Answer:
E
Step-by-step explanation:
NO
2
3
2
x
=2
5
x=
PLEASE HELPPPPPP
Answer: can you put it in diffrent form beucase the way you have it is really confusing me thanks
Step-by-step explanation:
A rubber bouncy ball is dropped at a height of 120.00 inches onto a hard flat floor. After each bounce, the ball returns to a height that is 20\% less than the previous maximum height. What is the maximum height reached after the 7th bounce? Round your answer to the nearest hundredth.
Answer:
To solve the problem, we need to find the maximum height reached by the ball after the 7th bounce, given that each bounce has a rebound height of 20% less than the previous maximum height.
Let's start by finding the maximum height reached by the ball on the first bounce. The ball is dropped from a height of 120.00 inches, so the maximum height reached on the first bounce is:
120.00 inches
For each subsequent bounce, the maximum height reached is 20% less than the previous maximum height. We can express this mathematically as:
maximum height = 0.8 * previous maximum height
Using this formula, we can calculate the maximum height reached on the second bounce as:
maximum height on 2nd bounce = 0.8 * 120.00 inches = 96.00 inches
On the third bounce, the maximum height reached is 20% less than 96.00 inches:
maximum height on 3rd bounce = 0.8 * 96.00 inches = 76.80 inches
We can continue this pattern for each subsequent bounce. The maximum height reached on the fourth bounce is:
maximum height on 4th bounce = 0.8 * 76.80 inches = 61.44 inches
The maximum height reached on the fifth bounce is:
maximum height on 5th bounce = 0.8 * 61.44 inches = 49.15 inches
The maximum height reached on the sixth bounce is:
maximum height on 6th bounce = 0.8 * 49.15 inches = 39.32 inches
Finally, the maximum height reached on the seventh bounce is:
maximum height on 7th bounce = 0.8 * 39.32 inches = 31.46 inches
Therefore, the maximum height reached by the ball after the 7th bounce is approximately 31.46 inches. Rounded to the nearest hundredth, this is 31.45 inches.
Un móvil parte del reposo acelerando a razón de 3m/. Calcular el espacio recorrido en el tercer segundo
Answer:
El espacio recorrido en el tercer segundo será de 9 m.
Step-by-step explanation:
In the scale drawing of the base of a rectanglar swimming pool, the pool is 8.5 inches long and 4.5 inches wide. If 1 inch on the scale drawing is equivalent to 4 meters of actual length, what are the actual length and width of the swimming pool
Answer:
34 m x 18 m
Step-by-step explanation:
No picture shown, but we can do it anyway. If one inch on the drawing is actually 4 meters, multiply each dimension by 4.
The actual length is (8.5 * 4) = 34 meters.
The actual width is (4.5 * 4) = 18 meters.
The actual dimensions of the pool are 34 meters long and 18 meters wide.
Compute the correlation coefficient for the following: X: -5, 1, 2, 11. Y: 5, 3, -3, 0
The correlation coefficient between X and Y is approximately -0.483.
We must first determine the mean and standard deviation for both X and Y in order to calculate the correlation coefficient between X and Y.
X has a mean of:
(-5 + 1 + 2 + 11)/4 = 2.25 is the mean of X.
Y has a mean of:
average of Y = (5 + 3 - 3 + 0)/4 = 1.
The value of X's standard deviation is
s_X = sqrt([(-5 - 2.25)^2 + (1 - 2.25)^2 + (2 - 2.25)^2 + (11 - 2.25)^2]/3) = 5.1478
The value of Y's standard deviation is
s_Y = sqrt([(5 - 1)^2 + (3 - 1)^2 + (-3 - 1)^2 + (0 - 1)^2]/3) = 3.7712
After that, we can figure out the correlation between X and Y:
cov(X, Y) = [(-5 - 2.25) × (5 - 1) + (1 - 2.25) × (3 - 1) + (2 - 2.25) × (-3 - 1) + (11 - 2.25) × (0 - 1)]/3 = -7.25
We can finally determine the correlation coefficient:
r = cov(X, Y)/(s X, s Y)=-7.25/(5.1478 3.7712)=-0.483
Thus, roughly -0.483 is the correlation coefficient between X and Y.
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X is a positive discrete uniform random variable. The mean and
the variance of X are equal to (µ,sigma2) = (5,4). Find
P(X>=6).
answers
(a) 3\7
(b) 1\2
(c) 2\7
As X is a discrete uniformly distributed random variable with a mean of 5, a variance of 4, and a range of values from 1, 2, 3, 5, 6, 7, 8, and 10, we know that X can have any one of these values with an equal probability of 1/10.
Calculating the likelihood that X will have a number equal to or greater to 6 is necessary to get [tex]P(X > =6)[/tex]. Due to the fact that X is a continuous uniformly distributed random variable.
We may calculate this probability simply counting all number of potential values for X that are greater or equal to to 6, dividing by the entirety of the potential values for X, and then adding the results together.
The probability of X is more than or equivalent to 6 is given by the fact there are a total of 5 variables of X that are at least equal to 6, namely: 6, 7, 8, 9, and 10.
[tex]P(X > =6) = 5/10 = 1/2[/tex]
Thus, (b) 1/2 is the right response.
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What is the length of x in the diagram below?
A triangle with vertical bisector forms 2 triangles with a right angle. One triangle has a side length of 5 and another angle with a measure 45 degrees. Another triangle has a hypotenuse with length x and another angle with measure 30 degrees.
StartFraction 5 Over StartRoot 3 EndRoot
StartFraction 10 Over StartRoot 3 EndRoot EndFraction
5 StartRoot 3 EndRoot
10
Answer:
The length of x is (10√3)/3.
Step-by-step explanation:
Using the trigonometric ratios of a 30-60-90 triangle, we know that the side opposite the 30-degree angle is half the length of the hypotenuse. Therefore, we have:
x/2 = (5/√3)
Multiplying both sides by 2, we get:
x = 10/√3, which can be simplified to:
x = (10√3)/3
So the length of x is (10√3)/3.
Hope this helps you! I'm sorry if it's wrong. If you need more help, ask me! :]
GEOMETRY Heron's formula states that the area of a triangle whose sides have lengths
1
a, b, and c is A = √s(s-a)(s - b)(s-c) where s =1/2 (a + b + c). If the area of
the triangle is 270 cm², s = 45 cm, a = 15 cm, and c = 39 cm, what is the length of side
b?
Answer:
Approximately 26.87 cm
Step-by-step explanation:
To find the length of side b using Heron's formula, we need to substitute the given values into the formula and solve for b:
A = √s(s-a)(s - b)(s-c)
270 = √45(45-15)(45-b)(45-39)
Simplifying the expression inside the square root:
270 = √45(30)(6)(6-b)
270 = 540√(6-b)
Squaring both sides:
72900 = 291600 - 54000b + 3240b^2
Rearranging:
3240b^2 - 54000b + 218700 = 0
Dividing both sides by 540:
6b^2 - 100b + 405 = 0
We can solve for b using the quadratic formula:
b = (-(-100) ± √((-100)^2 - 4(6)(405))) / (2(6))
b = (100 ± √13600) / 12
b ≈ 26.87 cm (rounded to two decimal places)
Therefore, the length of side b is approximately 26.87 cm.
3/4(8x+12)+x-5
this is hard can someone help
From the given expression, 3/4(8x+12)+x-5, the simplified expression is 7x + 4.
Simplifying an ExpressionFrom the question, we are to simplify the given expression.
To simplify the expression 3/4(8x+12)+x-5, we can follow the order of operations, which is commonly remembered using the acronym PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Using PEMDAS, we can simplify the expression as
3/4(8x+12)+x-5
Distributing 3/4 to the terms inside the parentheses
= 3/4 * 8x + 3/4 * 12 + x - 5
Simplifying the multiplication
= 6x + 9 + x - 5
Combining like terms
= 7x + 4
Hence, the simplified expression is 7x + 4.
Here is the complete question:
Simplify 3/4(8x+12)+x-5
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6 A cookery book shows how long it takes, in minutes, to cook a joint of meat. Electric oven time = (66 x weight in kg) + 35 Microwave oven time = (26 x weight in kg) + 15 a Compare the two formulae for cooking times. If a joint of meat takes about 2 hours to cook in an electric oven, roughly how long do you think it would take in a microwave oven? bi Work out how much quicker is it to cook a 2 kg joint of meat in a microwave oven than in an electric oven. il Does your answer to part a seem sensible?
a) the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.
b)a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.
c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.
Define equationThe definition of an equation is the claim that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, operations, and functions.
a) The two formulae for cooking times are:
(66 x weight in kg) + (35 x time in an electric oven
Microwave oven time = (26 x weight in kg) + 15
We can compare the two formulae by looking at their coefficients and constants. This suggests that the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.
b) (66 x weight in kg) + (35 x time in an electric oven
2 x 60 = (66 x weight in kg) + 35
120 - 35 = 66 x weight in kg
85 = 66 x weight in kg
weight in kg = 85 / 66
weight in kg ≈ 1.29
So, a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.
Microwave oven time = (26 x weight in kg) + 15
Microwave oven time = (26 x 1.29) + 15
Microwave oven time ≈ 48.34 minutes
Therefore, a 1.29 kg joint of meat would take about 48 minutes to cook in a microwave oven.
c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.
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Q28) A neighborhood depanneur has determined that daily demand for milk cartons has an approximate normal distribution, with a mean of 65 cartons and a standard deviation of 7 cartons. On Saturdays, the demand for milk is known to exceed 71 cartons. On the coming Saturday, what is the probability that it will be at least 81 cartons?
The probability that there will be at least 81 cartoons on a coming Saturday is given as follows:
0.011 = 1.1%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule 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, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 65, \sigma = 7[/tex]
The probability that there will be at least 81 cartoons is one subtracted by the p-value of Z when X = 81, hence:
Z = (81 - 65)/7
Z = 2.29
Z = 2.29 has a p-value of 0.989.
Hence:
1 - 0.989 = 0.011 = 1.1%.
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A packet contains 126 sweets. The sweets are all red, yellow or green in the ratio of 6 : 4 : 4Find how many yellow sweets are in the packet
If he sweets are all red, yellow or green in the ratio of 6 : 4 : 4, there are 36 yellow sweets in the packet.
To solve this problem, we need to use the concept of ratios. The ratio of red, yellow, and green sweets is 6:4:4, which means that for every 6 red sweets, there are 4 yellow and 4 green sweets.
We can use this ratio to find out how many yellow sweets there are in the packet. Since the ratio of yellow sweets to the total number of sweets is 4:14 (6+4+4=14), we can write:
Yellow sweets / 126 = 4 / 14
To solve for the number of yellow sweets, we can cross-multiply and simplify:
Yellow sweets = 126 x 4 / 14
Yellow sweets = 36
We can also use the same method to find the number of red and green sweets:
Red sweets = 126 x 6 / 14
Red sweets = 54
Green sweets = 126 x 4 / 14
Green sweets = 36
To check our answer, we can verify that the total number of sweets is equal to the sum of red, yellow, and green sweets:
54 + 36 + 36 = 126
Therefore, our answer is correct.
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Brian has $20,000 in a savings account that earns 5% annually. The interest is not
compounded. How much will he have in total in 5 years?
Answer:
Since the interest is not compounded, Brian will earn a simple interest of 5% per year on his initial deposit of $20,000. The formula for calculating simple interest is:
I = P * r * t
where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.
Substituting the given values, we get:
I = 20,000 * 0.05 * 5 = 5,000
Therefore, Brian will earn $5,000 in interest over the 5-year period. Adding this to his initial deposit of $20,000, we get:
Total amount = $20,000 + $5,000 = $25,000
Therefore, Brian will have a total of $25,000 in his savings account after 5 years.
Answer:
$25,000
Step-by-step explanation:
The total amount Brian will have in 5 years can also be calculated using the formula for simple interest:
A = P(1 + rt)
where:
A = the total amount
P = the principal (initial balance)
r = the annual interest rate
t = the time period (in years)
In this case:
P = $20,000
r = 0.05 (since 5% is the annual interest rate)
t = 5 (since we're calculating the total amount after 5 years)
Plugging these values into the formula, we get:
A = $20,000(1 + 0.05 x 5)
A = $20,000(1.25)
A = $25,000
So we get answer of $25,000, which is the total amount Brian will have in 5 years.
Find the equation of the linear function
represented by the table below in slope-
intercept form.
Answer:
X
-2
3
8
13
y
-8
7
22
37
Answer: y=3x-2
Step-by-step explanation
(-8)-(7)/ (-2)- (3) = -15/ -5= 3
y=3x+b
f(-2)= -8
y= 3x+ b
-8= 3(-2)+b
-8=-6+b
add 6 on both sides
b=-2
y=3x-2
The cuboid below is made of nickel and has a mass of 534 g. Calculate its density, in g/cm³. If your answer is a decimal, give it to 1 d.p
The sοlutiοn οf the given prοblem οf cubοid cοmes οut tο be the cubοid has a density οf abοut 6.0 g/cm³.
Describe the cubοid.In geοmetry, a hypercube is a cοncrete οr muti shape. A hypercube is a cοnvex pοlygοns with 12 sides, 6 rectangular faces, and 8 edges. A cubοid is anοther term fοr the creature. An οbject with six square sides is called a cube. Bricks and literature are amοng the items fοund in bοxes. The main differences between cubic but alsο cubic are as fοllοws.
Here,
This equatiοn can be changed tο read density = mass/vοlume. Since we already knοw the mass (534 g), we can use the rearranged methοd tο determine the vοlume.
=> Vοlume = L, W, and H, and mass = 534 g.
=> density equals mass/vοlume
=> weight = 534/ (L x W x H)
The CRC Encyclοpedia οf Chemistry and Physics states that nickel has a density οf 8.908 g/cm³.
Thus, we can enter this number as a substitute in οur fοrmula tο οbtain:
=> density = 534/(L, W, H)
=> 8.908 g/cm³.
Tο sοlve fοr density, we can rewrite this equatiοn as fοllοws:
=> density = 534/(L, W, H)
=> 6.0 g/cm³ (tο 1 decimal place)
Cοnsequently, the cubοid has a density οf abοut 6.0 g/cm³.
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Write an equation for each line
slope=5/6;through(22,12)
The equation for the line with a slope of 5/6 and passing through the point (22,12) is y=5/6x - 16.
The equation for the line with a slope of 5/6 and passing through the point (22,12) can be expressed as y=5/6x + b. To calculate the value of b, we can plug in the given point's coordinates, (22,12), into the equation. This will result in the equation 12=5/6(22)+b. Solving for b, we get b=-16. Therefore, the equation for the line is y=5/6x-16.
In summary, we can express the equation for the line with a slope of 5/6 and passing through the point (22,12) as y=5/6x - 16. To calculate the value of b, we plugged the point's coordinates, (22,12), into the equation, resulting in the equation 12=5/6(22)+b. Solving for b, we got b=-16. Thus, the equation for the line is y=5/6x - 16.
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Mariah's lunch bill was $13.00. What is the least amount
of bills she could use to pay for her lunch?
In circle H with m \angle GHJ= 90m∠GHJ=90 and GH=20GH=20 units, find the length of arc GJ.
HELP!!
The radius is equal to the length of the given line segment GH, which is 20 units. In this case, r = 20, and θ = 90° = π/2 radians.
Arc GJ is the portion of the circumference of circle H that lies between points G and J. Arc GJ can be calculated using the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = GH = 20 and θ = 90° = π/2 radians. Therefore, l = 20π/2 = 10π. Therefore, the length of arc GJ is 10π units.For example, if the radius of circle H is 10 units, l = 10π/2 = 5π. Thus, the length of arc GJ would be 5π units.To calculate arc GJ, we must first determine the radius of circle H. The radius is equal to the length of the given line segment GH, which is 20 units. We then use the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = 20, and θ = 90° = π/2 radians.
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the lengths of human pregnancies (gestations) can be modeled by a bell-shaped distribution with mean 266 days and standard deviation 16 days. use the empirical rule to answer the questions below. what is the 84th percentile of the gestations?
The 84th percentile of gestations which can be ruled by standard deviation is 282 days.
The lengths of human pregnancies (gestations) can be modeled by a bell-shaped distribution with a mean of 266 days and a standard deviation of 16 days. Use the empirical rule to determine the 84th percentile of the gestations. The empirical rule, also known as the 68-95-99.7 percent rule, is a statistical guideline that states that within one standard deviation of the mean, 68 percent of the data is distributed.
Within two standard deviations of the mean, 95% of the data is distributed. Finally, 99.7 percent of the data is distributed within three standard deviations of the mean. As a result, it's necessary to locate the corresponding z-score for the given percentile to use the empirical rule.
Since we have the mean and standard deviation, we can use the following equation to compute the z-score using the formula: z = (X - µ)/σ where X is the value of interest, µ is the mean, and σ is the standard deviation. From the formula: z = (X - µ)/σX = µ + zσ Substituting the given values in the formula, we get: X = 266 + z(16)We need to find the 84th percentile.
This means that the remaining 16 percent of the data is distributed outside of the mean plus one standard deviation. As a result, the corresponding z-score can be found using a standard normal distribution table or calculator. The standard normal distribution table or calculator gives us the z-score of 1.00 for the 84th percentile. Using this, we can compute the value of X as follows: X = µ + zσX = 266 + (1.00)(16)X = 266 + 16X = 282
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Quadratic formula in standard form for points (2.5, 1.5), (2,0) and (3,0)
The Quadratic formula in standard form for points (2.5, 1.5), (2,0) and (3,0) are x²-4x + 3.75 = 0 and x² -2x = 0
What is the standard for for quadratic equation?The standard form of a quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number
The given parameters that will help us to find the equations are
x = 2.5, and x = 1.5
(x-2.5) (x- 1.5)
Opening the brackets we have
x²-1.5x -2.5x + 3.75 = 0
x²-4x + 3.75 = 0
and the second is given as 2,0
x=2 and x=0
(x-2)(x-0)
Opening the brackets we have
x² -0 -2x+0 = 0
x² -2x = 0
Therefore the standard forms for the quadratic equations are x²-4x + 3.75 = 0 and x² -2x = 0
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For a relationship between variables x and y, the value of y is 24 when x=0, and the value of y increases by 65% for every unit increase of x. What is an exponential equation that relates x and y?
Answer:
The answer would be the second one.
Step-by-step explanation:
The answer is this because 65% as a decimal is .65 and the second equation is the only one with a .65 in it. It is also the only equation with 24 in it as well.
The area of the rectangle to the right is 18x² - 6x, and its width is 6x. Find the length of the rectangle.
Answer:
length = 3x - 1
Step-by-step explanation:
Area of a rectangle = length x width
or using l = length, w = width and A = area
A = l x w
or
l = A/w
Given
A = 18x² - 6x
w = 6x
l = 18x²- 6x/6x
= 18x²/6x - 6x/6x
= 3x - 1
Answer:
3x - 1
Step-by-step explanation:
Area of the Rectangle:
18x^2 - 6x
6x (3x - 1)
Width = 6x
Length =?
Area of Rectangle = Length * Width
Length = Area/breadth
6x (3x -1) / 6x cross out 6x
Thus, Length of Rectangle = 3x - 1
Pleaseeeeee helppp!!!!
Answer:
≈ 18.8 cm
Step-by-step explanation:
Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.
The area of the square is given as 36 cm^2, so we can find the side length of the square as:
side length = √(area) = √(36 cm^2) = 6 cm
The diameter of the circle is therefore also 6 cm, and the radius of the circle is half the diameter, or 3 cm.
The circumference of a circle is given by the formula:
circumference = 2πr
where r is the radius of the circle.
Substituting in our values, we get:
circumference = 2π(3 cm) = 6π cm
Using a calculator to approximate π to one decimal place, we get:
circumference ≈ 18.8 cm
Therefore, the circumference of the circle inside the square is approximately 18.8 cm.
10. Suppose y = x2 - 2x - 3. What is a linear equation that intersects the graph of
y=x²-2x-3 in exactly two places? Name the two points of intersection.
well, let's pick any two random x-values on the quadratic, hmmm say let's use x = 4 and x = 7, so hmm f(4) = 5 and f(7) = 32, that'd give us the points of (4, 5) and (7 , 32).
To get the equation of any straight line, we simply need two points off of it, let's use those two above.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{32}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{32}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{ 27 }{ 3 } \implies 9[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 9}(x-\stackrel{x_1}{4}) \\\\\\ y-5=9x-36\implies {\Large \begin{array}{llll} y=9x-31 \end{array}}[/tex]
Check the picture below.
Refer to the attached images.
What is a quadratic function (f) whose zeros are -2 and 11
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 11 &\implies x -11=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -11 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{3em}1( x +2 )( x -11 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-9x-22=f(x) \end{array}} ~\hfill[/tex]
help me pleasee still stuck
Answer:
90*
Step-by-step explanation:
Answer: 90 degrees
Step-by-step explanation:
Not sure what its asking but x is at the angle part which is definitely 90 degrees
The point (2,3) lies on the line 2x+ky=19. Find the value of k.
Since the point (2, 3) lies on the line 2x + ky = 19, the value of k is equal to 5.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Making k the subject of formula, we have the following:
k = (19 - 2x)/y
Since the point (2, 3) lies on the line, we have:
k = (19 - 2(2))/3
k = (19 - 4)/3
k = 15/3
k = 5.
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After the last ice age began, the number of animal species in Australia changed rapidly. The relationship between the elapsed time, ttt, in years, since the ice age began, and the total number of animal species, S(t)S(t)S, left parenthesis, t, right parenthesis, is modeled by the following function: S(t)=4,200,000⋅(0. 72)t Complete the following sentence about the yearly percent change of the number of animal species
The yearly percent change in the number of animal species is approximately -67.68%. This means that the number of animal species is decreasing by about 67.68% each year after the last ice age began.
The yearly percent change of the number of animal species after the last ice age began can be calculated by taking the derivative of the function given, S(t)=4,200,000⋅(0.72)t. Using the power rule, the derivative of this function is S'(t)=2,976,000⋅(0.72)t-1. This tells us that the yearly percent change in the number of animal species is -72%. This means that every year, the total number of animal species decreases by 72%.
The yearly percent change of the number of animal species can be determined by finding the derivative of the function [tex]S(t) = 4,200,000(0.72)^t.[/tex]
The derivative of the function can be calculated as follows:[tex]S'(t) = 4,200,000 ln(0.72) (0.72)^t[/tex] The yearly percent change can be calculated by finding the percentage change in the total number of animal species for each year. This can be done by finding the percentage change in the value of the function for each year.
The percentage change in the value of the function can be calculated using the formula:% change = [(new value - old value) / old value] x 100Substituting the values of the function for different years in the above formula, we can find the percentage change for each year.
For example, if we want to find the percentage change in the number of animal species after 10 years, we can substitute t = 10 in the function and calculate the new value of S(t). Then, we can use the above formula to find the percentage change in the value of the function for 10 years.S(10) = 4,200,000(0.72)^10 ≈ 1,357,747% change = [(1,357,747 - 4,200,000) / 4,200,000] x 100 ≈ -67.68%
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