Answer:
B ) ellipse.Domain: { -4 ≤ x ≤ 4 }Range: { -3 ≤ y ≤ 3 }
posted whole test on jiskha under RandomSophomore
The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. Its domain is \([-4, 4]\) and its range is \([-3, 3]\).
The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. To identify its domain and range, we need to understand its shape and orientation.
Step 1: Standard Form of an Ellipse
The standard form of an ellipse with its center at the origin is [tex]\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)[/tex], where \( a \) and \( b \) are the semi-major and semi-minor axes lengths, respectively.
Step 2: Compare Equations
Comparing the given equation [tex]\( 9x^2 + 16y^2 = 144 \)[/tex] with the standard form, we see that [tex]\( a^2 = \frac{144}{9} = 16 \)[/tex] and [tex]\( b^2 = \frac{144}{16} = 9 \).[/tex]
Step 3: Determine Axis Lengths
This means the semi-major axis length \( a \) is [tex]\( \sqrt{16} = 4 \)[/tex]and the semi-minor axis length \( b \) is [tex]\( \sqrt{9} = 3 \).[/tex]Step 4: Shape of the Ellipse
Since \( a > b \), the ellipse is stretched more horizontally than vertically, meaning it's wider than it is tall.
Step 5: Domain and Range
The domain of the ellipse is determined by the values of \( x \) and the range by the values of \( y \). For this ellipse, the \( x \)-values vary from \( -4 \) to \( 4 \) (domain), and the \( y \)-values vary from \( -3 \) to \( 3 \) (range).
Therefore, the domain is \([-4, 4]\) and the range is \([-3, 3]\).
Myra's stamp collection consisted of 120 stamps in october by the following march her collection had grown to 138 by how much did her collection increase between october and march
i know this is really late but this is for anyone else that wants to know the answer
138 -120 = 18 18/120 X 100 = 15%
A salesperson earns $300.50 per week plus 7% of her weekly sales. Which of the following describes the sales necessary for the salesperson to earn at least $900.85 in one week?
A. x is greater then or equal to 900.85
B. x is greater then or equal to 8576.43
C. x is greater then or equal to 600.35
D. x is greater then or equal to 17162.14
salesperson earns $300.50 per week plus 7% of her weekly sales .To have the sales necessary for the salesperson to earn at least $900.85 in one week we can form an inequality equation. Let x denote his weekly sales.
300.50+7% x ≥ 900.85
Subtracting 300.50 both sides:
7%x≥ 600.35
0.07x ≥ 600.35
Dividing both sides by 0.07
x≥8576.428
Option B . x is greater then or equal to 8576.43 is the right answer.
The average distance between the variable scores and the mean in a set of data is the __________.
a. range
b. standard deviation
c. mean
d. median user: all of the following are limitations of statistics except that it __________.
a. provides limited information
b. cannot be influenced by inaccurate assumptions
c. promotes limitations in perceptions
d. can be misrepresented
The B. standard deviation is the measure that represents the average distance between the variable scores and the mean in a dataset. Statistics can indeed be b. cannot be influenced by inaccurate assumptions
The average distance between the variable scores and the mean in a set of data is the standard deviation. The standard deviation quantifies the variation or dispersion from the average of a dataset. It provides insight into how spread out the data points are relative to the mean. A low standard deviation suggests that the data points tend to cluster near the mean, whereas a high standard deviation indicates a wider spread of data points.
As for the limitations of statistics, they do not include that statistics cannot be influenced by inaccurate assumptions. In fact, statistics can be greatly influenced by assumptions, and care must be taken to ensure that the data and the assumptions upon which the analyses are based are accurate. Otherwise, the conclusions drawn from statistical analyses may be misleading.
. Identify the converse of the conditional statement. Determine the truth values of the original conditional and its converse. If an angle is a right angle, then its measure is 90.
A.
If the measure of an angle is 90, then it is a right angle.
Original: true
Converse: true
B.
If an angle is not a right angle, then its measure is not 90.
Original: true
Converse: true
C.
If an angle is not a right angle, then its measure is 90.
Original: true
Converse: false
D.
If the measure of an angle is 90, then i ...?
Compensation for 195x5
A box has a length of 5 cm, a width of 10 cm, and a height of 2 cm. The volume of the box is
Answer:
100 cm3
Step-by-step explanation:
To find the solution to this problem, we have to use the formula for volume, which is Length x Width x Height. So, we have to do 5cm x 10cm x 2cm, which is 100. Finally, we have to square the centimeters, which gives us
100 cm3
Hope this helped!
