Answer:
67.97%
Step-by-step explanation:
Answer:
67.97%
Step-by-step explanation:
Mabel's salary is 1/3 higher than Lens. Lens salary is 1/4 higher than the hiring rate. how will you represent Mabel's salary (in terms of the original hiring rate h) if the hiring rate will be increased by 40%
Answer:
points cuzo
but if i find it out i will edit
Step-by-step explanation:
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
16 yd
6 yd
14 yd
8 yd
7 yd
The missing side length on the figure is 9 yards
How to determine the missing side lengthFrom the question, we have the following parameters that can be used in our computation:
The figure
The missing length on the figure is represented with ?
Using the above as a guide, we have the following equation
? + 7 = 16
Evaluate
? = 9
Hence, the missing side length is 9 yards
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The missing side length is equal to 9 yd.
Rectangles
The rectangle is a quadrilateral. The classification for quadrilaterals is given by the length of sides and angles. For a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
A rectangle is a geometric figure that has 4 sides called: length and width (W). Due to its characteristics, the rectangle presents two lengths (L) and two widths (W).
For solving this question, you should:
Identify the basic shapes;Find the missing side length;STEP 1 - Identify the basic shapes.The figure is composed of two rectangles:
Rectangle 01 whose sides are: 6 yd (W) and 16 yd (L).
Rectangle 02 whose sides are: 8 yd (W) and 7 yd (L).
STEP 2 - Find the missing side length.
If the length (L) of rectangle 01 is 16 yd, which is equal to the sum between the missing side and the length of rectangle 02 (7 yd). Thus
16=s+7
s=16-7
s=9
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Macroeconomics
The regular price for a set of four tires is $250, but Erin finds a store that has the tires she needs on sale for $175?
Which graph correctly illustrates this scenario?
The graph for the given question is mentioned below.
What is graph?A graph is a visual representation of data or information that is used to display and communicate relationships between variables or categories. Graphs can take many forms, including line graphs, bar graphs, pie charts, and scatter plots, among others. They are commonly used in fields such as science, economics, and statistics.
As the price of a set of four tires has decreased from $250 to $175, we can illustrate this scenario using a demand and supply graph with quantity on the horizontal and size on the vertical axis.
The graph should show a leftward shift of the demand curve, indicating that consumers are willing to buy more tires at a lower price. The supply curve remains constant, indicating that the supplier is willing to sell the same quantity of tires at a lower price. Therefore, the correct graph should be:
| P
250 | \
| \ Supply
| \
| \
175 | \
| \
| \ Demand (after discount)
| \
Q
where P is the price, Q is the quantity, and the demand curve has shifted to the right.
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Which insect measurement was the most frequent?
Length of insects (in inches)
The insect measurement that was the most frequent is given as follows:
1 and 1/4 inches.
How to obtain the most frequent insect measurement?A dot plot is a simple graphical display that uses dots to represent data values. It is also sometimes called a dot chart or a scatterplot. In a dot plot, each data point is represented by a dot along a number line or axis, where the position of the dot corresponds to the value of the data point.
Hence, a dot plot shows the number of times that each observation appeared in the data-set.
The observation with the most dots is the observation 2/8 of the way between 1 and 2, hence the most frequent observation is given by the following mixed number:
1 and 2/8 = 1 and 1/4 inches.
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Sheri's deck design is shown below. Which shape has the same perimeter but a different area than Sheri's design?
The shape that has the same perimeter but a different area than Sheri's design is option D.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
The figure contains sides with the measurements, 2 units, 4 units, 4 units, 2 units, 2 units, and 2 units.
The perimeter of the figure will be sum of all sides -
Perimeter = 2 + 4 + 4 + 2 + 2 + 2
Perimeter = 16 units
Therefore, the figure has perimeter of 16 units.
The area of the figure can be determined by adding the area of rectangle and square.
Side of the square measures 2 units.
The length of the rectangle is 2 units.
The breadth of the rectangle is 4 units.
So, the equation will be -
Area = Area of rectangle + Area of square
Area = (l × b) + (side)²
Area = (2 × 4) + (2)²
Area = 8 + 4
Area = 12 units²
Therefore, the figure has area of 12 units².
The diagram in option D contains sides with the measurements, 3 units, 1 unit, 1 unit, 3 units, 4 units, and 4 units.
The perimeter of the figure will be sum of all sides -
Perimeter = 3 + 1 + 1 + 3 + 4 + 4
Perimeter = 16 units
Therefore, the figure has perimeter of 16 units.
The area of the figure can be determined by adding the area of the two rectangles.
The length of the first rectangle is 1 unit.
The breadth of the first rectangle is 3 units.
The length of the second rectangle is 3 units.
The breadth of the second rectangle is 4 units.
So, the equation will be -
Area = Area of rectangle 1 + Area of rectangle 2
Area = (l × b) + (l × b)
Area = (1 × 3) + (3 × 4)
Area = 3 + 12
Area = 15 units²
Therefore, the figure has area of 12 units².
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36/84 simplify plsss
Answer:3/7
Step-by-step explanation:
36 divided by 12 then 84 divided by 12
therefore 36/84 simplified to the lowest terms is 3/7
Solve this system of equations for x using the addition method. (Must show steps of addition method to get credit. Do not solve using the substitution method.)
The solution for the inequality expression given is x > -2.154.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given linear inequality is,
-5/7 (21x + 35) < 1/3 (9 - 6x)
We have to solve the inequality.
Using the distributive property,
(-5/7 × 21x) + (-5/7 × 35) < (1/3 × 9) - (1/3 × 6x)
-15x - 25 < 3 - 2x
-15x + 2x < 3 + 25
-13x < 28
-x < 2.154
Multiplying throughout by negative 1.
x > -2.154
Hence the solution is x > -2.154.
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what is the value of the star?
Answer:
Star = 62
Step-by-step explanation:
To solve this, we need to find out what the value of the blue triangle is. To do this, we can take the right column, which adds up to -72, and divide that by 3.
-72 ÷ 3 = -24So, the value of the blue triangle is -24.
Now that we know this, we can solve for the value of the green trapezoid. (Top row going horizontally). To do this, we need to take the total value and subtract the value of the blue triangle from it.
138 - (-24) = 162Now divide that by 2 to get the value of each trapezoid:
162 ÷ 2 = 81So, the value of the green trapezoid is 81.
To solve for the value of the orange diamond (middle row going down), we can take the total and subtract 2 green trapezoids from it.
105 - 81 - 81 = -57To check, we can now do the middle horizontal row. Adding up the shapes:
-24 + 81 + (-57) = 0This is the proper value, meaning that the value of the orange diamond is -57.
Just to recap:
Blue triangle = -24Green trapezoid = 81Orange diamond = -57Now, to solve for the value of the star, we can solve the row on the right going vertically. To solve for this, we must take the total value and subtract the value of the diamond and trapezoid from it.
86 - 81 - (-57) = 62To check once again, we can now do the row on the bottom going horizontally. Adding up the numbers:
-24 + (-57) + 62 = -19This is the proper value, meaning that the value of the star is 62.
There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5 : 4. There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4: 5. The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?
We have the following response after answering the given question: equation Hence, there are 22/45 female students at the dance.
What is equation?In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.
Now, let's determine how many boys and females attend each school:
Middle School in Colfax
Boys: (5/9) * 270 = 150
Girls: (4/9) * 270 = 120
School in Winthrop:
Boys: (4/9) * 180 = 80
Girls: (5/9) * 180 = 100
Now, we can determine how many males and girls attended the dance overall:
Boys: 150 + 80 = 230
Girls: 120 + 100 = 220
Thus, the proportion of female students attending the dance is:
220 / (230 + 220) = 220 / 450 = 44/90 = 22/45
Hence, there are 22/45 female students at the dance.
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Henry claims that MN is a midsegment of AJKL. Explain why this is not true.
help with homework pls
Answer:
no
Step-by-step explanation:
orka:sweet potato
15:8 = 1.875
350:160 = 2.1875
Please help me!!!!!!
Answer:
4.5%
Step-to-Step Explanation:
[tex]y=8700*1.045^{x}[/tex]
[tex]y=a(1+r)^{x}[/tex]
1 + r = 1.045
r = 1 - 1.045
r = 0.045
Multiply 0.045 by 100 to ger 4.5%
r = 4.5%
There is something that looks like a backwards y. If the "backwards y" (∠2)=98°, find the following angle measures.
Angles 1 = 2 = 3 = 98° and 4 = 82° are measured.
