Volume of the cone is 1/3 of the volume of the cylinder, so volume of the cone = 40in³.
What is the volume of a cylinder and cone?One-third of the volume of a cylinder is the formula for the volume of a cone. The product of the base area and the height is used to calculate a cylinder's volume. As a result, the formula for a cone's volume is given as V = (1/3) r²h, where "h" stands for the cone's height and "r" for its base radius.
A cylinder's volume is determined by how many unit cubes (cubes of the same length) can fit inside of it. It is the area the cylinder takes up, just as any three-dimensional shape's volume is the area it occupies.
We are aware that a circle serves as the base of a right circular cylinder and that r² is the area of a circle of radius r. As a result, using the formula above, V = r²h is the right circular cylinder's volume.
Now in the given question, volume of the cylinder = 120in³.
Volume of cone = 1/3(volume of the cylinder)
= 1/3 × 120
40in³.
Therefore, volume of the cone = 40in³.
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What is the quotient of 16sup(x,-2)-8sup(x,-2)-2sup(x,-9) and 2x?
The required quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.
What is arithmetic?Arithmetic involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Here,
To simplify the given expression, we can start by factoring out the common factor of 2x from the numerator. This gives:
(16x⁻² - 8x⁻² - 2x⁻⁹) / 2x
Next, we can simplify the terms in the numerator by combining the like terms:
= (4x⁻² - x⁻⁹) / x
= 4x⁻²⁻¹ - x⁻⁹⁻¹
= 4x⁻³ - x⁻¹⁰
= 4x⁻³ - x⁻¹⁰
Therefore, the quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.
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help with homework pls
Answer:
no
Step-by-step explanation:
orka:sweet potato
15:8 = 1.875
350:160 = 2.1875
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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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%
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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1.1 Measure the diameter of the tin in mm and write down the real diameter in mm 1.2 Hence, determine the circumference of the base of the tin in mm. You may us the formula: C = 2лr π = 3,142 Hint: radius = half of diameter 1.3 Measure the height of the tin in mm and write down the real height in mm. MATHEMATICAL LITERACY GRADE 11, 2023 SBA GUIDELINE
We can write the diameter and circumference of the base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
Mathematically, we can write,
y = f(x) = ax + b.
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumference as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumference of the base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
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help me pls i will give brainless
. Aisha went to the local gas station to get a gallon of milk. She saw that the store had quart containers of milk for $1.19 while a gallon was $4.66. Aisha bought four quarts instead of the gallon because she thought it would be cheaper for the same amount of milk. Did Aisha save money? Explain your reasoning.
Therefore , the solution of the given problem of unitary method comes out to be she actually paid more for the same quantity of milk in the end.
What does unitary method mean?Divide the measures of just this microsecond portion by two variable in order to complete the task using the unitary technique. Briefly stated, the characterised by a group and colour subgroups are both removed from the unit method expression when a wanted item is present. For example, 40 pens with a changeable price would cost Rupees ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this.
Here,
4 gallons of milk make up a gallon of milk. Four pints would cost $1.19 each, or
=> $1.19 x 4 = $4.76.
Instead of purchasing a gallon of milk for $4.66,
Aisha opted to purchase four pints for $4.76.
Thus, by purchasing four pints rather than a gallon, Aisha did not save money.
She actually paid more for the same quantity of milk in the end.
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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:
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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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.
Step-by-step explanation:
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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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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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
squared root of x-45 equals squared root of x minus 3
Answer:
No solution
Step-by-step explanation:
[tex]\sqrt{x-45} =\sqrt{x-3} \\(\sqrt{x-45} )^2=(\sqrt{x-3} )^2\\x-45 = x-3\\x-x = 45-3\\0 = 42\\[/tex]
The population of Mexico between 1921 and 2010 can be modeled as
p(t) = 8.028e^0.025t million people, where t is the number of years since 1900.†
(a) What was the population of Mexico in 2006? (Round your answer to three decimal places.)
____________ million people
How rapidly was the population of Mexico growing in 2006? (Round your answer to three decimal places.)
____________ million people per year
(b) Write a linearization of p in 2006. (Round all numerical values to three decimal places.)
pL(t) = ______________
(c) Use linearization to estimate the population of Mexico in 2011. (Round your answer to three decimal places.)
_______________ million people
By answering the above question, we may state that As a result, in 2006, equation Mexico's population was expanding at a pace of around 2.708 million people each year.
What is equation?When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.
We must enter t = 2006 - 1900 = 106 into the population model and do the following calculations to get the population of Mexico in 2006:
p(106) = 8.028e (0.025 * 106) million individuals
108.191 million individuals, or p(106) (rounded to three decimal places)
Finding the derivative of the population model with respect to time t will allow us to determine how quickly Mexico's population was rising in 2006:
Each year, p'(t) = 0.025 * 8.028e(0.025t) million individuals.
We may then calculate the derivative at time t = 106 as follows:
P'(106) = 0.025 * 8.028e(0.025*106) million individuals annually P'(106) 2.708 million individuals annually (rounded to three decimal places)
As a result, in 2006, Mexico's population was expanding at a pace of around 2.708 million people each year.
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O
The value of "y" varies directly with "x"!
If y = 100, then x = 20.
Solve for y when x = 18.
k = 5
y = [?
Remember: y=kx
Answer:
Step-by-step explanation:
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below.
Course grades from A to F
Question content area bottom
Part 1
Choose the correct answer below.
A.
The ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural starting point.
B.
The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.
C.
The nominal level of measurement is most appropriate because the data cannot be ordered.
D.
The interval level of measurement is most appropriate because the data can be ordered, differences obtained by subtraction can be found and are meaningful and there is no natural staring point 
Option (B): The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.
What are the levels of measurement?
You may find out how accurately variables are recorded using levels of measurement, also known as scales of measurement. A variable in scientific research is anything that can have several values depending on the data collection.
Four levels of measuring exist:
Nominal: The information is only classifiable.Ordinal: The information is classifiable and rankableInterval: Data can be categorised, rated, and spaced evenly.Ratio: The data is equally distributed, categorised, ranked, and has a natural zero.You might only be able to perform a limited amount of data analysis depending on the level of measurement of the variable. From low (nominal) to high, there is a hierarchy in the complexity and precision of the level of measurement (ratio).
We have to find the appropriate level of measurement for the data course grades from A to F.
Here there is an order for ranking. This is because A is the highest grade followed by B, C, D, E and F respectively.
So nominal level of measurement is out of the question.
Now, there are no numerical values associated with the grades. We have no means to find the difference between the two grades.
Therefore the most appropriate level of measurement for Course grades from A to F is,
Option (B): The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.
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What is the output?
listC=[3, 2.5, 10]
listC.pop()
print(listC)
O There is no output because there is an error in the program.
O [2.5, 3, 10]
OI
O [3, 2.5]
Answer: [3, 2.5]
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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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:
What are the values of x when x²+x-6 = -4?
OA. x = -4 and x = 6
OB. x = -2 and x = 1
OC. x = -3 and x = 2
OD. x = -5 and x = -6
edu
play
Answer:
0
Step-by-step explanation:
for x x^2+x-6=-4. x2+x−6=−4 x 2 + x - 6 = - 4. Step 1. Add 4 4 to both sides of the equation. x2+x−6+4=0 x 2 + x - 6 + 4 = 0.
(hope it helps!)
Graph the following feature
Y intercept =2
Slope = -6/5
your given information is important because your first piece of info is the y intercept. The y intercept can be interpreted as (0,2). this is your initial point.
once you have that point, you can then use the slope to finish off your linear function. the slope is rise/run.
this means that you have to travel in the y direction, which is your rise. this means you have to go either in the positive or negative, depending on the number. in this case, it's -6, so we would go down 6.
then we would run 5 units in the x direction and same like the x it would be depending on the number being positive or negative. since we have a +5 it means we have to move 5 units to the right should have a graph that looks like a (\).
hope it helps.
learner sell 300 vetkoet every week for 12 they charge 10 for each vetkoet calculate the profit they will if the cost for each vetkoet is 3.80
The profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To calculate the profit for selling 300 vetkoek every week, we need to first calculate the total revenue generated and the total cost of producing the vetkoek.
Total revenue = Price per vetkoek x Number of vetkoek sold
Total revenue = 10 x 300 = 3000
Total cost = Cost per vetkoek x Number of vetkoek sold
Total cost = 3.80 x 300 = 1140
Profit = Total revenue - Total cost
Profit = 3000 - 1140 = 1860
Therefore, the profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.
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find the area of this semi circle with radius r=19cm give your answer rounded to 1 dp
the answer is 283.4
I can't write a formula
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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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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The distribution of heights of young women is approximately Normal with mean 64 inches and standard deviation 2.7 Use the 68-95-99.7 rule to answer the questions.
Therefore, the height range that encompasses 99.7% of adolescent women is roughly between 55.9 and 68.1 inches.
What can you infer from standard deviation?It reveals the average deviation of each number from the norm. When it comes to normally distributed, a large standard deviation denotes that values are typically out of the mean, whereas a smaller standard deviation denotes that values are grouped closely around the mean.
The 68-95-99.7 rule is a way to remember the percentage of data that falls within certain numbers of standard deviations from the mean in a normal distribution. Specifically:
About 68% of the data falls within 1 standard deviation of the meanAbout 95% of the data falls within 2 standard deviations of the meanAbout 99.7% of the data falls within 3 standard deviations of the meanUsing this rule, we can answer the following questions:
What is the range of heights that includes about 68% of young women?About 68% of young women have heights within 1 standard deviation of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 1 standard deviation from the mean:
64 inches ± 2.7 inches
So the range of heights that includes about 68% of young women is approximately 61.3 inches to 66.7 inches.
2. What is the range of heights that includes about 95% of young women?
About 95% of young women have heights within 2 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 2 standard deviations from the mean:
64 inches ± 2(2.7 inches)
So the range of heights that includes about 95% of young women is approximately 58.6 inches to 69.4 inches.
3. What is the range of heights that includes about 99.7% of young women?
About 99.7% of young women have heights within 3 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 3 standard deviations from the mean:
64 inches ± 3(2.7 inches)
So the range of heights that includes about 99.7% of young women is approximately 55.9 inches to 68.1 inches.
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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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2x(x+4) in standard form
Answer:
To write 2x(x+4) in standard form, we need to expand the product and simplify:
2x(x+4) = 2x^2 + 8x
Therefore, the standard form of 2x(x+4) is 2x^2 + 8x.
Step-by-step explanation: