The amount of money una earns in a week she serves $355 worth of meals including her base earnings is $177.25
How to solve equation?Amount una makes in a week= $64
Additional amount una earn = 15% of x
Cost of meal she serves = x
Total amount she makes= y
y = 0.15x + 64
If she serves $355 worth of meals.
y = 0.15x + 64
y = 0.15(355) + 64
= 53.25 + 64
y = $177.25
In conclusion, una makes a total of $177.25 in a week.
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I need help, can y’all explain to me how to solve it? Linear Equations
Necesito ayuda, ¿alguien puede explicarme cómo resolverla? Son ecuaciones lineales
x+y=25
2x+2y=50
The value of
x₁/x₂ = y₁/y₂ = c₁/c₂
the given lies are parallel to each other having no solution .
What are system of Equation?A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are no solutions when the lines are parallel, and there are a finite number of solutions when the two equations graph as the same line.
The equation are
x + y = 25
2x + 2y = 50
The value of
x₁/x₂ = y₁/y₂ = c₁/c₂
So the given lies are parallel to each other having no solution .
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Rani has several identical solid right circular metal cylinders of unknown base radius and height 10 cm. To find the base radius r of a cylinder, she puts them one by one into the above container half filled with water. When exactly 25 of them are put, the water reaches the level of the container being completely filled.
[tex]show \: that \: r = 5 \sqrt{ \frac{5}{\pi} } cm[/tex]
Find the value of r in centimetres to the first decimal place, by using 3.14 for the value of
[tex]\pi[/tex]
Answer:
The volume of each cylinder is given by the formula: V = πr^2h, where r is the base radius and h is the height of the cylinder.
When 25 cylinders are put into the half-filled container, the water level rises to the top of the container, which means that the total volume of the 25 cylinders is equal to the volume of the container. Let's assume the volume of the container is V_container.
So, 25 * πr^2 * h = V_container
Dividing both sides by 25πh gives: r^2 = V_container / (25πh)
Taking the square root of both sides gives: r = √(V_container / (25πh))
Since h = 10 cm, we can substitute this value in the formula above: r = √(V_container / (25π * 10))
Since r is the base radius of the cylinder, it must be positive. So, the final equation becomes:
r = √(V_container / (25π * 10)) cm = 5√(5/π) cm. shown
By using 3.14 for the value of π, we can calculate the value of r:
r = 5√(5/π) = 5√(5/3.14) = 5 * √(5/3.14)
= 5 * √(1.5873) = 5 * 1.259 = 6.295 cm (rounded to the first decimal place)
So, the base radius of the cylinder is approximately 6.3 cm.
Mary is looking to lease a car. Gerald's Auto has a car available with a money factor of 0.00355. Hillspring's Auto has the exact same car available with a money factor of 0.00324. Which of the following statements is true? a. The lower money factor with Gerald's Auto will give Jennifer the lowest monthly payment. b. The lower money factor with Hillspring's Auto will give Jennifer the lowest monthly payment. c. The higher money factor with Gerald's Auto will give Jennifer the lowest monthly payment. d. The higher money factor with Hillspring's Auto will give Jennifer the lowest monthly payment.
The statement that is true in this situation is "the lower money factor with Hillspring's Auto will give Jennifer the lowest monthly payment" (option B).
What is the money factor?This is a term used when you lease a car or a similar product. This term is a synonym for the "lease fee", which means it is a percentage of money that you need to pay for the lease.
What money factor is the most convenient?Based on the previous ideas a lower money factor is better because this means the payment will be lowered and this is offered by Hillspring's Auto (option B).
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Hey if anybody could please give me a hand and explain this question to me and help me out that would be great
Answer:
Step-by-step explanation:
We can use similar triangles to solve this. The bigger triangle is made up of the water tower as the height and the long horizontal line as its base, and the smaller triangle fitted inside the larger is made up of the tripod of the camera as the height and the distance Brian lies on the ground beyond it as the base for that triangle. We have to add this distance to the distance of the larger triangle's base. Setting it up as a proportion:
[tex]\frac{watertower}{base} =\frac{camera}{base}[/tex]
but since everything is in different measurements, we have to sort that out first. Let's change everything to feet.
The water tower's distance is 100 yards + 2 feet 9 inches:
[tex]100yds*\frac{3ft}{1yd}=300'[/tex] and now we add in 2 feet 9 inches which is 2.75 feet to get a total of 302.75 feet from the base of the water tower to the point of the triangle. Since we have already converted Brian's distance to feet we're ready to set up the proportion:
[tex]\frac{x}{302.75} =\frac{5}{2.75}[/tex] and we cross multiply.
2.75x = 1513.75 and divide to get
x = 550.45 feet tall.
Why is the symbol for standard deviation and variance the same?
The ith observation in the data set is represented by the number xi. The sample's average value is. V stands for variation. All of the values in a data set are added up to form x.
Do standard deviation and standard variance equate to one another?Variance, as opposed to range and interquartile range, is a measure of dispersion that considers the spread of each data point within a data collection. In addition to the standard deviation, which is just the variance's square root, it is the measure of dispersion that is most frequently employed.Symbols,It is common to use the formula x = the mean, or average, of all the data points in the problem to represent standard deviation and variance. A single data point is denoted by X.The ith observation in the data set is represented by the number xi. The sample's average value is. V stands for variation. All of the values in a data set are added up to form x.To learn more about stands for variation refer to:
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describe three techniques for analyzing data. how are they organized and summarized, and what are they used for?
The three types of Data analysis can be : Descriptive Analysis, Diagnostic Analysis nad Predictive Analysis.
What is Data Analysis ?In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data.
Using both recent and old data, descriptive analytics seeks out patterns and connections. Because it only describes patterns and associations without going any further, it is frequently referred to as the most basic kind of data analysis.
A type of advanced analytics called diagnostic analytics looks at data or information to determine "why it happened." Techniques like drill-down, data discovery, data mining, and correlations are used to describe it.
Using data, statistical algorithms, and machine learning approaches, predictive analytics determines the likelihood of future events based on previous data. The objective is to provide the most accurate prediction of what will happen in the future in addition to understanding what has already occurred.
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what should be t-value to indicate that curve is not over flattening in smoothening of time series data
When smoothing time series data, it's important to ensure that the curve is not over-flattened, as this can lead to important information being lost.
What should be t-value to indicate that curve is not over flattening?To avoid over-flattening, one approach is to use a threshold value, or "t-value", to determine the maximum amount of smoothing that can be applied.Here are some steps to consider when choosing a t-value:Plot the original time series data and the smoothed curve to visualize the smoothing effect.Compare the slope of the smoothed curve to the slope of the original data.Choose a t-value that preserves the important features of the original data, such as trends, seasonality, and outliers.Ensure that the smoothed curve still accurately represents the underlying pattern in the data, while reducing noise and variability.Re-evaluate the t-value if necessary, based on the visual comparison of the original data and the smoothed curve.The t-value should be chosen such that the smoothed curve captures the underlying pattern in the data, while retaining important features such as trends and seasonality. If the t-value is set too high, the curve may become over-flattened and important information may be lost. On the other hand, if the t-value is set too low, the curve may not effectively reduce noise and variability in the data.To learn more about T-value refer:
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Can you please solve for me please?
Answer:
[tex]\boxed{\sin D = 0.39 }[/tex]
Step-by-step explanation:
DEF is a right triangle with hypotenuse = 18 and one leg = 7
The law of sines states that the ratios of the sides of a triangle to the sine of the angle opposite that side must be the same for all sides
[tex]\dfrac{18}{\sin 90} = \dfrac{7}{sin D}[/tex]
sin(90) is 1
So the above equation becomes
[tex]18 = \dfrac{7}{\sin D}[/tex]
Cross multiplying we get
[tex]\sin D = \dfrac{7}{18}\\\\\sin D = 0.3889\\[/tex]
Rounded to the nearest hundredth ( i.e. 2 decimal places):
[tex]\sin D = 0.39 \quad \quad \textrm{ANSWER}\\\\[/tex]
huck can paint a fence in 5 hours. if tom helps him paint the fence they can do it in 3 hours. how long would it take for tom to paint the fence by himself? (hint: use the equation from
Assuming that the rates are constant, we can see that Tom can paint the fence in 7.5 hours.
How long would it take for tom to paint the fence by himself?Here we will use equations of the form:
(rate at which person x paints)*(time) = 1 fence painted.
We know that Chuck can paint a fence in 5 hours, then if C is the rate (assuming this is constant), we can write:
C*5 hours = 1 fence
C = (1/5) fences per hour.
And let's say that Tom's rate is T.
When they work together, the rate is:
(C + T)
And they can paint the fence in 3 hours, then:
(C + T)*3 hours = 1 fence
Replacing the value of T we will get:
( 1/5 fences per hour + T)*3 hours = 1 fence
1/5 fences per hour + T = 1/3 fences per hour.
T = (1/3 - 1/5) fences per hour
T = (5/15 - 3/15) fences per hour
T = 2/15 fences per hour.
Then Tom paints the fence in:
(15/2) hours = 7.5 hours.
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Let f be a continuous function such that f changes from increasing to decreasing, and the graph of f changes fro concave up to concave down. Which of the following is true about the midpoint Riemann sum approximation for definite integral from 1 to 3 of f(x^2 + x) using 4 subintervals?a. The midpoint Riemann sum approximation underestimates the definite integral.b. The midpoint Riemann sum approximation overestimates the definite integral.c. The midpoint Riemann sum approximation cannot be determined to be an underestimate or an overestimate.
The true statement is Option B, The midpoint Riemann sum approximation overestimates the definite integral.
Given data,
In this case, since the function f changes from increasing to decreasing and the graph of f changes from concave up to concave down, we can infer that the function has a local maximum point within the interval [1, 3].
The midpoint Riemann sum approximation for the definite integral breaks the interval [1, 3] into four subintervals of equal width, and it uses the midpoint of each subinterval to approximate the value of the function within that subinterval.
Now, when the function is increasing, the midpoint Riemann sum approximation will tend to underestimate the value of the definite integral since it approximates the function using values that are smaller than the actual function values.
However, when the function changes from increasing to decreasing, the midpoint Riemann sum approximation will tend to overestimate the value of the definite integral since it approximates the function using values that are larger than the actual function values.
Hence , the midpoint Riemann sum approximation overestimates the definite integral.
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Vectors A and B are shown in the figure. Vector C is given by C = B-A. The magnitude of vector A is 16.0 units, and the magnitude of vector B is 7.00 units.
Write vectors A, B, and C in unit vectors notation.
Determine the magnitude and direction (Direction should be given ccw from the positive x-axis) of the vector C?
The magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.
Explain the term cosine theory in vectors? A sum of the products of the individual components of a two vectors, multiplied by the total of the magnitude of a two vectors, is the cosine of a angle between the two vectors.The dot product of a vectors divided by all product of its lengths equals the cosine of angle formed by two nonzero vectors. Only when the dot product of two vectors is zero do they become orthogonal.For the stated question:
C = B-Avector A = 16.0 unitsvector B = 7.00 unitsBy using the cosine theory of the vectors:
C² = A² + B² - 2A.B cosФ
C² = 16.0² + 7.00² - 2(16.0)(7.00).B cosФ79°
On solving:
C = 16.19 units
Thus, the magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.
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The figure for the question is attached.
I’m not sure how to do this
On solving the provided question, we can say that so the equation formed is 1540-6x = 236 +6 x and in 108 2/3 minutes the tanks become equal with 888 gallons each
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
when does tank 1 = tank 2 when there is 6 gpm
tank 1 = 1540
tank2 = 236
so the equation formed is
1540-6x = 236 +6 x
1304 = 12x
108 * 2/3 = x
6*108*2/3 = 652 gallons
236+652=888
1504-652=888
in 108 2/3 minutes the tanks become equal with 888 gallons each
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. how can the directed graph of a relation r on a finite set a be used to determine whether a relation is asymmetric?
The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.
Let the relation R R R be asymmetric. A loop in the directed graph corresponds to an ordered pair of the form ( a , a ) (a , a) (a , a). By the definition of asymmetric, the relation R R R cannot contains any ordered pairs of the form ( a , a ) (a , a) (a , a) and thus the directed graph cannot contain any loops.
They are typically represented by labeled points or small circles. We connect vertex a to vertex b with an arrow, called an edge, going from vertex a to vertex b if and only if arb. This type of graph of a relation r is called a directed graph or digraph .
It is a set where either there are many components or only the beginning or ending are provided. By n(A), we refer to the total number of components, and if n(A) is a characteristic number, then the set is constrained.
Let A be finite non-empty set.
Then the exist relation R on A which is both equivalence and order relation.
Suppose A = {[tex]a_{1} , a_{2} , a_{3} , ...... a_{n} ,[/tex]}
And, R = { [tex](a_{1} ,a_{1}) , (a_{2} ,a_{2} ) ,(a_{3} ,a_{3} )........(a_{n} ,a_{n} )[/tex] }
R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric.
Then R is equivalence relation and an order relation.
Therefore,
The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.
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What is the value of s?
The value of s on the right triangle is s = 4.
How to get the value of s?Here we can assume that the two triangles are similar triangles, then, the measures of the hypotenuses of the right triangles must be the same one.
Remember that the hypotenuse is the side that is opposite to the 90° angle, then we can write the equation:
s + 43 = 47
s = 47 - 43 = 4
That is the value of s.
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consider the formula k = 1/(1-s). what happens to the variable k when s grows in value?
When s grows in value, the value of variable k decreases.
Consider the formula k = 1/(1 - s)
We know that when the value of one quantity 'm' increases with respect to decrease in the value of other 'n' or vice-versa, then we say that the two quantities 'm' and 'n' are inversely proportional to each other.
We write this as,
m∝ 1/n
m = p/n
where p is the constant of proportionality
From the formula k = 1/(1 - s) we can observe that the quantities k and s are inversely proportional to each other.
this means, when the value of variable s increases, there is decrease in value of variable k.
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three computer viruses arrived as an email attachment. virus a damages the system with probability 0.4. independently of it, virus b damages the system with probability 0.5. independently of a and b, virus c damages the system with probability 0.2. what is the probability that the system gets damaged? 0.96 0.24 0.76 0.04
The probability that the system gets damaged is P(AUBUC)=0.76
If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events.
The two events are said to be independent events if the outcome of one event does not affect the outcome of another.
The formula can be defined as:
P(A and B) = P(A)×P(B)P(A and B) = P(A)×P(B)
For independent events U and V we have P(U∩V)=P(U)P(V)
if the viruses are truly independent then the probability that the system gets damaged=
P(AUBUC)=P(A)+P(B)+P(C)-P(AnB)-P(anc)-P(bnc)+P(AnBnC).
0.4+0.5+0.2-0.4*0.5-0.4*0.2-0.5*0.2+0.4*0.5*0.2=1.1-0.2-0.08-0.1+0.04
P(AUBUC)=0.76
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Find the weighted average of the numbers 1 and 5 with one fourth of the weight on the first number and three fourths on the second number.
The Correct answer for the weighted average of given numbers is 4.
What is Weighted average?
Weighted average is one of the most commonly employed measures in statistical data to find the average of quantities when each quantity has a certain weight.
Formula for weighted average:
x= Σ(Weights × Quantity)/Σ(Weights)
In the given question,
first number is 1, Weight of the one of the number given is [tex]\dfrac{1}{4}[/tex](one fourth of first number (1)), The weight of three fourth of the second number is [tex]\dfrac{3}{4}*5[/tex], second number is 5.
Weighted average,
[tex]\dfrac{(\dfrac{1}{4}*1 + \dfrac{3}{4}*5)}{\dfrac{1}{4}+\dfrac{3}{4}}[/tex]
[tex]= \dfrac{16}{4}\\\\=4[/tex]
The weighted average of the numbers 1 and 5 with given condition is 4.
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For question #3:A) Express the general solution of the given system of equations in terms of real-valued functions.B) Also, draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as t approachs infinity.
The solutions of the system tend towards zero, as the exponential term dominates the other terms.
The general solution of the given system of equations can be expressed as:
x(t) = c1e^(-t) + c2te^(-t)
y(t) = c3e^(-t) + c4te^(-t)
where c1, c2, c3 and c4 are constants of integration.
The direction field of the system can be drawn by plotting the slopes of the two equations at each point. The trajectories of the solutions can be sketched by plotting the solutions of the system at different points in time. As t approaches infinity, the solutions of the system tend towards zero, as the exponential term dominates the other terms.
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For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500. g of sulfuric acid is produced and the theoretical yield is 575 g of sulfuric acid.
A. 89.3%
B. 86.9%
C. 85.2%
D. 88.1%
The percentage of actual yield to theoretical yield of SO3 + H2O → H2SO4
is B. 86.9%
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500g but the theoretical yield is 575g.
Therefore, The percentage of actual yield to theoretical yield is,
= (500/575)×100%.
= 0.8695×100%.
= 86.95%.
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At Silver Gym, membership is $45 per month, and personal training sessions are $30 each. At Fit Factor, membership is $75 per month, and personal training sessions are $20 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
To make the price at the two gyms equal, Sarah would have to purchase three training sessions.
what is unitary method ?The unit is a method of conundrum that entails measuring the value of an individual unit, multiplied that value, and then calculating the required value. To put it plainly, using unit method is employed to derive a minimum unit value from just a specified multiple. One writer costs Four rupees, thus 40 pens would pay 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mathematics of matrices or operators, discrete mathematics, mathematical analysis, and its adjoint and reciprocal are all equivalent.
given
Let S stand in for the monthly membership fee for Silver Gym.
Let F stand in for the monthly expense of using Fit Factor.
The number of training sessions used during the month will be denoted by T.
S = 45 +25T
F = 75 +15T
In order for the expenses to be equal, we need to find T. S = F, where 45 + 25T
= 75 + 15T,
10T = 30, and deduct 45+15T.
T = 3 is divided by 10 using the following formula:
To make the price at the two gyms equal, Sarah would have to purchase three training sessions.
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Two similar figures have a side ratio of 4:3. If the perimeter of the smaller figure is 15 units, what is perimeter of the larger figure?
Enter fractions as decimals.
The perimeter of the larger figure is: 20 units.
How to Find the Perimeter of Similar Figures?Similar figures have perimeters and side lengths that are related in such a way that, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Therefore, if x represents the perimeter of the larger figure, then:
x/15 = 4/3
Cross multiply to find x:
3x = 60
x = 60/3
x = 20
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A typing examination found that susan's typing accuracy was 93%. Which decimal number represents susan's typing accuracy?.
Representing fractional values, if a typing examination found that Susan's typing accuracy was 93%, the decimal number representing Susan's typing accuracy is 0.93.
How the decimal number is determined?The decimal number of Susan's typing accuracy is a direct conversion from percentage to decimal since both are fractional values.
We know that the percentage sign represents over 100. When 93 is divided by 100, the decimal value is 0.93.
93% = 93/100 = 0.93
Thus, as a fractional value, Susan's typing accuracy of 93% is the same as 0.93.
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a number n to the power of n, where n is a positive integer, is called interesting. find all interesting numbers that divide 2023 to the power of 2023
4^4 and 678^678 are the only two interesting numbers that divide 2023^2023.
To find all interesting numbers that divide 2023^2023, we need to find all positive integers n such that n^n divides 2023^2023.
Since 2023^2023 = 2023 * 2023 * ... * 2023 (2023 times), we can see that the factors of 2023^2023 are simply the powers of 2023.
So, a number n^n divides 2023^2023 if and only if 2023^(n-1) divides 2023^2023. This means that n-1 must be a factor of 2023.
The factors of 2023 are 3 and 677. Therefore, the values of n that satisfy the condition are 4 (3+1) and 678 (677+1), which correspond to the interesting numbers 4^4 and 678^678. These are the only two interesting numbers that divide 2023^2023.
Therefore, 4^4 and 678^678 are the only two interesting numbers that divide 2023^2023.
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Convert the below equation into y=mx b form 2x-y=-3
Answer: y=2x+3
Step-by-step explanation:
2x−y=−3
Step 1:
Add -2x to both sides.
2x−y+−2x=−3+−2x−y=−2x−3
Step 2: Divide both sides by -1.−y−1=−2x−3−1y=2x+3
What is the volume of the sphere? Use 3.14 for π and round to the nearest whole number. Enter your answer in the box.
The volume of the sphere with radius 5 is 523 units³.
What is Sphere?A sphere is a three dimensional figure which consists of set of all the points which are at an equal distance from a point called the center of the sphere.
Volume of a three dimensional shape is the space occupied by the shape.
Volume of a sphere can be found using the formula,
Volume = [tex]\frac{4}{3}[/tex] π r³, where r is the radius of the circle.
Given the radius of the circle = 5.
And π = 3.14
Substituting the values,
Volume = [tex]\frac{4}{3}[/tex] × 3.14 × (5)³
= 523.33 ≈ 523 units³
Hence the volume of the given sphere is 523 units³.
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if x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth?
If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Given that,
If x and y each represent a single digit
The number 8.3xy round to 8.3
Then, the nearest tenth value is,
Round to the nearest tenth means to write the given decimal number up to one decimal place. This is done in such a way that after rounding off, there is one digit after the decimal point.
To round to the nearest tenth using a number line, look at the tenth place value closest to the number you are rounding. Round 2.12, 2.28 and 2.44 to the nearest tenth.
We can write,
If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth,
We have the radius, 8.3, so we have all necessary information to solve this problem.
8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Therefore,
If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
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If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Given that,
If x and y each represent a single digit
The number 8.3xy round to 8.3
Then, the nearest tenth value is,
Round to the nearest tenth means to write the given decimal number up to one decimal place. This is done in such a way that after rounding off, there is one digit after the decimal point.
To round to the nearest tenth using a number line, look at the tenth-place value closest to the number you are rounding. Round 2.12, 2.28, and 2.44 to the nearest tenth.
We can write,
If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth,
We have a radius, of 8.3, so we have all the necessary information to solve this problem.
8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Therefore,
If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
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Determine if the triangles are similar by side-angle-side similarity
Answer:
Step-by-step explanation:
note that all adjacent triangles will share an angle.
for 13 and 14 this is the case.
for 13 and 14 the adjacent sides are also multiples of each other proportionately. find this by dividing one side by the other for both triangles. if equal they are proportionately larger.
13 and 14 are both similar
for 15 and 16 the same logic can be applied to the side lengths. however, we are not given any information on the angles and cannot determine the angles mathematically.
for 17 and 18 the same logic can be applied again for the sides and given that the angles are confined within each other, the angles are the same.
for 17 and 18 you must add the side lengths for each side together and divide to determine the ratio and compare that to the ratio of the initial triangle
solve for x
8x+16 9x+11
Answer:
x = 9
Step-by-step explanation:
(8x+16) + (9x+11) = 180
17x + 27 = 180
180 - 27 = 153
17x = 153
153/17 = 9
x = 9
Answer:
To solve the equation 8x+16+9x+11=180, add 8x and 9x to both sides to get 17x+27=180. Subtract 27 from both sides to get 17x=153. Divide both sides by 17 to get x=9.
1. What are some differences between arithmetic and geometric sequences and series? What about finite and infinite sequences and series?
2. What are the explicit and recursive formulas for the nth term of an arithmetic sequence?
3. What are the explicit and recursive formulas for the nth term of a geometric sequence?
4. What is the formula for the sum of a finite arithmetic series?
5. What are the formulas for the sum of a finite and an infinite geometric series?
This refers to a sequence in which each term increases by adding/subtracting some constant k.
What is geometric sequences?
This refers to a sequence where each term increases by dividing/multiplying some constant k.
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we have an urn with 3 green and 4 yellow balls. we draw 3 balls one by one without replacement. (a) find the probability that the colors we see in order are green, yellow, green. (b) find the probability that our sample of 3 balls contains 2 green balls and one yellow ball.
The probability of getting colors in order green-yellow-green is 24/245 and the probability of getting 2 green and 1 yellow ball is 72/245.
(a) The probability that the first ball drawn is green is 3/7. Given that the first ball is green, the probability that the second ball drawn is yellow is 4/6. Given that the first two balls are green and yellow respectively, the probability that the third ball drawn is green is 2/5. The final answer is (3/7) * (4/6) * (2/5) = 24/245.
(b) There are several ways to order 2 green and 1 yellow ball, such as green-green-yellow or green-yellow-green. The total number of such combinations is C(3,2) * C(4,1) = 3 * 4 = 12. The probability of getting any of these combinations is (3/7) * (2/6) * (4/5), so the total probability is 12 * (3/7) * (2/6) * (4/5) = 72/245.
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The probability of getting colors in order green-yellow-green is 24/245 and the probability of getting 2 green and 1 yellow ball is 72/245.
(a) The probability that the first ball drawn is green is 3/7. Given that the first ball is green, the probability that the second ball drawn is yellow is 4/6. Given that the first two balls are green and yellow respectively, the probability that the third ball drawn is green is 2/5. The final answer is (3/7) * (4/6) * (2/5) = 24/245.
(b) There are several ways to order 2 green and 1 yellow ball, such as green-green-yellow or green-yellow-green. The total number of such combinations is C(3,2) * C(4,1) = 3 * 4 = 12. The probability of getting any of these combinations is (3/7) * (2/6) * (4/5), so the total probability is 12 * (3/7) * (2/6) * (4/5) = 72/245.
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