An ellipse has a vertex at (5,0), a co-vertex at (0, -3), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer:

P=0.954 or 95.4%

Step-by-step explanation:

Using the formula for the standardized normal distribution to find Z:

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

Where μ is the mean (μ=20) and σ is the standard deviation (σ=2.6).  

[tex]Z_{1} =\frac{14.8-20}{2.6}=-2.0[/tex]

[tex]Z_{1} =\frac{25.2-20}{2.6}=2.0[/tex]

In the table of the normal distribution, we can look for positive values z, and these values are going to represent the area under the curve between z=0 and the values searched. the negatives values are found by symmetry (with the corresponding positive value but remember this area is under the left side of the curve).  To find a value in the table, find the units in the first column and the follow over the same row till you find the decimals required.

[tex]P_1=0.4772[/tex]

[tex]P_2=0.4772[/tex]

[tex]P_1[/tex] represents the probability of length being between 14.8 and 20 (the mean) and [tex]P_2[/tex] represents the probability of length being between 20 and 25.2, The requested probability is the sum of these two.

[tex]P=P_1+P_2=0.954[/tex]

Answer:

95%

Step-by-step explanation:

Answer:

Step-by-step explanation:

We will use the pattern f(x)= a(b)^t where a is the initial value, b is the base of the exponent. All these questions are about exponent function

A) Number of trout fish in the pound = 7 , it means a =7

population increases double every year. It means b=2

f(x)= a(b)^t

f(x)=7(2)^t

B) Cost of machine = $3000

The value depreciated every year = 7%

It means 100%-7%= 93% which is equal to 0.93

Therefore,

a = 3000

b = 0.93

f(x)= a(b)^t

f(x)=3000(0.93)^t

C) Initial population of a colony of ants = 300

The number of ants increase at a rate of 1.5%

It means 100%+1.5%=101.5%

101.5% = 1.015

Therefore,

a= 300

b = 1.015

f(x)= a(b)^t

f(x)=300(1.015)^t

D) A research laboratory is testing a new vaccine on 300 infected cells

The decay rate is 1.5% per minute

It means 100%-1.5% =98.5%

98.5% = 0.985

Therefore,

a = 300

b = 0.985

f(x)= a(b)^t  

f(x)= 300(0.985)^t ....

[tex]x\in(-3,\infty)[/tex]

Answer:

m = -5/2

Step-by-step explanation:

Solve for slope with the following equation:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(4 , -12) = (x₁ , y₁)

(-2 , 3) = (x₂ , y₂)

Plug in the corresponding numbers to the corresponding variables:

m = (3 - (-12))/(-2 - 4)

m = (3 + 12)/(-2 - 4)

m = (15)/(-6)

Simplify the slope:

m = -(15/6) = -5/2

-5/2 is your slope.

~

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

[tex]\bf\dfrac{y_2-y_1}{x_2-x_1}}\leftarrow\text{is the slope formula}[/tex]

[tex]\bf{y_2=-12}\\\bf{y_1=3}\\\bf{x_2=4}\\\bf{x_1=-2}[/tex]

[tex]\dfrac{-12-3}{4-(-2)}\\\\\\\text{-12 - 3 = -15}\\\\\\\text{4 - (-2) = 6}[/tex]

[tex]= \dfrac{-15}{6}[/tex]

[tex]\boxed{\boxed{\bf{Answer: \dfrac{-15}{6}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer: -2 PLEASE GIVE BRAINLIEST

Step-by-step explanation:

Subbing 8 for x

-5(-8)-5y=50

Simplifying

40 + -5y = 50

Solving

40 + -5y = 50

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-40' to each side of the equation.

40 + -40 + -5y = 50 + -40

Combine like terms: 40 + -40 = 0

0 + -5y = 50 + -40

-5y = 50 + -40

Combine like terms: 50 + -40 = 10

-5y = 10

Divide each side by '-5'.

y = -2

Simplifying

y = -2

Answer:

$5000

Step-by-step explanation:

25% of 4,000 is 1,000.

4,000 + 1,000 = 5,000

Answer:

5000 is correct

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

If x=5...

2/3(5)=10/3

That would be true.

Answer:

x=5

Step-by-step explanation:

2/3 x = 10/3

Multiply each side by 3

3 *2/3 x = 10/3*3

2x = 10

Divide each side by 2

2x/2 = 10/2

x = 5

Answer:

C. 7$

Step-by-step explanation:

Answer:

Samantha should plan to spend $7.

Step-by-step explanation:

Let the price of 1 pizza be = p

Let the price of 1 coke = c

Let the price of 1 pack of chips = b

As per table, we get following equations:

[tex]p+c+b=9[/tex] or [tex]p=9-c-b[/tex]   ......(1)

[tex]p+2c=10[/tex]     .......(2)

[tex]2p+2b=12[/tex]    ......(3)

Substituting the value of p from (1) in (2)

[tex]9-c-b+2c=10[/tex]

=> [tex]c-b=1[/tex]    ......(4)

Substituting the value of p from (1) in (3)

[tex]2(9-c-b)+2b=12[/tex]

=> [tex]18-2c-2b+2b=12[/tex]

=> [tex]18-2c=12[/tex]

=> [tex]2c=18-12[/tex]

=> [tex]2c=6[/tex]

c = 3

We have [tex]c-b=1[/tex]

=> [tex]b=c-1[/tex]

=> [tex]b=3-1[/tex]

b = 2

And [tex]p=9-c-b[/tex]

[tex]p=9-3-2[/tex]

p = 4

We get the following cost now.

Cost of 1 pizza = $4

Cost of 1 coke = $3

Cost of 1 chips bag = $2

We have been given that Samantha wants two bags of chips and a coke.

So, she should spend [tex](2\times2)+3[/tex]= [tex]4+3=7[/tex]

Hence, Samantha should plan to spend $7.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}12x=76-20y&\text{change the signs}\\8x=84-20y\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x=-76+20y\\8x=84-20y\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-4x=8\qquad\text{divide both sides by (-4)}\\.\qquad x=-2\\\\\text{put the value of x to the second equation}\\\\8(-2)=84-20y\\-16=84-20y\qquad\text{subtract 84 from both sides}\\-100=-20y\qquad\text{divide both sides by (-20)}\\5=y\to y=5[/tex]

Answer: $1578

Step-by-step explanation:

1) Take your discount rate of 3.5% and convert it to decimal form (0.035)

2) Then, 0.035 * 13.5 = 1.59109

3) 1.59109 * 992 = $1578

Answer:

tan(45°) = 1

Step-by-step explanation:

We know that sin (45°) = √2/2, and cos(45°) = √2/2.

Given that tan(x) = sen(x) / cos(x), we get:

tan(45°) = (√2/2) / (√2/2) = 1

Therefore, tan(45°) = 1

Attached you will find the important angles summary

Answer:

D

Step-by-step explanation:

The line segments drawn from each vertex of the triangle and intersecting at H are the Altitudes of the triangle.

The point H is called the Orthocenter

Answer:

D. Ortho-center.

Step-by-step explanation:

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option D is the correct choice.

Answer:

the degree measure of pie/4 is 45

Step-by-step explanation:

=pie/4

=180/4

=45

The basic formula that need to be recalled is:

Circular Area = π x R²

Circle Circumference = 2 x π x R

where:

R = radius of circle

The area of sector:

[tex]\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}[/tex]

The length of arc:

[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]

Let us now tackle the problem!

This problem is about conversion unit of angles

Remember that :

[tex]\large {\boxed {1 \pi ~ \text{radians} = 180^o} }[/tex]

[tex]\frac{\pi}{4} = \frac{1}{4} \times 180^o = \boxed {45^o}[/tex]  

Another Example:

[tex]\frac{\pi}{6} = \frac{1}{6} \times 180^o = \boxed {30^o}[/tex]  

[tex]\frac{\pi}{3} = \frac{1}{3} \times 180^o = \boxed {60^o}[/tex]  

[tex]\frac{\pi}{2} = \frac{1}{2} \times 180^o = \boxed {90^o}[/tex]

[tex]\frac{3\pi}{2} = \frac{3}{2} \times 180^o = \boxed {270^o}[/tex]

[tex]\frac{3\pi}{4} = \frac{3}{4} \times 180^o = \boxed {135^o}[/tex]

[tex]\frac{4\pi}{3} = \frac{4}{3} \times 180^o = \boxed {240^o}[/tex]

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area , Radian , Degree , Unit , Conversion

This is a right triangle and to solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 60

b = x

c = 65

^^^Plug these numbers into the theorem

[tex]60^{2} +x^{2} =65^{2}[/tex]

simplify

3600 + [tex]x^{2}[/tex] = 4225

Now bring 3600 to the right side by subtracting 3600 to both sides (what you do on one side you must do to the other). Since 3600 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

3600 - 3600 + [tex]x^{2}[/tex] = 4225 - 3600

0 + [tex]x^{2}[/tex] = 625

[tex]x^{2}[/tex] = 625

To remove the square from x take the square root of both sides to get you...

x = √625

x = 25

(option C)

Hope this helped!

Just a girl in love with Shawn Mendes

The function f(x) = -3x is always decreasing, has a domain of all real numbers, and also has a range of all real numbers. The statement about the function always increasing is false.

When considering the function f(x) = -3x, we can evaluate its properties to determine which statements are true. First, since the coefficient in front of x is negative, the function has a negative slope, indicating that it is always decreasing, not increasing. This rules out the first statement.

Second, the domain of this function is indeed all real numbers because there are no restrictions on the values that x can take in the equation. So, the second statement is true.

Third, because x can take on any real number value and there's a constant multiplier of -3, the output can also take on any real number value, but will always be the opposite sign of x or zero. This means the range of the function is also all real numbers. Therefore, the statement about the range is incomplete as provided, but it is true that the range of f(x) is all real numbers.

Answer:

x = -2

x = -10

Step-by-step explanation:

Step 1 : Rearrange

x² + 12x + 20 = 0

Step 2: Factorise

(x + 2)(x + 10)

Step 3: Find the roots / values of x

Make each bracket equal zero.

(x + 2) = x = -2

(x + 10) = x = -10

Hope this helps!

Answer:

1) y = (x + 8)² + 7; 5) y = (x - 6)² + 10; 7) y = (x - 3)² - 4

Step-by-step explanation:

Complete the square in order to figure these out. To complete the square, use the formula [½B]². Each time you do this, you get a perfect trinomial in the form of a product of two monomials [h], then you have to figure out how much more to deduct from or add on to your C they gave you in each exercise [k].

If you are still in need of assistance, do not hesitate to let me know and subscribe to my channel [username: MATHEMATICS WIZARD].

I am joyous to assist you anytime.

Answer:

undefined

Step-by-step explanation:

Answer:

It's the image that is more compressed. This is because the period is decreased.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

To convert from polar to rectangular form

• x = rcosΘ , y = rsinΘ

• r = [tex]\sqrt{x^2+y^2}[/tex] ⇒ r² = x² + y²

Given

r = 8cosΘ

r = 8 × [tex]\frac{x}{r}[/tex] ( multiply both sides by r )

r² = 8x, hence

x² + y² = 8x ⇒ D

Answer:

The correct answer is D

Step-by-step explanation:

Plato

Answer:

A hole at x=-4.

Step-by-step explanation:

This is a fraction so we have to worry about division by zero.

The only time we will be dividing by 0 is when x+4 is 0.

Solving the equation

x+4=0 for x:

Subtract 4 on both sides:

x=-4

So there is either a vertical asymptote or a hole at x=-4.

These are the kinds of discontinuities we can have for a rational function.

If there is a hole at x=-4, then x=-4 will make the top zero and can be cancelled out after simplification.

If is is a vertical asymptote, x=-4 will make the top NOT zero.

Let's see what -4 for x in x^2+6x+8 gives us:

(-4)^2+6(-4)+8

16+-24+8

-8+8

0

Top and bottom are 0 when x=-4.

Let's see what happens after simplication.

We are going to factor a^2+bx+c if factorable by finding two numbers that multiply to be c and add up to be b.

So what 2 numbers together multiply to be 8 and add up to be 6.

I hoped you said 4 and 2 because (4)(2)=8 where 4+2=6.

[tex]\frac{x^2+6x+8}{x+4}=\frac{(x+4)(x+2)}{x+4}=x+2[/tex]

We we able to cancel out that factor that was giving us x=-4 is a zero.  

Therefore there is a hole at x=-4.

Answer:

A. 500 transistors

B. 50,000 capacitors

C. 100 capacitors

Step-by-step explanation:

The width of one transistor =0.004 mm

The total length filled by the 0.004 mm transistors is 2 mm.

A. In 2 mm there are: 2 mm/ 0.004 mm/transistor =500 transistors.

B. In 2 mm there are 2 mm/ 0.00004 mm/capacitor= 50,000 Capacitors.

C. The number of capacitors to fit in one transistor is given by the quotient between the width of a transistor and the width of  a capacitor.

=0.004 mm ÷0.00004 mm

=100 capacitors/transistor

Thus only 100 capacitors can fit into 1 transistor

Answer:

C. x-5y = 12 and 3x+2y = -15

Step-by-step explanation:

We need to substitute the solution into the equations

A. x-5y = -12 and 3x+2y = -15

    -3 -5(-3) = -12

   -3 +15 = -12

  False

B. x-5y = -12 and 3x+2y = 15

 -3 -5(-3) = -12

   -3 +15 = -12

  False

C. x-5y = 12 and 3x+2y = -15

 -3 -5(3) = 12      3(-3) +2(-3) = -15

   -3 -15 = 12          -9 -6 = -15

  True                     True

D. x-5y = 12 and 3x+2y = 15

-3 -5(3) = 12      3(-3) +2(-3) = 15

   -3 -15 = 12         -9 -6 = 15

  True                       False

Answer:

5

Step-by-step explanation:

20*5=100

Answer:

10 meters

Step-by-step explanation:

Let at 100 degrees Celsius, the aluminum bar is x m long.

We have been given that aluminum bar is 2 m long at a temperature of 20 degrees Celsius.

Thus, we have the equation

[tex]\frac{2}{20}=\frac{x}{100}[/tex]

Solve the equation for x

[tex]x=\frac{2\times100}{20}\\\\x=10[/tex]

Thus, at 100 degree Celsius, the aluminium bar is 10 meters long.

Answer:

x ≥ -2; -2 ≤ x

Step-by-step explanation:

Your number line shows a closed diamond -2.

That shows that 2 is a member of the solution set.

One interpretation of the inequality is

x ≥ -2

Another inequality with the same solution set is

-2 ≤ x

Answer:

x≥ -2

-2≤x

Step-by-step explanation:

In the given number line, the arrow is towards right. We know that if the arrow is towards right then the sign of the inequality is greater than >

Now, at the end point, which is 2, there is a solid circle. Hence, we must include 2 in our solution set.

Thus, there must be ≥ sign.

Hence, the inequality is x≥ -2

We can rewrite this as -2≤x

Sixth and seventh options are correct.

Answer:

[tex]y = -\frac{1}{3} x[/tex]

Step-by-step explanation:

We are given the following two points and we are to find the equation of the line which passes through them:

(-3, 1) and (0,0)

Slope = [tex]\frac{0-1}{0-(-3)} =-\frac{1}{3}[/tex]

Substituting the given values and the slope in the standard form of the equation of a line to find the y intercept:

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

[tex]0=-\frac{1}{3} (0)+c[/tex]

[tex]c=0[/tex]

So the equation of the line is [tex]y = -\frac{1}{3} x[/tex]

Answer:

[tex]y = -\frac{1}{3}x[/tex]

Step-by-step explanation:

The equation of a line in the pending intersection is:

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

Where m is the slope of the line and b is the intercept with the y axis.

If we know two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] then we can find the equation of the line that passes through those points.

[tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]b=y_1-mx_1[/tex]

In this case the points are  (-3, 1) and (0,0)

Therefore

[tex]m =\frac{0-1}{0-(-3)}[/tex]

[tex]m =\frac{-1}{3}[/tex]

[tex]b=1-(\frac{-1}{3})(-3)[/tex]

[tex]b=0[/tex]

Finally the equation is:

[tex]y = -\frac{1}{3}x[/tex]

[tex]\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{-9})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=-2(x-10)\implies y+9=-2(x-10)[/tex]

Answer:

d. 45%

Step-by-step explanation:

In total there are 30 + 25 = 55 students in total that like rock. From these there are 25 who are in grades 11-12. This makes that (25/55) * 100% = 45.45% of the students that like rock are in grades 11-12.

Answer: d. 45%

Step-by-step explanation:

According to the frequency table there are 30 sudents who like rock in grades 9-10 and 25 students that like rock and are in grades 11-12.

25 ÷ 55 = n ÷ 100          

25 · 100 = 55 · n      

2500 ÷ 55 = n         n  = 45.454545        n = 45%

55 is the total amount of students that like rock

25 is the total amount of students that like rock in grades 11-12

100 is the total percentage

Answer:

(6, - 31)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = (x - 6)² - 31 ← is in vertex form

with vertex = (6, - 31 )

Answer:

Option D is correct.

Step-by-step explanation:

We are given c = 12

m∠B = 27°

a = 9

We need to find b

We would use Law of Cosines

[tex]b = a^2 + c^2 -2ac\,cosB[/tex]

Putting values and solving

[tex]b^2 = (9)^2 + (12)^2 -2(9)(12)\,cos(27°)\\b^2 = 81 + 144 - 216(0.891)\\b^2 = 81 + 144 - 192.456\\b^2 = 32.54\\taking\,\,square\,\,roots\,\,on\,\,both\,\,sides\\\\\sqrt{b^2} = \sqrt{32.54}\\ b = 5.7[/tex]

So, Option D is correct.

Answer:

D. 5.7

Step-by-step explanation:

We have been given that in △ABC,c=12, m∠B=27°, and a=9. We are asked to find the value of b.

We will use law of cosines to solve for b.

[tex]b^2=a^2+c^2-2ac\cdot \tect{cos}(B)[/tex]

Upon substituting our given values in law of cosines, we will get:

[tex]b^2=9^2+12^2-2\cdot 9\cdot 12\cdot {cos}(27^{\circ})[/tex]

[tex]b^2=81+144-216\cdot 0.891006524188[/tex]

[tex]b^2=225-192.457409224608[/tex]

[tex]b^2=32.542590775392[/tex]

Now, we will take square root of both sides of our equation.

[tex]b=\sqrt{32.542590775392}[/tex]

[tex]b=5.70461136059[/tex]

[tex]b\approx 5.7[/tex]

Therefore, the value of b is 5.7 and option D is the correct choice.

Answer:

A. (1, 10).

Step-by-step explanation:

I'm going to assume that it is 2*5^x, then

2 * 5^1

= 2 * 5 = 10.

So a point on the grapg is (1, 10).

(0, 1) is on the graph of [tex]f(x)=2.5^{x}[/tex].

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given function

[tex]f(x)=2.5^{x}[/tex]

Drawing this function in a graph we can see that (0, 1) is on the graph.

Hence,

(0, 1) is on the graph of [tex]f(x)=2.5^{x}[/tex].

Find out more information about graph here

https://brainly.com/question/21372452

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