Answers
In response to the aforementioned query, we may say that here, the exponent is [tex](x^2)^5 / (x^3)^2[/tex] = [tex]x^n[/tex] => [tex]x^4 = x^n[/tex] => so, n=4
what are exponents?Exponentiation, sometimes referred to as "b raised to the nth power," is a mathematical operation that includes two numbers: a base number, b, and an exponent, or power, n. It is represented by the sign bn. A number's exponent reveals how many times it has been multiplied by itself. For instance, the number 2-3 (written as 23) means 2 × 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that shows how many times a number has been multiplied by itself is called an exponent. As an example, multiplying 6 by 4 results in 6 x 6 x 6.
here, the exponent is
[tex](x^2)^5 / (x^3)^2[/tex] = [tex]x^n[/tex]
[tex]x^{10} / x^{6}[/tex]
[tex]x^{10 - 6}[/tex]
[tex]x^4 = x^n[/tex]
so, n=4
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Related Questions
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
Answers
First, we need to find the value of k:
k = y/x = 100/20 = 5
Now that we know k, we can solve for y when x = 18:
y = kx = 5(18) = 90
Therefore, when x = 18, y = 90.
Brainliest answer, please.
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 
Answers
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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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%
Answers
Answer:
points cuzo
but if i find it out i will edit
Step-by-step explanation:
Explain how you know 21/100 is greater then 1/5
Answers
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/
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]
Answers
Answer: [3, 2.5]
Step-by-step explanation:
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?
Answers
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:
Which insect measurement was the most frequent?
Length of insects (in inches)
Answers
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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Please help me!!!!!!
Answers
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%
help me pls i will give brainless
Answers
help with homework pls
Answers
Answer:
no
Step-by-step explanation:
orka:sweet potato
15:8 = 1.875
350:160 = 2.1875
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?
Answers
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.
Answers
find the area of this semi circle with radius r=19cm give your answer rounded to 1 dp
Answers
the answer is 283.4
I can't write a formula
36/84 simplify plsss
Answers
Explanation: Reduce the expression, if possible, by cancelling the common factors
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
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 =
Answers
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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2x(x+4) in standard form
Answers
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:
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
Answers
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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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.
Answers
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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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
Answers
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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discuss the implications for classroom practice relative to understanding learning difficulties in mathematics. 1.variations in teaching strategies
Answers
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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what is the value of the star?
Answers
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.
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.)
Answers
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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Graph the following feature
Y intercept =2
Slope = -6/5
Answers
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.
squared root of x-45 equals squared root of x minus 3
Answers
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]
There is something that looks like a backwards y. If the "backwards y" (∠2)=98°, find the following angle measures.
Answers
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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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.
Answers
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:
Sheri's deck design is shown below. Which shape has the same perimeter but a different area than Sheri's design?
Answers
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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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.
Answers
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:
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?
Answers
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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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).
Answers
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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