Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.

Answer:

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]

[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

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:

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:

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:

-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:

Step-by-step explanation:

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

Answer:

m= 0 /(−3np+v2 )

Step-by-step explanation:

Answer:

Hey there!

The overlapping part is the product.

Thus, the product is 1/8.

Hope this helps :)

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:

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:

30.0g

Step-by-step explanation:

In order to determine the amount of each chemical to the nearest tenth of gram prior to computing the sum is shown below:

Like

10.357, 57 > 50, rounded to 10.4

12.062, 62 > 50, rounded to 12.1

7.506, 06 < 50, rounded to 7.5

Now

The Sum is

= 10.4g + 12.1g + 7.5g

= 30.0g

Hence, 30.0g medicine required to make in grams

Answer:

2/3

Step-by-step explanation:

Bag A: WWB

Bag B: B

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:

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

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.

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:

A, C

Step-by-step explanation:

Only B is containing a variable .

The  -5 is not variable.

We have given that,

A.3x2

B. y

A

C. -5

In the expression 3x^2 + y -5

We have to determine which of the following terms does not have a variable.

variable, In algebra, a symbol stands in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Only C contains a variable.

The  -5 is not variable.

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Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5

Answer:

The total volume of the solid is 1.67 cubic units.

Step-by-step explanation:

Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.

1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2= 0.833

Therefore, the volume of each pyramid will be

= cubic units.

So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)

Hope it helped ya!

Mark me BRAINLIEST

Tysmm

The total volume of the solid is 1.67 unit³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Each pyramid has a height of 2 units.

and the rectangular base with dimensions of 5 units × 0.25 units.

So, the Volume of each Pyramid is

= 1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2

= 0.833

and, the total volume of the solid

= (2 × 0.833)

= 1.67 cubic units.

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Answer:

21 miles

Step-by-step explanation:

Since every single hour she runs 7miles.

In 3 hours she will run 7*3 miles.

21 miles

Hey there! I'm happy to help!

If Sue ran with an average speed of 7 miles an hour for 1 hour, she would have run 7 miles. So, if she ran at this speed for 3 hours, she would have run 3 times the distance she would if she ran for one hour!

7×3=21

Therefore, Sue ran 21 miles that day.

Have a wonderful day! :D

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:

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:

6

Step-by-step explanation:

Doing the fourth root of something is the equivalent of doing said number to the power of 1/4. So in this case I will convert the fourth root into an exponent and simplify:

6^(4*1/4) = 6^1 = 6

Hope this helps!

To find the area of a triangular prism you have to do A 1/2 bh or A bh/2 which means you have to multiply those two fractions and reduce them

Answer:

Find the area of the 2 triangle faces first and then find the area of the 3 rectangle faces and add them together to get [tex]159cm^{2}\\[/tex]

Step 1: Find the surface area of the 2 triangles

[tex]\frac{(6)(5.5)}{2}[/tex] x2 = [tex]33cm^2\\[/tex]

Step 2: Find the surface area of the 3 rectangles

(6x7) x 3 = [tex]126cm^2[/tex]

Step 3: Add the 2 surface areas together

[tex]33cm^2\\[/tex] + [tex]126cm^2[/tex] = [tex]159cm^2[/tex]

Therefore the surface area of the prism is [tex]159cm^{2}[/tex]

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:

It will take 6.118 minutes to fill up the pool to a depth of 20 cm

Step-by-step explanation:

The first step is to calculate the volume of the wading pool.

we will assume it is a cylinder, hence the volume will be = [tex]\pi r^{2}h[/tex]

Where r= radius of the pool = 115/2 = 57.5cm

h = depth of the pool =20 cm

The volume of the pool will be [tex]\pi \times57.5^{2} \times 20 =2.08 \times 10^{5} cm ^{3}[/tex]

We are filling a pool of 208,000cm ^{3} at the rate of 34000cm^3, cubed per minute.

To get the time it will take to fill up the pool, we will have to divide as follows:

208,000cm ^{3} / 34000cm^3 =6.118 minutes

Therefore it will take 6.118 minutes to fill up the pool to a depth of 20 cm

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/

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:

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