What angles are appropriate?The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The image serves as a right angle indicator. The angle formed when two chords cross paths inside of a circle is equal to half the sum of the chords' intercepted arcs. Hence, m1 = 50° and m2 = 130°.
The other angle measurements can be calculated using the diagram as follows:
∠1: ∠1 is a vertical angle to ∠2, so it is also 98°.
∠3: ∠3 is a corresponding angle to ∠2, so it is also 98°.
∠4: ∠4 and ∠2 form a straight angle, which means they add up to 180°. Therefore, ∠4 = 180° - ∠2 = 180° - 98° = 82°.
So, the angle measures are:
∠1 = ∠2 = ∠3 = 98°
∠4 = 82°
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Substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place.
S=4LW+2WH; S=138, L=9, W=3. (Surface area of a special rectangular box)
H=
Step-by-step explanation:
We have the formula for the surface area of a rectangular box given by:
S = 4LW + 2WH
Substituting the given values, we get:
138 = 4(9)(3) + 2(3)H
Simplifying, we get:
138 = 108 + 6H
6H = 138 - 108
6H = 30
H = 30/6
H = 5
Therefore, the value of the unknown variable H is 5.
Explain how you know 21/100 is greater then 1/5
Answer:
To compare two fractions, we need to make sure that they have the same denominator. In this case, we can convert 1/5 to an equivalent fraction with a denominator of 100 by multiplying both the numerator and denominator by 20:
1/5 = (1/5) x (20/20) = 20/100
Now we can compare 21/100 and 20/100. Since the numerator of 21/100 is greater than the numerator of 20/100, we know that 21/100 is greater than 20/100 or 1/5. Therefore, 21/100 is indeed greater than 1/5.
Step-by-step explanation:
Answer:
1/5 is equal 2/10 equals 20/
Instructions for a chemical procedure state to mix salt, baking soda, and water in a 18:9:25
ratio by mass. How many grams of baking soda would be required to make a mixture that contains 64 grams of salt?
From the ratio of baking soda and salt, we found that when the mass of salt is 64 grams, the mass of baking soda in the mixture should be 128 grams.
What is meant by ratio?
A ratio in mathematics demonstrates how many times one number is present in another. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. Here, the dividend is referred to as the "antecedent" and the "consequent" is the divisor. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio describes the relationship between two separate entities or groups, whereas the part-to-whole ratio describes the relationship between a particular group and the entire.
The ratio of salt, baking soda and water is given as :
18 : 9 : 25
We are asked to find the mass of baking soda in a mixture when the mass of salt is 64g.
The ratio of baking soda and salt is 18:9
Let the mass of baking soda required be x.
x : 64 = 18 : 9
x/64 = 18/9
x = 18/9 * 64 = 2 * 64 = 128
Therefore from the ratio of baking soda and salt, we found that when the mass of salt is 64 grams, the mass of baking soda in the mixture should be 128 grams.
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270 calories in 3 servings : 450 calories 5 servings
There are 90 calories to 1 serving.
What is rate of quantities?Rate is a term which compares two things. It simply relates the amount of one variable to the amount of the other variable. An example is the rate of the distance covered by an object with time taken.
In the given question, we can deduce that;
270 calories in 3 servings would give;
amount of calories in 1 serving = 270/ 3
= 90
Also,
450 calories in 5 servings would give;
amount of calories in 1 serving = 450/ 5
= 90
Therefore, there are 90 calories to 1 serving.
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K
State (a) the precision, (b) the accuracy of the following measurement number.
11,000 tons
(a) The measurement is precise to the nearest
(b) The measurement number is accurate to significant digit(s).
(Type a whole number.)
ton(s).
The precision and accuracy of the measurement of 11,000 tons are;
(a) The precision of the measurement is to the nearest ton
(b) The accuracy of the measurement is to two significant digits
What is the precision and accuracy of a measurement?The precision of a measurement
The precision of a measurement indicates the level to which the measurement can be repeated or reproduced. The precision indicates the level to which the same measurement of the same quantity made using the same condition produces the same outputs.
A measurement with a high precision is one which has the measurement value of the quantity when the measurement is performed using the same conditions, produces similar results, while a measurement made with a low precision produces varying or different results under the same conditions
The precision is indicated by the number of significant digits of the measurement, and it depends on the quality of the measuring instrument, the skill of the person performing the measurement and the measurement conditions
The accuracy of a measurement
The accuracy of the measurement indicates the closeness of the value measured to the true value of the measured quantity, such that the accuracy indicates the effectiveness of the measurement, compared to the actual measured value.
The above definitions and examples indicates;
(a) The measurement of 11,000 tons which specifies the values in tons, indicating the thousands, hundreds, tens, and units, values is precise to the nearest ton.
(b) The number of significant digits in 11,000, is 2 significant digits, therefore, the measurement is accurate to 2 significant digits
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Find RQ in the image below (HELP ASAP PLEASE)
The length of RQ is 15. The solution has been obtained by using the properties of rectangle.
What is a rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle.
We are given a figure PQRS which is a rectangle.
We know that the opposite sides of a rectangle are equal.
So,
⇒PS = RQ
⇒-1 + 4x = 3x + 3
⇒x = 4
On substituting x = 4 in 3x + 3, we get
3(4) + 3 = 15
Hence, the length of RQ is 15.
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n a circle graph displaying the most popular fruit sold to students in the school cafeteria, the ratio of apples to the total pieces of fruit sold is 3/5
.
What is the angle measure of the apples section of the graph?
Answer:
Since the ratio of apples to the total pieces of fruit sold is 3/5, we know that the apples section of the graph represents 3/5 of the total angle of the circle graph.
The total angle of a circle is 360 degrees, so we can set up the equation:
3/5 x 360 = angle measure of the apples section
Simplifying the left side, we get:
216 = angle measure of the apples section
Therefore, the angle measure of the apples section of the graph is 216 degrees.
Solve the indicated quantity.
the angle between the length of a rectangle and it's diagonal is 30⁰.if the length of the rectangle is 6cm.find the length of the diagonal.
Answer:
I can not help you do you have picture that i can use so i can give u the correct answer
Step-by-step explanation:
Answer:
ik....
Step-by-step explanation:
The perimeter of a square is the product of four and the length of a side. Which of the following function rules could be used to find the perimeter of a square, represented by y, given the length of a side, represented by x?
x=y+4
y=x+4
x= 4y
y=4x
The equation it find the perimeter is y = 4x
What is perimeter?Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.
Therefore the perimeter of a square e will be given as; l+l+l+l = 4l
if the sides of a square is x and the perimeter is given by y
then, y = x+x+x+x
y = 4x
therefore the equation that represents the perimeter of a square is y = 4x
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3. Shawn opened a money market account that has a 3.25% annual interest rate,
compounded yearly. He deposits $2,750 into the account each year. How much
interest will the account eam after 25 years?
Answer:
To find the total interest earned by the account after 25 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the total amount after t years
P = the principal (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $2,750, r = 0.0325, n = 1 (compounded yearly), and t = 25. Plugging these values into the formula, we get:
A = 2,750(1 + 0.0325/1)^(1*25)
A = 2,750(1.0325)^25
A = 2,750(2.0154)
A = $5,534.85
To find the total interest earned, we need to subtract the initial deposit from the total amount:
Interest = $5,534.85 - ($2,750 x 25)
Interest = $5,534.85 - $68,750
Interest = $-63,215.15
This result indicates that the account holder would have lost money over the 25-year period, as the interest earned was not enough to offset the annual deposits. However, it's worth noting that this calculation assumes no additional deposits or withdrawals were made during the 25 years. If the account holder had made additional deposits or withdrawals, the total interest earned would be different.
Function: g(x) = 2x² - 8
For x ≥ 0, the inverse function is f(x)=
X
For x ≤ 0, the inverse function is d(x)= -
-8
0
10
DONE
f(x) d(x)
0
r
S
q
-2
t
q
√√₂x+4
SE
√₁x +4
0000
11
t =
Step-by-step explanation:
for the function
�
(
�
)
=
2
�
2
−
8
g(x)=2x
2
−8
, q = 0, r = 2, s = 3, t = -3
The given function is:
�
(
�
)
=
2
�
2
−
8
g(x)=2x
2
−8
The inverse of
�
(
�
)
=
2
�
2
−
8
g(x)=2x
2
−8
for x ≥ 0 is
�
(
�
)
=
1
2
�
+
4
f(x)=
2
1
x+4
The inverse of
�
(
�
)
=
2
�
2
−
8
g(x)=2x
2
−8
for x ≤ 0 is
�
(
�
)
=
−
1
2
�
+
4
d(x)=−
2
1
x+4
For x = -8
�
(
−
8
)
=
−
1
2
(
−
8
)
+
4
�
(
−
8
)
=
0
d(−8)=−
2
1
(−8)+4
d(−8)=0
q = d(-8) = 0
r = f(0)
�
(
�
)
=
1
2
�
+
4
�
(
0
)
=
1
2
(
0
)
+
4
�
(
0
)
=
4
�
(
0
)
=
2
f(x)=
2
1
x+4
f(0)=
2
1
(0)+4
f(0)=
4
f(0)=2
r = 2
s = f(10)
�
(
�
)
=
1
2
�
+
4
�
(
10
)
=
1
2
(
10
)
+
4
�
(
10
)
=
9
�
(
10
)
=
3
f(x)=
2
1
x+4
f(10)=
2
1
(10)+4
f(10)=
9
f(10)=3
s = 3
t = d(10)
�
(
�
)
=
−
1
2
�
+
4
�
(
10
)
=
−
1
2
(
10
)
+
4
�
(
10
)
=
−
9
�
(
10
)
=
−
3
d(x)=−
2
1
x+4
d(10)=−
2
1
(10)+4
d(10)=−
9
d(10)=−3
Therefore, for the function
�
(
�
)
=
2
�
2
−
8
g(x)=2x
2
−8
, q = 0, r = 2, s = 3, t = -3
The value of variables are,
q = 0
r = 2
s = - 3
t = 3
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
g (x) = 2x² - 8
Now, We have;
For x ≥ 0;
The inverse function is,
⇒ f (x) = √1/2x + 4
And, For x ≤ 0;
The inverse function is,
⇒ d (x) = - √1/2x + 4
Hence, For x = - 8;
⇒ d (x) = - √1/2x + 4
⇒ q = - √1/2 × - 8 + 4
⇒ q = - √- 4 + 4
⇒ q = 0
For x = 0;
⇒ f (x) = √1/2x + 4
⇒ r = √1/2 × 0 + 4
⇒ r = √0 + 4
⇒ r = 2
For x = 10;
⇒ d (x) = - √1/2x + 4
⇒ t = - √1/2 × 10 + 4
⇒ t = - √5 + 4
⇒ t = - 3
For x = 10;
⇒ f (x) = √1/2x + 4
⇒ s = √1/2 × 10 + 4
⇒ s = √5 + 4
⇒ s = 3
Thus, The value of variables are,
q = 0
r = 2
s = - 3
t = 3
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1. Assume that f is an increasing, nonnegative function on [a, b]. What can be concluded about the relationships among LRAMn f, RRAMn f, and the area on [a, b]?
2. Assume that f is a decreasing, nonnegative function on [a, b]. What can always be concluded about the relationships among LRAMn f, RRAMn f, and the area on [a, b]?
3. Prove or disprove the following statement: MRAMn f is the average of LRAMn f and RRAMn f. Give specific examples.
4. Given the function f(x) = 2x over the interval [0, 3], explain how to find a formula for the Riemann sum obtained by dividing the interval into n subintervals and using the right-hand endpoint for each ci. Then take a limit of these sums as n approaches infinity to calculate the area under the curve over the interval.
The area under the curve of function f on [a, b] is the limit of both LRAMn f and RRAMn f as n approaches infinity.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The Left Riemann Sum (LRAM) and Right Riemann Sum (RRAM) of a non-negative, increasing function f on the interval [a, b] are defined as follows -
LRAMn f = (b - a)/n × [ f(a) + f(a + (b-a)/n) + f(a + 2(b-a)/n) + ... + f(a + (n-1)(b-a)/n) ]
RRAMn f = (b - a)/n × [ f(a + (b-a)/n) + f(a + 2(b-a)/n) + ... + f(a + n(b-a)/n) ]
As f is an increasing, non-negative function on [a, b], both LRAMn f and RRAMn f will be non-negative, and the area under the curve of f will also be non-negative.
Since f is increasing on [a, b], we have -
f(a) ≤ f(a + (b-a)/n) ≤ f(a + 2(b-a)/n) ≤ ... ≤ f(a + (n-1)(b-a)/n) ≤ f(b)
Therefore, LRAMn f will be less than or equal to the area under the curve of f on [a, b], which is less than or equal to RRAMn f.
That is -
LRAMn f ≤ Area under curve of f on [a, b] ≤ RRAMn f
So we can conclude that the area under the curve of f on [a, b] is bounded between LRAMn f and RRAMn f.
Therefore, as n increases, both LRAMn f and RRAMn f converge to the area under the curve of f on [a, b].
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is 9/18 a rational number?
Therefore , the solution of the given problem of rational numbers comes out to be that 9/18 is a rational number
What are rational numbers, exactly?Rational numbers are those that can be written as the ratio (not the fraction) of two integers. A fraction with a nonzero denominator is considered sensible. Examples of rational numbers include 1/2, 1/5, but it also 3/4. Additionally, "0" can be written in many different ways as a real purpose, such as 0/1, 0/2, as well as 0/3. But 1/0, 2/0, 3/0, and so forth. The number of seven is reasonable. Two parameters can be divided to produce a rational figure.
Here,
Because 9/18 can be written as a ratio of two numbers, it is a rational number. By dividing the numerator and denominator by their largest common factor, which is 9 in this instance, we can simplify the expression 9/18:
=> 9/18
=> (9 ÷ 9) / (18 ÷ 9) = 1/2
We can see that 9/18 is a rational number because 1/2 is also a ratio of two numbers.
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Fill in each blank with ONE word to create a sentence to explain slope in the context of this problem: The amount of blank is blank at a rate of slope number per blank.
Answer:
Fill in each blank with ONE word to create a sentence to explain slope in the context of this problem: The amount of [dependent variable] is [changing] at a rate of [slope] [units of dependent variable] per [unit of independent variable].
Step-by-step explanation:
discuss the implications for classroom practice relative to understanding learning difficulties in mathematics. 1.variations in teaching strategies
The implications for classroom practice relative to understanding implications for mathematics teaching .
What are the social cognitive theory's guiding principles?
The five following social cognition and behavior principles are discussed: (1) the influence of situation on conduct; (2) blindness to situational influences; (3) social perception and self-perception are constructive processes; (4) blindness to the constructed character of social and self-perception; and (5) self.
What does SCT mean by self-regulation?
When faced with externally imposed stimuli, self-regulation enables a person to maintain control over their behavior or response. A person's ability to self-regulate is strengthened through feedback, an externally imposed control that enables behavior modification.
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As seen in the diagram below, Austin is building a walkway with a width of xx feet to go around a swimming pool that measures 8 feet by 10 feet. If the total area of the pool and the walkway will be 360 square feet, how wide should the walkway be?
Answer:
We can start the problem by using the formula for the area of a rectangle:
Area = length x width
The total area of the pool and the walkway is given as 360 square feet. Let's assume that the width of the walkway is w feet. Then, the dimensions of the entire area can be represented as (8 + 2w) by (10 + 2w) feet, since there is an additional width of w feet on both sides of the pool. Therefore, we can set up the equation:
(8 + 2w) x (10 + 2w) = 360
Expanding the left side and simplifying, we get:
4w^2 + 36w - 80 = 0
We can solve for w using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 4, b = 36, and c = -80. Substituting these values into the formula, we get:
w = (-36 ± sqrt(36^2 - 4(4)(-80))) / 8
w = (-36 ± sqrt(1872)) / 8
w ≈ -5.6 or w ≈ 3.6
Since the width cannot be negative, we can discard the first solution. Therefore, the width of the walkway should be approximately 3.6 feet.
Step-by-step explanation:
Answer:
We can start the problem by using the formula for the area of a rectangle:Area = length x widthThe total area of the pool and the walkway is given as 360 square feet. Let's assume that the width of the walkway is w feet. Then, the dimensions of the entire area can be represented as (8 + 2w) by (10 + 2w) feet, since there is an additional width of w feet on both sides of the pool. Therefore, we can set up the equation:(8 + 2w) x (10 + 2w) = 360 Expanding the left side and simplifying, we get:4w^2 + 36w - 80 = 0We can solve for w using the quadratic formula:w = (-b ± sqrt(b^2 - 4ac)) / 2aIn this case, a = 4, b = 36, and c = -80. Substituting these values into the formula, we get:w = (-36 ± sqrt(36^2 - 4(4)(-80))) / 8w = (-36 ± sqrt(1872)) / 8w ≈ -5.6 or w ≈ 3.6Since the width cannot be negative, we can discard the first solution. Therefore, the width of the walkway should be approximately 3.6 feet.
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