in scientific notation
1.6 x 10^3/ 8 x 10^7

Answer:  Focus = (7.5, -3)

Step-by-step explanation:

The Vertex form of a horizontal parabola is: x = a(y - k)² + h   where

Rewrite the equation in Vertex form to identify a, h, & k:

2x = (y + 3)² + 14

[tex]x=\dfrac{(y+3)^2+14}{2}\\\\x=\dfrac{1}{2}(y+4)^2+7[/tex]

       Vertex: (h, k) = (7, -3)

         [tex]a=\dfrac{1}{2}[/tex]

Find p and then find the focus:  Focus = (h + p, k)

[tex]a=\dfrac{1}{4p}\quad \rightarrow \quad \dfrac{1}{2}=\dfrac{1}{4p}\quad \rightarrow \quad 4p=2\quad \rightarrow \quad p=\dfrac{2}{4}\quad \rightarrow p=\dfrac{1}{2}\\[/tex]

Focus: (7 + [tex]\frac{1}{2}[/tex] , -3) = (7.5, -3)

Answer:

"A" seems to be incorrect....

Step-by-step explanation:

"A" seems to be incorrect....

[tex]\frac{\left(\sin \left(60^{\circ \:}\right)\cdot \:300\right)}{\sin \left(90^{\circ \:}\right)}=150\sqrt{3}\quad \begin{pmatrix}\mathrm{Decimal:}&259.80762\dots \end{pmatrix}[/tex]

[tex]\\ \sf\longmapsto 7x-20=6x-1[/tex]

[tex]\\ \sf\longmapsto 7x-6x=-1+20[/tex]

[tex]\\ \sf\longmapsto x=-19[/tex]

Now

[tex]\\ \sf\longmapsto m<A=7x-20=7(-19)-20=133-20=113[/tex]

Answer:

(x-9)(x+2)

Step-by-step explanation:

x^2-7x-18

What 2 numbers multiply to -18 and add to -7

-9*2 = -18

-9+2 = -7

(x-9)(x+2)

Answer:

Below.

Step-by-step explanation:

x^2 - 7x - 18

-9 * 2 = -18 and -9 +2 = -7 so the factors are:

(x - 9)(x + 2)

Answer:

<R = 30 degrees

LM = 6 sqrt(3)

Step-by-step explanation:

RST = LMN

We know that angle R equals angle L

<L = 30 degrees so <R = 30 degrees

Side RS = side LM

RS = 6 sqrt(3)  so LM = 6 sqrt(3)

Answer:

M<C = 20°

Step-by-step explanation:

Because they’re vertical angles, that means they’re equal to each other so:

m<C = m<D

x = -3x + 80

x + 3x = 80

4x = 80

x = 20

Since m<C equals x, that means m<C is 20°

Answer:

The probability that a randomly selected person gets incorrect result is 2.2 × 10⁻⁴

Step-by-step explanation:

The parameters given are;

The accuracy of the test for a person who has the respiratory synctial virus = 97%

The accuracy of the test for a person who does not have the respiratory synctial virus = 99%

We have;

a = TP =

b = FP

c = FN

d = TN

a/(a + c) = 0.97

d/(d + b) = 0.99

a/(a + b) = 0.97*0.0055/(0.97*0.0055 + (1 - 0.99)*(1-0.0055))

PPV = 0.349 = 34.9%

Therefore, we have;

a/(a + c) = 0.97 and

a/(a + b)  =  0.349

0.97(a + c) =0.349(a + b)

(0.97 - 0.349)a = 0.349·b - 0.97·c

a = (0.349·b - 0.97·c)0.621

b × (1 - 0.0055) = (1 - 0.97)×(1 - 0.0055)

b = 1 - 0.97 = 0.03

Similarly,

c = 1 - 0.99 = 0.01

The proportion of the population that have false positive and false negative = 0.03 + 0.01 = 0.04 = 4%

The probability that a randomly selected person gets incorrect result = 0.04×0.0055 = 0.00022.

Answer:

0.01011

Step-by-step explanation:

Answer:

[tex](\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]

Step-by-step explanation:

[tex]a=4-\sqrt{15}[/tex]

[tex]a^{4} +\frac{1}{a^{4} }\\=a^{2^{2} } +\frac{1}{a^{2^{2} } }\\\\=(x^{2} +\frac{1}{a^{2} } )^{2} -2a^{2} \frac{1}{a^{2} } \\=(a +\frac{1}{a } )^{2} -2a \frac{1}{a}-2\\=(4-\sqrt{15} +\frac{1}{4-\sqrt{15} }) ^{2} -4\\\=(\frac{16-15-4+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\=(\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{18 - 20}}\\\huge\boxed{=\mathsf{18 + (-20)}}\\\huge\boxed{\mathsf{= -2}}\\\huge\boxed{\textsf{Answer: 18 + (-20)}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

pi

Step-by-step explanation:

A rational number can be written as a fraction

18/1 is a fraction

2.6666666 can be written as 2 2/3 = 8/3

-16/3 is a fraction

pi is a non repeating non termination decimal which is irrational

Answer:

The answer is π

Step-by-step explanation:

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio.

Answer:

42 green marbles

Step-by-step explanation:

sum the parts of the ratio, 7 + 2 = 9 parts

Divide the number of marbles by 9 to find the value of one part of the ratio.

54 ÷ 9 = 6 ← value of 1 part of the ratio , then

7 parts = 7 × 6 = 42 ← number of green marbles

Answer:

Area of the shaded region= 82.2 cm²

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

the dad is 60 im not sure about the son

Step-by-step explanation:

Answer:

The number to be added is 6.89

Step-by-step explanation:

Here, we want to know what number must be added to the expression to make it equal to zero.

Let the number be x

Thus;

-6.89 + 14.52 -14.52 + x = 0

-6.89 + x = 0

x = 6.89

For some reason, the scores your teacher gave you and the answer choices don't match up. I'm not sure why this is. Perhaps some kind of typo. Please double check and get back to me.

Answer:

[tex]x + a = \frac{3}{4} \\ x = \frac{3}{4} - a[/tex]

for a:

[tex]a = \frac{3}{4} - x[/tex]

[tex]\\ \sf \longmapsto x+a=\dfrac{3}{4}[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{3}{4}-a[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{3-4a}{4}[/tex]

And

[tex]\\ \sf \longmapsto a=\dfrac{3}{4}-x[/tex]

[tex]\\ \sf \longmapsto a=\dfrac{3-4x}{4}[/tex]

Answer:

40

Step-by-step explanation:

Total is 150

Germany=1/3 *150 = 50

Italian= 2/5 * 150 = 60

Total - Germany- Italian= French

150 - 50 -60= 40

Answer:

The center of the circle is

Step-by-step explanation:

Equation of a circle is given by

where r is the radius

(h, k) is the center of the circle

The center of a circle is given by

( - h , - k)

From the question equation of the circle is

( x + 4)² + ( y - 2)² = 16

Comparing with the general equation above

( h , k) = ( 4 , - 2)

The center of the circle is

( - h , - k) = ( - 4 , -(-2))

We have the final answer as

Hope this helps you

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

We can represent each ratio as a fraction, then use the cross products property to find the value of x.

[tex]\frac{3}{12} = \frac{x}{16} \\\\\\16\cdot3=48\\\\48\div12=4[/tex]

Hope this helped!

Answer:

x = 5

Step-by-step explanation:

x² - 5x = 0

(x² - 5x) /x = 0/x

x²/x - 5x/x = 0

x - 5 = 0

x = 5

Check:

x² - 5x = 0

5² - 5*5 = 0

25 - 25 = 0

The solution to the equation is:

x = 0 or x = 5

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

We have:

x²-5x = 0

We can solve the equation as follow:

x²-5x = 0

Factorize:

x(x - 5) = 0

x = 0 or (x -5) = 0

x = 0 or x = 5

Learn more about quadratic equation on:

brainly.com/question/29228193

#SPJ6

Answer:

4fg

Step-by-step explanation:

regrouping terms leaves 4 f variables along with the 4 g variables, since f is also multiplied by g, that would leave the answer to be 4fg. (socratic)

(4g)

Step One: Remove/ Alter the equation= f(gx4)

Step Two: Do the equation= f(gx4); f (4)

I hope I've helped! If you need anything, ask away!

Answer & Step-by-step explanation:

Take the last  expression:

[tex](3*3)*(4*4)[/tex]

This can be simplified using exponents. [tex]x*x=x^2[/tex] :

[tex]3^2*4^2[/tex]

So, take the two numbers within the parentheses from the first expression and write separately, including the exponent with each. Do this with the next problem:

[tex](5*6)^3=5^3*6^3[/tex]

:Done

Answer:

1. Data point A

4. Data point D

Step-by-step explanation:

In a scatter plot, the closer the clustered data points are close to the best line of fit, the greater the correlation that would exist between the two variables.

If we are to draw a best line of fit in the scatter plot that is shown above, the closest data points amongst data points A, B, C, D, and E, that would be close to the best line of fit are data points A and D.

Therefore, removing data point A and point D would cause the correlation to decrease the most.

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5

Answer: x = 3

Step-by-step explanation:

Sqrt(x+7) - 1  = x

Sqrt(x+7) = x + 1

x+7 = x^2 + 1

x = x^2 - 6

x=3

Answer:

First. 115°

Second. 65°

Third. 65°

Fourth. 7

Fifth. 425.25

First

angle DAB = angle ADC (since this is an isosceles trapezoid)

Second

In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)

180-115 is 65°

Third

(Same reason as second)

Fourth

The side 3x+4 is same as the opposite side

So 3x + 4 = 25

on solving you get x = 7 in

Fifth

[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]

area = 1/2 × 13.5 (20+43)

area = 1/2 × 13.5 × 63

Thus area is 425.25

Answer:

Step-by-step explanation:

1)As ABCD is isosceles trapezium,

∠ADC= ∠DAB

∠ADC = 115°

2) AD //BC

∠ADC + ∠DCB = 180°   {co interior angles}

115 + ∠DCB = 180

 ∠DCB = 180 - 115

 ∠DCB = 65°

3) As ABCD is isosceles trapezium,

∠CBA = ∠DCB

∠CBA = 65°

4) As ABCD is isosceles trapezium, non parallel sides are congruent.

AB = DC

3x + 4 = 25 in

3x = 25 - 4

3x = 21

x = 21/3

x = 7 in

5) height = 13.5 in

a= 43 in

b= 20 in

Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]

                   [tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]

A regular heptagon (7-sided figure) cannot be constructed with a compass and straightedge.

Answer:

d. physical features and locations tell historians about the ways people lived.

Step-by-step explanation:

I believe this is the correct answer