Which of the following correctly names one of the vertices of the triangle
below?

Answer:

68% of exam scores lie within one std. dev. of the mean

Step-by-step explanation:

Because the standard deviation is 100, one standard deviation above the mean comes out to 600.  Likewise, one std. dev. below the mean comes out to 400.  By the Empirical Rule, 68% of exam scores lie within one std. dev. of the mean.

Answer:

[tex]P(400<x<600) = 68.3\%[/tex]

Step-by-step explanation:

We know that the average [tex]\mu[/tex] is:

[tex]\mu=500[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=100[/tex]

The Z-score is:

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

We seek to find

P(400<x<600)

This is:

[tex]P(400<x<600)=P(\frac{400-500}{100}<\frac{x-\mu}{\sigma}<\frac{600-500}{100})\\\\P(400<x<600)=P(-1<Z<1)[/tex]

Looking for the value of z in a normal table we have to:

[tex]P(Z>1) =0.1587\\\\P(Z>-1) = 0.8413[/tex]

So

[tex]P(-1<Z<1)=P(Z>-1) - P(Z>1) =0.8413-0.1587=0.6826\\\\P(400<x<600) = 68.3\%[/tex]

Answer:

The slope of the line is -7/8

When the point (7, –4) is used, the point-slope form of the line is

y+4=(-7/8)(x-7)

The slope-intercept form of the line is y=(-7/8)x+(17/8)

Step-by-step explanation:

Answer:

y+4=(-7/8)(x-7)

Step-by-step explanation:

Answer:

Your total investment increase by $105.00 by second year.

Step-by-step explanation:

You bought 200 shares at the price = $15.25 per share

Total cost of 200 shares = 200 × 15.25 = $3050

First year your investment gains profit = 10%

10% of 3050 = [tex]\frac{10}{100}[/tex] × 3050

= 0.10 × 3050 = $305

Total value of 200 shares on first year = 3050 + 305 = $3,355

Then loses $1.00 per share the second year = 200 × 1.00 = $200

on second year the value of 200 shares would be = 3,355 - 200 = $3,155

So profit by second year = 3,155 - 3050 = $105

Your total investment increase by $105.00 by second year.

I think it would be x = 3 and y = 2 based on another question I read like this.

Answer:

incorrect

Step-by-step explanation:

this is because it would be 1/2 and 1/6. you would have to multiply the bases for a probability of 1/12

Answer:

Yes. because it ends.

Step-by-step explanation:

Rational numbers are numbers that end, or have a repating patern. Examples;

2.252525252525.......

2.369

5

8

8.69

8.541254125412

Hope this helped!

Hello There!

Yes indeed it is. 24 is a rational number because it can be expressed as the quotient of two integers: 24÷ 1

output B= -1-7*(6)

so -7*6=-42

-1-42= -43

The value of the linear equation B = - 1 - 7a at a = 6 will be negative 43.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The equation is given below.

B = - 1 - 7a

The value of the equation at a = 6. Then we have

B = - 1 - 7 × 6

B = - 1 - 42

B = - 43

The value of the linear equation B = - 1 - 7a at a = 6 will be negative 43.

More about the solution of the equation link is given below.

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Try searching it up on the internet maybe?? I tried doing some research but all I found was 2 I don’t know if the answer maybe be “2” but that’s what came up‍♀️

Final answer:

8/4 of a dollar is equivalent to 2 dollars, as 1/4 of a dollar is 0.25 dollars and multiplying this by 8 yields 2.

Explanation:

The question, what is 8/4 of a dollar?, falls under the category of elementary Mathematics, specifically fractions and monetary equivalence. To find the value of 8/4 of a dollar, you first need to understand that 4 quarters make up a dollar, which means that each quarter is worth 0.25 dollars or 25 cents. Therefore, to compute 8/4 of a dollar, you simply multiply 8 by the value of 1/4 of a dollar (0.25 dollars).

Here is the step-by-step calculation:

Understand that 1 quarter is 0.25 dollars.

Multiply 8 by 0.25 (1 quarter): 8 x 0.25 = 2.

So, 8/4 of a dollar is the same as 2 dollars

Answer:

(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12)

Step-by-step explanation:

Given:

Polynomial 27a^3 b^9+8c^18

Factoring the given polynomial

27a^3b^9 can be written as

=3^3.a^3.b^3^3

=(3ab^3)^3

Also 8c^18 can be written as

=2^3.c^6^3

=(2c^6)^3

Hence Polynomial 27a^3 b^9+8c^18 can be written as

=(3ab^3)^3+(2c^6)^3

Applying sum of cubes formula i.e. a^3 + b^3=(a+b)(a^2 – ab + b^2)

=(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12) !

Answer:

1- none of the choices are correct.

2-none of the answer choices are correct.

Step-by-step explanation:

1- there is no k therefore none are correct because they all offer a solution for k

2- yes the parabola opens upward but none are right in the right mix for the other two. the vertex is at (0,-5) and the axis of symmetry is x = 0 (not only because I calculated it and the graph showed it but because (x,y) And the x spot is a 0)

any time you just see a plain x^2 or really anything like that in the same vanilla sense wether the exponent is changed or there is a coefficient and all it has is a plus or minus whatever it will just be along the y axis where the plus or minus number was. (can't remember any vanilla advice for parabolas sorry)

Answer:

1. a=5,h=0,k=0

2. None of the choices are correct

Step-by-step explanation:

1. The function given is:[tex]f(x)=5x^2[/tex]

We can rewrite this in vertex form as: [tex]f(x)=5(x-0)^2+0[/tex].

Comparing this to [tex]f(x)=a(x-h)^2+k[/tex], we have a=5,h=0 and k=0.

The first choice is correct

2. The function given is: [tex]f(x)=x^2-5[/tex]

This can be rewritten in the vertex form as:

[tex]f(x)=a(x-0)^2-5[/tex]

Comparing this to [tex]f(x)=a(x-h)^2+k[/tex], we have a=1,h=0 and k=-5.

Since 'a' is positive, the parabola opens upwards, and has its vertex at (h,k)=(0,-5), and line of symmetry at x=0.

Based on this, the correct choice is none of the choices are correct

Answer:

Domain: {-12, 0, 24, 60}

Step-by-step explanation:

Function:

f(x) = [tex]\frac{x}{12}[/tex]

Range: { -1, 0, 2, 5}

For range = -1,

Domain: -1 = [tex]\frac{x}{12}[/tex] ⇒ x = -12

For range = 0,

Domain: 0 = [tex]\frac{x}{12}[/tex] ⇒ x = 0

For range = 2,

Domain: 2 = [tex]\frac{x}{12}[/tex] ⇒ x = 24

For range = 5,

Domain: 5 = [tex]\frac{x}{12}[/tex] ⇒ x = 60

Domain: {-12, 0, 24, 60}

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$700\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(700)(0.15)(3)\implies I=315[/tex]

I'll split this figure up in three sections, 65*60, 70*190, and 95*140.

95*140=13300

70*190=13400

65*60= 3900

Add the three areas of the three figures I have split the original figure into and you get 30600 ft²

The answer is:

x=-8

Because:

If you pick a number(-8) to fill in the equation written below

5x+20+5x=5x-20

After applying the -8 to x you get

-40+20-40=-40-20

When you simply the both sides you get

-60=-60

And that’s right -60 is equal to -60!

Answer:

Third option : x = -8

Step-by-step explanation:

Given

5x+20+5x=5x-20

in order to solve the equation, Subtracting 5x on both sides

5x+20+5x-5x=5x-20-5x

5x+20= -20

20 will be subtracted from both sides

5x+20-20= -20-20

5x= -40

Dividing by 5 on both sides

5x/5=  (-40)/5

x= -8

So, the value of x is -8 ..

For this case we must make a conversion. By definition, we have to:

1 liter equals 1000 milliliters.

So, we make a rule of three:

1L ------------> 1000mL

x ---------------> 1580mL

Where the variable "x" represents the amount of liters equivalent to 1580 milliliters.

[tex]x = \frac {1580 * 1} {1000}\\x = 1.58[/tex]

Thus, 1580 milliliters equals 1.58 liters.

Anwer:

1.58 liters

Answer:

2.28i

Step-by-step explanation:

u divide the -125/216

then u square root it

and multiply it times 3

YES THE I IS FOR A REASON IT MEANS IT IS IMAGINARY

2.28i I think that’s the answer but I am not sure

Answer:

Equation:

HCL + HCL = HCL

0.30x + 0.45(50-x) = 0.35*50

Multiply thru by 100 to get:

30x + 45*50 - 45x = 35*50

-15x = -10*50

x = (2/3)50

x = 33 1/3 liters (amt. of 30% solution needed in the mixture)

50-x = 16 2/3 liters (amt. of 45% solution needed in the mixture)

=============

Step-by-step explanation:

Answer:

about 36 and 24 liters  

Step-by-step explanation:

    a+b = 60     1

let A multiplied by  10 percent and B multiplied by 35 percent then

  10 a + 35 b = 1500 ( 60 * 25 ) 2

add no. 1 to 2 and multiply no.1  by -10

-10 a+ -10 b = -600

10 a+ 35 b = 1500  adding

then     25 b = 900 then         b = 36 liter

then     a = 24 liter    

Answer:

<2 =66

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles.

58 + <2 = <4

58 + <2 = 124

Subtract 58 from each side

58-58 + <2 = 124-58

<2 =66

Answer:

The volume of the figure is [tex]320\ units^{3}[/tex]

Step-by-step explanation:

we know that

The figure is a pyramid

The volume of a pyramid is equal to

[tex]V=(1/3)BH[/tex]

where

B is the area of the rectangular base of pyramid

H is the height of pyramid

Find the area of the base B

The area of the base B is equal to

[tex]B=AB*AC[/tex]

we have that

[tex]AB=8\ units[/tex] ---> see the graph

[tex]AC=10\ units[/tex] ---> see the graph

substitute

[tex]B=8*10=80\ units^{2}[/tex]

we have

[tex]H=EF=12\ units[/tex] ---> see the graph

Find the volume

[tex]V=(1/3)(80*12)=320\ units^{3}[/tex]

Answer:

20

Step-by-step explanation:

Write as an equation (in order to represent the question better):

9x - 4 = 176

Add 4 to both sides (to remove the '-4' on the left-hand side):

9x = 180

Divide both sides by 9 (to find x):

x = 20

Answer:

[tex]\sqrt{\frac{x}{4}}[/tex]  and  [tex]-\sqrt{\frac{x}{4}}[/tex]

Step-by-step explanation:

The function is given as  [tex]f(x)=4x^2[/tex]

to find inverse, we follow the steps shown below:

1. write "y" in place of "f(x)"

2. interchange "x" and "y"

3. solve for the new "y"

4. replace y with f^-1(x)

Let's do this:

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

These 2 are the inverse functions.

For this case we must find the inverse of the following function:

[tex]f (x) = 4x ^ 2[/tex]

We follow the steps below:

Replace f (x) with y:

[tex]y = 4x ^ 2[/tex]

We exchange variables;

[tex]x = 4y ^ 2[/tex]

We solve for y:

[tex]4y ^ 2 = x[/tex]

We divide between 4 on both sides of the equation:

[tex]y^ 2 = \frac {x} {4}[/tex]

We apply square root to both sides to eliminate the exponent:

[tex]y = \pm \sqrt {\frac {x} {4}}[/tex]

We substitute y for [tex]f ^ {- 1} (x)[/tex]:

 [tex]f ^ {- 1} (x) =\pm \sqrt {\frac {x} {4}}[/tex]

Answer:

[tex]f^{-1}(x)=\pm\frac{\sqrt{x}}{2}[/tex]

Answer:

[tex]\$16.64[/tex]

Step-by-step explanation:

we know that

The exponential function while the player is still active is equal to

[tex]y=3(1.07)^{x}[/tex]

where

y ----> is the value of the baseball card

x ----> the time in years

Find the value of y for x=7 years (7 years still active)

[tex]y=3(1.07)^{7}=\$4.82[/tex]

After 20 years

x=20-7=13 years (13 years retired player)

The initial value is [tex]\$4.82[/tex]

The new equation is equal to

[tex]y=\$4.82(1.1)^{x}[/tex]

substitute

x=13 years

[tex]y=\$4.82(1.1)^{13}=\$16.64[/tex]

Answer:

She buy 6 pounds of coffee

Step-by-step explanation:

8.22 × 6 = 49.32

90 - 49.32 = 40.68

Answer:

85 kilometers is equal to 85 000 meters

Step-by-step explanation:

1 kilometer is equivalent to 1000 meters. Then to convert from kilometers to meters use the following conversion factor

[tex]x\ kilometers * \frac{1000\ meter}{1\ kilometers }[/tex]

In this case [tex]x=85[/tex]

Then

[tex]85\ km* \frac{1000\ m}{1\ km} =85,000\ m[/tex]

Finally 85  kilometers = 85,000 meters

Answer:

Step-by-step explanation:

1km - one kilometer

kilo - 1,000 times more

1km = 1,000m

therefore

85km =85 × 1,000m = 85,000m

The composite number among options A. 23, B. 11, C. 25, D. 19 is C. 25. Composite numbers have more than two factors, and 25 has factors 1, 5, and 25.

The question is asking to identify which of the given options is a composite number. A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In simpler terms, composite numbers have more than two factors.

Now let's evaluate the given numbers:

Therefore, 25 is the composite number among the given options.

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The composite number among the options is C. 25.

A composite number is a positive integer greater than 1 that has more than two distinct positive divisors. In other words, it is not a prime number. Examples include 4 (divisible by 1, 2, and 4) and 9 (divisible by 1, 3, and 9).

Thus, a composite number is a positive integer that has more than two divisors. To determine whether a number is composite or not, we check if it is divisible by any number other than 1 and itself.  Among the given options, 25 is a composite number because it can be divided evenly by 5 and 1, in addition to 25 and itself.

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it's D because when you distribute the -x the 5x multiplies to -5x^2 then -4 multiplies to 4x since the negatives cancel out.

Answer:

16

Step-by-step explanation:

18-(7-5)

18-2=16

Answer:

16

Step-by-step explanation:

12 ÷ 2 × 3 - (7 - 5)

= 12 ÷ 2 × 3 - (2)

= 6 × 3 - 2

= 18 - 2

= 16

x^2+8x-2=18

x^2+8x-2-18= 18-18

x^2+8x-20= 0

(x-2)(x+10)=0

x-2= 0 , x+10=0

x-2+2= 0+2, x+10-10= 0-10

x=2 , x=-10

Answers are x= 2 -B, x=-10 -A.

Answer:

Option A and B

Step-by-step explanation:

Given : Quadratic equation [tex]x^2+8x-2=18[/tex]

To find : Complete the square to solve the equation below check all that apply ?

Solution :

Re-write, [tex]x^2+8x-2=18[/tex]

[tex]x^2+8x-20=0[/tex]

Applying quadratic formula,

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, a=1 , b=8, c=-20

[tex]x=\frac{-8\pm\sqrt{8^2-4(1)(-20)}}{2(1)}[/tex]

[tex]x=\frac{-8\pm\sqrt{64+80}}{2}[/tex]

[tex]x=\frac{-8\pm\sqrt{144}}{2}[/tex]

[tex]x=\frac{-8\pm12}{2}[/tex]

[tex]x=-4\pm6[/tex]

[tex]x=-4+6,-4-6[/tex]

[tex]x=2,-10[/tex]

The solution of the equation is x=2,-10.

Therefore, Option A,B satisfy the equation.

Answer:

37.5 [tex]units^2[/tex]

Step-by-step explanation:

As the area of each of the side of the cube are the same we can multiply the area of one side by 6.

The area of one side is

[tex]2.5*2.5=6.25\\\\6.25*6=37.5[/tex]

Answer:

37.5

Step-by-step explanation:

Surface area of a rectangular prism (a cube is a rectangular prism) is 2B + Ph

B is area of the base so do width x length. In cube all side lengths are the same, so do 2.5 x 2.5.

B= 6.25

P is perimeter of base so do 2.5 + 2.5 + 2.5 + 2.5 = 10

P=10

h is the height of the prism, but all sides are the same anyway so it's 2.5

h=2.5

2(6.25) + 10(2.5)

12.5 + 25

37.5

Answer:

Word Form: two and nine thousandths

Expanded Form:  

2  

+   0.0

+   0.00

+   0.009

Step-by-step explanation: