The inverse of this function can be written as x=log(y/100)/log(1.05), where log is the natural logarithm (base e).
What is function?A function is a set of instructions that performs a specific task when called upon. It is a fundamental concept in programming languages that allows code to be written once and reused multiple times. Functions are used to break down complex tasks into smaller, more manageable pieces of code that can be tested and debugged independently. This modular approach to software development helps make code more efficient, easier to read and maintain, and less prone to errors. Functions can accept input in the form of parameters, or variables, and may optionally return a result.
This inverse function can be interpreted as the number of years it has taken for the cost per night at the hotel to reach a given value y. In other words, x represents the number of years since the hotel opened at which the cost per night is y.
To learn more about function
https://brainly.com/question/22340031
#SPJ1
help me find the missing sides to solve this equation
For the equilateral triangles we have:
1) x = 5, y = √50
2) a = 2, b = √8
3)y = 8, x = √128
4) a = b = 7/√2
How to find the missing sides?We can see some triangles, remember that for a right triangle whose angles are 45°, we have an equilateral triangle.
So the two legs have the same measure.
1) Here we can see that x = 5, and the hypotenuse is given by:
y^2 = 5^2 + 5^2
y^2 = 50
y = √50
2) Here we have a = 2, then the hypotenuse is:
b^2 = 2^2 + 2^2
b^2 = 8
b = √8
3) Here we have y = 8, then the hypotenuse is:
x^2 = 8^2 + 8^2
x^2 = 128
x = √128
On the last triangle we can see that the hypotenuse is 7, and we know that a = b
then:
7^2 = a^2 + b^2
7^2 = a^2 + a^2
49 = 2*a^2
(49/2) = a^2
√(49/2) = a
7/√2 = a = b
Learn more about equilateral triangles at:
https://brainly.com/question/17264112
#SPJ1
I dont know what 28x76 is
Answer:
28
x 76
----
168 (units digit of 76 multiplied by 28)
1408 (tens digit of 76 multiplied by 28)
----
2128
Therefore, 28x76 is equal to 2128.
Step-by-step explanation:
1. Draw a scatter plot that shows a positive linear association and clustering.
2. Draw a scatter plot that shows a negative non-linear association and no clustering.
The grouping of data or sample points is a component of the machine learning process known as clustering.
What is Clustering?The task of arranging a set of objects into an identical group in a way that makes them more similar to one another than those found in different groups is known as cluster analysis or clustering.
A scatter plot is an unique type of plot or mathematical diagram that displays data for usually 2 parameters for a collection of data. It uses Cartesian coordinates.
Coordinates, it is a set or group of values that show an exact or accurate position.
To learn more about Clustering, visit:
https://brainly.com/question/30883020
#SPJ1
Use the equation y = 7x to complete the table. What are the missing values of
y?
O A. When x = 2, y = 16.
When x = 4, y = 30.
O B. When x = 2, y = 14.
When x = 4, y = 28.
C. When x = 2, y = 8.
When x = 4, y = 22
D. When x = 2, y = 12.
When x = 4, y = 24.
Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.
The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.
When x = 2, we can substitute this value into the equation:
y = 7(2) = 14
Therefore, when x = 2, y = 14.
Similarly, when x = 4, we can substitute this value into the equation:
y = 7(4) = 28
Therefore, when x = 4, y = 28.
So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.
In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.
To learn more about equation click on,
https://brainly.com/question/28355030
#SPJ4
Leeanne plans to sell her car and places an x-line ad. The newspaper charges p dollars for the
first k lines and e dollars per extra line, to run the ad for a week.
When x > k, write an algebraic expression for the cost of running the ad for a week.
a.
b. When x
Answer:
a. When x > k, the cost of running the ad for a week can be expressed as:
C = p + e(x - k)
where C is the cost in dollars, p is the cost per k lines, e is the cost per extra line, and (x - k) is the number of extra lines over k.
b. When x ≤ k, the cost of running the ad for a week can be expressed as:
C = p
where C is the cost in dollars and p is the cost per k lines. Since the number of lines x is less than or equal to k, there are no extra lines and the cost is simply the base cost of p dollars for k lines.
Hope this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
HELPPPPPPPPPPPPpppppppppppppppppppppppp
Answer:C
Step-by-step explanation:
[tex](x-3)^2=5\\we \ should \ find \ square \ root \ of \ each \ side,\\\sqrt{(x-3)^2}=\sqrt{5}\\1)x-3=\sqrt{5}x=\sqrt{5}+3\\2)3-x=\sqrt{5}\\x=3-\sqrt{5}\\\\so,x=3\± \sqrt{5}[/tex]
URGENTTTTT!!!!!!!!!! please complete the chart with the correct angle measures
(numbers 6-9 please!)
Answer:
9 hope u get it right budddyyyy
A company's profit (in millions of dollars) can be represented by y=x^2 -16x +67 where x is the number of years since the company started. When did the company have a profit of 7 million dollars?
For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
What exactly are quadratic equations?
A quadratic equation is a second-degree polynomial equation of the form:
ax²+ bx + c = 0
where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.
Now,
We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.
We want to find when the company had a profit of 7 million dollars.
So, we can set y = 7 in the equation:
7 = x² - 16x + 67
Rearranging and simplifying:
x² - 16x + 60 = 0
Now, we can solve for x using the quadratic formula:
x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)
x = (16 ± √(16)) / 2
x = 8 ± 2
Therefore, the solutions are x = 10 or x = 6.
This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
To know more about quadratic equations visit the link
brainly.com/question/30098550
#SPJ1
the basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population mean is . a. the empirical rule b. chebyshev's theorem c. bayes' theorem d. the central limit theorem
The cοrrect answer tο the given questiοn is d. the central limit theοrem.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
The basis fοr using a nοrmal prοbability distributiοn tο apprοximate the sampling distributiοn οf the sample means and pοpulatiοn mean is the central limit theοrem.
The central limit theοrem states that fοr a sufficiently large sample size, the sampling distributiοn οf the sample means will be apprοximately nοrmal, regardless οf the shape οf the pοpulatiοn distributiοn. This theοrem allοws us tο make statistical inferences abοut the pοpulatiοn mean based οn the sample mean using the prοperties οf the nοrmal distributiοn, such as the mean and standard deviatiοn.
Therefοre, the cοrrect answer tο the given questiοn is d. the central limit theοrem.
Learn more about frequency distribution, by the following link
https://brainly.com/question/16698786
#SPJ1
Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
Step-by-step explanation:
Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
Solve 5(p−3q)<12 for q
The value of q in the question is q>-12/15
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions
The given inequality is 5(p−3q)<12
Opening the bracket we have
5p - 15q < 12
The solution can only be gotten if we assume p = 0
the substitute p=0 in the inequality to have
-15q < 12
dividing both sides by -15 to have
-15q/-15 < 12/-15
therefore q > 12/-15
Learn more about inequality on https://brainly.com/question/30231190
#SPJ1
Given: S is on the segment RT. RS = x + 2, ST = 3x + 1, and RT = 15.
On solving the question we have that We can see that RS + ST = RT, equation confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:
RS + ST = 3x + 1 + (x + 2) = 15
To simplify this equation, we can combine similar terms:
4x + 3 = 15
Subtraction of 3 from both sides yields:
4x = 12
When we divide both sides by 4, we get:
x = 3
RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.
We can see that RS + ST = RT, confirming that S is on segment RT:
RT = RS + ST = 5 + 10 = 15
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Determine the value of x
Answer:
12 × 3 = 36
the top of the diagram will also equal 36
138-72=66
66 ÷2= 33
33÷3 =11
therefore x=11
Answer:
perimeter = 138
p=2(138+12)
p=2×150
p=300
x=300
Please I really need help the blank boxes are from 0-9.
For no solution 7x+10
For one solution8x+0
For infinite solution 7x+5
Define infinite solutionAn infinite solution is a solution to a system of equations that has an infinite number of possible solutions. In other words, any value for the variables in the system will satisfy all the equations.
2x+5+2x+3x
On adding the values with variables, x=7
On adding constant values=5
2x+5+2x+3x=7x+5
For no solution
7x+5=7x+10
For one solution
7x+5=8x
x=5
For infinite solution
7x+5=7x+5
Hence, For no solution 7x+10
For one solution 8x+0
For infinite solution 7x+5.
To know more about variables, visit:
https://brainly.com/question/17344045
#SPJ1
The table contains the number of M&M’s of each color that were found in a case.
M&M Distribution
Blue Brown Green Orange Red Yellow Total
399 538 364 393 507 351 2552
Round answers to four decimal places, if necessary.
Find the probability of choosing a green or red M&M.
P(green or red) =
Find the probability of choosing a blue, red, or yellow M&M.
P(blue, red, or yellow) =
Find the probability of not choosing a brown M&M.
P(not brown) =
Find the probability of not choosing a green M&M.
P(not green) =
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
What is probability?
Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
The total number of M&M's is 2552.
(a) P(green or red) = P(green) + P(red)
= 364/2552 + 507/2552
= 0.2692
(b) P(blue, red, or yellow) = P(blue) + P(red) + P(yellow)
= 399/2552 + 507/2552 + 351/2552
= 0.4917
(c) P(not brown) = 1 - P(brown)
= 1 - 538/2552
= 0.7891
(d) P(not green) = 1 - P(green)
= 1 - 364/2552
= 0.8575
Hence,
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
To know more about probability visit :
https://brainly.com/question/13604758
#SPJ1
PLEASE SHOW WORK!!!!!!!!!
Answer:
K
Step-by-step explanation:
[tex]c + d \: - 2(c + d) \\ = c + d - 2c - 2d \\ = - c - d \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Determining the functions that have complex rootsFrom the question, we are to determine the functions that have complex roots in the given coordinate plane.
In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.
Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.
The graph will have complex roots.
In the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Hence, the functions b, d, and f have complex roots.
Learn more on Determining the functions that have complex roots here: https://brainly.com/question/20127973
#SPJ1
If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. How many hours does Bill work in 5 days?
If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. Bill works for 36.25 hours in 5 days.
What is work per day?Work per day typically refers to the amount of time or effort expended by an individual during a typical working day.
According to question:First, let's find out how many hours Bill works in one day.
From 8:15 AM to 4:45 PM, Bill works for 8 hours and 30 minutes (since there are 60 minutes in an hour, we can convert the 45 minutes to 0.75 hours, so 8 hours and 45 minutes is the same as 8.75 hours):8 hours and 45 minutes - 90 minutes of breaks
= 7 hours and 15 minutes
= 7.25 hours of work per day.
To find out how many hours Bill works in 5 days, we can simply multiply his daily hours by the number of days:7.25 hours per day x 5 days = 36.25 hours.
Therefore, Bill works for 36.25 hours in 5 days.
To know more about work per day visit:
https://brainly.com/question/17202309
#SPJ1
How many terms are in the expression: 12p + 8m + 2
Answer: I THINK 4.
Step-by-step explanation:
Sorry if it is wrong!! :'D
PLEASE HELP I OS EASY\
Find the surface area of the rectangular prism.
A storage container is in the shape of a rectangular prism. The container has a length of 5 feet, and a width of 9 feet, and a height of 8 feet. What is the surface area of the container?
360 ft2
314 ft2
157 ft2
22 ft2
ANswer __________________
The surface area οf the cοntainer is 314 ft².
What is rectangle?A rectangle is a geοmetric shape that has fοur sides and fοur right angles (90 degrees) with οppοsite sides being parallel and equal in length. It is a type οf quadrilateral, a pοlygοn with fοur sides.
Tο find the surface area οf a rectangular prism, we need tο add the areas οf all six faces. The fοrmula fοr the surface area οf a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height οf the rectangular prism.
Substituting the given values, we get:
Surface area = 2(5)(9) + 2(5)(8) + 2(9)(8)
Surface area = 90 + 80 + 144
Surface area = 314 square feet
Therefοre, the surface area οf the cοntainer is 314 ft².
Answer: 314 ft².
To learn more about rectangle from the given link:
https://brainly.com/question/29123947
#SPJ1
Let X be a normally distributed random variable. Given that the
mean is 2 and P(X < 2.24) = 0.7257, what is the variance?
a. 0.5266
b. None of the suggested answers are correct
c. 0.6
d. 0.4
e. 0.1
e [0.1}
We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.
Learn more about normal distribution random variable
brainly.com/question/30002338
#SPJ4
Find the sum or difference
The sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]
What is sum?
In mathematics, the term "sum" refers to the result obtained by adding two or more numbers or quantities together. It also be used to refer to the total amount of something, such as the sum of money you have in your bank account, or the sum of the lengths of all the sides of a polygon.
To find the sum or difference of [tex]-2x^2+x+6 + (5x^2-4x-2)[/tex] we need to combine like terms.
[tex]-2x^2+x+6 + (5x^2-4x-2) &\\\\= (-2x^2 + 5x^2) + (x - 4x) + (6 - 2)[/tex]
[tex]&= 3x^2 - 3x + 4[/tex]
Therefore, the sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]
To learn more about sum visit:
https://brainly.com/question/24205483
#SPJ1
The graph shows a straight line.
a) What is the equation of the straight
line shown?
b) Another straight line has equation
y = 3x + 5
Complete the following statement: -5
'y = 3x + 5 passes through (0,
c) A straight line has the same gradient
as y = 3x + 5 and it passes through
the point (0, 12).
What is the equation of this straight line? y=
5
5 x
The equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex] and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex]
What are equations used for?A mathematical equation, such as 6 x 4 Equals 12 x 2, states that two quantities or units are similar. A noun that ranks. When two or more components must be taken into account together in to fully understand or describe the whole scenario, this is known as an equation.
a) To find the equation of the straight line shown, we need to determine its slope (or gradient) and [tex]y-[/tex]intercept. We can do this by choosing two points on the line and using the point-slope formula:
slope [tex]=[/tex] (change in y) / (change in x)
Let's choose the points [tex](1, 3)[/tex] and [tex](4, 7)[/tex] from the line.
slope [tex]= (7 - 3) / (4 - 1) = 4 / 3[/tex]
Now we can use the point-slope formula with one of the points to find the equation:
[tex]y - y1 = m(x - x1)[/tex]
where m is the slope and (x1, y1) is one of the points on the line.
Let's use the point (1, 3):
[tex]y - 3 = (4/3)(x - 1)[/tex]
Simplifying:
[tex]y = (4/3)x + 1[/tex]
So, the equation of the straight line shown is [tex]y = (4/3)x + 1[/tex].
b) To complete the statement "[tex]y = 3x + 5[/tex] passes through [tex](0, -5)[/tex]", we need to substitute [tex]x = 0[/tex] and [tex]y = -5[/tex] into the equation and verify that it is true:
[tex]y = 3x + 5[/tex]
[tex]-5 = 3(0) + 5[/tex]
[tex]-5 = 5 - 5[/tex]
[tex]-5 = -5[/tex]
Since the equation is true, we can say that the point [tex](0, -5)[/tex] is on the line [tex]y = 3x + 5[/tex].
c) We know that the gradient of the line we want to find is the same as [tex]y = 3x + 5[/tex], which is [tex]3[/tex]. We also know that it passes through the point [tex](0, 12)[/tex].
Using the point-slope formula with [tex]m = 3[/tex] and [tex](x1, y1) = (0, 12)[/tex]:
[tex]y - 12 = 3(x - 0)[/tex]
Simplifying:
[tex]y = 3x + 12[/tex]
So, the equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex]and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex].
To know more about equation visit:
https://brainly.com/question/10413253
#SPJ1
the daily high temperature for chattanooga is normally distributed with mean 79 and standard deviation 4. find the probability that a randomly chosen temperature is between 70 and 75.
The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.
To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:
z = (x - μ) / σ
Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)
To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.
Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.
To know more about probability, refer here:
https://brainly.com/question/29272039#
#SPJ11
find the values of a, b, and c in the equation 5x^2-2=2x^2+10x+6
The value οf a = 3, b=-10, c-8
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.
The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.
The equatiοn given 5x²-2=2x²+10x+6
3x²-10x-8=0
values οf a = 3, b=-10, c-8
Hence the value οf a = 3, b=-10, c=8
Learn more about quadratic equation, by the following link.
https://brainly.com/question/1214333
#SPJ1
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 15 . Find
P 9
, which is the IQ score separating the bottom9%from the top 91%
. The IQ score that separates the bottom 9% from the top 91% is P 9
=
(Round to the nearest hundredth as needed.) Assume that adults have IQ
scores that are normally distributed with a mean of 105 and a standard deviation of 15 . Find the third quartile
Q 3
which is the IQ score separating the top 25% from the others. The third quartile, Q 3
is . (Round to one decimal place as needed.)
Value of Q3 is approximately 114.1 given mean and standard deviation.
We must identify the IQ score that separates the bottom 9% from the top 91% in order to determine P9. The normal distribution of IQ scores has a mean of 100 and a standard deviation of 15, as is well known. The z-score for the 9th percentile can be calculated using a calculator or a typical normal distribution table.
[tex]z = invNorm(0.09) = -1.34[/tex]
The formula for converting a z-score to an IQ score is as follows:
IQ equals z * standard deviation + mean, or -1.34 * 15 + 100, or 79.1.
P9 is therefore roughly 79.1.
We must identify the IQ score that distinguishes the top 25% from the rest in order to determine Q3. Assuming a normal distribution, IQ values have a mean of 105 and a standard deviation of 15. Since the top 25% and the 75th percentile are the same, we can use a calculator or a conventional normal distribution table to determine the z-score that represents the 75th percentile:
[tex]z = invNorm(0.75) = 0.67[/tex]
We can then use the formula for transforming a z-score to an IQ score:
IQ = z * standard deviation + mean = 0.67 * 15 + 105 = 114.05
Therefore, Q3 is approximately 114.1.
Learn more about standard deviation here:
https://brainly.com/question/23907081
#SPJ1
Harrison has a rectangular plank of wood that is 29 inches long. He creates a ramp by resting the plank against a wall with a height of 14 inches, as shown. Using Pythagoras' theorem, work out the horizontal distance between the wallI and the bottom of the ramp. Give your answer in inches to 1 d.p.
Answer:
Horizontal distance between the wall and the bottom of ramp = 25.4 inches.
Step-by-step explanation:
Pythagorean theorem:
AB -> wall ; AB = 14 inches
AC -> Wooden plank ; AC = 29 inches
BC -> horizontal distance between the wall and the bottom of ramp(pank).
Pythagorean theorem,
[tex]\boxed{\bf base^2 + altitude^2 = hypotenuse^2}[/tex]
BC² + AB² = AC²
BC² + 14² = 29²
BC² + 196 = 841
BC² = 841 - 196
= 645
BC = √645
BC = 25.4 inches
Horizontal distance between the wall and the bottom of ramp = 25.4 inches.
Given,
Length = 29 inches
Height = 14inches
Here,
Pythagorean theorem:
AB -> wall ; AB = 14 inches
AC -> Wooden plank ; AC = 29 inches
BC -> horizontal distance between the wall and the bottom of ramp (plank).
Pythagorean theorem,
Base² + Perpendicular² = Hypotenuse²
BC² + AB² = AC²
BC² + 14² = 29²
BC² + 196 = 841
BC² = 841 - 196
= 645
BC = √645
BC = 25.4 inches
Know more about pythogras theorem,
https://brainly.com/question/21926466
#SPJ2
Karen has two dogs. The larger dog weighs 1. 4 pounds more than the smaller dog. The combined weight of the two dogs is 12. 6 pounds
The weight of the smaller dog is 5.6 pounds.
Let the weight of the smaller dog be x, then,
The weight of the larger dog = 1.4 pounds.
The combined weight of the dogs = 12.6 pounds.
Therefore,
The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.
That is,
1.4 + x + x = 12.6
1.4 + 2x = 12.6
2x = 12.6 - 1.4
2x = 11.2
x = 11.2 ÷ 2
x = 5.6.
Hence, the weight of the smaller dog is 5.6 pounds.
?
To learn more about weight, refer to:
https://brainly.com/question/86444
#SPJ4
Your question is incomplete, and the complete question would be:
Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?
The populations P (in thousands) of Horry County, South Carolina, from 1971 through 2018 can be modeled by P-75.9e0.0316 where t represents the year, with t= 1 corresponding to 1971.
(a) Use the model to find the population in 1980, 1990, 2000, and 2010. (Round your answers to the nearest whole number.)
1980
1990
2000
2010
(b) According to the model, when will the population of Horry County reach 390,000? (Round your answer down to the nearest year.)
(c) Do you think the model is valid for long-term predictions of the population? Explain.
O Yes, as t increases, the population increases rapidly.
O Yes, as t increases, the population decreases rapidly.
O Yes, as t increases, the population remains constant.
O No, as t increases, the population decreases rapidly.
O No, as t increases, the population increases rapidly.
a) The populations in 1980, 1990, 2000, and 2010 are 157,000, 218,000, 269,000, and 308,000 respectively.
b) the population will reach 390,000 in 270 years
c) No, as t increases, the population increases rapidly
How to find the populations as required(a) To find the population in 1980, 1990, 2000, and 2010, we substitute the corresponding values of t into the given model and round the answers to the nearest whole number.
Population in 1980: P = 75.9e^(0.0316*10) = 156,604
Population in 1990: P = 75.9e^(0.0316*20) = 217,643
Population in 2000: P = 75.9e^(0.0316*30) = 269,099
Population in 2010: P = 75.9e^(0.0316*40) = 308,227
(b) To find when the population of Horry County will reach 390,000, we need to solve the equation 390 000 = 75.9e^(0.0316t) for t.
Taking the natural logarithm of both sides, we get:
ln(390,000/75.9) = 0.0316t
Simplifying, we get:
t = ln(390,000/75.9)/0.0316 ≈ 270.395
Rounding down to the nearest whole year, we get that the population will reach 390,000 in 270 years
(c) The model assumes that the population growth rate will remain constant over time. However, in reality, population growth rates can be affected by a variety of factors, such as changes in birth and death rates, immigration, emigration, and natural disasters.
Therefore, it is unlikely that the model will be valid for long-term predictions of the population. The model can provide a good estimate of the population for the short-term, but it is not reliable for predictions far into the future.
Learn more about population growth rate at:
https://brainly.com/question/25630111
#SPJ1
PLEASE HELP ASAP WILL GIVE BRAINLIEST
Answer:
3x+5x=8x
-3t+-t=-4t
3p+3p=6p
2n+n=3n
5g+-g=4g
7y+y=8y
4+12=16
Step-by-step explanation: