On solving the provided inequality equation we cans ay that therefore, 60x + 45 <250 is the necessary inequality for the given situation.
Describe inequality.An inequality in mathematics shows how two values are related in an imbalanced algebraic expression. According to inequality signals, one of the two variables on either side of the inequality may be larger than, greater than or equal to, less than, or less than or equal to another value.
If the daily cost for each crew member is $60, the daily wage for crew members is $60, and the daily cost of operations is $45; the amount paid equals the total of the wages for each crew member plus the cost of operations. In this case, let x indicate the size of the crew.
= 60x + 45
Since the maximum daily payment is $250,
In other words, the total payment cannot be more than $250.
60x + 45 ≤ 250
Therefore , the required inequality for given problem is 60x + 45 ≤ 250.
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The diagram shows two proportional right triangles.
What is the perimeter of the larger triangle?
Answer:
48 units.
Step-by-step explanation:
Since the triangles are similar (proportional), their dimensions are increased at the same ratio at any point, which means their perimeter too. So the base of the larger triangle is twice as long as the base of the smaller triangle.
The perimeter of the smaller triangle is 10 + 6 + 8 = 24 units.
24 * 2 = 48. Because the ratio of increase is 2:1 from the bigger triangle to the smaller triangle.
Hope you could understand this,
simpelest form of the ratio 2 weeks to 30 days
Answer:
7:15 ,2 weeks=14 days and 30 days divide by 2 = 7 and 15 put them to a ratio and you'll get 7:15.
Can u please help......,,,....
The length of the sides of ΔABC are; AB = 2√5, BC = √13, and AC = √17
The length of the sides of ΔDEF are; DE = 2√5, EF = √13, and DF = √17
By the SSS Congruence Theorem, ΔABC ≅ ΔDEF
How to prove triangle congruency postulate?We are given the coordinates of Triangles ABC and DEF as;
A(5, 3), B(7, 7), C(9, 4)
D(-8, 6), E(-12, 8), F(-9, 10)
The formula for distance between two coordinates is;
Distance = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus;
AB = √[(7 - 3)² + (7 - 5)²]
AB = √20
AB = 2√5
Similarly;
BC = √[(4 - 7)² + (9 - 7)²]
BC = √13
AC = √[(4 - 3)² + (9 - 5)²]
AC = √17
Likewise;
DE = √[(8 - 6)² + (-12 + 8)²]
DE = √20
DE = 2√5
Similarly;
EF = √[(10 - 8)² + (-9 + 12)²]
EF = √13
DF = √[(10 - 6)² + (-9 + 8)²]
DF = √17
Since the corresponding sides of the two triangles are equal and as such they can be said to congruent by SSS Congruency.
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Plot the remaining data point. 1
2
, 1 , 1
1
4
, 1
1
4
, 1
3
4
, 3 , 3
3
The information you gave was presented as a table with three columns: value, x-coordinate, and y-coordinate.
You would need to make a graph with the x-coordinate acting as the horizontal axis and the y-coordinate acting as the vertical axis in order to plot this data point. The size or colour of the data point would serve as a representation of the value.
Here is an illustration of a data point plot:
[tex]x | 12 | 14 | 14 | 34 \\ y | 1 | 1 | 3 | 3 \\ v | 1 | 1 | 3 | 3[/tex]
The value at the position (12,1) will be 1, the value at the point (14,1) will be 1, the value at the point (14,3) will be 3, and the value at the point (34,3) will be 3. It's vital to remember that the values on the graph can be depicted by many colours or shapes.
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Fwam went shopping for a new phone. Sales tax where he lives is 9%. The price of the phone is $33. Find the total price including tax. Round to the nearest cent.
Answer:
$35.97
Step-by-step explanation:
33 × .09 = 2.97
33 + 2.97 = $ 35.97
Consider the differential equation dy/dx=xy^4.
(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.
The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.
What is a differential equation?
A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.
The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.
Given,
[tex]\frac{dy}{dx} = xy^{4}[/tex]
a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]
In quadrant II, the values of x < 0 and the values of y >0.
So [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.
Therefore the concavity is up for of all solution curves of the given differential equation.
b)
[tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]
Now it is given that initial condition is f(4) = -1
So substituting x =4 and y = -1 is the above equation to find c, we get
[tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]
Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.
[tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]
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Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice. Which histogram represents Blanca’s lap times for the three days of practice?
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds
What is endurance race?
A type of motorsport racing known as endurance racing is designed to test both the participants' and the equipment's endurance. Teams of several drivers attempt to travel a long distance in a single race while being allowed to change drivers at any time.
The given table is attached below.
The number of laps in the range 82 to 84 seconds = 1
The number of laps in the range 84 to 86 seconds = 4
The number of laps in the range 86 to 88 seconds = 2
The number of laps in the range 88 to 90 seconds = 4
The number of laps in the range 90 to 92 seconds = 6
The number of laps in the range 92 to 94 seconds = 5
The number of laps in the range 94 to 96 seconds = 2
The number of laps in the range 96 to 98 seconds = 0
Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds.
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Answer:A
Step-by-step explanation:
find the value of x and y (2x+5) , (5x-17) and (3x-11)
The value of x and y in the diagram are 26° and 9° respectively.
What is linear pair theorem?Two adjacent angles formed a linear pair.
The linear pair property:
The sum of the angle measure of both the angles is 180°.
Given:
Using linear pair theorem,
(5x - 17)° + (3x - 11)° = 180°.
8x - 28°= 180°
8x = 180° + 28°
8x = 208°
x = 208/8
x = 26°
The value of x is 26°.
Now,
3x - 11° = 3×26°-11°
= 67°
Linear pair theorem,
67° + 90° + (2y+5)° = 180°
157°+2y+5° = 180°
2y + 162° = 180°
2y = 180° - 162°
2y = 18°
y = 9°
The value of y is 9°.
Therefore, the value of x is 26° and y is 9°.
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The complete question is given in the attached image.
What's the domain of a logarithmic function?
Answer:
all positive numbers
Step-by-step explanation:
You want to know the domain of the log function.
Log functionThe log function ln(x) is defined for all x > 0. A log function with any other base is similarly defined.
log function domain: all positive numbers
A parent log function has a vertical asymptote at x=0, and an x-intercept at x=1. Its vertical scaling will depend on the base of the logarithm. Like any function, it can be translated and scaled horizontally and vertically.
__
Additional comment
In the field of complex numbers, the log function is defined for any non-zero number. For example, ln(-1) = πi.
The range is all real numbers.
The diameter of a circle is 34 inches.What is the area of the circle in square inches?Use 3.14 as pi
Answer: 907.46 inches squared
Step-by-step explanation:
The formula for the area of the circle is:
[tex]A = \pi r^{2}[/tex]
In this question, pi is 3.14. The radius of a circle is half of its diameter. So:
[tex]\frac{34}{2} =17[/tex]
Plug these values into the equation:
[tex]A = (3.14)(17)^2[/tex]
Simplify:
[tex]A = 907.46[/tex]
The area of the circle is 907.46 inches squared.
What is dual and complement?
The Boolean dual are created by replacing AND operator with OR operator and the complement is defined as the negation of the statement .
What is Boolean Expression ?
The Boolean Expression is defined as a logical statement that is either TRUE or FALSE . It compares data of any type as long as both the parts of expression have same basic data type.
The Dual of Boolean Expression are calculated by simply replacing AND operator with OR and OR operator with AND .
The Compliment of Boolean Expression is defined as negation of variables with replacement .
For Example : if the statement is [tex]A+B[/tex] ,
then the dual will be [tex]AB[/tex] and the compliment will be [tex]A'B'[/tex] .
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A solution of 60 quarts of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar
On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
1200=300+5x
900 = 5x
x=180
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Similar figures review - Question 1
For a house that have a height of 6 meters and length of 4.5 meters. On a scale drawing if the height of the house is 30 mm the length of the house will be 22.5 mm
What is proportions?In general, the term proportion refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal.
How to find the length of the houseThe length of the house on the map is calculated using equality in proportions as follows
The required proportion is
= height of the house / length of the house
= 6 / 4.5
= 4/3
Using this proportion, the length of the house in the drawing is
= 30 mm / 4/3
= 22.5
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help i have 5 mins left
Answer: c = P - a - 5
Step-by-step explanation:
P= a + 5 + c
P - a - 5= c
Marvin used the money he received from high school graduation gifts to start a new savings account with a simple interest rate of 7. 5%. After 12 years, the account had earned $288. If there were no other deposits or withdrawals, what was the original amount placed in the account?
The original amount placed in the account is $320.
What is simple interest ?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
The simplest way to compute interest is as a percentage of the principal. For instance, if you borrow $100 from a friend and agree to pay back the money with 5% interest, the interest you would have to pay would simply be 5% of $100, or $5.
Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time.
The interest earned is calculated as follows:
I = P*r*t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
Marvin is saving money in a savings account with a simple interest rate of r=7.5%=0.075. It's known that after t=12 years, the account had earned $288 interest.
Substituting in the formula:
288 = P*0.075*12
Calculating:
288 = 0.9P
Dividing by 0.9:
P = $320
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Hexagon K is a scaled copy of Hexagon J
The scale factor 5/2 takes hexagon J to hexagon K.
What is Hexagon?A hexagon or sexagon in geometry is a six-sided polygon or 6-gon that forms the shape of a cube. Any basic hexagon has 720° in total internal angles. No matter the type of hexagon, all of them have six sides. As a result, all types of hexagons—regular, asymmetrical, concave, and convex—have six sides. The hexagon, which has six sides mathematically, is particularly intriguing because it covers a plane with units of equal size and leaves no empty space. Because of its 120-degree angles, hexagonal packing also reduces a given area's perimeter.Hexagon AB, a leader in virtual reality hardware and software, was founded in 1992 and is a publicly traded, multinational information technology business with its headquarters in Stockholm, Sweden. Hexagon's B share is listed among the top firms by the Stockholm Stock Exchange.From the given two Hexagon's K and L, the Hexagon K is copy to Hexagon K.
The scale factor = the ratio of edges
Scale factor = 20/8 = 30/12 = 5/2
Hence, the scale factor 5/2 takes hexagon J to hexagon K.
Complete question:
Complete question is attached below.
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N is an integer such that
3n+4 <19 and 10n/n^2+16Find all the possible values of n.
N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.
What is an integer?An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.
What are the steps to solving inequalities?Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.
Now we solve
3n+4 <19
3n+4-4<19-4
3n<15
n<5
so n is less than and equal to 5 it will be {3, 4, 5].
10n/[tex]n^{2}[/tex]+16 >1
10n> [tex]n^{2}[/tex] +16
0> [tex]n^{2}[/tex]-10n +16
0>[tex]n^{2}[/tex] -8n -2n +16
0> n(n-8)-2(n-8)
0> (n-8) (n-2)
So n-2<0 n-8<0
n<2 n<8
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2 + (4-3 (3-6) -4] +12=
Answer: 23
Step-by-step explanation:
Write and solve an equation to find the value of x.
Answer:
x = 60
Step-by-step explanation:
Let the two opposite angles be equal and let's call them y.
Because of the theory of angles on a straight line 120 +y = 180
y = 60
Because of the theory of angles on a straight line 2x + y = 180
2x + 60 = 180
2x = 120
x = 60
Alternatively. (also a lot easier)
120 and 2x are opposite angles so they are equal and so;
2x = 120
x = 60
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Help me on this question.
The value of y from the equation is y = 5
The measure of RS = 38
The measure of ST = 18
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , on the number line , the measures of the sides are
The measure of RS = 7y + 3 be equation (1)
The measure of ST = 2y + 8 be equation (2)
The measure of RT = 56
Now , from the line segment ,
RT = RS + ST be equation (3)
Substituting the values in the equation , we get
7y + 3 + 2y + 8 = 56
On simplifying the equation , we get
9y + 11 = 56
Subtracting 11 on both sides of the equation , we get
9y = 45
Divide by 9 on both sides of the equation , we get
y = 5
Substitute the value of y in equations (1) and equation (2) , we get
The measure of RS = 7 ( 5 ) + 3 = 38
The measure of ST = 2 ( 5 ) + 8 = 18
Hence , the equations are solved and the value of y = 5
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A researcher wants to set up a hypothesis test to determine if there is a difference in the mean exam scores of students who are visual learners, versus auditory learners, versus kinesthetic learners. What would be the correct setup for the null and alternative hypotheses for this test
On solving the provided question we can say that here in null hypothesis a negative relationship; as anxiety rises less items are remembered
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
here,
in null hypothesis a negative relationship; as anxiety rises less items are remembered
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Sara's mom takes the parkway to work. It takes her 30 minutes to travel from mile marker 88 where she enters to her exit at mile marker 121. What is her average speed
Sara's mom average speed is 66mph. The next step is to divide the distance by the time: 33/0.5 = 66 mph.
What is average speed ?You may estimate the average pace at which an object will go a distance by looking at its average speed. Average speed is calculated by dividing a quantity by the time required to obtain that quantity.
Finding the distance and the time is necessary to calculate speed.
In this situation, you must deduct mile marker 88 from 121 to determine the distance.
121 - 88 = 33mile
Even though the time is 30 minutes, you're probably interested in miles per hour. 30 minutes must be converted to 0.5 hours.
The next step is to divide the distance by the time: 33/0.5 = 66 mph.
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(d) At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave.
The lower bound for the number of minutes that it takes for all people to leave is of:
70 minutes.
How to obtain the lower bound for the number of minutes that it takes for each person to leave?At a football match, there are 29 800 people, correct to the nearest 100. The fewest number of people that can be there, hence, is of:
29,750.
(as 29749 would be rounded to 29,700).
At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people, hence the fastest rate is given as follows:
424 people per minute.
(as 425 people would be rounded to 450).
Hence the time it would take is obtained applying the proportion as follows:
29750/424 = 70 minutes.
(lower bound is fewest time, hence lowest number of people leaving at the fastest rate).
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What is the value of W?
Answer:
Step-by-step explanation:
Let angle A = w - 15 degree , angle B = -w + 1 degree and angle X = w + 34 degrees then:
We know that the exterior angle of a triangle is equal to the sum of two interior opposite angles.
therefore, w + 34 = w - 15 + (-w +1)
w + 34 = w - 15 - w + 1
w = -15 - 34 = - 49 degrees
since angle cannot be negative
therefore w = 49 degrees
Is 0 the middle of a number line?
Zero is the middle point of a number line.
On the number line, all positive (natural numbers) numbers are on the right side of zero, while all negative numbers are on the left. A number's value lowers as we turn to the left. As an illustration, 1 is greater than -2.
A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point. [1]
The integers are frequently represented as specially designated, uniformly spaced dots on a line. It is frequently employed as a teaching tool for basic addition and subtraction, particularly when negative numbers are involved.
The number line may also be referred to as a real line or real number line in advanced mathematics.
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Given the lengths of two sides of a triangle, determine the range, a, of possible side lengths of the third side.
5 km and 11 km
12 mi and 12 mi
25 yd and 10 yd
By using the triangular inequality, we will get the possible lengths:
a) 6km < x < 16km
b) 0mi < x < 24mi
c) 15yd < x < 30yd
How to estimate the lengths of the possible third side?If A, C, and D are the lengths of the sides of a triangle, then the triangular inequality says that:
A + C > D
A + D > C
C + D > a
Now, if the two sides are 5km and 11 km, and the other side is x, then we can write:
x + 5km > 11km
x + 11km > 5km
11 km + 5 km > x
From these inequalities we can get:
16km > x
x > 11km - 5km
x > 6km
Then the possible lengths of the third side are:
6km < x < 16km
b) Now the sides are 12 mi and 12mi, then the inequalities are:
x + 12mi > 12mi
12mi + 12mi > x
The first one gives:
x > 0mi
The second:
24mi > x
The possible lenghts are 0mi < x < 24mi
c) 25 yd and 10 yd
Here we will get:
25yd + 10yd > x ----- > 30yd > x
x + 10 yd > 25yd -------> x > 15yd
The possible lengths are:
15yd < x < 30yd
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\frac { 32 x ^ { 2 } } { y } + \frac { 108 y ^ { 2 } } { x } y 32x 2 + x 108y 2
Therefore , the solution of the given problem of fraction comes out to be 4((2x)³ + (3y)³) /xy.
What exactly is a fraction?To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the fraction to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the exponent or population of a complicated fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces. For instance, 12 is used to denote half of a total number or item.
Here,
Given : 32x²/y + 108y²/x
=> (32x³+ 108y³ ) /xy
=> 4(8x³ + 27y³) /xy
=> 4((2x)³ + (3y)³) /xy
Therefore , the solution of the given problem of fraction comes out to be
4((2x)³ + (3y)³) /xy.
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An instructor gives four -hour exams and one final exam, which counts as three -hour exams. Find a student's grade if she received , , , and on the -hour exams and on the final exam. Round your answer to one decimal place if necessary.
One final test that lasts three hours is given in addition to four-hour exams that are given by the teacher. The student's last grade is an 83.29.
What is students final average ?The final exam result was an 80, which counts as 31 hour examinations if the exam scores range from 60 to 81, which totals to 97,87. In order to accomplish this, we must multiply three eighty by 62, 81, 97, and 87, which equals a 31-hour exam.
The whole time for the final exam, which is 31 hours, will be added up and divided by 7, giving us an average final grade for the student of 81.To reduce the number's number of significant digits in order to approximate it. Rounding down from 15.4 to 15.5, from 15.51 to 15.5 or 16, from 0.499 to 0, and from 970,000 to 1 million.
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Which strategies can be used to find the product of 1,587 x 1,000? Select two options
Answer:
Step-by-step explanation:
you can multiple and get 1,587,000]and then you divide to get 8 [tex]\sqrt{1587000[/tex]Is 4x² 3x 7 a polynomial in one variable?
'x' is the only variable in the provided polynomial. As a result, the polynomial 4x² - 3x + 7 has one variable.
what is polynomial ?A polynomial is an expression in mathematics made up of variables (sometimes referred to as indeterminates) and coefficients that only employs the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that combines variables, constants, and exponents utilizing addition, subtraction, multiplication, and division of numbers (No division operation by a variable).
given
'x' is the only variable in the provided polynomial. As a result, the polynomial 4x² - 3x + 7 has one variable.
The following list includes a few examples of polynomials with one variable: x+2. x2+3x+2.
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