The diagram shows 3 identical circles inside a rectangle.
each circle touches the other 2 circles and the side of the rectangle, as shown in the diagram.
Radius of each circle is 28mm.
work out the area of the rectangle.
Give your answer correct to three significant figures
Answers
The area of the rectangle is 6272 mm² (to three significant figures).
What is area?Area is a physical quantity that refers to the amount of space within a two-dimensional shape or surface. It is typically measured in square units such as square meters, square centimeters, or square feet.
What is radius?Radius is a measure of the distance from the center of a circle to any point on its circumference. It is often denoted by the letter "r" and is usually expressed in units of length, such as meters or millimeters.
In the given question,
We can start by drawing lines connecting the centers of the circles and the rectangle.
Let's call the width of the rectangle "w" and the height of the rectangle "h".
Since each circle touches the side of the rectangle, we know that the diameter of each circle is equal to the width of the rectangle, so:
diameter of each circle = radius of each circle = 28 mm
Therefore, we can write:
2 x 28 mm + w + w = h
Simplifying, we get:
w + 56 mm = h/22w + 56 mm = h
Now we can find the area of the rectangle by multiplying its width and height:
Area of rectangle = w x h
Substituting for "h", we get:
Area of rectangle = w x (2w + 56 mm)
Expanding and simplifying, we get:
Area of rectangle = 2w² + 56w mm²
To find the value of "w", we can use the fact that the radius of each circle is 28 mm and the circles touch each other, so:
w + 2 x 28 mm + w = 3 x diameter of each circle
Simplifying, we get:
2w + 56 mm = 3 x 2 x 28 mm
2w + 56 mm = 168 mm
2w = 112 mmw = 56 mm
Now we can substitute this value of "w" into the formula for the area of the rectangle:
Area of rectangle = 2w² + 56w mm²
Area of rectangle = 2 x (56 mm)² + 56 mm x 56 mm
Area of rectangle = 6272 mm²
Therefore, the area of the rectangle is 6272 mm² (to three significant figures).
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Related Questions
help plssss explainnn!!
Answers
Answer:
[tex]xy^8[/tex]
Step-by-step explanation:
Notice if you have the same base you can ADD the exponent, for example:
[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]
[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]
so the answer is
[tex]xy^8[/tex]
4. A pet store has eight dogs and cats. Three are dogs. What fraction represents the number of cats?
A. 1/4
B. 3/8
C. 1/2
D.5/8
Answers
There are 3 dogs out of 8 pets
Dogs=3/8
1-3/8=5/8
Cats=5/8
Answer:
Step-by-step explanation:
Number of cats = 8 - 3 = 5
Fraction that are cats [tex]=\frac{5}{8}[/tex]
If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + 5), what is the value of r?
F.:3
H. 7
J. 12
K. Cannot be determined from the given information
Answers
Answer:
H. 7
Step-by-step explanation:
Given x² + rx + 12 is equivalent to (x + 3)(x + s), equate the two expressions and expand the right side of the equation:
[tex]\begin{aligned}x^2+rx+12&=(x + 3)(x + s)\\ x^2+rx+12&=x^2 + sx + 3x + 3s\\x^2+rx+12&=x^2 + (s+3)x + 3s\end{aligned}[/tex]
To find the value of r, first find the value of s.
The constant term of the right-hand side must be equal to the constant term of the left-hand side. Therefore:
[tex]\implies 3s = 12[/tex]
Solve for s by dividing both sides of the equation by 3:
[tex]\implies s = 4[/tex]
Compare the coefficients of the terms in x:
[tex]\implies r = s + 3[/tex]
Substitute the value of s into the equation and solve for r:
[tex]\begin{aligned} \implies r &= s + 3\\&= 4 + 3\\&= 7\end{aligned}[/tex]
Therefore, the value of r is 7.
Answer:
[tex]\large\boxed{\sf r = 7 }[/tex]
Step-by-step explanation:
Correct question:- If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + s), what is the value of r?
Here we are given that , the expression (x+3)(x+s) is equal to r² + rx + 12 .
Firstly, expand the expression (x+3)(x+s) as ,
[tex]\implies (x+3)(x+s) \\[/tex]
[tex]\implies x(x+s)+3(x+s) \\[/tex]
[tex]\implies x^2 + xs + 3x + 3s \\[/tex]
Take out x as common,
[tex]\implies x^2 + (3+s)x + 3s \\[/tex]
Now according to the question,
[tex]\implies x^2 + (3+s)x + 3s = r^2 + rx + 12\\[/tex]
On comparing the respective terms , we get,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies 3s = 12 \\[/tex]
Solve the second equation to find out the value of s , so that we can substitute that in equation 1 to find "r" .
[tex]\implies 3s = 12 \\[/tex]
[tex]\implies s =\dfrac{12}{3}=\boxed{4} \\[/tex]
Now substitute this value in equation (1) as ,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies r = 3 + 4 \\[/tex]
[tex]\implies \underline{\underline{ \red{ r = 7 }}} \\[/tex]
and we are done!
Let A and B be events with P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.03. Are A and B mutually exclusive? Explain why or why not.
Answers
Answer:
A and B are not mutually exclusive
Step-by-step explanation:
A and B are not mutually exclusive because P(A and B) > 0. If A and B were mutually exclusive, then they would have no outcomes in common and the probability of their intersection would be zero. However, in this case, they do share some outcomes, since P(A and B) is greater than zero.
Management estimates that 5% of credit sales are eventually uncollectible. Of the collectible credit sales, 65% are likely to be collected in the month of sale and the remainder in the month following the month of sale. The company desires to begin each month with an inventory equal to 70% of the sales projected for the month. All purchases of inventory are on open account; 30% will be paid in the month of purchase, and the remainder paid in the month following the month of purchase. Purchase costs are approximately 60% of the selling prices. Budgeted January cash payments for December inventory purchases by Collection Corporation are:
Answers
Answer:
Step-by-step explanation:
Unfortunately, there is no information provided about the sales projections for the month of January or the selling prices of the inventory. Without this information, it is not possible to calculate the budgeted January cash payments for December inventory purchases.
Use the gradient to find the directional derivative of the function at P in the direction of PQ. f(x, y) = 3x2 - y2 + 4, P(1, 5), 2(4,2)
Answers
The directional derivative of f(x,y) at point P(1,5) in the direction of PQ is -2√2.
Find the directional derivative of the function f(x,y) = 3x² - y² + 4 at point P(1,5) in the direction of PQ, where P(1,5) as well as Q(4,2), we need to first calculate the gradient of f(x,y) at point P.
The gradient of f(x,y) at P is:
∇f(x,y) = [∂f/∂x, ∂f/∂y] = [6x, -2y]
Evaluating this at point P(1,5), we get:
∇f(1,5) = [6(1), -2(5)] = [6, -10]
Now, we need to find the unit vector in the direction of PQ. This can be calculated as follows:
u = PQ/|PQ|
where PQ = Q - P = [4 - 1, 2 - 5] = [3, -3] and |PQ| = √(3² + (-3)²) = √18 = 3√2
So, u = PQ/|PQ| = [3/3√2, -3/3√2] = [1/√2, -1/√2]
The directional derivative of f(x,y) at P in the direction of PQ is then given by:
D_u f(P) = ∇f(P) · u
where · represents the dot product.
Substituting the values we obtained earlier, wehave:
D_u f(P) = [6, -10] · [1/√2, -1/√2]
D_u f(P) = (6/√2) + (-10/√2)
D_u f(P) = -2√2
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please help !! Given l, m, n, find the value of x.
(7x-2)° (5x+14)°
Answers
Answer:
Step-by-step explanation:
7x - 2 = 5x + 14
2x - 2 = 14
2x = 16
x = 8
Find the definite integral of f(x)=
fraction numerator 1 over denominator x squared plus 10x plus 25 end fraction for x∈[5,7]
Answers
the definite integral of f(x) over the interval [5, 7] is (-5 / 600).
How to find?
The given function is:
f(x) = 1 / (x² + 10x + 25)
To find the definite integral of this function over the interval [5, 7], we can use the following steps:
Rewrite the function using partial fraction decomposition:
f(x) = 1 / (x² + 10x + 25)
= 1 / [(x + 5)²]
Using partial fraction decomposition, we can write this as:
f(x) = A / (x + 5) + B / (x + 5)²
where A and B are constants to be determined. Multiplying both sides by the common denominator (x + 5)², we get:
1 = A(x + 5) + B
Setting x = -5, we get:
1 = B
Setting x = 0, we get:
1 = 5A + B
= 5A + 1
Solving for A, we get:
A = 0
Therefore, the partial fraction decomposition is:
f(x) = 1 / [(x + 5)²]
= 0 / (x + 5) + 1 / (x + 5)²
Use the formula for the definite integral of a power function:
∫ xⁿ dx = (1 / (n + 1))× x²(n + 1) + C
where C is the constant of integration.
Using this formula, we can find the antiderivative of the function 1 / (x + 5)²:
∫ 1 / (x + 5)² dx = -1 / (x + 5) + C
Evaluate the definite integral over the interval [5, 7]:
∫[5,7] 1 / (x + 5)² dx
= [-1 / (x + 5)] [from 5 to 7]
= (-1 / 12) - (-1 / 10)
= (-5 / 600)
Therefore, the definite integral of f(x) over the interval [5, 7] is (-5 / 600).
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The expression 1.05x calculates what change to the value of x?
Answers
With comparison to the initial value of x, this signifies an increase of 5%.
What is an illustration of an initial value?If, for instance, we have the mathematical problem y′=2x y ′ = 2 x, then y(3)=7 y (3) = 7 is an initial value, so when these equations are combined, they create an initial-value problem.
The calculation of a 5% increase in the value of x is done by the phrase 1.05x.
We may modify the phrase as follows to understand why:
1.05x = x + 0.05x
Thus, 1.05x is the same as increasing x by 5% from its initial value.
For example, if x = 100, then:
1.05x = 1.05 × 100 = 105
The initial value of x has increased by 5% as a result of this.
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With comparison to the initial value of x, this signifies an increase of 5%. Thus, option A is correct.
What is an illustration of an initial value?If, for instance, we have the mathematical problem y′=2x y ′ = 2 x, then y(3)=7 y (3) = 7 is an initial value, so when these equations are combined, they create an initial-value problem.
The calculation of a 5% increase in the value of x is done by the phrase 1.05x.
We may modify the phrase as follows to understand why:
1.05x = x + 0.05x
Thus, 1.05x is the same as increasing x by 5% from its initial value.
For example, if x = 100, then:
1.05x = 1.05 × 100 = 105
The initial value of x has increased by 5% as a result of this.
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Complete question:
The expression 1.05x calculates what change to the value of x?
a. increase of 5%
b. Power of 5
c. decrease of 5%
d. fraction of 5
Given the coefficient of correlation in the relationship to be - 0.73 , what percentage of the variation in hours of sleep cannot be explained by the time spent on social media?
Answers
The coefficient of determination, denoted by r^2, represents the proportion of the variation in one variable that can be explained by the other variable in a linear regression model.
The proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is equal to 1 - r^2.
Given the coefficient of correlation, r = -0.73, we can find the coefficient of determination:
r^2 = (-0.73)^2 = 0.5329
So, the proportion of the variation in hours of sleep that can be explained by the time spent on social media is 0.5329.
Therefore, the proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is:
1 - 0.5329 = 0.4671
Multiplying this by 100, we get:
0.4671 x 100 = 46.71%
So, approximately 46.71% of the variation in hours of sleep cannot be explained by the time spent on social media.
can you help me to solve this question?
Answers
The asymptotes of the function f(x) = (2x² - 5x + 3)/(x - 2) are given as follows:
Vertical asymptote at x = 2.Oblique asymptote at: y = 2x - 3/2.How to obtain the asymptotes of the function?The function for this problem is defined as follows:
f(x) = (2x² - 5x + 3)/(x - 2)
The vertical asymptote is the value of x for which the function is not defined, hence it is at the zero of the denominator, and thus it is given as follows:
x - 2 = 0
x = 2.
The oblique asymptote is at the quotient of the two functions, hence:
(mx + b)(x - 2) = 2x² - 5x + 3
mx² + (b - 2m) - 2b = 2x² - 5x + 3.
Hence the values of m and b are given as follows:
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Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
Part A: Write the explicit equation for f (n) that represents the number of lionfish in the bay after n years. Show all necessary math work.
Part B: How many lionfish will be in the bay after 6 years? Round to the nearest whole number and show all necessary math work.
Part C: If scientists remove 1,300 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.
Answers
The number of lionfish after 6 years will be 85,609. The recursive equation for [tex]f(n)[/tex] will be [tex]f(n) = 4242.42(1.65)^n - 1300n[/tex].
What is an exponent?Consider the function:
[tex]y = a (1 \pm r)^x[/tex]
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
lionfish are considered an invasive species, with an annual growth rate of 65%.
Then the equation will be
[tex]f(n) = P(1.65)^n[/tex]
[tex]\text{P = initial population}[/tex]
A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
[tex]7000 = P(1.65)[/tex]
[tex]P = 4242.42[/tex]
Then the equation will be
[tex]f(n) = 4242.42(1.65)^n[/tex]
The number of lionfish after 6 years will be
[tex]f(n) = 4242.42(1.65)^6[/tex]
[tex]f(n) = 85608.58[/tex]
[tex]f(n) \cong 85,609[/tex]
If scientists remove 1,300 fish per year from the bay after the first year.
Then the recursive equation for f(n) will be
[tex]f(n) = 4242.42(1.65)^n - 1300n[/tex]
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Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from a standard deck of 52 playing cards.
Event A: The Result is a club
Event B: The result is a king
Are they mutually exclusive or not mutually exclusive?
Answers
In general, two events are mutually exclusive if they cannot both occur at the same time, meaning that there is no overlap between them. In this case, since there is one card that is both a club and a king, the events A and B are not mutually exclusive.
Cant figure out the surface area
Answers
Answer:
[tex]96 \: {m}^{2} [/tex]
The correct answer is B
Step-by-step explanation:
First, we have to find the area of one side of the cube:
[tex]a(side) = 4 \times 4 = 16[/tex]
Now multiply this number by 6 (since the cube has 6 sides in total):
[tex]a(surface) = 16 \times 6 = 96[/tex]
Answer: B - 96 sq m
Step-by-step explanation:
The surface area is the area of all the squares added up. To find the area of one square, you multiply 4 x 4, which equals 16. Then, count the number of sides on the cube. There are 6 sides on this cube. So, you multiply 16 x 6. 96 is your total. And you can eliminate C because it says meters instead of square meters.
Really Need help asap!
Answers
Step-by-step explanation:
h(-2) = 25
h(-1) = 5
h(0) = 1
h(1) = 1/5
h(2) = 1/25
A salesperson earns 4% commission on furnace sales.
What is the commission that the salesperson earns on the sale of $33,000 worth of furnaces.
Answers
The commission earned 4 percentage on the salesperson on the sale of furnaces is $1320.
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. The word per cent means per 100. The letter "%" stands for it. The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator.
by the question.
the commission that the salesperson earns on the sale of $33,000 worth of furnaces= 4% of 33,000 = 4× 330 = $1320
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Part A
Use GeoGebra to graph points A, B, and C to the locations shown by the ordered pairs in the table. Then join each pair of
points using the segment tool. Record the length of each side and the measure of each angle for the resulting triangle.
Location
A(3,4), B(1,1).
C(5.1)
A(4.5), B(2.1).
C(7.3)
—————-
AB=
BC=
AC=
Answers
Answer:
Step-by-step explanation:
Answer:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]
Step-by-step explanation:
Step 1Place points A, B and C on the coordinate grid.
Alternatively, type the following into the input field as 3 separate inputs:
Triangle 1
A = (3, 4)B = (1, 1)C = (5, 1)Triangle 2
A = (4, 5)B = (2, 1)C = (7, 3)Step 2Use the Segment tool to join each pair of points.
Alternatively, type Segment( <Point>, <Point> ) into the input field (replacing <Point> with the letter name of the point) to create a segment between two points.
Record the length of each side.
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]
Step 3Use the Angle tool to measure each angle in the resulting triangle.
Alternatively, type Angle(Polygon(A, B, C)) into the input field to create all interior angles.
Record the measure of each angle.
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]
Note: All measurements have been given to the nearest hundredth (2 decimal places).
write an algebraic expression to represent the phrase twelve dollars less than the original price. let p represent the unknown.
Answers
Answer:
p=O-12
Step-by-step explanation:
original price:O
12 less than O is "O-12"
therefore p=O-12
Find the distance from Link to the Octorok so Link can attack
Answers
The distance from Link to the Octorok is 10.63 units.
How to find the distance?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below:
distance = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here we want to find the distance from Link to the Octorok so Link can attack, so we need to get the distance between the points (-4, -5) and (3, 3).
The distance will be:
distance = √( (3 + 4)² + (3 + 5)²)
distance = √( (7)² + (8)²)
distance = √113
distance = 10.63
The distance is 10.63 units.
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performed 100 trials of a simulation to see what difference in proportions would occur due to chance variation
Answers
Performing a simulation with 100 trials is a common technique used to assess the impact of chance variation on the results of an experiment or study. The simulation can help you understand how likely it is to see certain results due to chance variation alone, rather than any underlying difference in proportions.
To perform this simulation, you would first need to define the two proportions that you want to compare. For example, you might want to compare the proportion of people who prefer brand A to brand B in a survey.
Next, you would randomly assign each trial to either brand A or brand B based on the defined proportions. For example, if the proportion of people who prefer brand A is 0.6, you would assign 60 out of the 100 trials to brand A and 40 trials to brand B.
After assigning each trial, you would then calculate the difference in proportions between the two groups. This would give you a distribution of differences that you would expect to see due to chance variation alone.
If the observed difference falls within the range of differences expected due to chance variation, you can conclude that the difference in proportions you observed is not statistically significant and may be due to chance.
However, if the observed difference is larger than what you would expect to see due to chance variation, you can conclude that the difference is statistically significant and likely due to an underlying difference in proportions.
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What value of Y and Z will make DEF correspond to JKI?
Answers
[tex]\bold{Solution:}[/tex]
[tex]\Delta[/tex][tex]DE[/tex][tex]F[/tex] congruent to [tex]\Delta[/tex][tex]JKI[/tex]
[tex]\bold{FD=JI} \text{(corresponding angles of congruent triangles)}[/tex]
[tex]z + 22 = 3z[/tex]
[tex]\text{or,} \ z-3 z= -22[/tex]
[tex]\text{or,} \ -2z = -22[/tex]
[tex]\text{or,} \ z = \bold{11}[/tex]
[tex]\bold{EF=KI} \text{(corresponding angles of congruent triangles)}[/tex]
[tex]5y+13=6y[/tex]
[tex]\bold{y=13}[/tex]
Which operation do you use to simplify a ratio after finding the greatest common factor (GCF)?
division
addition
multiplication
subtraction
Answers
Answer:
hey baby
Step-by-step explanation:
hi thwrw honey i love you lol
The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To simplify a ratio after finding the greatest common factor (GCF), we use division.
We divide both terms of the ratio by the GCF.
This reduces the ratio to its simplest form.
Thus,
The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.
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Mrs. Young has p goats and q cows on his farm. He has 23 fewer cows than goats.
What are the missing values in the table?
PLSSSS QUICK
Answers
Step-by-step explanation:
35:12
40:17
45:22
50:27
55:32
A company produced in the first quarter 6,905 pieces in the second quarter the same company produced 795 pieces more than in the first quarter under these conditions how many pieces did the company produce in the first semester?
Answers
Answer: 14,605 pieces.
Step-by-step explanation:
In the second quarter, the company produced 795 pieces more than in the first quarter.
So, the total pieces produced in the second quarter can be calculated as:
6905 + 795 = 7700
The total pieces produced in the first semester (two quarters) can be calculated as:
6905 + 7700 = 14,605
Therefore, the company produced 14,605 pieces in the first semester.
The number of pieces the company produced in the first semester was 14,605 pieces.
How many?The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.
In the first quarter, the company produced 6,905 pieces, as indicated in the question.
Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:
6,905 + 795 = 7,700 pieces.
To know the company's total production in the first semester, just add the productions of the two quarters:
6,905 + 7,700 = 14,605 pieces
In the inequality, x (< with line underneath) 8, represents the number of books on a shelf.
How do you know if 8 is a possible value of x?
Answers
Answer:
The numbers 8 and lower are possible values of x.
Step-by-step explanation:
The inequality [tex]x\leq 8[/tex] means x is less than or equal to 8. Therefore, 8 is a possible value of x.
Construct a 99% confidence interval of the population proportion using the given information.
x = 75, n = 250
Answers
The 99% confidence interval for the population proportion p is :lower bound= 0.225, upper bound 0.375
What does a confidence interval actually mean?
Your estimate's mean is added to and subtracted from by the estimate's range to create a confidence interval. If you repeat your test, within a specific level of confidence, this is the range of values you anticipate your estimate to fall within.
Given that,
n = 250
x = 75
Point estimate = sample proportion = p = x / n = 75/250=0.3
1 - p =1 - 0.3=0.7
At 99% confidence level the z is ,
α = 1 - 99% = 1 - 0.99 = 0.0
α / 2 = 0.01 / 2 = 0.005
Z /2 = Z0.005 = 2.576 ( Using z table )
Margin of error = E = Zα / 2 * √(( p * (1 - p)) / n)
= 2.576 (√((0.3*0.7) /250 )
E = 0.075
A 99% confidence interval for population proportion p is ,
p - E < p < p + E
0.3 -0.075 < p < 0.3 + 0.075
0.225< p < 0.375
The 99% confidence interval for the population proportion p is :lower bound= 0.225, upper bound 0.375.
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HELP Whats the Answer to this Stand Deviation Question?
Answers
Answer: he would be 2 standard deviations above the
Step-by-step explanation:
for autonomous equations, find the equilibria, sketch a phase portrait, state the stability of the equilibria.
Answers
Understanding the equilibria, sketching a phase portrait, and determining the stability of equilibria for autonomous equations are important tools for analyzing and understanding the behavior of systems over time.
Autonomous equations are differential equations that do not depend explicitly on time. To find the equilibria of an autonomous equation, we set the derivative of the function to zero and solve for the values of the independent variable that satisfy the equation. These values represent points at which the function does not change over time and are known as equilibrium points.
To sketch a phase portrait for an autonomous equation, we plot the slope field of the function and then draw solutions through each equilibrium point. The resulting graph shows the behavior of the function over time and helps us understand how the solutions behave near each equilibrium point.
The stability of an equilibrium point is determined by examining the behavior of nearby solutions. If nearby solutions move toward the equilibrium point over time, the equilibrium point is stable. If nearby solutions move away from the equilibrium point over time, the equilibrium point is unstable. Finally, if the behavior of nearby solutions is inconclusive, further analysis is needed.
Here is the sketch for [tex]dx/dt = x - x^3[/tex]
/ <--- (-∞) x=-1 (+∞) ---> \
/ \
<--0--> x=-1 x=1 0-->
\ /
\ <--- (-∞) x=1 (+∞) ---> /
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Find dz/dt in two ways: by using the Chain Rule, and by first substituting the expressions for x and y to write z as a function of t. Do your answers agree?z= x^2y+xy^2, x = 3t y = t^2
Answers
The derivative of the function z= x^2y+xy^2, x = 3t y = t^2 using the chain rule is given by dz/dt = 36t^3 + 15t^4.
Expressions are equals to,
z= x^2y+xy^2
x = 3t
y = t^2
Using the chain rule calculate dz/dt,
which states that if z is a function of x and y,
And x and y are both functions of t, then,
dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)
Using these expressions, calculate the value of dz/dt using the chain rule,
z= x^2y+xy^2
This implies,
dz/dx = 2xy + y^2
dz/dy = x^2 + 2xy
x = 3t
⇒ dx/dt = 3
y = t^2
⇒ dy/dt = 2t
Substituting these values into the chain rule formula, we get,
dz/dt = (2xy + y^2)(3) + (x^2 + 2xy)(2t)
= [2(3t)(t^2 ) + (t^2)^2 ]3 + [(3t)^2 + 2(3t)(t^2)](2t )
= [ 6t^3 + t^4 ]3 + [ 9t^2 + 6t^3 ]2t
= 18t^3 + 3t^4 + 18t^3 + 12t^4
= 36t^3 + 15t^4
Substituting the given expressions for x and y into z, we get,
z = (3t)^2(t^2) + (3t)(t^2)^2
= 9t^4 + 3t^5
here also,
dz/dt = 36t^3 + 15t^4
Therefore, the value of the function using the chain rule dz/dt is equals to 36t^3 + 15t^4.
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5 Mrs. Newsome bought a piece of fabric 142 centimeters long to make a quilt for her son's bedroom. She bought a piece of fabric 2 meters long for curtains. How could Mrs. Newsome find the total length, in centimeters, of both pieces of fabric? Multiply 2 by 2,000, then add 142. Add 2 and 142, then multiply by 100. Divide 142 by 100, then add 2,000. O Multiply 2 by 100, then add 142. B C
Answers
Answer:
Step-by-step explanation:
To find the total length of both pieces of fabric in centimeters, we need to add the length of the first piece of fabric (142 cm) and the length of the second piece of fabric (2 meters).
However, we need to make sure that the units are consistent before we add the lengths. We can convert the length of the second piece of fabric from meters to centimeters by multiplying by 100. Therefore, the total length in centimeters is:
142 cm + 2 meters * 100 cm/meter = 142 cm + 200 cm = 342 cm
The option that correctly gives the answer is "Multiply 2 by 100, then add 142" (Option C).
