The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
What is a linear function?
A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.
We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:
D(x) = 65 - 0.8x
where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
Therefore, the equation for the function is D(x) = 65 - 0.8x.
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Katya is going on a 7-night trip. She is staying in a hotel that costs $129 per night and her airfare is $375. If she budged $2.000 for the trip, how much money will she have left for the trip?
A. $672
B. $686
C.$704
D.$722
Answer: D. $722
Step-by-step explanation:
$2,000 - $375 (initial airfare cost which will only be once)
= 1,625
7 x 129 = 903 (cost of the 7 nights in a hotel)
1,625 - 903 = 722
$722 left for the trip
if y is inversely proportional to the square root of x, and y is 16 when x is 0.25.find the value of y when x is 0.64
By inverse proportions, 6.4 is the value of y .
What are some examples of inverse proportions?
In the case of two quantities that are inversely proportional, one quantity falls as the other rises. The number of hours needed to construct a wall serves as an illustration of inverse proportion. The time required to build a wall decreases as more people work on the same project.
suppose that y =√kx
enter (0.25,16) to y =√kx
0.5k = 16
k = 5
y = 8√x
when x = 0.64
y = 8√0.64
y = 6.4
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I need some helpppppppppppppppp
Answer:
Step-by-step explanation:
The corresponding equal angles must be written in the same order. So the first one is the correct answer.
A town was founded with a population of 8,000. The population then doubled every decade. Write the function, p(n), that expresses the
town's population after n decades
p(n)= 8000 + 2 n
p(n) = 8000 +2( n - 1)
p(n)=8000-2
p(n) = 8000
The correct function that expresses the town's population after n decades is: p(n) = 8000 × 2ⁿ. So the initial population of the town is 8,000, which is consistent with the problem statement.
What is function?A function is a mathematical concept that describes the relationship between a set of inputs, called the domain, and a set of outputs, called the range.
A function assigns a unique output to each input, meaning that for a given input, there is only one possible output.
Starting with a population of 8,000, the population doubles every decade, which means it multiplies by 2.
After n decades, the population will have doubled n times, so we can express the population as 8,000 multiplied by 2 raised to the power of n:
p(n) = 8000 × 2ⁿ
This function gives us the population of the town after n decades, where n is a non-negative integer. If we substitute n=0 into the function, we get:
p(0) = 8000 × 2⁰ = 8000
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Find the volume of this cylinder.
Give your answer to 1 decimal place.
20 cm
9 cm
Step-by-step explanation:
the answer will be 1272.7cm3
the formula of the volume of the cylinder is pie×radius squared×height so,
we will get the radius and the radius is half of the diameter and the diameter is 9 so 9÷2=4.5 and then it will be squared so it will be 20.25cm2 and so we will write it this way
3.14×20.25×20=1271.7cm3
hope this helped
xoxo adham
Describe the series of transformations which transforms f left parenthesis x right parenthesis equals x squared onto f left parenthesis x right parenthesis equals x squared minus 6 x plus 18.
f(x) = [tex]x^{2}[/tex] -> f(x) = [tex]x^2[/tex] - 18 (translation) -> f(x) = [tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x (vertical stretching)
how to transform given function?To transform the function f(x) =[tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18, we need to apply a series of transformations. Here are the steps:
Translation: We need to shift the graph of f(x) = [tex]x^{2}[/tex] down by 18 units to obtain f(x) = [tex]x^{2}[/tex] - 18. This can be done by subtracting 18 from the function, which results in f(x) = [tex]x^2[/tex]- 18.
Horizontal translation: Next, we need to shift the graph of f(x) = [tex]x^{2}[/tex] - 18 to the right by 3 units to obtain f(x) =[tex](x-3)^2[/tex] - 18. This can be done by replacing x with (x-3) in the function, which results in f(x) =[tex](x-3)^2[/tex]- 18.
Vertical stretching: Finally, we need to vertically stretch the graph of f(x) = [tex](x-3)^2[/tex] - 18 by a factor of -6 to obtain f(x) = [tex](x-3)^2[/tex] - 6x + 18. This can be done by multiplying the function by -6, which results in f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x.
So, the series of transformations required to transform f(x) = [tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18 is:
f(x) = [tex]x^{2}[/tex] -> f(x) =[tex]x^{2}[/tex] - 18 (translation) -> f(x) =[tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex]+ 18 - 6x (vertical stretching)
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If the light is coming from the same position, the length of a person's shadow is proportional to their height. Adam and Cara are standing side-by-side, facing their shadows. Adam is 159 centimeters tall and casts a shadow 105 centimeters in height. If Cara is 140 centimeters tall, how many centimeters will she need to walk forward for the tip of her shadow to be directly in line with Adam's?
need an answer NOW!! id prefer if sin cos and/or tan was used to find the side length, but its okay if you use pythagorean theorem
The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.
Equilateral triangle:An equilateral triangle is a type of triangle where all three sides have the same length, and all three angles are equal to 60 degrees.
The formula for the height of an equilateral triangle is given by
Height (h) = ½(√3a)Where 'a' is the equal side of the equilateral
In the given problem we use the height of the triangle to calculate the side of the triangle tenth.
Here we have
The height of the tent is 5 ft which is the height of the equilateral triangle
As we know,
Height of equilateral triangle = ½(√3a)
Let 'a' be the side of the triangle tent
=> 5 ft = ½(√3a)
Multiply by 2 on both sides
=> 5 × 2 = 2(1/2)√3a
=> √3a = 10
=> (1.732) a = 10 [ ∵ √3 1.732 ]
=> a = 5.8
Therefore,
The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.
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Stanley wants to know how many students in his school enjoy watching talk shows on TV. He asks this question to all 24 students in his history class and finds that 55% of his classmates enjoy watching talk shows on TV. He claims that 55% of the school's student population would be expected to enjoy watching talk shows on TV. Is Stanley making a valid inference about his population? (1 point)
a
No, it is not a valid inference because he asked all 24 students in his history class instead of taking a sample from his math class
b
No, it is not a valid inference because his classmates do not make up a random sample of the students in the school
c
Yes, it is a valid inference because his classmates make up a random sample of the students in the school
d
Yes, it is a valid inference because he asked all 24 students in his history class
Answer:
B.......................
URGENT! 35 POINTS!
The expression tan theta - sec^2theta/tan theta simplifies to what expression?
−tan θ
−cot θ
cos θ
sec θ
by simplifying the expression, option d ,sec θ is the correct answer.
how can we solve this expression?
We can simplify the given expression as follows:
(tan θ - [tex]sec^2[/tex] θ) / tan θ
= (tan θ / tan θ) - ([tex]sec^2[/tex] θ / tan θ) ,
by diving it by tan θ
= 1 - (1/[tex]cos^2[/tex] θ)([tex]sin^2[/tex] θ / cos θ),
since sec = 1/cos and tan=sin/cos
placing the value in expression and solving it , we get
= 1 - ([tex]sin^2[/tex] θ / ([tex]cos^3[/tex] θ))
= [tex]cos^3[/tex] θ / [tex]cos^3[/tex] θ - [tex]sin^2[/tex] θ
= [tex]cos^3[/tex]θ / [tex]cos^2[/tex] θ (1 - [tex]tan^2[/tex] θ)
We can simplify the given expression as follows:
= cos θ ( [tex]cos^2[/tex]θ - [tex]sin^2[/tex]θ) / ([tex]cos^2[/tex] θ)
= cos θ (cos θ / [tex]cos^2[/tex]θ)
= 1/cos θ is equal to sec θ
Therefore, the simplified expression is sec θ.
Hence, the answer is option (d) sec θ.
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A local doctor wants to test the effects of a new diet she decided to lower triglycerides on 10 randomly selected patients. The triglyceride level of each patient is checked twice, once before they start the diet, and again at three weeks after that time. The results are in the table below, (the photo). All data is in milligrams per deciliter (mg/dL).
The Noel and alternative hypothesis for the study are (in the photo)
Please let me know which one of the answers in the photo is correct ! Thank you , 100 points!!
With a significance level of 0.05, the. option that shows the correct test statistic, P- value, and conclusion is A. Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
What is a significance level?In statistics, the significance level (denoted by α) is the probability of making a Type I error, which is rejecting a true null hypothesis. In other words, it is the maximum allowable probability of observing a result as extreme as or more extreme than the one observed, assuming the null hypothesis is true.
The significance level is typically set by the researcher before conducting a hypothesis test and is usually set to 0.05 (5%) or 0.01 (1%). If the p-value of the test is less than or equal to the significance level, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected.
The correct option is A.
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With a significance level of 0.05, which of the following shows the correct test statistic, P- value, and conclusion?
Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, = 0.3619; P-value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, -1.952; P-value, 0.0509. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, t=0.3651; P-value, 0.6425. There is insufficient evidence to reject the null hypothesis of
no difference between the triglyceride test levels.
6 2/5 subtract 2 9/10
Answer: 9 3/10
Step-by-step explanation:
6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1 3/10= 8 + 1 + 3/10= 9 3/10
A bank account gathers compound interest at a rate of 5% each year. Another bank account gathers the same amount of money in interest by the end of each year, but gathers compound interest each month. If Abraham puts £4300 into the account which gathers interest each month, how much money would be in his account after 2 years and 5 months? Give your answer in pounds to the nearest 1p.
Answer:
$6235 1
' 1 . ' 8
Answer:
Step-by-step explanation:
Consider the quadratic function: f(x)=x²-8x-9 Vertex: (08) What is the vertex of the function? ( ,-25)
the vertex of the quadratic function is (4,-25).
What is a quadratic function?A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is 2. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree two. It carries out algebraic functions.
examples of quadratic functions are:
f(x) = 2x2 + 4x - 5; Here a = 2, b = 4, c = -5f(x) = 3x2 - 9; Here a = 3, b = 0, c = -9f(x) = x2 - x; Here a = 1, b = -1, c = 0Given quadratic equation:f(x)=x²-8x-9
x-coordinate of vertex:
x=-b/2a
Putting the values, we get
x=-(-8)/2=4
Y-coordinate vertex:
y(4)=16-32-9=-16-9=-25
Vertex(4,-25)
Hence, the vertex of the function =(4,-25).
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A pyramid has a height of 5 inches and a volume of 60 cubic inches. Which of the following figures could be the base for this pyramid?
Select 3 answers that apply.
A a hexagon with an area of 36 square inches
11 a right triangle with one leg 5 inches and the hypotenuse 13 inches
ca circle with radius 4 inches
Da 4-inch by 9-inch rectangle
a 3-inch by 4-inch rectangle
a square with side length 6 inches
E
The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:
A hexagon with an area of 36 square inches (option A)A 4-inch by 9-inch rectangle (option D)A 3-inch by 4-inch rectangle (option E)How do we calculate?The formula to find the base of a pyramid given its height and volume,
Volume of pyramid = (1/3) * Base area * Height
Substituting in the given values, we have:
60 = (1/3) * Base area * 5
Base area = 36 square inches
In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.
The following figures have a base area of 36 square inches:
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hello guys can someone help me with this. because my dead line is too close
→ no trolling please i really need it right now ←
→ i will give brainliest ←
We are given the following lengths:
XY (median) = 4m+3CO (upper base) = 2m-10PY (lower base) = 3m+37We will solve it by using this formula:
[tex]\boxed{\mathfrak{\purple {Median = \frac{1}{2}(lower \: base+upper \: base)}}}[/tex]
[tex]\boxed{\mathcal{\purple { XY = \frac{1}{2}( CO+PY)}}}[/tex]
Lets solve it down now, #16[tex] \green{ \sf4m + 3 = \frac{1}{2} (2m - 10 + 3m + 37)}[/tex]
[tex] \red \implies \green{ \sf4m + 3 = \frac{1}{2} (5m+ 27)}[/tex]
[tex] \red \implies \green{ \sf4m + 3 = \frac{5}{2} m + \frac{27}{2} }[/tex]
[tex] \red \implies \green{ \sf8m + 6 = 5m + 27 }[/tex]
[tex] \red \implies \green{ \sf8m + 6 - 5m = 27 }[/tex]
[tex] \red \implies \green{ \sf8m - 5m= 27 - 6 }[/tex]
[tex] \red \implies \green{ \sf3m = 21 }[/tex]
[tex] \boxed{ \mathfrak{ \red{m = 7}}}[/tex]
#17[tex] \blue \longmapsto \orange{ \tt \: XY =4m + 3}[/tex]
[tex] \blue \longmapsto \orange{ \tt \: XY =4(7) + 3}[/tex]
[tex] \blue \longmapsto \orange{ \tt \: XY =28 + 3}[/tex]
[tex] \boxed{ \underline{ \underline{ \blue \longmapsto \orange{ \tt \: XY =31}}}}[/tex]
#18[tex] \purple \longmapsto \pink{ \tt \: CO = 2m - 10}[/tex]
[tex] \purple \longmapsto \pink{ \tt \: CO = 2(7) - 10}[/tex]
[tex] \purple \longmapsto \pink{ \tt \: CO = 14 - 10}[/tex]
[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:CO=4}}}}[/tex]
#19[tex] \purple \longmapsto \pink{ \tt \: PY = 3m + 37}[/tex]
[tex] \purple \longmapsto \pink{ \tt \: PY = 3(7) + 37}[/tex]
[tex] \purple \longmapsto \pink{ \tt \: PY = 21 + 37}[/tex]
[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:PY=58}}}}[/tex]
Answer:
[tex]\textsf{16.}\quad m = 7[/tex]
[tex]\textsf{17.} \quad \overline{XY}=31[/tex]
[tex]\textsf{18.} \quad \overline{CO}=4[/tex]
[tex]\textsf{19.} \quad \overline{PY}=58[/tex]
[tex]\textsf{20.} \quad \overline{EV}=80.5\; \sf meters[/tex]
Step-by-step explanation:
The median of a trapezoid is the line segment that connects the midpoints of the non-parallel sides. It is parallel to the bases, and its length is equal to the average of the lengths of the two bases.
Given line segments:
[tex]\bullet \quad \overline{CO}=2m-10[/tex]
[tex]\bullet \quad \overline{PY}=3m+37[/tex]
[tex]\bullet \quad \overline{XY}=4m+3[/tex]
As the length of the median XY is equal to the average of the lengths of the two bases we can set up the following equation:
[tex]\overline{XY}=\dfrac{\overline{CO}+\overline{PY}}{2}[/tex]
Substitute the expressions for each line segment into the equation and solve for m:
[tex]\begin{aligned}4m+3&=\dfrac{(2m-10)+(3m+37)}{2}\\2(4m+3)&=(2m-10)+(3m+37)\\8m+6&=5m+27\\8m+6-5m&=5m+27-5m\\3m+6&=27\\3m+6-6&=27-6\\3m&=21\\3m \div 3&=21 \div 3\\m&=7\end{aligned}[/tex]
Therefore, the value of m is 7.
Now we have calculated the value of m, simply substitute this value into each line segment expression to determine their measures:
[tex]\begin{aligned} \overline{XY}&=4m+3\\&=4(7)+3\\&=28+3\\&=31\end{aligned}[/tex]
[tex]\begin{aligned} \overline{CO}&=2m-10\\&=2(7)-10\\&=14-10\\&=4\end{aligned}[/tex]
[tex]\begin{aligned} \overline{PY}&=3m+37\\&=3(7)+37\\&=21+37\\&=58\end{aligned}[/tex]
[tex]\hrulefill[/tex]
The length of the median of a trapezoid is equal to the average of the lengths of the two bases.
Given the bases of trapezoid LOVE are LO and EV, and the median is XY, we can set up the following equation:
[tex]\overline{XY}=\dfrac{\overline{LO}+\overline{EV}}{2}[/tex]
Given line segments:
[tex]\bullet \quad \overline{LO} = 48.5[/tex]
[tex]\bullet \quad \overline{XY} = 64.5[/tex]
To find the measure of the lower base EV, substitute the given values of the line segments into the equation and solve for EV:
[tex]\begin{aligned}\overline{XY}&=\dfrac{\overline{LO}+\overline{EV}}{2}\\\\64.5&=\dfrac{48.5+\overline{EV}}{2}\\\\2(64.5)&=48.5+\overline{EV}\\\\129&=48.5+\overline{EV}\\\\129-48.5&=48.5+\overline{EV}-48.5\\\\\overline{EV}&=80.5\end{aligned}[/tex]
Therefore, the measure of the lower base EV is 80.5 meters.
heya i need some help yall
if you have 2 bags of candy each with 4 pieces of candy in them you will have 8 because 2x4=8
Answer:
Step-by-step explanation:
ex 2
4444
2
4444
Yes, that's correct I even tried to show you.
The 2 is the bags of candy
4 pieces of candy per bag
equals to 8 in total
HELP PLEASE
Lee puts $5,000 into a stock market index mutual fund That grew at an average of 6.5% per year for 10 years. Without any added deposits or withdrawals, about how much is in Lee's mutual fund account after only 8 years, if you ignore the come pounding?
You are thinking about changing employment. Your goal is to work for three years and then return to university full-time, in pursuit of an advanced degree. A potential employer just offered you an annual salary of R55 000, R60 000, and R65 000 a year for the next three years, respectively. All salary payments will be made as lump sum payments at the end of each year. The offer also includes a starting bonus of R4 500, payable immediately. What is this offer worth to you today, at a discount rate of 8,25%?
Answer:
55K+60K+65K=184K
100% - 8.25%=91.75%
184000x91.75%=168820
Ans:168K
Answer:
Step-by-step explanation:
To determine the value of the offer today, we need to calculate the present value of all the cash flows using a discount rate of 8.25%.
First, let's calculate the present value of the salary payments.
PV(year 1 salary) = R55 000 / (1 + 0.0825)^1 = R50 760.87
PV(year 2 salary) = R60 000 / (1 + 0.0825)^2 = R51 423.95
PV(year 3 salary) = R65 000 / (1 + 0.0825)^3 = R52 110.69
Next, let's calculate the present value of the starting bonus.
PV(starting bonus) = R4 500 / (1 + 0.0825)^0 = R4 500
Finally, we can add up all the present values to find the total present value of the offer:
PV(total offer) = PV(year 1 salary) + PV(year 2 salary) + PV(year 3 salary) + PV(starting bonus)
PV(total offer) = R50 760.87 + R51 423.95 + R52 110.69 + R4 500
PV(total offer) = R158 795.51
Therefore, the offer is worth R158 795.51 to you today at a discount rate of 8.25%.
If the circumference of a circle is 88 cm, find its area.
Answer:
24328.49 cm
Step-by-step explanation:
as (A = π r²). r is 88 so and is 24328.49cm
Circle p has a radius of 8 inches
The area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
the angle of the sector = 70°
the radius = 8 ft
hence the area of the sector is calculated as follows:
(70°/360°) × 22/7 × 8 in × 8 in
we simplify by division and multiplication
1/36 × 22 × 64 in²
352 in²/9
39.1111 in²
Therefore, the area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.
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Ken made a scale drawing of a neighborhood park. He used the scale 2 inches : 1 yard. The actual width of a soccer field in the park is 58 yards. How wide is the field in the drawing?
The width of the soccer field in the drawing is 116 inches if the ratio is 2 inches to 1 yard
How wide is the field in the drawing?If 2 inches on the drawing represents 1 yard in reality, then 1 inch on the drawing represents 1/2 yard in reality.
So, to find the width of the soccer field in the drawing, we can use the following proportion:
1 inch on drawing / (1/2) yard in reality = x inches on drawing / 58 yards in reality
Simplifying this proportion, we get:
x inches on drawing = (1 inch on drawing / (1/2) yard in reality) * 58 yards in reality
x inches on drawing = 2 * 58
x inches on drawing = 116
Therefore, the width of the soccer field in the drawing is 116 inches.
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Please see attachment
The binary number 1001100 is equivalent to the decimal number 76.
HOW TO CONVERT BINARY TO DECIMAL?
To convert a number in base 2 (binary) to base 10 (decimal), we need to multiply each digit of the binary number with its corresponding power of 2 and then sum up the results. The rightmost digit corresponds to 2, the next digit to 2 the next to 2², and so on, with each successive digit corresponding to the next higher power of 2.
For example, to convert the binary number 1001100 to decimal, we would start by multiplying the rightmost digit (0) by 2 raise the power 0, which equals 1. We would then multiply the next digit (0) by 2 raise the power 1, which equals 0, and so on, until we reach the leftmost digit (1), which corresponds to 2 raise the power 6. We then add up all of these products to get the decimal equivalent of the binary number.
So, using this method, we have:
1 x 2⁶ + 0 x 2⁵ + 0 x 2⁴ + 1 x 2³+ 1 x 2² + 0 x 2¹ + 0 x 2°= 64 + 0 + 0 + 8 + 4 + 0 + 0 = 76
Therefore, the binary number 1001100 is equivalent to the decimal number 76.
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The volume of a cuboid is 630cm3.
The length is 14cm and the width is 90mm.
Whatt is the height of the cuboid in cm.
Answer:
Height = 630 / (14 x 0.9) = 47.5 cm
PLEASE HELP! URGENT AND WORTH 50 POINTS!!!
As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.
what is length ?Length, which is typically expressed in units like meters, feet, or inches, is a measurement of an object's size or the separation between two locations. It alludes to the measurement of an object's longest dimension or the separation between two ends. The term "length" can also be used to describe the extent of a line or the linear separation between two locations, such as the length of a triangle's side, a road, or a length of rope. In geometry, length is a crucial mathematical notion that is used to gauge an object's size, shape, and location.
given
The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. Here are the facts:
60° sine + (BC/AB)
Using sin 60°, whose value is 3/2, as an example:
√3/2 = (BC/AB)
Multiplying AB by both sides:
BC = AB * √3/2
The hypotenuse's length is determined by adding the squares of the lengths of the other two edges. Here are the facts:
We have the following by substituting the earlier-obtained formulas for AC and BC:
Adding 3 to both sides:
4AB2 + 9AB2 = 12AB2
AB = 3x
As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.
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the worlds population hit 8 billion in 2022. suppose the population increases exponentially with doubling time of 60 years. what population can we expect in the year 2100. Answer in billions
The population in the year 2100 will be approximately 18.8 billion.
Determine exponential equation
The exponential equation to model the world population (in billions) after t years is P(t) = 8(1.011)[tex]^t[/tex], where P(t) is the population in billions and t is the number of years after 2022.
To write this equation, we need to use the information provided in the question. The initial population in 2022 is 8 billion, so this is our starting value. The growth rate is 1.1% per year, which can be written as 1.011 in decimal form.
We can use the formula for exponential growth, P(t) = P0(1 + r[tex])^t[/tex]where P0 is the initial population, r is the growth rate, and t is the number of years.
Substituting the values for [tex]P_0[/tex]and r into the equation, we get:
P(t) = 8(1.011[tex])^t[/tex]
2100-2022=78
This equation can be used to find the population after t years.
For example, to find the population after 5 years, we can substitute t = 78 into the equation and get:
P(5) = 8(1.011[tex])^78[/tex] ≈ 18.8 billion
Therefore, the population in year 2100 will be approximately 18.8 billion.
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3) Given that f(x) = 3x – 5 g(x) = 2x – 6 and h(x) = x + 4
4 2x
Find:- i) f(-3) = ii) g[f(0)] = iii) f[h(2)] =
iv) hᴏf(x) v) h-1(1) =
The Answer for the given functions are:
i) f(-3) = -14.
ii) g[f(0)] = -16.
iii) f[h(2)] = 13.
iv) hᴏf(x) = 3x - 1.
v) h-1(1) = -3.
What is the functiοn nοtatiοn?Functiοn nοtatiοn is a way οf representing a functiοn using algebraic symbοls. It is a shοrthand way οf expressing a relatiοnship between twο quantities οr variables, where οne variable depends οn the οther.
i) Tο find f(-3), we substitute x = -3 in the expressiοn fοr f(x) and simplify:
f(-3) = 3(-3) - 5 = -9 - 5 = -14
Therefοre, f(-3) = -14.
ii) Tο find g[f(0)], we first evaluate f(0) and then substitute that value intο g(x):
f(0) = 3(0) - 5 = -5
g[f(0)] = g(-5) = 2(-5) - 6 = -10 - 6 = -16
Therefοre, g[f(0)] = -16.
iii) Tο find f[h(2)], we first evaluate h(2) and then substitute that value intο f(x):
h(2) = 2 + 4 = 6
f[h(2)] = f(6) = 3(6) - 5 = 18 - 5 = 13
Therefοre, f[h(2)] = 13.
iv) Tο find hᴏf(x), we substitute f(x) intο the expressiοn fοr h(x) and simplify:
hᴏf(x) = h[f(x)] = f(x) + 4 = (3x - 5) + 4 = 3x - 1
Therefοre, hᴏf(x) = 3x - 1.
v) Tο find h-1(1), we need tο sοlve fοr x in the equatiοn h(x) = 1:
h(x) = x + 4 = 1
Subtracting 4 frοm bοth sides, we get:
x = 1 - 4 = -3
Therefοre, h-1(1) = -3.
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One paperclip has the mass of 1 gram. 1,000 paperclips have a mass of 1 kilogram. How many kilograms are 5,600 paperclips?
Answer: 5.6 kilograms.
Step-by-step explanation:
We know that 1,000 paperclips have a mass of 1 kilogram.
Therefore, one paperclip has a mass of 1/1000 kilograms, or 0.001 kilograms.
To find out how many kilograms 5,600 paperclips have, we can multiply the mass of one paperclip (0.001 kilograms) by the number of paperclips:
0.001 kilograms/paperclip * 5,600 paperclips = 5.6 kilograms
Therefore, 5,600 paperclips have a mass of 5.6 kilograms.
Identify the rate, base, and percent in each statement. Place them in
the correct columns to complete the table.
1) 25 is 25% of 100
2) 15 is 25% of 60
318 is 20% of 90
4) 18 is 30% of 60
5) 20% of 150 is 30
What it is rate?
What it is base?
What it is percentage?
Answer:
In each statement:
The rate is the percentage or ratio that relates the quantity being described to the base.
The base is the total quantity or amount that the rate is applied to.
The percent is the rate expressed as a percentage, or the part of the base that corresponds to the rate.