A parabola can be drawn given a focus of (0, 4) and a directrix of y =
be said about the parabola?

The required answers are

a) b = -4

b) x = 23.45

c) p = 201

The distributive property implies that multiplying a number by the sum of two or more addends yields the same result as dividing the multiplier, multiplying each addend individually, and combining the products . It can be given as,

a (b+c) = d

[tex](a*b) + (a*c) = d[/tex]

Now in the given question,

a) −1/2(b−6)= 5

by distributive property , we have

[tex](\frac{-1}{2} *b)-(\frac{-1}{2}*6 )=5\\\frac{-1}{2}b+3=5\\\frac{-1}{2}b=2\\b=-4[/tex]

b) 0.4(x−0.45)= 9.2

by distributive property , we have

0.4x - 0.4(0.45) =9.2

0.4x -0.18 = 9.2

0.4x = 9.38

x = 23.45

c) −4(p−212)=44

by distributive property , we have

-4p +4 (212) = 44

-4p + 848 =44

-4p = 44 - 848

-4p = -804

p = 201

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Answer:

8

Step-by-step explanation:

8x3 = 24

24 + 4 = 28

The probability of randomly selected patient selected for coronary, oncology or both is equal to P( H∪C ) = 0.24.

Let patient admitted with heart disease represented by P(H)

P(H) = 12%

       = 0.12

And patient admitted for cancer disease represented by P(C)

P(H) = 16%

       = 0.16

Percent of patient received both coronary and oncology = 4%

P( H∩C ) = 0.04

Probability of randomly selected patient admitted for coronary, oncology or both is :

P( H∪C ) = P(H) + P(C) - P(H∩C )

⇒P( H∪C ) = 0.12 + 0.16 - 0.04

⇒ P( H∪C ) = 0.24

Therefore, the probability of randomly selected patient getting treatment for coronary, oncology or both is given by  P( H∪C ) = 0.24.

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Answer:

58585

Step-by-step explanation:

i know

Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles

We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles

Depth of Mariana Trench (d) = 11 km = 11 × 0.62136

                                                          = 6.835 miles

Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189

                                                              = 5.492 miles

Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by

H = Depth of Mariana Trench + Height of Mount Everest

H = d + h

H = 6.835 miles + 5.492 miles

H = 12.327 miles

H = 12.3 miles

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The height of the flagpole is 110 feet.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

tan 19 = f/x

tan 21 = f/(600 - x)

Now,

tan 16 x = tan 21 x (600 - x)

0.34x = 0.38 x 600 - 0.38x

0.34x = 230 - 0.38x

0.34x + 0.38x = 230

0.72x = 230

x = 319

Now,

tan 19 = f/319

0.34 x 319 = f

f = 109.8

f = 110 feet

Thus,

110 feet is the height of the flagpole.

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Answer:

[tex]-\dfrac{4}{5}[/tex]

Step-by-step explanation:

We have the following expression

[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x[/tex]

and asked to evaluate this expression at  [tex]\[x = {2\over\displaystyle 5\][/tex]

First convert [tex]3 \; \dfrac{1}{2}[/tex]   and  [tex]5 \; \dfrac{1}{2}[/tex]  to mixed fractions

[tex]3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\[/tex]

[tex]5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}[/tex]

Therefore
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\[/tex]

[tex]\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}[/tex]

Answer:

[tex]\frac{y^2}{4x^5}[/tex]

Step-by-step explanation:

Used Exponents Properties :

[tex]\blacksquare \left( a\times b\right)^{n} =a^{n}\times b^{n}\\\blacksquare \left( a^{n}\right)^{m} =a^{n\times m}\\\blacksquare \left( \frac{a}{b} \right)^{n} =\frac{a^{n}}{b^{n}}[/tex]

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

[tex]\begin{aligned}\left(\frac{256 \times x^{20}}{y^8}\right)^{-\frac{1}{4}} & =\left(\frac{y^8}{2^8 \times x^{20}}\right)^{\frac{1}{4}} \\& =\frac{\left(y^8\right)^{\frac{1}{4}}}{\left(2^8 \times x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{8 \times \frac{1}{4}}}{\left(2^8\right)^{\frac{1}{4}} \times\left(x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{\frac{8}{4}}}{2^{\frac{8}{4}} \times x^{\frac{20}{4}}} \\& =\frac{y^2}{2^2 x^5}\\& =\frac{y^2}{4 x^5}\end{aligned}[/tex]

Answer:

if the angle has the arrow on top pointing straight up thats a right angle if it is leaning towards the left instead it is obtuse and if is getting closer to the right side it is acute.

Step-by-step explanation:

i can't tell you anything else if there is no picture to base this question.

The average rate of change of f(x) over the interval 3≤x≤4 is 15

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table, we have

f(3) = -4

f(4) = 11

The average rate is then calculated as

Average rate = [f(4) - f(3)]/[4 - 3]

Substitute the known values in the above equation, so, we have the following representation

Average rate = (11 + 4)/(4 - 3)

Evaluate

Average rate = 15

Hence, the average rate is 15

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Complete question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.

X f(x)

3 -4

4 11

5 8

6 10

7 11

8 14

The probability that the first box was the one selected given that the marble is white is [tex]\frac{7}{12}[/tex] .

Probability is the likelihood that an event will occur.

The likelihood of an occurrence A provided that an earlier event B has already happened is known as conditional probability.

the two boxes are marked as B1, B2

Number of black balls: 1

Number of white balls: 1

Number of black balls in the box: 2,

Number of white balls: 1.

B and W should stand for black and white marble.

Therefore, the likelihood that either box will be selected is [tex]\frac{1}{2}[/tex]

Probability of selecting a black ball from a box: [tex]\frac{1}{2}[/tex]

Probability of selecting a black ball from a box: [tex]\frac{2}{3}[/tex]

To determine: the likelihood that the marble is black.

Solution:

The likelihood that the marble being black is equal to

[tex]\frac{1}{2} (\frac{1}{2} ) + \frac{1}{2} (\frac{2}{3} )\\= \frac{7}{12}[/tex]

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Answer:

see explanation

Step-by-step explanation:

given sinΘ = - [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

the negative sign indicates sinΘ is in the third quadrant where sinΘ < 0

this is a 3- 4- 5 right triangle with opposite = 3 and hypotenuse = 5

then the adjacent side = 4

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{4}{5}[/tex] ( since cosΘ < 0 in third quadrant )

secΘ = [tex]\frac{1}{cos0}[/tex] = [tex]\frac{1}{-\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]

tanΘ

= [tex]\frac{sin0}{cos0}[/tex]

= [tex]\frac{-\frac{3}{5} }{-\frac{4}{5} }[/tex]

= - [tex]\frac{3}{5}[/tex] × - [tex]\frac{5}{4}[/tex]

= [tex]\frac{3}{4}[/tex]

The profit that they will make if they have 24 dogs for adoption is given as follows:

$160.

The profit is obtained with the subtraction of the revenue by the costs.

The revenue and the costs for this problem are obtained as follows:

Hence the profit made is obtained as follows:

Profit = 45 x 24 - 920

Profit = $160.

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In the given case where 860 observations are drawn from a bell-shaped distribution, there are 2 observations of more than 112.

Total number of observations = 860

Mean of the observations = 76

Standard deviation = 18

The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the observations utilizing the Z- score -

Z = X - u/a

Calculating the observations -

Where X = 112 u = 76 and a = 18

Z = 112 - 76/18

= 36/18

= 2

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Answer:

2x(5x+7)

Step-by-step explanation:

[tex]x^2+2x^2+14x+7x^2\\=10x^2+14x\\=2x(5x+7)[/tex]

The angle that the ladder makes with the ground is ∠B = 67.38°.

The distance between the ladder from the building is 5 feet.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Given that a 13-foot ladder is placed up against a wall.

The ladder's top touches the wall at a height of 12 feet.

As per the given question, we have the right triangle ΔABC

Using sine ratio to find angle ∠B as:

sin ∠B = AC/ AB

sin ∠B = 12/13

∠B = sin ⁻¹(12/13)

∠B = 67.38°

Now, using Pythagoras's theorem to find distance x as:

AC² + BC² = AB²

12² + x² = 13²

144 + x² = 169

x² = 169 - 144

x² = 25

x = 5

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We can write the equivalent expression as -

{5.95 × 10⁸ + 8.87 × 10⁸} = {10⁸ x 14.82}.

In mathematics, an expression or mathematical expression is combination of terms both constants and variables. For example -

23 + 54

2x + 5

3x + 5y + z

Given is that after gathering information, Kara decided to add up some distances. She decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. He wrote -

5.95 × 10⁸ + 8.87 × 10⁸

The given expression is -

5.95 × 10⁸ + 8.87 × 10⁸

10⁸ x (5.95 + 8.87)

10⁸ x 14.82

Therefore, we can write the equivalent expression as -

5.95 × 10⁸ + 8.87 × 10⁸ = 10⁸ x 14.82.

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{Question in english -

1) Operations with numbers written in scientific notation

a) After gathering information, Kara decided to add up some distances. decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. Here is what he wrote.

5.95×108 + 8.87×108

Do you know what the result is?}

Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)And the column is (2x+1).

Expanding this makes -2x²+3x+2

Answer:

83%

Step-by-step explanation:

To find the percentage divide 40 by 48

40/48 = 0.83333333333333

Round to 0.83

Multiply by 100

The patient has only eaten 83% of her daily intake.

To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.

Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:

a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.

Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.

b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.

Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.

c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).

Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.

d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).

Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.

Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.

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Answer:

x = 8 - 3y - 2z

Step-by-step explanation:

Step-by-step explanation:

x + 3y + 2z = 8

3x + y + 3z = -10

-2x - 2y - z = 10

we solve this by eliminating variables or expressing sine variables by others, and then solve for the remaining one. with that value we then cancer back to solve for the other variables.

in our case the easiest way is the elimination via combinations of equations.

let's first multiply equating 1 by -3 and then add that to equation 2 :

-3x - 9y - 6z = -24

3x + y + 3z = -10

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

0 - 8y - 3z = -34

8y + 3z = 34

then multiply equation 1 by 2 and add it to equation 3 :

2x + 6y + 4z = 16

-2x - 2y - z = 10

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

0 4y + 3z = 26

now we subtract this result from the previous result :

8y + 3z = 34

- 4y + 3z = 26

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

4y 0 = 8

y = 8/4 = 2

4×2 + 3z = 26

3z = 18

z = 18/3 = 6

x + 3×2 + 2×6 = 8

x = -10

so,

x = -10

y = 2

z = 6

Answer:

37

Step-by-step explanation:

AAA   1 way

AAB, AAC, AAD      3 ways each     3*3=9  ways

ABB, ACC, ADD      3 ways each     3*3=9 ways

ABC, ABD, ACD       3*2=6 ways each     3*6=18ways

1+9+9+18 = 37 ways

Answer: 83 3/5

Step-by-step explanation:

hope this helps !! :3

The equation 5x + 6y = 4, 10x + 12y = 8 has infinitely many solution.

System of equation can be solved using elimination method, substitution method and graphical method.

Therefore, let's solve the system of equation using elimination method.

5x + 6y = 4

10x + 12y = 8

multiply equation(i) by 2

Hence,

10x + 12y = 8

10x + 12y = 8

subtract the equations

0 = 0

Therefore, the equation has infinitely many solution.

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Check the picture below.

so the polygon is really just a 5x7 rectangle with a triangle that has a base of 7 units(vertically) and a height of 2 units.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(5)(7)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(2)}}\implies 35~~ + ~~7\implies \text{\LARGE 42}~units^2[/tex]

The hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

We can use the time it takes the hare to run 100 m to determine how long he can afford to nap.

First, let's find the time it takes the hare to run the 100 m:

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the hare.

t = 100 m / 15 m/s

t = 6.67 s

Next, let's find the time it takes the tortoise to run 1 km (1000 m):

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the tortoise.

t = 1000 m / 0.27 m/s

t = 3700 s

So, the time it takes the tortoise to run the race is 3700 s. The time it takes the hare to run the first 900 m is 7 s. Therefore, the time the hare has left to nap is:

3700 s - 7 s = 3693 s

And the time it takes the hare to run the last 100 m is 6.67 s. Therefore, the hare can afford to nap for:

3693 s - 6.67 s = 3686.33 s

So, the hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

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Answer:

The equation of the line of symmetry of triangle ABC is:

Step-by-step explanation:

The line of symmetry of an isosceles triangle bisects the vertex angle (the angle opposite the base) and is perpendicular to the base of the triangle.

As AB = AC, then angle A is the vertex angle of the isosceles triangle ABC.

If B and C lie on the line with equation 3y = 2x + 12, then the line of symmetry is the line that is perpendicular to this line and passes through A (4, 37).

Rearrange the given equation 3y = 2x + 12 to slope-intercept form by dividing both sides by 3:

[tex]\implies y=\dfrac{2}{3}x+4[/tex]

Perpendicular lines have slopes that are negative reciprocals of one another.  Therefore, the slope of the perpendicular line is -³/₂.

Substitute the found slope and point A (4, 37) into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-37=-\dfrac{3}{2}(x-4)[/tex]

Rearrange the equation to standard form:

[tex]\implies 2y-74=-3(x-4)[/tex]

[tex]\implies 2y-74=-3x+12[/tex]

[tex]\implies 3x+2y-74=12[/tex]

[tex]\implies 3x+2y=86[/tex]

Therefore, the equation of the line of symmetry of triangle ABC is:

a. The two firing angles of the projectile are 5.65° and 174.35°

b. The time it takes the projectile to hit the ground is 4.02 s

A projectile is an object that follows a parabolic path when thrown into the air.

Given that a projectile travels a distance of 800 meters with an initial velocity of 200 m/s, to find the firing angles, we use the formula for the range of a projectile.

The range of a projectile is its horizontal distance. It is given by R = u²sin2Ф/g where

Given that we require Ф, the angle of projection. Making it subject of the formula, we have that

Ф = [sin⁻¹(gR/u²)]/2

Given that

Substituting the values of the variables into the equation, we have

Ф = [sin⁻¹(gR/u²)]/2

Ф = [sin⁻¹(9.8 m/s² × 800 m/(200 m/s)²)]/2

Ф = [sin⁻¹(9.8 m/s² × 800 m/(40000 m²/s²)]/2

Ф = [sin⁻¹(9.8 m²/s² × 1/50 m²/s²)]/2

Ф = [sin⁻¹(0.196)]/2

Ф = 11.30°/2

Ф = 5.65°

Since sin is positive in the second qudrant also, the second angle is

Ф = 180° - 5.65°

= 174.35°

So, the angle are 5.65° and 174.35°

To find how long it takes the projectile to hit the ground, we use the formula for time of flight of a projectile.

T = 2usinФ/g where

Since

Substituting the values of the variables into the equation, we have

T = 2usinФ/g

T = 2(200 m/s)sin5.65° ÷ 9.8 m/s²

T = 400 m/s × 0.09845 ÷ 9.8 m/s²

T = 39.381 m/s ÷ 9.8 m/s²

T = 4.02 s

So, the time it takes the projectile to hit the ground is 4.02 s

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The mean number of days to maturity for dollars invested in these five money market funds is approximately 8.95 days.

To calculate the weighted mean of the days to maturity, we need to multiply each value of days to maturity by its corresponding dollar value, sum the products, and divide the result by the total dollar value.

The calculation for the weighted mean is as follows:

Weighted Mean = (D1 x V1 + D2 x V2 + D3 x V3 + D4 x V4 + D5 x V5) / (V1 + V2 + V3 + V4 + V5)

where D represents the days to maturity and V represents the dollar value.

Using the given values, we can plug them into the formula and get:

Weighted Mean = (15 x 15 + 11 x 10 + 7 x 25 + 5 x 15 + 4 x 10) / (15 + 10 + 25 + 15 + 10)

Weighted Mean = 8.95 (rounded to two decimal places)

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Answer: [tex]-\frac{9}{8}[/tex]

Step-by-step explanation:

If you are given two points of a line, the slope is defined as rise/run. Rise is the difference in y coordinates, (think about it, going UP is RISING), and Run is the difference in x coordinates, (again its pretty intuitive.)

So Slope = [tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]

This can be calculated with the coordinates of the two points, (order wont matter youll get the same answer).

Slope = (-3-6)/(6-(-2)) = -9/8

OR, (going the other way)

Slope = (6-(-3))/(-2-6) = 9/-8 = -9/8

Easy!