The conjecture that can be made about the other number is option A: the other number is odd.
Let's assume that the two even numbers are x and y. Then, we can write their sum as x + y = 2a, where a is some even number.
Now, let's consider the sum of 6 and another number, which we can represent as 6 + z, where z is some unknown number. If this sum is even, then we can write it as 2b, where b is some even number.
So, we have the equations:
x + y = 2a (since the sum of two even numbers is even)
6 + z = 2b (since the sum of 6 and another number is even)
We can subtract 6 from both sides of the second equation to get:
z = 2b - 6
Now, we can substitute this expression for z into the first equation:
x + y = 2a
And we get:
x + y + z - 2z = 2a
x + (y + z) - 2z = 2a
x + (2b - 6) - 2z = 2a
x + 2b - 2z - 6 = 2a
This equation tells us that x + 2b - 2z - 6 is an even number (since 2a is even). Since x and 2b are even, the expression -2z - 6 must also be even. Therefore, -2z must be even. This means that z is odd (since an even number minus an even number is even, and -6 is even).
So, we can conclude that the other number (z) is odd. Option A is the correct answer.
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A 360-ounce bag of rice has a serving size of 7 ounces on its label. How many full servings does the bag contain?
One positive integer is 2 less than twice another. The sum of their squares is 260 . Find the integers.
Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.
what is integers ?All entire numbers (optimistic, negative, and zero) as well as their opposites are included in the category of integers. These can be visualised as evenly spaced-apart points with zero in the middle on a number line. The following numbers are part of the set of integers, which is represented by the symbol Z . The numbers of pupils in an educational setting, the weather in degrees Celsius, or the location of an object in relation to a reference point are all examples of quantities that can be represented by integers and are counted or measured in whole units. They adhere to specific arithmetic laws and can be added, deducted, multiplied, and divided.
given
Assume that x and y are the two positive integers, with x being the greater of the two. Finally, we may convert the provided data into equations:
In order to remove x, we can replace the first equation with the second equation as follows:
[tex](2y-2)^2 + y^2 = 260[/tex]
Adding and subtracting:
[tex]4y^2 - 8y + 4 + y^2 = 260[/tex]
combining comparable phrases
[tex]5y^2 - 8y - 256 = 0[/tex]
Using the quadratic formula, we can solve this quadratic equation:
y = [8 ± sqrt(8^2 - 45(-256))] / (2*5)
y = [8 ± sqrt(3368)] / 10
y ≈ 8.6 or y ≈ -9.4
Y must be 8 because we are seeking for positive integers. The first equation can then be used to determine x:
x = 2y - 2 = 2(8) - 2 = 14
Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.
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HELP QUICK!
The owners of the pet sitting business have set aside $96 to purchase chewy toys for dogs, x, and collars for the cats, y. They are pricing the items at two different stores and wondering if there are any combinations of these items that could be purchased at both stores for the same price.
Marco’s Market: The price of a chewy toy for dogs is $2 while the price of a cat collar is $8.
Sonia’s Superstore: The price of a chewy toy for dogs is $4 and the price of a cat collar is $4.
Create an equation to represent the quantities of each item that can be purchased at each store. Then, graph the equations on the coordinate axes with proper labels and scale. Use the graph to find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores.
Answer:Let's assume that the number of chewy toys for dogs purchased at Marco's Market is represented by x, and the number of cat collars purchased at Marco's Market is represented by y. Similarly, let's assume that the number of chewy toys for dogs purchased at Sonia's Superstore is represented by a, and the number of cat collars purchased at Sonia's Superstore is represented by b.
The total cost of chewy toys for dogs and cat collars at Marco's Market is given by:
2x + 8y
The total cost of chewy toys for dogs and cat collars at Sonia's Superstore is given by:
4a + 4b
We want to find values of x, y, a, and b such that:
2x + 8y = 4a + 4b
Simplifying the equation, we get:
x + 4y = 2a + b
We also know that the total amount set aside for the purchases is $96. Therefore, we have:
2x + 8y + 4a + 4b = 96
Simplifying the equation, we get:
x + 4y + 2a + b = 48
Now, we can plot the graph of the equation:
x + 4y = 2a + b
To plot the graph, we can rearrange the equation as follows:
4y - b = 2a - x
y = (2a - x + b)/4
We can choose values of x and b, and then calculate the corresponding values of y and a using the equation. For example, let's choose x = 0 and b = 8. Then, we have:
y = (2a - 0 + 8)/4 = (2a + 8)/4 = 0.5a + 2
Similarly, we can choose other values of x and b, and calculate the corresponding values of y and a. We can then plot the points on the graph and join them to get the line representing the equation.
Here is the graph:
Graph
To find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores, we need to find the point where the line intersects the line representing the equation of the total cost:
x + 4y + 2a + b = 48
We can find this point by solving the two equations simultaneously. However, we can also use the graph to estimate the point. From the graph, we can see that the point of intersection is approximately (12, 6). This means that we can purchase 12 chewy toys for dogs and 6 cat collars at Marco's Market, and 4 chewy toys for dogs and 10 cat collars at Sonia's Superstore, and the total cost would be $48 at both stores.
Step-by-step explanation:
There is a straight road between town 4 and town B of length 130 km. Maxi travels from town 4 to town B. Pippa travels from town B to town A. Both travel at a constant speed of 40 km/h. Maxi leaves 30 minutes before Pippa. Work out how far from town A they will be when they pass each other
The distance from town A that they will be, when they will pass each other is 44 4/9 .
How can the distance be calculated?It should be noted that time traveled in each segment is constant, which implies that in this case the average speed can be regarded as the simple mean of speeds. An in the case whereby the distance traveled in each segment is constant, average speed can be described to be the reciprocal of simple mean .
This can be expressed mathematically as
Average speed = Reciprocal [ 1/40 & 1/50].
Average speed = Reciprocal of (1/40 + 1/50)/2
= Reciprocal of [(5+4)/400]
= 44 4/9 .
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5. The population, P, of a city has grown according to the mathematical model P = 50 000(1.15), where t
is the number of years since 2005.
Using a graphing tool or by hand answer the questions below.
a) What was the population of the town in 2005?
I
b) In what year will the population exceed 100 000?
Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.
Step-by-step explanation: a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:
P = 50,000(1.15)^0 = 50,000
Therefore, the population of the town in 2005 was 50,000.
b) We need to find the value of t when the population P exceeds 100,000:
100,000 = 50,000(1.15)^t
Divide both sides by 50,000:
2 = 1.15^t
Take the natural logarithm of both sides:
ln 2 = ln (1.15^t)
Apply the power rule of logarithms:
ln 2 = t ln 1.15
Divide both sides by ln 1.15:
t = ln 2 / ln 1.15
Using a calculator, we get:
t ≈ 10.73
Jackie, a marine biologist, is tracking migratory patterns of a group of whales. The endpoints
of the whales' current migration route are 9 inches apart on Jackie's chart. If the scale of the
map is 1 inch: 0.6 miles, then what is the actual distance between the whales' starting and
ending points?
Answer:
1 inch = 0.6 miles
= 9 inches = 0.6 miles*9
= 9 inches = 5.4 miles
Hence, the answer is 5.4 miles.
Please mark me as brainliest...
The average score of 22 students on a math online quiz is 86.3 with a standard deviation of 7.2. The average population score is 83.5. What is the
t-value?
Based the provided information, the t-value is approximately 1.824.
How do we determine the t-value?We shall work out the t-value by calculating the difference between the sample mean and the population mean, divided by the standard error of the mean.
We shall use the t-test formula to calculate the t-value:
t = (sample mean - population mean) / (sample standard deviation / [tex]\sqrt(sample size)[/tex])
where:
sample mean = 86.3
population mean = 83.5
sample standard deviation = 7.2
sample size = 22
Plugging in these values, we have:
t = (86.3 - 83.5) / (7.2 / √22)
t = 2.8 / (7.2 / 4.69)
t = 2.8 / 1.535
t ≈ 1.824
Therefore, the t-value is approximately 1.824.
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NEED HELP ASAP PLS AND THX PIX IS ATTACHED
Sin A Cos A, and Tan A can be found respectively as follows:
1. 41.81°.
2. 44.19 degrees
2. 60 degrees
How to find the anglesThe angles can be found by following the rules for right-angled triangles. This can be achieved in the following ways:
1. sin A= opposite/hypotenuse
sin A = 6/9
Now we take the sine inverse:
sin^-1(6/9)
= 41.81°.
2. Cos 45° = Adjacent/hypotenuse
= cos 45° = x/4
x = cos 45° × 4
= 0.707 × 4
= 2.82
cos A = b2 + c2 – a2 ÷ 2bc
2.8² + 4² - a² ÷ 2×2.8×4
23.84 - 2.8² ÷ 22.4
23.84 - 7.84 ÷ 22.4
Cos A = 0.7142
= 44.19 degrees
3. tan A = Opposite/Adjacent
tan 60° = 4/x
x = 4/tan 60°
x = 4/1.732
= 2.309
Tan A = 4/2.309
= 1.732
= 60 degrees
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solve 2,401=7^6-2x
x=
The solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.
Define logarithmIn mathematics, a logarithm is the inverse operation to exponentiation. Given a base b and a positive number y, the logarithm of y with respect to the base b is the exponent to which b must be raised to yield y. In other words, if x is the logarithm of y with respect to base b, then bˣ = y.
We can begin solving this equation by isolating the exponential term on one side of the equation and taking the logarithm of both sides.
2,401 = 7⁶⁻²ˣ
Taking the logarithm base 7 of both sides:
log₇(2,401) = log₇(7⁶⁻²ˣ )
Using the property of logarithms that states that log base a (aᵇ) = b, we can simplify the right-hand side of the equation:
log₇(2,401) = (6-2x)log₇(7)
Since log₇(7) = 1, we can further simplify:
log₇(2,401) = 6-2x
-2x = log₇(2,401) - 6
x = (6 - log₇(2,401))/2
Using a calculator, we find:
x ≈ 1.4076
Therefore, the solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.
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8 = -4 + v
v = what does v equal
Find the missing angle:
After 8 years, Fabian earned $1430 in simple interest from a CD into which he
initially deposited $5500. What was the annual interest rate of the CD?
A. 0.48%
B. 4.8%
C. 0.325%
D. 3.25%
Answer:
D. 3.25%
Step-by-step explanation:
The formula for simple interest is:
I = Prt
where I is the interest earned, P is the principal, r is the annual interest rate, and t is the time in years.
We are given that:
I = $1430
P = $5500
t = 8 years
Substituting the values:
$1430 = $5500 * r * 8
Simplifying, we get:
r = $1430 / ($5500 * 8)
r = 0.0325 or 3.25%
Therefore, the annual interest rate of the CD is 3.25%.
Answer: D. 3.25%
Pls pls someone one help me with this
Answer:
Triangle A = scalene
Triangle B = scalene
Triangle C = equilateral
Step-by-step explanation:
scalene triangle = all lengths are different
isosceles triangle = 2 side lengths are the same
equilateral triangle = all 3 side lengths are the same
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
The surface area of the triangular prism is 1740cm²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a prism is expressed as;
SA = 2B + ph
where B is the base area
p is the perimeter of the base
h is the height of the prism.
Base area = 1/2 bh
= 1/2 × 10 × 24
= 24×5
= 120 cm²
The perimeter of the base = 24+10+26
= 60cm
height = 25 cm
Therefore the surface area of the prism is
SA = 2 × 120 + 60 × 25
SA = 240+ 1500
SA = 1740 cm²
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If you want get 60000 in 8 years how much do you need to deposit in the bank today if the account pays an interest rate of 9%
Answer:
FV = PV x (1 + r)^n
where:
FV = future value
PV = present value (the amount to be deposited today)
r = interest rate per period (in this case, per year)
n = number of periods (in this case, 8 years)
Plugging in the given values, we get:
$60,000 = PV x (1 + 0.09)^8
Simplifying this equation:
PV = $60,000 / (1 + 0.09)^8
PV = $60,000 / 1.999^8
PV = $60,000 / 3.058
PV = $19,602.68
Therefore, the amount that needs to be deposited in the bank today to accumulate $60,000 in 8 years with an interest rate of 9% is $19,602.68.
I hope this helps.
College Level Trigonometry Question Any Help will do
The expression of angle in radian is -0.071.
What is the measure of angles in radian?Angles can be measured in two units: degrees and radians.
Radian is a unit of measurement for angles, and it is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
To be more precise, an angle of one radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
The expression of angle in radian is calculated as follows;
θ = tan⁻¹ (-0.071)
θ = -0.071
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HELPPPP PLS ILL GVIE BRAINLY 30 POINTS
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
A. Area of the rectangle, in standard form is: 14x² + 19x - 3
B. The degree of a polynomial is: 4. It has 4 terms (4x², 3y, -6x^4y, and 4.); C ALWAYS result in another polynomial.
What is a Polynomial?A polynomial is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.
Part A:
Area of the rectangle = (7x - 1)(2x + 3) = 7x(2x + 3) -1(2x + 3)
= 14x² + 21x - 2x - 3
Combine like terms:
Area of the rectangle = 14x² + 19x - 3 (standard form)
Part B: Given the expression, 4x² + 3y - 6x^4y + 4,
The degree of a polynomial is the highest exponent of its variable.
Therefore, the degree is 4.
It has 4 terms, which are: 4x², 3y, -6x^4y, and 4.
Part C: When two polynomials are subtracted, multiplied, or added, it will ALWAYS result in another polynomial.
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The data table shows the
numbers of eggs laid by
individual chickens in a year
What is the median number of
eggs laid in a year?
A. 231
B 229
C. 230
D. 234.6
The median number of eggs laid in a year is 231 from the given data, option A is correct.
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median = (7 + 1)/2
= 4th term
= 231
Hence, the median number of eggs laid in a year is 231, option A is correct.
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What type of conic section is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone?
The conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle
Determining type of conic section formedThe summary statement from the question is given as
A plane parallel to the base of a circular cone that intersects the cone.
By definition, a circle is the cross-section that is parallel to the base of a cone
This means that when a cone is cut through the base, the resulting shape is a circle
So, the conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle
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A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds to a complete and total stop. What was the initial velocity of the car before the brake was pulled?
The initial velocity of the car before the brake was pulled is 30m/s
What was the initial velocity of the car before the brake was pulled?From the question, we have the following parameters that can be used in our computation:
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds
This means that
Acceleration = -4.0m/s^2
Time = 7.5 seconds
Using the above as a guide, we have the following:
Initial velocity = -Acceleration * Time
substitute the known values in the above equation, so, we have the following representation
Initial velocity = 4 * 7.5
Evaluate
Initial velocity = 30
Hence, the initial velocity is 30
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SOLVE THE FOLLOWING INEQUALITY: x^3-5x^2+10 > 0
________________________________
x³ - 5x² + 10 > 0 = x³ - 5x² + 10 = 0= x² - 5x² + 10 - 10 = 0 - 10= x² - 5x² = - 10 = x² - 5x² = - 4x² - 4x² = - 10= - 4x² = - 10 = - 4x² / - 4 = - 10 / - 4x² = 5 / 2 x = √ 5 / 2________________________________
Help with this pleaseee
The reduced form of the matrix is [tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]
A matrix is a rectangular array of numbers arranged in rows and columns. In linear algebra, matrices can be used to represent linear transformations and solve systems of linear equations.
In the given matrix, we need to perform a row operation to get a 1 in row 1, column 1. Row operations are operations performed on the rows of a matrix to transform it into another matrix that is equivalent in terms of solutions to a system of linear equations.
The three types of row operations are:
Swapping two rows.
Multiplying a row by a non-zero constant.
Adding a multiple of one row to another row.
To perform this row operation, we first multiply row 1 by 12 to get a multiple of 12 in the first column of row 1:
[tex]\begin{bmatrix}84 &-48 &96 \\-12& 7& -13\end{bmatrix}[/tex]
Next, we add row 1 to row 2 multiplied by 2 to get a 0 in column 1 of row 2:
[tex]\begin{bmatrix}84 &-48 &96 \\0& 11& 79\end{bmatrix}[/tex]
Finally, we can divide row 1 by 84 to get a 1 in row 1, column 1:
[tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]
Now we have a 1 in row 1, column 1, and the matrix is in row echelon form.
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Two similar cones have surface areas of 1883 square meters and 7532 square meters, respectively. If the height of the smaller cone is 36 meters, what is the height of the larger cone?
The height of the larger cone is 71.13 meters
What is the height of the larger cone?From the question, we have the following parameters that can be used in our computation:
Two similar cones have surface areas of 1883 square meters and 7532 square meters. Height of the smaller cone is 36 metersUsing the above as a guide, we have the following:
Scale factor = h1/h2
So, we have
h1/h2 = √(1883/7352)
substitute the known values in the above equation, so, we have the following representation
36/h2 = √(1883/7352)
So, we have
h2 = 36 * √(7352/1883)
Evaluate
h2 = 71.13
Hence, teh height is 71.13
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What is the slope intercept form of the equation y-5=-1/4(x-12)
What is the equation of the line that passes through the point ( 4 , 0 ) and has a slope of − 2?
Step-by-step explanation:
y=m(x-x1)+y1
y=-2(x-4)+0
y=2x-8+0
y=2x-8
Solve the inequality and graph the solution on the line provided.
> ≤ ≥ or
Inequality Notation:
Number Line:
-12 -10
4x + 45 57
-4-2 0 24
Click and drag to plot line.
6
10 12
The solution of the given inequality is x ≤ 13/4
Since Inequality can be defined as the relation which makes a non-equal comparison between two given functions.
We are given the Inequality as;
4x + 45 ≤ 57
Solving;
4x + 45 ≤ 57
4x ≤ 57 - 45
4x ≤ 13
x ≤ 13/4
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Each container holds 3 L 456 mL of water. How much water is in 206 identical containers?
Answer:
711 L 936 mL
Step-by-step explanation:
3 L 456 ml times 206=711L 936mL
I hope this helps
Please help me i am so confused
The interval that will have the highest frequency will be: C. 11 - 15.
Which interval will have the highest frequency?The interval that will have the highest frequency will be 11 - 15. This interval will have the highest frequency because there are a total of 6 sales within this range.
The other intervals have sales that are 5 and below. So, since this interval has up to 6 sales, it can be regarded as the interval with the highest frequency. Frequency refers to how often something occurs. When an outcome happens several times, then we can refer to it as the highest frequency.
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Type the correct answer in each box.
Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of its square base. Nathan
uses the formula for the volume of a pyramid to determine the dimensions of the sculpture
V= }ah
Here, a is the side length of the pyramid's square base and h is its height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x? +
= O can be used to find that the length of
the sculpture's base is
centimeters.
The sculpture's base length = 9 cm and the height of sculpture is found as 6 cm.
Explain about the pyramid:The base and apex are joined to form a pyramid. To identify them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.
volume of a pyramid = V=1/3 a²h Given volume V = 162 cm³Let 'x' be the side length.Then , (x - 3) be the height of sculpture.Put the values and find the length.
162 = 1/3 (x)² (x-3)
162 * (3) = (x)² (x-3)
486 = x²(x-3)
486 = x³ - 3x²
x³ - 3x² - 486 = 0
(use a graphing tool or calculator equation mode).
x = 9
Thus,
side length of sculpture = 9 cm
height of sculpture = 9 - 3 = 6cm
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Correct question:
Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.
V=1/3 a^2h
Here, a is the side length of the pyramids square base and h is it’s height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3 + _x^2+ _ =0 can be used to find that the length of the sculptures. base is _ centimeters.