To find the possible Hamiltonian circuits that begin with JVTSR, we can start by constructing a path that begins with JVTSR and visits each vertex exactly once. Such a path must be of the form JVTSRX, where X is the remaining vertex.
Case 1: JVTSRQX
To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to Q are S and R. Thus, we must have X = S or X = R, and the circuits are JVTSRQS and JVTSRQR.
Case 2: JVTSRXQ
To find the possible value of X, we note that the only edges incident to X are S and L. Thus, we must have X = L, and the circuit is JVTSRLQ.
Case 3: JVTSRLX
To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to L are T and R. Thus, we must have X = R, and the circuit is JVTSRLR.
Case 4: JVTSRXL
To find the possible value of X, we note that the only edges incident to Q are S and R, and the only edges incident to X are L and S. Thus, we must have X = L, and the circuit is JVTSRQL.
Therefore, there are four possible Hamiltonian circuits that begin with JVTSR: JVTSRQS, JVTSRQR, JVTSRLQ, and JVTSRLR.
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1. Un ciclista ha recorrido 145. 8 km en una etapa, 136. 65 km en otra etapa y 162. 62 km en una tercera etapa. ¿Cuántos kilómetros le quedan por recorrer si la carrera es de 1000 km?
Esta es una y la segunda es otra ayúdenme
2. Una clinica dental tiene una tarifa de $ 19,99 para las calzas de piezas dentales. Si en un mes se registraron 109 calzas realizadas, ¿ que cantidad de dinero ingreso a la clinica?
1) The distance left in the race is 554.93km
2) The total amount earned is $2,178.91
How many kilometers remain in the race?We know that the total race is of 1000km, to find the distance missing, we need to take that total distance and subtract the amounts that the cyclist already traveled.
Then we will get:
distance left = 1000km - 145.8km - 136.65km - 162.62 km
distance left = 554.93km
That is the distance left in the race.
2) We know that each piece costs $19.99, and 109 pieces are sold, then the amount earned is the product between these two numbers.
Earnings = 109*$19.99 = $2,178.91
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to measure the length of a hiking trail, a worker uses a device with a 2-foot-diameter wheel that counts the number of revolutions the wheel makes. if the device reads 1,100.5 revolutions at the end of
the trail, how many miles long is the trail, to the nearest tenth of a mile?
The length of the trail is determined as 1.3 miles.
What is the length of the trail?The length of the trail is calculated as follows;
The circumference of the circle is calculated as;
S = πd
where;
d is the diameter of the circleS = π x 2 ft
S = 2π ft
I revolution = 1 circumference = 2π ft
1 rev = 2π ft
1,100.5 rev = ?
= 1,100.5 rev/rev x 2π ft
= 6,914.65 ft
5280 ft -------> 1 mile
6,914.65 ft ------> ?
= 1.3 miles
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Jessica has 300 cm of matenal. She uses 12. 6 cm to make a nght triangular prism She wants to make a second prism that is a
dilation of the first prism with a scale factor of 3
How much more material does Jessica need in order to make the second prism?
Select from the drop-down menu to correctly complete the statement
cm of material to make the second prism
Jessica needs an additional Choose
To make the second prism, Jessica needs an additional 25.2 cm of material.
To answer your question, since Jessica wants to create a second triangular prism with a scale factor of 3, she will need 3 times the material used for the first prism.
She used 12.6 cm for the first prism, so for the second prism, she would need 12.6 cm × 3 = 37.8 cm of material.
Jessica already has 300 cm of material, so to find out how much more she needs, subtract the amount used for the first prism: 37.8 cm - 12.6 cm = 25.2 cm.
Jessica needs an additional 25.2 cm of material to make the second prism.
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A ball is drawn randomly from a jar that contains 8 red balls, 7 white balls, and 3 yellow balls. Find the probability of the given event. Write your answers as reduced fractions or whole numbers. (a) P(A red ball is drawn) = (b) P(A white ball is drawn) = (c) P(A yellow ball is drawn) = (d) P(A green ball is drawn) =
(a) P(A red ball is drawn) = 4/9
(b) P(A white ball is drawn) = 7/18
(c) P(A yellow ball is drawn) = 1/6
(d) P(A green ball is drawn) = 0
(a) To find the probability that a red ball is drawn, we'll use the following formula:
P(A red ball is drawn) = (Number of red balls) / (Total number of balls)
There are 8 red balls and a total of 8+7+3 = 18 balls in the jar. So, the probability of drawing a red ball is:
P(A red ball is drawn) = 8/18 = 4/9
(b) To find the probability that a white ball is drawn:
P(A white ball is drawn) = (Number of white balls) / (Total number of balls)
There are 7 white balls, so the probability of drawing a white ball is:
P(A white ball is drawn) = 7/18
(c) To find the probability that a yellow ball is drawn:
P(A yellow ball is drawn) = (Number of yellow balls) / (Total number of balls)
There are 3 yellow balls, so the probability of drawing a yellow ball is:
P(A yellow ball is drawn) = 3/18 = 1/6
(d) To find the probability that a green ball is drawn:
P(A green ball is drawn) = (Number of green balls) / (Total number of balls)
There are no green balls in the jar, so the probability of drawing a green ball is:
P(A green ball is drawn) = 0/18 = 0
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In a nuclear disaster, there are multiple dangerous radioactive isotopes that can be detected. If 91.9% of a particular isotope emitted during a disaster was still present 6 years after the disaster, find the continuous compound rate of decay of this isotope
The decay of isotope at compound rate is approximately 0.0140.
To find the continuous compound rate of decay of this isotope, we can use the following formula:
Nₜ = N₀e^(-λᵗ)
Where:
Nₜ is the amount of the isotope present after time t (years),
N₀ is the initial amount of the isotope,
λ is the continuous compound rate of decay, and
t is the time in years.
In this case, 91.9% of the isotope is still present 6 years after the disaster,
so Nₜ = 0.919 * N₀, and t = 6 years.
We want to find λ, the continuous compound rate of decay.
We can rewrite the formula as follows:
0.919 * N₀ = N₀ * e^(-λ * 6)
Divide both sides by N₀:
0.919 = e^(-λ * 6)
Now, take the natural logarithm (ln) of both sides:
ln(0.919) = -λ * 6
Divide by -6 to solve for λ:
λ = ln(0.919) / (-6)
Calculate the value:
λ ≈ 0.0140
So, the continuous compound rate of decay of this particular radioactive isotope is approximately 0.0140.
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PLEASE HELP FAST!!!!
On Monday a group of students took a test and the average ( arithmetic mean ) score was exactly 80. 4. A student who was absent on Monday took the same test on Tuesday and scored 90. The average age test score was then exactly 81. How many students took the test on Monday?
A) 14
B) 15
C) 16
D) 17
E) 18
With steps please
The number of students who took the test on Monday is found to be 15, hence the correct option is B.
Let us assume that the number of student taking test on Monday is n. The total score for Monday's test is n times the average score of 80.4,
Monday's total score = 80.4n
When the student who missed the test on Monday took the test on Tuesday and scored 90, the total score became,
Total score = 80.4n + 90
The new average score of 81 can be expressed as,
81 = Total score / (n+1)
Substituting the value of the total score, we get,
81 = (80.4n + 90)/(n+1)
Multiplying both sides by n+1, we get,
81(n+1) = 80.4n + 90
Expanding the brackets,
81n + 81 = 80.4n + 90
Simplifying,
0.6n = 9
n = 15, so, the number of students who took the test on Monday is 15.
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A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
The confidence level represents the degree of certainty that the interval contains the true population parameter.
The statement "determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520" means that if the farmer were to repeat the sampling process many times and calculate the confidence interval each time, 95% of those intervals would contain the true mean number of suitable apples per tree.
Therefore, we can be 95% confident that the true mean number of suitable apples produced per tree is within the interval of 375 to 520 for this particular sample of 40 trees.
The confidence level represents the degree of certainty that the interval contains the true population parameter.
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A recipe for maroon paint says, "mix 5 ml of red paint with 3 ml of blue paint."
use snap cubes to represent the amounts of red and blue paint in the recipe. then, draw a sketch of your snap-cube representation of the maroon paint.what amount does each cube represent?
Assuming that one snap cube represents one milliliter (ml) of paint, we can use five red snap cubes to represent 5 ml of red paint and three blue snap cubes to represent 3 ml of blue paint. We can arrange these snap cubes in a row to represent the recipe:
RRRRR BBB
This indicates that we mix 5 ml of red paint with 3 ml of blue paint to create the maroon paint.
To draw a sketch of the snap-cube representation of the maroon paint, we can combine the red and blue snap cubes into a single row:
RRRRR BBB
This gives us a row of eight snap cubes, which represents the maroon paint. Visually, the maroon paint will appear as a blend of red and blue, with a darker, richer hue than either color alone.
Each snap cube represents one milliliter (ml) of paint. Therefore, in this representation, each snap cube represents a fixed amount of paint, regardless of the color. In other words, each cube represents a unit of volume, rather than a unit of color or pigment.
A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μ and variance σ2 of a single roll are 3. 5 and 2. 92, respectively. What is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2?
The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.
The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.
The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0
The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)
where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.
Since each roll of the die is independent, the variance of the sample mean for each sample is given as:
σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584
σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292
Substituting these values in the above equation, we get:
σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468
Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:
σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)
Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.
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Qué expresión es igual a 4.6?
a. 1.6 + (3 × 4) – 2 ÷ 2
b. 1.6 + 3 × 4 – 2 ÷ 2
c. [1.6 + (3 × 4)] – (2 ÷ 2)
d. (1.6 + 3) × (4 – 2) ÷ 2
The correct expression that is equal to 4.6 is option c. [1.6 + (3 × 4)] – (2 ÷ 2)
Let's evaluate each expressions using the BODMAS rule of mathematics,
a. 1.6 + (3 × 4) – 2 ÷ 2
= 1.6 + 12 - 1
= 12.6
b. 1.6 + 3 × 4 – 2 ÷ 2
= 1.6 + 12 - 1
= 12.6
c. [1.6 + (3 × 4)] – (2 ÷ 2)
= [1.6 + 12] - 1
= 12.6
d. (1.6 + 3) × (4 – 2) ÷ 2
= 4.6 × 2 ÷ 2
= 4.6
BODMAS is an acronym used to remember the order of operations in mathematics: Brackets, Orders, Division, Multiplication, Addition, Subtraction. It is used to perform calculations in the correct order to obtain the correct result. Therefore, the correct answer is (c).
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Complete question - Which expression is equal to 4.6?
a. 1.6 + (3 × 4) – 2 ÷ 2
b. 1.6 + 3 × 4 – 2 ÷ 2
c. [1.6 + (3 × 4)] – (2 ÷ 2)
d. (1.6 + 3) × (4 – 2) ÷ 2
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Which expression is equivalent to 1/2(2n+6
1/2+2n+6
2 1/2 + 6 1/2
n + 6
n+ 3
After an antibiotic is taken, the concentration of the antibiotic in the bloodstream is modeled by the function C(t) = 4te-397, where t is measured in hours and C is measured in ag Use the closed interval methods to mg detremine the maximum concentration of the antibiotic between hours 1 and 7. Write a setence stating your result, round answer to two decimal places, and include units.
To find the maximum concentration of an antibiotic between hours 1 and 7, first find the critical points of the function C(t), then evaluate C(t) at the critical points and endpoints to choose the highest value.
To determine the maximum concentration of the antibiotic between hours 1 and 7, follow these steps:
1. Find the critical points of the function C(t) = 4te^(-397). To do this, find the first derivative of the function, C'(t), and set it equal to 0.
2. Check the value of C(t) at the critical points and the endpoints of the interval, t=1 and t=7.
3. Choose the highest value of C(t) among the critical points and the endpoints.
1: Find the first derivative, C'(t).
C(t) = 4te^(-397)
C'(t) = 4e^(-397)(1-397t)
2: Set the first derivative equal to 0 and solve for t.
4e^(-397)(1-397t) = 0
1 - 397t = 0
t = 1/397
3: Evaluate C(t) at the critical point t = 1/397 and the interval endpoints t = 1 and t = 7.
C(1/397) = 4(1/397)e^(-397(1/397)) ≈ 0.01 ag/mg
C(1) = 4(1)e^(-397(1)) ≈ 0.00 ag/mg
C(7) = 4(7)e^(-397(7)) ≈ 0.00 ag/mg
The maximum concentration of the antibiotic occurs at t = 1/397 hours, with a concentration of approximately 0.01 ag/mg. What is Titration: Titration is a technique by which we know the concentration of unknown solution using titration of this solution with solution whose concentration is known.
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I absolutely hate IQR so can someone help pls
Answer:5
Step-by-step explanation: The median of the lower quartile is 23 and the median of the upper quartile is 28. 28-23=5. The IQR is 5.
Use the given facts about the functions to find the indicated limit.
lim x->3 f(x)=0, lim x->3 g(x)=4 lim x->3 h(x)=2
lim x->3 6h/ 4f+g (x)
*there are no answer choices. Its a prompt*
The value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
Given, [tex]\lim_{x \to 3} f(x)=0[/tex]
[tex]\lim_{x \to 3} g(x)=4[/tex]
[tex]\lim_{x \to 3} h(x)=2[/tex]
We have to find the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex]
[tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)=\lim_{x \to 3} \frac{6h(x)}{4f(x)+g(x)}[/tex]
[tex]= \frac{\lim_{x \to 3}6h(x)}{\lim_{x \to 3}4f(x)+\lim_{x \to 3}g(x)}[/tex]
[tex]=\frac{6\times 2}{4\times0+4}[/tex]
= 12/4
= 3
Hence, the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
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The volume of a cylinder is twice the volume of a cone. The cone and the
cylinder have the same diameter. The height of the cylinder is 5 meters.
What is the height of the cone?
The height of the cone that the volume of a cylinder is twice the volume of a cone is 7.5 meters.
How to determine the height of the coneLet's first define some variables to represent the dimensions of the cone and cylinder. Let's use r for the radius of both shapes, h for the height of the cone, and 5 for the height of the cylinder.
The volume of a cone is given by V_cone = (1/3)πr^2h, and the volume of a cylinder is given by V_cylinder = πr^2h.
We are told that the volume of the cylinder is twice the volume of the cone:
V_cylinder = 2V_cone
Substituting the formulas for the volumes of the cone and cylinder, we get:
πr^2(5) = 2[(1/3)πr^2h]
Simplifying, we can cancel the π and the r^2 terms on both sides:
5 = (2/3)h
Multiplying both sides by 3/2, we get:
h = 7.5
Therefore, the height of the cone is 7.5 meters.
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Suppose we used a between subjects design to see if caffeine influenced levels of alertness. We had three groups of participants: participants who received 8 ounces of a caffeinated beverage, participants who received 24 ounces of a caffeinated beverage, and participants who received no caffeine. If this was a between subjects design with 30 total participants, how many participants would be in each condition
If we have 30 total participants in a between-subjects design with three groups, we can assign any number of participants to each group as long as the sum of participants in each group adds up to 30. The number of participants in each group is 10 in the 8-ounce group, 15 in the 24-ounce group, and 5 in the no-caffeine group.
If we have a total of 30 participants in a between-subjects design, we need to divide them into three groups according to the conditions.
Let x be the number of participants who received 8 ounces of a caffeinated beverage, y be the number of participants who received 24 ounces of a caffeinated beverage, and z be the number of participants who received no caffeine. Since we have a total of 30 participants, we can write
x + y + z = 30
We don't know the specific number of participants in each group, but we do know that they must add up to 30.
However, we also know that each participant can only be in one group, which means that we have mutually exclusive groups. Therefore, we can assume that there is no overlap between the groups, which means that the total number of participants in each group is
x + y + z = 30
z = 30 - (x + y)
So, we can assign any value to x and y, as long as the sum of x and y is less than or equal to 30. Then, we can find the value of z using the equation above.
For example, if we assign 10 participants to the 8-ounce group and 15 participants to the 24-ounce group, we would have
x = 10
y = 15
z = 30 - (10 + 15) = 5
So, there would be 10 participants in the 8-ounce group, 15 participants in the 24-ounce group, and 5 participants in the no-caffeine group.
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Pythagorean theorem
1. a surveyor walked eight miles north, then three miles west. how far was she from her starting point?
2. a four meter ladder is one meter from the base of a building. how high up the building will the ladder reach?
3. what is the longest line you can draw on a paper that is 15 cm by 25 cm?
4. how long a guy wire is needed to support a 10 meter tall tower if it is faster
the foot of the tower?
5. the hypotenuse of a right triangle is twice as long as one of its legs.the other leg is nine inches long. find the length of the hypotenuse.
The distance traveled by the surveyor is √73 miles. The height of the building that the ladder reaches is √15 meters. The longest line that can be drawn is 5√34 cm. The length of the guy wire that is needed is 5√5 meters. The length of the hypotenuse of the given right triangle is 6√3 inches.
In a right-angled triangle that is a triangle with one of the angles with magnitude 90° following is true according to Pythogaras' Theorem:
[tex]A^2=B^2+C^2[/tex]
where A is the hypotenuse
B is the base
C is the height
1. According to the question,
the distance between the starting and the ending point is the hypotenuse of a right-angled triangle
B = 8 miles
C = 3 miles
A = √(64 + 9)
= √73 miles
2. Hypotenuse in the given question is the length of the ladder, thus,
A = 4 m
B = 1 m
16 = 1 + [tex]C^2[/tex]
C = √15 meters
3. The longest line that can be drawn on the paper is described as the hypotenuse of the triangle
C = √225 + 625
= 5√34 cm
4. The length of the guy wire is the hypotenuse of the triangle.
C = √100 + 25
= 5√5 meters
5. Let the base of the triangle be x
the hypotenuse be 2x
height = 9 inches
[tex]4x^2=x^2[/tex] + 81
[tex]3x^2[/tex] = 81
x = 3√3 inches
Hypotenuse = 2x = 6√3 inches
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Use the slope of a line formula to find the slope of the following points: (3, 9) and (8, 15)
Answer:
m = 6/5
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (3, 9) and (8, 15)
We see the y increase by 6 and the x increase by 5, so he slope is
m = 6/5
Answer:
The slope of the points is 6/5.
Step-by-step explanation:
SOLUTION :
Using slope of a line formula to find the slope of the points :
[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]\pink\star[/tex] m = slope[tex]\pink\star[/tex] [tex](x_1, y_1)[/tex] coordinates of first point in the line[tex]\pink\star[/tex] [tex](x_2, y_2) [/tex] = coordinates of second point in the lineSubstituting all the given values in the formula to find the slope of the points :
[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]\blue\star[/tex] y_2 = 15[tex]\blue\star[/tex] y_1 = 9[tex]\blue\star[/tex] x_2 = 8[tex]\blue\star[/tex] x_1 = 3[tex]\quad\dashrightarrow{\sf{m = \dfrac{15 - 9}{8 -3}}}[/tex]
[tex]\quad\dashrightarrow{\sf{m = \dfrac{6}{5}}}[/tex]
[tex]\quad{\star\underline{\boxed{\sf{\red{m = \dfrac{6}{5}}}}}}[/tex]
Hence, the slope of the points is 6/5.
————————————————Find the exact values of sin 2u, cos2u, and tan2u using the double-angle formulas cot u= square root 2, pi < u < 3pi/2
sin 2u = -1/2, cos 2u = -1/2, tan 2u = 1, because cot u = sqrt(2) and the range of u is between pi and 3pi/2.
How to find the trigonometric function?
Given cot u = sqrt(2) and the range of trigonometric of u, we can determine the values of sine, cosine, and tangent of 2u using the double-angle formulas. First, we can find the value of cot u by using the fact that cot u = 1/tan u, which gives us tan u = 1/sqrt(2). Since u is in the third quadrant (i.e., between pi and 3pi/2), sine is negative and cosine is negative.
Using the double-angle formulas, we can express sin 2u and cos 2u in terms of sin u and cos u as follows:
sin 2u = 2sin u cos u
cos 2u =[tex]cos^2[/tex] u - [tex]sin^2[/tex] u
Substituting the values of sine and cosine of u, we get:
sin 2u = 2*(-sqrt(2)/2)*(-sqrt(2)/2) = -1/2
cos 2u = (-sqrt(2)/2[tex])^2[/tex] - (-1/2[tex])^2[/tex] = -1/2
To find the value of tangent of 2u, we can use the identity:
tan 2u = (2tan u)/(1-[tex]tan^2[/tex] u)
Substituting the value of tan u, we get:
tan 2u = (2*(1/sqrt(2)))/(1 - (1/sqrt(2)[tex])^2[/tex]) = 1
Therefore, sin 2u = -1/2, cos 2u = -1/2, and tan 2u = 1.
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If f(x)
4e^x find f(4) rounded to the nearest tenth.
The value of f(4) rounded to the nearest tenth is approximately 194.9.
The value of f(4) can be found by substituting x=4 in the given function f(x) = [tex]4e^x[/tex], so we get:
f(4) = [tex]4e^4[/tex]
Using a calculator, we can evaluate this expression as:
f(4) ≈ 194.92
Rounding this to the nearest tenth gives:
f(4) ≈ 194.9
Therefore, the value of f(4) rounded to the nearest tenth is approximately 194.9.
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Element x decays radioactively with a half life of 15 minutes. if there are 960 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 295 grams?
y=a(.5)^(t/h)
It would take approximately 21.2 minutes for 960 grams of Element X to decay to 295 grams.
The time it takes for 960 grams of Element X with a half-life of 15 minutes to decay to 295 grams can be found using the formula y = a [tex](0.5)^\frac{t}{h}[/tex] .
1: Identify the variables.
a = initial amount = 960 grams
y = final amount = 295 grams
h = half-life = 15 minutes
t = time in minutes (this is what we want to find)
2: Plug the variables into the formula.
295 = 960 [tex](0.5)^\frac{t}{15}[/tex]
3: Solve for t.
Divide both sides by 960.
(295/960) = [tex](0.5)^\frac{t}{15}[/tex]
4: Take the logarithm of both sides to remove the exponent.
log(295/960) = log [tex](0.5)^\frac{t}{15}[/tex]
5: Use the logarithm property to move the exponent to the front.
log(295/960) = (t/15) * log(0.5)
6: Solve for t.
t = (15 * log(295/960)) / log(0.5)
7: Calculate t.
t ≈ 21.2 minutes
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Find an exponential function that passes through (2,8) and (4,128)
The final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
To find an exponential function that passes through the points (2,8) and (4,128), follow these steps:
Step 1: Recall the general form of an exponential function: y = ab^x
Here, 'a' and 'b' are constants that need to be determined using the given points.
Step 2: Substitute the first point (2,8) into the equation:
8 = ab^2
Step 3: Substitute the second point (4,128) into the equation:
128 = ab^4
Step 4: Divide the second equation by the first equation to eliminate 'a':
(128 = ab^4) / (8 = ab^2)
16 = b^2
Step 5: Solve for 'b':
b = √16
b = 4
Step 6: Substitute the value of 'b' back into the first equation:
8 = a(4^2)
Step 7: Solve for 'a':
8 = 16a
a = 8/16
a = 1/2
Step 8: Write the final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
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On a certain hot summer's day,670 people used the public swimming pool. The daily prices are for children 1.25 and for adults.2.00 The receipts for admission totaled 1118.00 How many children and how many adults swam at the public pool that day
Based on simultaneous equations, the number of children and adults who swam at the public pool that hot summer's day is as follows:
Children = 296Adults = 374.What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Simultaneous equations are also referred to as a system of equations because the equations are solved at the same time.
The total number of people who used the public swimming pool = 670
The unit price for children = $1.25
The unit price for adults = $2.00
The total amount collected that day = $1,118
Let the number of children who swam at the public pool that day = x
Let the number of adults who swam at the pool that day = y
Equations:x + y = 670 ... Equation 1
1.25x + 2y = 1,118 ... Equation 2
Multiply Equation 1 by 2:
2x + 2y = 1,340 Equation 3
Subtract Equation 2 from Equation 3:
2x + 2y = 1,340
-
1.25x + 2y = 1,118
0.75x = 222
x = 296
y = 670 - 296
= 374
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Obtain the equation of the line that passes through the point (4 , 6) and is parallel to the line y= -2x+4.
Answer:
y = -2x + 14
Step-by-step explanation:
OK so first u have to do y = -2x + b cuz its parallel
then u gotta just plug in the ordered pair so
6 = -2(4)+b
6 = -8 +b
14 = b
So now u have to do
y = -2x + 14
The altitude to the hypotenuse of a right angled triangle is 8 cm. If the hypotenuse is 20 cm long, find the lenghs of the two segments of the hypotenuse
someone help pls!! giving brainlist to anyone who answers
Answer: csc M = [tex]\frac{\sqrt{86} }{8}[/tex]
Step-by-step explanation:
The csc is related to sin
csc x = 1/sin x
find sin M first then flip it to find csc M
sin M= opposite/hypotenuse
sin M= [tex]\frac{8}{\sqrt{86} }[/tex] >flip that
csc M = 1/sin M
csc M = [tex]\frac{\sqrt{86} }{8}[/tex] >root cannot be simplified it breaks down into 2 and 43
which are 2 prime numbers
The ratio of Adults to Girls in a tennis club is 5:1
The ratio of Girls to Boys in the same club is 3:4
What is the ratio of adults to boys?
The ratio of adult to boys is 35:24
What is ratio?A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. For example, if the ratio of boys to girls in a class is 4:1. This means that the for every 4 boys therefore is a girl.
Represent the total number of adult, boys and girls in the club by x
This means number of boys = 4/7× x
number of adult = 5/6 × x
Therefore the ratio of adults to boys will be
5x/6 : 4x/7
= 5/6 : 4/7
multiply through by 42
= 35 : 24
therefore the ratio of adult to boys is 35: 24
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36 inches in 3 feet
rate=____ unit rate ___
Answer:
Rate: 36:3
Unit Rate: 12:1
Step-by-step explanation:
The total distance in d,in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, is the time in seconds. At a time of 10. 0 seconds the total distance is traveled by the objects is 50. 0 meters and at a time of 20. 0 seconds the total distance traveled by the object is 200. 0 meters if the object was at a distance of 0 meters when t=0 then what is the total distance traveled in meters, by the object after 30. 0 seconds
Let's denote the total distance traveled by the object as `d` and time as `t`.
We can use the given information to set up a system of equations:
When t = 10.0 seconds, d = 50.0 meters
50.0 = a(10.0)^2 + b(10.0) + c (Equation 1)
When t = 20.0 seconds, d = 200.0 meters
200.0 = a(20.0)^2 + b(20.0) + c (Equation 2)
When t = 0 seconds, d = 0 meters
0 = a(0)^2 + b(0) + c (Equation 3)
Simplifying Equation 3, we get c = 0.
Substituting c = 0 in Equations 1 and 2, we get:
50.0 = 100a + 10b (Equation 4)
200.0 = 400a + 20b (Equation 5)
We can solve Equations 4 and 5 simultaneously to get the values of `a` and `b`:
From Equation 4, we get:
10b = 50 - 100a
b = 5 - 10a
Substituting this value of `b` in Equation 5, we get:
200.0 = 400a + 20(5 - 10a)
200.0 = 400a + 100 - 200a
200.0 = 200a + 100
100.0 = 200a
a = 0.5
Substituting this value of `a` in Equation 4, we get:
50.0 = 100(0.5) + 10b
50.0 = 50 + 10b
b = 0
Therefore, the quadratic function that models the total distance traveled by the object is:
[tex]d = 0.5t^2[/tex]
To find the total distance traveled by the object after 30.0 seconds, we can substitute `t = 30.0` in the above equation:
[tex]d = 0.5(30.0)^2[/tex]
d = 450.0 meters
Therefore, the object will travel a total distance of 450.0 meters after 30.0 seconds.
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