The value of the variable x = π³ - π/π
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.
These algebraic expressions are also comprised of arithmetic operations, such as;
DivisionMultiplicationSubtractionFloor divisionAdditionBracketParenthesesFrom the information, we have that;
y = π³
y = πx + π
Substitute the values, we get;
π³ = πx + π
collect like terms
π³ - π = πx
Divide both sides by the coefficient of x
x = π³ - π/π
Thus, the value is x = π³ - π/π
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Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?
Answer: 41 years ago, when Sally was 13 and her mother was 39.
Answer: 41 years
Step-by-step explanation:
I reckon the question is asking when her mother was 3 times her age.
S = 54
M = 80
54 - 41 = 13
80 - 41 = 39
39/13 = 3
of course, quadratic equations don't always come with the coefficients labeled , , and . for example, assuming the solutions are real and , the larger solution of -bx^2 c^2x a^3
The equation -bx2 + c2x + a3 has a larger solution of x = (-c + sqrt(c2 - 4ab))/2a.
We must first move the constants to the right side of the equation in order to find the solution to the equation
-bx2 + c2x + a3 = 0.
As a result, we have the equation -bx2 + c2x = -a3. The result is x2 - (c2/b)x = -a3/b after dividing both sides by -b. The quadratic formula can be used to resolve this quadratic equation. x = (-c + sqrt(c2 - 4ab))/2a is the equation's more complex solution. We enter the coefficient values into the quadratic formula to verify this. The broader solution is
x = (-4 + sqrt(4 - 24))/4 = (-4 + sqrt(-20))/4 = (-4 + 25)/4 = 0.55 - 1,
for instance, if a = 2, b = 3, and c = 4. This demonstrates that the comprehensive answer.
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Evaluate 2( L+ 8Z) + L, when Z = 3 and L = 4.2
Answer:
Okay so z is 3.
We are going to put taht into our equation
2(L + 8(3)) + L
2(L + 24) + L
Now we do the 2
2L + 48 + L
Okay now L is 4.2
SO
2(4.2) + 48 + (4.2)
8.4 + 48 + 4.2 = 60.6
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2(l + 8z) + l}\\\mathsf{= 2(4.2 + 2(8)(3)) + 4.2}\\\mathsf{= 2(4.2) + 2(8)(3) + 4.2}\\\mathsf{= 8.4 + 16(3) +4.2}\\\mathsf{= \mathsf{8.4 + 48 + 4.2}}\\\mathsf{= 56.4 + 4.2}\\\mathsf{= 60.6}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{\mathsf{60.6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
❗️PLEASEE HELPPPPPP ILL GIVE YOU BRAINLIESTTTTTT ❗️
Find the value of v that makes quadrilateral PQRS a parallelogram.
P v+38°
s 8v-56°
R 6v–72°
Q v+98°
PLEASEE HELPPPPPP ILL GIVE YOU BRAINLIESTTTTTT
Answer:
there is no value of v that makes quadrilateral PQRS a parallelogram.
Step-by-step explanation:
Hopefully this helps, may be wrong so...
A quadrilateral is a parallelogram if and only if opposite angles are equal. Therefore, in order for quadrilateral PQRS to be a parallelogram, angle P must be equal to angle S, and angle Q must be equal to angle R. From the given information, we know that:
angle P = v + 38°
angle S = 8v - 56°
angle Q = v + 98°
angle R = 6v - 72°
To find the value of v that makes quadrilateral PQRS a parallelogram, we must set angle P equal to angle S and angle Q equal to angle R:
v + 38° = 8v - 56°
v + 98° = 6v - 72°
Solving for v in the first equation:
v + 38° = 8v - 56°
-7v = -94°
v = 13.428571428571429
Solving for v in the second equation:
v + 98° = 6v - 72°
-5v = -170°
v = 34
We can see that both values of v do not match, therefore there is no value of v that makes quadrilateral PQRS a parallelogram.
A quadrilateral is a parallelogram if and only if the opposite angles are equal. In this case, the opposite angles are P and S, and Q and R.
Therefore, for the quadrilateral PQRS to be a parallelogram, we must have:
v+38° = 8v-56° and v+98° = 6v–72°
Solving the first equation for v:
v+38° = 8v-56°
38 = 7v
v = 38/7
Now we use this value of v to check if the second equation is true:
v+98° = 6v–72°
(38/7) +98 = 6(38/7) - 72
98 = -34
As we can see, the second equation is not true, so the value of v = 38/7 doesn't make quadrilateral PQRS a parallelogram.
No value of v exists that would make quadrilateral PQRS a parallelogram, as the opposite angles are not equal in this case.
What is the slope of the line through the points (5, −5) and (6, 0) ?
Answer:
5
Step-by-step explanation:
the slope is Δy/Δx
0-(-5) =5
6-5 =1
slope is 5
First solve the system for x and y.
-3y+8x=18
y=6x-6
Step-by-step explanation:
given = y = 6x-6 .
therefore ,
=) -3(6x-6)+8x=18 - ( from given ) .
=) -18x+18+8x=18 .
=) -10x=18-18 .
=) -10x = 0 .
=) x = 0/10 = 0.
therefore ,
y=6(0)-6 .
= -6 .
therefore , x = 0 & y = -6 .
[ it takes so much time to write and solve so plzzz => ]
MARK ME AS BRAINLIEST ...Use the distributive property to write each expression as an equivalent
algebraic expression.
12(y+14)
Answer: 12y+168
Step-by-step explanation:
Basically, multiply each of the numbers that are in the parenthesis by the number outside the parenthesis (12). So 12·y=12y and 12·14=168. Therfore the answer is 12y+168 .
Classify the variables in the data if it’s (qualitative, nominal, ordinal, quantitative, discrete, or continuous etc)
The sample may or may not be representative depending on the sampling method that was used. If the sample was randomly selected from the population, it may be representative.
Classify the variables in the data if it’s?However, if the sample was not randomly chosen, then it may not be representative and may have bias.Gender: Nominal
Age: Ordinal
Number of Family Members: Quantitative, Discrete
Income: Quantitative, Continuous
Education Level: Ordinal
This sample may not be representative of the population as a whole, as it is a small sample size and may not accurately reflect the population.Additionally, the sample is not randomly selected and some groups may be over or underrepresented.Moreover, the sample is not stratified and the data may not be equally distributed across all categories.Therefore, this sample may not be representative and could lead to biased results.To learn more about data classification refer to:
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use ratio test to see if this series converges
This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] diverges.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given a series, [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] we need to see if the series converges or not.
the ratio test will fail if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | =1[/tex]. Otherwise, the series converges absolutely if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | < 1[/tex] and diverges if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | > 1[/tex]
Testing for the series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}\\[/tex],
=> [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right |[/tex]
=> [tex]\displaystyle \lim_{n\to \infty} \left |\frac{(n+1)!}{n!} \right | \\[/tex]
=> [tex]\lim_{n \to \infty} (n + 1)[/tex]
This value will always be greater than 1 for any positive value of n.
Therefore, This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] does not converge.
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HELPPP! Find the surface area of the triangular prism
here we are given a triangular prism and we are interested in finding its surface area .
The given prism comprises of 2 triangular faces and 3 rectangular faces . We can separately find the area and then add them up to find the resultant surface area.
Finding area of triangle:-
There are 2 triangles so the total area would be ,
Area = 2(ar. of one ∆)
Area = 2 ( 1/2 * base * height)
Area = 2 ( 1/2 * 16m * 5m )
Area = 80m²
Finding area of rectangle:-
Area = 3 ( length* breadth)
Area= 3 ( 17m * 10m)
Area = 3 * 170m²
Area = 510m²
Total area,
Net Surface area= area of rectangle+ area of triangle= (80+510)m² = 590m² [ required answer]
And we are done!
If the x-intercepts of a function are 2 and 5, then f(2) = _______. and f(5) = ________. The x-intercepts, 2 and 5, are called the _______ of the function.
If the x-intercepts of a function are 2 and 5, then f(2) = ____0___. and f(5) = ____0____. The x-intercepts, 2 and 5, are called the _zeros_ of the function.
What are the x-intercepts of the function?
The x-intercepts of a function y = f(x) are the values of x such that the graph of the function intercepts the x-axis, that means that are the values of x such that f(x)= 0
Then if 2 and 5 are x-intercepts of the function, then:
f(2) = 0
f(5) =0
The x-intercepts are allso called the zeros of the function.
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1. Last Monday Micah bought 5 % pounds of plant food. He used 1 7/8 pounds
for his tomato plants and 1 1/2 pounds for his pepper plants.
a. How many pounds of plant food did he have left? Write one or more
equations to show how you reached your answer.
5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds
What is algebra?The theory used in this question is algebra. Algebra is the branch of mathematics that studies the rules of operations and relations and the constructions and concepts arising from them.
In this question, algebra was used to solve for the number of pounds of plant food that Micah had left after using some for his tomato and pepper plants.
Step 1: Calculate the total amount of plant food that Micah bought: 5 % pounds
Step 2: Calculate the amount of plant food that Micah used for his tomato plants: 1 7/8 pounds
Step 3: Calculate the amount of plant food that Micah used for his pepper plants: 1 1/2 pounds
Step 4: Calculate the amount of plant food that Micah had left by subtracting the total amount of plant food used from the total amount of plant food bought: 5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds
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Draw the taste of the values for the relation y = x² for the Interval -3≤x≤4.
Answer: I don't have the capability to draw images. However, I can explain how to graph the equation y = x² for the interval -3≤x≤4.
To graph the equation, we can plot a set of points by substituting values of x from the given interval into the equation and solving for y.
For example:
when x = -3, y = (-3)² = 9
when x = -2, y = (-2)² = 4
when x = -1, y = (-1)² = 1
when x = 0, y = (0)² = 0
when x = 1, y = (1)² = 1
when x = 2, y = (2)² = 4
when x = 3, y = (3)² = 9
when x = 4, y = (4)² = 16
We can plot these points on a coordinate plane, and then connect them with a smooth curve.
The graph of y = x² for the interval -3≤x≤4 will be a parabola that opens upward and its vertex is located at (0,0) point.
The x-coordinates of the vertex are in the center of the inte
Step-by-step explanation:
A party hat is in the shape of a cone with dimensions shown.
Find the height of the hat. Round to the nearest tenth.
4.3 in.
10 in.
The height of the hat is 9.0 inches.
How to find the height of a cone?A party hat is in the shape of a cone with dimensions shown . Therefore, the height of the cone can be found as follows:
The radius of the cone is 4.3 inches and the slanted height of the cone is 10 inches.
Therefore, Pythagoras's theorem can be used to find the height of the cone. The radius and the slanted height of the cone forms a right angle triangle.
Therefore,
10² - 4.3² = h²
h² = 100 - 18.49
h² = 81.51
square both sides
h = √81.51
h = 9.02828887442
h = 9.0 inches
Therefore,
height of the hat = 9.0 inches
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Using Tiles to Multiply Two Binomials
Multiply: (x + 3)(x – 4)
The middle term in the simplified product for (x + 3)(x – 4) will be B. -x.
How to calculate the binomial?A polynomial with only terms is a binomial. For instance, the binomial x + 2 is composed of the terms x and 2.
Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is also referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form.
The product of (x + 3)(x – 4) will be:
= x² - 4x + 3x - 12
= x² - x - 12
In this case, the middle term in the simplified product is -x.
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the distribution system for the herman company consists of three plants, two warehouses, and four customers. plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows: customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows: choose the correct network representation of this problem. (i) (ii) (iii) (iv) formulate a linear programming model of the problem. for subtractive or negative numbers use a minus sign even if there is a sign before the blank. let xij represents relation between plants to warehouses or relation between warehouses to customers. min fill in the blank 2 x14 fill in the blank 3 x15 fill in the blank 4 x24 fill in the blank 5 x25 fill in the blank 6 x34 fill in the blank 7 x35 fill in the blank 8 x46 fill in the blank 9 x47 fill in the blank 10 x48 fill in the blank 11 x49 fill in the blank 12 x56 fill in the blank 13 x57 fill in the blank 14 x58 fill in the blank 15 x59 s.t. 1) fill in the blank 16 x14 fill in the blank 17 x15 < fill in the blank 18 2) fill in the blank 19 x24 fill in the blank 20 x25 < fill in the blank 21 3) fill in the blank 22 x34 fill in the blank 23 x35 < fill in the blank 24 4) fill in the blank 25 x46 fill in the blank 26 x47 fill in the blank 27 x48 fill in the blank 28 x49 fill in the blank 29 x14 fill in the blank 30 x24 fill in the blank 31 x34
All variables must be greater than or equal to 0, indicating that no shipping is allowed if the cost is negative.
The network representation of the Herman Company distribution system is as follows:
Plants (P1, P2, P3) -> Warehouses (W1, W2) -> Customers (C1, C2, C3, C4).
A linear programming model of the problem can be formulated as:
Minimize Z = 2x14 + 3x15 + 4x24 + 5x25 + 6x34 + 7x35 + 8x46 + 9x47 + 10x48 + 11x49 + 12x56 + 13x57 + 14x58 + 15x59
Subject to:
x14 + x15 ≤ 2
x24 + x25 ≤ 3
x34 + x35 ≤ 4
x46 + x47 + x48 + x49 ≤ 5
x14 + x24 + x34 ≤ 6
x15 + x25 + x35 ≤ 7
x46 + x56 + x66 ≤ 8
x47 + x57 + x67 ≤ 9
x48 + x58 + x68 ≤ 10
x49 + x59 + x69 ≤ 11
All variables ≥ 0
The objective of this problem is to minimize the total shipping cost from plants to warehouses and warehouses to customers. The constraints represent the limited capacities of each plant, warehouse and customer and the maximum number of units that can be shipped from each plant to each warehouse or each warehouse to each customer. All variables must be greater than or equal to 0, indicating that no shipping is allowed if the cost is negative.
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Do these data (Mod2-2Commercials (Links to an external site.)Links to an external site.) allow us to infer that the mean number of commercials watched during the game is different from 16? Assume the level of significance is 10%.
No, the data provided in the link does not allow us to infer that the mean number of commercials watched during the game is different from 16.
To test the hypothesis that the mean number of commercials watched is different from 16, we would need to perform a statistical hypothesis test. The level of significance (10%) would be used to determine the critical value(s) for the test statistic, which would then be used to make a decision about the null hypothesis (that the mean number of commercials watched is equal to 16).
Without the results of such a test, it is not possible to make a conclusion about the difference between the mean number of commercials watched and 16.
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The store is selling lemons at $0.52 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon juice?
A cause-and-effect relationship between two variables can best be determined from which of the following? When the two variables have a correlation. An observational study where the observational units are chosen randomly. A survey conducted using a simple random sample of individuals. A survey conducted using a stratified random sample of individuals. A controlled experiment where the observational units are assigned randomly to treatments.
The answer is A cause- and- effect relationship between two variables can best be determined When the two variables are identified.
Because the cause and effect relationship is chancing when the variables are identified or there exists a direct relationship between the variable. i.e. when the variables are identified or have a retrogression between the variables.The use of a controlled study is the most effective way of establishing reason between variables. In a controlled study, the sample or population is resolve in two, with both groups being similar in nearly every way.
There are three criteria that must be met to establish a cause- effect relationship. The cause must do before the effect. Whenever the cause occurs, the effect must also do. There mustn't be another factor that can explain the relationship between the cause and effect.
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An insurance company crashed 4 cars in succession at 5 miles per hour . The cost of the repair for each of the four crashes was $427, $451, $412, $212 compute the range ,sample variance and sample standard deviation cost of repair
The range is $______
Which method(s) of distributing supplies is best suited for specific items and quantities?
Direct delivery is coordinating with a specific location such as a shelter, feeding site or hospital for the delivery of specific items and quantities
What is distributing supplies?Distributing can be defined as the means of spread the product throughout the market place such that a large number of people can buy it.
There are five types of Distribution such as:
Direct distribution. This first system comprises directly performing merchandise distribution activities.Indirect distribution. A third-party-involved indirect distribution system is the second type.Intensive distribution.Exclusive distribution.Selective.Distributing channels are important to businesses as they allow for the smooth delivery of goods.
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Let $x$ be a real number selected uniformly at random between 100 and 200. If $\lfloor {\sqrt{x}} \rfloor = 12$, find the probability that $\lfloor {\sqrt{100x}} \rfloor = 120$. ($\lfloor {v} \rfloor$ means the greatest integer less than or equal to $v$.)
$\text{(A)} \ \frac{2}{25} \qquad \text{(B)} \ \frac{241}{2500} \qquad \text{(C)} \ \frac{1}{10} \qquad \text{(D)} \ \frac{96}{625} \qquad \text{(E)} \ 1$
The probability of successful region is =241/2500 Option b is correct.
Since √x=12, 12 ≤√x<13 and thus 144 ≤ x < 169.
The successful region is when 120 ≤ 10√x < 121 in which case 12 ≤√x< 12.1
Thus, the successful region is when
144 ≤ x < 146.41
The successful region consists of a 2.41 long segment, while the total possibilities region is 25 wide. Thus, the probability is
=2.41/25
=241/2500 (B)
In mathematics, a real number is a quantity that can be expressed as an infinite decimal expansion. In contrast to the natural numbers 1, 2, 3,..., which are derived from counting, real numbers are used in measurements of continuously varying quantities such as size and time.
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write in the form a b, where a and b are positive integers:
The expression of the fraction 256^-3/4 in the form of a / b is equal to 1 / 64 where highest common factor between 1 and 64 is 1.
Expression of the fraction 256^-3/4 in the form a /b .
Where 'a' and 'b' are positive integers .
'a' and 'b' have no common factor than 1.
256^-3/4
= ( 1 / 256^3/4 )
= 1 / 2^ (8 × 3/4 )
= 1 / 2 ^ ( 2 × 3 )
= 1 / 2^6
= 1 / 2⁶
= 1 / 64 in the form of ( a / b )
Greatest common factor between 1 and 64 is equal to 1.
1 and 64 are positive integers.
Therefore, the expression of 256^-3/4 in the a/b fraction form is equal to 1/64.
The given question is incomplete, I answer the question in general according to my knowledge:
Express 256^-3/4 as a fraction. Write the fraction in the form a/b, where a and b are positive integers with no common factor greater than 1 .
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For an experiment, Kelly poured equal amounts of distilled water into each of 30 beakers. She used a total of 4.2 liters of distilled water. How many liters did she pour into each beaker?
The required amount of water in each beaker would be 0.14 liters.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Kelly poured equal amounts of distilled water into each of the 30 beakers. She used a total of 4.2 liters of distilled water.
Amount of liters she put in a beaker,
= 4.2 / 30
= 0 .14 liters per beaker
Thus, the required amount of water in each beaker would be 0.14 liters.
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Below is the data for the unemployment rates from September 2017 issue of the Economist from 10 different countries. Country Unemployment Rates US 4.4 China 4 France 9.8 Spain 17.1 India 5 Greece 21.2 Chile 6.9Mexico 3.2 Egypt 12 Turkey 10.2 You can enter the data into R using this line of code below. GlobalRates<-c(4.4.4,9.8.17.1,5,21.2,6.9.3.2,12,10.2) Constuct a box and whisker plot and deterimine if there are any outliers in the Global Unemployment Rates. O There is one outlier, Greece, O There are two outliers, Greece and Spain.O There are three outliers, Spain, Greece and Turkey. O There are no outliers.
The answer is -There are no outliers.
According to the question, there are no outliers in the Global Unemployment Rates. From the given data, no outliers are observed.
An outlier is an observation that lies an abnormal distance from other values in a sample from a population. In a sense, this explanation leaves it up to the analyst to decide what will be considered abnormal.
An outlier is a single data point that goes far outside the average value of a set of statistics. Outliers may be exceptions that stand outside individual samples of populations.
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Rachel's health-related budget is as follows: The percentage budgeted for health Insurance is four times the percentage for health club dues. The percentage budgeted for prescriptions is equal to one-fourth the percentage budgeted for health insurance. The percentage budgeted for doctor visits is twice the percentage budgeted for prescriptions. a. What is the percentage for health insurance? 12.5% b.What are the percentages budgeted for all categories?
The percentages budgeted for all categories is 14.06%
What is the percentage for health insurance?A total of $900 seems to be spent on various health-related expenses:
medication costs, health club dues, and health insurance
seeing a doctor
If we go back in time, we can observe that the rate of doctor visits is double that of prescriptions, which is half that of health insurance,
which is 1/4 times that of health club dues.
As a result, if we consider x to be health club dues, health insurance is included.
4x medical visits, medicines, and health club dues 2x \s
sums to $900 = 8
The amount set up for health insurance is thus $112.5.
112 .5 * 12.5% = 14.06%
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which of the following options correctly describe scientific notation? select all that apply. multiple select question. one digit is present to the right of the decimal point in all cases. the exponent can be a positive or negative integer. the number must be a positive integer. one digit is present to the left of the decimal point in all cases.
"At least one digit is present to the left of the decimal point in all cases" and "the exponent can be a positive or negative integer" are the correct option for the given question.
Decimal numbers, also known as base-10 numbers. They use a system of digits from 0 to 9 and a decimal point to represent values. The decimal point separates the integer part of the number from the fractional part.
For example, in the decimal number 56.36, 56 is the integer part and 36 is the fractional part.
Hence, at least one digit is present to the left of the decimal point in all cases.
In scientific notation, the exponent is used to represent very large or very small numbers. The number is written in the form of a x [tex]10^n[/tex] where 'a' is a decimal number between 1 and 10 (inclusive) and 'n' is an integer (positive or negative) exponent.
Say, for example, 0.00006 can be written as 6 x [tex]10^{-5}[/tex] where 6 is the coefficient and -5 is the exponent.
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16 multiplied by what gives you 1600?
Answer:
The answer is 100. One way to find it out is 1600/16, and then you get 100.
find the rang of te function for the given domain
The range of the f(x) is {- 4, 0, 4, 8, 12}
Range of the function:A collection of numbers that represent every possible value of x is said to be the function's domain. The set of numbers that a function can produce is known as its range.
To find the range of a function substitute the domine values into the given function f(x).
Here we have
Give domain of f(x) = 4x + 4; { -2, -1, 0, 1, 2}
The range of the f(x) can be calculated as follows
Take x = -2 => f(x) = 4(-2) + 4 = -8 + 4 = - 4
Take x = -1 => f(x) = 4(-1) + 4 = - 4 + 4 = 0
Take x = 0 => f(x) = 4(0) + 4 = 0 + 4 = 4
Take x = 1 => f(x) = 4(1) + 4 = 4 + 4 = 8
Take x = 2 => f(x) = 4(2) + 4 = 8 + 4 = 12
Therefore,
The range of the f(x) is {- 4, 0, 4, 8, 12}
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A boat travels 10 miles upstream in 2 hours. Going downstream, it can travel 18 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water.
The speed of the current is 7 miles per hour,
and the speed of the boat in still water is 2 miles per hour.
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
Given A boat travels 10 miles upstream in 2 hours. Going downstream, it can travel 18 miles in the same amount of time.
let the speed of the boat and current be x and y,
for downstream,
x + y = D₁/t₁
D₁ = distance traveled in downstream = 18 miles
t₁ = time taken = 2 hours
x + y = 18/2
x + y = 9 .........(1)
for upstream,
x - y = D₂/t₂
D₂ = distance traveled in upstream = 10 miles
t₂ = t₁ = time taken = 2 hours
x - y = 10/2
x - y = 5 .......(2)
adding both equations
x + y + x - y = 9 + 5
2x = 14
x = 7 miles per hour
and x + y = 9
7 + y = 9
y = 9 - 7
y = 2 miles per hour
speed of the boat is 7 miles per hour and the speed of the current is 2 miles per hour.
Hence boat's speed is 7 miles per hour and the current speed is 2 miles per hour.
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