Find the 7th term of the geometric sequence with the given terms:
a2 = 768 and a4 = 48; a7 = _____. ...?
To find the 7th term in the geometric sequence, determine the common ratio using given terms, a2 and a4, then use the formula for the nth term to calculate a7. The common ratio is 1/4, and the 7th term is 0.75.
Explanation:The student is asking to find the 7th term (a7) of a geometric sequence for which the 2nd term (a2) is 768 and the 4th term (a4) is 48. To solve for the 7th term, we must first determine the common ratio of the sequence.
We know that in a geometric sequence, each term is the product of the previous term and the common ratio (r). The formula for the nth term of a geometric sequence is an = a1 * r^(n-1), where a1 is the first term and n is the term number.
Since a4 is the 4th term and a2 is the 2nd term, we can write these equations:
a4 = a2 * r^(4-2)48 = 768 * r^2
By solving this equation, we get:
r^2 = 48 / 768 = 1 / 16, which means r = 1 / 4.
Now that we know the common ratio, we can find the 7th term (a7) by using the formula from above with n = 7:
a7 = a2 * r^(7-2) = 768 * (1/4)^(7-2) = 768 * (1/4)^5 = 768 * 1/1024 = 0.75
Hence, the 7th term of the given geometric sequence is 0.75.
what is a proportional relationship
Sari is factoring the polynomial 2x2 + 5x + 3. What is the missing number in her factorization?
2x2 + 5x + 3
Answer:
the factor of polynomial [tex]2x^{2}+5x+3[/tex] is [tex]=\left(x+1\right)\left(2x+3\right)[/tex]
Step-by-step explanation:
We need to factor the polynomial [tex]2x^{2}+5x+3[/tex]
Break the expression into groups,
[tex]=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c[/tex]
[tex]x^2=xx[/tex]
then
[tex]2x^2+2x=2xx+2x[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}2x[/tex]
[tex]=2x\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]
[tex]=2x\left(x+1\right)+3\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]
[tex]=\left(x+1\right)\left(2x+3\right)[/tex]
Hence, the factor of polynomial [tex]2x^{2}+5x+3[/tex] is [tex]=\left(x+1\right)\left(2x+3\right)[/tex]
An automobile travels 34.o mpg of gasoline . how many kilometers does it travel per liter of gasoline ? use these equalities : 1 mile=1.61 kilometers ; 1 gallon = 3.79 liters
11x-1+5x+5+3x+5=180
geometry solve for x
A. A band leaves a free T-Shirt under every 6th seat at a concert. They leave a free backstage pass under every 4th Street.
Which of these seat numbers get a free T-SHirt? Which Get a backstage pass? Which get both? Explain Your reasoning
Bianca's bank offers a savings account with a 2.1% APR, compounded monthly. What is the actual annual percentage yield on this account?
Answer:
2.12
Step-by-step explanation:
I'm takingit rn :/
Five different written driving tests are administered by the Motor Vehicle Department. One of these five tests is selected at random for each applicant for a driver's license. A group consisting of two women and three men apply for a license. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the five will take the same test?
The probability that exactly two of the five applicants will take the same test is approximately 0.384.
To solve the problem of finding the probability that exactly two of the five applicants for a driver's license will take the same written driving test, we can use the principles of combinatorial probability.
Identify the Total Number of Tests:
The Motor Vehicle Department administers 5 different tests.Identify the Total Number of Applicants:
There is a group of 5 applicants (2 women and 3 men).Understand the Requirement:
We need to find the probability that exactly 2 out of the 5 applicants take the same test, and the remaining 3 take different tests.Select the Applicants Who Share the Same Test:
Choose 2 out of the 5 applicants to take the same test. This can be done in:
[tex]\binom{5}{2} = 10 \text{ ways}[/tex]
Choose the Test for the Selected Applicants:
Any of the 5 tests can be taken by the 2 selected applicants. Thus, we have 5 choices for the test.Assign Tests to the Remaining Applicants:
The remaining 3 applicants must take different tests. Since one test is already taken by the 2 applicants, there are 4 tests left available for the other 3.
We need to choose 3 tests from the remaining 4, which can be selected in:
[tex]\binom{4}{3} = 4 \text{ ways}[/tex]
The arrangement of these selected tests among the 3 remaining applicants can happen in:
[tex]3! = 6 \text{ ways}[/tex]
Calculate the Total Ways to Arrange Tests:
The total ways to assign tests involving both the shared test and unique tests is calculated as:
[tex]10 \times 5 \times 4 \times 6 = 1200 \text{ ways}[/tex]
Total Possible Assignments Without Restrictions:
Without any restriction, each of the 5 applicants could take any of the 5 tests, leading to:
[tex]5^5 = 3125 \text{ total combinations}[/tex]
Calculate the Probability:
The probability that exactly two applicants take the same test is then:
[tex]P(X=2) = \frac{1200}{3125} \approx 0.384[/tex]
omar is 3 times as old as jason.
henry is 5 years older than jason.
if their total age is 80 years old,how much older is omar than henry?
