Answer:37c − 32d
2:7p+3w
Step-by-step explanation:
Answer:
1. c - 5d
2. 7p + 3w
Step-by-step explanation:
1.)
5c - 8d - 4c + 3d =
5c + -8d +-4c + 3d
Combine like terms:
(5c + -4c) +(-8d + 3d) =
c - 5d
2.)
6p - 2w + p + 5w =
6p + -2w + p + 5w
Combine like terms:
(6p + p) + (-2w + 5w) =
7p + 3w
Select the expression that represents this real-world situation.
Josie has 12 yards of fabric. She is making identical dresses for d dolls. What is the length of fabric used for each doll??
12 + d
12 − d
12 x d
12 ÷ d
which transformation carries the rhombus below onto itself?
1. a rotation of 180 clockwise about (-2,-2)
2. a rotation of 90 counterclockwise about (-2,-2)
3. a reflection over the line y=x+10
4. a reflection over the line y=-x-6
Therefore, the answer is option 4: a reflection over the line y=-x-6.
What is transformation?In mathematics, a transformation is a process that changes the position, size, or shape of a geometric object in some way. Transformations are often used in geometry and other branches of mathematics to study the properties of shapes and their relationships to each other.
Here,
To determine which transformation carries the rhombus onto itself, we need to identify the symmetries of the rhombus. A rhombus has two types of symmetry: rotational symmetry and reflectional symmetry.
Option 1: a rotation of 180 degrees clockwise about (-2,-2)
This transformation takes each point of the rhombus and rotates it 180 degrees clockwise about the point (-2,-2). Since the rhombus has rotational symmetry of order 2 (i.e., a rotation of 180 degrees carries the rhombus onto itself), this transformation carries the rhombus onto itself.
Option 2: a rotation of 90 degrees counterclockwise about (-2,-2)
This transformation takes each point of the rhombus and rotates it 90 degrees counterclockwise about the point (-2,-2). Since the rhombus does not have rotational symmetry of order 4 (i.e., a rotation of 90 degrees does not carry the rhombus onto itself), this transformation does not carry the rhombus onto itself.
Option 3: a reflection over the line y=x+10
This transformation reflects each point of the rhombus over the line y=x+10. Since the rhombus does not have reflectional symmetry over this line, this transformation does not carry the rhombus onto itself.
Option 4: a reflection over the line y=-x-6
This transformation reflects each point of the rhombus over the line y=-x-6. Since the rhombus has reflectional symmetry over this line, this transformation carries the rhombus onto itself.
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Help pls this is due soon 10 points
The slope of the line is -1, and the y-intercept is 4.
What is linear function ?
A linear function is a type of mathematical function where the graph of the function is a straight line. It is a function that has a constant rate of change (or slope) between any two points on the line.
In the form of the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). This equation represents a linear function since the graph of the function is a straight line.
Linear functions are used in many areas of mathematics and science, as well as in real-world applications such as engineering, economics, and physics. They are useful in modeling and predicting relationships between variables that have a constant rate of change over time.
To find the equation of the linear function in the form y = mx + b, we need to determine the slope (m) and y-intercept (b) of the line.
From the graph, we can see that the y-intercept is 4, since the line intersects the y-axis at the point (0, 4).
To find the slope, we can choose two points on the line and use the slope formula:
slope (m) = (y2 - y1) / (x2 - x1)
Let's choose the points (2, 6) and (6, 2):
slope (m) = (2 - 6) / (6 - 2) = -4 / 4 = -1
Therefore, the equation of the linear function is:
y = -x + 4
So, the slope of the line is -1, and the y-intercept is 4.
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2. Describe the solution to this system of equation below. Justify your thinking.
3. Look at the system of equation.Solve the system algebraically. Show all of your work.
Ted tried to evaluate the expression 21 divided by 3 plus 5 times 3 is his work correct
Ted's work to evaluate the expression 21 ÷ 3 + 5* 3 is incorrect, as he evaluated the division before the multiplication. He follow the wrong order of operations. The correct answer is 22, not 36.
Ted's work is incorrect. In step 1, he evaluated the division before the multiplication, which is incorrect according to the order of operations (PEMDAS). According to the order of operations, multiplication and division should be done before addition and subtraction. Therefore, the correct way to evaluate the expression is as follows:
21 ÷ 3 + 5 * 3
= 7 + 15 (evaluating multiplication before addition)
= 22
Thus, the correct answer is 22, not 36 as Ted calculated. It is important to follow the order of operations in order to arrive at the correct answer.
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_____The given question is incomplete, the complete question is given below:
Ted tried to evaluate the expression 21 ÷ 3 + 5* 3. Here, is his work:
21 ÷ 3 + 5* 3
= 7 + 5 * 3 step 1
= 12 * 3 step 2
= 36
Is his work correct?
Please help !!!!!!!!!!!
The simplified expressions are, 6. [tex]16^{\frac{1}{2} }[/tex] = 4, 7. [tex]125^{\frac{1}{3} }[/tex] = 5, 8. [tex]36^{\frac{1}{2} }[/tex] = 6, 9. [tex]27^{\frac{1}{3} }[/tex] = 3,10. [tex]49^{\frac{1}{2} }[/tex] = 7.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical operations and structures using symbols and letters to represent numbers and quantities. It involves manipulating mathematical expressions and solving equations to find unknown values.
In algebra, the basic operations include addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions can also include variables, which represent unknown quantities, and coefficients, which are the constant values that appear in front of variables.
The study of algebra begins with the basic concepts of arithmetic, such as addition, subtraction, multiplication, and division, and then progresses to more advanced topics, such as equations, inequalities, functions, matrices, and abstract algebra. Algebraic concepts are widely used in other areas of mathematics, including geometry, trigonometry, calculus, and number theory
[tex]16^{\frac{1}{2} }[/tex] = 4
[tex]125^{\frac{1}{3} }[/tex] = 5
[tex]36^{\frac{1}{2} }[/tex] = 6
[tex]27^{\frac{1}{3} }[/tex] = 3
[tex]49^{\frac{1}{2} }[/tex] = 7
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Select the expression that makes the equation true.
16 x (4.5 + 3) ÷ 10 = ___.
20.8 + (3 x 4) ÷ 4
24 ÷ (8 − 4) + 8.2
30 ÷ (15 ÷ 2.5) + 7
36 ÷ (9 − 4.2) + 3
30 ÷ (15÷2.5) + 7
Step-by-step explanation:Given: 16 · (4.5 + 3) ÷ 10= ____
First let us do PEMDAS (Parenthesis, Equation, Multiply, Divide. Add, Subtract) upon the given value.
16 · (7.5) ÷ 10 = ____
120 ÷ 10 = ____
= 12
We now understand that the given is equal to the value of 12, now we will calculate each equation with PEMDAS until we find the equivalent value.
20.8 + (3 · 4) ÷ 4 =
20.8 + 12 ÷ 4 =
20.8 + 3 =
= 23.8
24 ÷ (8 − 4) + 8.2 =
24 ÷ 4 + 8.2 =
6 + 8.2 =
= 14.2
30 ÷ (15 ÷ 2.5) + 7 =
30 ÷ 6 + 7 =
5 + 7 =
= 12
36 ÷ (9 − 4.2) + 3 =
36 ÷ 4.8 + 3 =
7.5 + 3 =
= 10. 5
It is safe to say the following:
16 · (4.5 + 3) ÷ 10 ≠ 20.8 + (3 x 4) ÷ 4
16 · (4.5 + 3) ÷ 10 ≠ 24 ÷ (8 − 4) + 8.2
16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7
16 · (4.5 + 3) ÷ 10 ≠ 36 ÷ (9 − 4.2) + 3
Therefore, the answer is:
16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7
Hope this helps =D, happy learning !
Using the quadratic formula, solve 0 = 2x²8x + 5 Give each of your answers to 2 d.p.
Answer:
(i) 4x
2
−5x−3=0
Let us consider, a=4,b=−5,c=−3
So, by using the formula,
x=
2a
−b±
b
2
−4ac
So let, b
2
−4ac=D
x=
2a
−b±
D
D
=b
2
−4ac
=(−5)
2
−4(4)(−3)
=25+48
=73
So
x=[−(−5)±
73
]/2(4)
=[5±8.54]/8
=[5+8.54]/8 or [5−8.54]/8
=13.54/8 or −3.54/8
=1.6925 or -0.4425
∴ Value of x=1.69 or -0.44
Hope it helps
really need help please ASAP The graph of a function is shown below.
Use the graph of the function to find its average rate of change from x=0 to x=3
Simplify your answer as much as possible.
accualy in math one but they dont have 9th grade on hear.
As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as the average rate of change of the function from x = 0 to x = 3.
what is function ?A function is a rule in mathematics that links every element of one set, known as the domain, to a certain element of some other set, known as the range. A function is just a relationship between the values of the input and the output, where the outcome specifically depends on the input. A function can be depicted in a number of different ways, including as an equation, a chart, or a list of values. For instance, the function f(x) = 2x multiplies the input value x by two to get the output value f. (x). The range of this function is indeed the set of all real numbers, and its domain is any set of real numbers.
given
To determine (3, f(3)) on the function graph the average rate of change of the function from x = 0 to x = 3.
According to the graph, the point (0, f(0)) is on the y-axis and has a y-coordinate of 2, while the point (3, f(3)) is on the line that connects the points (2, 0) and (4, 6) and has a slope of m = 3. As a result, we have:
f(0) = 2 and f(3) = 6
We can determine the slope of the line connecting these two points using the slope formula:
m = (f(3) - f(0)) / (3 - 0) = (6 - 2) / 3 = 4/3
As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as the average rate of change of the function from x = 0 to x = 3.
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Mrs. Klein was shopping for her family. She saw that blueberries were on sale. The Kroger brand was $3.75 with 15% off. The regular brand was 2 for $6.25. If she wanted to buy 2 containers of blueberries, which is the better deal?
a Kroger Brand
bRegular Brand
Thus, the price of regular brand blueberries is less than the Price of 2 container of Kroger brand blueberries. Hence, Regular Brand is better deal.
Define about the 2-variable linear equation?A linear equation with two variables is shown by the equation axe + by = r if a, b, and r are all real values and they are not equal to 0. The equation's two variables are represented by the letters x and y. The coefficients are denoted by the numerals a and b.
Given data:
Price of 1 container of Kroger brand blueberries with discount: 3.75 with 15% off.
= 3.75 - 0.15*3.75
= 3.1875
Price of 1 container of Kroger brand blueberries: $3.1875
Price of 2 container of Kroger brand blueberries:
= 3.1875 * 2
= $6.375
Now,
Price of 2 container of regular brand blueberries: $6.25
Thus, the price of regular brand blueberries is less than the Price of 2 container of Kroger brand blueberries. Hence, Regular Brand is better deal.
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sylvia wants to go on a cruise in 4 years. she could earn 7.3 percent compounded monthly in a bank account if she were to deposit the money today. she needs to have 14,000 dollars in 4 years. how much will she have to deposit today? (round to the nearest dollar).
The amount Sylvia should deposit today: P = A / (1 + r/n)^(nt)Where:P = P = $ ___The principal amount is $9,463. So, Sylvia has to deposit $9,463 today.
Sylvia wants to go on a cruise in 4 years. She could earn 7.3% compounded monthly in a bank account if she were to deposit the money today. She needs to have $14,000 in 4 years. To determine the amount Sylvia should deposit today to earn $14,000 in 4 years with a 7.3% interest rate compounded monthly,
we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where:A = the amount of money at the end of the time periodP = the principal, or initial amount of moneyr = the annual interest raten = the number of times interest is compounded per yeart = the time period, in yearsWe need to solve for P.
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a middle school classroom contains 15 students. out of them, nine are boys. a teamis to be formed with ten students, of them six must be boys. in how many ways can the team be formed?
As per the combination method, there are 1260 ways in which a team of 10 students with 6 boys and 4 girls can be formed from a middle school classroom containing 15 students with 9 boys.
To solve this problem, we need to use the concept of combinations. A combination is a way of selecting items from a larger group where the order of selection does not matter. In this problem, we are selecting a team of 10 students, and the order in which we select the students does not matter.
Using this formula, we can find the number of ways to select 6 boys from a group of 9 as:
⁹C₆ = 9! / (6! x (9-6)!) = 84
Similarly, the number of ways to select 4 girls from a group of 6 is:
⁶C₄ = 6! / (4! x (6-4)!) = 15
To find the total number of ways to form a team of 10 students with 6 boys and 4 girls, we need to multiply the number of ways to select 6 boys and 4 girls. This is because the selection of boys and girls is independent of each other, and we can choose them in any order.
Therefore, the total number of ways to form a team of 10 students with 6 boys and 4 girls is:
84 x 15 = 1260
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In 1980 a value of home is 81600 since then it's value has increased by 12 percentage each year what is the appoxmate value of the home in the 1987 round to the nearest hundred dollars
The approximate value of the home in 1987 is approximately $161,872.
The formula to calculate the approximate value of a home in 1987 is:
V1987 = 81600 x (1 + 0.12)^7
V1987 = 81600 x 1.987
V1987 = 161872
Therefore, the approximate value of the home in 1987 is approximately 161,872.
To arrive at this answer, we first started with the value of the home in 1980, which was 81,600. We then multiplied this value by 1.12, which is the 12% increase every year, to the seventh power. This resulted in a value of 1.987. We then multiplied this value by the original value of the home in 1980, which gave us the approximate value of the home in 1987. We then rounded the answer to the nearest hundred dollars, which resulted in the answer of 161,872.
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Equations with fractions
Can someone please show me step by step how to answer this, thank you.
Answer:
x=7
Step-by-step explanation:
The equation can be represented as following:
[tex](\frac{x}{14} +3\frac{1}{2})=2(\frac{x}{21} +1\frac{2}{3})[/tex]. If we open the parenthesis, we can get as following:
[tex]\frac{1}{14}x +3\frac{1}{2}=\frac{2}{21}x +3\frac{1}{3} \\[/tex], which then subtract [tex]2\frac{2}{21} x[/tex] from both sides to get the following:
[tex]\frac{7}{2}-\frac{1}{42} x=\frac{10}{3}[/tex];
subtract [tex]\frac{7}{2}[/tex] from both sides to get [tex]\frac{-1}{42} x=\frac{-1}{6}[/tex], and multiply both sides by -42 to get our final answer of x=7
Simplify each difference. 7) (1 + 2x) - (6x+2-524)
the simplified difference is -1 - 4x + 524. To simplify the difference (1 + 2x) - (6x+2-524), we need to first distribute the negative sign to the second expression inside the parentheses:
(1 + 2x) - (6x+2-524) = 1 + 2x - 6x - 2 + 524
Now we can simplify by combining like terms:
1 + 2x - 6x - 2 + 524 = (1 - 2) + (2x - 6x) + 524
Simplifying further:
-1 - 4x + 524
Therefore, the simplified difference is -1 - 4x + 524.
It's worth noting that this expression could be simplified further by combining like terms, but it depends on the context and purpose of the expression. For example, if we were trying to solve an equation involving this difference, we might want to simplify it further to make it easier to solve. However, if we were simply asked to simplify the expression, then the answer we have above is sufficient.
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Which fractions are less than 1/2 ? choose all the correct answers
The fractions less than [tex]\frac{1}{2}[/tex] are:
a. [tex]\frac{2}{5}[/tex]
d. [tex]\frac{1}{6}[/tex]
e. [tex]\frac{3}{8}[/tex]
To see why, we can compare each fraction to [tex]\frac{1}{2}[/tex], which is equivalent to [tex]\frac{4}{8}[/tex]:
[tex]\frac{2}{5}[/tex] < [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 40, we get [tex]\frac{16}{40}[/tex] < [tex]\frac{20}{40}[/tex].[tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] > [tex]\frac{1}{2}[/tex], because when we convert both fractions to have a common denominator of 8, we get [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] and [tex]\frac{1}{2}[/tex] = [tex]\frac{4}{8}[/tex], and [tex]\frac{3}{4}[/tex] > [tex]\frac{4}{8}[/tex].[tex]\frac{4}{5}[/tex] > [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 40, we get [tex]\frac{32}{40}[/tex]> [tex]\frac{20}{40}[/tex].[tex]\frac{1}{6}[/tex] < [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 24, we get [tex]\frac{4}{24}[/tex] < [tex]\frac{6}{24}[/tex].[tex]\frac{3}{8}[/tex] < [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 8, we get [tex]\frac{3}{8}[/tex] < [tex]\frac{4}{8}[/tex].[tex]\frac{5}{6}[/tex] > [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 12, we get [tex]\frac{10}{12}[/tex] > [tex]\frac{6}{12}[/tex].The complete question is:-
Which fractions are less than 1/2 ? choose all the correct answers
a. 2/5 b. 6/8 c. 4/5 d. 1/6 e. 3/8 f. 5/6
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What is the slope of the line y = 2.5x - 7
Answer:
2.5
Step-by-step explanation:
The slope of the line represented by the equation y = 2.5x - 7 is 2.5. This means that for every unit increase in x, the value of y increases by 2.5 units.
The slope of the line y = 2.5x - 7 can be identified as the coefficient of the 'x' variable in the equation. Here, the term in front of 'x' is 2.5, so the slope of the line is 2.5. In other words, for every unit increase in x, y will increase by 2.5 units. This is a key concept in linear equations, which are used to represent straight lines in a coordinate system.
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Help me me me help me
See pics for answers
a 500-foot cable is attached to the top of a tower and is stretched tight to a point that is 350 feet away from the base of the tower. what is the angle of depression formed by the cable?;
The angle of depression formed by the cable is approximately 41.4 degrees.
The angle of depression is the angle formed by the horizontal line and the line of sight from the observer to an object that is lower than the observer's position. In this case, the observer is at the top of the tower and the object is at the end of the cable that is stretched to a point 350 feet away from the base of the tower.
To find the angle of depression, we can draw a diagram as follows:
where h is the height of the tower, d is the horizontal distance from the base of the tower to the point where the cable is attached, and θ is the angle of depression that we want to find.
From the diagram, we can see that
tan(θ) = h / d
We know that the length of the cable is 500 feet and the horizontal distance from the base of the tower to the point where the cable is attached is 350 feet. We can use the Pythagorean theorem to find the height of the tower:
h^2 = 500^2 - 350^2
h = sqrt(500^2 - 350^2)
h = 300
Now we can substitute the values we have found into the equation for tan(θ) to get:
tan(θ) = 300 / 350
θ = tan^-1(300/350)
θ ≈ 41.4 degrees
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Slope intercept formula
Answer:
y = mx + b
the is the slope intercept formula
When Fredrick buys a cup of coffee he is given change of €1.65 when he should have received €1.50. Find percentage error
When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%
Explain about the percentage error?The variation between the real value and the predicted value, in relation to the theoretical value, is known as percentage error.
When compared to the real number and expressed in percent format, percentage error seems to be the gap between the anticipated amount and the actual number. The equation is as follows:
To put it another way, you divide the deviation between the true answer and the answer you guessed by the true answer to get the percent.
Amount paid by Fredrick for cup of coffee: €1.65
Actual amount: €1.50.
percentage error = (amount paid - actual amount)/amount paid * 100 %
percentage error = (1.65 - 1.50)/1.65 * 100
percentage error = 9.09%
Thus, When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%
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Please Help
Jake has a summer job as a photographer at an amusement park. He wants to save 3500.He must choose whether to sell large photos or small photos. For each photo, he will earn the amounts shown in the table. How many of each kind of photo will he need to sell to reach his goal of 3500?
Answer:
Large Photos: 500
Small Photos: 3000
Step-by-step explanation:
school ski trip each winter the pta organizes a ski trip students pay a upfront cost cost which includes a 2 night stay transportation meals and 6 hours of skiing each day this
*this year the PTA has 7 chaperones going on the trip and each chaperone will supervise exactly 15 students
*the PTA collected $25,515 from the students to pay for the trip
*the chaperones pay for their own hotel rooms but the PTA pays for the hotel rooms for the students. each room can hold 4 students
*students and chaperones take the school buses from the school to the ski resort. each bus seat 48 people
*students can choose to go snow tubing during the trip but this is not included in the cost of the trip the cost for tubing is $23 for the lift ticket plus the cost of renting specialty snow boots the total cost of snow tubing is 29
use this information to write and solve equations to determine the number of students going on the trip the cost per student, the number of hotel rooms needed for the students,the number of buses needed, and the cost to rent snow boots for turbing
your work should include:
defined variables(2 points)
equations to represent each situation (3 points)
an explanation of how each equation represents the situation (3 points)
solved equations (3 points)
statements interpreting solutions (2 points)
The number of students going on the trip is 105 students. The cost per student is $ 243 per student. The number of hotel rooms needed is 27 hotel rooms.
The number of buses needed is 3 buses. The cost to rent snow boots for turbing is $ 6.
How to find the number of students?Let's define the variables:
s = number of students going on the trip
c = cost per student
h = number of hotel rooms needed for the students
b = number of buses needed
r = cost to rent snow boots for tubing
The equations would then be:
s = 7 chaperones × 15 students/chaperone
$25,515 = s × c
h = ceil (s / 4)
b = ceil ((s + 7) / 48)
$29 = $23 + r
Solving the equations then gives:
Number of students on trip:
s = 7 × 15 = 105 students
Cost per student :
$25,515 = 105 × c
c = $25,515 / 105
= $243 per student
Number of hotel rooms :
ceil(105 / 4) = 27 hotel rooms
Number of buses :
= ceil((105 + 7) / 48)
= ceil(112 / 48)
= 3 buses
Cost per student for snow boots ;
r = $29 - $23
= $6
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person 1 writes internal operating procedures 3 times faster than person 2. most of the procedures took 15 minutes each to create, but three of the procedures for person 1 took 1 hour each. calculate how long it took person 1 to complete 12 procedures.
Answer: 4 hours
Step-by-step explanation:
3/1=12/x
3x=12
x=4
The vertices of triangle ABC are A(2, 2), B(4, 2), and C(4, 3).
If the given triangle is dilated by a factor of 2, which coordinates are A'B'C'?
=
A A'(0, 0), B'(2, 0), C'(3, 1)A'(0, 0), B'(2, 0), C'(3, 1)
B A'(4, 4), B'(6, 4), C'(6, 5)A'(4, 4), B'(6, 4), C'(6, 5)
C A'(4, 4), B'(8, 4), C'(8, 6)A'(4, 4), B'(8, 4), C'(8, 6)
D A'(1, 1), B'(2, 1), C'(2, 32
The vertices after the dilation arE:
C A'(4, 4), B'(8, 4), C'(8, 6)
Which are the vertices after the dilation?The original vertices are A(2, 2), B(4, 2), and C(4, 3). And we apply a dilation of scale factor 2, then to get the new coordinates ust multiply all the coordinates by 2, we will get.
A' = (2*2, 2*2) = (4, 4)
B' = (4*2, 2*2) = (8, 4)
C' = (4*2, 3*2) = (8,6)
Then the correct option in this case is:
C A'(4, 4), B'(8, 4), C'(8, 6)
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Look at the second Model It. How does using the partial quotients strategy help you find the quotient of 2,125 ÷ 4?
Finding a quotient of [tex]2,125/4[/tex] is [tex]531.25[/tex] with the use of partial quotients is possible.
What are fractional quotients?A fraction's quotient is the whole integer that results from simplifying the fraction. The division is the fraction's decimal form if the simplified fraction yields a non-whole number. The answer to a division issue involving two fractions can also be found in the quotient.
What makes it a quotient?Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the second number enters the first. The number being divided is referred to as the payout, and the number being divided by it is referred to as the divisor.
40)2125(531.25
20
-------
12
-12
------
5
-4
--------
10
-8
--------
20
-20
----------
00
----------
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Mary had a sum of money.
She spent $49 on a dress 2/5 of the remaining money on a pair of shoes.
She then had 1/4 of the sum of money left.
How much money did Mary have at first?
Answer:
$84
Step-by-step explanation:
Let's assume, Mary had x $
Now we can make an equation:
[tex]x - 49 - \frac{2}{5} \times (x - 49) = \frac{1}{4} x[/tex]
(After she spent $49, she had (x - 49) dollars left)
Let's multiply this whole equation my 20 (since it's a common denominator):
20x - 980 - 8(x - 49) = 5x
20x - 980 - 8x + 392 = 5x
20x - 8x - 5x = -392 + 980
7x = 588 / : 7
x = 84
is x^2+3x+4 linear or quadratic equation?
Answer: The equation x^2+3x+4 is a quadratic equation.
A quadratic equation is a second-degree polynomial equation in one variable (usually x), where the highest power of the variable is squared (x^2).
In this case, x^2+3x+4 is a second-degree polynomial with the variable x raised to the power of 2. Therefore, it is a quadratic equation.
Linear equations, on the other hand, are first-degree polynomial equations in one variable, where the variable is not raised to any power higher than 1.
Step-by-step explanation:
A survey found that women's heights are normally distributed with mean 63.4 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
After answering the provided question, we can conclude that As a result, normal distribution the new height requirement for women to join this branch of the military is 57.1 inches to 68.6 inches.
what is normal distribution?The normal distribution is an example of a constant distribution of probabilities, in which the majority of the points cluster near the range's center and the ones that are left decrease symmetrically towards one of the extremes. The mean of the spread is another term for the range's centre. According to the bell curve, also known as the Distribution function, which is symmetrical well about mean, data that are near the median are more frequent than data that are far from the mean. I'm using heuristics in normality to obtain a child's SAT scores from an innovative exam prep course. The data have a normal distribution with a mean (M) of 1150 and a standard deviation (SD) of 150.
a. To calculate the percentage of women who meet the height requirement, find the area under the normal distribution curve between 58 and 80 inches.
For x = 58 inches: z = (58 - 63.4) / 2.5 = -2.16
For x = 80 inches: z = (80 - 63.4) / 2.5 = 6.64
This means that all women with heights ranging from 58 to 80 inches meet the requirement.
b. For the shortest 1%, we need to find the height that corresponds to z = -2.33:
-2.33 = (x - 63.4) / 2.5
x = 57.1 inches
So the new minimum height requirement is 57.1 inches.
For the tallest 2%, we need to find the height that corresponds to z = 2.05:
2.05 = (x - 63.4) / 2.5
x = 68.6 inches
So the new maximum height requirement is 68.6 inches.
As a result, the new height requirement for women to join this branch of the military is 57.1 inches to 68.6 inches.
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A soccer player kicks a ball with a velocity of 28 feet per second. The expression 28r - 16r2 represents the height of the ball after seconds. What are
the factors of this expression?
the factors of the expression 28r - 16r² are 4r and (-4r + 7).
define factorizationFactorization is the process of expressing a number or an algebraic expression as a product of its factors, which are numbers or expressions that multiply together to give the original number or expression. In other words, factorization involves breaking down a larger number or expression into smaller factors.
To factor the expression 28r - 16r², we can first rearrange it to put it in descending order of powers of r:
-16r² + 28r
Then we can factor out the greatest common factor, which in this case is 4r:
4r(-4r + 7)
Therefore, the factors of the expression 28r - 16r² are 4r and (-4r + 7).
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