The solution to the simultaneous equations log₂x − log₂y = 2 and log₂(x − 2y) = 3 is x = 8 and y = 4.
Solving the simultaneous equationsGiven the following equations
log₂x − log₂y = 2
log₂(x − 2y) = 3
We can simplify the first equation by using the rule of logarithms that states:
log a - log b = log(a/b)
Using this rule, we have:
log₂(x/y) = 2
Rewriting this in exponential form, we get:
x/y = 2²
xy = 4
Multiplying both sides by y, we get:
x = 4y
Substituting this into the second equation, we get:
log₂(4y − 2y) = 3
log₂(2y) = 3
Rewriting this in exponential form, we get:
2y = 8
Dividing both sides by 2, we get:
y = 4
Substituting this value into the equation 2y = x, we get:
x = 2 * 4
x = 8
Hence, the solution to the simultaneous equations is x = 8 and y = 4.
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Complete question
Solve the simultaneous equations :
log2x − log2y = 2
log2(x − 2y) = 3
Three and seven tenths times five
Answer:
6.5
Step-by-step explanation:
3 + (and) 7/10 x 5 = 6.5
Hope this helps!
Please HELP I have a math test tommorow and I ned to study!!
This is one of the questions..
If y is directly proportional with x and y = 36 when x = 30, what is the value of y when x = 25?
THANK YOU!! <3
The value of y when x = 25 is 30
What are direct variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
given y is directly proportional to x then the equation connecting them is
y = kx ← k is the constant of proportionality
To find k use the condition y = 36 when x = 30
So, 36=k(30)
=> k = 36/30 = 1.2
equation of proportionality:
y=1.2x
When x = 25 then
y=1.2(25) = 30
The value of y when x = 25 is 30
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Franklin is an ecologist monitoring the catfish population in Athena Lake each year. When he first started monitoring the population one year ago, he estimated that there were 800 catfish in the lake. Today, Franklin estimates the population has decreased to 760 and it will continue decreasing each year.
The exponential model for the population of catfish in Athena Lake is:
P(t) = 800 × e^{-0.0513t}
What is exponential ?
an exponential function is a function of the form:
f(x) = a^{x}
where a is a positive constant called the base, and x is the exponent. The base represents the factor being repeatedly multiplied, while the exponent represents the number of times the base is being multiplied by itself.
To model the decreasing population of catfish in Athena Lake, we can use an exponential function of the form:
P(t) = P0 × e^{-rt}
where:
P(t) is the population at time t
P0 is the initial population
r is the annual growth rate (in this case, a negative value representing a decreasing population)
e is the mathematical constant e (approximately 2.71828...)
t is the time elapsed (measured in years)
In this case, we know that the initial population P0 is 800, and that the current population P(1) is 760 (since Franklin started monitoring one year ago and estimates the population has decreased to 760). So we can use these values to solve for the annual growth rate r:
760 = 800 × e^{-r}
Dividing both sides by 800, we get:
0.95 = e^{-r}
Taking the natural logarithm (ln) of both sides, we get:
ln(0.95) = -r
Solving for r, we get:
r ≈ 0.0513
So the exponential model for the population of catfish in Athena Lake is:
P(t) = 800 × e^{-0.0513t}
where t is the time elapsed (measured in years).
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What is the value of m ?
Answer:
Step-by-step explanation:
90-28=62
62 is the answer
A plane is 148 mi north and 167 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree
Therefore, the pilot should turn by approximately 41.8 degrees to fly directly to the airport.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It has applications in various fields, such as engineering, physics, architecture, and astronomy. Trigonometry is based on the use of six fundamental trigonometric functions, which are sine, cosine, tangent, cosecant, secant, and cotangent. These functions are defined in terms of the ratios of the sides of a right triangle. In a right triangle, one angle is a right angle, which measures 90 degrees, and the other two angles are acute angles, which are less than 90 degrees. The three sides of a right triangle are called the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the longest side, and it is always opposite to the right angle. The adjacent side is the side that is adjacent to the angle of interest, and the opposite side is the side that is opposite to the angle of interest.
Here,
We can use trigonometry to find the angle x that the pilot should turn in order to fly directly to the airport.
First, let's draw a diagram of the situation:
A(airport)
|\
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
P x mi
In the diagram, P represents the position of the plane, which is 148 miles north and 167 miles east of the airport A. The line labeled "x mi" represents the distance that the plane needs to fly in order to reach the airport, and the angle x is the angle between the line x mi and the line representing the eastward direction.
To find x, we can use the trigonometric ratio for tangent (tan):
tan(x) = opposite/adjacent
In this case, the opposite side is 148 miles (the distance north of the airport) and the adjacent side is 167 miles (the distance east of the airport). Therefore:
tan(x) = 148/167
Using a calculator, we can find that:
tan(x) ≈ 0.8868
To find x, we need to take the arctangent (tan⁻¹) of both sides:
x = tan⁻¹(0.8868)
Using a calculator, we find that:
x ≈ 41.8°
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a regular hexagon is truncated to form a regular dodecagon (12-gon) by removing identical isosceles triangles from its six corners. what percent of the area of the original hexagon was removed? express your answer to the nearest tenth.
0%.
The area of a regular hexagon is given by A = (3√3/2)s2, where s is the length of one side of the hexagon. To calculate the percent of the area of the original hexagon that was removed, we need to calculate the area of the dodecagon and subtract it from the area of the hexagon.
The area of a regular dodecagon is given by A = 3(3 + 2√3)s2, where s is the length of one side of the dodecagon.
Let's assume that the side length of the original hexagon is s, and the side length of the resulting dodecagon is sd. Since each of the isosceles triangles removed has base length of s and height of s/2, we can find the side length of the dodecagon as sd = √3s.
Substituting this into the area formula for the dodecagon, we get:
Ad = 3(3 + 2√3)sd2
Ad = 3(3 + 2√3) (√3s)2
Ad = 3(3 + 2√3)(3s2)
Ad = 27s2
Therefore, the area of the dodecagon is 27 times the area of the original hexagon.
The percent of the area of the original hexagon that was removed is given by the following formula:
Percent removed = 100 x (Ahex - Adod) / Ahex
Percent removed = 100 x (Ahex - 27Ahex) / Ahex
Percent removed = 100 x (1 - 27) / 1
Percent removed = 100 x (-26) / 1
Percent removed = -2600 / 1
Percent removed = -2600%
Since the percent of the area of the original hexagon that was removed cannot be negative, the correct answer is 0%.
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Profit is the money made when a business' income is more than its expenditure. Loss is the money lost when a business' expenditure is more than its income. For each of the businesses below, state whether they made a profit or a loss. Business A B C Income £100 £49.85 £21,357 Expenditure £200 £71.24 £7,028
For each of the businesses below:
Business A: Loss (Income £100 - Expenditure £200 = -£100)
Business B: Loss (Income £49.85 - Expenditure £71.24 = -£21.39)
Business C: Profit (Income £21,357 - Expenditure £7,028 = £14,329)
What is percent?Percent is a term used to describe a fraction or ratio as a portion of 100. It is commonly denoted by the symbol %, which means "per hundred." For example, the percentage 50% means 50 out of 100 or 0.5 as a fraction. Percentages are often used to express change, growth, or comparison between different quantities. Percentages are commonly used in many fields, including finance, science, and statistics, to express values in a more convenient and easily interpretable way.
Here,
Business A:
Income = £100
Expenditure = £200
Profit/Loss = Income - Expenditure = £100 - £200 = -£100
Since the result is negative, the business made a loss.
Business B:
Income = £49.85
Expenditure = £71.24
Profit/Loss = Income - Expenditure = £49.85 - £71.24 = -£21.39
Since the result is negative, the business made a loss.
Business C:
Income = £21,357
Expenditure = £7,028
Profit/Loss = Income - Expenditure = £21,357 - £7,028 = £14,329
Since the result is positive, the business made a profit.
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WILL GIVE BRAINLIEST. IM IN A HURRY! A cube-shaped box has an edge length of 4/5 meter.
What is the volume of the container?
Enter your answer, as a fraction in simplest form, in the box.
The hypotenuse of a right triangle measures 5 cm and one of its legs measures 3 cm. Find the measure of the other leg
Answer:
16
Step-by-step explanation:
a^2 + b^2 = c^2
a^2= 3^2 = 9
c^2=5^2 = 25
25-9= b^2
25-9=16
b^2 = 16
Calculate the Value of x.
Answer:
[tex]\large\boxed{\mathtt{x=44^{\circ}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the value of x.}[/tex]
[tex]\textsf{We should know that} \ \angle \textsf{CAB is an Interior Angle.}[/tex]
[tex]\large\underline{\textsf{What is an Interior Angle?}}[/tex]
[tex]\textsf{An Interior Angle is any angle that is inside of a circle. It's formed by 2 Chords.}[/tex]
[tex]\large\underline{\textsf{What is a Chord?}}[/tex]
[tex]\textsf{A Chord is any line segment inside of a circle. Its' endpoints are on the circumference.}[/tex]
[tex]\textsf{Because Interior Angles are formed by Chords, the arc within its endpoints is}[/tex]
[tex]\textsf{half of the measurement of the Interior Angle.}[/tex]
[tex]\large\underline{\textsf{For this problem;}}[/tex]
[tex]\mathtt{x=\frac{1}{2} \widehat{BC}}[/tex]
[tex]\textsf{We can't find x right away. We should find} \ \mathtt{ \widehat{BC}} \ \textsf{first.}[/tex]
[tex]\textsf{We are given} \ \mathtt{\widehat{AC} = 92^{\circ}.}[/tex]
[tex]\textsf{The Arcs around a circle add up to 360}^{\circ}.[/tex]
[tex]\overline{AB} \ \textsf{is a diameter. The arc will equal 180}^{\circ}.[/tex]
[tex]\large\underline{\textsf{Solve for BC;}}[/tex]
[tex]\mathtt{92^{\circ}+180^{\circ}+\widehat{BC} = 360^{\circ}.}[/tex]
[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]
[tex]\mathtt{272^{\circ}+\widehat{BC} = 360^{\circ}.}[/tex]
[tex]\large\underline{\textsf{Subtract 272 from both sides of the equation:}}[/tex]
[tex]\mathtt{\widehat{BC} = 88^{\circ}.}[/tex]
[tex]\large\underline{\textsf{Remember that;}}[/tex]
[tex]\mathtt{x=\frac{1}{2} \widehat{BC}}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{x=\frac{1}{2} (88^{\circ})}[/tex]
[tex]\large\underline{\textsf{Multiply:}}[/tex]
[tex]\large\boxed{\mathtt{x=44^{\circ}}}[/tex]
suppose a class has 50 students, and 10 of them are math majors. in how many ways can the students be lined up so that all the math majors are in the front half of the line?
If the class has 50 students, and 10 of them are math majors There are a total of 50! (50 factorial) ways to line up the 50 students.
To ensure that all the 10 math majors are in the front half of the line, the first 10 positions in the line must be filled by the math majors, leaving 40 positions in the second half to be filled by the remaining 40 students.
Thus, there are 10! (10 factorial) ways to fill the first 10 positions and 40! (40 factorial) ways to fill the second half.
Therefore, the total number of ways to line up the students so that all the math majors are in the front half of the line is
10! × 40! = 30,240,000.
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Determine whether each expression can be used to find the length of segment AB.
AB= 10sinC
AB = 10cosA
AB = 8tanA
AB= 8tanC
A
B
27
8
10
C
The length of segment AB, is calculated using the formulae velow
AB = 10 sin CAB = 10 cos AAB = 8 tan CHow to the formulae for length of ABInformation from the question
a figure of right triangle
The length of AB is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The length of AB is solved using sin, cos and tan as follows
Sin = opposite / hypotenuse - SOH
sin C = AB / 10
AB = 10 Sin C
Cos = adjacent / hypotenuse - CAH
cos A = AB / 10
AB = 10 cos A
Tan = opposite / adjacent - TOA
tan C = AB / 8
AB = 8 tan C
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how much greater is 4/5 than 3/4?????
Answer:
To find how much greater 4/5 is than 3/4 we can turn them into decimal values:
4/5 = 0.8
3/4 = 0.75
0.8 - 0.75 = 0.05
4/5 is 0.05 or 1/20 greater than 3/4
(2)
Each hemisphere has three basic wind systems. The first, at 30( latitude north and south,
is known as the (3).
There, air sinks, warms, and moves toward the
equator from northeast to southwest in the northern hemisphere and from southeast to
northwest in the southern hemisphere. When the air reaches the equator, it rises, then moves
back toward 30( to start the cycle again. These winds from both hemispheres converge at the
equator. They are forced upward, creating an area of (4)
This area
near the equator is called the (5).
The second wind system, called the (6)
flows between 300 and
60 Latitude north and south of the equator. Its circulation pattern is opposite that of the
wind system discussed above. These winds are responsible for the movement of many
weather systems across much of (7)
The third wind system, the (8).
Latitude. In the northern hemisphere, these winds flow from the (9)
to the (10)
lies between the poles and 60(
They flow in the opposite direction in the southern
hemisphere.
Narrow bands of fast, high-altitude, westerly winds called (11)
flow at the boundaries between wind zones in the middle latitudes. These bands of
wind steer weather systems in the middle latitudes. The most important one, the
(12)
separates the polar easterlies from the prevailing westerlies.
En la situación de la alberca olímpica cuyo volumen es de 3750m³.¿Que capacidad de agua tiene?
Answer:
Step-by-step explanation:
Y
in 2005 the population of a district was 35,700 with a continuous annual growth rate of approximately 4%, what will the population be in 2030 according to the exponential growth function?
The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.
The formula for the continuous exponential growth is given by the formula:
P = Pe^(rt)
where,P is the population in the future.
P0 is the initial population.
t is the time.
r is the continuous interest rate expressed as a decimal.
e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.
Therefore, t = 25.We will now use the formula:
P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.
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Answer: I got 97,042.7
Step-by-step explanation:
Find the value of M.
A) 20,
B)10,
C)36,
D)100
In the given parallelogram, The value of M is option B) 10 , so values of given angles is 50°.
What is parallelogram?Parallelogram is type of quadrilateral with two pairs of parallel sides.
The opposite sides of parallelogram are congruent in length.
The opposite angles of parallelogram are congruent in measure.
The adjacent angles of parallelogram are supplementary (add up to 180 degrees).
The area of parallelogram can be calculated by multiplying the length of its base by its height.
Since ABCD is parallelogram, then opposite angles are congruent. Therefore, we have:
∠ABD = ∠ABC = 5M° (opposite angles in a parallelogram)
∠ABD = ∠CBD (alternate interior angles formed by transversal BD)
∠CBD = ∠BCD = 3M+20° (opposite angles in a parallelogram)
Thus, we have:
5M° = ∠ABD = ∠CBD = 3M+20°
Solving for M, we get:
5M° - 3M - 20° = 0
2M = 20°
M = 10°
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The surface area of the right triangular prism is 376.8 cm²
What is the value of x? Show your work.
In response to the stated question, we may state that As a result, the prism value of x is around 6.432 cm.
what is prism?A prism is a polyhedron with either an n-sided polygonal basis, a second base that is a shifted copy of the original base, and n extra faces (essentially all parallelograms), with two connecting the corresponding sides of the base. Any cross sections those are parallel to the base are translations of it. A prism is a three separate, solid, three-dimensional object with two faces. It has the same merge, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with out any bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by planes that are obliquely oriented to one another. A typical prism has two triangular faces and parallel square faces. They are made of either glass or metal.
Two congruent triangles and three rectangular faces make up the right triangular prism.
L is the length of the rectangular faces.
W is the width of the rectangular faces.
H is the height of the rectangular faces and the prism.
B is the triangle's base.
x is the height of the triangles.
SA = 2B + PH
B = 1/2 * base * height
B = 1/2 * 13 cm * x = 6.5x cm²
P = 13 cm + 5 cm + x = 18 cm + x
SA = 2B + PH
376.8 cm² = 2(6.5x cm²) + (18 cm + x)(12 cm)
376.8 cm² = 13x cm² + (18 cm)(12 cm) + 12x cm²
376.8 cm² = 25x cm² + 216 cm²
25x cm² = 376.8 cm² - 216 cm²
25x cm² = 160.8 cm²
x = 6.432 cm
As a result, the value of x is around 6.432 cm.
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in a sample of men, said that they had less leisure time today than they had years ago. in a sample of women, women said that they had less leisure time today than they had years ago. at , is there a difference in the proportions? use for the proportion of men with less leisure time
The test static for sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago is 0.2377.
A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.
In order to determine whether to accept or reject your null hypothesis, the test statistic is utilised to calculate the p value of your findings.
In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago.
In a sample of 50 women, 48 women said that they had less leisure time than they
had 10 years ago.
p-hat men:: 44/50 = 0.22
p-hat women:: 48/50 = 0.24
Test Stat:
z(0.24-0.22) =[tex]\frac{0.02}{\sqrt{[(0.22*0.78/50)+(0.24*0.76/50)]} }[/tex] = 0.2377
At [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women
[tex]p-value = 2*P(z > 0.2377) = 0.8121[/tex]
Since the p-value is greater than 5%, fail to reject H.
H: p(men)-p(women) = 0
Ha: p(men)-p(women) # 0 = .05, is there a difference in the proportions between the men and women
p-value = 2*P(z > 0.2377) = 0.8121
Since the p-value is greater than 5%, fail to reject H.
H: p(men)-p(women) = 0
Ha: p(men)-p(women) # 0
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Complete question:
In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. What is the test statistic? At [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women?
the diameter of a gazebo is 15 ft. what is its circumference? round the answer to one decimal place:
The circumference of a gazebo is 47.1 ft
To calculate the circumference, you can use the formula C=2πr. This formula states that the circumference of a circle is equal to two times the constant π (approximated as 6.28) multiplied by the radius of the circle. The radius of a circle is equal to half of the diameter, so in this case the radius would be 7.5 ft (half of 15 ft).
Therefore, to calculate the circumference of a gazebo with a diameter of 15 ft, you can use the formula C=2πr. Plugging in the radius of 7.5 ft, the equation would become C=2π(7.5) which results in a circumference of 47.12 ft. To round this answer to one decimal place, the final answer is 47.1 ft
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which of the following is not a characteristic of the normal probability distribution? 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
The false statement regarding the normal distribution is given as follows:
99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The percentage of scores within 1 standard deviation of the mean is obtained considering that:
The p-value of Z = 1 is of 0.8413.The p-value of Z = -1 is of 0.1587.Hence the percentage is given as follows:
84.13 - 15.87 = 68.26%, which is different of 99.72%.
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The correct answer is that all of the following are characteristics of the normal probability distribution as given below.
What is a probability?A subfield of statistics known as probability studies random events and their likelihood of happening.
The statement "99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean" is actually a characteristic of the normal probability distribution.
The correct answer is that all of the following are characteristics of the normal probability distribution:
It is a continuous probability distribution, which means that it can take on any value within a certain range.It is symmetric around its mean.It is described by two parameters: its mean and standard deviation.The area under the curve of the probability density function is equal to 1.A large proportion (68.27%) of the data falls within one standard deviation of the mean, an even larger proportion (95.45%) falls within two standard deviations of the mean, and an even larger proportion (99.73%) falls within three standard deviations of the mean.To know more about probability, visit:
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You See I Have This Monster Under My Bed And Every 8 Hours He Eats 4 Cupcakes , Id Like To Buy Egnogh For The Next 24 Hours How Many Would I Need To Buy
Answer: 12 cupcakes
Step-by-step explanation:
24/8 = 3
3x4=12
Answer:
The answer to your problem is, 12
Step-by-step explanation:
First, we want to know the problem:
24 ÷ 8 = ?
? = 3
Next, we can do some easy multiplication such as the following:
3 x 4 = ?
? = 12.
Thus, the answer to your problem is, 12
I’m a little confused on this, also this is about complementary and supplementary angles.
Answer:
1. 48
2. 103
3. 47
4. 60
hope this helps
A cone has a radius of 3 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 9 inches?
We can use the fact that the ratio of the corresponding lengths in two similar shapes is equal to the ratio of their corresponding surface areas. Since we are looking for the surface area of a similar cone with radius 9 inches, we need to find the ratio of the surface area of that cone to the surface area of the original cone with radius 3 inches.
The surface area of a cone is given by:
surface area = πr(r + l)
where r is the radius and l is the slant height.
For the original cone with radius 3 inches and slant height 12 inches, we have:
surface area of original cone = π(3)(3 + 12) = 45π
For the similar cone with radius 9 inches, we can find the slant height using the fact that the slant height and radius are proportional in similar cones. Specifically, the ratio of the slant heights is equal to the ratio of the radii. Therefore:
slant height of similar cone = (9/3)(12) = 36 inches
Using this slant height and the radius of 9 inches, we can find the surface area of the similar cone:
surface area of similar cone = π(9)(9 + 36) = 405π
Finally, we can find the ratio of the surface areas:
ratio of surface areas = surface area of similar cone / surface area of original cone
= (405π) / (45π)
= 9
Therefore, the surface area of the similar cone is 9 times the surface area of the original cone. The exact surface area of the similar cone is 9 times the surface area of the original cone, or:
9 × 45π = 405π square inches
Answer:405pi in^2
Step-by-step explanation:
Which statements about this system of equations are true? Check all that apply
2 x minus 7 y = negative 13. Negative 2 x + 11 y = 1.
The x-variable will be eliminated when adding the system of equations.
The y-variable will be eliminated when adding the system of equations.
The sum of the system of equations is 4 y = negative 12.
x = 17
y = negative 3
There are infinitely many solutions to the system of equations.
As a result, (x, y) = is the answer to a set of equations. (-17, -3). There aren't an endless number of answers because there is a single one.
What sort of equation would that be?The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.
The statements that are true about this system of equations are:
The x-variable will be eliminated when adding the system of equations.
There are infinitely many solutions to the system of equations.
To eliminate the x-variable, we can add the two equations as follows:
(2x - 7y) + (-2x + 11y) = -13 + 1
Simplifying the left-hand side and the right-hand side gives:
4y = -12
Dividing both sides by 4 yields:
y = -3
Substituting y = -3 into either of the original equations gives:
2x - 7(-3) = -13
Simplifying this equation yields:
2x + 21 = -13
Subtracting 21 from both sides yields:
2x = -34
Dividing both sides by 2 yields:
x = -17
Therefore, the solution to the system of equations is (x, y) = (-17, -3). Since there is a unique solution, there are not infinitely many solutions.
The statement "The sum of the system of equations is 4y = -12" is false since the sum of the equations does not simplify to that expression.
The statement "x = 17" is false since the correct solution is x = -17.
The statement "The y-variable will be eliminated when adding the system of equations" is false since adding the equations only eliminated the x-variable.
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a mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 24,000 miles and a standard deviation of 2700 miles. he wants to give a guarantee for free replacement of tires that don't wear well. how should he word his guarantee if he is willing to replace approximately 10% of the tires?
To word his guarantee for free replacement of tires, the mechanic needs to determine the minimum life expectancy that the tires must meet in order to replace approximately 10% of them.
Since the life expectancy of the tires is normally distributed, we can use the standard normal distribution and the z-score formula to determine the minimum life expectancy that corresponds to a probability of 10%:
z = (x - μ) / σ
where z is the z-score, x is the minimum life expectancy, μ is the mean life expectancy of 24,000 miles, and σ is the standard deviation of 2700 miles.
Solving for x, we get:
x = zσ + μ
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to a probability of 10%, which is approximately -1.28. Plugging this into the formula, we get:
x = (-1.28) * 2700 + 24000
x ≈ 20,856 miles
Therefore, the mechanic should guarantee free replacement of tires that wear out before reaching a mileage of approximately 20,856 miles, in order to replace approximately 10% of the tires.
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What is the area of the parallelogram? 50 points each if u answer 100 points in total answer please
Responses
18 square units
21 square units
16 square units
28 square units
Answer:
A = 21 units²
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height between parallel sides )
here b = 7 and h = 3 , then
A = 7 × 3 = 21 units²
A little help :) Appreciated - 40 points
Select the true statements. Select the two correct answers. A. 1 . 01 < 0 . 99 1 . 01 < 0 . 99 B. 4 . 5 = 4 . 50 4 . 5 = 4 . 50 C. 3 . 5 < 3 . 39 3 . 5 < 3 . 39 D. 1 . 51 > 1 . 15 1 . 51 > 1 . 15 E. 2 . 09 = 2 . 9
The true statements are:
B. 4.5 = 4.50 (both sides are equal to 4.5, with the same number of significant figures)
D. 1.51 > 1.15 (1.51 is greater than 1.15)
What is system of inequalities ?
A system of inequalities is a set of two or more inequalities with one or more variables. The solution to a system of inequalities is the set of all possible values of the variables that satisfy all the inequalities in the system simultaneously. In other words, it is the intersection of the solution sets of each individual inequality in the system.
According to the question:
The two correct statements are B and D.
B is true because trailing zeros after a decimal point do not change the value of a number, so 4.5 is equal to 4.50.
D is true because 1.51 is greater than 1.15, as the digits to the right of the decimal point represent fractions of a whole number, so 0.51 is greater than 0.15.
A is false because 1.01 is greater than 0.99.
C is false because 3.5 is greater than 3.39.
E is false because 2.09 is not equal to 2.9.
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A company records the value of a machine used for production at $25,000. As the machine ages, its value depreciates, that is, decreases in value. If the depreciation is estimated to be 20% of the value of the machine at the end of each year, what is the expected value of the machine after 6 years?
The expected value of the machine after 6 years is approximately $4086.
To find the value of the machine after each year, we can use the formula:
Vn = V0 x (1 - r)ⁿ
where Vn is the value of the machine at the end of year n, V0 is the initial value of the machine, r is the depreciation rate (0.20 in this case), and n is the number of years.
For the first year, we have:
V1 = 25000 x (1 - 0.20)¹ = 20000
For the second year, we have:
V2 = 25000 x (1 - 0.20)² = 16000
Continuing this pattern, we find that the value of the machine at the end of the sixth year is:
V6 = 25000 x (1 - 0.20)⁶ = 4085.76
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