Answer:
12
Step-by-step explanation:
i
Evaluate the following by writing it as a difference of two squares first:
103^2 − 97^2
Answer:
1200
Step-by-step explanation:
A difference of 2 squares factors in general as
a² - b² = (a - b)(a + b) , then
103² - 97²
= (103 - 97)(103 + 97)
= 6 × 200
= 1200
The correct answer is 1200.
What is the difference between two squares called?Where one perfect square is subtracted from another, is called a difference of two squares. It arises when (a − b) and (a + b) are multiplied together. This is one example of what is called a special product.
A difference of 2 squares factors in general is written as
a² - b² = (a - b)(a + b) , then
103² - 97²
= (103 - 97)(103 + 97)
= 6 × 200
= 1200
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The low temperature on Wednesday was –15°F. What was the absolute value below zero for the temperature on Wednesday?
A)-15
B)0
c)15
D)30
Answer:
C. 15
Step-by-step explanation:
Absolute value is just how far away the number is on the number line and is always positive.
Help me with this....
Match each expression with its greatest common factor. 4a + 8 2a2 + 8a 12a2 − 8a 4 − 6a Greatest Common Factor Expression 4 : 2 : 2a : 4a :
Answer:
see explanation
Step-by-step explanation:
4a + 8 4
2a² + 8a 2a
12a² - 8a 4a
4 - 6a 2
Match each expression with its greatest common factor as follows;
4a + 8 4
2a² + 8a 2a
12a² - 8a 4a
4 - 6a 2
What is the greatest common factor?The largest number that is found in the common factors is called the greatest common factor.
The given expression are;
4a + 8
2a² + 8a
12a² - 8a
4 - 6a
The greatest common factor of the expression are as follows;
4a + 8 = 4(a+2) = common factor = 4
2a² + 8a = 2a(a+4a) = common factor = 2a
12a² - 8a = 4a(3a-2) = common factor = 4a
4 - 6a = 2(2-3a) = common factor = 2
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Is the following number rational or irrational? sqrt(50) Choose 1 answer ?
Answer:
its irrational
7.07106781187
look at how the decimals are all over the place
if it was rational it would've been something like this
7.070707070707 or 7.071071071071
hope that answers your question
Step-by-step explanation:
A storage tank consist of a hemisphere and a cylinder which share a common base. The tank has a height of 16.5 m and the cylinder has a base diameter of 4.7m. Find the total capacity of the tank.
The total capacity of the tank is 272.675 cubic meters.
Given that,
A storage tank consist of a hemisphere and a cylinder which share a common base.
The base of both hemisphere and cylinder will be the same circle with the same radius.
Also, we have,
Height of the tank = 16.5 m
Base diameter of the cylinder = 4.7 m
Radius of the base of the cylinder = 4.7 / 2 = 2.35 m
Radius of the hemisphere = 2.35 m
Height of the cylinder = Total height of the tank - Height or radius of the hemisphere
Total capacity of the tank = Volume of hemisphere + Volume of cylinder
= 2/3 π r³ + π r² h
= 2/3 π (2.35)³ + π (2.35)² (16.5 - 2.35)
= 8.652π + 78.143π
= 272.675 cubic meters
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The scatter plot below shows the relationship between two variables, x and y. Which line best fits the data? У 30 25 20 15 10 5 У 30 25 20 15 10 5- 0 2 3 5 x 1 2 3 4 5 X y 30- 25 20- 15- у 30 25 20- 15 10- 5- 0 0 10- 5- 0 0 1 2 x 3 4 5 5 4 1 2 3
The variables on a scatter plot are related using the equation of a straight line graph; y = mx + c.
What is a scatterplot?Since the options are unclear, I will try to help you as much as possible. A scatter plot is an arrangement in which one variable is plotted on the vertical axis and another is plotted on the horizontal axis.
The variables on a scatter plot are related using the equation of a straight line graph; y = mx + c. Using this relation, we can establish the equation of the scatter plot.
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Find the volume of the cylinder
What is the exact volume in terms ofx?
What is the approximate volume using 3 14 forx?
9514 1404 393
Answer:
5000π mm³ ≈ 15,700 mm³
Step-by-step explanation:
The volume of the cylinder is given by the formula ...
V = πr²h
For the given radius and height, the volume is ...
V = π(10 mm)²(50 mm) = 5000π mm³
Using 3.14 for π, the volume is ...
5000(3.14) mm³ = 15,700 mm³
consider the sequence {12, 5, -2, -9, -16 ... } select all the items that define the sequence
Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.
What is arithmetic sequence ?
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.
The sequence {12, 5, -2, -9, -16 ... } can be defined by the following items:
The first term: 12
The common difference: -7
The pattern of adding the common difference to find the next term.
Therefore, all the items that define the sequence are:
The first term: 12
The common difference: -7
This sequence is an arithmetic sequence.
Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.
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the least squares method for determining the best fit minimizes
The least squares method minimizes the sum of the squared differences between the observed data points and the predicted values.
The least squares method is a mathematical technique used to find the best fit line or curve for a set of data points. It is commonly used in regression analysis to determine the relationship between two variables.
The method works by minimizing the sum of the squared differences between the observed data points and the predicted values from the line or curve. This sum is known as the residual sum of squares (RSS) or the sum of squared residuals (SSR).
The least squares method aims to find the line or curve that minimizes this sum, meaning it minimizes the overall error between the observed data and the predicted values. By minimizing the sum of squared differences, the method finds the line or curve that best represents the data.
In other words, the least squares method seeks to find the line or curve that provides the best balance between fitting the data closely and avoiding extreme deviations from the data points.
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The least squares method for determining the best fit minimizes the sum of the squared differences between the observed data points and the corresponding values predicted by the mathematical model or regression line.
In other words, it aims to minimize the sum of the squared residuals, where the residual is the difference between the observed data point and the predicted value. By minimizing the sum of squared residuals, the least squares method finds the line or curve that best fits the data by minimizing the overall error between the predicted values and the actual data.
Mathematically, the least squares method minimizes the objective function:
E = Σ(yᵢ - ŷᵢ)²
where yᵢ is the observed value, ŷᵢ is the predicted value, and the summation Σ is taken over all data points. The goal is to find the values of the parameters in the mathematical model that minimize this objective function, usually by differentiating it with respect to the parameters and setting the derivatives equal to zero.
By minimizing the sum of squared differences, the least squares method provides a way to estimate the parameters of a mathematical model that best represents the relationship between the independent and dependent variables in a data set.
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Help me plssssssssss
Answer:
4 quarters, 10 dimesStep-by-step explanation:
x + y = 14 --> x = 14 - y
$0.10x + $0.25y = $2.00, or 10x + 25y = 200
- we can plug this value for x from the first equation into the second:
10(14 - y) + 25y = 200
140 - 10y + 25y = 200
140 + 15y = 200
15y = 60
y = 4 --> 4 quarters ($0.25 x 4 = $1.00)
if y = 4, then x = 14 - y --> x = 10 --> 10 dimes (0.10 x 10 = $1.00)
matches the second equation where these add up to $2.00
Answer:
1 way is 10 dimes and 4 quartes
I can only come up with one way
pls help!
Eva is short on frosting! She works in a bakery and has 12 cakes to frost, but she is short 4 1/8 cups on the amount of frosting required. She decides that she will spread the frosting she has among the 12 cakes. She makes a sign for the cakes and names them by the value that represents the amount of frosting on each cake compared to the amount it should have. What does the sign say? Drag a value to the box to correctly complete the statement. Cakes for sale. We are calling these cups. You should ask why!
A. -33/8
b. -11/8
C. -33/32
d. -11/32
Answer:
11/32
Step-by-step explanation:
I took the test Please make brainlyest if can
Jill walks 3/5 mile in 1/2 hour. How fast is this in miles per hour?
Answer:1.2mph
Step-by-step explanation:
3/5*2=1.2 and 1/2*2=1 so it’s 1.2 mph
There are 2.3^3 slices of pizza and ther are 3 friends how much do they all get
Answer:
the answer is 3/8
Step-by-step explanation:
the answer is 3/8
1. Find the slope of a line passing though the points. Write the formula and indicate
the type of slope (2, 9 ) and (-3, 6).
Answer:
The answer is 3/5
Step-by-step explanation:
try math caculators to help you with these questions thats where i go the solution from.
-Best of luck
A distribution is given as X ~ Exp(0. 75). Find P(x < 4)
The probability of P(x < 4) is 0.6922 or approximately 69.22%.
The exponential distribution is often used to model the time between events that occur randomly and independently at a constant rate over time. The probability density function of the exponential distribution with parameter λ is given by f(x) = λe^(-λx) for x ≥ 0.
In this case, X ~ Exp(0.75) means that the parameter λ is 0.75. To find P(x < 4), we need to calculate the area under the curve of the probability density function to the left of 4. This can be done by integrating the function from 0 to 4 as follows
P(x < 4) = ∫₀⁴ λe^(-λx) dx
= [-e^(-λx)]₀⁴
= -e^(-0.75 * 4) + 1
= 0.6922
Therefore, the probability that X is less than 4 is 0.6922 or approximately 69.22%.
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If the concentration of the product COCl2 were to double, what would happen to the equilibrium constant
If the concentration of the product COCl2 were to double, the equilibrium constant of the reaction would not be affected.
The equilibrium constant (K) is a measure of the ratio of product concentrations to reactant concentrations at equilibrium for a given chemical reaction. It is determined solely by the temperature of the reaction and is independent of the initial concentrations or changes in concentrations during the reaction.
Therefore, doubling the concentration of the product COCl2 would not alter the equilibrium constant of the reaction. The equilibrium constant reflects the relative concentrations of reactants and products at equilibrium and remains constant as long as the temperature remains the same. Any changes in concentration would simply shift the reaction towards the formation of reactants or products until a new equilibrium is reached, without affecting the equilibrium constant itself.
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A newsvendor orders the quantity that maximizes expected profit for two products, x and y. The critical ratio for both products is 0. 8. The demand forecast for both products is 9,000 units and both are normally distributed. Product x has more uncertain demand in the sense that it has the larger standard deviation. Of which of the two products does the newsvendor order more?.
Following are the calculation to the standard deviation:
Cr = 0.8, which is the critical ratio.
The value of Z corresponding to the critical ratio of 0.8 from the standard normal distribution tables is 0.8416
Unless the quantity ordered by the newsvendor is Q, then
Q = Mean value of demand+Z×Standard deviation of demand
Below are the specifications of the two products:
The mean requirement for both X and Y is 900O units.
Z value for both X and Y = 0.8416
Let
Sd₁ = Demand standard deviation for product X
Sd₂ = Demand standard deviation for product Y
Assuming that Sd₁ > Sd₂ (Product X does have a higher standard deviation than Product Y),
quantities for
X = Mean value of demand + Z × standard deviation of demand
= 9000 + 0.8416.Sd₂
X₁ > X₂ because
As a result 9000 + 0.8416Sd₁ > 9000 + 0.8416Sd₂
OR
The quantity ordered for X is > the quantity ordered for Y. As a result, Newsvendor orders Product X more frequently because it has a higher level of certainty.
In this question, all the estimates are wrong so, the correct answer is "Product X because it has less certain demand".
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help please!
thank you
The range of the picewise function is R: [5, ∞)
Which is the range of the function?Here we have a piecewise function. We can see that for x ≥ 2 we have a line with positive slope, so that part will go to ∞.
Now we need to analize the left part to find a minimum.
g(x) = x² + 5 for x < 2
The minimum there is when x = 0 (it minimizes the square part) we will get:
g(0) = 0² + 5 = 5
Then the range of the function is:
R: [5, ∞)
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1,5,9,13 generalize the pattern by finding the nth term
Answer:
an= a1 +(n-1)*4
Step-by-step explanation:
a1 = 1, a2 =5, a3 = 9, a4= 13,... an= ?
we see that each term is getting bigger so usually that will happen because of addition or multiplication-in our case add 4 to previous term
a1 = 1,
a2 = a1+(2-1) 4 = 1+4 = 5,
a3 = a1 + (3-1)*4 = a1+8 = 1 + 8 = 9,
a4= a1 + (4-1)*4 = a1 + 12 = 1+12= 13,
...
an= a1 +(n-1)*4
If m∠A is less than 90°, then ∠A is an acute angle. m∠A = 75°. What can you logically conclude using the Law of Detachment?
A. ∠A is acute.
B. ∠A is right.
C. ∠A is obtuse.
D. Not enough information
Answer:
A. ∠A is acute.
Step-by-step explanation:
An acute angle is any angle < 90°
Please help me!!!!!!!!!!
YO HELP ME OUT!!!! Question is in the screenshot below PLEASE answer correctly, I am running out of time!
Answer:
V = 696.91
Step-by-step explanation:
Volume of a sphere formula:
V = 4/3πr³
Given:
d = 11
r = d/2
r = 5.5
Work:
V = 4/3πr³
V = 4/3π(5.5)³
V = 4/3π(166.375)
V = 696.91
In certain circle the endpoints of the diameter is (0, 6) and (10, 6); what is the coordinate of the center of the circle?
The coordinate of the center of the circle are (5,6).
To find the center of a circle:
The center of the circle lies at the midpoint of the diameter, which is the line segment connecting the two endpoints.
In this scenario, the endpoints of the diameter is given as (0, 6) and (10, 6). Applying the midpoint formula, we can find the required coordinates of the center.
The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints:
x-coordinate of the midpoint = (0 + 10) / 2
= 10 / 2 = 5
The y-coordinate of the midpoint is the average of the y-coordinates of the endpoints:
y-coordinate of the midpoint = (6 + 6) / 2
= 12 / 2 = 6
Therefore, the coordinates of the center of the circle are (5, 6).
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In this square, all the angles are equal. What is the measure of angle x°?
720°
180°
90°
360°
Answer:
90degrees
Step-by-step explanation:
I'm pretty sure, terribly sorry if I'm wrong
~Animaljamissofab ♥
nice green square lol
90° is the measure of angle x°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
We know that, a ray is a line that continues on forever inn one direction with a point at it's start.
Here, given that,
the figure is a square,
so, all its angle = 90 degrees
Now, the x = (180-90)=90
Hence, 90° is the measure of angle x°.
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Okay I really need someone help rn this is for my geometry test!!! Please take time
Answer:
13.7Step-by-step explanation:
the triangle is ... 1/2 b h = 1/2 * 3.6 * 4.8 the semi-circle is ... 1/2 π r^2 = 1/2 * 3.14 * 1.8^2
in other words
What you do is 4.8*3.6=A then divide your answer in half which is the area of the triangle than to find the area of the semi circle you do 3.14*1.8^{2}=A then divide that in half than add the two together then round to the nearest tenth.
If a pet grooming salon hires an additional groomer, that worker can groom 4 additional pets per day. the average grooming fee is $25. the most the salon would be willing to pay that groomer is
The most the salon would be willing to pay that groomer is $25×4 = $100.
What is unitary method?The unitary method is a technique that determines the worth of a single unit from value of multiple units, as well as the quality of multiple units from value of a single unit.
Some key features regarding the unitary method are-
It's a method which we use for the majority of math calculations. This method will come in handy when answering questions about ratio & proportion, algebra, geometry, and other subjects.We can determine the missing value using the unitary method. For example, if one carton of juice pays $5, how much would five such packets cost? We can then easily determine the price of 5 packets, which is $25.To know more about the unitary method, here
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Using Green's Theorem, calculate the area of the indicated region. The area bounded above by y=7 and below by y=7/25x^2
The area of the indicated region bounded by y=7 and y=7/25x^2 is XXX square units.
To calculate the area using Green's Theorem, we need to express the region in terms of a curve. Green's states that closed the line Theorem line integral integral of over a a vector field around a closed curve is equal to the double integral of the curl of the vector field over the region bounded by the curve.
In this case, we can rewrite the given equations in terms of x and y to define the boundary of the region. The upper boundary is y=7, and the lower boundary is y=7/25x^2. To find the points of intersection between these two curves, we can equate them:
7 = 7/25x^2
Solving this equation, we find x = ±5. Now we have the boundaries of the region in terms of x values.
To express the region in terms of a line integral, we need to define a vector field F = (M, N). In this case, we can take M = 0 and N = x. Now we can apply Green's Theorem:
Area = ∬ D dA = ∮ C N dx = ∮ C x dx
To calculate the line integral, we need to parameterize the curve C that encloses the region. Since the region is bounded by two curves, we need to split the curve into two parts. Let's consider the upper curve C1: y = 7.
Parameterizing C1, we have:
x = t
y = 7, for t ∈ [5, -5]
Now we can calculate the line integral over C1:
∮ C1 x dx = ∫[5,-5] t dt = [t^2/2] evaluated from -5 to 5 = 25/2 - 25/2 = 0
Next, let's consider the lower curve C2: y = 7/25x^2.
Parameterizing C2, we have:
x = t
y = 7/25t^2, for t ∈ [-5, 5]
Now we can calculate the line integral over C2:
∮ C2 x dx = ∫[-5,5] t dt = [t^2/2] evaluated from -5 to 5 = 25/2 - 25/2 = 0
Since both line integrals are zero, the area of the region bounded by y=7 and y=7/25x^2 is 0 square units.
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A salt solution was made by mixing 16 quarts of 2% salt solution and 12 quart of a 51% salt solution. Find the concentration of the new mixture .
The concentration of the new mixture is ___%
Answer:
.33 or 33%
Step-by-step explanation:
multiply 16 times .02, then multiply 12 times .51 add your two answers together. 3.2 + 6.12=28X add 3.2 and 6.12 give you 9.32=28x, divide both sides by 28 which give an answer of .33 or 33%
27⅔ multiply by 32 minus 2 over 5 divided by 64 raised to the power of 5 over 6
Using BODMAS, the answer of the given question is 13232 / 15.
What is the math rule of BODMAS?The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEDMAS rule are applied.
The other operations must be solved in the same order. Brackets (B) are followed by the order of powers or roots, which is then followed by multiplication, addition, subtraction, and finally division.
According to the question,
\(27 \frac{2}{3} \times 32 - \frac{2}{5} \div 64^{\frac{5}{6} }\)
Using BODMAS,
⇒ 83/3 × 32 - \(\frac{2}{5}\) ÷ \(64^{\frac{5}{6} }\)
⇒ 83/3 × 32 - 2/5 ÷ \((2^{6})^{\frac{5}{6} }\)
⇒ 83/3 × 32 - 2/5 ÷ 2⁵
⇒ 83/3 × 32 - 2/5 × 1/2⁵
⇒ 83/3 × 32 - 2⁴/5
⇒ 2656 / 3 - 2⁴/5
⇒ 2656 / 3 - 16/5
⇒ 13280 - 48 / 15
⇒ 13232 / 15
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