Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.
To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:
tan(θ) = x/15
We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:
d^2 = x^2 + 25^2
Taking the derivative of both sides with respect to time t, we get:
2d (dd/dt) = 2x (dx/dt)
Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):
tan(θ) = x/15
sec^2(θ) (dθ/dt) = (1/15) (dx/dt)
(dθ/dt) = (1/15) (dx/dt) sec^2(θ)
We can use the equation for d to solve for x:
x^2 = d^2 - 25^2
2x (dx/dt) = 2d (dd/dt)
(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)
(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)
Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):
(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))
(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))
(dθ/dt) = (13/375) sec^2(arctan(15/25))
(dθ/dt) ≈ 0.039 radians per second
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HELP ASAP ! Write a function rule for the table.
A. ƒ(x) = 3x
B. ƒ(x) = x + 3
C. ƒ(x) = –3 – x
D. ƒ(x) = x – 3
Answer:
The correct answer is D. ƒ(x) = x – 3.
The function rule for a table is a mathematical expression that relates the input values to the output values. In this case, the input values are the numbers in the first column of the table, and the output values are the numbers in the second column of the table.
To find the function rule, we can look for a pattern in the table. We can see that each output value is 3 less than the corresponding input value. For example, when the input value is 1, the output value is -2. When the input value is 2, the output value is -1.
This pattern can be expressed mathematically as ƒ(x) = x – 3. This function rule tells us that the output value is equal to the input value minus 3.
Step-by-step explanation:
find dy/dx and d2y/dx2. x = 2 sin t, y = 3 cos t, 0 < t < 2π
Therefore, the value of derivatives dy/dx = -3 tan t/2 and d2y/dx2 = -3(1 - cos t)/(2(1+cos t)^2).
To find dy/dx and d2y/dx2, we need to first express y in terms of x:
x = 2 sin t --> sin t = x/2 --> cos t = ±sqrt(1 - sin^2 t) = ±sqrt(1 - x^2/4)
y = 3 cos t = ±3sqrt(1 - x^2/4)
Since 0 < t < 2π, we can determine the sign of cos t by looking at the quadrant that x lies in. Since x = 2 sin t, we have x > 0 when 0 < t < π and x < 0 when π < t < 2π. Therefore, when 0 < t < π, we have:
cos t = sqrt(1 - sin^2 t) = sqrt(1 - x^2/4)
y = 3 sqrt(1 - x^2/4)
dy/dx = -3x/2 sqrt(1 - x^2/4)^(-1)
Taking the derivative of dy/dx with respect to x, we get:
d2y/dx2 = -3/2 [sqrt(1 - x^2/4)^(-1) - 3x^2/8 (1 - x^2/4)^(-3/2)]
Plugging in x = 2 sin t and simplifying, we get:
dy/dx = -3 sin t / sqrt(4 - 4 sin^2 t) = -3 sin t / 2 cos t = -3 tan t/2
d2y/dx2 = -3/4 (sec^2 t/2 - 3 tan^2 t/2) = -3/4 [(2/(1+cos t) - 3 tan^2 t/2)]
Using the identity cos^2(t/2) = (1+cos t)/2 and simplifying, we get:
d2y/dx2 = -3/4 [(4/(1+cos t) - 3) / (1+cos t)] = -3(1 - cos t)/(2(1+cos t)^2)
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questionthere are 76 ounces of fluid in container a. this is about 8 times the amount of fluid in container how many ounces of fluid are there in container b?select the numbers that correctly complete the are between choose... ounces of fluid in container b.
The amount of fluid in container B is 9.5 ounces.
to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.
To determine the amount of fluid in container B, we can divide the amount of fluid in container A by the given ratio of 8. Since container A contains 76 ounces, we divide 76 by 8 to find that each unit of the ratio represents 9.5 ounces. Therefore, container B would contain 9.5 ounces of fluid.
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Is it negative or positive to say that your gonna “destroy” someone in a race?
Saying you will destroy someone in a race could be positive or negative depending on the context of the situation.
What does it mean to destroy someone in a race?Using the word "destroy" to describe beating someone in a race can be viewed as negative or positive, depending on the context and the relationship between the individuals.
In some situations, it may be seen as a playful or friendly challenge, indicating a competitive but good-natured spirit. However, in other cases, it may come across as aggressive or intimidating, potentially damaging the relationship between the participants.
It is important to consider the tone and the relationship when using language that could be interpreted as confrontational or threatening.
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In AABC, mA = 58° and m2 B = 45°.
Select the triangle that is similar to AABC.
A. APQR, in which mZP = 58° and
mZR= 70°
B. AXYZ, in which mZX= 45° and
mZY= 103°
OC. AHIJ, in which mZH= 58° and
mZJ= 77°
OD. AMNP, in which m/M = 58° and
mZN = 103°
The triangle similar to ΔABC is ΔSTU, in which m∠S = 87° and m∠U = 70°. Option C
We have,
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
In ΔABC, we know that m∠A = 87° and m∠B = 23°.
The angle m∠C must therefore be 70°,
since the sum of the angles in a triangle is always 180°.
now, we have,
In ΔSTU, we are given that m∠S = 87°, which corresponds to ∠A in ΔABC.
We are also given that m∠U = 70°, which corresponds to ∠C in ΔABC.
so, we get,
as, This is because two triangles are similar if their corresponding angles are congruent.
Therefore, ΔSTU is similar to ΔABC.
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The above answer is in response to the full question below
In Δ ABC, m∠A = 87° and m∠B = 23°.
Select the triangle that is similar to ΔABC.
A. ΔXYZ, in which m∠X= 87° and m∠z = 50°
B. ΔLMN, in which m∠M=20° and m∠N=87°
C. ΔSTU, in which m∠s = 87° and m∠U=70°
D. ΔPQR, in which m∠P= 110° and m∠R = 23°
The formula PV - FV(1 + n) will determine the present value of $1. True/False
False. The formula PV - FV(1 + n) does not determine the present value of $1.
But rather it is a formula used to calculate the present value of a future cash flow or investment. PV stands for present value, FV stands for future value, and n represents the number of periods for which the investment will be held. The formula states that the present value of an investment or cash flow is equal to the future value of that investment or cash flow, discounted at a specified rate of return over a specific period of time.
In other words, the formula is used to determine the value today of a future cash flow or investment based on the time value of money. By discounting the future value of the cash flow or investment at a specified rate, the formula calculates the present value that would be equivalent to receiving that cash flow or investment at a future date.
Therefore, the correct statement would be: The formula PV - FV(1 + n) is used to determine the present value of a future cash flow or investment.
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Pump A and Pump B fill the pool in 35 minutes, Pump B and Pump C fill it in 40
minutes, and Pump A and Pump C fill it in 56 minutes. How many minutes will it take
all three pumps, working together, to fill the pool?
It will take all three pumps, Working together, 1.56 minutes to fill the pool.
The given information, we can write three equations as follows:
1) (1/A + 1/B)*35 = C ---(Equation 1)
2) (1/B + 1/C)*40 = C ---(Equation 2)
3) (1/A + 1/C)*56 = C ---(Equation 3)
We want how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".
When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.
Using the rate formula, we can write the following equation:
1/A + 1/B + 1/C = 1/t ---(Equation 4)
We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".
First, we can simplify Equations 1, 2, and 3 as follows:
1) 1/A + 1/B = C/35
2) 1/B + 1/C = C/40
3) 1/A + 1/C = C/56
Next, we can substitute these equations into Equation 4 to get:
(C/35) + (C/40) + (C/56) = 1/t
Now, we can simplify and solve for "t":
LCD = 39200
1120C + 980C + 700C = 39200
2800C = 39200
C = 14
Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:
1/A + 1/B = 14/35
5(A+B) = 98
A+B = 19.6
Now we can use A+B+C = 1/t to solve for "t":
t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes
Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.
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g) a car rental agency has ten mid-sized and fifteen compact cars on its lot, from which six will be selected. assuming that each is equally likely to be selected, and that they will be selected at random, what is the probability that exactly two mid-sized cars and four compact cars will be selected?
The probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.
The answer to this question involves using the formula for combinations and multiplying the probabilities of each selected car.
Calculate the number of ways to select two mid-sized cars and four compact cars.
- Choose 2 mid-sized cars from 10: C(10, 2) = 10! / (2! * (10 - 2)!) = 45 ways
- Choose 4 compact cars from 15: C(15, 4) = 15! / (4! * (15 - 4)!) = 1365 ways
There are a total of 25 cars to choose from and we need to select 2 mid-sized cars from the 10 available and 4 compact cars from the 15 available. Using the formula for combinations, we get:
C(10,2) * C(15,4) = 45 * 1365 = 61,425
This represents the number of ways we can select exactly 2 mid-sized cars and 4 compact cars. To find the probability, we divide this number by the total number of possible selections:
C(25,6) = 53,130
So the probability of selecting exactly 2 mid-sized cars and 4 compact cars is:
61,425 / 53,130 ≈ 0.1156 or 11.56%
In conclusion, the probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.
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two balls are drawn simultaneously from a bag containing 2 yellow and 4 green balls. what is the probability of drawing 2 green balls
The probability of drawing 2 green balls simultaneously from a bag containing 2 yellow and 4 green balls can be determined using the following method:
First, calculate the total number of balls in the bag. There are 2 yellow balls and 4 green balls, so the total is 6 balls.
Now, let's find the probability of drawing 2 green balls. To do this, consider the number of green balls (4) and the total number of balls (6). When drawing the first green ball, there are 4 green balls out of 6 total balls. Therefore, the probability of drawing one green ball is 4/6.
Since the balls are drawn simultaneously, there's no change in the number of balls for the second draw. So, the probability of drawing a second green ball remains 4/6.
Now, we can calculate the probability of both events occurring simultaneously by multiplying the probabilities:
(4/6) * (4/6) = 16/36
To simplify the fraction, divide both numerator and denominator by their greatest common divisor (4):
16/36 = 4/9
So, the probability of drawing 2 green balls simultaneously is 4/9.
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graph each image as well as the figure after each dilation with the origin as it's center and the given scale factor.
X(-3, 1), Y(-1, 2), Z(2, 1) K = 2
Answer:
Step-by-step explanation:
To perform a dilation with a center at the origin and a scale factor of 2, we multiply each coordinate by 2.
For point X(-3, 1):
x-coordinate: -3 * 2 = -6
y-coordinate: 1 * 2 = 2
So the image of point X after the dilation is X'(-6, 2).
For point Y(-1, 2):
x-coordinate: -1 * 2 = -2
y-coordinate: 2 * 2 = 4
So the image of point Y after the dilation is Y'(-2, 4).
For point Z(2, 1):
x-coordinate: 2 * 2 = 4
y-coordinate: 1 * 2 = 2
So the image of point Z after the dilation is Z'(4, 2).
Graph of the original triangle XYZ:
Y(0, 2)
/\
/ \
/____\
X(0, 0) Z(3, 0)
Graph of the triangle after dilation
Y'(-2, 4)
/\
/ \
/____\
X'(-6, 0) Z'(4, 0)
its hard
if the standard error is smaller than the standard deviation when conducting a regression, what can you conclude?
If the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable.
When conducting a regression, the standard error is a measure of the precision of the estimated regression coefficient. On the other hand, the standard deviation is a measure of the variability of the data points from the mean. If the standard error is smaller than the standard deviation, it means that the estimated regression coefficient is more precise than the variation of the data points. This indicates that the model is more reliable and accurate in predicting the outcome variable.
In practical terms, a smaller standard error means that the predicted values of the outcome variable will be closer to the actual values, resulting in more accurate predictions. However, it is important to note that a smaller standard error does not necessarily mean that the regression model is better. Other factors such as the goodness of fit, significance of the coefficients, and the overall explanatory power of the model should also be considered when evaluating the performance of a regression model.
In conclusion, if the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable. However, other factors should also be taken into account to evaluate the overall performance of the model.
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Hi can someone who is great at math help me with this math questions and show the steps! I’m struggling with it. Find the area of the middle shape.
The calculated area of the middle shape is 18 square units
Finding the area of the middle shape.From the question, we have the following parameters that can be used in our computation:
The figures
From the figure, we have the middle shape to be a rectangle
The width of the rectangle is
Width = 6
The length of the rectangle is calculated as follows
15 = 3 * 5
27 = 3 * 3 * 3
The common factor is 3
So, we have
Length = 3
The area of the rectangle is calculated as
Area = Length * Width
So, we have
Area = 3 * 6
Evaluate
Area = 18
Hence, the area of the middle shape is 18 square units
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
0.714
Step-by-step explanation:
5/7
(5X100) / 7 = 500/7.
50/7 = 7 remainder 1. carry that one over and place it before last zero in 500.
10/7 = 1 remainder 3.
we have 71 remainder 3.
3/7: 300/7 = 42.83
we now have answer of 0.714282
= 0.714 to nearest thousandth
Find the angles plssss hurry
Answer:
a = 157
b = 23
c = 157
Step-by-step explanation:
Angle b is a vertical angle to the angle measuring 23 so they are equal.
b = 23
Angle c and the angle measuring 23 forms a straight line so they add to 180.
c+23 =180
c = 180-23
c = 157
Angle c and a are vertical angles so they are equal.
c = a = 157
Answer:
a = 157°
c = 157°
b = 23°
Step-by-step explanation:
We know that vertically opposite angles are equal.
∴ b = 23°
We know that angles in a straight line are added up to 180°.
∴ b + c = 180
23 + c = 180
c = 180 - 23
c = 157°
a = 157° ( vertically opposite angles ⇒ c = a )
Jayna lives 2 ⅗ miles away from school. Ava lives 3 ⅖ miles away from school. How much further from the school is Ava than Jayna?
Answer:
Ava lives 8/5 or 1 3/5 miles further from the school compared to Jayna.
Step-by-step explanation:
PLEASE HELP I AM GROUNDED AND NEED THIS ANSWER
Answer: 39
Step-by-step explanation: 180-141= 39
What is the following product?
sq root 30 product sq root 10
2 sq root 10
3 sq root 10
4 sq root 10
10 sq root 3
The product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10}[/tex] is 10[tex]\sqrt{3}[/tex].
The correct answer would be 10[tex]\sqrt{3}[/tex].
To find the product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10\\}[/tex], we can simplify it by multiplying the square roots and simplifying the result.
[tex]\sqrt{30 * 10 = (30 * 10) = 300}[/tex]
Now, let's simplify [tex]\sqrt{300}[/tex]. To do this, we can find the prime factorization of 300:
[tex]300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2[/tex]
Taking the square root of 300:
[tex]\sqrt{300}[/tex] = ([tex]\sqrt{(2^2 * 3 * 5^2)}[/tex]
Using the properties of square roots, we can split the square root into separate square roots:
[tex]\sqrt{300}[/tex] = [tex]\sqrt{2^2}[/tex] * [tex]\sqrt{3}[/tex] * [tex]\sqrt{5^2 }[/tex]
Simplifying each square root separately:
[tex]\sqrt{2^2}[/tex] = 2
[tex]\sqrt{3[/tex] = [tex]\sqrt{3[/tex]
[tex]\sqrt{5^2 }[/tex]= 5
Combining the simplified square roots:
[tex]\sqrt{300}[/tex] = 2[tex]\sqrt{3}[/tex] * 5 = 10[tex]\sqrt{3}[/tex]
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Calculate the Curved Surface area of a Cone whose height IS 8Cm and radius is 5cm
The curved surface area of the cone is 148.19 square cm
Calculating the curved surface area of the coneFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 5 cm
Height, h = 8 cm
The slant height l of the cone is calculated as
l² = 8² + 5²
So, we have
l² = 89
This gives
l = √89
The curved surface area of the cone is then calculaed as
Area = πrl
So, we have
Area = π * 5 * √89
Evaluate
Area = 148.19
Hence, the curved surface area of the cone is 148.19 square cm
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2. When making a full batch of tuna, you will mix one pouch of tuna with 26oz (737g) of mayonnaise. How much tuna and mayonnaise would you need when making a double batch?
These measurements are based on the Original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.
If one pouch of tuna is mixed with 26 oz (737g) of mayonnaise to make a full batch, then to make a double batch of tuna, we need to double the amounts of both the tuna and the mayonnaise.
we simply need to multiply the amount of tuna in a single batch by 2:
1 pouch of tuna x 2 = 2 pouches of tuna
So, we need 2 pouches of tuna for a double batch.
26 oz (737g) of mayonnaise x 2 = 52 oz (1474g) of mayonnaise
So, we need 52 oz (1474g) of mayonnaise for a double batch.
Therefore, to make a double batch of tuna, we would need 2 pouches of tuna and 52 oz (1474g) of mayonnaise. It's important to note that these measurements are based on the original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.
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Find the area of the triangle. Simplify your answer.
The area of the triangle with base 2x and height (x - 7) in simplified form is x² - 7x
What is the area of the triangle?Area of a triangle = ½ × base × height
Base = 2x
Height = (x - 7)
Area of a triangle = ½ × base × height
= ½ × 2x × (x - 7)
= (2x² - 14x) / 2
= x² - 7x
Hence, the triangle given the dimensions has an area of x² - 7x
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What is the growth factor?
Hint: the "growth factor" is the number that each term is multiplied by, to get the next term.
With exponential decay, the "growth factor" will be a fraction.
Growth Factor:
The calculated value of the exponential decay factor is 1/5
Calculating the growth factor or exponential decay?From the question, we have the following parameters that can be used in our computation:
The table of values
From the table of values, we can see that
x f(x)
1 625
2 125
3 25
This show that as x increases by 1, the function f(x) values decreases by a constant factor
This means that
The function is a decay function and the rate of decay is calculated as
Rate = 125/625
Evaluate
Rate = 1/5
Hence, the exponential decay factor is 1/5
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An army contingent of 1000 members is to march behind an army of 56 members in a parade. The 2 groups are to march in the same number of columns. What is the maximum number of columns in which they can march ?
The value of number of columns in which they can march is, 8
According to the problem ,
Members in army contingent = 1000
And, Members in army band = 56
Hence, To find maximum number of columns to march behind army band in the same number of columns,
we have to find HCF of 1000 and 56
1000 = 56 × 17 + 48
56 = 48 × 1 + 8
48 = 8 × 6 + 0
Here, Remainder has become zero.
Since, the divisor in this is, 8 .
HCF ( 1000 , 56 ) = 8
Thus, Required columns = HCF ( 1000 , 56 ) = 8
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do you think the question or problem you described could be investigated using a mathematical population model? why or why not?
It is possible that the question or problem described could be investigated using a mathematical population model. A population model is a mathematical representation of a population, which can be used to make predictions about the population’s behavior and characteristics.
The usefulness of such a model would depend on the specific question or problem at hand. If the question involves understanding how a population will grow or change over time, a mathematical model could be very helpful. However, if the question is more complex and involves multiple factors or variables, a mathematical model may not be sufficient on its own.
For example, if the question is about predicting the spread of a disease in a population, a mathematical model that takes into account the size of the population, the infectiousness of the disease, and the effectiveness of various interventions could be very useful. On the other hand, if the question is about understanding the motivations and behavior of individuals within a population, a mathematical model may not be the best approach. In this case, other methods such as surveys or interviews may be more appropriate.
In summary, whether or not a mathematical population model is appropriate for investigating a question or problem depends on the specific details of that question or problem. In some cases, a population model can provide valuable insights and predictions, while in other cases it may not be sufficient on its own.
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5x-4y=34
-x+8y=22
find the solution of the system of equations.
The solution of the system of equations 5x-4y=34 and -x+8y=22 is x = -6 and y = 4, or (x, y) = (-6, 4).
What is the solution to the system of equation?Given the system of equation in the question;
5x - 4y = 34 _____1
-x + 8y = 22 _____2
To solve the system of equation, first solve for x in equation 2 and plug it into equation 1.
-x + 8y = 22
x = 8y - 22 _____ 3
Plug equation 3 into equation 1
5x - 4y = 34
Plug in x = 8y - 22
5( 8y - 22 ) - 4y = 34
Solve for y
40y - 110 - 4y = 34
40y - 4y = 34 + 110
36y = 144
y = 144/36
y = 4
Plug y = 4 into equation 3
x = 8( 4 ) - 22
x = 32 - 22
x = 10
Therefore, the solution is x = 10 and y = 4.
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what is the surface area
The total surface area of the pyramid is: 208.88 m²
What is the surface area of the pyramid?The surface area of the pyramid is simply the sum of the areas of all the given surfaces.
Formula for the area of a triangle is:
Area = ¹/₂bh
where:
b is base
h is height
Area of four side triangles = 4(¹/₂ * 8 * 12) = 192 m²
Using Pythagoras theorem, the height of the base triangle is:
x = 4.22
Area of base = ¹/₂ * 8 * 4.22 = 16.88 m²
Total surface area = 192 + 16.88
= 208.88 m²
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Biologists introduced a population of bacteria to a test environment. The function � ff models the population size (in thousands) as a function of time (in days) after introduction.
The number of bacteria that were present when the antibiotic was first introduced is 14
How many bacteria were present when the antibiotic was first introduced?From the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
The number of bacteria that were present when the antibiotic was first introduced is when the graph intersects with the y-axis
In this case, the graph intersects with the y-axis at
y = 14
Hence, the number of bacteria that were present when the antibiotic was first introduced is 14
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Complete question
Biologists introduced a population of bacteria to a test environment. The function f models the population size (in thousands) as a function of time (in days) after introduction.
The graph shows a bacteria population (see attacment)
How many bacteria were present when the antibiotic was first introduced?
Use the compound interest formula A = P(1 + r) to find the annual interest rate, r, if in 2 years an investment of $5,000 grows to $6,050.
The annual interest rate, r, is 0.1 or 10%. A 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.
To find the annual interest rate, r, we can rearrange the compound interest formula A = P(1 + r) and solve for r.
Given that an investment of $5,000 grows to $6,050 in 2 years, we can substitute these values into the formula:
$6,050 = $5,000
[tex] {1 + r}^{2}[/tex]
Dividing both sides by $5,000, we have:
1.21 =
[tex](1 + r)^2[/tex]
Taking the square root of both sides, we get:
√1.21 = 1 + r
Simplifying, we have:
1.1 - 1 = r
0.1 = r
This means that the investment grew by 10% annually over the 2-year period. Compound interest is calculated by adding the interest earned to the initial amount, and as time passes, the interest is earned on both the initial amount and the accumulated interest from previous periods. In this case, a 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.
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How are the pairs of figures alike? How are they different?
Answer: they all have the same amount of squares but are placed differently in each example.
Step-by-step explanation:
there are 6 yellow squares and 10 blue squares for each of the 4 examples. The only difference is how they’re arranged.
HELP ASAP PLEASE :(((
The values of the third side that would make this a right triangle are C. √ 73 m.
Which values make this a right triangle ?The value that should make the shape a right triangle would be the value that obeys the Pythagorean Function which is:
Longest side ² = Side A ² + Side B ²
Picking √ 73, we have a value of :
= 8. 544 m
Plugging into the formula, we have:
8. 544 ² = 3 ² + 8 ²
72. 99 = 9 + 64
73 = 73
This shows that the value would be 8. 544 or any value that is around 8. 5 m as this can be rounded off.
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Forty volunteer drivers are separated into two groups of 20 drivers each at random. The first group is asked to pay particular attention to braking smoothly when approaching a red light or stop sign. The second group is given no special instructions. All drivers report, at the end of a month, the gallons of gasoline used. The mean for the first group is 43.16 gallons of gas. The mean for the second group is 54.63 gallons of gas. The difference in means for the two groups is -11.47 gallons of gas. The data for both groups are combined and redistributed at random into two groups of 20. The means for each redistributed group are calculated, and the difference in means is recorded. The differences are represented in the histogram.
Which of these conclusions and justifications is the most reasonable?
The most reasonable conclusion is that the instruction to brake smoothly resulted in a decrease in gas consumption, as evidenced by the lower mean and negative difference in means between the two groups.
Based on the information provided, the most reasonable conclusion would be that the instruction given to the first group of drivers to brake smoothly when approaching a red light or stop sign resulted in a decrease in the mean gallons of gas used compared to the second group.
The justification for this conclusion is supported by the fact that the mean for the first group is 43.16 gallons of gas, which is lower than the mean for the second group, which is 54.63 gallons of gas. This indicates that the first group, who received the specific instruction to brake smoothly, consumed less gas on average.
The histogram displaying the differences in means after the data for both groups were combined and redistributed also supports the conclusion. It likely shows a distribution that is centered around a negative value, indicating that the majority of the redistributed groups had a lower mean gas consumption compared to the initial second group.
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