6. Complete the two-column proof.
Given:x/6+2=15
Prove: x = 78
Statement: x/6+2=15 Reason: A:
x/6=13 B:
x=78 C:
Answer:
Given: [tex]\frac{x}{6} + 2 = 15[/tex] ......[1]
To prove : x =78
Subtraction property states that you subtract the same number to both sides of an equation.
Subtract 2 from both sides of an equation [1];
[tex]\frac{x}{6} + 2 - 2= 15 -2[/tex]
Simplify:
[tex]\frac{x}{6} = 13[/tex] ......[2]
Multiplication property states that you multiply the same number to both sides of an equation.
Multiply 6 to both sides of an equation [2];
[tex]\frac{x}{6} \times 6 = 13 \times 6[/tex]
Simplify:
[tex]x = 78[/tex] proved!
Statement Reason
1. [tex]\frac{x}{6} + 2 = 15[/tex] Given
2. [tex]\frac{x}{6} = 13[/tex] Subtraction property of equality
3. [tex]x = 78[/tex] Multiplication property of equality
Final answer:
To solve for x, subtract 2 from both sides of the equation, then multiply both sides by 6. This yields that x equals 78, completing the proof.
Explanation:
To complete the two-column proof, we start with what is given and use algebraic manipulation to prove that x equals 78. Here are the steps formatted into a proof:
Statement: x/6 + 2 = 15what is the nth term of 3 8 15 24 35
I am part of a whole. i am greater than three fourths,but less than nine tenths. i am a decimal with a 3 in my hundredths place. what number am i?______________
A spinner used for a game is divided into 4 sections: Yellow, Brown, Red and Orange. The spinner is spun 50 times and lands on brown 18 times. What is the experimental probability that the spinner does NOT land on brown?
Answer:
[tex]\frac{16}{25} =0.64[/tex]
Step-by-step explanation:
Given : A spinner used for a game is divided into 4 sections: Yellow, Brown, Red and Orange. The spinner is spun 50 times and lands on brown 18 times
To Find: What is the experimental probability that the spinner does NOT land on brown
Solution :
Since we are given that the spinner is spun 50 times .
Ans the spinner lands on brown 18 times
Probability of landing on brown = [tex]\frac{18}{50} =\frac{9}{25}[/tex]
Since we know that the sum of probabilities is 1
So, probability that the spinner does NOT land on brown is :
⇒ 1 - prob. of landing on brown
⇒[tex]1-\frac{9}{25}[/tex]
⇒[tex]\frac{25-9}{25}[/tex]
⇒[tex]\frac{16}{25}[/tex]
Thus probability that the spinner does NOT land on brown is 16/25=0.64
Lois has 36 colored pencils. They are either green or red. For every green pencil, Lois has 3 red pencils. How many red pencils does Lois have?
Answer:
12
Step-by-step explanation: 36/3=12
evaluate the expression 5/12-4/9
Ron bought 2 dvds for 12.95 each. he spent $25. did he spend more on dvds or magazines
The data set represents the number of snails that each person counted on a walk after a rainstorm. 12, 13, 22, 16, 6, 10, 13, 14, 12 The outlier of the data set is .
Answer: 22
Step-by-step explanation:
Given : The data set represents the number of snails that each person counted on a walk after a rainstorm.
The given data : 12, 13, 22, 16, 6, 10, 13, 14, 12
Arrange in order : 6,10 , 12, 12, 13, 13, 14, 16, 22
We can see that all data values are closer to each other except 22.
22 is an extreme value as compare to the entire data values.
Therefore, the outlier of the data set is 22 .
A bank requires a four-digit access code for each account. The access code is generated using the digits 0–9, and the digits can be repeated. What is the probability of an access code “1234”?
Answer:
Hence, the probability of an access code “1234”= [tex]\dfrac{1}{10000}[/tex]
Step-by-step explanation:
" The probability of an event is defined as the ratio of total number of favourable outcomes to the total number of possible outcomes ".
A bank requires a four-digit access code for each account. The access code is generated using the digits 0–9, and the digits can be repeated.
The total number of outcomes possible are 10×10×10×10=10000
since the first place any of the 10 digits are possible, similarly for the second, third and fourth place.
Also each code is a unique representation in itself.
Hence the code "1234" is unique.
Hence, the probability of an access code “1234”= [tex]\dfrac{1}{10000}[/tex]
What is the surface area of this design?
Answer:
256
Step-by-step explanation:
Answer:
Surface Area of Design = 256 in.²
Step-by-step explanation:
Given: a Shape which is made by placing two cuboid on one another.
To find: Surface area of shape.
Figure is attached.
Surface Area of Design
= Lateral Surface Area of Base Cuboid + Lateral Surface area of Top Cuboid + Area of rectangle CDLJ + Area of rectangle EFNM + Area of rectangle ABHG
Dimensions of Base Cuboid:
Length, CJ = 8 in.
Width, CD = LJ = MN = 5 in.
Height, AD = 4 in.
Dimensions of Top cuboid:
Length, HI = BI - BH = 8 - 4 = 4in.
Width, GH = KI = MN = 5 in.
Height, FH = JN - JI = 8 - 4 = 4 in.
Length of rectangle ABHG, AB = 5 in.
Width of rectangle ABHG , BH = 4 in.
Length of rectangle DCJL, DC = 5 in.
Width of rectangle DCJL , CJ = 8 in.
Length of rectangle EFNM, EF = 5 in.
Width of rectangle EFNM , FN = 4 in.
Lateral Surface Area of Base Cuboid = 2 × Height ( length + Width )
= 2 × 4 ( 8 + 5 )
= 8 ( 13 )
= 104 in²
Lateral Surface Area of Top Cuboid = 2 × Height ( length + Width )
= 2 × 4 ( 5 + 4 )
= 8 ( 9 )
= 72 in²
Area of rectangle DCJL = length × breadth
= 5 × 8
= 40 in.²
Area of rectangle ABHG = length × breadth
= 5 × 4
= 20 in.²
Area of rectangle EFNM = length × breadth
= 5 × 4
= 20 in.²
⇒ Surface Area of Design = 104 in.² + 72 in.² + 40 in.² + 20 in.² + 20 in.²
= 256 in.²
Therefore, Surface Area of Design = 256 in.²
Tabitha bought peppers that cost $0.79 per pounds. she paid $3.95 for the peppers. how many pounds of peppers did she buy? show your work
Tabitha bought 5 pounds of peppers for $3.95 at a rate of $0.79 per pound by dividing the total cost by the price per pound.
Explanation:The student asked how many pounds of peppers Tabitha bought if she paid $3.95 for them at a cost of $0.79 per pound.
To answer this, we need to divide the total cost by the price per pound.
So, we calculate $3.95 / $0.79 per pound to get the total pounds of peppers.
Here's how the calculation is done step-by-step:
Write down the total amount spent on peppers: $3.95.Write down the cost per pound of peppers: $0.79.Divide the total cost by the cost per pound to find the quantity purchased: $3.95 / $0.79 = 5 pounds.Therefore, Tabitha bought 5 pounds of peppers.
find a polynomial function of degree 4 with -1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
f(x)=? ...?
Consider the function f(x) = ax+3 over x-b.
Find a and b given that y=f(x) has asymptotes with equations x = -1 and y = 2.
The value of 'a' is determined from the horizontal asymptote y=2, which gives a=2. The value of 'b' is derived from the vertical asymptote x=-1, leading to b=1. Hence, the function with the given asymptotes is f(x) = 2x+3 over x-1.
To find the values of a and b for the function f(x) = ax+3 over x-b, given the horizontal and vertical asymptotes, we need to consider the general behavior of rational functions. A vertical asymptote occurs where the denominator of a rational function is zero, while a horizontal asymptote is determined by the relationship between the degrees of the numerator and the denominator.
Since the vertical asymptote is x = -1, we know that the denominator of the function must be zero when x = -1. Thus, we can determine that b = 1, since the denominator is x - b and -1 - b = 0.
The horizontal asymptote is given by y = 2. This indicates the value that the function approaches as x goes to infinity. For the function f(x) = ax+3 over x-b, the degrees of the numerator and denominator are both one. Therefore, the horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and the denominator, which means a / 1 = 2, so a = 2.
Therefore, the values of a and b are 2 and 1, respectively.
If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (c * d ) (x)?
A ) 4x3 + 18x2 – 10x
B ) x2 + 9x – 2
C ) 16x2 + 4x – 6
D ) 4x2 + 20x – 2
Smith high school offers a baseball camp that is 75$ for 4 days of camp and a basketball camp for that 100$ for 5 days of camp.which is a a better deal and by how much?