Answer: 6+1=7
Step-by-step explanation:
Writing an equation of an ellipse given the foci and major axis length
Given
Major axis of length = 12
Foci at ( 9 ,1 ) and ( -1, 1 )
Find
Equation of an ellipse
Explanation
As we know , major axis = 2a = 12
thus a = 6
the midpoint between the foci is the center , so
[tex]\begin{gathered} C:(\frac{8}{2},\frac{2}{2}) \\ C:(4,2) \end{gathered}[/tex]the distance between the foci is equal to 2c
[tex]\begin{gathered} 2c=\sqrt{\left(9+1\right)^2+0^2} \\ 2c=10 \\ c=5 \end{gathered}[/tex]now,
[tex]\begin{gathered} c^2=a^2-b^2 \\ b^2=a^2-c^2 \\ b^2=36-25 \\ b^2=11 \end{gathered}[/tex]so , the equation of an ellipse is
[tex]\begin{gathered} \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2} \\ \frac{(x-4)^2}{11}+\frac{(y-2)^2}{36} \end{gathered}[/tex]Final Answer
The equation of an ellipse
[tex]\frac{(x-4)^{2}}{11}+\frac{(y-2)^{2}}{36}[/tex]
NEED DONE ASAP
A bakery prepares boxes of desserts. Each box contains twice as many cookies as brownies. Which line on the graph depicts the number of cookies relative to the number of brownies?
A
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 0), (10, 5) connected through a line.
B
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 0), (10, 10) connected through a line.
C
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 2), (10, 2) connected through a line.
D
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 0), (5, 10) connected through a line.
Answer:
Answer is the last graph which shows 10 cookies and 5 brownies.
Step-by-step explanation:
There are more cookies (y-axis) than brownies (x-axis), the slope is 2.0 so the line must be > 45 degrees.
Jenny wants to buy a new dress for her first school dance. She borrows $25.63 from her sister to help pay for the dress. Then Jenny earns $16.33 helping her dad organize his home office. If she gives all the earnings to her sister, Jenny will still owe her sister $ .
Answer:
Jenny owes her sister 9.3 dollars.
Step-by-step explanation:
23.63 - 16.33 = 9.3
suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. if 83 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams? round your answer to four decimal places.
The probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams is 0.4339.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 3316 grams - 54 grams = 3262
μ = mean = 3316 grams
σ = standard deviation = 324 grams
z-score = (3262 - 3316) / 324
z-score = -54 / 324
z-score = -0.1667
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = -0.1667
Using interpolation of values,
probability = 0.4339
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What is an equation in point-slope form for the line perpendicular to y =-5x - 14 that contains (10, -4)?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-5}x-14\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {-5\implies \stackrel{slope}{\cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5}\implies \cfrac{1}{5}}}[/tex]
so we're really looking for the equation of a line whose slope is 1/5 and it passes through (10, -4)
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \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-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \implies {\large \begin{array}{llll} y +4= \cfrac{1}{5} (x -10) \end{array}}[/tex]
You toss a coin and roll a number cube. Find P(heads and an even number)
1- 1
2- 1/12
3- 1/6
4- 1/4
The probability of a head and an even number is 1/4.
What is probability?Probability is the occurrence of a certain event out of the total events than can occur in a given context.
Given event is a coin is tossed and then a die is rolled.
∴ The sample space (S) is = (H,1), (T,1), (H,2), (T,2), (H,3),(T,3), (H,4), (T,4), (H,5), (T,5), (H,6), (T,6).
So, the number of sample spaces N(S) = 12.
The number of heads and an even number N(H,E) = 3.
∴ The probability of a head and an even number is = N(H,E)/N(S).
= 3/12.
= 1/4.
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Expand & simplify
(
x
+
3
)
2
(
2
x
−
5
)
Answer:
4x²+2x-30
Step-by-step explanation:
(x+3) 2(2x-5)
(x+3) (4x-10)
4x²-10x+12x-30
4x²+2x-30
what is the mean of 45,68,77,90,90,95,100,100,86,90,50,55
Answer:
78.8
Step-by-step explanation:
how much time has elapsed 2:20 pm to 5:57 pm
Answer:
2:20 pm to 5:57 pm is 3 hours and 37 minutes.
Answer:
3 hours and 37 minutes.
Step-by-step explanation:
5:57
-2:20
= 3:37
classify as =1 , <1 , >1 . for n>1.
|1.1n|
a. <1
b. >1
c. =1
The value of the absolute value expression given; | 1.1n | for n > 1 as required in the task content can be classified as; Choice B; >1.
What is the best classification of the expression | 1.1n | for n > 1?It follows from the task content that the best classification of the expression | 1.1n | for n > 1 be determined.
Since the domain of variable n is such that n > 1, it follows that 1.1 × n > 1.1.
There, it follows that; 1.1n > 1.1 > 1.
By definition; The absolute value |n| of any real number n is the non-negative value of x irrespective of its sign. For instance, the absolute value of 15 is 15, and also the absolute value of −15 is also 5.
Hence, the absolute value sign; | 1.1n | indicates positive values.
Ultimately, the correct classification of.the expression is; Choice B; > 1.
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A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.04.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.
The correct answer is 0.4834
There can only be one tornado every year on the calendar. This indicates that there are only two conceivable outcomes of the event: either there will be one tornado or none at all.
The likelihood of a tornado in any given year is 0.14. This indicates that an event's chance of occurring is fixed. p = 0.14
The frequency of tornadoes in one year is unrelated to the quantity in other years. This indicates that the incidents are unrelated to one another.
The likelihood that there won't be more than two tornadoes in a 12-year period has to be calculated. This indicates that the number of trials, n, is set at 12.
p = 0.14
q = 1 - p = 1 - 0.14 = 0.86
n = 12
x = 2
We need to find: P( x < 2)
Fewer than 2 tornadoes means either 1 or 0 tornado. So,
P(x < 2) = P(x=0) + P(x=1)
the likelihood of less than two tornadoes occurring in a 12-year period is 0.4834
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Is 1/1 a terminating or repeating decimal
a school Liberian ordered new books for the library of the new books covered 1/3 are science 2/5 are biography,and the rest of the books are friction. what fraction of the books ordered are fiction?
Given that of the new books the new books the new liberian ordered;
-1/3 are science
-2/5 are biography
Let s, b and f represent the fraction of science, biography and fiction of the new book.
[tex]s+b+f=1[/tex]substituting the values of s and b given;
[tex]undefined[/tex]y/31.25 = 5 solve for y please
Answer:
Step-by-step explanation:
y=652/4
convert decimal to a fraction
46/125=5
multiplying by both sides of the equation by 125/4
y=652/4 = 156 1/4
Tommy deposited $2,000 into a savings account that earns 5% interest per year. What
equation would be used to determine how much money Tommy has after x number of years?
Answer:
7A, 8D
Step-by-step explanation:
The compound interest formula is as followed
[tex]A = P(1+\frac{r}{n} )^{nt}\\[/tex]
A = accumulated amount
P = principle
r = interest rate
n = compounding
t = time
The accumulated amount is represented by f(x).
The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000
The interest rate is 5%. This needs to be converted into a decimal.
5% = 0.05 = r
The money is compounded annually, thus n = 1.
The time is represented by x. x = t.
thus
[tex]f(x) = 2000(1+0.05)^{x}[/tex]
After six years, you simply find f(6), or substitute 6 into x.
f(6) = 2000(1.05)^6 = $2,680.19
The equation of a line is y=4/3x + 4 . Is the point (6, 13) on the line? [ Select ] Is the point (9, 16) on the line?
The point (9, 16) is on the line.
Given,
The equation of the line = y = 4/3x + 4
We have to find whether the given points are on this line or not.
For that substitute the points into the equation.
That is,
Point (6, 13)
x = 6 and y = 13
Equation;
y = 4/3x + 4
13 = 4/3 x 6 + 4
13 = 8 + 4
13 ≠ 12
That is, the point (6, 13) is not in the line.
Next,
Point (9, 16)
x = 9 and y = 16
Equation;
y = 4/3x + 4
16 = 4/3 x 9 + 4
16 = 12 + 4
16 = 16
Therefore, the point (9, 16) is in the line.
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Pleasehelp Name the reciprocal
Answer:
x = 12
Step-by-step explanation:
3/4x = 9
x = 9/1(4/3)
x = 12
Find the circumference of each circle round answer to the nearest tenth
Answer: ask your teacher
Step-by-step explanation:u have to multiply
The answer to x/-2+1>4
Answer: x < -6
Step-by-step explanation:
1) Bring 1 to the other side
x/-2 > 3
2) Bring -2 to the other side. The sign flips when the number multiplied or divided is negative
x < -6
In a school of 2000 students, the ratio of teachers to students is 3:80.
Some teachers join the school and the ratio changes to 1:20.
Find the number of teachers who joined the school.
25 new teachers joined the school such that the new ratio is 1 : 20 .
In mathematics, a ratio illustrates how frequently one number appears in another. For instance, the ratio of oranges to lemons on a fruit platter would be eight to six if there were eight oranges and six lemons.
Ratios can be decreased by dividing each quantity by the sum of all the common components of the numbers (much like fractions are). When the ratio's numbers are the smallest practical integers, the fraction is said to be in its simplest form.The ratio's antecedent and consequent are frequently referred to as A and B, respectively.The total number of students is 2000
The ratio of teachers to students is 3:80 .
Therefore the number of teachers = 3 × 2000 ÷ 80 = 75
Let x teachers joined the school.
Therefore new ratio = (x+75) : 2000
but the new ratio is 1 : 20
Therefore 1 : 20 = (x+75) : 2000
Simplifying we get:
x + 75 = 100
or, x = 25
Therefore the number of teachers who joined the school is 25 .
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You run $2\frac{1}{2}$ miles as a part of an exercise routine. you run $\frac{1}{3}$ of that distance on a hill. you run down a slope for the last $\frac{1}{2}$ of the hill. on how many miles of your run do you run down the slope?
Given,
Total distance [tex]=2\frac{1}{2}[/tex] miles
You run 1/3 of that distance on a hill.
Distance on a hill[tex]=\frac{1}{3} * 2\frac{1}{2}[/tex] miles
You run down a slope for the last 1/2 of the hill=[tex]\frac{1}{3} * 2\frac{1}{2}*\frac{1}{2}[/tex] miles[tex]=\frac{5}{12}[/tex] miles
Distance you run down the slope [tex]=\frac{5}{12}[/tex] miles
It takes 0.5 gallon of cream to make 1 pound of butter.
How much butter could you make with 0.25 gallons of cream?
How much cream would you need to make 2.5 pounds of butter?
What is 955 divided by 36 rounded to the nearest tenth?
(8d+4)⁰
(6d+8)°
3. Find d. Show a picture of your work.
d =
pic goes here (or ok to type your steps)
Answer:
d=12
Step-by-step explanation:
8d+4+6d+8 = 180 (Straight angle = 180)
14d+12=180
14d=168
d=12
:]
Answer:
D =12
Step-by-step explanation:
8d+4+6d+8 =180 (being a linear pair)
14d+12=180
14d=180-12
14d=168
d= 168/14
d=12#
the accounting department at weston materials inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the red barn model. assume the assembly times follow the normal distribution. a-1. determine the z values for 29 and 34 hours. (negative amount should be indicated by a minus sign. round z value to 2 decimal places and your final answer to 2 decimal places.) a-2. what percent of the garages take between 32 hours and 34 hours to erect? (round z value to 2 decimal places and your final answer to 2 decimal places.) b. what percent of the garages take between 29 hours and 34 hours to erect? (round z value to 2 decimal places and your final answer to 2 decimal places.) c. what percent of the garages take 28.7 hours or less to erect? (round z value to 2 decimal places and your final answer to 2 decimal places.) d. of the garages, 5% take how many hours or more to erect? (round your answer to 1 decimal place.)
The z-value for 29 and 34 hours is z(32) = 0, the garages take between 32 hours and 34 hours to erect 34%, the garages take between 29 hours and 34 hours to erect 77.45%, and the garages, 5% take 35.29 hours of time.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
Weston Materials, Inc., a national manufacturer of detached garages, states that erecting the Red Barn type takes two construction workers a mean of 32 hours and a standard variation of 2 hours. Assume that the assembly times are distributed normally.
Calculating the z values for 29 and 34 hours.
z(29) = (29-32)/2 = -3/2
z(34) = (34-32)/2 = 1
z(32) = 0
The percentage of garages take between 32 hours and 34 hours to erect as:
⇒ P(32 < x < 34) = P(0< z < 1) = 0.34
The percentage of garages take between 29 hours and 34 hours to erect as:
⇒ P(29 < x < 34) = P(-1.5 < z < 1) = 0.7745
The percentage of garages take 28.7 hours to erect as:
⇒ z(28.7) = (28.7-32)/2 = -3.3
⇒ P(0 < x < 28.7) = P (-10 < z < -3.3) = 0.00048348...
The z-value corresponds to a 95% left area and only
5% to the right under the curve.
Use z-chart or InvNor(0.95) = 1.645
x-value that corresponds to the z-value.
1.645 = (x-32)/2
x-32 = 2×1.645
x = 35.29 hours
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The first three terms of an arithmetic sequence are as follows.-26, -19, -12Find the next two terms of this sequence.-26, – 19, -12,
1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:
[tex]\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ d=7 \end{gathered}[/tex]2) Based on that, we can do the following to find the next two terms:
[tex]\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ -12+7=-5 \\ -5+7=2 \\ \\ -19,-12,-5,2 \\ Or \\ \\ a_4=a_1+d(n-1) \\ a_4=-26+7(4-1) \\ a_4=-26+21 \\ a_4=-5 \\ \\ a_5=-26+7(5-1) \\ a_5=-26+7(4) \\ a_5=-26+28 \\ a_5=2 \end{gathered}[/tex]Thus, the next terms are -5 and 2
Travis got a charging fee of 20$.He has an outstanding charge of 7.50 how much will he need to pay to not get feed by the bank
(X-3)^2=5 to 3 significant figures
The solution to the equation is x = 5.24
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The equation is given as
(x - 3)^2 = 5
Take the square root of both sides
So, we have
x - 3 = 2.24
Add 3 to all sides of the equation
So, we have
x = 5.24
Hence, the solution is x = 5.24
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You have 8 nickels, 5 dimes, 6 quarters and 4 pennies. How much money do you
have?
$2.49
$2.44
$2.54
$2.59
[23+4x(2+5)<15-5x(8-7)]2^5
Answer:
[tex]23+4x(2+5)<15-5x(8-7)]2^5[/tex]