The minimal number of employees who did not get their preferred shift that week was 20.
Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.
But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.
We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.
But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.
Thus, 20 is the minimum number of staff members who failed to receive her preference of shift that week.
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Teresa wrote this expression to describe the total distance she was going to swim during two swim classes s+3 which situation could be described by this expression
The correct answer of expression 's+3' is (c) Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class. She used the sign "+" instead of "x" or any other notation.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression is (Number/variable, Math Operator, Number/variable)
The answer here should be Option C, as she used the sign "+" instead of "x" or any other notation. She wanted to add something.
And as it is very clear that she wanted to write the information about two classes, so that makes the second term for second class and first term for first class.
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The complete Question is:
Teresa wrote this expression (s+3) to describe the total distance she was going to swim during two swim classes. Which situation could be described by this expression?
A. Teresa wasn't sure how far she would swim during the first class. She would swim 3 fewer laps during the second class.
B. Teresa wasn't sure how far she would swim during the first class. She would swim the same distance for 3 classes.
C. Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class.
D. Teresa wasn't sure how far she would swim during the first class. She would swim 3 times farther during the second class.
3x-3y=-6
3x+y=10 use subtraction please help thank you
need an ordered pair
Answer:
x=2, y=4. (2, 4).
Step-by-step explanation:
3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.
-----------------------------
x-y=-2
3x+y=10
---------------
4x=8
x=8/4=2
2-y=-2
y=2-(-2)=2+2=4
ractical Work/Activities A problem on the purification of the impurities present in the pond is given by t 8100p C(p) = 100-P where p is the percentage impurities present in the polluted water and C(p), the pr Rs. needed to remove p% of the impurities. a) Find the cost of removing 90% of the impurities. lim Find C(p). What does the value mean? p→19 Is it possible to purify completely? Give reason. b) c) O oved by Curriculum Development Centre (CDC), Nepal
Therefore , the solution of the given problem of ratio comes out to be
lim C(p) as p->19 = 152900.
Define ratio.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Here,
a) To find the cost of removing 90% of the impurities, we can substitute 90 for p in the equation:
C(p) = 8100p / (100-p)
C(90) = 8100(90) / (100-90)
C(90) = 729000
So the cost of removing 90% of the impurities is Rs. 729000.
b) To find the limit of C(p) as p approaches 19, we can substitute 19 for p in the equation:
lim C(p) as p->19 = 8100(19) / (100-19)
lim C(p) as p->19 = 152900
The value of the limit of C(p) as p approaches 19 means that as the percentage of impurities approaches 19, the cost of purification approaches Rs. 152900.
c) It is not possible to purify completely as the percentage of impurities approaches 100. It's because as the percentage of impurities becomes closer to 100, the denominator of the fraction becomes smaller, thus the value of the cost of purification becomes larger, and it is impossible to pay an infinite amount of money.
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Which simplified ratio correctly compares 5 meters to 100 centimeters?
A. 5:1
B. 20:1
C. 1:5
D. 1:20
The simplified ratio that compares 5 meters to 100 centimeters is 5: 1 .Option A
How to determine the ratioRatio is simply described as the non equal comparison of two numbers, variables, or events.
It shows how many times a number or variable contains another.
The comparison is also based on size.
From the information given, we have;
5 meter to 100 centimeters
It is important to note that;
100 centimeters = 1 meters
Also, 1 meter= 100 centimeters
5 meters = x centimeters
cross multiply
x = 100(5)
Multiply the values
x = 500 centimeters
Then,
5 meters = 1 meter
Hence, the ratio is 5:1
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Find the lengths of the diagonals of rectangle WXYZ
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.
A rectangle is a four-sided geometric shape where opposite sides are parallel and congruent. The diagonals of a rectangle are two lines that connect the opposite corners of the rectangle, and they bisect each other at 90 degrees.
Briefly defined, what is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Given the sides of rectangle WXYZ are WY = 14x + 10 and XZ = 11x + 22. We can find the length of the diagonals using the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the diagonal of the rectangle) is equal to the sum of the squares of the other two sides (the sides of rectangle)
Diagonal WX: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)
Diagonal YZ: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)
So, the lengths of the diagonals of rectangle WXYZ are √(317x^2 + 940x + 584) units.
Note that the diagonals of a rectangle are congruent and the value of x is not a known, the diagonal of rectangle is the value of the square root of the expression.
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Answer: 66
Step-by-step explanation:
I skipped it to see the answer hope this helps
Williamston Daily is a new daily newspaper. When they first started printing three years ago they had 5900 home delivery subscribers. The number of subscribers increases by 66 every month. Write an equation that expresses the number of subscribers B in terms of n, the number of months the paper has been printed.a.B
this is a question of set of equations and solution is as follows,
Williamston Daily newspaper started printing newspaper.
Three years ago they had 5900 subscribers.
every month there is an increase of 66 new subscribers.
n is the number of months the paper has been printed.
so, the linear model will be
B= early subscriber + number of month × increments
B= 5900 + n × 66
B= 66 n + 5900
Example - subscribers after 3 months,
n = 3
= 66 x 3 +5900
= 198 + 5900
= 6000
set of equations
A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Linear equations
Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
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9) Express the roots of the equation 2x² + 4x + 5 = 0 in simplest a + bi form.
2x2+4x5=0 is a quadratic equation that can be solved. 2 x 2 + 4 x - 5 = 0. To find the answers, start with the quadratic formula.
What is the quadratic equation of 2x² 3x 5 0?Using the quadratic formula, determine the roots of the quadratic equations 2x2-3x-5= 0. The equation's roots must be located. As a result, the equation's roots are 5/2 and -1. Which equation with 2 as a root must be identified. As a result, 2 is not a root of x2-4x + 5= 0.
Since 2 is not a root, x2 + 3x-12= 0 cannot be solved. Thus, 2 is the root of the equation 2x2-7x + 6= 0. The roots of the quadratic equation ax2 + bx + c= 0 are real and equivalent if the discriminant is equal to zero (b2-4ac=0), a, b, and c are real values, and a0. The roots in this situation arex= -b/2a.
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Select the correct answer. Solve the quadratic equation by factoring.
9x -16 = 0
Answer:
x = 16/9
Step-by-step explanation:
9x -16 = 0
9x = 16
x = 16/9
Let's check
9(16/9) -16 = 0
144/9 - 16 = 0
16 - 16 = 0
0 = 0
So, x = 16/9 is correct!
Answer:
Step-by-step explanation:
9x = 16
x = 16/9
What is the equation of the straight line shown below? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms. Y 14- 13- 12- 11- 10- 9 8- 97654 MNE 7- 6- 5- 4- 3- 2- 1- -10-9-8-7-6-5-4-3-2 0 1 2 3 4 5 6 7 8 9 10 x -1 -2- -3- بنا -4- 56 -5- -6+
Answer:
y = 2x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line
m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2
the line crosses the y- axis at (0, 10 ) ⇒ c = 10
y = 2x + 10 ← equation of line
Question 12
In the figure shown, if J, P, and L are the midpoints of KH, HM, and MK, respectively, find the values of x, y, and z.
Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility test for three.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
add all number
9+9+0 = 18
and 18/3 = 6
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On solving the provided question, we can say that in this triangle 2x-6 = 3 => 2x = 9 => x = 9/2 and 2z = 4 => z = 2
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
in this triangle
2x-6 = 3
2x = 9
x = 9/2
2z = 4
z = 2
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What is the probability that this year's graduation will fall on the birthday of exactly one of the 68 Seniors? What is the probability that there is more than one such Senior?
The probabilities are given as follows:
Birthday of one student: 0.1550 = 15.50%.Birthday of more than one student: 0.0152 = 1.52%.What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 68, as the class is composed by 68 Seniors.p = 1/365, as the year has 365 days, hence the probability of a person having a given day as a birthday is of 1/365.Hence the probability of one senior having the birthday on the same day as the graduation is of:
P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.
The probability of more than one is given as follows:
P(X > 1) = 1 - P(X <= 1).
In which:
P(X <= 1) = P(X = 0) + P(X = 1)
Hence:
P(X = 0) = (364/365)^68 = 0.8298.P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.Finally:
P(X <= 1) = 0.8298 + 0.1550 = 0.9848.P(X > 1) = 1 - P(X <= 1) = 1 - 0.9848 = 0.0152.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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Amelie is making a recipe that uses 134 cups flour. She is making 212 times the original recipe. Amelie draws this model to represent the number of cups of flour she needs. How many cups of flour does Amelie need
Amelie needed 335 cups of flour for the recipe.
How is quantity calculated?The whole centre line length, as well as the construction's breadth and depth, must be multiplied in order to determine the required amount of quantity. Every time the main wall is attached to a cross wall, a partition, or a verandah, the centre line length will be halved at that intersection.Any number, variable, or algebraic combination of other numbers can be a quantity in a mathematical equation. Seven, ten, x, and the product of x and seven, or x + seven, are the four numbers in the equation x + 7 = 10.The unit price is the cost per unit of the product you are purchasing. The amount might be given per thing or per measurement type, such ounces, grammes, gallons, or litres.Given data :
She is making 2 1/2 or 2.5 times the original recipe.
Cups in original recipe= 134 cups
cups Amelie will need= 2.5 × 134
= 335 cups
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What is the solution of 7x =- 63?
The answer to 7^2 is 49. This means that 7 is multiplied by itself two times. To solve the given problem following steps should be followed :
Step 1: To calculate the value of 7 power 2, we need to use the exponentiation operator (^).
Step 2: The operator is written as 7^2, which is read as "seven to the power of two".
Step 3: We can calculate the value of 7 power 2 by multiplying 7 by itself 2 times.
Step 4: 7 × 7 = 49
Therefore, 7 power 2 = 49.
An expression known as "power" is defined as the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.
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How do you write no solution?
No solution is when a system of equations has no solution. This means that the equations are inconsistent, and there is no set of values that can make the equations true.
For example, if the system of equations is 2x + 3y = 4 and 2x + 3y = 5, then there is no solution. This is because no matter what values are chosen for x and y, the equations cannot both be true. This means that the system of equations is inconsistent, and there is no solution.
To symbolically represent no solution, you can use the following notation:
2x + 3y = 4, 2x + 3y = 5 No solution
This notation is used to indicate that the equations are inconsistent and that there is no solution.
Complete question: What is the solution to the equation 2x + 3y = 4 and 2x + 3y = 5?
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You want to ride your bike down the street to your friend's house, which is 340 meters from your house. The trip takes you 68 seconds from start to finish. How fast are you traveling on your bike?
The speed of the Bike is 5 meters per second
What is speed?Speed is a scalar quantity that describes how fast an object is moving . It is defined as the distance an object travels divided by the time it takes to travel that distance. The units of speed are typically meters per second (m/s) or kilometers per hour (km/h).
To find out how fast you are traveling on your bike, you can use the formula:
Speed = [tex]\frac{Distance}{Time}[/tex]
In this case, the distance is 340 meters and the time is 68 seconds. So, you can plug these values into the formula and get:
Speed = 340 meters / 68 seconds
Speed = [tex]\frac{340 meters}{68 seconds}[/tex] = 5 meters per second
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The sum of -3 times x +6.3 what are all the possible values of x
So x = 2.1 is the only possible value of x that makes the equation true.
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
The equation is given as follows:
-3x + 6.3 = 0
To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:
-3x + 3x + 6.3 = 0 + 3x
6.3 = 3x
Now we can divide both sides by 3:
x = 6.3/3
x = 2.1
So x = 2.1 is the only possible value of x that makes the equation true.
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Clare made an error when solving -4x+3<23−4x+3<23.
The solution of the inequality is,
⇒ x > - 5
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 4x + 3 < 23
Now,
Since, The inequality is,
⇒ - 4x + 3 < 23
Solve as;
⇒ - 4x < 23 - 3
⇒ - 4x < 20
⇒ - x < 5
⇒ x > - 5
Thus, The solution is,
⇒ x > - 5
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Find the measure of the indicated angle to the nearest degree.
Answer:
70⁰
Step-by-step explanation:
We need to use the knowledge of trigonometry to find the indicated angle. Given the information in relation to the angle we have the opposite and the hypotenuse.
we therefore use Sine in this calculations
Sin ? = opposite/ hypotenuse
= 16/17
= 0.9412
to get the angle we get the sine inverse
Sine inverse of 0.9412 = 70.25⁰
= 70⁰
Answer:
? ≈ 70°
Step-by-step explanation:
using the sine ratio in the right triangle
sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then
? = [tex]sin^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 70° ( to the nearest degree )
Write the Riemann sum to find the area under the graph of the function f(x) = x4 from x = 5 to x = 7.
Answer:
Refer to the attached image.
Step-by-step explanation:
Octagon ABCDEFGH with side lengthsABCDEFGII 10 and BC=DE FG = HA= 11 isformed by removing 6-8-10 triangles from the corners of a 23 x 27 rectanglewith side AH on a short side of the rectangle, as shown. Let J be the midpointof AH, and partition the octagon into 7 triangles by drawing segments JB,JC, JD, JE, JF, and JG. Find the area of the convex polygon whosevertices are the centroids of these 7 triangles.
Area of the convex polygon whose vertices are the centroids of these 7 triangles is 184.
What is a convex polygon?
A polygon that forms the edge of a convex set is said to be convex polygon. This indicates that the union of the interior and the boundary of the polygon has the line segment connecting two points of the polygon.
Given,
AB = CD = EF = GH = 10
BC = DE = FG = HA = 11
Triangles of side length 6,8,10 is cut from corners 23×27 rectangle.
Using the above information, we marked the position of A,B,C,D,E,F,G,H and J, taking the upper left corner of rectangle as origin.
The centroid of a triangle can be found using the formula,
Centroid = [tex](\frac{x_{1} + x_{2}+x_{3}}{3} , \frac{y_{1} +y_{2}+y_{3}}{3})[/tex]
For ΔJAB,
[tex]C_{1}[/tex] = (8/3 , -35/6)
For ΔJBC,
[tex]C_{2}[/tex] = ( 9 , -23/6)
For ΔJCD,
[tex]C_{3}[/tex] = ( 46/3, -35/6)
For ΔJDE,
[tex]C_{4}[/tex] = ( 18 , -23/2)
Area of convex polygon = [tex]\frac{1}{2} [x_{1} y_{2} + x_{2}y_{3}+.........+x_{n}y_{1}] - [y_{1}x_{2}+y_{2}x_{3}+......+y_{n}x_{1}][/tex]
From figure we find the area of C₁C₂C₃C₄C₈, where C₈ = (8/3 , -23/2)
Area =
[tex]\frac{1}{2} [8/3 (-23/6 )+ 9(-35/6)+46/3(-23/2)+18(-23/2)+8/3(-35/6)] - [(-35/9)9+(-23/6)46/3+(-35/6)18+(-23/2)8/3+(-23/2)8/3][/tex]
= 184 / 2
Therefore total area of convex polygon = 2 × 184/2 = 184 sq. units
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Find the length of the third side. If necessary, round to the nearest tenth
Answer:
6.3
Step-by-step explanation:
This is a right triangle, so in order to solve you can use the Pythagorean theorem; which is a² + b² = c² (The hypotenuse, or the longest side, equals C. A and B equal the legs, or the shorter sides.) So once you plug in the values, your equation should look like this:
3² + b² = 7²
Square each side, or in other words multiply it by itself.
9 + b² = 49
Subtract 9 from both sides.
b² = 40
Take the square root of 40 and your done!
b = 6.3
I hope this helped you! :)
19. The Beaufort Scale measures the intensity of tornadoes. For a tornado
3
with Beaufort number B, the formula v = 1. 9B2 may be used to
estimate the tornado's wind speed in miles per hour. Estimate the wind
speed of a tornado with Beaufort number 9.
The the wind speed of a tornado with Beaufort number 9 is 51.3 miles per hour.
What is speed?
Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in meters per second (m/s) in this example because the distance is measured in meters (m) and the time is measured in seconds (s).
Given:
The Beaufort Scale measures the intensity of tornadoes. For a tornado
with Beaufort number B, the formula [tex]v = 1.9B^\frac{3}{2}[/tex] may be used to
estimate the tornado's wind speed in miles per hour.
We have to estimate the wind speed of a tornado with Beaufort number 9.
Plug B = 9 in the formula [tex]v = 1.9B^\frac{3}{2}[/tex]
⇒
[tex]v = 1.9(9)^\frac{3}{2} \\v = 1.9(27)\\v = 51.3[/tex]
Hence, the the wind speed of a tornado with Beaufort number 9 is
51.3 miles per hour.
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At what ordered pair will the function
f ( x ) = √ x + 2 - 2
begin on the coordinate plane?
( ? , ?)
Answer:(-2,-2)
Step-by-step explanation:
The radical has a value of 0 when x = -2. At that point, the function value is ...
f(-2) = √(-(-2)-2) -2 = √(0) -2
f(-2) = -2
Please help with all
−8≤2−10
Can you please help me find it?
Answer:
-8 [tex]\leq[/tex] -8
Step-by-step explanation:
-8[tex]\leq[/tex]2-10
-8[tex]\leq[/tex]-8
Answer:
-8
Step-by-step explanation:
-8≤2-10
2-10 = -8
-8≤-8
Reduce the fraction and find the domain
The simplification of all the given algebra fractions are;
1) a/c
2) (a - b)/(a - 1)
3) (x + 1)/(x - 4)
How to solve algebraic fractions?An algebraic fraction is defined as a fraction whose numerator and denominator are algebraic expressions.
1) (abc + ab²)/(b²c + bc²)
Factorizing numerator and denominator gives;
ab(c + b)/bc(b + c)
b(b + c) will cancel out to get; a/c
2) (a² - b²)/(a² - a + ab - b)
Factorizing numerator and denominator gives;
[(a + b)(a - b)]/[a(a - 1) + b(a - 1)]
= [(a + b)(a - b)]/(a + b)(a - 1)
(a + b) will cancel out to get;
(a - b)/(a - 1)
3) (x² - 2x - 3)/(x² - 7x + 12)
Expanding the numerator and denominator gives;
(x² - 3x + x - 3)/(x² - 4x - 3x + 12)
= ((x + 1)(x - 3))/((x - 3)(x - 4)
(x - 3) will cancel out to get;
(x + 1)/(x - 4)
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1. Write 7 example of mathematical expreion. 2. Larry had 5 3/6 yard of fabric. He ued 2 2/3 to make a bag for hi computer. Write an expreion that will how how much of the fabric Larry will have left. PLEASE HURRY UPPPPP!!! I HAVE 1 HOUR LEFT UNTIL SUBMISSION!!!
a) 7 examples are:
[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]
b) Fabric Larry will have left after using [tex]2\frac{2}{3}[/tex] yard out of [tex]5\frac{5}{6}[/tex] yard to make a bag for his computer is: [tex]3\frac{3}{6} yard[/tex]
What kinds of expressions are examples?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
7 examples of mathematical expression are:
[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]
For the second part of the question:
Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.
The mathematical expression that represents the amount of fabric Larry has left is:
5 3/6 - 2 2/3 = 2 7/18
You can simplify this further:
2 7/18 = 2 1/6
The amount of fabric Larry will have left is 2 1/6 yards.
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Courtney is in the process of buying a minivan. The car she wants to buy is $29,999. The required down payment is 20% . How much will she need to put down in order to purchase this car
Car insurance coverage covers damages caused by or other mishaps. The following damages are covered claims except :
A. A head on collisions .
B. A tree falls in your car during a windstorm
C. The sun weathers the paint on your car and it must be repainted
D. A thief breaks your back window and steals the guitar from your back seat
On observing the provided question we can say that - the function f(x) = a^x is Range : (−∞,∞) or all real numbers
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the number and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
The answer to the question is that all real numbers or (−∞,∞)
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Write an equation for the parabola that passes through (-2,7), (1, 10), and (2,27)
An equation for the parabola is y=.
Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.
Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k
y = a(x-h)^2 + k
Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get
7 = a(-2 - h)^2 + k
It passing through (1, 10), we can substitute the values of x and y in the equation and get
10 = a(1 - h)^2 + k
It passing through (2,27), we can substitute the values of x and y in the equation and get
27 = a(2 - h)^2 + k
Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k
Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.
Step-by-step explanation:
Rectangle A is similar to rectangle B by scale factor r. The length of rectangle A is 1. 5r+2. 25 units. The length of rectangle B is 3 unite. What is the scale factor
The scale factor of the two rectangles is 1.5
Describe the rectangle.According to Euclidean Plane Geometry, a rectangle is a quadrilateral with equal opposed sides and four right angles. In other words, a rectangle is a parallelogram with a right angle of 90 degrees or an equiangular quadrilateral (i.e., 360°/4 = 90°). A rectangle is referred to as a square if its four sides are all the same length.
The ratio of the matching side lengths of two comparable figures is known as the scale factor. We know that the ratio of the respective side lengths of the two rectangles equals equivalent to r since Rectangle A and Rectangle B are similar to one another by the scale factor r.
We can set up the following ratio to determine the scale factor if the lengths of rectangles A and B are 1.5r+2.25 units and 3 units, respectively.
(1.5r+2.25) / 3 = r
Solving for r, we get:
r = (1.5r + 2.25) / 3
multiply both sides of the equation by 3
3r = 1.5r + 2.25
Subtract 1.5r from both sides
1.5r = 2.25
divide both sides by 1.5
r = 2.25/1.5
r = 1.5
Therefore, the scale factor of the two rectangles is 1.5.
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