Answer:
The expression of the ellipse is: [tex]\frac{x^2}{4} + y^2 = 1[/tex]
Step-by-step explanation:
The equation of a ellipse can be written by the following expression:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Where 2a is the length of the major axis and 2b is the length of the minor axi. Since we were given the length of the minor vertex, then:
[tex]2b = 2\\b = 1[/tex]
The length of the major axis is the distance between the two vertices.
[tex]2a = \sqrt{[2 - (-2)]^2}\\2a = \sqrt{(2 + 2)^2}\\2a = \sqrt{4^2}\\2a = 4\\a = 2[/tex]
Therefore the expression of the ellipse is:
[tex]\frac{x^2}{2^2} + \frac{y^2}{1^2} = 1\\\\\frac{x^2}{4} + y^2 = 1[/tex]
Two cards are selected at random from a standard deck of cards. What is the probability that you select a king or a queen? (If your answer will reduce, you should reduce it.) Also show you're work
Answer:
2/13
Step-by-step explanation:
In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.
Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.
Hope this helps!
Write the number in scientific notation.
a) 423.6
b) 7,194,548
c) 500.23
d) 71.23884
e) .562
f) .0348
g) .000123
h) .5603002
Answer:
a) 4.236 x 10^2
b) 7.194548 x 10^6
c) 5.0023 x 10^2
d) 7.123884 x 10^1
e) 5.62 x 10^-1
f) 3.48 x 10^-2
g) 1.23 x 10^-4
h) 5.603002 x 10^-1
Hopefully this helps :)
Answer:
a) 423.6=4.236*10^2
b) 7,194,548=7.194548*10^6
c) 500.23=5.0023*10^2
d) 71.23884=7.123884*10^1
e) 0.562=5.62*10^-1
f) 0.348=3.48*10^-1
g) 0.000123=1.23*10^-3
h) 0.5603002=5.603002*10^-1
Step-by-step explanation:
The numbers in which the point lies must be between 0 and 10
Hope this helps ;) ❤❤❤
Given that C is at (-6, -1) and D (4, 8), find the point P that partitions CD into the ratio of 1:3.
Answer:
The coordinates of point P are (-7/2, 5/4)
Step-by-step explanation:
Here, we want to give the coordinates of the point P that divide CD in the given ratio
To do this , we shall be making use of a mathematical formula;
Let’s say the ratio 1:3 represents a:b, our formula those becomes
{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}
From the question, we can identify that
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
Plugging these values into the formula we have
3(-6) + 1(4)/(1+3) , 3(-1) + 1(8)/(1+3)
= (-18 + 4)/4 , (-3+ 8)/4
=-14/4, 5/4
= (-7/2, 5/4)
Using the linear combination method, what is the solution to the system of linear equations 5 x + 3 y = negative 10 and Negative 20 x minus 7 y = 15? (–5, 1) (–1, 5) (1, –5) (5, –1)
Answer:
work is shown and pictured
Answer:
The answer is C
Step-by-step explanation:
WILL MARK BRAINLIEST!!!!
Answer:
See below.
Step-by-step explanation:
SQUARE:
The area of the square is:
[tex]9x^2-12x+4[/tex]
Factor it:
[tex]=9x^2-6x-6x+4\\=3x(3x-2)-2(3x-2)\\=(3x-2)(3x-2)\\=(3x-2)^2[/tex]
Remember that all four sides of a square is equal. The area is simply the side squared. Therefore, all four sides of the square measure (3x-2).
RECTANGLE:
[tex]25x^2-16y^2\\[/tex]
Factor it. This resembles the difference of two squares, where:
[tex](x-a)(x+a)=x^2-a^2[/tex]
[tex]25x^2-16y^2\\=(5x)^2-(4y)^2\\=(5x-4y)(5x+4y)[/tex]
This cannot be simplified further. Note that the sides of rectangles doesn't necessarily have to be the same.
The dimensions of the rectangle is:
(5x-4y) by (5x+4y)
Answer:
Step-by-step explanation:
1. the area of square is 9x^2-12x+4 square units
shortcut: (a-b)^2= a^2-2ab+b^2
then simplify 9x^2-12x+4 to (3x-2)^2
area of square = s^2
then side equals sqrt((3x-2)^2)
s = (3x-2) units
2. the area of rectangle is (25x^2-16y^2) square units
shortcut: (a^2-b^2) = (a-b)(a+b)
then simplify (25x^2-16y^2) to (5x-4y)(5x+4y) square units
one side is: (5x-4y) units
one side is (5x+4y) units
!!!!!!WILL GIVE BRAINLEIST !!!!!!
Answer:
[tex]\boxed{Median = 152}[/tex]
Step-by-step explanation:
Observation = 568 , 254 , 152 , 101 , 100
In ascending order:
=> 100 , 101 , 152 , 254 , 568
Median is the middlemost no. So here:
Median = 152
Answer:
152
Step-by-step explanation:
If you set the data in an ascending order, you will find 152 to be the middle value, thus being the median
John is planning a party. There are 28 pieces of carrot cake and 7 pieces of marble cake. He wants to create plates with the same number of each type of cake. What is the greatest number of plates he can create?
Answer:
Hey there!
He can create 7 plates at most, with one carrot cake and one marble cake on each plate.
Hope this helps :)
Kaylee has $4,500 for a down payment and thinks she can afford monthly payments of $300. If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate), what is the maximum amount Kaylee can afford to spend on the car? [use the calculation in the text or the online calculators in the resource section]
Answer:
$17,028.06
Step-by-step explanation:
Given that :
Kaylee's down payment = $4500
monthly payment = $300
If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate).
the maximum amount Kaylee can afford to spend on the car is being calculated as the present value for all the payments.
= [tex]=\$4,500 +\dfrac{\$300}{(1+\frac{0.07}{12})} + \dfrac{\$300}{(1+\frac{0.07}{12})^2} +\dfrac{\$300}{(1+\frac{0.07}{12})^3} + ....+ \dfrac{\$300}{(1+\frac{0.07}{12})^{46}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{47}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{48}}[/tex]
Using the online desmos calculator to determine the maximum amount Kaylee can afford to spend on the car; we have:
= $17,028.06
Statistics question; please help.
Scott has hired you to check his machine prior to starting an order. To check it, you set the machine to create 1.5 inch screws and manufacture a random sample of 200 screws. That sample of screws has an average length of 1.476 inches with a standard deviation of 0.203 inches.
Does this sample provide convincing evidence that the machine is working properly?
Thank you in advance!
Answer:
Does this sample provide convincing evidence that the machine is working properly?
Yes.
Step-by-step explanation:
Normal distribution test:
[tex]$z=\frac{x- \mu }{ \frac{\sigma}{\sqrt{n}} }=\frac{ (x-\mu)\sqrt{n}}{\sigma} $[/tex]
Where,
[tex]x: \text{ sample mean}[/tex]
[tex]\sigma: \text{ standard deviation}[/tex]
[tex]n: \text{ sample size determination}[/tex]
[tex]\mu: \text{ hypothesized size of the screw}[/tex]
[tex]$z=\frac{(1.476-1.5)\sqrt{200} }{0.203 } $[/tex]
[tex]$z=\frac{(-0.024)10\sqrt{2} }{0.203 } $[/tex]
[tex]z \approx -1.672[/tex]
Once the significance level was not given, It is usually taken an assumption of a 5% significance level.
Taking the significance level of 5%, which means a confidence level of 95%, we have a z-value of [tex]\pm 1.96[/tex]
Therefore, we fail to reject the null. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!
Which values for h and k are used to write the function f of x = x squared + 12 x + 6 in vertex form?
h=6, k=36
h=−6, k=−36
h=6, k=30
h=−6, k=−30
Answer:
h=−6, k=−30
Step-by-step explanation:
did on edge
Considering the equation of the parabola, the coefficients of the vertex are:
h=−6, k=−30
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](h,k)[/tex]
In which:
[tex]h = -\frac{b}{2a}[/tex]
[tex]k = -\frac{b^2 - 4ac}{4a}[/tex]
In this problem, the equation is:
[tex]f(x) = x^2 + 12x + 6[/tex]
Hence the coefficients are a = 1, b = 12, c = 6, thus:
[tex]h = -\frac{12}{2} = -6[/tex]
[tex]k = -\frac{120}{4} = -30[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
Find the surface area of the regular pyramid shown to the nearest whole number
Answer:
740 m^2
Step-by-step explanation:
To which set or sets below does the number -7/8 belongs to ?
