Answers
The complete table of the algae area is:
Day 1 2 3 4 5 6
Area 1/2 1 2 4 8 16
What is meant by an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
The initial area exists given as;
A(1) = 1/2 square meters
When it doubles every day, we have:
A(n) = 2 × A(n - 1) where A(1) = 2
So, we contain the following values
A(2) = 1/2 × 2 = 1
A(3) = 1 × 2 = 2
A(4) = 2 × 2 = 4
A(5) = 4 × 2 = 8
A(6) = 8 × 2 = 16
Therefore, the complete table is:
Day 1 2 3 4 5 6
Area 1/2 1 2 4 8 16
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Related Questions
In how many ways can 3person study groups beselected from a class of 25students?Note: nrn!r!(n-r)!nEnter
Answers
Answer:
2,300
Explanation:
This is given as:
[tex]\begin{gathered} 25\text{ combination 3 represented as:} \\ ^nC_r=\frac{n!}{r!(n-r)!} \\ n=25 \\ r=3 \\ ^{25}C_3=\frac{25!}{3!(25-3)!} \\ ^{25}C_3=\frac{25\times24\times23\times22!}{3!\times22!} \\ ^{25}C_3=\frac{25\times24\times23}{3\times2\times1} \\ ^{25}C_3=2300 \end{gathered}[/tex]Therefore, there are 2,300 ways that 3 persons can be selected from 25 people
simplify (3^-2)^4 A 1/3^2B 3^2C 1/3^8D 3^8
Answers
Ok, so
We're going to simplify the following expression:
[tex](3^{-2})^4[/tex]Remember that if we have two exponents elevating each other in the same base, they multiply.
So, this is equivalent to write:
[tex](3^{-2})^4=(3)^{-8}[/tex]Now, we can rewrite the last expression in this new one:
[tex](3^{-2})^4=(3)^{-8}=\frac{1}{3^8}[/tex]R= {y | y is an integer and -5 ≤ y ≤ -4}
Answers
The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.
The set is
R= {y | y is an integer and -5 ≤ y ≤ -4}
An integer is a combination of number zero, all the positive numbers and negative numbers without any fraction.
Any set that does not contains any numbers or elements is called null set, which is also called empty set or void set. Null set can be denoted as {} or ∅.
The set is R= {y | y is an integer and -5 ≤ y ≤ -4}
There is no integers between -5 and -4, therefore it is a null set
Hence, The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.
The complete question is :
Write the set in roaster form R= {y | y is an integer and -5 ≤ y ≤ -4}
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HELP ME!!!!!
One interior angle of a triangle is 95.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
42.25°
47.75°
84.5°
90°
Answers
The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25° so option (A) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
Let's suppose the two congruent interior angles are x degrees.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠x+ m∠x + 95.5° = 180°
2m∠x = 180° - 95.5°
m∠x = 84.5/2 = 42.25°
Hence "The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25°".
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This graph shows the solutions to the inequalities y> 3x-2 and y<?x-10Does the system of inequalities have solutions? If so, which region containsthe solutions?108A84210-88441022 488BPopс-10A. There is a solution, and it is shown by region A.B. There is a solution, and it is shown by region C.C. There is no solution.D. There is a solution, and it is shown by region B.
Answers
there is no solution (option C)
Explanation:Given:
y > 3/2x - 2
y < 3/2x - 10
To find:
The solution to both graphs
To determine the solution of the graphs, we will consider their slopes
[tex]\begin{gathered} y\text{ > }\frac{3}{2}x\text{ - 2} \\ comparing\text{ with y = mx + b} \\ m\text{ = slope, b = y-intercept} \\ from\text{ the above, the slope = 3/2} \end{gathered}[/tex][tex]\begin{gathered} y\text{ < }\frac{3}{2}x\text{ - 10} \\ the\text{ slope = 3/2} \end{gathered}[/tex]The slope of both inequalities is 3/2. If the slopes of two lines are the same, the lines are said to be parallel. This means both inequalities are parallel lines
For parallel lines, there is no solution because the lines do not intersect (meet).
Since both inequalities give parallel lines, there will be no solution (option C)
Is (x+1) a factor of -2x^5-4x^4+x-10?
Answers
Notice that:
[tex]-2x^5-4x^4+x-10,[/tex]cannot be expressed as a product of factors, meaning that
[tex](x+1),[/tex]is not a factor of the given polynomial.
Answer: Not a factor.
(05.05 MC)A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete thetable to analyze the data and answer the questions:Likes hamburgersboes not like hamburgers TotalLikes burritos41Does not like burritos54135Total110205Part A: What percentage of the survey respondents do not like both hamburgers and burritos? (2 points)Part & What is the marginal relative frequency of all customers that like hamburgers? (3 points)Part C Use the conditional relative frequencies to determine which data point has strongest association of its two factors. Use completesentences to explain your answer. (5 points)
Answers
EXPLANATION:
Given;
We are given a frequency table which displays a survey of numbers of customers that like hamburgers and burritos and those that do not like hamburgers and burritos.
Required;
We are required to analyze the table and use the values to answer the questions that follow.
Solution;
We shall begin by completing the table as follows;
Part A:
What percentage of the survey respondents do not like both burritos and hamburgers?
The percentage that do not like hamburgers is
[tex]Does\text{ }not\text{ }like\text{ }hamburgers=\frac{95}{205}[/tex]The percentage that do not like burritos is
[tex]Does\text{ }not\text{ }like\text{ }burritos=\frac{135}{205}[/tex]The percentage that does not like both burritos and hamburgers is;
[tex]\frac{54}{205}=0.263414634146[/tex]Expressed as a percentage, this is
[tex]\begin{gathered} Percentage=0.263414634146\times100 \\ \\ Percentage=26.3414634146 \\ \\ Percentage=26.34\%\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }hundredth) \end{gathered}[/tex]The marginal relative frequency of all customers that like hamburgers is the total of all hamburger lovers divided by the total of all respondents.
[tex]\begin{gathered} Marginal\text{ }relative\text{ }frequency=\frac{hamburger\text{ }lovers}{total\text{ }respondents}=\frac{110}{205} \\ \\ Marginal\text{ }relative\text{ }frequency=0.536585365854 \\ \\ Marginal\text{ }relative\text{ }frequency=53.66\%\text{ }(rounded\text{ }to\text{ }2\text{ }decimal\text{ }places) \end{gathered}[/tex]ANSWER:
Part (a) 26.34%
Part (b) 53.66%
If f(x) = x² + 5 and g(x) = 3x, find (f o g)(x) and (g o f)(x) .
Answers
Answer:
[tex](f \circ g)(x) = 9x^2 + 5\\\\\\(g \circ f)(x) = 3x^2 + 15[/tex]
Step-by-step explanation:
We are given
[tex]f(x) = x^2+5\\\\g(x) = 3x\\\\(f\circ g)(x) = f(g(x))\\\\[/tex]
To find this, wherever you see an x in f(x) substitute the expression in g(x)
[tex](f\circ g)(x) = f(g(x))\\\\= f(3x)\\\\= (3x)^2 + 5\\\\=9x^2 + 5\\\\\\[/tex]
To find [tex](g \circ f)(x) = g(f(x))\\\\[/tex]
Wherever there is an x in the expression for g(x) substitute that x with the expression in f(x)
[tex](g \circ f)(x) = g(f(x))\\\\\\= g(x^2 + 5) = 3(x^2 + 5) \\\\= 3x^2 + 15[/tex]
find the percent of change. Round to the nearest whole percent original:26 new:30
Answers
We want to find the percentage change;
We can do that using the formula;
[tex]\text{ \%P}=\frac{New-Original}{\text{Original}}\times100\text{\%}[/tex]Given:
[tex]\begin{gathered} \text{Original = 26} \\ \text{New = 30} \end{gathered}[/tex]Substituting the given values;
[tex]undefined[/tex]Select the postulate that is illustrated for the real numbers.
25 + 0 = 25
A The commutative postulate for multiplication
B The multiplication inverse
C The addition inverse postulate
D Commutative postulate for addition
E The distributive postulate
F Additive identity
G Multiplication by one
Answers
Answer:
Additive Identity
Step-by-step explanation:
Hello!
Adding 0 to any number will give you that number itself, as proven by adding 0 to 25, which gave us 25.
This is the identity property of addition, as the output would be identical to the sum of the non-zero terms.
We can also experiment with these:
21 + 4 + 0 = 21 + 4 = 257(3 + 0) = 7(3) = 21A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is less than 5.
Event B: The number rolled is even.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event "A or B": {0}
(b) Event "A and B": {0}
(c) The complement of the event A
Answers
According to the solving the probability are as follows:
a) Event "A or B": {1, 2, 3, 4, 6}
(b) Event "A and B": {2, 4}
(c) The complement of the event A: {5, 6}
Define the experiment's sample space and event:The term "sample space" refers to a collection of probable results from a random experiment. The letter "S" indicates that this is the sample space. Events are a subset of what might happen in an experiment. Depending on the experiment, the outcomes in a sample area could change. In discrete or finite sample spaces, there are only a finite number of possible outcomes.
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
According to the given data:the sample space is, 1, 2, 3, 4, 5, 6 i.e., U = {1, 2, 3, 4, 5, 6}
Event A: The number rolled is less than 5
i.e., A = {1, 2, 3, 4}
Event B: The number rolled is even
i.e., B = {2, 4, 6}
Event A Or B A∪B = {1, 2, 3, 4} ∪ {2, 4, 6}
= {1, 2, 3, 4, 6}
Event "A and B"A∩B = {1, 2, 3, 4} ∩ {2, 4, 6}
= {2, 4}
Compliment of the event A
Comp(A) = U/ A = {1, 2, 3, 4, 5, 6} / {1, 2, 3, 4}
= {5, 6}
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i need tutor answer this two quedtion thabks you so much
Answers
5. Let the following inequality:
[tex]13-3m\text{ }<-2[/tex]this is equivalent to:
[tex]-13+3m\text{ }>2[/tex]this is equivalent to:
[tex]-13+13+3m\text{ }>2\text{ +13}[/tex]this is equivalent to:
[tex]3m\text{ }>15[/tex]solve for m:
[tex]m\text{ }>\frac{15}{3}=5[/tex]that is :
[tex]m\text{ }>5[/tex]6. Because of the graphic (real line), we can conclude that the correct interval would be:
[tex](-\infty,-3\rbrack\text{ = x}\leq-3[/tex]Then we have to find the inequalities that have this solution interval.
a) Let the inequality
[tex]\frac{x}{3}+2\leq1[/tex]this is equivalent to:
[tex]\frac{x}{3}+2-2\leq1-2[/tex]this is equivalent to:
[tex]\frac{x}{3}\leq-1[/tex]solve for x:
[tex]x\leq-3[/tex]then. A) represent the graph.
b)Let the inequality
[tex]8-5x\ge23[/tex]
this is equivalent to:
[tex]-8+5x\leq-23[/tex]this is equivalent to:
[tex]-8+8+5x\leq-23+8[/tex]this is equivalent to:
[tex]5x\leq-15[/tex]solve for x:
[tex]x\leq\frac{-15}{5}\text{ = -3}[/tex]then the solution interval would be:
[tex]x\leq\text{-3}[/tex]then. B) represent the graph.
c) Let the inequality:
[tex]-18\ge3+7x[/tex]this is equivalent to:
[tex]-18+18\ge3+18+7x[/tex]this is equivalent to:
[tex]0\ge21+7x[/tex]this is equivalent to:
[tex]-21\ge7x[/tex]solve for x:
[tex]x\text{ }\leq\frac{-21}{7}\text{ = -3}[/tex]that is:
[tex]x\text{ }\leq\text{-3}[/tex]then. C) represent the graph.
d) Let the inequality:
[tex]7x-3\leq18[/tex]this is equivalent to:
[tex]7x-3+3\leq18+3[/tex]this is equivalent to:
[tex]7x\leq21[/tex]solve for x:
[tex]x\leq3[/tex]We can conclude that this interval does not represent the graph because:
[tex]x\leq3\text{ }\ne\text{ }x\leq-3\text{ }[/tex]Finally:
e) Let the inequality:
[tex]1-\frac{x}{2}\text{ }\leq2\text{ +}\frac{1}{2}[/tex]this is equivalent to:
[tex]-1+\frac{x}{2}\text{ }\ge-2\text{ -}\frac{1}{2}[/tex]this is equivalent to
[tex]-2+x\text{ }\ge-4\text{ -}1[/tex]that is:
[tex]x\text{ }\ge-4\text{ -}1+2[/tex]that is:
[tex]x\text{ }\ge-3[/tex]THEN WE CAN CONCLUDE THAT THE CORRECT ANSWER ARE:
A), B), C) AND E)
Solve the compound inequality -8≤x+4<5
Answers
Answer:
-12≤x<1
Step-by-step explanation:minus both side by 4
Triangle ABC is dilated by a scale factor of 4 to form triangle A’B’C
The coordinates of Vertex A’ are
The Coordinates of Vertex B’ are
The coordinates of Vertex C’ are
PLS HELP!!
Answers
The coordinates of vertex B is -3,3
The coordinates of vertex C is -1,3
my apologies if im incorrect but i think this the answer.
Which set of measurement could be the interior angle measures of triangle.A. 10°, 10°, 160°B. 15°, 75°, 90°C. 20°, 80°, 100°D. 35°, 35°, 105°E. 60°, 60°,60°
Answers
The sum of the interior angles of a triangle must add 180°.
C : 20 + 80 + 100 = 200 NO
D : 35+35+105 = 175 NO
A : 10+ 10+160 = 180 Yes
B : 15 +75 + 90 = 180 Yes
E :60+60+60 = 180 Yes
Type the correct answer in each box.If matrix C represents (A − B) + A, the value of the entry represented by c41 is and the corresponding entry in (A + B) − A is .
Answers
Given the matrices A and B:
[tex]\begin{gathered} A=\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix} \\ \\ B=\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \end{gathered}[/tex]We know that:
[tex]C=(A-B)+A=2A-B[/tex]Then, using the matrices A and B:
[tex]\begin{gathered} C=2\cdot\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \\ \\ C=\begin{bmatrix}{-10} & {6} & {16} & {} \\ 6 & {12} & {-10} & {} \\ 10 & {-18} & {0} & {} \\ 14 & 6 & 8 & {}\end{bmatrix}+\begin{bmatrix}{7} & {8} & {5} & {} \\ -{7} & -{9} & -{2} & {} \\ -{2} & {-5} & {7} & {} \\ {-2} & -{8} & {7} & {}\end{bmatrix} \\ \\ \therefore C=\begin{bmatrix}{-3} & 14 & 21 & {} \\ -1 & {3} & {-12} & {} \\ 8 & {-23} & 7 & {} \\ 12 & -2 & 15 & {}\end{bmatrix} \end{gathered}[/tex]And the element C₄₁ (fourth row and first column) is:
[tex]C_{41}=12[/tex]Now, for the matrix (A + B) - A = B:
[tex]B_{41}=2[/tex]Part A answer and explanation pls
Answers
Answer:
[tex]\frac{3}{13}[/tex]
Step-by-step explanation:
the fraction is formed by the number who prefer historical movies to the total preferring all movies.
total = 24 + 18 + 6 + 30 = 78
number preferring historical movies = 18
then fraction preferring historical movies is
[tex]\frac{18}{78}[/tex] ( divide numerator/ denominator by 6 )
= [tex]\frac{3}{13}[/tex] ← in simplest form
Answer:
From the Graph the total number of students who preferred historical movies = 18.
Similarly total number of students = 24+18+6+30
= 78
Fraction of student who prefer Historical movies = 18/78
= 3/13.
Solve for x. Then find m
(8x+4)°
(10x-6)°
Both lines are intersecting and the two equations are vertical pairs
Answers
For the vertical angles, the value of x is found as 5. The measure of the angle ∠QRT = 44° for the two intersecting lines.
What is referred as the vertical angles?When two lines intersect at a point, vertical angles are formed. They are always on equal footing. In other words, four angles are formed anytime two lines pass or intersect. We can see that two opposite angles are equal, and these are referred to as vertical angles.For the given pair of angles in the question.
Two lines are intersecting to form two equations are vertical pairs.
∠QRT = ∠VRS (vertical angles)
Put the values.
8x + 4 = 10x - 6
Simplifying.
2x = 10
x = 5
Put the values of 'x' in the angle.
∠QRT = 8x + 4
∠QRT = 8×5 + 4
∠QRT = 44
Thus, the measure of the angles ∠QRT is found as 44°.
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There are 100 centimeters in a meter .63 centimeters is what fraction of a mater?
Answers
Since 1 meter = 100 cm
Then to change from cm to meter, divide by 100
Since there is 63 cm, then divide it by 100
[tex]\frac{63}{100}[/tex]The fraction of a meter is 63/100
which expression is equivalent to [tex] \sqrt{15} \times \sqrt{12} [/tex]
Answers
Consider that √15 and √12 can be written as follow:
√15 = √(3*5)
√12 = √(3*4)
Moreover, √15*√12 = √(15*12). Then, you can write:
√(15*12) = √(3*5*3*4) = √(3^2*2^2*5) = 3*2√5 = 6√5
Hence, the equivalent expression is 6√5
Find the value of x.1714X = 93x = 93x= 3x = 485
Answers
Given a right angle triangle:
The hypotenuse of the triangle = 17
The legs of the triangle are the sides 14 and x
We will find x using the Pythagorean theorem as follows:
[tex]x^2+14^2=17^2[/tex]Solve for x:
[tex]\begin{gathered} x^2=17^2-14^2=93 \\ \\ x=\sqrt[]{93} \end{gathered}[/tex]So, the answer is the first option
[tex]x=\sqrt[]{93}[/tex]How do I simplify radicals in simplest radical form?
Answers
Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots e.t.c
Examples of radicals are
[tex]\sqrt[]{4},\sqrt[2]{8},\sqrt[3]{16}[/tex]For exmaple,
Given the radical
[tex]\sqrt[]{12}[/tex]To simplify into the simplest radical,
Factorize the perfect square
[tex]\sqrt[]{12}=\sqrt[]{4\times3}[/tex]Then we take out the pairs
[tex]\begin{gathered} \sqrt[]{12}=\sqrt[]{4}\times\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2\times2}\times\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2^2}\times\sqrt[]{3} \end{gathered}[/tex]Simplify the result
[tex]\begin{gathered} \text{Where} \\ \sqrt[]{2^2}=2 \\ \sqrt[]{12}=2\times\sqrt[]{3} \\ \sqrt[]{12}=2\sqrt[]{3} \end{gathered}[/tex]Hence, the simplified radical of the example used is
[tex]\sqrt[]{12}=2\sqrt[]{3}[/tex]3.)The area of a regular polygon is 145.8 sq. cm. If the perimeter of this polygon is 108 cm,find the length of the apothem.
Answers
The area of the regular polygon is a= 145.8 sq.cm
Perimeter of the polygon is p=108 cm.
Let apothem length be a
We know,
a=p x a/2
Putting the values,
145.8=108xa/2
a=2.7 cm
The length of the apothem is 2.7 cm
Given the following table of values for f(x), find f(0).
x −3 −1 0 3 6 9
f(x) 1 8 1 0 13 −3
Answers
The value of the function at x = 0 will be 1.
What is a function?
A statement, principle, or rule that creates a relationship between two variables is known as a function. Functions are abundant in mathematics and are required for the creation of complex relationships.
When the required parameters and natural laws are given values, the expression yields the calculation result that the mathematical model represents.
The table represents a function.
x f(x)
-3 1
-1 8
0 1
3 0
6 13
9 -3
In the above table, we can see that at the value of x = 0 in the function the value of the whole function is 1.
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As assistant manager of a soccer specialty store you have been asked to review the inventory costs associated with the store's best selling soccer shoe. The information you have available concerning this shoe follows: Average Demand =18 pairs per week; Standard Deviation of demand = 6 pairs Lead time for ordering shoes= 1 week; Ordering cost = $32 per order Cost of a pair = $90; Carrying cost per pair per year = 10% of cost of per pair Service level =98%, Z =2.05; The store operates 50 weeks per year.
Answers
The annual demand when the manager reviews the stock is 900 units.
What is the annual demand?Mean demand, d = 18 units per week
Standard deviation of weekly demand, σd = 6 units per week
Lead Time, LT = 1 week
Order Cost, S = $32 per order
Unit Cost, C = $90 per unit
Holding Cost, H = 10% of C = $9 per unit per year
Service level, SL = 98%
z score = NORMSINV(SL) = NORMSINV(98%) = 2.05
Operating weeks = 50 weeks per year
The annual Demand, D will be:
= 50*18
= 900 units
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An invester invested a total of 3,300 in two mutual funds. One fund earned a 5% profit while the other earned a 2% profit. If the investor's total profit was $126, how much was invested in each mutual fund?
Answers
Given
Total investment of $3,300
5% profit and 2% profit totaling $126
[tex]\begin{gathered} \text{Let} \\ x\text{ be the investment on 5\% profit} \\ y\text{ be the investment on 2\% profit} \end{gathered}[/tex]The equations therefore will be
[tex]\begin{gathered} x+y=3300\text{ based on the total amount of investment} \\ 0.05x+0.02y=126\text{ based on the investor's total profit} \end{gathered}[/tex]Use substitution method using the first equation
[tex]\begin{gathered} x+y=3300 \\ y=3300-x \\ \\ \text{Substitute }y\text{ to the second equation} \\ 0.05x-0.02y=126 \\ 0.05x-0.02(3300-x)=126 \\ 0.05x-66-0.02x=126 \\ 0.05x-0.02x=126-66 \\ 0.03x=60 \\ \frac{0.03x}{0.03}=\frac{60}{0.03} \\ \frac{\cancel{0.03}x}{\cancel{0.03}}=\frac{60}{0.03} \\ x=2000 \end{gathered}[/tex]Now that we have solve for x, substitute it to the first equation to get the value of y
[tex]\begin{gathered} x+y=3300 \\ 2000+y=3300 \\ y=3300-2000 \\ y=1300 \end{gathered}[/tex]Therefore, the amount invested in mutual fund that earned 5% was $2000, and the amount invested that earned 2% was $1300.
Solve 1/3x + 4/9 = 7/9
Answers
We want to solve
[tex]\frac{1}{3}x+\frac{4}{9}=\frac{7}{9}[/tex]We can subtract 4/9 on both sides.
[tex]\begin{gathered} \frac{1}{3}x+\frac{4}{9}-\frac{4}{9}=\frac{7}{9}-\frac{4}{9} \\ \\ \frac{1}{3}x=\frac{7}{9}-\frac{4}{9} \\ \\ \frac{1}{3}x=\frac{7-4}{9} \\ \\ \frac{1}{3}x=\frac{3}{9} \end{gathered}[/tex]Now we have 3/9 on the right side, but we can simplify that fraction to 1/3
[tex]\begin{gathered} \frac{1}{3}x=\frac{3}{9} \\ \\ \frac{1}{3}x=\frac{1}{3} \end{gathered}[/tex]And now we have the result!
[tex]x=1[/tex]Therefore the final result is x = 1
A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 32 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t)=-16t²2 +32t+5.
How long will it take the rocket to reach its maximum height? What is the maximum height?
Answers
It takes the rocket to reach its maximum height h max = 17(ft).
The object's maximum height is the highest vertical position along its trajectory.How to find a maximum height?The object's maximum height is the highest vertical position along its trajectory. Before reaching the highest point, the object is flying upwards and then falls. It means that the vertical velocity is equal to 0 at the highest point of projectile motion (v y = 0 v y = 0 v_y=0).So, h(t) = -16+ 32t+5:
t max = time for maximum heightt max = 32 / 2*(-16)= 32 / 32 = 1h max = the maximum height above the groundh max = h(1) = -16() + 32*1 +5-16+32+5 = -16+ 37 = 21Then, h max rocket = the maximum height of the toy rocket
h max rocket = 21 -5 = 17(ft)t max = 1 secondh max = 17(ft)Therefore, it takes the rocket to reach its maximum height h max = 17(ft)
The object's maximum height is the highest vertical position along its trajectory.To learn more about maximum height, refer to:
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When Ross solved the equation 12 = 3x, he made a mistake. Hiswork is shown below. What mistake did Ross make?3x = 123x - 3= 12-3x=9
Answers
The mistake Ross has made was in line 2, and it is that we can only combine like terms, that is, terms that have the same variable at the same power. So
[tex]3x-3\ne x,[/tex]We cannot performe this operation.
John and Ariana bought school supplies. John spent $10.30 on 5 notebooks and 7 pens. Ariana spent $7.20 on 4 notebooks and 4 pens. What is the cost of 1
notebook and what is the cost of 1 pen?
Answers
Answer:
$ 0.75 for one pen
$1.05 per notebook
Step-by-step explanation:
John and Ariana bought school supplies. John spent $10.30 on 5 notebooks and 7 pens. Ariana spent $7.20 on 4 notebooks and 4 pens. What is the cost of 1 notebook and what is the cost of 1 pen?
John: 5n + 7p = 10.5
let's solve for n:
5n + 7p = 10.5
subtract 7p from both sides:
5n + 7p -7p = 10.5 - 7p
5n = 10.5 - 7p
divide both sides by 5:
5n/5 = (10.5 - 7p)/5
n = 2.1 - 7/5 p
Ariana: 4n + 4p = 7.20
Let's substitute in: n = 2.1 - 7/5 p
4n + 4p = 7.20
4(2.1 - 7/5p) + 4p = 7.20
multiply left side:
8.4 - 5.6p + 4p = 7.2
subtract 8.4 from both sides:
8.4 - 5.6p + 4p - 8.4 = 7.2 - 8.4
- 5.6p + 4p = -1.2
combine p terms on left side:
-1.6p = -1.2
divide both sides by -1.6:
-1.6p/(-1.6) = -1.2/(-1.6)
p = 0.75 cents for one pen
Now solve to find the price of a notebook:
4n + 4p = 7.20 when p = 0.75
4n + 4(0.75) = 7.20
4n + 3 = 7.20
subtract 3 from both sides:
4n + 3 - 3 = 7.20 - 3
4n = 4.2
divide both sides by 4:
4n/4 = 4.2/4
n = 1.05 per notebook
CHECK: when n = 1,05 and p = 0.75
John: 5n + 7p = 10.5
5(1.05) + 7(0.75) = 10.5
10.5 = 10.5
Ariana: 4n + 4p = 7.20
4n + 4p = 7.20
4(1.05) + 4(0.75) = 7.20
7.2 = 7.2
Answer assumes no additional sales tax.