These expressions represent four numbers. The value of the median of the expressions is 12.

Answer:

A. y = 600x, the jet travels 12,000 miles in 20 hours

Explanation:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Take two points: (2, 1200), (4, 2400)

[tex]\sf slope : \dfrac{2400-1200}{4-2 } = 600[/tex]

Equation:

y - 1200 = 600(x - 2)

y - 1200 = 600x - 1200

y = 600x

Miles the Jet travels at 20 hours:

Miles the Jet travels at 22 hours:

Answer:

y = 600x, the jet travels 12,000 miles in 20 hours

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]y = mx + b[/tex]

where:

To find the slope, define two points on the line and use the slope formula to find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1200-0}{2-0}=600[/tex]

From inspection of the graph, the y-intercept (where the line crosses the y-axis) is at (0, 0).  Therefore, the equation of the line is:

y = 600x

y is defined as the distance (in miles).  Therefore, to find the number of hours it takes for the jet to travel 12,000 miles, substitute y = 12000 into the found equation and solve for x:

[tex]\sf \implies 600x=12000[/tex]

[tex]\sf \implies x=\dfrac{12000}{600}[/tex]

[tex]\sf \implies x=\dfrac{120}{6}[/tex]

[tex]\implies \sf x=20[/tex]

Therefore, it takes the jet 20 hours to travel 12,000 miles.

Step-by-step explanation:

Using dimensional analysis, let convert km to cm.

[tex] \frac{4cm}{1km} \times \frac{km}{100000 \: cm} [/tex]

Cancel out the km

[tex] \frac{4cm}{100000 \: cm} [/tex]

[tex] \frac{1}{25000 } [/tex]

So n= 25000

iii.

Dimensional Analysis

[tex] \frac{3 \: cm}{1 } \times \frac{km}{100000 \: cm} [/tex]

[tex] \frac{3 \: km}{100000} [/tex]

Or

[tex]0.00003 \: km[/tex]

The base case of [tex]n=1[/tex] is trivially true, since

[tex]\displaystyle P\left(\bigcup_{i=1}^1 E_i\right) = P(E_1) = \sum_{i=1}^1 P(E_i)[/tex]

but I think the case of [tex]n=2[/tex] may be a bit more convincing in this role. We have by the inclusion/exclusion principle

[tex]\displaystyle P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1 \cup E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le P(E_1) + P(E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le \sum_{i=1}^2 P(E_i)[/tex]

with equality if [tex]E_1\cap E_2=\emptyset[/tex].

Now assume the case of [tex]n=k[/tex] is true, that

[tex]\displaystyle P\left(\bigcup_{i=1}^k E_i\right) \le \sum_{i=1}^k P(E_i)[/tex]

We want to use this to prove the claim for [tex]n=k+1[/tex], that

[tex]\displaystyle P\left(\bigcup_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]

The I/EP tells us

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cup E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right)[/tex]

and by the same argument as in the [tex]n=2[/tex] case, this leads to

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1})[/tex]

By the induction hypothesis, we have an upper bound for the probability of the union of the [tex]E_1[/tex] through [tex]E_k[/tex]. The result follows.

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^k P(E_i) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]

Answer:

Domain: (-∞, ∞)
Range: [-2, ∞)

Step-by-step explanation:

The domain of any parabola is (-∞, ∞)
The range of this parabola is [-2, ∞) because the vertex is at (-2, -2).

The confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41 where the lower limit is 97.59 and the upper limit is 102.41

We have:

Mean = 100

Sample size = 80

Standard deviation = 11

At 95% confidence interval, the critical z value is:

z = 1.96

The confidence interval is then calculated as:

[tex]CI = \bar x \pm z \frac{\sigma}{\sqrt n}[/tex]

So, we have:

[tex]CI = 100 \pm 1.96 \frac{11}{\sqrt {80}}[/tex]

Evaluate the product

[tex]CI = 100 \pm \frac{21.56}{\sqrt {80}}[/tex]

Divide

[tex]CI = 100 \pm 2.41[/tex]

Split

CI  = (100 - 2.41,100 + 2.41)

Evaluate

CI  = (97.59,102.41)

Hence, the confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41

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Answer:

6

Step-by-step explanation:

the blue factors are all the factors 12 and 18 have in common.

The true statement is:

"The range of the function is all real numbers less than or equal to 9."

Here we have the quadratic function:

[tex]f(x) = -x^2 - 4x + 5[/tex]

And we want to see which of the given statements are true.

The first one is:

"The domain is al real numbers less than or equal to -2"

This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).

The second statement is:

" The domain of the function is all real numbers less than or equal to 9."

Also false

Third one:

" The range of the function is all real numbers less than or equal to −2"

The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.

In this case, the quadratic function is:

[tex]f(x) = -x^2 - 4x + 5[/tex]

So the vertex is at:

[tex]x = 4/(2*-1) = -2\\[/tex]

Then the y-value of the vertex is:

[tex]f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9[/tex]

So the range is the set of all real numbers less than or equal to 9.

So the above statement is false, and the final one:

"The range of the function is all real numbers less than or equal to 9."

Is the true statement.

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Answer:

$2,120

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute the given values into the formula and solve for A:

⇒ A = 2000(1 + 0.06(1))

⇒ A = 2000(1.06)

⇒ A = 2120

Therefore, there will be $2,120 in the account at the end of the 1 year period.

Answer:

it will increase the production

Step-by-step explanation:

Answer:

option c (19.2, -6.7) is correct

Step-by-step explanation:

Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.

if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is

given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]

according to question :

given : end point T(-16.8, 31.7)  and mid point M(1.2, 12.5)

let coordinates of another end point S (a, b)

therefore, using mid point formula

1.2 = (-16.8 + a)/2

2.4= (-16.8 + a)

19.2 = a

and,

12.5 = (31.7 + b)/2

25 = 31.7 + b

-6.7 = b

so the option c (19.2, -6.7) is the correct answer

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The f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2) , Option D is the right answer.

A function is a law that defines relation between two variables.

The function given in the question is

f(x) = 8x² +2

h(x) = -8x²-2

The graph is plotted and the similarities or differences are studied ,

It can be seen from the graph that

f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2).

Therefore Option D is the right answer.

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Part 1: Finding slope

The slope is [tex]\frac{-3-15}{5-(-10)}=\frac{-18}{15}=\boxed{-\frac{6}{5}}[/tex]

Part 2: Finding the equation

Using the point (-10, 15) to substitute into point-slope form,

[tex]y-15=-\frac{6}{5}(x+10)\\\\y-15=-\frac{6}{5}x-12\\\\\boxed{y=-\frac{6}{5}x+3}[/tex]

Answer:

Using the given points we find that the slope is -1.2 and using the slope-point form we find that the equation of line is y+1.2x = 3.

Step-by-step explanation:

In the question, two points are given, (5,-3) and (-10,15). Using them we can find the slope using the formula, (y2 - y1) / (x2 - x1). So, the slope is

(-3-15) / (5+10) = -18 / 15 = -1.2

Now, we have to find the equation of line. We have two points and a slope. Using any one point and the slope, we can find the equation of line using slope-point form of line. Let us take (5,-3).

(y+3) / (x-5) = -1.2

y+3 = -1.2(x-5)

y+3 = -1.2x + 6

y+1.2x = 3

So, the slope of line is -1.2 and the equation of line is y+1.2x = 3.

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Caden needs to grow 4 inches tall enough to ride the Super Slide.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that:-

Caden's height = 4 feet

Min height to ride the Super slide is = 52 inches

Caden's height in inches will be:-

1 feet = 12 inches

4 feet = 12 x 4 = 48 inches.

The difference between the height will be given as:-

D = 50 - 48 = 4 inches

So Caden should grow his height by 4 inches to ride the super slide.

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Answer:

see explanation

Step-by-step explanation:

using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

[tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

then

[tex]\sqrt{500}[/tex]

= [tex]\sqrt{100(5)}[/tex]

= [tex]\sqrt{100}[/tex] × [tex]\sqrt{5}[/tex]

= 10 × 2.24

= 22.4

-------------------------------

[tex]\sqrt{0.5}[/tex]

= [tex]\sqrt{\frac{50}{100} }[/tex]

= [tex]\frac{\sqrt{50} }{\sqrt{100} }[/tex]

= [tex]\frac{\sqrt{50} }{10}[/tex]

= [tex]\frac{7.07}{10}[/tex]

= 0.707

Answer:

550g

Step-by-step explanation:

total g in 1 kg is 1000

so 1000 - 550 =450

Answer:

5 and a 250,000

Step-by-step explanation:

A quarter million = 1,000,000 · [tex]\frac{1}{4}[/tex] = 250,000

Answer:

It is: 5,250,000

Answer:

Unknown

Step-by-step explanation:

Hi! so you didn't add the ordered pair options but I will do my best :) so if you see the ordered pair (0.7) that could definitely be a solution because using the slope intercept form equation you gave I know that's our y Intercept. the slope is 4/1 so moving up 4 and to the right 1 or down 4 and to the left 1 on a graph could show you more points! If you don't want to draw it you could use Desmos and just put this equation in or give me the ordered pairs and I will give you your answer!

hope this helps :)

Answer:

errrrrr a not too sure but try

Step-by-step explanation:

i did the test got a 90

Answer:

Hence the age of Mikhail is 37 and the age of Grabrielle is 47

Answer:

Here;

Gabrielle age= 10yrs older that M..= 16 + 10= 26yrs old.

Sum of their age= 84

Now;

100 - 84

16,,

Answer:

6x = 9

Step-by-step explanation:

4x-5y  = 12

2x+5y  = -3

Add the equations together

4x-5y  = 12

2x+5y  = -3

-------------------

6x + 0y = 9

6x = 9

Answer:

B. 6x = 9

Step-by-step explanation:

4x - 5y = 12

+ 2x + 5y = -3

____________

6x + 0 = 9

Hence, option B. 6x = 9 is the correct answer.

Answer:

state Avogadro's hypothesis and prove that molecular weight

Answer:

$27,500.00

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 6%/100 = 0.06 per year.

Solving our equation:

A = 11000(1 + (0.06 × 25)) = 27500

A = $27,500.00

The total amount accrued, principal plus interest, from simple interest on a principal of $11,000.00 at a rate of 6% per year for 25 years is $27,500.00.

Answer:

AC = 2x - 13 Cm

BC = 3x + 4 Cm

AB = 36 Cm

AB = AC + BC

BC = AB - AC

= 36 - (2x - 13)

= 36 - 2x + 13

= 49 - 2x

but, BC = 3x + 4

so equating both the equation we get

3x + 4 = 49 - 2x

3x + 2x = 49 + 4

5x = 53

x = 53/5

x = 10.6

BC = 49- 10.6*2

= 49- 21.2

= 27.8 CM

Answer:

BC = 31 cm

Step-by-step explanation:

from the diagram

AC + CB = AB ( substitute values )

2x - 13 + 3x + 4 = 36

5x - 9 = 36 ( add 9 to both sides )

5x = 45 ( divide both sides by 5 )

x = 9

then

BC = 3x + 4 = 3(9) + 4 = 27 + 4 = 31 cm

Answer:

[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]

Step-by-step explanation:

The difference of squares formula gives us

[tex]a^2 - b^2 = (a+b)(a-b)[/tex]

(you can multiply this out to confirm)

[tex]0.09y^2 = (0.3y)^2[/tex]

and

[tex]0.81 = 0.9^2[/tex]

Thus, by the difference of squares formula

[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]

Answer:

Step-by-step explanation:

Solution by substitution method

3x+5y=7

and 4x-y=5

Suppose,

3x+5y=7→(1)

and 4x-y=5→(2)

Taking equation (2), we have

4x-y=5

⇒y=4x-5→(3)

Putting y=4x-5 in equation (1), we get

3x+5y=7

⇒3x+5(4x-5)=7

⇒3x+20x-25=7

⇒23x-25=7

⇒23x=7+25

⇒23x=32

⇒x=32/23

→(4)

Now, Putting x=32/23

in equation (3), we get

y=4x-5

⇒y=4(32/23)-5

⇒y=(128-115)/23

⇒y=13/23

∴y=13/23   and x=32/23

The two transformations for fx and gx would be to shift by 6 units and also go up by 18.

This is the term that is used in mathematics to describe the manipulation of a line or a shape.

a. The possible transformations that can be gotten here would be to shift to the left by 6 units from what we have in the graph and also shift to the top by 18.

g of x = f(x - k) then

g(x)= f(x) + k

C. The value of k should be based on the way it changes based on the given points.

Vertically, g(x)=f(x) +18

Horizontally , g(x)=f(x-6)

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A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The triangles ΔEST and ΔEFD are similar triangles, therefore, we can write,

[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}[/tex]

Since S and T are midpoints of EF and ED, the lines will be divided into two equal parts. Therefore,

[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}= \dfrac12[/tex]

Therefore, we can write it as,

[tex]FD = 2 (ST)[/tex]

In ΔEST and ΔTDR

∠T ≅ ∠T {Vertical angles}

ET ≅ TD {T is the midpoint of ED}

∠SET ≅ ∠TDR {Alternate interior angles}

Therefore,  ΔEST ≅ ΔTDR.

Since the two triangles are equal we can write,

ST ≅ TR

Further, it can be written as,

FD = 2(ST)

FD = ST + ST

FD = ST + TR

FD = SR

Hence, FD≅SR.

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Answer:

sin(cos^-1(-15/17))=8/17

Step-by-step explanation:

I apologize for the bad writing, I hope you can read it

The logical conclusion from the statement is that

B. The opposite sides of a rhombus are congruent.

From the information given, if shape is a parallelogram, then opposite angles are congruent.

In this case, since the rhombus is a parallelogram, then the opposite sides of a rhombus are congruent.

In conclusion, the correct option is B.

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