Answers
The equation of the circle graphed is (x + 4)^2 + (y + 5)^2 = 16
Determining the equation of the circle graphedFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (-4, -5)
Radius, r = 4 units
The equation of the circle graphed is represented as
(x - a)^2 + (y - b)^2 = r^2
So, we have
(x + 4)^2 + (y + 5)^2 = 4^2
Evaluate
(x + 4)^2 + (y + 5)^2 = 16
Hence, the equation is (x + 4)^2 + (y + 5)^2 = 16
Read more about circles at
https://brainly.com/question/24810873
#SPJ1
Related Questions
Use properties of exponents to verify that 2s − 1 and _1
2 (2)
s
are equivalent.
Answers
The properties of the exponents are solved and the expression is given by the relation ( 2s )⁻¹ = 1 / 2s
Given data ,
Let the expression be represented as A
Now , the value of A is
( 2s )⁻¹ = 1 / 2s
From the laws of exponents , we get
m⁻ᵃ = ( 1 / mᵃ )
So , on simplifying , we get
( 2s )⁻¹ = 1/ ( 2s )
On further simplification , we get
1/ ( 2s ) = ( 2s )⁻¹
Hence , the expression is ( 2s )⁻¹ = 1/ ( 2s )
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ1
The complete question is attached below :
Use properties of exponents to verify that ( 2s )⁻¹ = 1/ ( 2s ) are equivalent.
In a class of 50 students, they had a chance to read novel,comics and textbook 21 read novel,24 read comics and 18 read textbook 3 read only novel 9 read only comics and 2 read only textbook 5 read all the 3. illustrate your information on a venn diagram. use your diagram to find the number of students who read a. comics and novel only b. textbook and novel only c. none of the 3
Answers
The number of students are as follows:
novel and textbook is 7textbook and comics is 3comic and novel is 4What is the number of students who read comics and novels only?To find the number of students who read comics and novels only:
there are a total number of students 5021 students read novel24 students read comics18 students read textbook 3 read novel only9 read comic only2 read textbook only5 read all 3 booksLet novel and textbook = x
Let textbook and comics = y
Let comic and novel = z
y + x = 11 --- (1)
y + z = 10 --- (2)
x + z = 13 --- (3)
Make y subject of the formula in (2)
y = 10 - z
substitute for y in (1)
10 - z + x = 11 --- (4)
solve (3) and (4) simultaneously by addition
10 - z + x + x + z = 11 + 13
2x = 24 - 10
x = 7
y = 11 - 7
y = 3
z = 13 - 7
z = 4
Learn more about Venn diagrams at: https://brainly.com/question/2099071
#SPJ1
Use the long division method to find the result when 4x^3+15x^2+17x+6 is divide by 4x+3
Answers
The result when 4x³ + 15x² + 17x + 6 is divide by 4x + 3 using long dividion method will be x² + 3x + 2.
Given that:
Dividend, 4x³ + 15x² + 17x + 6
Divisor, 4x + 3
The division of the polynomial is given below.
4x + 3 ) 4x³ + 15x² + 17x + 6 ( x² + 3x + 2
- (4x³ + 3x²)
12x² + 17x
- (12x² + 9x)
8x + 6
- (8x + 6)
0 0
More about the polynomial link is given below.
https://brainly.com/question/17822016
#SPJ1
PLEASE HELP!!
What is the area of the circle? Approximate using pi equals 22 over 7. a circle with radius labeled 42 yards 22,176 square yards 5,544 square yards 264 square yards 132 square yards
Answers
The calculated value of the area of the circle is 5544 square yards
What is the area of the given circle?From the question, we have the following parameters that can be used in our computation:
Radius, r = 42
Using the above as a guide, we have the following:
Area = π * r^2
Substitute the known values in the above equation, so, we have the following representation
Area = 22/7 * 42^2
Evaluate the products and exponents
Area = 5544
Approximate
Area = 5544
Hence, the value of the area is 5544 square yards
Read mroe about cricle at
brainly.com/question/3883184
#SPJ1
Need help, pls!!!
ty!
Answers
The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.
The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.
The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.
The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).
Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.
To learn more about function here:
https://brainly.com/question/12431044
#SPJ1
HELP ASAP! What is the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the triangle?
Answers
Answer:
Step-by-step explanation:
To answer this question, we need to know the dimensions of the rectangle and the triangle. Assuming that the triangle is right-angled and has one side coinciding with one side of the rectangle, we can use the formula for the area of a triangle: \ ( \frac {1} {2} \) × base × height1. The base and height of the triangle are the same as the length and width of the rectangle. The area of the rectangle is length × width. The probability that a point chosen randomly inside the rectangle is in the triangle is then the ratio of the area of the triangle to that of the rectangle, which is: \ ( \frac {\frac {1} {2} \times length \times width} {length \times width} \) = \ ( \frac {1} {2} \). So, the probability is 0.5 or 50% to the nearest hundredth2.
Answer: C .08
Step-by-step explanation:
Probability is the part out of the whole. you first need to find the part, which is the triangle
In other words find out how much of the triangle is taking up the rectangle, which is done through area
A(triangle)=1/2 b h where b=6 h=9
A(triangle)=1/2 (6)(9) = 27
A(rectangle)= Lw where L=24 h=15
A(rectangle)= (24)(15) = 360
P(triangle in rectangle)= 27/360
=.075 rounded = .08
A cone has a diameter of 16 cm and a height of 35 cm. What is its volume?
Answers
Answer: if with 3.14 v= 37512.5333
if with pi v= 37531.56
Step-by-step explanation:
the formula is 1/3hπr^2
r= 2d so radius is 32
plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)
Ronald is walking at a rate of 3 miles per hour. If he walks for 2 hours and then runs at a rate of 6 miles per hour for another 1 hour, how far did Ronald travel in total?
Answers
Answer:
12Step-by-step explanation:
Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.
Someone rolls a die 180 times.
Given: 1. She can expect to see 30 aces in 180 rolls (aces means one spot) and 2. The give or take number for this result is 5 (standard deviation).
Question: What are the chances she gets between 20 and 40 aces? (inclusive of the endpoints 20 and 40)
Answers
The chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.
How to solve for the probabilityWe can first standardize the values of 20 and 40 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize (20 or 40), μ is the expected value (30), and σ is the standard deviation (5).
For x = 20, we get:
z = (20 - 30) / 5 = -2
For x = 40, we get:
z = (40 - 30) / 5 = 2
probability of getting a z-score between -2 and 2.
Using a standard normal distribution table or calculator, we find that the probability of getting a z-score between -2 and 2 is approximately 0.9544.
Therefore, the chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.
Read more on probability here:https://brainly.com/question/24756209
#SPJ1
Determine the equation of the circle with center (0,−1) containing the point ( − 8 , 10 )
Answers
To find the equation of the circle with center (0, −1) that contains the point (−8, 10), we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Since the center of the circle is given as (0, −1), we have:
(x - 0)^2 + (y + 1)^2 = r^2
We still need to find the radius, r. We know that the circle passes through the point (−8, 10), so we can substitute these values for x and y and solve for r:
(-8 - 0)^2 + (10 + 1)^2 = r^2
64 + 121 = r^2
r^2 = 185
So the equation of the circle is:
x^2 + (y + 1)^2 = 185
Alternatively, we can expand the equation to get it in standard form:
x^2 + y^2 + 2y + 1 = 185
x^2 + y^2 + 2y - 184 = 0
So another form of the equation is:
x^2 + (y + 1)^2 = 185
Based on the graph, is there an association between age and preferred mode of transportation?
O There is an association because the distribution of preferred transportation differs among the age groups.
O There is an association because the distribution of preferred transportation is the same among the age groups.
O There is no association because the distribution of preferred transportation differs among the age groups.
There is no association because the distribution of preferred transportation is the same among the age groups.
Answers
Based on the graph, there is no association because the distribution of preferred transportation differs among the age groups. The Option C is correct.
What influences difference in preferred transportation among all age group?The significant factors is accessibility and convenience because younger individuals may be more likely to use public transportation such as buses or trains because it is more affordable and convenient than owning a car.
But the older individuals may prefer to use personal cars because it provides more flexibility and control over their transportation needs. Another factor that influences is the cost of ownership, maintenance, and fuel.
Read more about graph association
brainly.com/question/26598523
#SPJ1
Using the integers −9 to 9 at most one time each, place a digit in each box ( ___ , ____) and. ( ___ , ____) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3)
Answers
Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).
To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).
In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:
(x₁ + x₂)/2 = 1
(y₁ + y₂)/2 = 3
We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:
(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2
(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6
Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:
x₁ + (2-x₁) = 2 => x₁ = 1
y₁ + (6-y₁) = 6 => y₁ = 3
So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.
To learn more about midpoint click on,
https://brainly.com/question/12885634
#SPJ1
La base de un rectangulo mide el doble de su altura. Cuales son sus dimensiones Si el perimetro mide 144 cm ?
Answers
Answer:
Las dimensiones del rectángulo son:
altura = 24 cm
base = 48 cm
Step-by-step explanation:
Consideración:
La formula del perímetro de un rectángulo es:
p = 2(altura+base)
Planteamiento:
144 = 2(a+b)
b = 2a
a = longitud de la base del rectángulo
b = longitud de la altura del rectángulo
de la primer ecuación del planteamiento:
144/2 = a+b
72 = a+b
b = 72-a
igualando este último valor con el de la segunda ecuación del planteamiento:
2a = 72 - a
2a + a = 72
3a = 72
a = 72/3
a = 24 cm
b = 2a
b = 2*24
b = 48 cm
Comprobación:
144 = 2(24+48)
144 = 2*72
what is debit and credit of this transactions? On December 1, NNC began an electro repair shop,Samson Quality Automotive. The following transactions occurred during December Dec. 1 Samson contributed birr 55,000 cash to the business in exchange for shares of common stock. 1 Purchased birr 9,000 of equipment paying cash. 1 Paid birr 1,500 for a five-month 9 Paid birr 16,000 cash to purchase land to be used in operations. insurance policy starting on December 1. 10 Purchased office supplies on account, birr 2,000. 19 Borrowed birr 12,000 from the bank for business use. Samson signed a notes payable to the bank in the name of the corporation. The note is due in five years. 22 Paid birr 1,700 for advertising expenses. 26 Paid birr 300 on account. 28 The business received a bill for utilities to be paid in January, birr 180. 31 Revenues earned during the month included birr 14,000 cash and birr 2,600 on account. 31 Paid employees' salaries birr 3,800 and building rent birr 1,300. Record as a compound entry. 31 The business received birr 1,400 for auto screening services to be performed next month.
Answers
Journal entries are a record of financial transactions in chronological order, showing the accounts and amounts debited and credited for each transaction. Below is the journal entries of the transactions:
Constitutes the journal entries :-
Below are the debit and credit entries for each transaction:
Dec. 1:
Debit: Cash (55,000)
Credit: Common Stock (55,000)
Debit: Equipment (9,000)
Credit: Cash (9,000)
Debit: Prepaid Insurance (1,500)
Credit: Cash (1,500)
Dec. 9:
Debit: Land (16,000)
Credit: Cash (16,000)
Dec. 10:
Debit: Office Supplies (2,000)
Credit: Accounts Payable (2,000)
Dec. 19:
Debit: Cash (12,000)
Credit: Notes Payable (12,000)
Dec. 22:
Debit: Advertising Expense (1,700)
Credit: Cash (1,700)
Dec. 26:
Debit: Accounts Payable (300)
Credit: Cash (300)
Dec. 28:
Debit: Utilities Expense (180)
Credit: Accounts Payable (180)
Dec. 31:
Debit: Cash (16,600)
Debit: Accounts Receivable (2,600)
Credit: Service Revenue (17,600)
Debit: Salary Expense (3,800)
Debit: Rent Expense (1,300)
Credit: Cash (5,100)
Debit: Unearned Revenue (1,400)
Credit: Cash (1,400)
Debit: Cash Dividends (4,000)
Credit: Cash (4,000)
learn more about journal entries: brainly.com/question/14279491
#SPJ1
I need help with questions 2-6 and I want to make sure I got question one right
Answers
graphing using calculator. what is the solution to this problem.
Answers
The solutions to the function y = -x^2 - 8x + 8 are (-8.9, 0) and (0.9, 0)
What is the solution to this functionFrom the question, we have the following parameters that can be used in our computation:
y = -x^2 - 8x + 8
To solve using a graphing calculator, we enter the equation in a graph and write out the solution
Having said that we have
When y = -x^2 - 8x + 8 is plotted, the soluton is (-8.9, 0) and (0.9, 0)
Read more about quadratic functions at
https://brainly.com/question/25841119
#SPJ1
simplify(-2+8i)(-2+6i)
Answers
The product between the complex numbers gives:
(-2 + 8i)*(-2 + 6i) = -44 - 28i
How to simplify the expression?Here we have the product of two complex numbers.
It is (-2 + 8i)*(-2 + 6i)
Expanding that we will get:
(-2 + 8i)*(-2 + 6i) = (-2)*(-2) + (-2)*(6i) + (-2)*(8i) + (8i)*(6i)
Remember that i² = -1, then we will get:
(-2)*(-2) + (-2)*(6i) + (-2)*(8i) + (8i)*(6i) = 4 - 12i - 16i - 48
= -44 - 28i
Then the expression simplified is:
(-2 + 8i)*(-2 + 6i) = -44 - 28i
Learn more about complex numbers at
https://brainly.com/question/10662770
#SPJ1
WXYZ is a parallelogram. If ZX = 104 and ZU = 11c-3, find the value of c.
Answers
The value of c for the parallelogram WXYZ is 5
What is Parallelogram?Parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary and the opposite sides need to be parallel.
How to determine this
When WXYZ is a Parallelogram
ZX = 104
ZU = 11-2c
By using the law of parallelogram
ZU = UX
Therefore, ZX = ZU + UX
Where ZU = UX
So, 104 = 11c- 23 + (11c -3)
104 = 11c - 3 + 11c - 3
104 = 11c + 11c - 3 - 3
104 = 22c - 6
Collect like terms
104 + 6 = 22c
110 = 22c
Divides through by 22
110/22 = 22c/22
5 = c
Therefore, the value of c = 5
Read more about Parallelogram
https://brainly.com/question/26624522
#SPJ1
attractiveness vaties inversely with the wiggles. At 300 wiggles the attractiveness is 10. What would the attractiveness be at 150 wiggles
Answers
Answer:
5
Step-by-step explanation:
300÷2=150 ⇒300 wiggles=10 wiggles⇒ 10÷2=5
A study of patients with insulin-dependent diabetes was conducted to investigate the
effects of cigarette smoking on renal and retinal complications. Before examining the
results of the study, you wish to compare the baseline measures of systolic blood pressure across four different subgroups: nonsmokers, current smokers, exsmokers, and tobacco chewers. A sample is selected from each subgroup; the relevant data are provided below [217]. Sample means and standard deviations are expressed in millimeters of mercury (mm Hg). Assume that systolic blood pressure is normally distributed.
(a) Calculate the estimate of the within-groups variance for the four populations.
(b) Calculate the estimate of the between-groups variance.
(c) Calculate the test statistic to evaluate the null hypothesis that the mean systolic blood
pressures of the four groups are identical.
(d) What is the probability distribution of the test statistic?
(e) If you are conducting the test at the 0.05 level of significance, do you reject or fail to reject the null hypothesis?
(f) What do you conclude?
Answers
The within-group sum of squares is 58250.44
The degrees of freedom are given as 355
The estimate of the within-groups variance is 164.0657
What is Variance?Variance, as a statistical measure, evaluates the level of variability or dispersion contained in a dataset by inspecting how distant each value in a set is from the mean of that same set.
If there is a higher variance, it signals that data points are more widely distributed and further removed from the mean, whereas if there is a lower variance, one can assume that they are primarily clustered more closely around the mean.
To obtain the variance value, one must determine an average signal-to-noise ratio for each squared difference derived from every respective value taken away from the arithmetic mean. It is no exaggeration to say that variance is progressively employed across diverse subject areas including finance, engineering, and science.
Read more about variance here:
https://brainly.com/question/9304306
#SPJ1
13x−6y=22
x=y+6
Please help first come first surve
Answers
Answer:
The answer is
x= -2
y= -8
Step-by-step explanation:
x=y+6
substitute into equation 1
13(y+6)-6y=22
13y+78-6y=22
13y-6y=22-78
7y=-56
divide both sides by 7
7y/7= -56/7
y= -8
x=y+6
x= -8+6
x= -2
In an ossicles triangle the base is 65 which of the following expressions is a way to calculate the measure of the third triangle
Answers
The measure of the third angle in an isosceles triangle can be expressed using the expression of option c. 180° - 2(65°).
In an isosceles triangle,
Measure of the base angles is equal to 65°.
Let us consider the measure of the third angle in an isosceles triangle is equal to x degrees.
The two base angles are congruent.
Since each base angle measures 65°, the sum of the base angles is.
65° + 65° = 130°
The sum of the angles in any triangle is 180°.
This implies,
The measure of the third angle in the isosceles triangle is equal to,
x° + 130° = 180°
⇒ x° = 180° - 130°
⇒ x° = 50°
Therefore, the correct expression to calculate the measure of the third angle in an isosceles triangle is option (c) 180° - 2(65°).
Learn more about isosceles triangle here
brainly.com/question/29169213
#SPJ1
The above question is incomplete, the complete question is:
In an isosceles triangle, the base angles measure 65°. Which of the following expressions is a way to calculate the measure of the third angle?
a. 180° - 65°
b. 180°+ 65°
c. 180° - 2(65°)
d. 180° + 2( 65°)
which expression represents the distance between point j and point k?
Answers
The calculated expression that represents the distance between point j and point k is |j - k|
Which expression represents the distance between point j and point k?From the question, we have the following parameters that can be used in our computation:
Point j and point k
The expression that represents the distance between point j and point k is the absolute difference of the points j and k
Using the above as a guide, we have the following:
Distance = |point j - point k|
So, we have
Distance = |j - k|
Hence, the expression that represents the distance between point j and point k is |j - k|
Read more about distance at
https://brainly.com/question/28551043
#SPJ1
The volume of a rectangle prism is 810 square centimeters .
Height = 15 cm
Width = 3 cm
Find the missing length
Answers
The length of the rectangular prism is 18 cm.
Volume of a Rectangular Prism Formula:The formula for the volume of a rectangular prism is given as:
Volume of a rectangular prism = (length x width x height) cubic units.
V = (l x w x h) cubic units
In a rectangular prism, the product of the length and the width is known as the base area. Therefore, we can also represent the volume of a rectangular prism formula as:
Volume of a rectangular prism = Base area x height
Now, We have :
The volume of a rectangle prism is 810 square centimeters .
Height = 15 cm
Width = 3 cm
To find the length of the rectangular prism
Now, Apply the formula of volume of rectangular prism
Volume of rectangular prism is(V) : (l x w x h) cubic units
Plug all the values in above formula:
810 = l x 3 x 15
810 = 45L
L = 810 / 45
L = 18cm
Hence, The length of the rectangular prism is 18 cm.
Learn more about Rectangular prism at:
https://brainly.com/question/21308574
#SPJ1
According to your graphing calculator what is the approximate solution to the trigonometric inequality tan(x/4)<1/5 over the interval 0<= x<=2pi radians 
Answers
The approximate solution to the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians is 0 <= x <= 0.75. Option 1 is correct.
To solve the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians, we can use a graphing calculator and follow these steps:
Press the "mode" button on the calculator and make sure it is in radian mode.Enter the function "tan(x/4)" into the calculator.Press the "y=" button and enter "1/5" as the second function.Press the "graph" button to plot both functions on the same graph.Use the "trace" function or the cursor to find the points where the two graphs intersect.Check the values of x for which the tan(x/4) function is less than 1/5.Using this method, we can see that the two graphs intersect at approximately x = 0.75, x = 4.6, and x = 8.4 (or their equivalents within the interval 0 <= x <= 2π). We can also see that the tan(x/4) function is less than 1/5 between the first two intersection points (0 <= x <= 0.75 and 4.6 <= x <= 2π), but not between the second and third intersection points. Hence Option 1 is correct.
Note: Since we are rounding to the nearest degree, the approximate values may not be exact and may need to be adjusted slightly to ensure accuracy.
To learn more about trigonometric inequality, here
https://brainly.com/question/20719017
#SPJ1
find the mean of brothers and sisters
Answers
The mean of brothers and sisters = 3
From the attached data set of brothers and sisters we can write the data values (frequency) as:
1, 5, 4, 2
We need to find the mean of brothers and sisters,
We know that the formula for the mean of data.
mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values
First we find the sum of all data values.
1 + 5 + 4 + 2 = 12
and the total number of data values = 4
Using above formula of mean,
mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values
mean([tex]\bar{x}[/tex]) = 12 / 4
mean([tex]\bar{x}[/tex]) = 3
Therefore, the required mean is: 3
Learn more about the mean here:
https://brainly.com/question/30891252
#SPJ1
Find the complete question below.
Square root of 1444. Yumikkpyn vo lyuyb
Answers
Answer:
38
Step-by-step explanation:
the square root of 1444 is 38.
the surface area of a rectangular prism is 1,648 inches, the width is 16 inches and the hight is 20 inches. What is the length
Answers
Answer:
14
Step-by-step explanation:
l = length, w = width, h = height.
The surface area of a rectangular prism is:
2lw + 2wh + 2lh.
If the total surface area is 1648, your equation will be:
2lw + 2wh + 2lh = 1648.
lw + wh + lh = 824.
Plug in your width and height values.
16l + 16*20 + 20l = 824.
36l = 504.
Length = 14.
[tex]\boxed{\sf l=14(in)}.[/tex]
Step-by-step explanation:1. Write the surface area equation for rectangular prisms.[tex]\sf SA=2(wl+hl+hw)[/tex]
2. Substitute the variables by the given values in the formula.Surface area (SA)= 1,648 inches;
Width (w)= 16 inches;
Height (h)= 20 inches.
[tex]\sf 1648(in)=2((16(in))l+(20(in))l+(20(in))(16(in)))[/tex]
3. Simplify the expression.Let's remove the units for these steps to make the algebra a little bit easier to understand.
[tex]\sf 1648=2(16l+20l+320)\\ \\1648=2(36l+320)[/tex]
Here, we apply the distributive property of multiplication. Check attached image 1.
[tex]\sf 1648=(2)(36l)+(2)(320)\\\\1648=72l+640[/tex]
Now solving the equation for "l" to find its value.4. Subtract "640" from both sides of the equation.[tex]\sf 1648-640=72l+640-640\\ \\1008=72l\\ \\72l= 1008[/tex]
5. Divide both sides by "72".[tex]\sf \dfrac{72l}{72} = \dfrac{1008}{72} \\ \\\\ \boxed{\sf l=14(in)}.[/tex]
6. Verification.If you want to verify this answer simply take the surface area formula for rectangular prisms and calculate the value for the SA using these values of lengh, width and height:
[tex]\sf SA=2((16)(14)+(20)(14)+(20)(16))=\boxed{\sf 1648}. That's\,correct![/tex]
-------------------------------------------------------------------------------------------------------
Learn more about calculating the area of different shapes here:brainly.com/question/31651027
brainly.com/question/31638424
brainly.com/question/31637968
-------------------------------------------------------------------------------------------------------
Learn more about solving equations here:brainly.com/question/28282032
brainly.com/question/28306861
brainly.com/question/28306307
Which of the following questions about a particular animal could NOT be answered using only the data collected for the tracking collars?
Answers
The question about a particular animal that could NOT be answered using only the data collected from the tracking collars would be do the movement patterns of the animal vary according to the weather? That is option C.
What are tracking collars?A tracking collars is a neck device that usually has a GPS device attached to it which is used by biologists to track the movement of animals that are under study.
The functions of the tracking collars include the following:
It allows them to note how many miles the animal can travel in a given time.It allows them to note the pattern of movement of the animals.It allows them to note the location preferred by the animal to travel.Learn more about tracking here:
https://brainly.com/question/30633995
#SPJ1
Complete question:
Biologists often attach tracking collars to wild animals. For each animal, the following geolocation data is collected at frequent intervals.
The time
The date
The location of the animal
Which of the following questions about a particular animal could NOT be answered using only the data collected from the tracking collars?
A. Approximately how many miles did the animal travel in one week?
B. Does the animal travel in groups with other tracked animals?
C. Do the movement patterns of the animal vary according to the weather?
D. In what geographic locations does the animal typically travel?
C. Do the movement patterns of the animal vary according to the weather?
When 1370 subjects were asked, "On how many days in the past 7 days have you felt lonely?" the mean was 1.5 and the standard deviation was 2.16. The margin of error for a 95% confidence interval for the population mean is 0.12. Construct that confidence interval, and interpret it. The confidence interval goes from nothing to nothing. (Round to two decimal places as needed.)
Answers
Answer:
Confidence Interval = (1.41, 1.59)
Step-by-step explanation:
To construct a confidence interval for the population mean, we can use the following formula:
Confidence Interval = sample mean ± (margin of error * standard error)
where the standard error is equal to the standard deviation divided by the square root of the sample size.
Given the information provided, we can calculate the standard error as:
standard error = 2.16 / sqrt(1370) = 0.058
Then, we can calculate the margin of error as 0.12.
Substituting these values into the formula, we get:
Confidence Interval = 1.5 ± (0.12 * 0.058)
Confidence Interval = (1.41, 1.59)
Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.
