Answer:
True
Explanation:
Bridget Riley was one of the most prominent artists associated with the 1960s 'Op Art' movement, which was an art movement that explored optical illusions and effects to create abstract art that played with the viewer's perception. However, there were many other artists associated with this movement, including Victor Vasarely, Richard Anuszkiewicz, and Yaacov Agam, among others.
The average temperature for a dog is 101.8° F, but it can vary by as much as 0.7° F. Write an inequality to represent the normal temperature range of a dog, where t represents body temperature.
|t − 101.8| ≥ 0.7
|t − 101.8| ≤ 0.7
|t − 0.7| ≥ 101.8
|t − 0.7| ≤ 101.8
The correct inequality to represent the normal temperature range of a dog is |t − 101.8| ≤ 0.7. So, correct option is B.
Here, |t - 101.8| represents the absolute value of the difference between the body temperature of the dog (t) and the average temperature of dogs (101.8° F). The inequality states that this absolute value must be less than or equal to 0.7° F, which is the maximum amount that the temperature of a dog can vary from the average.
If the temperature of a dog is within this range, it is considered to have a normal body temperature. If the temperature is outside this range, it may indicate an underlying health issue or illness.
The other answer choices are incorrect because they do not accurately represent the relationship between the body temperature of a dog and the normal temperature range. For example, |t - 0.7| ≥ 101.8 makes no sense in the context of the problem, as there is no logical reason to subtract 0.7 from the body temperature.
So, correct option is B.
To learn more about inequality click on,
https://brainly.com/question/28746337
#SPJ1
13x−6y=22
x=y+6
Please help first come first surve
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
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)
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
1. Simplify(3mks)
a + b / 2 - 2A - b / 3 =
Use the long division method to find the result when 4x^3+15x^2+17x+6 is divide by 4x+3
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
Gretta travels 77 miles per hour for 5 hours, find the distance traveled in miles
Answer: 358 miles
Step-by-step explanation:
Answer: 385
Step-by-step explanation: 77x5
Determine the equation of the circle with center (0,−1) containing the point ( − 8 , 10 )
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
Use properties of exponents to verify that 2s − 1 and _1
2 (2)
s
are equivalent.
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.
solve 5 to the power of x+2 is less than or equal to 3 to the power of x
Step-by-step explanation:
5^(x+2) <= 3^x
5^x * 5^2 <= 3^x
25 <= 3^x / 5^x
25<= (3/5)^x LOG both sides
log 25 <= x log (3/5)
log 25 / log (3/5) <= x
- 6.3 <= x
Faster please!! thanks!! 30 points + brainliest!!
Which is an example of simple random sampling created from each given population?
An example of simple random sampling is given as follows:
C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.Hence the samples for this problem are classified as follows:
A -> convenient.B -> stratified.C -> random.D -> cluster.More can be learned about sampling at https://brainly.com/question/9910540
#SPJ1
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.)
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.
Write a two-column proof for the following information. Upload your proof below.
Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2
Prove: x = 2
The required two column proof is explained below.
What is a midpoint?A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.
The two column proof for the information is given as:
M is the midpoint of CD (Given)
CD = CM + MD (addition property of a line segment)
CM = MD (definition of a midpoint)
So that;
5x – 2 = 3x + 2 (Definition of midpoint)#
Then,
5x - 3x = 2 + 2 (collecting like terms)
2x = 4
x = 2
Learn more about midpoint at https://brainly.com/question/24431553
#SPJ1
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
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
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
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
find the mean of brothers and sisters
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.
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)
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
find the polar coordinates of a point with Cartesian coordinates (x,y)=(5√3/2,−5/2).Select the correct answer below:
(5,5π/6)
(10,4π/3)
(5,11π/6)
(10,5π/6)
(5,4π/3)
(10,11π/6)
Answer: The correct answer is (5, 11π/6). or C
Step-by-step explanation:
The polar coordinates of the point (x, y) = (5√3/2, -5/2) are (r, θ) = (5, 11π/6).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((5√3/2)^2 + (-5/2)^2)
= √(75/4 + 25/4)
= √(100/4)
= 5
θ = atan2(-5/2, 5√3/2)
≈ 11π/6 radians
So, the correct polar coordinates of the point (5√3/2, -5/2) are (r, θ) = (5, 11π/6).
La base de un rectangulo mide el doble de su altura. Cuales son sus dimensiones Si el perimetro mide 144 cm ?
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
Solve for BC: 3√2 A B C
Sides AB = 3√2 and BC = 6.
The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.
In the given right triangle ABC,
Hypotenuse of the triangle = BC
Base and height = AC and AB.
Also, we see from the diagram that ∠ACB and ∠ABC are equal.
∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.
Now, by Pythagoras' theorem,
Hypotenuse² = Base² + Height²
Or, BC² = AC² + AB²
Or, BC² = (3√2)² + (3√2)²
⇒ BC² = 36
Or, BC = 6
Hence, sides AB = 3√2 and BC = 6.
For more about Pythagoras theorem,
https://brainly.com/question/343682
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
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
TONS OF POINTS - please help
The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will
travel follows a parabolic arch that can be described by this polynomial.
f(x) = -0.05(x2-26x-120)
He is supposed to land on a safety net 30 feet away. Does the function give you
enough information to tell you where he will land? If so, how far from the cannon will he land?
Make Sense of the Problem
3 points: 1 point for each answer.
-What do you know?
-What do you want to find out?
-What kind of answer do you expect?
1. The function f(x)=-0.05(x2-26x-120)
Represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent
2.what do the zeros of this function represent? Remember the zeros are where f(x)=0
3. Will the zeros tell you where the net should be placed? Why or why not?
4.to find zeros, set the function equal to 0, and then factor the polynomial start by setting the function equal to 0
5. Next factor the polynomial x2-26x-120. To identify the factors, complete the table: note this does not contain all the factors of -120, but it has enough to let you factor the polynomial
(I tried to type out the table )
pqp+q
P. q. p. |
————————— |
10. | 12 | blank. |
—————————.|
-10 | 12 |. Blank. |
—————————.|
30. |. -4. |. Blank. |
—————————-|
4. |. 30. | blank. |
—————————.|
6. Which values of p and w give the correct factors
7. Factor the polynomial completely
0=-0.05(x2 - 26x -120)
8. Find the roots of equation by setting each factor equal to 0 and solving for x.
Hint: there are three factors, but the constant factor, -0.05, does not equal zero
Solve for x with the other two factors
9. Identify the roots
Answer:
Step-by-step explanation:
2344
A cone has a diameter of 16 cm and a height of 35 cm. What is its volume?
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)
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 
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
hi how to integrate this
Integration of [tex]\int\limits^6_0 {\frac{8}{1+74e^{-0.3t} } } \, dt[/tex] is 2.199.
We can solve this integral using the substitution method, where u = 1 + 74[tex]e^{-0.3t}[/tex] . Taking the derivative of both sides, we have du/dt = -222[tex]e^{-0.3t}[/tex] .
We can rewrite the integral in terms of u:
∫[8/(1+74[tex]e^{-0.3t}[/tex] )]dt = ∫[8/u * (-1/222) * (-222[tex]e^{-0.3t}[/tex] )]du
Simplifying this expression, we have:
= (-8/222) ∫[1/u] du
= (-4/111) ln|u| + C
where C is the constant of integration.
Substituting back for u, we have:
= (-4/111) ln|1 + 74[tex]e^{-0.3t}[/tex] | + C
To evaluate the definite integral from 0 to 6, we plug in the limits of integration:
= (-4/111) [ln | 1 + 74[tex]e^{-0.3(6)}[/tex] | - ln | 1 + 74[tex]e^{-0.3(0)}[/tex] |]
= (-4/111) [ln|1 + 74[tex]e^{-1.8}[/tex]| - ln75]
≈ 2.199
Therefore, the value of the definite integral is approximately 2.199.
To learn more about Integration here:
https://brainly.com/question/18125359
#SPJ1
WXYZ is a parallelogram. If ZX = 104 and ZU = 11c-3, find the value of c.
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
Square root of 1444. Yumikkpyn vo lyuyb
Answer:
38
Step-by-step explanation:
the square root of 1444 is 38.
SOS need help on this math project with all the work
To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.
How to construct the shapes and anglesA key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a line AB.
Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.
Learn more about geometry here:
https://brainly.com/question/19241268
#SPJ1
In an ossicles triangle the base is 65 which of the following expressions is a way to calculate the measure of the third triangle
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°)
A scientist has 68 lbs of a material. In 40 years , there is 63.3 lbs left. How much will be there be left in 200 years?
Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.
How much will be there be left in 200 years?A general exponential decay is:
f(x) = A*(b)^x
Where A is the initial value, b is the rate of decay, x is the variable.
We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:
63.3 = 68*(b)^40
Where b defines how it decays, we can solve that equation for b to get:
(63.3/68)^(1/40) = b
0.9982 = b
Then the decay is:
f(x) = 68*(0.9982)^x
The amount left after 200 years will be:
f(200) = 68*(0.9982)^200 = 47.43
Learn more about exponential decays at:
brainly.com/question/27822382
#SPJ1
Callie uses leather cord to make necklaces. She has a pieces of leather cord that has a length of 4 yards. Each necklace will have a length of 28 inches. How many necklaces can Callie make? Show your work.
Callie can make 5 necklaces.
What is the formula for yards to inches?So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.
Now, She has a pieces of leather cord that has a length of 4 yards.
Each necklace will have a length of 28 inches.
We have to determine the how many necklaces can Callie make?
We know that :
1 yard= 36 inches
So, Multiply by 36 into 4 yards
4 yards= 36x4= 144
Length of leather cord is 4 yards
144/4 = 5.14
Callie can make 5 necklaces.
Learn more about Conversion yards into inches at:
https://brainly.com/question/1609326
#SPJ1
