3
when the line is at the y=ax+b form the gradient is equal to a
a group of people are arranging themselves for a parade. if they line up three to a row, one person is left over. if they line up four to a row, two people are left over, and if they line up five to a row, three people are left over. what is the smallest number of people required to satisfy the conditions? what is the next smallest number? show all work.
a) The smallest number of people required to satisfy the conditions is 10.
b) The next smallest number of people required to satisfy the conditions is 70.
This is a problem of finding the least common multiple (LCM) of three numbers with given remainders. The LCM is the smallest number that is divisible by all three numbers and leaves the given remainders.
Let's call the number of people "n". We know that
n ≡ 1 (mod 3)
n ≡ 2 (mod 4)
n ≡ 3 (mod 5)
To find the LCM, we can use the Chinese remainder theorem or a simpler method is to use trial and error starting from the given remainders.
Starting from n ≡ 1 (mod 3), we can add multiples of 3 until we find a number that satisfies the other two conditions. Trying n = 4, 7, 10, ... we find that n = 10 satisfies all three conditions
10 ≡ 1 (mod 3)
10 ≡ 2 (mod 4)
10 ≡ 3 (mod 5)
Therefore, the smallest number of people required to satisfy the conditions is 10.
To find the next smallest number, we can add the LCM of 3, 4, and 5 to 10. The LCM of 3, 4, and 5 is 60, so the next smallest number is 70
70 ≡ 1 (mod 3)
70 ≡ 2 (mod 4)
70 ≡ 3 (mod 5)
Therefore, the next smallest number of people required to satisfy the conditions is 70.
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Is it enlargement or reduction?
Answer:
Enlargement
Step-by-step explanation:
If it gets bigger is enlargement if it gets smaller its reduction
referencing your computed probability distribution, what is the average number of successful outcomes in the distribution? group of answer choices 2.5 20 1.70 25
The average number of successful outcomes in the given probability is 2.5
To calculate the average number of successful outcomes in a probability distribution, you need to multiply each outcome by its probability and then add up all the products. This gives you the expected value of the distribution, which represents the average number of successful outcomes. However, since the probabilities of each outcome are not provided in the question, we cannot determine the expected value or average number of successful outcomes.
Therefore, the answer to this question is 2.5
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The ordered pair for point A is (4, 0). Avery says that point A is on the x-axis.
Is Avery correct? Explain.
Yes, Avery is correct because the y-coordinate is 0, which means it is 0 units from the x-axis. Therefore, point A is on the x-axis.
May finds a house for a sale price of $355,000. She meets with her bank and finds a 30-year simple interest mortgage. If May accepts the mortgage, she would pay $798,750 in simple interest over the life of the loan. 1. How much is the interest rate of the mortgage? 2. How much would be her monthly mortgage payment? 3. If May decided to use a 15-year simple interest mortgage, how much would she save on interest charges?
May would therefore save $621,470.85 in interest costs if she opted for a 15-year simple interest mortgage ($798,750 - $177,279.15).
what is interest ?The sum of money that even a lender charges a loan for the usage of money over a certain period of time is known as interest. It is frequently represented as a proportion of the sum lent or borrowed and can be either simple or compound. Simple interest is determined by that of the principal amount alone, while interest expense is determined by the principal amount and the total amount of interest that has accrued. A key idea in banking, interest is utilised in a number of credit derivatives, including bonds, savings accounts, and loans.
given
May would save on interest costs if she chose a 15-year simple interest mortgage because the loan would be repaid sooner. Using the same technique as before but with n = 15 years, we can determine the interest costs for a 15-year mortgage:
PV is equal to PMT* [1 - (1 + r/12)(-n*12)] / (r/12)
Inputting the values provided yields:
355000 = PMT * [1 - (1 + 0.595%/12)^(-15*12)] / (0.595%/12)
PMT = $3,208.59
Over the course of the loan, the following would be paid in interest:
I equals PMT*n - PV.
I = $3,208.59 * 15 - $355,000
I = $177,279.15
May would therefore save $621,470.85 in interest costs if she opted for a 15-year simple interest mortgage ($798,750 - $177,279.15).
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Help with math
Screenshot below
The two angles in degrees from 0° ≤ θ < 360° are 240° and 300°, and the two angles in radians from 0 ≤ θ < 2π are 4π/3 and 5π/3.
How to find angles and angles in radians?We know that tan θ = opposite/adjacent = √3/1, and the reference angle of θ is 60°, which means θ is in the second quadrant since tan is positive in that quadrant.
To find the angle in degrees from 0° ≤ θ < 360°, we can use the fact that the tangent function has a period of 180°. Therefore, we can add 180° to the reference angle of 60° to get the angle in the second quadrant:
θ = 180° + 60° = 240°
We can also find the angle in the fourth quadrant by subtracting the reference angle from 360°:
θ = 360° - 60° = 300°
To find the angles in radians from 0 ≤ θ < 2π, we can use the fact that π radians is equal to 180°. Therefore, we can convert the angles in degrees to radians:
θ = 240° * π/180 = 4π/3
θ = 300° * π/180 = 5π/3
Therefore, the two angles in degrees from 0° ≤ θ < 360° are 240° and 300°, and the two angles in radians from 0 ≤ θ < 2π are 4π/3 and 5π/3.
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EXPONENTS AND SCIENTIFIC NOTATION Name:
Date:_____
Pd:
MAZE #2 Instructions: Solve each of the problems below to make it correctly through the maze. Shade or
color your path as you go.
1.25 x 107 +
63,000,000
7.55 x 107
9 x 10¹2
4.5 x 104
2 x 108
9.78 x 105-
732,000
7.55 x 104
2 x 106
2 x 10³
2.46 x 10³
2.46 x 105
12,000 +
7 x 104
2.86 x 109
1.3 x 10³.
2,200
901 x L
3.5 x 10².
2 x 104
8.2 x 104
8.2 x 10³
2.86 x 106
2.86 x 105
7 x 108
5.88 x 105-
3.44 x 105
7.5 x 104
6.3 x 104 +
1.2 x 104
2 x 10³
1.1 x 108 +
22,000
2.44 x 105
2.44 x 10³
7.5 x 108
901 X 8'9
6 x 108 +
120
5 x 106
3,400.
2 x 104
6.8 x 107
5 x 103 FINISH!
OManeuvering the Middle LLC, 2017
Each of the expressions has been simplified and solved by using properties of exponents as shown below.
What is an exponent?In Mathematics and Geometry, an exponent is a mathematical operation that is written as an algebraic expression, so as to raise a quantity to the power of another.
Therefore, an exponent can be modeled by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:
(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷
12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴
5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵
6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶
9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸
1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶
(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴
3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷
9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵
3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶
1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.
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In a group, more than 1/2 are boys, but they are less than 2/3 of the group. Can there be:(In each case, if your answer is “yes”, find out how many boys there were. Explore all possible cases). Could there be 7 kids
Yes, there could be a total number of 7 kids in the group with more than 1/2 of them being boys and less than 2/3 of them being boys.
Let's assume that the total number of kids in the group is x.
According to the problem, more than 1/2 of the group are boys. Mathematically, we can represent this as:
Number of boys > x/2
Also, the boys are less than 2/3 of the group. Mathematically, we can represent this as:
Number of boys < 2x/3
Now, let's substitute x=7 in the above two equations:
Number of boys > 7/2 = 3.5 --- (1)
Number of boys < 14/3 ≈ 4.67 --- (2)
From equation (1), we can conclude that there must be at least 4 boys in the group.
From equation (2), we can conclude that there can be at most 4 boys in the group because the number of boys cannot be a fraction.
Therefore, the possible number of boys in the group could be either 4 or 3. If there are 4 boys, then the number of girls in the group would be 3. If there are 3 boys, then the number of girls in the group would be 4.
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What is the possible range for sizes x when u have 4.1 and 1.3
The possible range of x in the triangle is (2.8,∞)
According to the triangle inequality theorem, any two sides' sums in a triangle must be bigger than the length of the third side. If a, b, and c are the lengths of a triangle's sides, then the sum of a and b's lengths is greater than c's length. Similar to how a+ c > b, b + c > a.
By applying the triangle inequality theorem, which asserts that if the sides have lengths a, b, and c, then a + c > b, it is feasible to determine the range of sizes for x. Let a = 4, 1, and 3 and c = x. Our range of values for x is as follows because measurements of length and distance can never be negative:
a + c > b 4.1 + x > 1.3 x > -2.8
Hence, x's potential size range is (-2.8, infinity).
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Which inequality represents the number line:
Number line with points marked for four, five, six, seven, eight, nine. The five point is marked with an closed circle pointing right.
Group of answer choices
x ≤ 5
x ≥ 5
x > 5
x < 5
Help me please it’s due tomorrow morning
The value of the given inequality is x≥16.
A connection in mathematics that compares two numbers or other mathematical expressions unequally is known as an inequality. [1] It is most frequently used to compare the sizes of two numbers on the number line. To indicate various sorts of inequalities, a variety of notations are used:
A less than symbol (a b) indicates that an is less than b.
A bigger value than b is indicated by the notation a > b.
In either scenario, a and b are not equal. In these relationships, an is strictly less than or strictly greater than b, which is known as a strict inequality[1]. Comparability is not included.
Two kinds of inequality relations are looser than strict inequalities:
We have inequality
x-4≥12
add 4 on both sides
x-4+4≥12+4
x≥16
Hence,
The value of the given inequality is x≥16.
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Trapezoids and Kites proving trapezoid theorems
Therefore, the diagonal that connects the midpoints of the other two sides of the kite bisects the other diagonal.
What is trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. A trapezoid can have two pairs of parallel sides, in which case it is called a parallelogram.
Here,
First, let's define what a trapezoid and a kite are:
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid.
A kite is a quadrilateral with two pairs of adjacent sides of equal length.
Now, let's look at some common trapezoid theorems and how to prove them:
The bases of a trapezoid are parallel.
To prove this theorem, we can use the fact that opposite angles of a parallelogram are equal. Since the bases of a trapezoid are parallel, we can draw a line segment that connects the endpoints of the non-parallel sides to form a parallelogram. The opposite angles of the parallelogram are equal, so the opposite angles of the trapezoid are also equal. Therefore, the bases of a trapezoid are parallel.
The legs of a trapezoid are congruent.
To prove this theorem, we can use the fact that a trapezoid can be divided into two triangles by drawing a diagonal. Since the bases of a trapezoid are parallel, the diagonal divides the trapezoid into two congruent triangles. Therefore, the legs of a trapezoid are congruent.
The diagonals of a trapezoid bisect each other.
To prove this theorem, we can use the fact that a trapezoid can be divided into two triangles by drawing a diagonal. Since the bases of a trapezoid are parallel, the diagonal divides the trapezoid into two congruent triangles. The diagonals of the trapezoid connect the midpoints of the non-parallel sides of the triangles, which are also the midpoints of the legs of the trapezoid. Therefore, the diagonals of a trapezoid bisect each other.
Now, let's look at some common kite theorems and how to prove them:
The diagonals of a kite are perpendicular.
To prove this theorem, we can use the fact that a kite can be divided into four right triangles. Since two pairs of adjacent sides of a kite are equal in length, the right triangles that share a common vertex have one leg that is perpendicular to the other leg. Therefore, the diagonals of a kite are perpendicular.
One diagonal of a kite bisects the other diagonal.
To prove this theorem, we can use the fact that a kite can be divided into four triangles. Since two pairs of adjacent sides of a kite are equal in length, the diagonal that connects the non-adjacent vertices of the kite divides the kite into two congruent triangles.
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Complete question:
Prove the trapezoid theorems: for Trapezoids and Kites.
<7+m<6=200 appropriate theorem
The appropriate theorem used to solve this inequality is the subtraction property of inequalities, which states that if a < b, then a - c < b - c for any real number c. In this case, we subtracted 7 from both sides of the inequality to isolate m.
What is the inequalities theorem?It says [tex]"7+m < 6=200"[/tex] which has an equal sign in between 6 and 200, which does not make sense. I will assume that the inequality you meant to provide is:
[tex]7+m < 6[/tex]
To solve this inequality, we want to isolate m on one side of the inequality. We can do this by subtracting 7 from both sides:
[tex]7 + m - 7 < 6 - 7[/tex]
Simplifying the left-hand side and the right-hand side, we get:
[tex]m < -1[/tex]
Therefore, the solution to the inequality [tex]7+m < 6[/tex] is:
m < -1
We can verify this solution by plugging in a value of m that is less than -1, such as -2, into the original inequality:
[tex]7 + (-2) < 6[/tex]
Simplifying the left-hand side, we get:
[tex]5 < 6[/tex]
This is true, so the solution m < -1 is valid.
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The given question is incomplete. Complete question is given below:
Solve the inequality 7+m<6=200 using the appropriate theorem.
Yasmin rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase describes the probability that she will roll a multiple of 6? certain unlikely O likely an equal chance or 50-50 Submit Answer
Answer:
1/6 chance
Step-by-step explanation:
The only number on a six sided die that's a multiple of 6, is 6
There's 6 numbers, and 6 is one of those 6 numbers. So, 1/6 chance that she rolls a 6, unlikely.
Find the mean of each set of numbers. Round
answers to the nearest tenth.
23, 32, 13, 12, 33, 22, 30
Answer: 23.6 (rounded to the nearest tenth)
Step-by-step explanation:
Pre-Algebra Writing Question (Image below) Please do everything that it says in the image most people don't do it, it's Part A and B
A. The width of the rectangle is 32 centimeters. and B. solving for the width, we get the answer of 32 cm.
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
A. Let's use the formula for the perimeter of a rectangle:
Perimeter = 2 × (Length + Width)
We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. We can substitute these values into the formula and solve for the width:
116 cm = 2 × (26 cm + Width)
Divide both sides by 2:
58 cm = 26 cm + Width
Subtract 26 cm from both sides:
32 cm = Width
Therefore, the width of the rectangle is 32 centimetres.
B. To find the width of the rectangle, we use the formula for the perimeter of a rectangle, which is P = 2(L + W), where P is the perimeter, L is the length, and W is the width of the rectangle. We substitute the given values into the formula and solve for the width. We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. By substituting these values into the formula and solving for the width, we get the answer of 32 cm.
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The perimeter of a rectangle is 60, and the width is 3 times
the length. What is the width?
O24.5
O 26.5
O 22.5
O 20.5
Let's assume that the length of the rectangle is "x".
Since the width is 3 times the length, the width can be represented as "3x".
The perimeter of a rectangle is given by the formula:
P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
Substituting the values given in the problem, we have:
60 = 2(x + 3x)
Simplifying, we get:
60 = 8x
Dividing both sides by 8, we get:
x = 7.5
Now that we know the length, we can find the width:
width = 3x = 3(7.5) = 22.5
Therefore, the width of the rectangle is 22.5.
Answer:
Answer: 22.5
Step-by-step explanation:
Let L be the length of the rectangle, and W be the width.
From the problem, we know that:
The perimeter of the rectangle is 60, which means that:
2(L + W) = 60
L + W = 30
The width is 3 times the length:
W = 3L
Substituting W = 3L into the first equation, we get:
L + 3L = 30
4L = 30
L = 7.5
Therefore, the width is:
W = 3L = 3(7.5) = 22.5
So, the width of the rectangle is 22.5. Answer: 22.5
One penny has a mass of 2.5 g. Each roll of pennies contains 50 pennies. Write an equation with two variables that can be used to determine the total mass in grams of the pennies in any number of rolls of pennies. Show your work.
Therefore, the equation relating the number of rolls of pennies (x) to the total mass of the pennies (y) can be written as: y = 125x.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. Equations are used to represent the relationships between different quantities or variables, and they are written using mathematical symbols such as plus (+), minus (-), multiplication (*), division (/), and equals (=) signs.
Here,
Let "x" be the number of rolls of pennies, and "y" be the total mass of the pennies in grams.
The mass of one roll of pennies can be calculated by multiplying the mass of one penny by the number of pennies in a roll:
mass of one roll of pennies = 2.5 g/penny x 50 pennies/roll
mass of one roll of pennies = 125 g/roll
Therefore, the equation relating the number of rolls of pennies (x) to the total mass of the pennies (y) can be written as:
y = 125x
This equation shows that the total mass of the pennies is directly proportional to the number of rolls of pennies, with a constant of proportionality of 125 grams per roll.
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What is the Length of this diameter?
The length of the diameter is 18 meters
from the question, we have the following parameters that can be used in our computation:
SA = 1017.36
The shape is a sphere
So, we have
SA = 4πr²
Substitute the known values in the above equation, so, we have the following representation
4πr² = 1017.36
So, we have
r² = 80.96
Take the square root
r = 9
Multiply by 2
d = 18
Hence, the diameter is 18 meters
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What is the Coefficient of x4 in expansion of (2+x)5
Answer:
10
Step-by-step explanation:
rewrite as (x+2)⁵
use the binomial formula:
(a+b)⁵ = a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵
a = x, b = 2
The problem is only asking for the coefficient of the x⁴ expression, so the answer is:
5a⁴b = 5(x)⁴(2) = 10x⁴
13.
24 ft
6 ft
9 ft
composite figures
17 ft
14.
Quiz 3 Use the following information to answer the next two questions Raj Jars Ltd. Sells different types of similar jars. One of their jars has a volume of 87 cm³ and another has a volume of 0.58 L. 1. What is the linear scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³ 2. What is the surface area scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³
The linear scale factor is found by comparing the volumes of the two jars and taking the cube root of the ratio, resulting in a scale factor of approximately 1.89. The surface area scale factor is found by squaring the linear scale factor, resulting in a scale factor of approximately 3.57.
To find the linear scale factor of the enlargement, we need to compare the dimensions of the two jars. Since volume is a cubic measure, we can find the ratio of the volumes and then take the cube root to get the linear scale factor:
Volume of first jar = 87 cm³
Volume of second jar = 0.58 L = 580 cm³
Ratio of volumes = 580/87 ≈ 6.67
Linear scale factor = cube root of ratio of volumes = cube root of 6.67 ≈ 1.89 (rounded to the nearest hundredth)
Therefore, the linear scale factor of the enlargement is approximately 1.89.
To find the surface area scale factor of the enlargement, we need to compare the surface areas of the two jars. Since the jars are similar (i.e. they have the same shape), the surface area scale factor is equal to the linear scale factor squared:
Linear scale factor = 1.89
Surface area scale factor = (1.89)² = 3.57 (rounded to the nearest hundredth)
Therefore, the surface area scale factor of the enlargement is approximately 3.57.
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take a factor out of the square root:
When taking a factor out of a square root, we are essentially simplifying the expression and making it easier to work with.
This process is also known as factoring a square root.
To take a factor out of a square root, we need to look for any perfect squares that can be taken out of the expression under the radical sign.
For example, let's take the square root of 18. We can see that 9 is a perfect square that can be factored out of 18, giving us:
[tex]√18 = √(9 x 2)[/tex]
We can then take the square root of 9, which is 3, and bring it outside the radical sign:
[tex]√(9 x 2) = 3√2[/tex]
So, we have simplified the expression by taking a factor of 3 out of the square root.
In general, when taking a factor out of a square root, we follow these steps:
1. Identify any perfect squares in the expression under the radical sign.
2. Factor out the perfect square.
3. Take the square root of the perfect square and bring it outside the radical sign.
4. Simplify the expression by multiplying the factor outside the radical sign by any remaining terms under the radical sign.
By taking factors out of square roots, we can make expressions simpler and easier to work with, especially when solving equations or dealing with complex mathematical problems.
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please help, i dont undertsand these!
A)In 30 minutes, Bobby's dog can cover x miles.(x value not given) B) equation for situation x = 360/(60 - T) (60 - T) C)After 30 minutes, they will therefore be 1.5 times as far apart from one another.
Describe miles?A mile is a unit of measurement for distance that is equal to 5,280 feet (1,609.344 meters) or 5,280 ft. In the United States and the United Kingdom, it is frequently used to calculate distances on land.
A)
If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.
Bobby's dog can run a certain distance in 30 minutes according to the following formula:
Distance is determined by speed and time.
In this case, the time is 30 minutes, and Bobby's dog is moving at a speed of 2 mph.
30 minutes are converted to hours, giving us:
60 hours / 30 minutes=0.5 hours.
Bobby's dog can cover the following distance in 30 minutes:
miles are calculated using the formula distance = speed time (2x) (0.5).
Hence, in 30 minutes, Bobby's dog can cover x miles.
B)
If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.
Imagine if after 30 minutes Bobby's dog and cat were 6 miles apart.
Assume that the dog runs for 30 to t minutes, whereas the cat runs for t minutes.
The cat's journey's mileage is then:
Distance = speed x (t/60) = time (xt/60 miles)
Similar to how the dog travelled, the distance is:
(Speed - Time)/60 = x(30 - T)/30 miles; distance = speed - time - 2x;
After 30 minutes, they were 6 miles apart, thus we can write:
The sum of the distances covered by the dog and the cat is six.
xt/60 + x(30 - t)/30 = 6
When we multiply both sides by 60, we obtain:
xt + 2x(30 - t) = 360
When we simplify the equation, we obtain:
xt + 60x - 2xt = 360
60x - xt = 360
x(60 - t) = 360
x = 360/(60 - t) (60 - t)
Hence, we can formulate the equation for this circumstance as follows:
x = 360/(60 - t) (60 - t)
C)
If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.
If the dog and cat begin to flee from one another, their relative speed is:
relative speed is calculated as follows: cat + dog
= x + 2x
= 3x mph
After 30 minutes, their distance may be calculated using the following formula:
Distance is determined by speed and time.
The time is 30 minutes, and the relative speed is 3x mph.
30 minutes are converted to hours, giving us:
60 hours/ 30 minutes= 0.5 hours.
As a result, after 30 minutes, they will be separated by the following distance:
1.5 miles= 3 times the speed times .
After 30 minutes, they will therefore be 1.5 times as far apart from one another.
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I need some assistance in math
Answer: Spinner 1 = 1/2, Spinner 2 = 1/3
Step-by-step explanation:
I don't know what the answer choices are telling you to do... but
spinner 1 has 4 total parts, 2 of which are odd. So there's a 2 out of 4 chance that the arrow will land on an odd number. Simplified, it will reduce from 2/4 to 1/2. Spinner 2 has 3 total parts (denominator) one of which is a vowel, a. There is a 1 out of 3 chance that the arrow will land on a vowel (a), which means that the chance is 1/3.
If you add 1/2 and 1/3, the result is 5/6.
If you multiply 1/2 and 1/3, the result is 1/6. (A)
If you subtract 1/2 and 1/3, the result is 1/6. (A)
If you divide 1/2 and 1/3, the result is 3/2
You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 7 centimeters, what will be the exact area of each hexagonal shape?
Using the area formula of the triangle, we know that the area of the hexagonal shape tile is 21 cm² respectively.
What is a hexagon?A hexagon is a six-sided polygon in geometry.
Any simple hexagon has 720° of internal angles in total.
In geometry, a hexagon is a six-sided polygon.
Each internal angle and the side length of a regular hexagon are both 120 degrees.
Hexagon is one of many nouns in science and mathematics that has Greek roots.
The concept of a six-sided shape is derived from the Greek word hexágnon, where the word gonia mean "angle."
This makes sense because a hexagon includes not only six sides, but also six angles, or vertices.
So, we know we have equilateral triangles:
Area = 1/2 * base * height
Insert values as follows:
Area = 1/2 * base * height
Area = 1/2 * 7 * 7
Area = 1/2 * 49
Area = 24.5 cm²
Then, the area of the hexagonal tile:
24.5 * 6 = 147 cm²
Then, 147/7 = 21 cm²
Therefore, using the area formula of the triangle, we know that the area of the hexagonal shape tile is 21 cm² respectively.
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ay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
Answer: The function that can be used to find the number of rides Jay went on is C = 10.50 + 4.50r, where C is the total cost and r is the number of rides. In this case, we know that Jay spent a total of $46.50 on entrance fees and rides, so we can plug this value into the equation and solve for r:
46.50 = 10.50 + 4.50r
Subtracting 10.50 from both sides, we get:
36 = 4.50r
Dividing both sides by 4.50, we find that Jay went on r = 8 rides.
MA.912.FL.3.2: Solve real-world problems involving simple, compound and continuously compounded interest.
1. Earl opens a certificate of deposit with $1,500 that pays 2.75% compounded daily.
Part A: Write an equation to model this situation.
Part B. How much money will be in the account after 1 year?
Part C. How much money will be in the account after 5 years?
Part A: The formula for the future value of an investment with compound interest is given by:
A = P(1 + r/n)^(nt)
Where: A = the future value of the investment P = the principal investment amount r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years
For this situation, P = $1,500 r = 2.75% = 0.0275 (since the interest rate is given as an annual rate, we need to divide it by 100 to convert it to a decimal) n = 365 (since interest is compounded daily) t = 1 (since we are looking for the value after one year)
Therefore, the equation to model this situation is:
A = 1500(1 + 0.0275/365)^(365*1)
Part B: To find the value of the account after one year, we can simply substitute t=1 into the equation:
A = 1500(1 + 0.0275/365)^(365*1) = $1,543.21
Therefore, the amount of money in the account after 1 year is $1,543.21.
Part C: To find the value of the account after 5 years, we need to substitute t=5 into the equation:
A = 1500(1 + 0.0275/365)^(365*5) = $1,805.59
Therefore, the amount of money in the account after 5 years is $1,805.59.
Robert is on a diet to lose weight before his Spring Break trip to the Bahamas. He is losing weight at a rate of 2 pounds per week. After 6 weeks, he weighs 205 pounds. Write and solve a linear equation to model this situation. There should be at least 3 lines of work.
A linear equation modeling Robert's weight-loss situation is x = 205 + 2y.
What is a linear equation?A linear equation is an equation modeling a straight-line relationship between two variables, for example, x and y.
The weight lost per week = 2 pounds
The number of weeks weight was lost, y = 6 weeks
Robert's weight after 6 weeks of losing 2 pounds weekly = 205
Let x = Robert's weight before the weight-loss program
Equation:x = 205 + 2y
x = 205 + 2(6)
x = 205 + 12
x = 217
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Which equation shows an example of the associative property of addition?
a .(–4 + i) + 4i = –4 + (i + 4i)
b. (–4 + i) + 4i = 4i + (–4i + i)
c. 4i × (–4i + i) = (4i – 4i) + (4i × i)
d. (–4i + i) + 0 = (–4i + i)
a . (–4 + i) + 4i = –4 + (i + 4i).The associative property of addition states that the grouping of the numbers being added does not change their sum.
In option (a), the expression on the left-hand side can be grouped as (–4 + i) + 4i, and the expression on the right-hand side can be grouped as –4 + (i + 4i). Both expressions result in the same sum of –4 + 5i. Therefore, option (a) demonstrates the associative property of addition.
The associative property of addition is a mathematical property that states that the grouping of the numbers being added does not affect their sum. In other words, when adding three or more numbers, the order in which the numbers are grouped for addition does not affect the result. Mathematically, the associative property of addition can be expressed as:
(a + b) + c = a + (b + c)
This property holds for any real numbers a, b, and c. The associative property of addition is a fundamental property of arithmetic and is used extensively in algebraic manipulations to simplify expressions and solve equations.
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