Therefore , the solution of the given problem of equation comes out to be rounded to three decimal places, is 17.483 grams.
What is equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Think about the information that y + 7 provides. When accompanied by generate y + 7, increasing results in b + 7 in this case rather than another method that could split 12 into two separate components.
Here,
We must enter t = 110 into the equation for y and solve for y in order to determine how much of the original mass is still present after 110 years:
=> y = 20(1 - 2^(-t/30))
=> y = 20(1 - 2^(-110/30))
=> y ≈ 2.517
As a result, there are roughly 2.517 grams of cesium-137 left after 110 years. We can deduct this amount from the original mass of 20 grams to determine how much of the initial mass is still present:
=> 20 - 2.517 ≈ 17.483
Thus, roughly 17.483 grams of the original 20 grams of cesium-137 are still present after 110 years.
The number, rounded to three decimal places, is 17.483 grams.
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PLEASE HELP ME.
(In picture)
Answer:
2nd option
Step-by-step explanation:
the temperature T, in degrees Fahrenheit, during the day can be modeled by the equation T(x)=-0.07x^2, where x is the number of hours after 6 a.m. At what time is the temperature a maximum? What is the maximun temperature?
Answer: To find the time at which the temperature is maximum, we need to find the vertex of the quadratic function T(x) = -0.07x^2. Recall that the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c is given by -b/2a. In this case, a = -0.07 and b = 0 (since there is no linear term), so the x-coordinate of the vertex is x = -b/2a = -0/(-0.14) = 0.
Since x is the number of hours after 6 a.m., the time corresponding to x = 0 is 6 a.m. Therefore, the temperature is a maximum at 6 a.m.
To find the maximum temperature, we evaluate T(0) = -0.07(0)^2 = 0. Therefore, the maximum temperature is 0 degrees Fahrenheit. Note that this result makes sense, since the quadratic function T(x) = -0.07x^2 is a downward-facing parabola, which means that the temperature decreases as the number of hours after 6 a.m. increases.
Step-by-step explanation:
24 = 3(y + 6) someone can help me please?
An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations can be used to model a wide range of real-world situations, and they are an essential tool in many fields of study, including physics, engineering, and economics.
How to solve the given equation?To solve for y, we need to isolate y on one side of the equation. We can do this by first distributing the 3 on the right-hand side:
24 = 3y + 18
Next, we can isolate 3y by subtracting 18 from both sides:
24 - 18 = 3y
6 = 3y
Finally, we can solve for y by dividing both sides by 3:
y = 2
Therefore, the solution to the equation 24 = 3(y + 6) is y = 2.
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type the correct answer in the box. use numerals instead of words. use / for the fraction bar. there are 57 houses on julian's street. of those houses, 12 have a skylight, 28 have a fireplace, and 5 have both a skylight and a fireplace. the probability, expressed as a fraction in the lowest terms, that julian lives in a house with a skylight or a fireplace is (what fraction in the lowest terms).
The probability that Julian lives in a house with a skylight or a fireplace is 35/57, which can be simplified to 5/8 in the lowest terms. So the answer is: 5/8.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To calculate the probability that Julian lives in a house with a skylight or a fireplace, we need to add the number of houses that have a skylight and the number of houses that have a fireplace, and then subtract the number of houses that have both a skylight and a fireplace, because we don't want to count those houses twice:
Number of houses with a skylight = 12
Number of houses with a fireplace = 28
Number of houses with both a skylight and a fireplace = 5
Number of houses with a skylight or a fireplace = (12 + 28) - 5 = 35
Therefore, the probability that Julian lives in a house with a skylight or a fireplace is 35/57, which can be simplified to 5/8 in the lowest terms.
So the answer is: 5/8.
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Write the statement in words. Let p="The plane is on time." Let q="The sky is clear."
Q->~P
It asserts that if the sky is clear, then it is not possible for the plane to be on time.
Define hypothesisIn general, a hypothesis is a proposed explanation or tentative answer to a research question or problem. It is a statement that can be tested through investigation and analysis of data.
The statement "q -> ~p" can be interpreted as "If the sky is clear, then the plane is not on time."
This is a conditional statement, where q represents the hypothesis or condition ("the sky is clear") and ~p represents the conclusion or result ("the plane is not on time").
It asserts that if the sky is clear, then it is not possible for the plane to be on time.
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Directions: Show all work. Round to the nearest tenth. 1. What is the volume of a cone with a diameter of 12 inches and a height of 16 inches?
Answer:
603.2 cubic inches
Step-by-step explanation:
First, we need to find the radius of the cone, which is half of the diameter:
radius = 12 inches / 2 = 6 inches
Next, we can use the formula to find the volume of a cone:
V = (1/3)πr^2h
where V is the volume, π is pi (approximately 3.14), r is the radius, and h is the height.
Substituting in the values we have:
V = (1/3)π(6 inches)^2(16 inches)
V = (1/3)π(36 square inches)(16 inches)
V = (1/3)π(576 cubic inches)
V = 192π cubic inches
Rounding to the nearest tenth, the volume of the cone is:
V ≈ 603.2 cubic inches
Hopes this helps
help asap will give brainliest hurry
Based on the given information, the value of y is 5.
What is a cyclic polygon?
A cyclic polygon is a polygon that can be inscribed inside a circle in such a way that all of its vertices lie on the circumference of the circle. In other words, a cyclic polygon is a polygon that can be circumscribed by a circle.
In a polygon with n sides, the sum of its interior angles is given by the formula: (n - 2) * 180 degrees. Since this polygon is inside a circle, it must be a cyclic polygon, which means that its opposite angles add up to 180 degrees.
We are given that the opposite angles are 23y and 13y, so we can write:
23y + 13y = 180
36y = 180
y = 5
Therefore, the value of y is 5.
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A survey of 240 families showed that
91 had a dog;
70 had a cat;
31 had a dog and a cat;
91 had neither a cat nor a dog, and in addition did not have a parakeet;
7 had a cat, a dog, and a parakeet.
How many had a parakeet only?
Ok
so the math that we need to do for this problem will be:
Total number of families = 240
minus the ones that don't have any pets = 91
minus the families that do have dogs = 91
minus the families that do have cats = 70
add back the overlap of dogs and cats = 31
add back the overlap of dogs cats parakeets = 7
240 - 91 - 91 - 70 + 31 + 7
^ this math will give us the families that ONLY have parakeets
so I stand by what I said before that this is the math you would to do get the answer to your problem
therefore its 26 buddy
Step-by-step explanation:
[tex]n(p) only= \: n(p) - n(c n d np) \\ = 91 - 7 \\ = 84[/tex]
Can someone do this for
Me
1. The two triangles are congruent, ASA criteria. angle H ≅ angle M, HY ≅ MN and EY ≅ AN using CPCT. 2. The two triangles are congruent, ASA criteria. AT ≅ AP, by CPCT. Angle T ≅ angle P. CT ≅ RP, by CPCT.
What are congruent triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.
If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.
1. For the given triangle HEY and triangle MAN we see that,
angle E ≅ angle A
angle Y ≅ angle N
and HE ≅ AM
Thus, the two triangles are congruent using the ASA criteria.
Also angle H ≅ angle M (CPCT)
HY ≅ MN
EY ≅ AN using CPCT.
2. For triangle CAT and PAR we have:
angle A ≅ angle A (vertically opposite angles)
Angle C ≅ angle R
AC ≅ AR
Thus, the two triangles are congruent using the ASA criteria.
Also, AT ≅ AP, by CPCT
Angle T ≅ angle P, by CPCT
CT ≅ RP, by CPCT.
3. For the triangles ACL and triangle ARS:
AC ≅ AR and angle 1 ≅ angle 2 (Given)
Also, angle A = angle A (Vertically opposite angle)
Thus, the two triangles are congruent using ASA criteria.
Now, angle 3 ≅ angle 4 using CPCT.
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Select the correct answer from each drop-down menu.
AABC is similar to ADEF. The ratio of the perimeter of AABC to the perimeter of ADEF is 1:10. The longest side of ADEF measures 4
The length of the longest side of AABC is
2
4
16
30
units. The ratio of the area of AABC to the area of ADEF is 1:100 v
Reset
Next
Triangle ABC's longest side is found as 4 units. Thus, Triangle DEF has a 100-times larger area than triangle ABC.
Explain about the ratios:A ratio is a tool being used compare the sizes of two or more quantities with relation to one another in mathematics. By making amounts easier to understand, ratios enable us to evaluate and express quantities.
Equivalent fractions equate to equivalent ratios.a is the antecedent whereas b is the consequent in the ratio a: b.In a ratio, the roles of antecedent with consequent cannot be switched.Given that both triangles remain similar, triangle DEF is 10 times larger than triangle ABC according to the ratio 1:10.
Triangle ABC's longest side will just be 1/10 of triangle DEF's longest side, or 4, since its longest side is 40.The square of a ratio of the sides of two comparable triangles is the ratio of respective areas.While the ratio of sides in this instance is 10/1 = 10, the ratio of areas forms : 10² = 100Thus, Triangle DEF has a 100-times larger area than triangle ABC.
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Solve the inequality and enter your solution as an inequality comparing the variable to your solution. 30 + x > 83
Answer:
x > 53
30 + x > 83
Subtract 30 from both sides:
x > 53
Therefore, the solution is:
x > 53
Name a radius
Name a chord
Name a tangent
Where is the point
of tangency?
B. C D
E
G
H
F
DH is radius.
EG is a chord
FI line is tangent to the circle
H is the point of tangency
Define the point of tangencyThe point of tangency is the point where a tangent line touches a curve or a circle at a single point, without intersecting it. At this point, the tangent line is perpendicular to the curve or circle at that specific point. The point of tangency is important in calculus and geometry, as it is used to calculate derivatives and solve problems related to circles, curves, and other geometrical figures.
In the given circle,
DH is radius.
(As it passes through center of circle and touches its circumference)
EG is a chord
(It divides the circle into two parts)
FI line is tangent to the circle
(It touches the line externally)
H is the point of tangency
(It is a point where the tangent of circle and circle meets)
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2. If Jon took a test and made the following scores: 72, 84, 92, 80, 96, 88, 45, 70, 79, 92, 87, and 103.
a. Box and Whisker plot:
b. What is the range:
IQR:
c. Are there any outliers?
3. If the mean is 77 and the standard deviation is 11 please find:
a.
A value 3 standard deviations above the mean
b.
A value 2.5 standard deviation below the mean
c. A value 2 standard deviations below the mean
d. A value 1 standard deviation above the mean
4. If 99.7 percent of the data is between 30 and 90, then please find the mean and the standard of deviation.
b. o:
a. u
5. If 68 percent of the data is between 42 and 58, then please find the mean and the standard of deviation.
b. a:
a. p
6. If 95 percent of the data is between 34 and 64, then please find the mean and the standard of deviation.
b. a:
a. µ
Someone please help with this page
Answer:
a)
103
|
96 +
|
92 | *
| * *
88 +--*
| *
84 |
|*
80 +
|
79 |
|
72 +
|
70 |
|
b)b. The range is the difference between the highest and lowest scores: 103 - 45 = 58.
The IQR is the interquartile range, which is the range of the middle 50% of the scores. To find it, we first need to find the first and third quartiles:
The first quartile (Q1) is the median of the lower half of the scores, which are 45, 70, 72, 79, and 80. The median of this set is (72+79)/2 = 75.5.
The third quartile (Q3) is the median of the upper half of the scores, which are 84, 87, 88, 92, and 96. The median of this set is (88+92)/2 = 90.
Therefore, the IQR is 90 - 75.5 = 14.5.
c)c. To find any outliers, we need to first define the "fences" of the box and whisker plot. The lower fence is Q1 - 1.5IQR = 75.5 - 1.514.5 = 53.25. The upper fence is Q3 + 1.5IQR = 90 + 1.514.5 = 112.75.
There is one score that is outside the fences: 103. Therefore, 103 is an outlier.
Step-by-step explanation:
need done asap only have 2 min
Answer 6
Step-by-step explanation: A = 1/2 bh, 6 x 2 is 12 and 1/2 of 12 is 6
Tami has two jobs and can work at most 20 hours each week. She works as a server and makes $6 per hour. She also tutors and makes $12 per hour. She needs to earn at least $150 a week. Choose the first inequality that represents this scenario
Answer:
B?
Step-by-step explanation:
Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise
her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.
Edward would like to use a round cast iron pan like his grandmother does.
What is the area of a 9-in. by 13-in. pan?
22 in.²
44 in.²
108 in.² 117 in.²
Answer:
117in
Step-by-step explanation: 9in x 13in=117in
So, Edward needs to use a round cast iron pan with a radius of 177 inches to have the same area as the rectangular pan. correct answer is (d).
How to find area of the circle?To find the area of a circle, you need to know its radius (the distance from the center of the circle to any point on its perimeter). Once you know the radius, you can use the following formula:
[tex]Area = \pi * radius^2[/tex]
where π (pi) is a mathematical constant approximately equal to 3.14159.
So, to find the area of a circle, follow these steps:
Measure the radius of the circle.
Square the radius (multiply it by itself).
Multiply the squared radius by π.
Round your answer to the desired number of decimal places (usually 1 or 2).
The area of a 9-in. by 13-in. rectangular pan is:
Area = length x width = 9 in. x 13 in. = 117 in.²
So, the area of the rectangular pan is 117 in.².
To use a round cast iron pan with the same area, Edward needs to find the radius of the circle with an area of 117 in.²:
Area of a circle = πr²
[tex]= \pi r^2[/tex]
[tex]= 117 in.^2 /[/tex]
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the complete question: Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise.
her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.
Edward would like to use a round cast iron pan like his grandmother does.
What is the area of a 9-in. by 13-in. pan?
[tex](a) 22in^{2} \\(b)44in^{2} \\(c)108in^{2} \\(d)117in^{2}[/tex]
Find the y-intercept for the equation:
y=2x+6
Y=2x+6
x=2y+6
2y=6-x/÷2
y=[tex]\frac{6-x}{2}[/tex]
A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box?
V = lwh
P = 2(l + w)
Answer: V(x) = -5x^2 + 70x
Step-by-step explanation:
Let the length and width of the rectangular base be represented by x and y, respectively.
Since the perimeter of the rectangular base is 28 cm, we have:
2x + 2y = 28
x + y = 14
The height of the box is given as 5 cm.
The volume of the box is given by:
V = lwh = xy(5)
V = 5xy
We can solve for y in terms of x from the equation x + y = 14:
y = 14 - x
Substituting this into the equation for the volume, we get:
V = 5x(14 - x)
Simplifying:
V = 70x - 5x^2
31. Given that f(x) = 55+x and g(x) = 5, it must be true
that (x) = ?
A. 11+
B. 11 + x
C. 11+5x
D. 55+
E. 55+5x
55 + 5x, because we substitute g(x) = 5 in f(x) and get the final function as f(g(x)) = 55 + 5x. option E
How determine if f(x) = 55+x and g(x) = 5 is trueWe are given two functions:
f(x) = 55 + x
g(x) = 5
We need to find the value of f(g(x)), which means we need to substitute g(x) in place of x in f(x).
f(g(x)) = f(5)
Therefore, we need to find f(5).
f(x) = 55 + x
f(5) = 55 + 5 = 60
So, the answer is E. 55 + 5x, because we substitute g(x) = 5 in f(x) and get the final function as f(g(x)) = 55 + 5x.
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The average 5-year-old child has a mass of 20 kg. Write this mass in
scientific notation. Approximately how many times larger is the elephant
than the child? Approximately how many water drops equal the mass of the
child? Explain your thinking.
Answer:
The mass of a 5-year-old child is 20 kg. We can express this mass in scientific notation as:
2 x 10^1 kg
To find approximately how many times larger an elephant is than a 5-year-old child, we need to know the mass of an elephant. According to National Geographic, an average elephant can weigh between 2,700 and 6,000 kg. Assuming an average weight of 4,350 kg for an elephant, we can calculate the ratio of elephant mass to child mass as follows:
4,350 kg / 20 kg ≈ 218
Therefore, an elephant is approximately 218 times larger than a 5-year-old child in terms of mass.
To determine approximately how many water drops equal the mass of a child, we need to know the mass of a single water drop. This can vary depending on the size of the drop and the substance it is made of. However, for the purposes of estimation, we can assume that the mass of a water drop is approximately 0.05 grams.
A specific bacteria is given a favorable growth medium, the bacteria has a growth rate of 30.5% every hour. In the beginning there are 100 bacteria, how many bacteria will there be in 36 hours? Round your answer to the nearest tenth.
a. 1550236.7 bacteria
b. 1452039.5 bacteria
c. 152.3 bacteria
d. 149.1 bacteria
Answer:
36hrs is 36/6.5=5.538 doubling periods. Initial population x0=100
Step-by-step explanation:
The rate of exponential growth of a bacterial culture is expressed as generation time, also the doubling time of the bacterial population. Generation time (G) is defined as the time (t) per generation (n = number of generations). Hence, G=t/n is the equation from which calculations of generation time (below) derive.
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These are just a few examples of real life situations where you might need to find the volume or surface area of a shape. There are many other situations where this knowledge is useful, including in scientific research, medical imaging, and many other fields.
What is volume?In mathematics, volume is the amount of space occupied by an object or a shape. It is a measure of how much three-dimensional space an object or a shape takes up. Volume is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or cubic inches (in³).
Here,
There are many real life situations where you might need to find the volume or surface area of a shape. Here are some examples:
Packaging and Shipping: In order to package and ship products, companies need to know the volume and surface area of the products and their packaging. For example, a shipping company needs to know the volume and surface area of a package in order to determine how much space it will take up in a truck or airplane, and how much packaging material will be required.
Construction: Architects, engineers and builders need to know the volume and surface area of building materials such as concrete, steel, bricks, and insulation in order to estimate the amount of materials required for a project. They also need to know the volume of a space to determine the amount of materials required to fill it, such as the amount of concrete required to fill a foundation or the amount of insulation needed to insulate a room.
Cooking and Baking: When cooking or baking, you may need to measure the volume or surface area of a container or cooking vessel to ensure that the recipe will fit and cook or bake properly. For example, you might need to measure the volume of a baking dish to know how much batter to use, or measure the surface area of a frying pan to know how much oil is needed.
Gardening and Landscaping: In gardening and landscaping, you may need to know the volume of soil required to fill a raised bed or the surface area of a lawn in order to determine the amount of fertilizer or weed killer required.
Industrial Design: In industrial design, designers need to know the volume and surface area of products in order to determine the materials required for production and to ensure that the product will fit in its intended location. For example, a designer may need to know the volume and surface area of a water tank to determine its capacity and the amount of materials required to build it.
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Of the 50 students Bryson surveyed, 15 are twelve years old, 20 are thirteen years old, and 15 are fourteen years old. If there are approximately 600 students at King Middle School, what is the best estimate of the proportion of students who are twelve, thirteen, and fourteen years old?
Answer:
Step-by-step explanation:
If 15 out of 50 students are twelve years old, we can estimate the proportion of twelve-year-olds in the whole school as follows:
Proportion of twelve-year-olds = 15/50
Simplifying this fraction by dividing both numerator and denominator by 5, we get:
Proportion of twelve-year-olds = 3/10
Similarly, if 20 out of 50 students are thirteen years old, we can estimate the proportion of thirteen-year-olds in the whole school as:
Proportion of thirteen-year-olds = 20/50
Simplifying this fraction by dividing both numerator and denominator by 10, we get:
Proportion of thirteen-year-olds = 2/5
Finally, if 15 out of 50 students are fourteen years old, we can estimate the proportion of fourteen-year-olds in the whole school as:
Proportion of fourteen-year-olds = 15/50
Simplifying this fraction by dividing both numerator and denominator by 5, we get:
Proportion of fourteen-year-olds = 3/10
Therefore, the best estimate of the proportion of students who are twelve, thirteen, and fourteen years old in the school, respectively, is:
3/10 are twelve years old
2/5 are thirteen years old
3/10 are fourteen years old
Solve the inequality, if possible. 3(5w+4)<12w+15
A. W<1
B. W<3/2
C. W>15
D. Not possible
Answer:
[tex]3(5w + 4) < 12w + 15[/tex]
[tex]15w + 12 < 12w + 15[/tex]
[tex]3w < 3[/tex]
[tex]w < 1[/tex]
A is the correct answer.
9x9x9x9 using an exponet
Answer:
9⁴
Step-by-step explanation:
If I'm understanding what you're asking correctly, it would just be the answer above, which evaluates to 6561.
Smithson Mining operates a silver mine in Nevada. Acquisition, exploration, and development costs totaled $7.6 million. After the silver is extracted in approximately five years, Smithson is obligated to restore the land to its original condition, including constructing a wildlife preserve. The company’s controller has provided the following three cash flow possibilities for the restoration costs: (1) $700,000, 25% probability; (2) $750,000, 40% probability; and (3) $850,000, 35% probability. The company’s credit-adjusted, risk-free rate of interest is 8%.
What is the book value of the asset retirement liability at the end of one year?
Assuming that the actual restoration costs incurred after five years are $796,000, what amount of gain or loss will Smithson recognize on retirement of the liability?
Smithson will recognize the loss. So,the amount of loss will Smithson recognize on retirement of the liability is $309,248.85.
What is profit or loss?Profit or loss is the financial gain or loss resulting from the difference between revenue and expenses in a business or financial context.
Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization
PV = PMT x (1 - 1 / (1 + r)ⁿ) / r
The formula for weighted average is:
Weighted average = (Cash flow 1 x Probability 1) + (Cash flow 2 x Probability 2) + (Cash flow 3 x Probability 3)
PV = (700,000 x 0.25 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (750,000 x 0.4 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (850,000 x 0.35 x (1 - 1 / (1 + 0.08)⁵) / 0.08)
PV = $2,317,283.36
Since this is the end of the first year, the accumulated depreciation and amortization is simply the present value of the estimated cash flows for the first year:
Accumulated depreciation and amortization = (700,000 x 0.25 / (1 + 0.08)) + (750,000 x 0.4 / (1 + 0.08)) + (850,000 x 0.35 / (1 + 0.08))
Accumulated depreciation and amortization = $1,830,532.21
Finally, we can calculate the book value of the ARL at the end of one year:
Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization
Book value of ARL = $2,317,283.36 - $1,830,532.21
Book value of ARL = $486,751.15
Therefore, the book value of the asset retirement liability at the end of one year is $486,751.15.
Loss = Actual restoration costs - Book value of ARL
Loss = $796,000 - $486,751.15
Loss = $309,248.85
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You pick a card at random. Without putting the first card back, you pick a second card at random. 4 5 6 7 What is the probability of picking a 7 and then picking a 7? Write your answer as a percentage.
The probability of picking a 7 and then picking a 7 is 8.33%.
EquationsSince we are not replacing the first card before drawing the second one, the probability of drawing a 7 on the first card is 1/4. After drawing the first card, there are three remaining cards, and only one of them is a 7. Therefore, the probability of drawing a 7 on the second card given that the first card was a 7 is 1/3.
Using the multiplication rule of probability, the probability of drawing a 7 on the first card and then drawing a 7 on the second card without replacement is
P(7 on the first card) x P(7 on the second card | 7 on the first card) = (1/4) x (1/3) = 1/12
P(7 on the first card and then a 7 on the second card) = 1/12 x 100% = 8.33%
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Quadrilateral ABCD with vertices A(0, 6), B(-3, -6), C(-9.-6), and D(-12, -3):
a) dilation with scale factor of 1/3 centered at the origin
b) translation along the vector (-5, -1)
Part (a)
Answers:
A' = (0, 2)
B' = (-1, -2)
C' = (-3, -2)
D' = (-4, -1)
Explanation:
Multiply each coordinate by 1/3.
For instance,
[tex]B(-3,-6) \to B( -3*(1/3), -6*(1/3) ) \to B \ '(-1, -2)[/tex]
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Part (b)
Answers:
A' = (-5, 5)
B' = (-8, -7)
C' = (-14, -7)
D' = (-17, -4)
Explanation:
Subtract 5 from the x coordinate. Subtract 1 from the y coordinate. This moves each point 5 units to the left and 1 unit down.
I'll show an example using point C.
[tex](\text{x},\text{y})\to(\text{x}-5,\text{y}-1)\\\\(-9,-6)\to(-9-5,-6-1)\\\\(-9,-6)\to(-14,-7)\\\\[/tex]
Therefore, C(-9,-6) moves to C ' (-14,-7)
Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial:
0.01b^2+ ∗ +100c^2
The square of the binomial that represents the trinomial is [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.
What is Trinomial ?
A trinomial is a polynomial that consists of three terms. In algebra, a term is a combination of a constant and one or more variables, multiplied together. A trinomial, therefore, is a polynomial that has three such terms.
To represent the trinomial 0.01[tex]b^{2}[/tex]+ ∗ +100[tex]c^{2}[/tex] as a square of a binomial, we need to find a monomial that can be added to it to form a perfect square trinomial.
To do this, we can take the square root of the first and last terms of the trinomial and multiply them together:
√(0.011[tex]b^{2}[/tex]) = 0.1b
√(100[tex]c^{2}[/tex]) = 10c
Multiplying these square roots together, we get:
0.1b * 10c = b * 1c * 10 = 10bc
So, the missing monomial is 10bc. Adding this monomial to the original trinomial gives us:
0.011[tex]b^{2}[/tex] + 10bc + 100[tex]c^{2}[/tex] = [tex](0.1b+10c)^{2}[/tex],
Therefore, the square of the binomial that represents the trinomial is [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.
To learn more about Trinomial from given link.
https://brainly.com/question/11202722
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PLEASE HELP ASAP!!!!
The distance between two cities on a map is 25 inches. The actual distance between the two cities is 500 miles. How many miles would 35 inches be on the map?
1.75 miles
20 miles
510 miles
700 miles
Question 2(Multiple Choice Worth 2 points)
(Circumference LC)
What is the circumference of a circle with a diameter of 21 cm? Approximate using pi equals 22 over 7.
7 cm
33 cm
66 cm
132 cm
Question 3(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures LC)
An image of a rhombus is shown.
A rhombus with a base of 17 inches and a height of 14 inches.
What is the area of the rhombus?
62 in2
119 in2
124 in2
238 in2
Question 4(Multiple Choice Worth 2 points)
(Surface Area of Cylinders LC)
Which equation would calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown?
a cylinder with the diameter labeled 2.8 centimeters and the height labeled 3.7 centimeters
SA = 2π(1.4)2 + 2.8π(3.7)
SA = 2π(1.4)2 + 1.4π(3.7)
SA = 2π(2.8)2 + 2.8π(3.7)
SA = 2π(2.8)2 + 1.4π(3.7)
Question 5(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 10 feet. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water will it take to fill up the pool completely? Use π = 3.14 and round to the nearest gallon.
63 gallons
471 gallons
1,409 gallons
3,523 gallons
Question 6(Multiple Choice Worth 2 points)
(Surface Area of Cylinders MC)
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
14 and 1 over 7 in2
23 and 4 over 7 in2
47 and 1 over 7 in2
84 and 6 over 7 in2
Question 7(Multiple Choice Worth 2 points)
(Area of Circles LC)
A circle with a diameter of 34 inches is shown.
circle with diameter of 34 inches
What is the area of the circle using π = 3.14?
53.38 in2
106.76 in2
907.46 in2
3,629.84 in2
Question 8(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A cylinder with a diameter of 8 yards has a volume of 452.16 yd3. What is the height of the cylinder? Use 3.14 for π.
2 yards
8 yards
9 yards
18 yards
Question 9(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.2 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
96.93 cubic inches
553.90 cubic inches
581.59 cubic inches
2,326.36 cubic inches
Question 10(Multiple Choice Worth 2 points)
(Surface Area of Cylinders MC)
A cylindrical can of vegetables has a label wrapped around the outside, touching end to end. The only parts of the can not covered by the label are the circular top and bottom of the can. If the area of the label is 100π square inches and the radius of the can is 5 inches, what is the height of the can?
25 inches
20 inches
10 inches
5 inches
Question 11(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 6 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 4 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 5 centimeters.
What is the area of the tile shown?
34.5 cm2
45 cm2
54 cm2
57.5 cm2
Question 12(Multiple Choice Worth 2 points)
(Area of Circles MC)
A circular cookie cake costs $12.56. If the diameter of the cookie cake is 8 inches, what is the approximate cost per square inch of the cookie cake? Use π = 3.14.
$0.04
$0.06
$0.16
$0.25
Question 13(Multiple Choice Worth 2 points)
(Surface Area of Cylinders MC)
The net of a right circular cylinder is shown.
net of a cylinder where the radius of each circle is labeled 4 meters and the height of the rectangle is labeled 8 meters
What is the surface area of the cylinder? Use π = 3.14 and round to the nearest whole number.
251 m2
301 m2
502 m2
804 m2
Question 14(Multiple Choice Worth 2 points)
(Scale Factor MC)
The state of Colorado is 4 centimeters long and 2 centimeters wide on a map. A cartographer wants to use a scale factor of 3.5 to enlarge the map. What is the area of the enlarged map?
98 cm2
42 cm2
28 cm2
8 cm2
Question 15(Multiple Choice Worth 2 points)
(Circumference MC)
A race car drove around a circular track that was 0.5 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.
124.20 feet
248.41 feet
420.38 feet
840.76 feet
Answer: first one is 700
Step-by-step explanation: