Answer: I think that this is the answer
standard form of equation for ellipse with vertical major axis (a^2 under y^2):
(x-h)^2/b^2+(y-k)^2/a^2=1,a>b, (h,k) being the (x,y) coordinates of the center.
For given equation: x^2/9+y^2/36=1
center: (0,0)
a^2=36
a=√36=6
length of vertical major axis=2a=12
Vertices are end points of major axis=(0,0�a)=(0,0�6)=(0,-6) and (0,6)
Vertices are at (0,-6) and (0,6)
Step-by-step explanation:
Answer:
Explanation: General formula for vertical ellipse Given: x24+y29=1 ... Use the equation provided above, and "plug it" in.
Suppose the eight committee members are ranked and the seating arrangements matter based off of rank. In how many ways can they sit in the 12 possible chairs
Answer:
They can sit in 19,958,400 ways
Step-by-step explanation:
The seating arrangements matter based off of rank, which means that we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
8 seats from a set of 12. So
[tex]P_{(12,8)} = \frac{12!}{(12-8)!} = 19,958,400[/tex]
They can sit in 19,958,400 ways
Represent the following sentence as an algebraic expression, where "a number" is the letter x.
The product of 6 and a number.
The product of 6 and a number.
factor the polynomial expression 16y^4-256x^12
Answer:
see explanation
Step-by-step explanation:
Given
16[tex]y^{4}[/tex] - 256[tex]x^{12}[/tex] ← factor out 16 from each term
= 16([tex]y^{4}[/tex] - 16[tex]x^{12}[/tex] ) ← difference of squares which factors in general as
a² - b² = (a - b)(a + b), thus
[tex]y^{4}[/tex] - 16[tex]x^{12}[/tex]
= (y² )² - (4[tex]x^{6}[/tex] )²
= (y² - 4[tex]x^{6}[/tex] )(y² + 4[tex]x^{6}[/tex] )
Now y² - 4[tex]x^{6}[/tex] ← is also a difference of squares
= y² - (2x³)²
= (y - 2x³)(y + 2x³)
Thus
16[tex]y^{4}[/tex] - 256[tex]x^{12}[/tex]
= 16(y - 2x³)(y + 2x³)(y² + 4[tex]x^{6}[/tex] )
Answer:
Step-by-step explanation:
4y^2+16x^6, 2y, 4x^3, 2y, 4x^3
How long will it take $4000 to grow into $5089.12 if it’s invested at 3.5% compounded annually?
Answer: 7 years
Step-by-step explanation:
From the formula A = P(1+(r/100))^t we have
5089.12 = 4000 (1+(3.5/100))^t
=> 1.27228 = (1.035)^t
Using calculator we find that 1.035^7 gives 1.272279
Hence in 7 years $4000 will grow to $5089.12 if it’s invested at 3.5%
Lancelot Manufacturing is a small textile manufacturer using machineminus−hours as the single indirect − cost rate to allocate manufacturing overhead costs to the various jobs contracted during the year. The following estimates are provided for the coming year for the company and for the Case High School band jacket job.
Company Cae High School Job
Direct materials $40,000 $2,000
Direct labor $10,000 $400
Manufacturing overhead costs $45,000
Machine-hours 100,000 mh 900 mh
What is the bid price for the Case High School job if the company uses a 40% markup of total manufacturing costs?
A. $1,122.
B. $3,927.
C. $960.
D. $3,360.
Answer:
The correct answer is B.
Step-by-step explanation:
Giving the following information:
Job:
Direct materials= $2,000
Direct labor= $400
Machine-hours= 900 mh
Company:
Manufacturing overhead costs $45,000
Machine-hours 100,000 mh
Selling price= 40% markup of total manufacturing costs
First, we need to calculate the predetermined overhead rate to allocate overhead:
Predetermined manufacturing overhead rate= total estimated overhead costs for the period/ total amount of allocation base
Predetermined manufacturing overhead rate= 45,000/100,000
Predetermined manufacturing overhead rate= $0.45 per machine hour
Now, we can calculate the total cost and the selling price:
Total cost= 2,000 + 400 + 0.45*900= $2,805
Selling price= 2,805*1.4= $3,927
An exponential function has:
A. a straight line that can be increasing or decreasing.
B.a curved line that can be increasing or decreasing.
C. U-shaped curved lines that increase then decrease or decrease then increase.
D. None of these choices are correct.
Answer:
Answer B is the correct one: a curved line that can be increasing or decreasing.
Step-by-step explanation:
Exponential functions are one-to-one functions, which means that cannot have a U shape. Also, they are not a straight line, since they grow of decrease exponentially (based on a fixed numerical base with the variable as the exponent) They can represent exponential growth showing a curve with increasing values as we move from left to right, or can represent exponential decay showing a curve with decreasing values as we move from left to right.
2. Solve the following.
a. 18:2/3
Answer:
Step-by-step explanation:
18 : 2/3
can also be written as 18 / 2/3 = 18 × 3/2
= 27
Hope it helps
plz mark as brainliest!!!!!
y=x2+3x+1 has how many real roots?
Answer:
2 real solutions
Step-by-step explanation:
hello,
[tex]\Delta = b^2-4ac=3^2-4*1*1=9-4=5>0[/tex]
as this is > 0 there are 2 different real solutions
hope this helps
The quadratic equation, y = x² + 3x + 1 has two real roots.
How to define the nature of roots in a quadratic equation?In a quadratic equation of the form, ax² + bx + c = 0, the nature of the roots depends upon the value of the discriminant (D), which is calculated by the formula, D = b² - 4ac.
If the value of D > 0, the equation has real and distinct roots.
If the value of D = 0, the equation has real and equal roots.
If the value of D < 0, the equation has imaginary roots.
How to solve the questionIn the question, we are given an equation y = x² + 3x + 1 and are asked to say how many real roots it has.
To find the roots, we first equate y to 0.
∴ y = x² + 3x + 1 = 0.
Now comparing the equation x² + 3x + 1 to the standard equation ax² + bx + c, we get a = 1, b = 3, and c = 1.
Now, the nature of the roots depends upon the discriminant (D),
D = b² - 4ac = 3² - 4.1.1 = 9 - 4 = 5.
∵ Discriminant (D) > 0, the quadratic equation, y = x² + 3x + 1 has both its root real and distinct.
∴ The quadratic equation, y = x² + 3x + 1 has two real roots.
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Suppose that 2 ≤ f ' ( x ) ≤ 3 for all values of x . What are the minimum and maximum possible values of f ( 7 ) − f ( 2 ) ? ≤ f ( 7 ) − f ( 2 ) ≤
Answer:
10 ≤ f ( 7 ) − f ( 2 ) ≤ 15
Step-by-step explanation:
Integrating the given inequalities along the interval from x = 2 to x = 7 yields the minimum and maximum possible values:
[tex]2 \leq f ' ( x )\leq 3\\\int\limits^7_2 {2} \, dx \leq \int\limits^7_2 {f'(x)} \, dx \leq\int\limits^7_2 {3} \, dx \\\\2*7-(2*2)\leq f(7)-f(2)\leq 3*7-(3*2)\\10\leq f(7)-f(2)\leq 15[/tex]
The minimum possible value is 10 and the maximum possible value is 15.
Which of the following shows the union of the sets? {1, 5, 10, 15} {1, 3, 5, 7}
Answer:
{ 1,3,5,7,10,15}
Step-by-step explanation:
The union means join together, or all the elements of both sets
{1, 5, 10, 15} U {1, 3, 5, 7}
= { 1,3,5,7,10,15}
Answer:
Step-by-step explanation:
Union of two sets contains the elements that belongs to A set or B set or both
A= {1,5,10, 15}
B ={1,3,5,7}
A U B = {1,3,5,7,10,15}
A race car is traveling at a constant speed of 150 miles per hour how many feet does it travel in 5 seconds
Answer:
50
Step-by-step explanation:
The requried, race car will travel approximately 1100 feet in 5 seconds at a constant speed of 150 miles per hour.
To find out how many feet a race car traveling at a constant speed of 150 miles per hour travels in 5 seconds, we need to convert the given speed from miles per hour to feet per second.
There are 5280 feet in a mile, and there are 3600 seconds in an hour.
First, let's convert 150 miles per hour to feet per second:
= 150 miles/hour * 5280 feet/mile / 3600 seconds/hour
= 220 feet/second (approximately)
Now, we can calculate the distance traveled by the race car in 5 seconds:
Distance = Speed * Time
Distance = 220 feet/second * 5 seconds
Distance = 1100 feet
Therefore, the race car will travel approximately 1100 feet in 5 seconds at a constant speed of 150 miles per hour.
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1. Bailey withdrew $135 from her checking account. Write an algebraic expression that describes Bailey's action.
Answer:
c − 135
Explanation:
Let's say that the amount of money in Bailey's checking account is
c dollars.
We also know that she took away $ 135
From this variable and number, we can state the algebraic expression
c − 135
Hope this helps!
How can you justify that the diagonals of a rhombus bisect opposite interior angles? A. Show that the diagonals form two congruent triangles using the definition of a rhombus and geometric properties. Then, use CPCTC (corresponding parts of congruent triangles are congruent) to show that the opposite interior angles are bisected. B. Show that the interior angles of each triangle created by the diagonals must add to 180°. C. Show that the exterior angles of the rhombus must sum to 360°. D. Show that the vertical angles created by the diagonals are congruent. Then, show that the opposite interior angles are supplementary to these angles.
Answer:
A. Show that the diagonals form two congruent triangles using the definition of a rhombus and geometric properties. Then, use CPCTC (corresponding parts of congruent triangles are congruent) to show that the opposite interior angles are bisected.
Step-by-step explanation:
Answer choice A is the only one that applies specifically to a rhombus.
The other answer choices are true of triangles and vertical angles in general. They do not relate specifically to the problem at hand.
What is the volume of the prism below?
8
A. 280 units3
B. 234 units3
C. 140 units 3
D. 560 units3
Answer:
140 units3
Step-by-step explanation:
The volume of the prism below is 420 cubic units.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The prism is a three-dimensional shape that has base area, and height. The volume of a prism is equal to the product of base area and height of a prism.
The volume of the prism= B×H
Where, B is base area of prism, and H is height of prism.
Given that,
Length of prism (L) = 12 centimeters
Width of prism(W) = 14 centimeters
B=1/2×12×5
=30
Now volume of prism = 30×14
=420 cubic units
Hence, the volume of the prism below is 420 cubic units.
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Find the indefinite integral by using the substitution x = 4 sec(θ). (Use C for the constant of integration.) x2 − 16 x d
Answer:
[tex]\frac{x^2-16}{2} + 16ln\frac{4}{x} +16C[/tex]
Step-by-step explanation:
Given the indefinite integral [tex]\int\limits{\frac{x^2-16}{x} } \, dx[/tex], using the substitute
x = 4 sec(θ)...1
The integral can be calculated as thus;
First let us diffrentiate the substitute function with respect to θ
dx/dθ = 4secθtanθ
dx = 4secθtanθdθ... 2
Substituting equation 1 and 2 into the integral function we will have;
[tex]\int\limits{\frac{(4sec \theta)^2-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{16sec^2 \theta-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{(16(sec^2 \theta-1)}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\from \ trig \ identity,\ sec^2 \theta - 1 = tan^\theta\\\\\int\limits{\frac{16 tan^2 \theta}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\\int\limits 16 tan^3 \theta d \theta\\\\[/tex]
Find the remaining solution in the attachment.
Find the cardinal number for the given set
A = {6, 11, 16,...,76)
The cardinal number is
Answer:
15
Step-by-step explanation:
A={6,11,16,...,76}
a=6,d=11-6=5
[tex]a_{n}=a_{1}+(n-1)d\\76=6+(n-1)5\\76-6=(n-1)5\\n-1=70/5=14\\n=14+1=15[/tex]
so the cardinal number is 15
helppppppppppppppppppppppppppppppppppppp
━━━━━━━☆☆━━━━━━━
▹ Answer
0.4 = 2.5, circle with 4 pieces shaded, and the rectangle with 40 squares shaded.
0.75 = Rectangle with 3 squares shaded and 75/100
0.9 = 90/100
▹ Step-by-Step Explanation
You can change the fractions into decimals, and count the shaded parts to determine the answer.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
.4= 2/5, the one with 10 equal parts that has 4 shaded, the one with 4/10 shaded
.75= 75/100,
.9= 90/100, the one with 2/3 shaded
Step-by-step explanation:
u have to reduce it to find ur answer
hope this helps
sorry if it was late
A repair shop repairs an average of 4.5 machines per hour. Let X be the time (in hours) before the first machine is repaired.(a) What is the probability that a repair time exceeds 4 hours?(b) What is the average time (in hours) it takes to repair the first machine?(c) The conditional probability that a repair takes at least 6 hours, given that it takes more than 4 hours?
Answer:
a) P(X>4)=e-4*4.5 =1.523*10-8 ~ 0.0000
b) 1/4.5 =0..2222 Hours
c) P(X>6|X>4) =P(X>2)=e-2*4.5 =0.000123
Step-by-step explanation:
Hey Which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression 5+3*(3*8)
A. (3*3)*8+8
B. 3*(3*8)+5
C. 5+3*(24)
D. 3*(8*3)+5
The commutative property of addition tells that there is no effect of orders of addends on the result. The associative property of multiplication tells that there can be any grouping of factors, without changing the result.
The expression which uses the commutative property of addition and the associative property of multiplication to rewrite the given expression is:
(3*3)*8 + 5
What is commutative property of addition?The order in which addends(quantities that are added) are written doesn't matter and the result will be same.
[tex]a + b = b + a[/tex]
What is associative property of multiplication?The associative property of multiplication tells that there can be any grouping of factors(any association), without changing the result.
[tex]a\times (b \times c ) = (a \times b) \times c[/tex]
For given expression 5 + 3*(3*8), using the commutative property of addition, we have:
[tex]5 + 3 \times (3 \times 8) = 3 \times (3 \times 8) + 5[/tex]
For the resultant expression [tex]3 \times (3 \times 8) + 5[/tex], using the associative property of multiplication:
[tex]3 \times (3 \times 8) + 5 = (3 \times 3) \times 8 + 5[/tex]
Thus, the expression which uses the commutative property of addition and the associative property of multiplication to rewrite the given expression is:
(3*3)*8 + 5
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www.g "7 Democrats and 6 Republicans. Four members are selected to attend a conference. Find the probability that the group will consist of all Republicans."
Answer:
2.10% probability that the group will consist of all Republicans.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the members are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
4 republicans from a set of 6.
[tex]D = C_{6,4} = \frac{6!}{4!2!} = 15[/tex]
Total outcomes:
4 members from a set of 6 + 7 = 13.
[tex]T = C_{13,4} = \frac{13!}{4!9!} = 715[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{15}{715} = 0.021[/tex]
2.10% probability that the group will consist of all Republicans.
What is the inverse of f(x)=3x+6 ?
Answer:
[tex]\boxed{\sf \ \ f^{-1}(x)=\dfrac{x-6}{3} \ \ }[/tex]
Step-by-step explanation:
hello,
we can write
[tex]fof^{-1}(x)=x \ and \ fof^{-1}(x)=f(f^{-1}(x))=3f^{-1}(x)+6 \ so\\3f^{-1}(x)+6=x \ \ subtract \ 6\\<=>3f^{-1}(x)=x-6 \ \ divide \ \ by \ \ 3\\<=> f^{-1}(x)=\dfrac{x-6}{3}[/tex]
hope this helps
Jamal is comparing his transportation options for an upcoming trip. He’s considering a rental car and a taxi service. Based on his planned routes during his trip, he expects a taxi service would cost about $128. Jamal could also get a rental car for a daily rate and unlimited miles. If Jamal’s trip will last 4 days and he expects to pay about $24 for gas, which graph shows the range of car rental rates that would be cheaper than the taxi service?
Answer:
Graph A
Step-by-step explanation:
Say that the car rental rate stands for c dollars ( $ ). We know that Jamal's trip lasts for 4 days, paying $ 24 in expenses for gas, and $ 128 for taxi services. Based on these requirements for his trip the question asks for a graph that models this situation, but lets start with the inequality.
______
The big key here is the part " which graph shows the range of car rental rates that would be cheaper than the taxi service. " Our inequality must thus have the variable " c " on the same side as the payment for gas ($ 24 ), and must be less than the taxi service ( $ 128 ), or in other words a less than sign. Another point is the car rental rate. We know it stands for c, but it is dependent on the number of days. Hence we can conclude the following inequality,
24 + 4c < 128 - Subtract 24 from either side,
4c < 104 - Divide by 4 on either side, isolating c,
c < 26
The range of car rental rates that would be cheaper than the taxi service should be { c | 0 ≤ c < 26 }, knowing variable c stands for the car rental rates.
______
The graph that models this range should be the first one, option A. This graph is not accurate however, as it extends infinitely in the negative direction, and you can't have negative money, or rather be in debt - in this situation.
Answer:
A is the answer
Step-by-step explanation:
help help help pls pls
Answer:
C. 2y = -12
Step-by-step explanation:
Well a function is when all x values have only one corresponding y value and on a graph we can use the vertical line test and in doing so we know that the answer is C. 2y = -12
Answer:
Step-by-step explanation:hi
(1,5), (9,85), (2,10), (6,38), (4,3), (12,107), (7,64), (12,86), (7,47), (9,64), (4,27) The line is in the form y=mx+b. What is the value of m?
Answer: The value of m = 10.
Step-by-step explanation:
Given points, (1,5), (9,85), (2,10), (6,38), (4,3), (12,107), (7,64), (12,86), (7,47), (9,64), (4,27)
Each point is represented in the form (x,y).
The line is in the form[tex]y=mx+b[/tex], where m is the rate of change of y with respect to x.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Take [tex]x_1=1\ \ , y_1=5;\ \ x_2=9,\ \ y_2=85[/tex]
Then,
[tex]m=\dfrac{85-5}{9-1}\\\\=\dfrac{80}{8}=10[/tex]
Hence, the value of m = 10.
Answer:
9.15
Step-by-step explanation:
I just took the test Hope this helped :D
In triangle ABC, the length of side AB is 18 inches and the length of side BC is 26 inches. Which of the following could be the length of side AC? A. 46 inches B. 49 inches C. 6 inches D. 32 inches
Answer:
D
Step-by-step explanation:
The Triangle Inequality states that the sum of the two largest side lengths of a triangle must be greater than the length of the largest side. Let's check these answers.
A: Since 18 + 26 > 46 is a false statement, A is not the answer.
B: Since 18 + 26 > 49 is false, B is not the answer.
C: Since 18 + 6 > 26 is false, C is not the answer.
D: Since 18 + 26 > 32 is false, D is the answer.
Answer:
since ab=18 and bc= 26 and if u draw out the shape and write them down u would mostly get d but I not too sure is d that the best I can do
Step-by-step explanation:
Q2) The isoscsles right triangle has 2 of it’s sides 10,10 it’s area is
Answer:
Step-by-step explanation:
side a = 10
Area of isosceles triangle = [tex]\frac{\sqrt{3}a^{2}}{4}\\\\[/tex]
= [tex]\frac{\sqrt{3}*10*10}{4}\\\\=\sqrt{3}*5*5\\\\=25\sqrt{3}\\\\=25*1.732[/tex]
= 43.3 square units
Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis and translated 1 unit to the right? f(x) = –|x| + 1 f(x) = –|x – 1| f(x) = |–x| + 1 f(x) = |–x – 1|
Answer:
Hello There. ♡ The correct answer is: f(x) = -|x-1|
The parent function is f(x) = |x|
Then the function is reflected over the x-axis, so the f(x) will become -f(x)'. The function will become:
f(x) = -|x|
-f(x)' = |x|
f(x)' = -|x|
After that, the function is translated 1 unit to the right. That mean x will become x'-1. The function will become:
f(x) = -|x|
f(x) = -|(x'-1)|
f(x) = -|x'-1|
Hope It Helps! :)
ItsNobody~ ♡
Answer:
its b on edge 2020
Step-by-step explanation:
How many normal distributions are there? (1, 10, 30, infinite—pick one)
Answer:
Infinate
Step-by-step explanation:
The normal distribution is dependent on the standard deviation and what the value of the mean is. But this then implies that a different standard deviation or a different mean leads to a different normal distribution. Making there many possibilities for normal distributions.
There are infinitely many possibilities for normal distributions as there are indefinitely many values possible for both the mean and standard deviation.
Use the given information to determine if the geometric series converges or
diverges. If it converges, find the sum.
ai = 0.75; r = 5
a) The series converges to 3.75.
b) The series converges to 0.15.
c) The series diverges. There is no sum.
d) The series converges to 20.
Answer:
c) The series diverges. There is no sum.
Step-by-step explanation:
A geometric series is a series of the form:
[tex]S = \Sigma_{i=0}^{n} a\cdot r^{i}[/tex], [tex]\forall i \in \mathbb{N}_{O}[/tex]
Where:
[tex]a[/tex] - First term of the series, dimensionless.
[tex]r[/tex] - Common ratio, dimensionless.
A geometric series converges only if [tex]|r| < 1[/tex]. As [tex]r > 1[/tex], the geometric series diverges. Hence, the right answer is C.
John is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he finds that it is 2.44 oz. The manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.44 oz or greater? Give your answer as a percentage precise to at least two decimal places.
Answer:
1.02% probability of the stick's weight being 2.44 oz or greater
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 2, \sigma = 0.19[/tex]
What is the probability of the stick's weight being 2.44 oz or greater?
As a decimal, this is 1 subtracted by the pvalue of Z when X = 2.44. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.44 - 2}{0.19}[/tex]
[tex]Z = 2.32[/tex]
[tex]Z = 2.32[/tex] has a pvalue of 0.9898
1 - 0.9898 = 0.0101
1.02% probability of the stick's weight being 2.44 oz or greater