Answer:
3
Step-by-step explanation:
The enrollment for a new program is 1,500 students. the program is expected to grow at a rate of 0.03. what is the expected enrollment in 7 years? round to the nearest whole number.
The expected enrolment in 7 years is 1845.
What is the expected enrolment?The formula for calculating future value of the number of students is an exponential equation with this form:
FV = P (1 + r) ^n
FV = Future populationP = Present populationR = rate of growth of the populationN = number of years1500 x (1.03)^7 = 1845
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answer...............
In the given graph point B is a relative maximum with the coordinates (0, 2).
The given function is [tex]y=x^{4}-2x^{2} +1[/tex].
In the given graph, we need to find which point is a relative maximum.
What are relative maxima?The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.
In the graph, the maximum point is (0, 2).
Therefore, in the given graph point B is a relative maximum with the coordinates (0, 2).
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You toss a coin and roll a number cube. Find P(heads and an even number.)
Answer:
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number)
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number) = P(head) × P(even number)
P(even number)Assuming a fair coin and a fair die:
P(even number)Assuming a fair coin and a fair die:P(head)
P(even number)Assuming a fair coin and a fair die:P(head) =50%
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number)
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50%
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number)
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number) =50%×50%=25%
The sum of ten and eight times a number is 162. What is the number?
Answer:
9
Step-by-step explanation:
10x + 8x = 162
18x = 162
x = 9
What is the principal, if a person paid an amount of $432 after 1 year at 8% rate of interest per annum
Answer:
principal = $400
Step-by-step explanation:
amount(a)=principal(p) + interest(y).........(1)
Interest(y)=principal(p) x rate(r) x time(t)....(2)
In (1), p= a - y...........(3)
putting (3) in (2),
y = (a - y) x r% x t
y = (432 - y) x 8% x 1
y = 3456%-8y%
y + 0.08y = 3456%
1.08y = 34.56
y = 32
but a - y = p
432 - 32 = p
p = 400
principal = $400
PLEASE HELP ASAP!!!!!!!1
Consider the series 1/4+3/2+11/4+4+21/4+....
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The series _____ (diverges or converges). You Consider conclude this because the series is _________ (Arithmetic, Geometric and the absolute value of the common ratio is greater than 1, Geometric and the absolute value of the common ratio is less than 1, neither arithmetic nor geometric)
The series diverges. You Consider concluding this because the series is in arithmetic progression.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
[tex]a_n = a_1 + (n-1)d[/tex]
where d is the difference and a₁ is the first term of the sequence.
The given series of numbers 1/4+3/2+11/4+4+21/4+.... is an arithmetic series because the difference between any two consecutive terms is 5/4. Therefore, the blanks can be filled as,
The series diverges. You Consider conclude this because the series is in arithmetic progression.
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Graph the rational function
f(x) = 2x+3
———
X-4
Answer:
Step-by-step explanation:
HELPPPP RIGHT NOW !!!!!!!!!
The equation can be used to find the time it took student to hike the trail will be 3t= 5(3-t)
What is the equation?
A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The formula for the distance for the to and fro motion is;
x= v × t
The total time required for to and fro motion is;
[tex]\rm t_1 + t_ 2 = 3 \\\\ \frac{x}{v_)1} +\frac{x}{v_2}=3 \\\\ \frac{x}{3} +\frac{x}{5}= 3 \\\\ x = \frac{45}{8} \\\\ x = 3 \times \frac{15}{8} \\\\\ x =v \times \frac{15}{8} \\\\ x = v \times t[/tex]
From the equation B;
3t= 5(3-t)
3t=15-5t
8t=15
t=15/8
The equation can be used to find the time it took Stu to hike the trail will be 3t= 5(3-t)
Hence option B is correct.
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Solve for w.
−16w-3 = 5w²
Answer:
w = -1/5
OR
w = -3
Step-by-step explanation:
Given equation:
−16w-3 = 5w²
Solution:
Subtracting 5w^2 from both sides,we get
-16w-3-5w² = 5w² - 5w²-5w²-16w-3=0Factor the LHS of this equation using middle term factor:
(-5w²-1)(w-3)Now,
[tex]( - 5w - 1) = 0 \: \: \: \: \: \: \: \: ...(1)[/tex][tex](w - 3) = 0 \: \: \: \: \: \: \: \: \: \: ... (2)[/tex]Solving for equation 1:
[tex] - 5w = 0 + 1[/tex][tex] - 5w = 1[/tex][tex] \boxed{w = - \cfrac{1}{5} }[/tex]Solving for equation 2:
[tex]w - 3 = 0[/tex][tex]w = 0 - 3[/tex][tex] \boxed{w = - 3}[/tex][tex] - 16w - 3 = 5 {w}^{2} \\ \\ 0 = 5 {w}^{2} + 16w + 3 \\ \\ 5 {w}^{2} + 16w + 3 = 0 \\ \\ 5 {w}^{2} + w + 15w + 3 = 0 \\ \\ (5 {w}^{2} + w) + (15w + 3) = 0 \\ \\ w(5w + 1) + 3(5w + 1) = 0 \\ \\ (w + 3)(5w + 1) = 0. [/tex]
The value of w is -3 and -1/5 .
The table shows the prices of different sizes of containers of vegetable oil.
A 3-column table with 3 rows. Column 1 is labeled Container size with entries 16 ounces, 24 ounces, 48 ounces. Column 2 is labeled Price with entries 4 dollars and 64 cents, 6 dollars and 24 cents, 16 dollars and 32 cents. Column 3 is labeled price per ounce with entries 29 cents, 26 cents, 34 cents.
Tony needs to purchase 3,600 oz of vegetable oil for his catering business. For the containers shown in the table, how much would he save by purchasing those with the lowest unit price than those with the highest unit price?
Total amount at lowest price:
Total amount at highest price:
Amount saved:
The total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The table is in the picture, please refer to the picture.
Tony needs to purchase 3,600 oz of vegetable oil for his catering business.
Lowest unit price = 26 cents per ounce
Total price at this rate = 3600×26 = 93600 cents = $936
The highest unit price = 34 cents per ounce
Total price at this rate = 3600×34 = 122400 cents = $1224
Total saving he purchases the container that has the lowest unit price:
= 1224 - 936
= $288
Thus, the total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.
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a bag contains 4 white marbles , 7 red marbles , and 5 black marbles. you randomly select 3 marbles from the bag. without replacement.the random variable represents the number of black marbles
please help .. . . .
Answer:
Step-by-step explanation:
The probability distribution for a random variable x is given in the table. Probability Find the probability that x=-10
Answer:.20
Step-by-step explanation:
According to what are written in the table the probability for x=-10 is .20
If f(x)=7^x and g(x)=15x/x+9, find a simplified formula for: g(f(x))=
Answer:
[tex]\frac{15*7^{x} }{7^{x} +9}[/tex]
Step-by-step explanation:
→ Substitute f(x) into g(x)
[tex]\frac{15*7^{x} }{7^{x} +9}[/tex]
Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $8.65 .How many of each type of coin do they have?
Solve this system of equations algebraically:
y – 10 = 11x + x2
y – 12x = 30
The first solution is (–4, –18).
The second solution is (
,
).
Answer:
(-4,-18) and (5,90)
Step-by-step explanation:
I'll assume the first equation is supposed to be y – 10 = 11x + x^2
This is a parabola. The second equation is a straight line:
y – 12x = 30
We want to find the points at which these lines intersect. They will intersect for any (x,y) that
Let's rearrange the second equation to isolate y:
y – 12x = 30
y = 30 + 12x
Now we can take the this value of y and substitute it into the first equation:
y – 10 = 11x + x^2
(30 + 12x) – 10 = 11x + x^2
20 + 12x = 11x + x^2
0 = x^2 -x -20
We can factor this into (x+4)(x-5)
That means x can be either -4 or 5.
Find the value of y using these values of x in both original equations:
For x = -4
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(-4)+(-4)^2 +10
y = -44 + 16 + 10
y = -18 The point both lines meet is at (-4, -18) which was already given in the problem.
For x = 5
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(5) + (5)^2 + 10
y = 55 + 25 + 10
y = 90
The second point both lines meet is (5,90).
We should use both solutions in the second equation to verify these values, but I'll graph them, instead. See the attached graph to prove these points are correct.
Which of the expressions are equivalent to the one below? Check all that
apply.
(14+4) 6
A. 14 (4+ 6)
B. (14+6) + 4
C. (4+6) (14+6)
D. (4+14) ÷ 6
Answer:
none of them match
Step-by-step explanation:
maybe something is typed wrong. the answer I got for the equation was 108 and none of them match
If the set U = {all positive integers} and set A = {x|x ∈ U and x is an odd positive integer}, which describes the complement of set A, Ac?
Ac = {x|x ∈ U and is a negative integer}
Ac = {x|x ∈ U and is zero}
Ac = {x|x ∈ U and is not an integer}
Ac = {x|x ∈ U and is an even positive integer}
Answer: Choice D) set of even integers
=======================================================
Explanation:
U = universal set = {all positive integers} = {1, 2, 3, 4, 5, ...}
A = {stuff in set U that is odd} = {1, 3, 5, 7, 9, ...}
[tex]A^c[/tex] = {stuff in set U but NOT from set A} = {2, 4, 6, 8, ...}
[tex]A^c[/tex] = {set of even numbers from set U}
In set theory, the complement is simply the complete opposite. If the number 7 is found in set A for instance, then 7 is not going to live in the complement [tex]A^c[/tex]
The opposite of the odd numbers is the set of even numbers.
Therefore, we go for choice D as our final answer.
Side note: if we union set A with its complement [tex]A^c[/tex] then we get the universal set as a result. [tex]A \cup A^c = \text{universal set} = \text{set of all positive integers}[/tex]
The solution is Option D.
Ac = {x|x ∈ U and is an even positive integer} where Ac represents the complement of set A
What is union and intersection of sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set U be = {all positive integers}
So , the values of set U = { 1 , 2 , 3 , 4 , 5 .. }
And , let the set A = {x|x ∈ U and x is an odd positive integer}
So , the value of set A = { 1 , 3 , 5 , 7 , ... }
And , the complement of set A is Ac
The value of set Ac is all the even positive odd integers
So , the value of set Ac = { 2 , 4 , 6 , 8 .. }
Therefore , the value of set Ac = { 2 , 4 , 6 , 8 .. }
Hence , the set Ac = {x|x ∈ U and is an even positive integer}
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A rectangular prism has a length of 8 in., a width of 4 in., and a height of 2 1/4 in.
The prism is filled with cubes that have edge lengths of 14 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
To fill the rectangular prism,
cubes are needed.
The number of cubes needed to fill the rectangular prism 4608 cubes.
How to find volume of rectangular prism and cube?volume of rectangular prism = lwh
where
l =lengthw = widthh = heightTherefore,
volume of the rectangular prism = 8 × 4 × 9 / 4 = 72 inches³
volume of the cube = l³
where
l = lengthTherefore,
volume = (1 / 4)³
volume of the cube = 1 / 64 inches³
Therefore,
The number of cubes needed to fill the rectangular prism = 72 ÷ 1 / 64
The number of cubes needed to fill the rectangular prism = 72 × 64 = 4608
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Which of the following sets of data will have the smallest Standard Deviation?
1, 6, 2, 100, 4, 0, 0, 0, 0, 1
3, 33, 103, 4, 122, 1, 0, 245, 7, 99
1, 2, 3, 4, 5, 6, 7, 8, 8, 9
79, 79, 79, 79, 79, 79, 79, 79, 79, 79
Answer:
Step-by-step explanation:
The last one: 79, 79, 79, 79, 79, 79, 79, 79, 79, 79 because there isn't any difference in the numbers.
S.D.: 0
ap:3, 2, 1....
what is its coomon difference
Answer:
-1
Step-by-step explanation:
3-1=2
2-1=1
Please Help
What does the missing angle in the triangle measure?
Answer:
x = 60
Step-by-step explanation:
The sum of the angles of a triangle is 180
95+25 +x = 180
120 +x = 180
Subtract 120 from each side
120+x-120 = 180-120
x = 60
Identify angles with terminology
I need help I’ve been stuck for hours
Nadine had 20 minutes to do a three-problem quiz. She spent 10 7/10 minutes on question A and 6 2/5 minutes on question B. How much time did she have left for question C?
Hi, could you help me with this substitution question?
I'd really appreciate if you added workings out as I'm terribly confused.
Thanks,
Answer:
[tex]-\dfrac{69}{14}[/tex]
Step-by-step explanation:
Substitute the given values of the variables into the given expression:
[tex]\implies \dfrac{60 \left(\dfrac{1}{3}\right)\left(-\dfrac{1}{5}\right)\left(\dfrac{1}{4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]
When multiplying fractions, simply multiply the numerators and the denominators:
[tex]\implies \dfrac{60 \left(\dfrac{1 \cdot -1 \cdot 1}{3\cdot 5 \cdot 4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]
[tex]\implies \dfrac{60 \left(-\dfrac{1}{60}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]
[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]
When adding or subtracting fractions, make the denominators the same:
[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20}{60}-\dfrac{12}{60}+\dfrac{15}{60}\right)}{\left(\dfrac{5}{15}-\dfrac{3}{15}\right)\left(\dfrac{4}{12}+\dfrac{3}{12}\right)}[/tex]
Now add the numerators and put that over the denominator:
[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20-12+15}{60}\right)}{\left(\dfrac{5-3}{15}\right)\left(\dfrac{4+3}{12}\right)}[/tex]
[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{23}{60}\right)}{\left(\dfrac{2}{15}\right)\left(\dfrac{7}{12}\right)}[/tex]
Again, multiply the fractions:
[tex]\implies \dfrac{\left(-1 \cdot \dfrac{23}{60}\right)}{\left(\dfrac{2 \cdot 7}{15 \cdot 12}\right)}[/tex]
[tex]\implies \dfrac{-\dfrac{23}{60}}{\dfrac{14}{180}}[/tex]
To divide the fractions, turn the second fraction upside down, then multiply it by the first fraction:
[tex]\implies -\dfrac{23}{60} \cdot \dfrac{180}{14}[/tex]
[tex]\implies -\dfrac{4140}{840}[/tex]
Finally, simplify:
[tex]\implies -\dfrac{4140 \div 60}{840 \div 60}[/tex]
[tex]\implies -\dfrac{69}{14}[/tex]
A short sale is when a house is sold _____.
Select the best answer from the choices provided.
A.
for less than what a person paid for it
B.
for less than the mortgage owed on it
C.
before the mortgage is paid out in full
D.
because the owner is in bankruptcy proceedings
a short sale is when a house is sold for less than what the mortgage is.
answer: B. for less than the mortgage owed on it
The diagonals of a rhombus are: A. are the same length and intersect at different angles B. bisect each other at right angles C. bisect each other and intersect at different angles D. are the same length and intersect at a right angle
Answer:
Step-by-step explanation:
Comment
Either you know the answer to this or you don't. There is no point in eliminating the wrong answers until you get to the right one. It is better to get to the right one immediately.
A rhombus and its diagonals have many interesting properties. This one is one of those properties. The diagonals are not the same length. The diagonals bisect each other at right angles.
Answer: B
Find the area of the rectangle
Answer:
Option A = 1*3 = 3 unit²[tex]area \: of \: rectangle \: = length \: \times breath[/tex]
[tex]length \: = distance \: between \: f \: and \: g \: or \: between \: e \: and \: h \: [/tex]
Distance between f and G = distance between E and HF = (3,7)
G = (6,4)
H = (5,3)
E= (2,6)
= (3 units)
Distance between FE = GH= 1 units
Area = 3* 1
= 3 units²
3. Error Analysis A classmate began an indirect
proof as shown below. Explain and correct
your classmate's error.
Given: AABC
Prove: LA is obtuse.
Assume temporarily that LA is acute.
could i get help with this equation?
Answer:
10
Step-by-step explanation:
use PEMDAS
PEMDAS order is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
2[32 — (4 − 1)³] =
2[32 — (3)³] =
2[32 — 27] =
2[5] =
10
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