Answer:
a. To find the weight corresponding to the highest 20 percent of coffees, we need to find the z-score that corresponds to the 0.8 cumulative probability.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.8 is 0.8416.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the highest 20 percent of coffees is approximately 448.32 g.
b. To find the weight corresponding to the middle 60 percent of coffees, we need to find the z-scores that correspond to the cumulative probabilities of 0.2 and 0.8.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.2 is -0.8416, and the z-score corresponding to a cumulative probability of 0.8 is 0.8416.
Next, we use the z-score formula to find the weights:
Weight Lower Bound = Mean + (z-score * Standard Deviation)
Weight Lower Bound = 400 + (-0.8416 * 20) = 351.68 g
Weight Upper Bound = Mean + (z-score * Standard Deviation)
Weight Upper Bound = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the middle 60 percent of coffees ranges from approximately 351.68 g to approximately 448.32 g.
c. To find the weight corresponding to the highest 80 percent of coffees, we use the same process as in (a) to find the z-score that corresponds to the cumulative probability of 0.8, which is 0.8416.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the highest 80 percent of coffees is approximately 448.32 g.
d. To find the weight corresponding to the lowest 15 percent of coffees, we need to find the z-score that corresponds to the cumulative probability of 0.15.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.15 is -0.9332.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (-0.9332 * 20) = 346.64 g
So, the weight corresponding to the lowest 15 percent of coffees is approximately 346.64 g.
Step-by-step explanation:
2 Δ Δ Δ Δ Δ
Δ.
57. If t is any real number, which of the following
statements must be true?
A. -t <0
B. -t
C. -t=t
D. ts|-t
E. (-t)2 = -12
58. Let a and h be positive real num
When t is any real number, the true statements will be:
A. -t < 0:
B. -t = 0
E. (-t)^2 = -t^2
How to get the true statementsIf t is any real number, then the following statements are true:
A. -t < 0: This statement is true if t > 0, and false if t <= 0.
B. -t = 0: This statement is true if t = 0, and false if t ≠ 0.
C. -t = t: This statement is false for all real numbers t, since the negative of any non-zero real number is not equal to the original number.
D. t|-t: This statement is false for all real numbers t, since the absolute value of any real number is non-negative.
E. (-t)^2 = -t^2: This statement is true for all real numbers t, since squaring a real number gives a non-negative result. Note that the negative sign in front of the square is distributive and can be moved inside the square.
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3. Explain how "a" affects the graph of a parabola. (f(x) = ax²)
The effect of "a" in the graph of parabola is value from the quadratic function.
How to determine the standard equation of the parabola?In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
y = a(x – h)2 + k or x = a(y – k)2 +h
Where:
(h, k) - The vertex of the parabola.
p - Least distance between the vertex and the focus of the parabola.
Given that;
The equation of parabola is f(x) = ax².
Now, Let's look at the graph of f(x) = x^2 + 3x + 1, which is below. The b-value in this equation is 3.
We see that our graph is indeed a parabola. Our parabola is curving up. The x-value of the vertex, the tip of the parabola, is -3 / 2 or -1.5. We can actually calculate this x-value by evaluating the expression -b / 2a, where a and b are the values from the quadratic function.
Therefore, the role of a in parabola is stated.
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{y=1/2x−4
{ y=−2x+1
What is the y-
coordinate for the solution to the system of equations?
The y-coordinate for the solution to the system of equations is y = -3.
What is substitution method?The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.
Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be chosen over other algebraic methods for straightforward equations that don't require complicated calculations.
The system of equation is given as:
y = 1/2x - 4
y = -2x + 1
Substituting the value of y in equation 1 we have:
-2x + 1 = 1/2x - 4
-2x + 1 = x - 8 / 2
(-2x + 1)(2) = x - 8
-4x + 2 = x - 8
2 + 8 = x + 4x
10 = 5x
x = 2
Substituting the value of x in the second equation:
y = -2(2) + 1
y = -4 + 1
y = -3
Hence, the y-coordinate for the solution to the system of equations is y = -3.
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A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 22 mg every six hours. This antihistamine also comes in a liquid form with a concentration of 12.3 mg/ 6mL. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take in a week?
On solving the provided question, we can say that equation is 532/13.5 = 39.4 doses.
What exactly is an equation?A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2.
the equation is the week * 7 (weekdays) * 24 (hours/day) * 19/6 (MILIGRAMS/HOURS)
532 mg per week (532/13.5 = 39.4 doses)
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Suppose you invest $500 into an account earning simple interest. The APR is 2% and you invest it for 5 years. Choose two answers: How much would your investment be worth at the end? What equation should you use to calculate this?
1a. $2500.10
2a. $550
3a. $1000
4a. $2550
5a. $5500
1b. A = 500 ( 1 + 2(5))
2b. A = 500 (1 + 0.2(5))
3b. A = 500 (1 + 0.02(5))
Answer:
a=1000.10
Step-by-step explanation:
pls help me i’ll give you brainlist!
For the linear equation 3x + y = 9 we have:
x-intercept (3, 0)y-intercept (0, 9).How to find the x and y-intercepts?Here we want to find the two intercepts for the linear equation:
3x + y = 9
First, the x-intercept is the point that we get when we evaluate on y = 0.
3x + 0 = 9
3x = 9
x = 9/3
x = 3
Then we get: x-intercept (3, 0)
And for the y-intercept we need to evaluate in x = 0.
3*0 + y = 9
y = 9
Then the y-intercept is (0, 9).
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A quantity with an initial value of 3600 decays continuously at a rate of 80% per year.
What is the value of the quantity after 0.2 decades, to the nearest hundredth?
Answer:
Step-by-step explanation:
The decay rate of 80% per year means that after each year, the value of the quantity decreases by 80/100 * 3600 = 2880.
To find the value of the quantity after 0.2 decades, we need to multiply the number of years by 10, since a decade is equal to 10 years. In this case, 0.2 decades is equal to 0.2 * 10 = 2 years.
The value of the quantity after 2 years can be found using the formula:
3600 * (1 - 0.8)^2
Plugging in the values, we get:
3600 * (1 - 0.8)^2 = 3600 * (0.2)^2 = 3600 * 0.04 = 144
So, the value of the quantity after 0.2 decades, to the nearest hundredth, is 144.
Answer: 726.83
Step-by-step explanation:
What is the y intersecpt of y=-4x-5
Answer:
-5
Step-by-step explanation:
The equation is in slope intercept form,
y = mx+b
where m is the slope and b is the y intercept.
y = -4x-5
The slope is -4 and the y intercept is -5.
Need help with how to do this one...
Find the domain of
x ¹ -2
x + 1
A. x ≠ -1
B. x ≠ 1
C. x ≠ -2
D. x ≠ -1, 1
E. x ≠ 2
F. x ≠ 0
Alyssa bought a pair of shoes online for $53. She used a coupon code to get a 20% discount. The website also applied a 20% processing fee to the price after the discount. How much was the discount , in dollars and cents?
Answer:
The original price of the shoes was $53.
The discount percentage was 20%.
The discount amount was 53 * 0.2 = 10.6.
The sale price after the discount was 53 - 10.6 = 42.4.
The processing fee percentage was 20%.
The processing fee amount was 42.4 * 0.2 = 8.48.
The final price after the processing fee was 42.4 + 8.48 = 50.88.
Therefore, the discount was $10.60, and the final price was $50.88.
Step-by-step explanation:
1 The difference between the simple interest and compound interest on a sum put out for 2 years at 5% was 6.90 .find the sum
so we're assuming the compounding period is annual, so hmmm let's call our sum "P", how much is it at simple and compound interest anyway?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P[1+(0.05)(2)] \implies \boxed{A = 1.10P} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annual, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P\left(1+\frac{0.05}{1}\right)^{1\cdot 2} \implies \boxed{A = 1.1025P}[/tex]
now, the larger one will be the compound interest one, so, let's subtract the simple interest one from it to get 6.90
[tex]1.1025P~~ - ~~1.10P~~ = ~~6.90\implies 0.0025P=6.90 \\\\\\ P=\cfrac{6.90}{0.0025}\implies {\Large \begin{array}{llll} P=2760 \end{array}}[/tex]
Kelsey orders several snow globes that each come in a cubic box that measures 14
foot on each side. Her order arrives in the large box shown below. The large box is completely filled with snow globes.
The number of snow globe in box is x³/ 2744.
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given:
length of one small cube = 14 foot.
Volume of small cube = l³
= 2744 ft³
let the edge of one large cube be x.
So, volume of large cube= x ft³
Thus, number of globes in larges box
= Volume of large box/ Volume of small box
= x³/ 2744
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the function of G takes a student's first name for its input and gives the number of letters in the first name for its output
Describe the meaning of G(jada)=4
Find the value of G(Diego).
Answer:
Step-by-step explanation:
The meaning of the function notations are
G(Jada) = 4 means that the first name Jada has four letters
C(11-15)= chemistry means that the Monday class for 11-15 is chemistry
How to interpret the function notations?
The meaning of the function G
From the question, we have the following parameters that can be used in our computation:
Function G gives the number of letters in the first name for its output.
Next, we have
G(Jada) = 4
Using the meaning of the function, we have
G(Jada) = 4 means that the first name Jada has four letters
The meaning of the function C
From the question, we have the following parameters that can be used in our computation:
Function C gives a student's Monday class for its output.
Next, we have
C(11-15)= chemistry
Using the meaning of the function, we have
C(11-15)= chemistry means that the Monday class for 11-15 is chemistry
50x2\10 es para orita urge
Answer:
= 10.
Step-by-step explanation:
=
[tex]50 \times \frac{2}{10} \\ = 5 \times 2 \\ = 10.[/tex]
The answer becomes for the given expression is: 10.
What is multiplication?Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in mathematics refers to the continual addition of sets of the same size. One of the fundamental mathematical processes is multiplication. The result of multiplying two or more integers together is known as the product. The first number used in a multiplication operation between two numbers is referred to as the multiplicand.
Given that,
= 50 × (2/10)
= 50 × (1/5)
= 10
Thus, for the given expression the answer becomes: 10
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write an absolute value inequality for each length x with the given tolerance
1. a length of 4.2 cm with a tolerance of 0.01 cm
2. a length of 3.5 cm with a tolerance of 0.2 cm
show work pls
The absolute value inequalities for the different lengths are
1) 4.19 ≤ x ≤ 4.21
2) 3.3 ≤ x ≤ 3.7
What is an absolute value inequality?
The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|.
An expression using absolute functions and inequality signs is known as an absolute value inequality. One example of an absolute value inequality with a larger than symbol is the statement |x + 3| > 1.
1) length x = 4.2 cm with a tolerance of 0.01 cm
Absolute value inequality is:
|x - 4.2| ≤ 0.01
This can be written as:
x - 4.2 ≤ 0.01x ≤ 4.21
x - 4.2 ≥ - 0.01x ≥ 4.19
2) length x = 3.5 cm with a tolerance of 0.2 cm
Absolute value inequality is:
|x - 3.5| ≤ 0.2
This can be written as:
x - 3.5 ≤ 0.2x ≤ 3.7
x - 3.5 ≥ - 0.2x ≥ 3.3
Therefore the absolute value inequalities for the different lengths are
1) 4.19 ≤ x ≤ 4.21
2) 3.3 ≤ x ≤ 3.7
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Mike is working on solving the exponential equation 37^x= 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation
Hint Use the change of base formula: logby=
log y over log b
Answer:
should" (and any subsequent words) was ignored because we limit queries to 32 words.
Castroville requires all dogs to be registered with the city and keeps records of the distribution of different breeds. Golden Retrievers 45% Boxers 55% Dog ownership If 60 dogs are registered, how many more of them are Boxers than Golden Retrievers?
If 60 dogs are registered in Castroville, we can find the number of Golden Retrievers and Boxers by using the given percentages.
Number of Golden Retrievers = 0.45 x 60 = 27
Number of Boxers = 0.55 x 60 = 33
To find how many more Boxers there are than Golden Retrievers, we can subtract the number of Golden Retrievers from the number of Boxers:
Boxers - Golden Retrievers = 33 - 27 = 6.
Therefore, there are 6 more Boxers than Golden Retrievers in the group of 60 registered dogs in Castroville.
What is the total percentage of all other dog breeds among registered dogs in Castroville?The given information only provides the percentages of Golden Retrievers and Boxers among registered dogs in Castroville, so we don't have enough information to directly calculate the percentage of all other dog breeds. However, we know that the total percentage of all dog breeds must add up to 100%. Since Golden Retrievers and Boxers make up 45% and 55% of the registered dogs, respectively, the percentage of all other dog breeds must be 100% - 45% - 55% = 0%. This means that there are no other registered dog breeds in Castroville, and all registered dogs belong to either the Golden Retriever or Boxer breed.
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I need to know why the medians differ relative to the data set and the best measure of center?
Explanation:
In this case the median value is more representative of the 'center' of the population. The median is a better measure when the data set is skewed, has fat tails as compared to a normal didtribution, or has outliers. Otherwise you should use the arithmetic mean.
Find the value of x for the following
Answer: x = 10
Step-by-step explanation:
4x+89=129
(2 parallel straight lines have congruent angles)
then solve for x.
Step 1: Subtract 89 from both sides of the equation.
4x = 40
(We want to isolate the variable x on one side of the equation. To do this, we need to get rid of the number 89 that is currently on the right side of the equation. To do this, we subtract 89 from both sides of the equation.)
Step 2: Divide both sides of the equation by 4.
x = 10
(To isolate the variable x further, we need to get rid of the coefficient 4 that is currently in front of x. To do this, we divide both sides of the equation by 4.)
A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.
Answer: The momentum of the truck before the collision is given by the formula:
p_i = m_i * v_i, where m_i is the mass of the object and v_i is its velocity.
The momentum of the truck before the collision is:
p_i (truck) = 3000 kg * 10 m/s = 30000 kg m/s
The momentum of the car before the collision is:
p_i (car) = 1000 kg * 0 m/s = 0 kg m/s
The total initial momentum of the system is the sum of the initial momenta of the truck and car:
p_i (total) = p_i (truck) + p_i (car) = 30000 kg m/s + 0 kg m/s = 30000 kg m/s
After the collision, the final momentum of the system is the sum of the final momenta of the truck and car:
p_f (total) = p_f (truck) + p_f (car)
Let's call the velocity of the truck after the collision v_f (truck). The final momentum of the truck is:
p_f (truck) = 3000 kg * v_f (truck)
The final momentum of the car is:
p_f (car) = 1000 kg * 15 m/s = 15000 kg m/s
Using the conservation of momentum, we can write an equation:
p_f (total) = p_i (total)
30000 kg m/s = p_f (truck) + p_f (car)
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
v_f (truck) = (30000 kg m/s - 15000 kg m/s) / 3000 kg = 7.5 m/s
So, the velocity of the truck immediately after the collision is 7.5 m/s.
Step-by-step explanation:
In one lottery game, contestants pick six numbers from 1 through 23 and have to match all six for the big prize (in any order).
You'll get twice your money back if you match four out of six numbers. If you buy five tickets, what's the probability of matching four out of six numbers?
If you buy five tickets, the probability of matching four out of six numbers is…?
(Enter your answer as a fraction in lowest terms.)
The answer is 0.360, or approximately 36/100.
What is probability?
Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.
The probability of matching four out of six numbers in a single ticket can be calculated as follows:
There are C(23, 6) = 8,145 possible combinations of six numbers from 1 through 23.
There are C(23, 4) = 1,531 possible combinations of four numbers from 1 through 23.
So, the probability of matching four out of six numbers in a single ticket is 1,531/8,145 = 19/102.
If you buy five tickets, the probability of matching four out of six numbers in at least one of them is 1 - (1 - 19/102)⁵ , which can be calculated as:
1 - (1 - 19/102)⁵ = 1 - 0.848⁵ = 1 - 0.640 = 0.360
Therefore, The answer is 0.360, or approximately 36/100.
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Whats the answer to these please provide steps.
The trigonometric identities can be proved as follows;
32. Using the substitution, tan(x) = sin(x)/cos(x), and cot(x) = cos(x)/sin(x), we get;
cot(x) - tan(x) = (1 - 2·sin²(x))/(sin(x)·cos(x)) = sec(x)·(csc(x) - 2·sin(x))
36. tan(θ)/(1 + sec(θ)) = sin(θ)/(1 + cos(θ)) = (1 - cos(θ))/(sin(θ)) = -cot(θ) + csc(θ)
What are trigonometric identities?Trigonometric identities are equations involving trigonometric functions which are valid for the values of the input variable.
as follows;
cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))
The left hand side of the equation can be expressed using sin(x) and cos(x) as follows;
cot(x) = cos(x)/sin(x)
tan(x) = sin(x)/cos(x)
Therefore;
cot(x) - tan(x) = cos(x)/sin(x) - sin(x)/cos(x) = (cos²(x) - sin²(x))/(sin(x)·cos(x))
cos²(x) = 1 - sin²(x), therefore
(cos²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - sin²(x) - sin²(x))/(sin(x)·cos(x))
(1 - sin²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - 2·sin²(x))/(sin(x)·cos(x))
(1 - 2·sin²(x))/(sin(x)·cos(x)) = csc(x)·sec(x)·(1 - 2·sin²(x))
csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))
Therefore;
cot(x) - tan(x) = csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))
cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))36. tan(θ)/(1 + sec(θ)) = -cot(θ) + csc(θ)
The left hand side can be manipulated as follows;
tan(θ) = sin(θ)/cos(θ)
sec(θ) = 1/cos(θ)
Therefore; tan(θ)/(1 + sec(θ)) = (sin(θ)/cos(θ))/(1 + (1/cos(θ)))
(sin(θ)/cos(θ))/(1 + (1/cos(θ))) = (sin(θ)/cos(θ))/((cos(θ) + 1)/(cos(θ)))
((sin(θ)/cos(θ))×cos(θ))/((cos(θ) + 1)/(cos(θ)) × cos(θ))) = sin(θ)/(cos(θ) + 1)
tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1)
sin(θ)/(cos(θ) + 1) = sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ)))
sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ))) = ((sin(θ)·(1 - cos(θ))/(1 - cos²(θ)))
((sin(θ)·(1 - cos(θ))/(1 - cos²(θ))) = ((sin(θ)·(1 - cos(θ))/(sin²(θ)) = (1 - cos(θ))/(sin(θ))
sin(θ)/(cos(θ) + 1) = (1 - cos(θ))/(sin(θ)) = csc(θ) - cot(θ) = -cot(θ) + csc(θ)
tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1) = -cot(θ) + csc(θ)
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Determine the area of this composite figure below
Answer:
The area is 510 in^2.
Step-by-step explanation:
You need to find two areas. The area of the rectangle and then the area of the triangle above.
The formula for a rectangle's area is base x height. The base is 20 inches, and the height is 15 inches as shown on the side. So, you multiply 20 x 15, and the product is 300.
The formula for a triangle's height is 1/2(base x height). The 3 ft on the side is equal to 36 inches. To find the height of the triangle alone, you take the 36 inches and subtract by 15 inches, resulting in a difference of 21 inches. The base of the triangle is 20 inches, so multiply 20 x 21 = 420. Then multiply 420 by 1/2 (or divide by 2) and you get 210.
Now that we have the areas of both shapes, 210 + 300 = 510.
The area of the composite figure is 510in².
Step-by-step explanation:1. Identify the different shapes that form this composite figure.Check attached image 1.
2. Identify the dimensions of each shape.a) For the rectangle, we have that the base is 20 inches, and that the height is 15 inches.
b) For the triangle, we see that the base is also 20 inches long, and the height must be the difference between the height of the rectangle and the total height of the composite figure.
3. Convert all the units to a single unit.First, convert the 3 feet to inches, because we need to have the same unit in order to make the calculations.
We know that 12 inches is 1 feet, therefore, to covert 3 feet to inches we do the following operation:
[tex]3feet*\frac{12inches}{1feet}[/tex]
The feet unit cancel out and the 3 is multiplied by 12, leaving us with the following result:
[tex]36inches[/tex]
4. Find the height of the triangle.Check attached image 2.
So the height of the triangle must given by the following expression:
[tex]36in-15in=21in[/tex]
5. Find the individual area of each shape.a) For the rectangle:
[tex]A=b*h[/tex]; where "b" is the length of the base and "h" is the height.
[tex]A=(20in)(15in)=300in^{2}.[/tex]
b) For the triangle:
[tex]A=\frac{b*h}{2} =\frac{(20in)(21in)}{2} =210in^{2} .[/tex]
6. Find the total area.So if the figured is formed by a triangle and a rectangle, the sum of the area of the 2 shaped equals the area of the composite figure. Let's add up the areas and calculate:
[tex]300in^{2} +210in^{2} =510in^{2} .[/tex]
7. Conclude.The area of the composite figure is 510in².
A positive integer is 3 less than another. If the sum of the reciprocal of the smaller and
twice the reciprocal of the larger is 9/10 then find the two integer
Answer:
Step-by-step explanation:
Let the smaller integer be x, then the larger integer is x + 3.
The sum of the reciprocal of the smaller and twice the reciprocal of the larger is 9/10:
1/x + 2/(x + 3) = 9/10
Expanding both sides:
10/x + 20/(x + 3) = 90/10
Combining like terms on the left side:
(10 + 20)/(x(x + 3)) = 90/10
30/(x(x + 3)) = 9/10
Cross multiplying both sides:
30 * 10 = 9 * (x(x + 3))
300 = 9x(x + 3)
Expanding the right side:
300 = 9x^2 + 27x
Subtracting 27x from both sides:
273 = 9x^2 + 27x - 27x
273 = 9x^2
Taking the square root of both sides:
√273 = √(9x^2)
√273 = 3x
Dividing both sides by 3:
√273/3 = x
The smaller integer is √273/3 and the larger integer is √273/3 + 3.
The grass in the photo above can be found in the __________ ecosystem.
The tropical savanna environment is home to the grass in the picture above.
What is Southeast Asia's ecosystem like?The two primary types of forests are deciduous or monsoon rainforests and tropical evergreen rainforests, which have leaves all year round (these loose their leaves during the dry season). Human activity causes deforestation because it endangers the local ecosystem's ability to sustain life.
What is the ecosystem of the rainforest?Rainforests are a type of forest habitat that have a dense canopy, great species variety, and high rainfall rates. The Amazon is made up of a variety of ecosystems and plant life, including savannas, deciduous woods, seasonal forests, and rainforests.
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Find the perimeter of the figure.
Answer:
≈29.93 [units].
Step-by-step explanation:
according to the attachment the required perimeter is:
P=2*6+4.25*2+3.1415*3=12+8.5+9.4245=29.9245 [units].
etry E.7 Find the distance between a point and a line GWC
Q Search
Line & has equation y=x+1. Find the distance between t and the point V(-5-6).
Round your answer to the nearest tenth.
Submit
Work it
The distance between the line and the point is 2 units
How do we calculate the distance between a line and a point?A perpendicular line will give the shortest distance between a point and a line.
From the equation of the line y = x+1. Therefore the slope is 1
using the equation (y-y1) = m(x-x1)
equation of the line joining the point and the line
= y-(-6) = -1(x - (-5)
= y+6 = -x-5
y = -x-11
x-1 = -x-11
2x = -10
x = -5
y = -5+1
y = -4
(x,y) = (-5,-4)
d = √ -5-(-5)²+ -4-(-6)²
d = √ 0+ 4
d = √4
d = 2 unit
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Subtract 5m + 11 and m + 8
The expression (m + 8) - (5m + 11) simplifies to -4m - 3.
How to subtract the expresisonsFrom the question, we have the following parameters that can be used in our computation:
Subtract 5m + 11 and m + 8
To subtract (5m + 11) from (m + 8), we need to distribute the negative sign to each term inside the first set of parentheses:
(m + 8) - (5m + 11)
Open the brackets
= m + 8 - 5m - 11
Evaluate the like terms
= -4m - 3
Hence, (m + 8) - (5m + 11) simplifies to -4m - 3.
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Find the value of x that makes AABC~ADEF.
B
8
12
光
A x+7 C
X =
D
24
E
48
3(x+3)
F
Answer:e
Step-by-step explanation:t
3. The number of pages
in my book is less
than 96 and greater
than 90.
Who could I be?
2
I have 3 letters in my
'name.
Who am I?
4.
The number of pages in the book is given by the inequality 90 < A < 96 , where A is the number of pages
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the number of pages in the book be A
And , it is more than 90 and less than 96
So , the value of A is { 91 , 92 , 93 , 94 , 95 }
On simplifying , we get
90 < A < 96 , where A is the number of pages
Hence , the inequality is 90 < A < 96
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