The tires can be arranged in 24 ways. Computed using permutation.
The permutation is a way of selecting a smaller set from a larger set when the order of selection is not of concern.
For selecting r number of items, from n number of items, with the order of selection not being a concern, we can calculate the number of ways using permutation:
nPr = n!/(n - r)!.
In the question, we are asked the number of ways in which the four tires can be arranged on a car.
As we need to select 4 tires, from 4 tires, with any order, we will use permutation.
Thus, the number of ways can be calculated as 4P4, which can be calculated using the formula, nPr = n!/(n - r)!.
Thus, 4P4 = 4!/(4 - 4)! = 4!/0! = 24/1 = 24.
Thus, the tires can be arranged in 24 ways. Computed using permutation.
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Identify the method that will be used to solve for x: 5x + 6x = 22
The method that will be used in solving for x in the expression 5x + 6x = 22 is simplifying using addition and division operation
solving the equation gives x to be equal to 2
How to solve for the expressionThe expression given 5x + 6x = 22 is a linear function having one unknown variable and the solution is sought by using the relevant mathematical operations
Applying addition operation in solving for x
5x + 6x = 22
11x = 22
Applying division operation in solving for x
11x = 22
x = 2
hence, the solution of the the expression is x = 2
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In the diagram below, PQ is parallel to MN. If PQ is 2 more than MP,
PO = 12, and MN = 12, find the length of MP. Figures are not necessarily
drawn to scale. State your answer in simplest radical form, if necessary.
Therefore , the solution to the given problem of triangle comes out to be the length MP is measured at 6 units.
Explain the triangle.Due to its three vertices and three sections, a component is a polygon. It has a simple geometric form. Triangle ABC refers to a triangle only with points A, B, and C. When components are not collinear, a singular plane and triangle are found. Triangles are regarded as polygons since they have three corners and a right side. The points where a triangle's three sides intersect are known as the triangle's corners. By compounding three triangle angles, one gets 180 degrees.
Here,
Triangle OMN is provided.
Now, OMN and OPQ are comparable. It follows that the side lengths are in proportion to one another. We can write:
=>OP = OM = PQ = MN
=>OM = PQ/MN in 12
=>(OP + PM)/12 = PQ/MN
Considering that -
=>PQ = MP + 2
=>12/(OP plus PM) = (MP plus 2)/MN
=>12MN equals (MP + 2)(OP + PM).
=>12 × 12 = (MP + 2)(MP + 12)
=>2 MP plus 12 MP plus 2 MP plus 24 = 144
=>(MP)² + 14(MP) - 120 = 0
We can write - if MP = x.
=>x² + 14x - 120 = 0
=>(x + 20)(x - 6) = 0
=>(x + 20) = 0 and (x - 6) = 0
x = - 20 and x = 6
There can be no negative lengths, hence x = 6
Consequently, the length MP is measured at 6 units.
Therefore , the solution to the given problem of triangle comes out to be the length MP is measured at 6 units.
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The table and the graph each show a different relationship between the same two variables, x and y:
X
3
4
5
6
100
110
190
Y
200
270
360
450
540
How much more would the value of y be in the table, than its value on the graph, when x = 11? (1 point)
800
640
480
320
160
0
246810
The value of y in the table would be greater than the value on the graph, when x = 11 by: B. 110.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the points.For the table, an equation which represent its data points is given by:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 270 = (360 - 270)/(4 - 3)(x - 3)
y = 90(x - 3) + 270
y = 90x - 270 + 270
y = 90x.
When x = 11, the value of y is given by:
y = 90(11)
y = 990.
For the graph, an equation which represent its data points is given by:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 160 = (320 - 160)/(4 - 2)(x - 2)
y = 80(x - 2) + 160
y = 80x - 160 + 160
y = 80x.
When x = 11, the value of y is given by:
y = 80(11)
y = 880
Next, we would determine the difference:
Difference = 990 - 880
Difference = 110.
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Hurry i'm timed - please help
Outputs represent your y - values in coordinate.
Input represent your x - values in coordinate.
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
We know that;
A relation is said to be a function if set of inputs having one output each.
Hence, In coordinate (x, y);
All x - values represents inputs and all y - values represent outputs.
Hence, Outputs represent your y - values in coordinate.
And, Input represent your x - values in coordinate.
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A polynomial of the fourth degree has both non-real roots and real roots with multiplicities.
If two of the roots are -3 and 7 - 2i, identify this polynomial.
The polynomial is x^4 - 8x^3 - 30x^2 + 144x + 405 = 0. The solution is obtained using the concept of bi-quadratic equation.
What is bi-quadratic equation?A 4-degree equation is a bi-quadratic equation.
Sometimes the phrase "bi-quadratic equation" is used as a substitute for the phrase "quartic equation." Such problems variable are straightforward to resolve because they can be reduced to quadratic equations in the variable x=z^2, which can then be solved for x using the quadratic formula and then in terms of the original variables by calculating the square roots.
Here,
We are given two roots of the bi-quadratic equation which are -3 and 7 - 2i.
Now, we will find the other two roots of the bi-quadratic equation by using the conjugates of the given roots.
In order to find the conjugate of complex numbers, we have to change the sign of the imaginary part.
So, we will get the conjugate of 7 - 2i = 7+2i
Thus, all the four roots of the bi-quadratic equation are -3, 7+2i, 7 - 2i and -3.
If two roots of an equation are given as a and b, then we can express the equation as (x-a) (x-b) = 0.
So, using this, we will form the equation with two imaginary roots 7+2i and 7−2i, which is given as:
[x-(7−2i)][x-(7+2i)]=0
⇒[x-7+2i][x-7-2i]=0
⇒[(x-7)+2i][(x-7)−2i]=0
Using the identity (a+b)(a-b)=a^2-b^2 , we get
(x-7)^2-(2i)^2=0
∵i=√-1
⇒(x-7)^2+(√-4)^2=0
⇒(x-7)^2+(-4)=0
⇒(x-7)^2 - 4=0
Now we will form the equation with roots -3 and -3, which is
[x-(-3)][x-(-3)]=0
⇒(x+3)^2=0
Finally, we will now find the product of these two quadratic equations to get the required bi-quadratic equation
⇒[(x-7)^2 - 4] [(x+3)^2]=0
⇒[x^2 + 49 - 14x -4] [x^2 + 9 + 6x]=0
⇒[x^2 + 45 - 14x] [x^2 + 9 + 6x]=0
⇒x^4 + 9x^2 + 6x^3 + 45x^2 + 405 + 270x - 14x^3 - 126x - 84x^2 = 0
⇒x^4 - 8x^3 - 30x^2 + 144x + 405 = 0
Hence, the required polynomial is x^4 - 8x^3 - 30x^2 + 144x + 405 = 0
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Almost a billion people on the planet don't have access to clean drinking water." if there were 7.8×10^9 people in the world in 2014, then approximately what percent of them lived without clean drinking water? round to the nearest tenth of a percent.
If almost a billion people on the planet don't have access to clean drinking water. The percent of them that lived without clean drinking water is 12.82%.
How to find the Percentage of people without clean drinking water?Given data:
Total number of people = 7.8×10^9
Number of people that lived without clean water = 1 billion
Number of people that lived without clean water = 1,000,000,000 = 1 × 10^9
So,
Percentage of people without clean water= Number of people that lived without clean water / Total number of people
Percentage of people without clean water = 1 × 10^9 / 7.8×10^9 × 100
Percentage of people without clean water = 1/ 7.8 × 100
Percentage of people without clean water= 12.82%
Therefore 12.82% people lived without clean water.
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A new car is purchased for $26, 000 and over time its value depreciates by one half every 5 years. What is the value of the car 7 years after it was purchased, to the nearest hundred dollars?
Answer:
$203
Step-by-step explanation:
Please mark brainliest
The velocity v(t) of a sprinter on a straight track is shown in the graph below. 15 13 11 : 10 Determine the evaluaton of each definite integral Jot v() dt = 26 J4' v() dt = 3 6l v() dt =-10 v(t) dt = 19 You are correct: Your receipt no. is 161-2313 Previous Tries S' (t) =v(t) , then s(t) is the position of the runner at time t. Let s(0) ~2, determine the following values s(4) s(5) s(7) s(9) Submit Answer Incorrect _ Tries 2/8 Previous_ Tries
The position of the sprinter is equal to the value of definite integral of the given velocity function v(t). The position at t = 4, 7, and 9 is 8, 8, 0.
The velocity is the first derivative of the position function. The position function is given in the attached picture.
s'(t) = v(t)
The position at time t is therefore equal to the definite integral from t = 0 to time t.
Since the graph is linear, the evaluation of each definite integral is equal to the area of triangles underneath the lines.
∫₀⁴ v(t) dt = (1/2) x 2 x 6 = 6
∫₄⁷ v(t) dt = (1/2) x 1 x 8 - (1/2) x 2 x 4 = 0.
∫₇⁹ v(t) dt = 2 x (-4) = -8
The position at t = 0 is s(0) = 2
Hence,
s(4) = s(0) + ∫₀⁴ v(t) dt = 2 + 6 = 8
s(7) = s(0) + ∫₀⁴ v(t) dt + ∫₄⁷ v(t) dt = 2 + 6 + 0 = 8
s(9) = s(0) + ∫₀⁴ v(t) dt + ∫₄⁷ v(t) dt + ∫₇⁹ v(t) dt = 2 + 6 + 0 - 8 = 0
The graph in your question was missing. Most likely it was like on the attached picture.
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A number cube is tossed 60 times.
Outcome | Frequency
1 | 12
2 | 13
3 | 11
4 | 6
5 | 10
6 | 8
Determine the experimental probability of landing on a number less than 2.
A. 35 over 60
B. 25 over 60
C. 13 over 60
D. 12 over 60
Answer:
D. 12 over 60----------------------------
Total number of frequencies:
12 + 13 + 11 + 6 + 10 + 8 = 60Number of frequencies with the outcome of less than 2:
12 of 1'sProbability of a number less than 2:
Probability = favorable outcomes / total outcomesP = 12/60 = 1/5 or 20%The matching choice is D.
Answer:
[tex]\sf D. \quad \dfrac{12}{60}[/tex]
Step-by-step explanation:
Experimental probability is based on the actual results of an experiment.
Theoretical probability is based on possible outcomes based on assumptions.
Experimental probability
Calculated by dividing the number of times an event happens by the total number of trials in an actual experiment.
[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]
From inspection of the given table, the actual results (frequency) of landing on a number less than 2 is 12.
The total number of trials is 60.
Therefore:
[tex]\sf \implies P(x < 2)=\dfrac{12}{60}[/tex]
After giving the final exam, the professor found that many of his students failed the test,
so he decided to give a remedial exam. The probability that a student passes the final
exam is 0.6. Given that a student fails the final exam, the probability that the student
passes the remedial exam is 0.8. What is the probability that Jay fails the final exam and
passed the remedial exam?
The probability that Jay fails the final exam and passed the remedial exam is P(fail the final and passed the remedial) = 0.32.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
After giving the final exam, the professor found that many of his students failed the test, so he decided to give a remedial exam.
The probability that a student passes the final exam is 0.6. Given that a student fails the final exam, the probability that the student passes the remedial exam is 0.8.
We are given the following probabilities:
P(passes the final exam) = 0.6
P(fail the final exam = (1 - 0.6) = 0.4
P(passes through the remedial | failed the final) = 0.8
We have to find P(fail the final and passed the remedial).
P(fail the final and passed the remedial) = P(passes the remedial | failed the final)*P(failed the final)
P(fail the final and passed the remedial) = 0.8 x 0.4
P(fail the final and passed the remedial) = 0.32
Hence, the probability that Jay fails the final exam and passed the remedial exam is P(fail the final and passed the remedial) = 0.32.
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find the coordinate matrix of x relative to the orthonormal basis b in rn.
The coordinate matrix of x relative to an orthonormal basis b in [tex]R^n[/tex] can be found by computing the inner product of x with each basis vector and representing these inner products as the entries of a column vector.
To find the coordinate matrix of x relative to an orthonormal basis b in R^n, we need to express x as a linear combination of the basis vectors in b. This can be done by computing the inner product (dot product) of x with each basis vector and representing these inner products as the entries of a column vector. The resulting vector is the coordinate matrix of x relative to the orthonormal basis b.
For example, let x be a vector in [tex]R^n\\[/tex], b = [tex]{b_1, b_2, ..., b_n}[/tex] be an orthonormal basis in R^n, and let A be the coordinate matrix of x relative to b. Then the entries of A are given by:
A = [tex]( x, b_1 , x, b_2 , ..., x, b_n )^T[/tex] where [tex]x, b_i[/tex] denotes the inner product of x and [tex]b_i[/tex].
It is important to note that the basis b must be orthonormal for the coordinate matrix to have this form, if the basis is not orthonormal, the process will be different.
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Enter the Correct 3 Digit Code (don't forget the decimal) *
Answer:
4.85
Step-by-step explanation:
8.09-3.24+4.85
I need help in my hw ASAP, this is ki11ing me ~.~
Answer:
look back through your lessons.
Step-by-step explanation:
what do you know about this question? if you go back through your lessons, you might be able to find a way to do this equation.
The time needed to paint a fence varies directly with the length of the fence. If it takes 5 hours to paint 200 feet of the fence, how long will it take to paint 500 feet of fence?
Answer:
Step-by-step explanation:
The Answer is 12.5 because...
200/5=40
40x12.5=500
So that means 12.5x40=500
A rectangle is dilated by a scale factor of 1/2, centered about the origin.
What should the area of the pre-image be multiplied by to obtain the area of the image rectangle?
2
4
1/4
1/2
30 points
What the area of the pre-image should be multiplied by to obtain the area of the image rectangle is; 4
How to interpret the scale of dilation?The scale factor in the dilation of a mathematical object is one that determines how much larger or smaller the image will be when compared to the original image.
Now, the formula for area of a rectangle is;
A = LW
Where;
L is length
W is width
If the rectangle is dilated by a scale factor of 1/2, then it means that;
New length = ¹/₂L
New Width = ¹/₂W
New Area = ¹/₂L * ¹/₂W
= ¹/₄LW
Thus, to get the pre image are, we have;
Area of pre-image = 4 * Area of new image
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Here is a table that shows the ratio of flower to water in an art pace, complete the table with values in the equivalent ratio
The table with values in the equivalent ratio is completed as
1 : 1/2
4 : 2
6 : 3
1/2 : 1/4
What equivalent ratio?When we compare ratios, equivalent ratios are the ones that don't change. In order to determine whether or not different ratios are equivalent, we compare them side by side. An example makes it clear that the ratios 1:2 and 2:4 are equivalent. With the aid of division and multiplication, we can determine the two equivalent ratios.
In order to create a ratio that is equal to one that is already given, we must multiply or divide the given ratio's two terms by a non-zero number.
1 cup of flour = 1/2 cup of water
4 cups of flour = 1/2 × 4
= 2 cups of water
1/2 cup of flour = 1/2 × 1/2
= 1/4 cups of water
2 cups of water = 4 cups of flour
1 cup of water = 4/2
= 2 cups of flour
3 cups of water = 2 × 3
= 6 cups of flour
Thus, the table with values in the equivalent ratio is completed as 1 : 1/2, 4 : 2, 6 : 3 and 1/2 : 1/4.
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if a^1/n=r 10 which of the following are true statements
Correct options are C, D. On simplifying, a^(1/n) = r can be written as n√a = r and a = rⁿ.
The fundamental guidelines and procedures to simplify any algebraic statement are as follows:
By multiplying factors, remove any grouping symbols like brackets and parenthesis.
If the words contain exponents, use the exponent rule to eliminate grouping.
Add or subtract like terms to combine them.
Add the constants together.
Given,
a^(1/n) = r ...........(1)
It can be written as -
n√a = r
secondly,
multiplying power n on both sides of equation (1)
we get,
a = rⁿ
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Find a spot at a whiteboard and complete the following:
There are two malls that open at the same time.
The number of people in Mall A is modeled by -t² +9t + 36,
and the number of people in Mall B is modeled by - t² + 11t + 12,
where t represents the number of hours since the mall opened.
A) Write an expression that models how many more people are in Mall A than Mall B at time t.
B) How many people are in Mall A when t = 3 hours?
On solving the provided question, we can say that we have two quadratic equations; t² +9t + 36 > t² + 11t + 12 => t>12
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
here,
we have two quadratic equations
Mall A is modeled by -t² +9t + 36,
Mall B is modeled by - t² + 11t + 12,
t² +9t + 36 > t² + 11t + 12
-2t > -24
t>12
Mall A when t = 3 hours = [tex]3^2 +9*3 + 36 = 9+27+36 = 72[/tex]
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Illustrative Mathematics
Cool-down: Fundraising for the Animal Shelter
Noah raised $54, which is 60% of his fundraising goal to support the animal shelter.
5
Noah's ambition was $90, and he raised $54 toward that total, or 60% of his fundraising target, in order to benefit the animal sanctuary.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.
given
60% x what= $54
Then, by converting 60% to a decimal, we can turn it into a useful number: 0.6. We will substitute x for what because we also need to make "what" simpler to use:
0.6x=54
Get x by itself next, which is referred to as isolating the variable. To accomplish this, divide both sides by 0.6, which is referred to as employing inverse operations.
You must obtain x=90.
Noah's ambition was $90, and he raised $54 toward that total, or 60% of his fundraising target, in order to benefit the animal sanctuary.
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Rhombus DEFG with vertices D(1, 4), E(5, 5), F(4, 1),
and G(0, 0); 270° clockwise rotation about R(6,8)
On solving the provided question, we can say that vertices D(1, 4), E(5, 5), F(4, 1) and G(0, 0), area of rhombus = S*S = 5*5 = 25 cm sq.
what is Rhombus?A rhombus is an equal-sided quadrilateral in Euclidean plane geometry. The term "equilateral triangle" also refers to a quadrilateral whose sides are of the same length. A parallelogram has a unique variation known as a rhombus. In a rhombus, the opposite sides and angles are parallel and equal. A rhombus's diagonal is split in half by a right angle, and each of its sides is the same length. Rhombic diamonds and diamonds are other names for rhombuses. The length of every side is the same. Diagonals are equal in a rhombus. At a 90° angle, parallel lines split in half. 180 degrees is the sum of adjacent angles.
here,
vertices D(1, 4), E(5, 5), F(4, 1) and G(0, 0)
so area of rhombus = S*S = 5*5 = 25 cm sq.
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1. The height of a right triangular prism is 1 5/6 inches. Each side of the triangular base measures 10 inches, and the height of the base is 8 2/3 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.What is the surface area of the solid formed?
100 POINTS AND IF YOU INCLUDE ACCURATE DIAGRAM, BRAINLIEST!!!!!!!
Answer:Therefore the surface area of the solid formed is about 598.33 in²
Step-by-step explanation:If the height of a right triangular prism is 1 5/6 inches. The surface area of the solid formed is: 598.33 in².
Surface area
First step
Right triangular prism=1 5/6 inches= 11/6 inches
Height of the base=8 2/3 inches = 26/3 inches
Second step
Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)
Surface area = 5(100) +43.33+ 3(18.33)
Surface area = 500) +43.33 + 55
Surface area = 598.33 in²
Edgar works in the shipping department of a toy manufacturer. Toy cars weigh 6 pounds apiece and are shipped in a container that weighs 5 pounds when empty. Toy trucks, which weigh 3 pounds apiece, are shipped in a container weighing 20 pounds. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the number of toys?
The number of toys based on the information will be 5.
How to calculate the number of toys?From the information, Edgar works in the shipping department of a toy manufacturer. Toy cars weigh 6 pounds apiece and are shipped in a container that weighs 5 pounds when empty. Toy trucks, which weigh 3 pounds apiece, are shipped in a container weighing 20 pounds.
This will be Illustrated as:
5 + 6t = 20 + 3t
Collect the like terms
6t - 3t = 20 - 5
3t = 15
Divide.
t = 15 / 3
t = 5
The number of toys is 5.
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please answer all questions 30 points
Answer:
20) Rhombus | 21) Rhombus | 22) Square
Step-by-step explanation:
20) All sides are congruent, but there is no right <'s, and therefore it is just a Rhombus.
21) A Rhombus has diagonals that bisect each other and are congruent, which is shown in 21.
22) A square is a shape with all sides congruent and at least 1 right angle, which the diagram meets.
Hopefully this helps!
Which gives the correct values for points A, B, C, and D?
Option (D) A: -2/5, B: -1/5, C: -4/5, and D: -2/5 given the correct value of the number line.
What is a number line?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics.
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
The set R of all real numbers, considered as a geometric space, namely the Euclidean space of dimension one, is the formal definition of the number line in advanced mathematics, also known as a real line or real number line.
So, according to the given number line:
A: -2/5
B: -1/5
C: -4/5
D: -2/5
Therefore, option (D) A: -2/5, B: -1/5, C: -4/5, and D: -2/5 given the correct value of the number line.
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what’s the answer?? because I don’t understand this
Answer:
The answer is (A) 57
Step-by-step explanation:
[tex]4x^{2} + 3y = 4(3^{2}) + 3(7) \\= 4(9) + 21 \\= 36 + 21 \\= 57[/tex]
Hope this helps!
Answer:
A. 57
Step-by-step explanation:
If x is equal to 3 and y is equal to 7 then the equation should be written like this,
4 x (3)² + 3 x 7
Then solve it
First solve the number in the bracket
(3)² = 9
Then
4 x 9 + 3 x 7
According to BODMAS, we should solve numbers that need to be multiplied
4 x 9=36
3 x 7= 21
Then add those two numbers
36+21
The answer is 57
Hope this helps
what is[tex]254 ÷ 6[/tex] 254 ÷ 6
The value of expression 254 ÷ 6 is, 42.33.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ 254 ÷ 6
Divide the numbers as;
⇒ 254 ÷ 6
⇒ 254 / 6
⇒ 42.33
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Which equation is a linear function?
Answer: the third one
y=2^x-1
Step-by-step explanation:
Example: 300 000 + 5 < 300 500
a.75001+9____75100
The correct answer is 75001+9< 75100.The 75010 is less than 75100.Because we can count to prove it.
When can we use greater than and less than symbols?The greater than and less than symbols are generally used to represent the inequality expressions. The symbol used to represent greater than is “>” and less than is “<”. If one value is larger than the other value we use greater than. Similarly,if we want to represent one value that is less than the other value we use less than.
How do we find less than greater than?Many teachers use the Alligator Method analogy to teach greater than and less than. They will draw an Alligator mouth on the greater than and less than signs.We can say the alligator is going to want to eat more.
Now
75001+9= 75010
This will seventy five thousand and ten
75100 = seventy five thousand and one hundred
So, 75001+9 <75100
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Last summer, the Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. This summer, they purchased a larger kiddie pool that holds 150 gallons of water.
If the Abrams fill the larger pool at the same rate, how long will it take to fill it?
The answer is 10 minutes
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. Thus speed = 30/2
=15 gallons per day
Thus to fill 150 gallons the time required is 150/15=10 mins
Hence, The answer is 10 minutes
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$940 has been put into an investment account that grows at 5.14% compounded semi-annually. (NOT MULTIPLE CHOICE)
a. Create a table that shows this growth
b. Write an equation that models this situation
c. State what x represents in your equation
d. State what y represents in your equation
e. How much will in the account after 12 years?
Answer:
a) See below.
[tex]\textsf{b)} \quad y=940\left(1.0257\right)^{2x}[/tex]
c) x is the number of years.
d) y is the account balance in dollars.
e) $1728.29
Step-by-step explanation:
Part (a)Interest is compounded semi-annually, so:
5.14% ÷ 2 = 2.57%Therefore, calculate 1.0257% of the balance every 6 months:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \rm Years& \rm Account\;balance\;(\$) \\\cline{1-2} \vphantom{\dfrac12} 0& 940.00\\\cline{1-2} \vphantom{\dfrac12} 0.5& 964.16\\\cline{1-2} \vphantom{\dfrac12} 1& 988.94\\\cline{1-2} \vphantom{\dfrac12} 1.5&1014.35\\\cline{1-2} \vphantom{\dfrac12} 2&1040.42\\\cline{1-2} \vphantom{\dfrac12} 2.5&1067.16\\\cline{1-2} \vphantom{\dfrac12} 3&1094.59\\\cline{1-2} \end{array}[/tex]
Part (b)An equation that models this situation is:
[tex]\implies y=940\left(1+\dfrac{0.0514}{2}\right)^{2x}[/tex]
[tex]\implies y=940\left(1.0257\right)^{2x}[/tex]
Part (c)x is the number of years.
Part (d)y is the account balance in dollars.
Part (e)To calculate how much will be in the account after 12 years, substitute x = 12 into the equation from part (b):
[tex]\implies y=940\left(1.0257\right)^{2 \times 12}[/tex]
[tex]\implies y=940\left(1.0257\right)^{24}[/tex]
[tex]\implies y=940\left(1.8386054...\right)[/tex]
[tex]\implies y=1728.2890...[/tex]
Therefore, $1728.29 will be in the account after 12 years.