term + d

                 = 13 + 6 = 19

nth term = a +(n-1)*d

              = -5 + (n-1)*6

              = -5 + 6n - 6  {add like terms}

              = -5 - 6 + 6n

             = -11 + 6n

Pattern: 6n -11

Answer:

x = - 6

Step-by-step explanation:

3x - 4 = 2x - 10

3x -2x = 4 - 10

x = - 6

For the equation 3x-4=2x-10, the value of x is -6.

The given equation is 3x-4=2x-10.

x is the variable in the equation.

Plus and minus are operators.

To solve for x, subtract 2x from both sides:

3x-2x-4=2x-2x-10

x-4=-10

Add 4 on both sides:

x=-10+4

x=-6

Hence, the value of x is -6.

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Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5

Answer:

0.7967

Step-by-step explanation:

We know that population proportion p=0.31.

We have to find P(phat<0.33).

Mean=p=0.31

[tex]Standard deviation=\sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]Standard deviation=\sqrt{\frac{0.31(0.69)}{373} }[/tex]

standard deviation=0.024 (rounded to three decimal places)

[tex]P(phat<0.33)=P(Z<\frac{0.33-0.31}{0.024})[/tex]

[tex]P(phat<0.33)=P(Z<\frac{0.02}{0.024})[/tex]

[tex]P(phat<0.33)=P(Z<0.83)[/tex]

[tex]P(phat<0.33)=0.5+0.2967[/tex]

[tex]P(phat<0.33)=0.7967[/tex]

Thus, the required probability that sample proportion of households spending more than $125 a week is less than 0.33 is 79.67%

Answer:

Approximately 439.6 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cone is the following:

[tex]A=\pi r^2+\pi r l[/tex]

Where, r is the radius and l is the slant height.

The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:

[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]

Answer:

292.77

Step-by-step explanation:

πr(r+[tex]\sqrt{h2+r2}[/tex])

13 x 2 = 26

7 x 2 = 14

26 + 14 = 40

[tex]\sqrt{40}[/tex] = 6.32

7 + 6.32 = 13.32

3.14 x 7 = 21.98

21.98 x 13.32 =

292.77

Answer:

2/3

Step-by-step explanation:

Bag A: WWB

Bag B: B

Answer:

43

Step-by-step explanation:

Using Thales theorem:

● SP/LN = RP /RN

Notice that RN = 2×RP

● SP/LN = RP/2RP

● SP /LN = 1/2

● SP / (5x-14) = 0.5

● (2x+3)/(5x-14) = 0.5

● 2x+3 = 0.5(5x-14)

● 2x+3 = 2.5x -7

Add 7 to both sides

● 2x+3+7 = 2.5x-7+7

● 2x+10 = 2.5x

Sustract 2x brom both sides

● 2x+10-2x = 2.5x-2x

● 10 = 0.5x

Multiply both sides by 2

● 10×2 = 0.5x×2

● 20 = x

Replace x with 20 in Sp expression:

● SP = 2x+3

● SP = 2×20+3

● SP = 43

The answer is shown below:

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.

1+5.2 + (1+3)²

=1+10 + 16

=27

0.25*4³-1

=0.25*64-1

=16-1

=15

4+8(1/4+2)

=4+8(9/4)

=4+2*9

=4+18

=22

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Answer:

m= 0 /(−3np+v2 )

Step-by-step explanation:

Answer:

D. 9%, 440.36 million

Step-by-step explanation:

w = 221(1.09)t

9%, 440.36 million

Answer:

[tex] d = 55h [/tex]

Step-by-step explanation:

We are given that Chantal drives at a constant speed of 55 miles per hour.

If, d represents the total distance in miles, and

h represents number of hours, the following equation can be used to express the given situation:

[tex] d = 55h [/tex]

For every hour, a distance of 55 miles is covered.

Thus, if h = 1, [tex] d = 55(1) = 55 miles [/tex]

If h = 2, [tex] d = 55(2) = 110 miles [/tex].

Therefore, [tex] d = 55h [/tex] , is an ideal equation that represents the situation given in the question above.

Answer:

[tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex]

Step-by-step explanation:

[tex]\frac{4x}{(x-3)}+\frac{6}{(x+2)}[/tex]

= [tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]

Now we have done the denominators of each term of the expression equal.

Further we add the terms,

[tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]

= [tex]\frac{4x(x+2)+6(x-3)}{(x-3)(x+2)}[/tex]

= [tex]\frac{4x^{2}+8x+6x-18}{(x-3)(x+2)}[/tex]

= [tex]\frac{4x^{2}+14x-18}{(x-3)(x-2)}[/tex]

Now factorize the numerator of the fraction.

4x² + 14x - 18 = 2(2x² + 7x - 9)

                     = 2(2x² + 9x - 2x - 9)

                     = 2[x(2x + 9) - 1(2x + 9)]

                     = 2(x - 1)(2x + 9)

Therefore, [tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex] will be the answer.

Answer:

The equation is a quadratic equation because there is an x2-term.

Step-by-step explanation:

x(x−6)=−5

Distribute

x^2 -6x = -5

The equation is a quadratic equation because there is an x^2-term.

Answer:

Your required answer is option A.

Step-by-step explanation:

Here,

The given equation is;

x(x-6)=-5

now,

while finding x.

either or,

x=-5 (x-6)=-5

x= 1 (shifting-6 in next side)

now, the value of x is -5,1.

so, it's a quadratic equation.

( in quadratic equation the variable always has two values after solution)

Hope it helps..

Answer: The Answer is (-5,-3)

hope so my answer is correct

Step-by-step explanation: