After calculating the perimeters, both the square and the rectangle have the same perimeter of 32 inches when the square has each side measuring 8 inches and the rectangle has dimensions of 6 inches by 10 inches.
Explanation:To determine which shape has the greater perimeter, calculate the perimeter of both the square and the rectangle. The formula for the perimeter of a square is 4 × side length, and the formula for the perimeter of a rectangle is 2 × (length + width).
For the square with each side measuring 8 inches, its perimeter is 4 × 8 = 32 inches.
For the rectangle with a width of 6 inches and a length of 10 inches, its perimeter is 2 × (10 + 6) = 2 × 16 = 32 inches.
Therefore, both the square and the rectangle have the same perimeter of 32 inches.
What is the total number of digits required in numbering the pages of a book which has 53 pages?
Answer:
The total number of digits required in numbering the pages of a book that has 53 pages would be: 97.
Step-by-step explanation:
This answer would be 97 due to the first nine digits being singular.
The next 44 digits are double, so therefore, you multiply 44 by 2, and you end up with 88.
After that, you take 88 and add the 9, which, is 97 digits in total that you would need to number a 53 page book.
If the radius of a circle is 14 ft, then the diameter of the circle is _____.
7 ft
28 ft
42 ft
87.92 ft
Answer:
The answer is 28ft.
Step-by-step explanation:
A radius will always be exactly half of the diameter: meaning, the diameter is double the length of the radius.
What is the value of x?
Last question please!
Answer:
x = -1
Step-by-step explanation:
-2 to 2 is 4 units, so -3x + 1 = 4.
We subtract 1 from both sides to get -3x = 3.
Then we divide each side by -3 to get x = -1.
True or false (Picture provided)
The answer is: True.
Why?A counterexample is a way that we can prove that something is not true about a mathematical expression or equation, it could be considered as an exception to a rule, so to check if the answer is true or false, we must prove that a counterexample of the given expression is 0°, so:
The given expression is:
[tex]sinytany=cosy[/tex]
Then,
[tex]sin(0)*\frac{sin(0)}{cos(0)}=cos(0)\\\\0*\frac{0}{1}=1\\\\0*0=1\\0=1[/tex]
We can see that the equation is not fulfilled, so 0° is a counterexample of [tex]sinytany=cosy[/tex] and the answer is true.
Have a nice day!
What is the mean absolute deviation of Dean's homework scores? 70, 95, 35, 90, 85
Answer:
18.
Step-by-step explanation:
Mean of the values = (70+95+35+90+85) / 5
= 75.
Mean absolute deviation :-
70 - 75 = |-5| = 5 (absolute value is taken
95 - 75 = 20
35-75 = 40
90-75 = 15
85-75 = 10
Mean Absolute Deviation = (5 + 20 + 40 + 15 + 10) / 5
= 18.
Answer: 18
Step-by-step explanation: it was correct on ttm
The rate of change of a bacteria (N) with respect to time is directly proportional to itself. When t=0, N=500. When t=4, N=3000. How many bacteria will be present when t=8?
Carbon-14 has a half-life of 5715 years. Find the rate of decay, if the initial amount of carbon-14 is 10 units.
Please explain (step by step is preferred)
Fine the average rate of change by the difference in N over the difference in T:
3000 - 500 / 4-0 = 2500 / 4 = 625
This means for every 1 T, N = 625.
Now multiply 625 by 8:
625 x 8 = 5000
When T = 8 N = 5,000
The decay rate can be found by dividing -ln(2) by the half life.
Decay rate = -ln(2) / 5715 = -0.00012
Which expression is equivalent to 1/2x - 1? *
a) 1/3(3/2x - 1)
b) (3/2x + 1) - (x - 2)
c) 2/3(3/4x - 3/2)
d) (3/4x - 2) + (1/4x + 1)
Ans: It's C
'Cause (2/3 * 3/4x)+(2/3 * (-3/2)) = 1/2x - 1.
The expression which isequivalent to (1/2)x - 1 will be 2/3(3/4x - 3/2). Then the correct option is C.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Let's check all the options, then we have
a) 1/3(3/2x - 1), simplify the expression, then we have
⇒ 1/3(3/2x - 1)
⇒ (1/2)x - 1/3
b) (3/2x + 1) - (x - 2), simplify the expression, then we have
⇒ (3/2x + 1) - (x - 2)
⇒ (1/2)x + 3
c) 2/3(3/4x - 3/2), simplify the expression, then we have
⇒ 2/3(3/4x - 3/2)
⇒ (1/2)x - 1
d) (3/4x - 2) + (1/4x + 1), simplify the expression, then we have
⇒ (3/4x - 2) + (1/4x + 1)
⇒ x - 1
The expression which isequivalent to (1/2)x - 1 will be 2/3(3/4x - 3/2). Then the correct option is C.
More about the equivalent link is given below.
https://brainly.com/question/889935
#SPJ2
the base are of a cylinder is the quotient of its volume and its height true or false
Answer:
True.
Step-by-step explanation:
Volume of a cylinder = π r^2 h where h = height and π r^2 = the base area.
Volume / height = π r^2 h / h = π r^2 = base area.
The base area of a cylinder is not the quotient of its volume and its height; it is determined by the area of its circular base. Understanding the relationship between base area and volume in a cylinder is essential in mathematics.
False. The base area of a cylinder is not the quotient of its volume and height. The base area of a cylinder is the same as the area of its circular base, which is equal to πr2 where r is the radius of the base.
The volume of a cylinder is calculated by multiplying the base area with the height of the cylinder. Thus, base area ≠ volume / height.
When the height of a cylinder is equal to its diameter, it minimizes the surface area, but it does not affect the calculation of the base area itself.
The length of a rectangle is twice its width. If the area of the rectangle is 5 , find its perimeter
Answer:
9.48
Step-by-step explanation:
The perimeter of a rectangle is the distance around the the shape. It can be found by adding each side of the shape to find a total. In contrast, the area of a shape is the amount inside a shape. It is found using multiplication or A = l*w. Since the width is w and the length is twice its width or 2w, use these expressions in the area formula to find their amount. Then add them together to find the perimeter.
[tex]A = l*w5 = w(2w)\\5 = 2w^2\\2.5 = w^2\\1.58 = w[/tex]
The width of the rectangle is w = 1.58. The length is 2w = 2 (1.58) = 3.16.
Add these amounts by P = l + l + w + w to find the perimeter.
P = 3.16 + 3.16 + 1.58 + 1.58 = 9.48
Estimate the limit.
Answer:
a. 0.25
Step-by-step explanation:
The given expression is
[tex]\lim_{x \to 2} \frac{x-2}{x^2-4}[/tex]
Factor the denominator using difference of two squares.
[tex]\lim_{x \to 2} \frac{x-2}{(x-2)(x+2)}[/tex]
Cancel out common factors;
[tex]\lim_{x \to 2} \frac{1}{(x+2)}[/tex]
We plug in 2 to get
[tex]\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{2+2}[/tex]
[tex]\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{4}=0.25[/tex]
Answer:
The correct answer option is A. 0.25.
Step-by-step explanation:
We are given the following expression and we are to find its limit:
[tex] lim_\left \{ {{ x = 2 } [/tex] [tex] \frac { x - 2 } { x ^ 2 - 4 } [/tex].
First of all, we will simplify the expression by factorizing the term in the denominator:
[tex] \frac { x - 2 } { x ^ 2 - 4 } = \frac { x - 2 } { ( x - 2 ) ( x + 2 ) }[/tex]
Cancelling the common terms to get:
[tex]\frac{1}{x+2}[/tex]
Substituting the given value for x to get:
[tex]\frac{1}{2+2}[/tex] = 0.25
Which measurements could NOT represent the side lengths of a right triangle? * 1 point A. 6 cm, 8 cm. 10 cm B. 12 cm, 35 cm, 37 cm C. 4 cm, 6 cm, 10 cm D. 10 cm, 24 cm, 26 cm
Answer:
C. 4cm, 6cm, 10cmStep-by-step explanation:
Is a ≤ b < c are the side lengths of a right triangle, then
[tex]a^2+b^2=c^2[/tex]
A. 6cm, 8cm, 10cm.
Substitute:
[tex]6^2+8^2=10^2\\36+64=100\\100=100\to TRUE[/tex]
B. 12cm, 35cm, 37cm.
Substitute:
[tex]12^2+35^2=37^2\\144+1225=1369\\1369=1369\to TRUE[/tex]
C. 4cm, 6cm, 10cm.
It's not the side lengths of a triangle, because 4 + 6 = 10.
Without looking at it, we will check equality
[tex]4^2+6^2=10^2\\16+36=100\\52=100\to FALSE[/tex]
D. 10cm, 24cm, 26cm.
Substitute:
[tex]10^2+24^2=26^2\\100+576=676\\676=676\to TRUE[/tex]
The measurement that could not represent the side length of a right triangle is 4 cm, 6 cm, 10 cm.
What is a right triangle?A right triangle is a triangle that consists of three sides. The longest side is the hypotenuse. The other sides are the base and the length. The sum of angles in a triangle is 180 degrees.
What is the Pythagoras theorem?According to this theorem, the square of the hypotenuse should be equal to the sum of the square of the other two sides.
The Pythagoras theorem: a² + b² = c²
where:
a = length
b = base
c = hypotenuse
Which measurements do not represent the side lengths of the right triangle?6² + 8² = 10²
36 + 64 = 100
Option B = 12² + 35
= √144 + 1225
= √1369
= 37
Option C = 4² + 6²
16 + 36
= √52
= 7.2
Option D: 10² + 24² = 26²
100 + 576
= √676
= 26
Please find attached an image of a right triangle. To learn more about Pythagoras theorem, please check: https://brainly.com/question/14580675
Which equation can be used to find the volume of the right rectangular prisms
A) V = (10)(5)
B) V = (10)(2)
C) V = (10)(5)(2)
D) V = 10(5 + 2)2
The answer is C because it’s length x width x height
Answer:
C) V = (10)(5)(2)
Step-by-step explanation:
V = (10)(5)(2) To find the volume of a right rectangular prisms, multiply the length times the width times the height. -- V = lwh.
A pendulum swings an arc with a length equal to 15 meters. Each subsequent swing is 95% of the previous swing.
a) How far with the pendulum travel on its 6th swing?
b) How far will the pendulum swing before it essentially stops? Hint: This is an infinite geometric series.
Show all work and explain your reasoning.
Answer:
The answers for your two questions are the following
a)11.606 m
b) As the number of swings approaches infinity
Step-by-step explanation:
We are dealing with an exponential equation series, where the length of each swing can be represented as
l = [ 15 *(0.95)^(n-1) ]
n is the corresponding number of the swing.
So, for the first swing, n = 1
[ 15 *(0.95)^(1-1) ] = 15 m
a) How far with the pendulum travel on its 6th swing?
We just need to evaluate the previous formula for n = 6
[ 15 *(0.95)^(6-1) ] =
[ 15 *(0.95)^(5) ] =
[ 15 *(0.7737) ] =
[ 15 *(0.7737) ] = 11.606 m
b) How far will the pendulum swing before it essentially stops? Hint: This is an infinite geometric series.
We previously stated that the length of the arc of each swing can be represented as
l(n) = [ 15 *(0.95)^(n-1) ] , for n>=1
Since the function approaches zero if and only if n approaches infinity, we can say that the pendulum never stops.
Of course, this only happens mathematically, we can always fin a threshold for which the movement cannot be registered anymore.
Please see attached graph for a representation of the function
Answer:
a) It will travel approx 79.47 meters,
b) It will travel 300 meters.
Step-by-step explanation:
Given,
The initial distance travel on first swing = 15 meters,
Also, Each subsequent swing is 95% of the previous swing.
Thus, there is a G.P. that shows this situation,
Having first term, a = 15,
And, the common difference, r = 95 % = 0.95,
a) Also, for the 6th swing,
Number of terms, n = 6,
Hence, the distance covered by the pendulum on its 6th swing,
[tex]S_{n}=\frac{a(1-r^n)}{1-r}[/tex]
[tex]S_{6}=\frac{15(1-0.95^6)}{1-0.95}[/tex]
[tex]=79.4724328125\approx 79.47\text{ meters}[/tex]
b) When [tex]n=\infty[/tex]
The distance will the pendulum swing before it essentially stops is,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]
[tex]=\frac{15}{1-0.95}[/tex]
[tex]=300\text{ meters}[/tex]
the starting salary at a company is $38000 per year.the company automatically gives a raise of 3.5% per year.write the explicit and recursive frmulas for the geometric sequence formed by the salary increase.
Final answer:
The explicit formula for the salary increases represented as a geometric sequence is a_n= 38,000(1.035)^(n-1), and the recursive formula is a_1= $38,000 and a_n= a_(n-1) × 1.035 for n > 1, reflecting an annual raise of 3.5%.
Explanation:
The starting salary at a company is $38,000 per year with an annual raise of 3.5%. To represent the salary increases as a geometric sequence, we need both explicit and recursive formulas.
The explicit formula for a geometric sequence is an= a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number. In this case, a1= $38,000 and r = 1.035 (since the salary increase is 3.5%, or 0.035 in decimal form, plus the original amount, hence 1 + 0.035). Therefore, the explicit formula is an= 38,000(1.035)(n-1).
The recursive formula defines each term based on the previous term. It can be written as a1= $38,000, an= a(n-1) × 1.035, for n > 1. This means that starting from the second year (when n > 1), the salary is obtained by multiplying the previous year's salary by 1.035.
Please answer this question! 25 points and brainliest!
chur answer is gonna be 63787 km
12 decreased by twice a number is the same as 8 times the sum of the number and four. What is the number?
Shannon is putting a fence around the garden, except where there is a gate that is 3 feet wide. One foot of the fence costs $43. The cost of the gate is $128. Write an expression that represents the total cost of the fence and the gate. Explain how you determined your expression.
Answer:
The expression would be 43x + 128
Step-by-step explanation:
43 dollars is multiplied by however many feet is used. Then, the exception(the gate) is added to the charge that is 43x
Simplifying the expression results in what binomial expression?
The answer is 2x−5
Step-by-step explanation:see the image
The temperature in frostville was at 50*F at midnight,and it dropped at a constant rate for the next 10 hours.
After 10 hours the temperature is shown on the graph as 30 degrees.
50 degrees - 30 degrees = 20 degrees.
The temperature dropped 20 degrees in 10 hours.
Divide the change by the time:
20 degrees / 10 hours = 2 degrees per hour.
Because the temperature dropped, the change would be negative.
The answer is D. -2 degrees per hour.
Please help!!!
The area of the green square is 9 ft2. The area of the yellow square is 25 ft2.
What is the area of the red square (labelled "b" in the diagram)?
Answer:
the answer is 16Ft^2
Step-by-step explanation:
Square A's area is 9 so take its square root =3
then do the same for Square c =5
then use pythagram theory which is
3^2 + 5^2 = 4^2 = 16
Answer:
area = 16 ft²
Step-by-step explanation:
The area of the green square = 9 ft²
area of the yellow square = 25 ft²
Area of the red square can be computed as follows:
area of a square = L²
Since one side of each triangle forms a part of the triangle knowing the length of sides of the green and yellow triangle can be use to get the sides of the red square and invariably the area.
Green square
L² = 9
square both sides
√L² = √9
L = 3 ft
Yellow square
L² = 25
square both sides
√L² = √25
L = 5 ft
use Pythagoras theorem to get the third side of the triangle which is the b
c² = a² + b²
b² = c² - a²
a = 3 ft
c = 5 ft
b² = 5² - 3²
b² = 25 - 9
b² = 16
square both sides
√b² = √16
b = 4
Red square
area = L²
area = 4²
area = 16 ft²
Can someone help me ? i have no clue how to figure this out
[tex] \cos t (\sec t - \cos t) = \sin^2 t [/tex]
[tex] \cos t (\dfrac{1}{\cos t} - \cos t) = \sin^2 t [/tex]
[tex] \dfrac{\cos t}{\cos t} - \cos^2 t = \sin^2 t [/tex]
[tex] 1 - \cos^2 t = \sin^2 t [/tex]
Use the identity: [tex] \sin^2 t + \cos^2 t = 1 [/tex] and solve for [tex] \sin^2 t [/tex]. You get: [tex] \sin^2 t = 1 - \cos^2 t [/tex]
Do the substitution on the left side to get:
[tex] \sin^2 t = \sin ^2 t [/tex]
[tex] \cos \: t ( \sec \: t - \cos \: t) = \sin^{2}t \\ \\ 1. \: 1 - \frac{ \cos \: t }{ \sec \: t } = \sin^{2} t \\ 2. \: 1 - \cos \: t \cos \: t = \sin^{2} t \\ 3. \: 1 - \cos^{2} t = \sin^{2} t \\ 4. \: 1 - \cos^{2} t - \sin^{2} t = 0 \\ 5. \: 1 - 1 = 0 \\ 6. \: 0 = 0 \\ 7. \: infinitely \: many \: solutions[/tex]
The temperature in Franklin city is -5°C. The temperature in Silver city is 4° less what is the temperature in Silver city .
Answer:
-9 C
Step-by-step explanation:
Subtract 4 from -5 will equal -9
Find the measure of an angle with measure between 0 degrees and 360 degrees that is coterminal with an angle measuring 800 degrees.
To find a coterminal angle to 800 degrees within the 0 to 360-degree range, divide 800 by 360 and find the remainder, which is 80 degrees. Hence, 80 degrees is the angle that's coterminal with 800 degrees.
Explanation:To find an angle that is coterminal with 800 degrees, which means an angle that shares the same terminal side as the 800-degree angle but is between 0 degrees and 360 degrees, we use the concept of coterminal angles. Since a complete circle has 360 degrees, we can subtract or add multiples of 360 degrees to any angle to find a coterminal angle.
Here’s how we find it for 800 degrees:
Divide 800 by 360 to find how many complete turns the angle makes: 800 ÷ 360 = 2.22. This shows the angle makes more than 2 full rotations.Find the remainder when 800 is divided by 360 to find the coterminal angle within the 0 to 360-degree range. The remainder is 80 degrees (800 - 720 = 80).Therefore, 80 degrees is the angle between 0 degrees and 360 degrees that is coterminal with an angle measuring 800 degrees.
Conrad paid $52.26 for a pair of shoes. Michelle paid $3.89 more for a pair of shoes than Conrad paid for his. How much did Michelle pay for her shoes
Answer:Michelle paid $56.15 for her shoes
Step-by-step explanation:
Since Michelle paid $3.89 more for her shoes compared to Conrad, who paid $52.26. This means you have to add $3.89 to $52.26.
$3.89+$52.25= $56.15
Final answer:
Michelle paid $56.15 for her shoes, which is $3.89 more than the $52.26 that Conrad paid for his.
Explanation:
The question involves a simple arithmetic calculation to determine how much Michelle paid for her shoes. To find the answer, we will add $3.89, which is the additional amount Michelle paid, to $52.26, which is the amount Conrad paid for his shoes.
Step-by-step calculation:
Conrad's shoe price: $52.26Additional amount paid by Michelle: $3.89Michelle's shoe price: $52.26 (Conrad's price) + $3.89 = $56.15Therefore, Michelle paid $56.15 for her shoes.
Plz Help Me
Select the correct answer from each drop-down menu.
In a given year, two tennis academies each had 120 players who went on to play professionally. In the following years, the number of players who went on to play professionally from academy A increased by 10 players every year. The number of players who went on to play professionally from academy B increased by 10% every year.
Use the given information to complete the sentence.
The number of players who went on to play professionally at (academy A, academy B, both academy) can be represented by (an arithmetic, a geometric) sequence because the numbers of players who went on to play professionally in successive years have a common (difference, ratio) of 10
Answer:
Academy A, Arithmetic, and difference makes most sense to me.
Academy A's professional tennis player numbers can be described by an arithmetic sequence due to a constant increase of 10 every year. In contrast, Academy B's numbers can be represented by a geometric sequence because the increase each year is proportionate to the current number of students, at a rate of a 10% increase per year.
Explanation:The number of players who went on to play professionally at Academy A can be represented by an arithmetic sequence because the numbers of players who went on to play professionally in successive years have a common difference of 10. For Academy A, each year the number increased by a consistent amount, 10 more players, hence the use of an arithmetic sequence.
On the other hand, the number of players who went on to play professionally at Academy B can be represented by a geometric sequence because the numbers of players who went on to play professionally in successive years have a common ratio of 10%. For Academy B, the rate of increase is proportional to the current number of students, which makes it a geometric sequence.
Learn more about Sequence here:https://brainly.com/question/36944481
#SPJ11
This sphere has a diameter of 12 meters.
What is its exact surface area and its exact volume?
Show the formulas and show your work.
Answer:
area: 144π m²volume: 288π m³Step-by-step explanation:
The formula for the surface area of a sphere is ...
A = 4πr²
For a radius of 6 meters, that is ...
A = 4π(6 m)² = 144π m²
___
The formula for the volume of a sphere is ...
V = (4/3)πr³ = A·(r/3)
For the same sphere, this is ...
V = (144π m²)(6 m/3) = 288π m³
Need help with Geometry
Answer:
Answer: 56*pi
Step-by-step explanation:
The easiest way is to find the area of the circle and subtract the area of the sector.
Area of the circle
d = 16 cm given
d = 2*r definition
16 = 2*r divide by 2
16/2 = 2r/2
r = 8
Area of the circle = pi * r^2
Area of the circle = pi * 8^2
Area of the circle = 64 pi
Area of the sector
Area of sector = (theta/360) * pi * r^2
Area of sector = 45/360 * pi * 64
Area of sector = 1/8 * pi * 64
Area of sector = 8 * pi
Area of the shaded area
Area of the shaded area = 64 * pi - 8*pi = 56*pi
Note: There is a shorter way, but one can never be confident of getting an angle greater than 180 correct.
360 - 45 = 315
Area of the sector = 315/360 * pi * r2
Area of the sector = 7/8 * pi * 64
Area of the sector = 7 * pi * 8
Area of the sector = 56*pi
Find the zeros of f(x)=-3x^3+6x+5.
Answer:
x = 1.723
Step-by-step explanation:
The zeros of a function f(x) are the points where the function crosses the x-axis. At these points, the function will have a value of zero, that is;
f(x) = 0
We simply graph the function and determine the points where it crosses the x-axis. From the attachment, f(x) crosses the x-axis at;
x = 1.723
Answer:
Step-by-step explanation:
We have given the function:
f(x)=-3x³+6x+5.
We have to find the zeros of the function.
The zeros of the function are the points where the function cuts the x-axis.
And at that points function has value zero.
So to find these points put f(x)= 0 we get,
-3x³+6x+5=0
As from the graph the function cuts the x-axis at x = 1.723 so, this is the zero of the function.
Jim Juice treats that are in the shape of a cone. The molds he bought are each 3 inches (in.) deep with a diameter of 3 in. What is the approximate volume of juice needed for Jim to make 6 juice treats?
A.169.6 in
B.127.2 in
C.84.8 in
D.42.4 in
Answer:
Option D. [tex]42.4\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the cone (juice treats) is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter
[tex]h=3\ in[/tex]
assume
[tex]\pi=3.14[/tex]
substitute
[tex]V=\frac{1}{3}(3.14)(1.5)^{2}(3)=7.065\ in^{3}[/tex]
Multiply the volume of one juice treats by 6
[tex](6)7.065=42.39=42.4\ in^{3}[/tex]
How does f(x) = 5x change over the interval from x = 7 to x = 8?
A) f(x) increases by 5
B) f(x) decreases by 5
C) f(x) increases by a factor of 5
D) f(x) decreases by a factor of 5
Answer:
the answer is a
Step-by-step explanation:
5x7= 35, 5x8= 40 40-35=5