Answer:
-7/8
Step-by-step explanation:
PLEASE help me with this question!!! I really need help...
Answer:
The last option
Step-by-step explanation:
The centroid is the point that is equidistant from all the vertices, not the incenter. Furthermore, the incenter is formed by finding the point of concurrency (intersection) of the angle bisectors.
N students joined the radio control club. Some had boats, some had airplanes, and some had cars. They divided into 3 equal groups according to what model each one had. Ten more students joined the radio-controlled airplane group. There are 15 students in this group now. How many students joined the radio control club in the beginning?
Answer:
36 people joined the radio control club.
Step-by-step explanation:
15-3= 12
12*3=36
Where is the function increasing?
A)1
B)3< X
C)-infinity < x < 1
D)-infinity
Answer:
A) [tex]1<x<\infty[/tex]
Step-by-step explanation:
Given:
A graph of a function.
When we analyze the given graph, it is of a parabola.
To find:
The interval of values of [tex]x[/tex] where the function is increasing.
Solution:
First of all, let us learn about the meaning of increasing and decreasing functions.
1. A function [tex]y=f(x)[/tex] is known as increasing in an interval [tex]a<x<b[/tex] when
Value of y keeps on increasing when we move from the value of x from a to b.
2. A function [tex]y=f(x)[/tex] is known as decreasing in an interval [tex]a<x<b[/tex] when
Value of y keeps on decreasing when we move from the value of x from a to b.
On analyzing the given graph , we can see that the graph is decreasing on the interval: [tex]-\infty<x<1[/tex]
and is increasing on the interval: [tex]1<x<\infty[/tex]
When we choose from the options,
The correct answer is option A) [tex]1<x<\infty[/tex]
Someone pls help me I put numbers so it will be more easier
Answer:
1.road 1
2. scooter
3. walk
Answer:
1. road 1
2. scooter
3. walk
Step-by-step explanation:
1. in the corresponding point on the tree, you have road 2. therefore, the most logical answer would be road 1.
2. you are given three options of travel. as "walk" and "bike" are already provided, they cannot be the answer to fill in for box 2. therefore, you are left with "scooter."
3. similarly, you are given three options of travel. as "bike" and "scooter" are already provided, they cannot be the answer to fill in for box 3. therefore, you are left with "walk."
Last week Lisa had a gross earning of $1441.30. Cathy receives a base salary of $375 and a commission on sales exceeding her quota of $5000. What is her rate of commission if her sales were $6560?
Answer:
4.25%
Step-by-step explanation:
Commision = 441.30 - 375 = 66.30
Commision is based on = 6560-5000 = 1560
Rate of Commision = (in decimal) 66.30/1560 = 0.0425
Rate of Commision = 0.0425 * 100 = 4.25 %
Convert -(3)^1/2 - i to polar form
Answer:
2(cos30°+isin30°)
Step-by-step explanation:
Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
Substituting in the rectangular form of the comlex number above;
z = rcosθ + irsinθ
z = r(cosθ+isinθ)
r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Given the complex number in rectangular form z = -(3)^1/2 - i
z = -√3 - i
x = -√3 and y = -1
r = √(-√3)²+(-1)²
r = √3+1
r = √4
r = 2
θ = tan⁻¹ (-1/-√3)
θ = tan⁻¹ (1/√3)
θ = 30°
Hence the complex number in polar form will be z = 2(cos30°+isin30°)
Find the 12th term of the arithmetic sequence whose common difference is d=6 and whose first term is a, = 2.
Answer:
The 12th term is 68Step-by-step explanation:
Since the sequence is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
d = 6
a = 2
n = 12
So the 12th term of the sequence is
A(12) = 2 + (12-1)6
= 2 + 11(6)
= 2 + 66
A(12) = 68Hope this helps you
The Greenpoint factory produced two-fifths of the Consolidated Brick Company's bricks in 1991. If the Greenpoint factory produced 1,400 tons of bricks in 1991, what was the Consolidated Brick Company's total output that year, in tons?
Answer:
3,500 tons
Step-by-step explanation:
We know that 1,400 tons is 2/5 of the Consolidated Brick Company's output.
This means that 1/5 must be equal to 700 tons if 2/5 is 1,400.
So, we can find the total output by multiplying 700 by 5, since 700 is 1/5 of the total.
700(5) = 3,500 tons
A hair color manufacturer performed a survey which was normally distributed. They found that the average age at which a person's hair starts turning gray is 32 years, with a standard deviation of 4 years. Which of the following graphs displays the normal distribution of the average age at which a person's hair starts turning gray?
W.
X.
Y.
Z.
Answer: X
Step-by-step explanation:
what is the vertex of g(x)=3x^2-12x+7? a) (-6,-5) b) (-2,-5) c) (2,-5) d) (6,-5)
Step-by-step explanation:
Answer:
The answer is C.) (2, -5)
URGENT!!! Please help me with this question!!!!!! I will not accept nonsense answers!
Answer:
B
Step-by-step explanation:
The inscribed angle's arc measures 36°, and central angle's arc measures 72°.
Answer:
the answer is B
Step-by-step explanation:
1 Calculator What is the area of this figure? Enter your answer in the box. units²
Answer:
44 units²
Step-by-step explanation:
For triangles: (bases and heights of both triangles are equal)
Base = 4 units, height = 3 units
For trapezoid:
Base 1 = 5 units, base 2 = 3 units, height = 8 units
Area of figure = Area of two triangles + Area of trapezoid
= 2 *1/2 * base * height + 1/2(base 1+ base 2) *height
=4*3 + 1/2(5+3)*8
= 12 + 8*4
= 12 + 32
= 44 units²
The required area of the figure shown in the graph is given as 44 square units.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
here,
The area of the given figure is given as,
Area = Area of 1 + Area of 2 + Area 3 + Area 4
Area = length × width + [1/2× base × height] + [1/2× base × height] + [1/2× base × height]
Area = 8 × 3 + 1/2 × 4 × 3 + 1/2 × 4 × 3 + 1/2 × 8 × 2
Area = 44 square units.
Thus, the required area of the figure shown in the graph is given as 44 square units.
Learn more about the surface area here: https://brainly.com/question/2835293
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I need help with this!
Part A
Answer: 33.2 degrees F
Explanation: Adding on a negative is the same as subtracting. So 72.3 + (-39.1) = 72.3 - 39.1 = 33.2
================================================
Part B
Answer: 70 + 2 + 0.3 + (-30) + (-9) + ( -0.1 )
Explanation:
Think of 72 as 70+2. Furthermore, think of 72.3 as 70+2+0.3; we just break the number up into its corresponding digits (adding zeros when needed). The 7 is in the tens place, the 2 is in the units or ones place, and the 3 is in the tenths place.
Similarly, we have 39.1 break down into 30+9+0.1, in which all three terms are made negative to represent -39.1
================================================
Part C
Answer: 70 + (-30) + 2 + (-9) + 0.3 + ( -0.1 )
Explanation: Arrange the tens place value items to be next to each other. Same goes for the units place value, and also the tenths place value.
================================================
Part D
Answer: [70 + (-30)] + [ 2 + (-9) ] + [ 0.3 + ( -0.1 ) ]
Explanation: Take the result of part C and surround each pair of terms in square brackets to show how the terms pair up.
This is the last one but how do you find y ? what do I subtract 5 from ?
Answer:
y = 250
Step 1:
To solve, we plug in 50x for y.
[tex]50x=200+10x[/tex]
Then, we subtract the 10x from the right side. Our goal is to get the x by itself first.
[tex]40x=200[/tex]
Then, we divide both sides by 40, since we have to get the x by itself.
[tex]\frac{40x}{40}=x\\\\\frac{200}{40} =5[/tex]
x = 5
Step 2:
Now that we found x, we plug in 5 to the original equation and solve from there.
[tex]y=200+10(5)\\y=200+50\\y=250[/tex]
y = 250
What is the function rule for the line
4(2n + 3) =44 pls someone help me with this??
Answer:
n = 4
Step-by-step explanation:
4(2n + 3) = 44
Expand the brackets.
4(2n) + 4(3) = 44
8n + 12 = 44
Subtract 12 on both sides.
8n + 12 - 12 = 44 - 12
8n = 32
Divide both sides by 8.
(8n)/8 = 32/8
n = 4
54x^3y+ 81x^4y^2 factorise
Answer:
I hope it helps you......
What is the coefficient of the second term in the expression 12x+xy-7y?
Answer:
1
Step-by-step explanation: