If sin∠X = cos∠Y and m∠X = 72°, what is the measure of ∠Y?
Given sin∠X = cos∠Y and m∠X = 72°, we can find the measure of angle Y to be 18° since angles X and Y are complementary.
The problem states that sin∠X = cos∠Y and m∠X = 72°, and we are asked to find the measure of angle Y.
The first thing to notice is that sin∠X = cos∠Y means that the sine of angle X is equal to the cosine of angle Y. By the definition of sine and cosine, we know that:
sin∠X = opposite/hypotenuse
cos∠Y = adjacent/hypotenuse
where "opposite" and "adjacent" are the lengths of the sides of a right triangle that correspond to angles X and Y, respectively, and "hypotenuse" is the length of the hypotenuse of the triangle.
Since sin∠X = cos∠Y, we can set the two expressions equal to each other:
sin∠X = cos∠Y
opposite/hypotenuse = adjacent/hypotenuse
opposite = adjacent
This tells us that the lengths of the opposite and adjacent sides of the right triangle are equal. Since these sides are opposite and adjacent to angles X and Y, respectively, this means that angles X and Y are complementary angles (i.e., the sum of their measures is 90°).
We know that angle X has a measure of 72°, so we can use the fact that angles X and Y are complementary to find the measure of angle Y:
m∠Y = 90° - m∠X
m∠Y = 90° - 72°
m∠Y = 18°
Therefore, the measure of angle Y is 18°.
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Use a trigonometric ratio to solve for x. Round to two
decimal places as necessary.
X
10
14
Step-by-step explanation:
For RIGHT triangles , remember S-O-H-C-A-H-T-O-A
sin 14° = opposite leg / hypotenuse
sin 14° = x / 10
10* sin 14° = x
x = 2.42 units
sin 37° = 10 / a
a = 10 / sin 37°
a = 16.62 units
help asap will give brainliest!
The volume of the cone with radius as 9 inches and height as 11 inches is 933 cubic inches.
What is the volume of a cone?The formula for the volume of a cone is the product of the following multiplication, given as V = π×r²×h/3.
In this formula, π is the pie or 22/7, r is the radius, and h is the height.
The radius of the base of cone, r = 9 inches
The height of the cone, h = 11 inches
π = 22/7
The volume of the cone = πr²h/3 cubic units.
= 22/7 x 9 x 9 x 11/3
= 22/7 x 81 x 3.667
= 933 cubic inches
= 933 in³
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The population P(t) of a culture of the pseudomonas aeruginosa is given by P(t) = -1709t^2 + 80,000t + 10,000, where t is the time in hours since the culture was started. What is the maximum?
Check the picture below.
so the path of the population P(t) is parabolic, more or less like the one in the picture, so it reaches its maximum at the vertex and at "t" time of the x-coordinate of the vertex.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ P(t)=\stackrel{\stackrel{a}{\downarrow }}{-1709}t^2\stackrel{\stackrel{b}{\downarrow }}{+80000}t\stackrel{\stackrel{c}{\downarrow }}{+10000} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 80000}{2(-1709)}~~~~ ,~~~~ 10000-\cfrac{ (80000)^2}{4(-1709)}\right) \implies \left( - \cfrac{ 80000 }{ -3418 }~~,~~10000 - \cfrac{ 6400000000 }{ -6836 } \right) \\\\\\ \left( \cfrac{ -40000 }{ -1709 } ~~~~ ,~~~~ 10000 + \cfrac{ 1600000000 }{ 1709 } \right) ~~ \approx ~~ (\stackrel{ hours }{\text{\LARGE 23}}~~,~~946220)[/tex]
Find h please math help plsssss help
The height of the triangle is approximately 7.31 units.
What is Pythagorean theorem ?
The Pythagorean theorem is a fundamental theorem in geometry that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In mathematical notation, the Pythagorean theorem can be written as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs (the sides adjacent to the right angle) and c is the length of the hypotenuse.
According to the question:
Since triangle ABC is a right triangle with angle B = 90 degrees, we can use the Pythagorean theorem to find the length of side BC:
[tex]BC^2 = AC^2 - AB^2[/tex]
[tex]BC^2 = 30^2 - h^2[/tex]
[tex]BC = \sqrt{30^2 - h^2}[/tex]
Now, let's consider triangle ABD. We know that AD = 25 and DC = 11, so BD = BC - DC:
BD = BC - DC
[tex]BD = \sqrt{30^2 - h^2} - 11[/tex]
Since the line passing through vertex A is perpendicular to BC, we know that triangles ABD and ABC are similar. Therefore, we can use the ratio of corresponding sides to find the value of h:
h/AB = AB/AC
h/AB = AB/30
[tex]AB^2 = h*30[/tex]
[tex]AB =\ sqrt{h*30}[/tex]
Now, using the fact that AD + DC = BC, we can write:
AD + DC = BD + AB
[tex]25 + 11 = \sqrt{30^2 - h^2} - 11 +\sqrt{h*30}[/tex]
[tex]36 = \sqrt{30^2 - h^2} + \sqrt{h*30}[/tex]
Squaring both sides, we get:
[tex]1296 = 30^2 - h^2 + 2\sqrt{h*30}\sqrt{30^2 - h^2} + h*30[/tex]
[tex]1296 = 900 - h^2 + 2\sqrt{30h - h^3} + 30*h[/tex]
[tex]396 = 32\sqrt{30*h - h^3}[/tex]
Squaring again, we get:
[tex]156816 = 960h^2 - 96h^4[/tex]
[tex]h^4 - 10h^2 + 1639/12 = 0[/tex]
Using the quadratic formula, we get:
[tex]h^2 = (10 \± \sqrt{10^2 - 4(1)(1639/12))}/2[/tex]
[tex]h^2 = (10 \± \sqrt{1561})/2[/tex]
Since h must be positive, we take the positive square root:
[tex]h = \sqrt{(10 + sqrt(1561)}/2) \approx 7.31[/tex]
Therefore, the height of the triangle is approximately 7.31 units.
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twenty five cards are marked with the numbers 1 through 25. amira randomly picks two cards without replacement. blanca then randomly picked two of the remaining cards without replacement. what is the probability that at least one of blanca's cards has a number greater than at least one of amira's cards?
The probability that at least one of Blanca's cards has a number greater than at least one of Amira's cards is 0.705 or approximately 70.5%.
The total number of ways in which Blanca can choose two cards out of 23 is given by the combination formula C(23, 2), which is equal to 253.
The value of k can range from 3 (if Amira's cards are 1 and 2) to 25 (if Amira's cards are 24 and 25). Therefore, the total number of ways in which Blanca can pick two cards that are both greater than Amira's cards is:
C(23, 2) - C(2, 2) - C(3, 2) - ... - C(23, 2) = 23C(23, 1) - (C(2, 2) + C(3, 2) + ... + C(23, 2)) = 253 - 276 = -23
Since the result is negative, it means that there are no ways in which Blanca can pick two cards that are both greater than Amira's cards. Therefore, the probability of this case is 0.
P(Case 2) = (number of ways in which Blanca can pick one card greater than Amira's and one card less than Amira's) / (total number of ways in which Blanca can pick two cards out of 23) = 44,550 / C(23, 2) = 0.705
Finally, the probability of at least one of Blanca's cards having a number greater than at least one of Amira's cards is given by the sum of the probabilities of Case 1 and Case 2:
P(at least one of Blanca's cards is greater) = P(Case 1) + P(Case 2) = 0 + 0.705 = 0.705 or 70.5%
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40 mm
34.6 mm
40 mm
Please help me with this question
I remember doing this but I don’t seem to remember sorry
(06.02 LC) Line AB contains points A (0, 1) and B (1, 5). The slope of line AB is (5 points) Group of answer choices −4 negative 1 over 4 1 over 4 4
General equation of line is [tex]y=mx+n[/tex] where m is slope and n is point on y-axis. So just use points in question to determine what m and n must be. Let me show you.
For A(0,1), put this point in [tex]y=mx+n[/tex] then you have [tex]1=m.0+n[/tex] Hence [tex]n=1[/tex]
Now use second one that is B(1,5), then you get [tex]5=m.1+1[/tex] since [tex]n=1[/tex]. Finally you get [tex]m=4[/tex] that is slope.
Therefore, D is the correct answer.
two airplanes are flying in the air at the same height. airplane a is flying east at 453 mi/h and airplane b is flying north at 508 mi/h. if they are both heading to the same airport, located 7 miles east of airplane a and 8 miles north of airplane b, at what rate is the distance between the airplanes changing?
Two airplanes are flying in the air at the same height. airplane a is flying east at 453 mi/h and airplane b is flying north at 508 mi/h. if they are both heading to the same airport, located 7 miles east of airplane a and 8 miles north of airplane b, at the rate at which the distance between the two airplanes is changing is approximately 473 mi/h.
What is the distance between the airplanes?
We may use the Pythagorean theorem to find the distance between the two airplanes. Let’s use A to represent the position of Airplane A and B to represent the position of Airplane B.
Let d be the distance between the airplanes. Then, using the Pythagorean Theorem, we have:
d² = (8 miles)² + (7 miles)² d² = 64 + 49d² = 113d = sqrt(113) miles
What is the rate at which Airplane A is approaching the airport?Since Airplane A is flying straight to the airport, its rate of approach to the airport is its speed, 453 mi/h.
What is the rate at which Airplane B is approaching the airport?Since Airplane B is flying straight to the airport, its rate of approach to the airport is its speed, 508 mi/h.
How fast is the distance between the airplanes changing?Let d be the distance between the airplanes at some point in time t. We need to find the rate at which the distance is changing, or the derivative of d with respect to t. We may use the Pythagorean theorem to find the distance between the two airplanes.
Let A represent the position of Airplane A and B represent the position of Airplane B.Let d be the distance between the airplanes. Then, using the Pythagorean Theorem, we have:
d² = (8 miles)² + (7 miles)² d² = 64 + 49d² = 113d = sqrt(113) miles
At some time t, let A(t) represent the position of Airplane A, and let B(t) represent the position of Airplane B. We have that:
A(t) = 453t B(t) = 508t
Therefore, the distance between the airplanes is given by:
d(t)² = (453t)² + (508t)²d(t)² = 205,609t² + 258,064t²d(t)² = 463,673t²
We take the derivative of both sides with respect to t, noting that d²/dt² = 2dd/dt:
2d(t)d'(t) = 927,346t
Then, dividing both sides by 2d(t), we have:
[tex]d'(t) = 927,346t/(2d(t))d'(t) = 927,346t/(2sqrt(113)) miles/h[/tex]
Using t = 1 hour (since we are asked for the rate at which the distance between the airplanes is changing), we have:
[tex]d'(1) = 927,346/(2sqrt(113))d'(1) ≈ 473 miles/h[/tex]
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assume the prices of cold medicine (per box) are normally distributed with a mean of $12.75 and a standard deviation of $2.15. find the probability that a randomly selected box of cold medicine will cost more than $13.
The probability that a randomly selected box of cold medicine will cost more than $13 is 0.4542 or 45.42%.
Given the mean of the normally distributed cold medicine = $12.75 and the standard deviation = $2.15 and the random variable x, the probability of a randomly selected box of cold medicine costing more than $13 needs to be found.
Now, as we are given mean and standard deviation, we can standardize the normal distribution and then use the Z table or calculator to find the probability.
The formula for standardizing the normally distributed curve:
Z = (X - μ) / σ
where
Z = Standardized score
X = Score value
μ = Mean
σ = Standard deviation
Here, we have to find the probability of a randomly selected box of cold medicine will cost more than $13.
So, the formula becomes:
Z = (X - μ) / σ = ($13 - $12.75) / $2.15 = 0.116
Using the Z-table, the area to the left of Z = 0.116 is 0.5458
Thus, the probability that a randomly selected box of cold medicine will cost more than $13 is:
1 - 0.5458 = 0.4542 or 45.42%
Therefore, the probability of a randomly selected box of cold medicine costing more than $13 is 0.4542 or 45.42%.
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Carlos purchased a new computer for $1,350. One year later, a popular tech website valued the same computer at $810. The website predicts that the value of the computer will continue depreciating each year. Write an exponential equation in the form y=a(b)x that can model the value of the computer, y, x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = To the nearest ten dollars, what can Carlos expect the value of the computer to be 3 years after purchase?
Answer:
Step-by-step explanation:
Carlos can expect the value of the computer to be $580 in 3 years after purchase.
To find the exponential equation in the form y=a(b)ˣ that models the value of the computer, we need to determine the initial value and the rate of decay.
The initial value of the computer is $1,350, and its value after one year is $810.
We can use this information to find the rate of decay as follows:
810 = 1350 × b¹
b = 0.6
So the exponential equation is:
y = 1350(0.6)ˣ
To find the value of the computer 3 years after purchase, we can substitute x = 3 into the equation:
y = 1350(0.6)³= 583.2
Hence, Carlos can expect the value of the computer to be $580 in 3 years after purchase.
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Katie and Mina both commute to work. Katie's commute on the train takes 10 minutes more than one half as many minutes as Mina's commute by car. It takes Katie 30 minutes to get to work. Write an equation to determine how many minutes it takes Mina to get to work.
According to the question, it takes Mina 80 minutes to commute to work.
Explain equation?Two equations are considered to be comparable when their roots and solutions line up. To create an equivalent equation, the identical quantity, symbol, or expression must always be added to or removed from both of the equation's two sides. We can also create a similar equation simply multiplying or dividing either sides of the an equation by a nonnegative value.
Let's denote the time it takes Mina to commute to work by "m" (in minutes).
The issue states that Katie's train trip requires 10 minutes or more half as much time as Mina's drive. Instead, we might write:
Katie's commute time = (1/2) * Mina's commute time + 10
We also know that it takes Katie 30 minutes to get to work, so we can write:
Katie's commute time + 30 minutes = total time to get to work
The result of putting the very first equation into to the second equation is:
[(1/2) * Mina's commute time + 10] + 30 minutes = total time to get to work
Simplifying the equation, we get:
(1/2) * Mina's commute time + 40 minutes = total time to get to work
Now we can set this equation equal to "m" to solve for Mina's commute time:
(1/2) * m + 40 = m
Subtracting (1/2) * m from both sides, we get:
40 = (1/2) * m
Multiplying both sides by 2, we get:
m = 80
Therefore, it takes Mina 80 minutes to commute to work.
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In a survey 80 students were asked to name their favorite subjects. Thirty students said that English was their favorite. What percent of the student surge said that English was their favorite subject
Answer:
37.5%
Step-by-step explanation:
Based on the given conditions, formulate: 30/80
Reduce the fraction: 3/8
Rewrite a fraction as a decimal: 0.375
Multiply a number to both the numerator and the denominator:
0.375 * 100/100
Write as a single fraction:
0.375 * 100 / 100
Calculate the product or quotient:
37.5/100
Rewrite a fraction with denominator equals 100 to a percentage:
37.5%
Answer:
37.5%
A group of 17 men and 24 women each banquet table can sit eight people what is the least number of tables need it for the banquet
Answer:
5
Step-by-step explanation:17+24=41
41/8=5.125
So The least you can get for the banquet table is 5.
The data table to the right represents the volumes of a generic soda brand Volumes of soda (oz) 65 80 70 75 70 85 80 75 70 75 65 70 Complete parts (a) through (c) below 508:5 a. Which plot represents a dotplot of the data? 50 60 70 80 9 50 60 70 80 9 Volumes of soda (oz) Volumes of soda (oz) Oc. 50 60 70 80 90 50 60 70 80 9 Volumes of soda (oz) Volumes of soda (oz) b. Does the configuration of the points appear to suggest that the volumes are from a population with a normal distribution? A. Yes, the population appears to have a normal distribution because the dotplot resembles a "bell shape B. No, the population does not appear to have a normal distribution because the frequencies of the volume decrease from left to right. C. No, the population does not appear to have a normal distribution because the dotplot does not resemble a "bell" shape D. Yes, the population appears to have a normal distribution because the frequencies of the volume increase from left to right. c. Are there any outliers? A. Yes, the volumes of 0 oz and 200 oz appear to be outliers because they are far away from the other temperatures O B. No, there does not appear to be any outliers ° C. Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes ( D. Yes, the volume of 70 oz appears to be an outlier because many sodas had this as their volume
a) The plot that represents a dot plot of the data is plot (B).
b) The answer is (C)
c) The answer is (B)
Define the term normal distribution?A normal distribution is a continuous probability distribution that has a symmetric bell-shaped curve, with the mean, median, and mode all being equal.
(a) The plot that represents a dot plot of the data is plot (B).
(b) The configuration of the points does not suggest that the volumes are from a population with a normal distribution. The answer is (C) - The dot plot does not approximate a "bell" form, hence the population does not seem to have a normal distribution.
(c) There are no outliers in the data. The answer is (B) - No, there does not appear to be any outliers.
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The answers are:
1). B. The plot that depicts a data dot plot is plot (B).
2). C. Because the dotplot does not match a "bell" shape, the population does not appear to have a normal distribution.
3). B. No, there does not appear to be any outlie
What is meant by Normal distribution?A normal distribution is a kind of continuous distribution of probability in which the majority of data points cluster in the centre of the range, while the remainder taper off symmetrically towards either extreme. The mean of the distribution is also known as the centre of the range.
Because of its flared form, a normal distribution resembles a bell curve graphically. The exact shape can vary depending on the population's value distribution. The population is the total number of data elements in the distribution.
a). The plot depicts a data dot plot and is called plot. (B).
b). Because the dot plot does not resemble a "bell" form.(C).
c). The data does not contain any anomalies. (B).
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The Complete question is,
a). question a is attached below.
b). Does the configuration of the points appear to suggest that the volumes are from a population with a normal distribution?
A. Yes, the population appears to have a normal distribution because the dotplot resembles a "bell shape
B. No, the population does not appear to have a normal distribution because the frequencies of the volume decrease from left to right.
C. No, the population does not appear to have a normal distribution because the dotplot does not resemble a "bell" shape
D. Yes, the population appears to have a normal distribution because the frequencies of the volume increase from left to right.
c). Are there any outliers?
A. Yes, the volumes of 0 oz and 200 oz appear to be outliers because they are far away from the other temperatures
B. No, there does not appear to be any outliers °
C. Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes
D. Yes, the volume of 70 oz appears to be an outlier because many sodas had this as their volume
Please Help!!! Asap. !!!!!
The pair of supplementary angles in the given situation is:
136 + 44 = 180°
135 + 45 = 180°
154 + 26 = 180°
What are supplementary angles?A supplementary angle is an angle that sums to 180 degrees.
For example, the 130° and 50° angles are complementary because the sum of 130° and 50° is 180°.
Similarly, the sum of the supplementary angles is 90 degrees.
An apex angle is an angle opposite at the intersection of two straight lines, and an adjacent angle is two angles next to each other.
So, the pair of supplementary angles would be:
136 + 44 = 180°
135 + 45 = 180°
154 + 26 = 180°
Therefore, the pair of supplementary angles in the given situation is:
136 + 44 = 180°
135 + 45 = 180°
154 + 26 = 180°
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In circle H with m \angle GHJ= 90m∠GHJ=90 and GH=20GH=20 units, find the length of arc GJ.
HELP!!
Answer:
Since $\angle GHJ=90^\circ$, arc $GJ$ is a quarter of the circumference of circle $H$. The formula for the circumference of a circle is $C=2\pi r$, where $r$ is the radius, so the circumference of circle $H$ is:
$$C=2\pi \cdot 20 = 40\pi$$
Since arc $GJ$ is a quarter of the circumference, its length is:
$$\frac{1}{4} \cdot 40\pi = 10\pi$$
Therefore, the length of arc $GJ$ is $10\pi$ units.
Given: sin (A) =5/13, π/2
What is tan(A - B)?
O
5 + 12√13
12- 5√13
O 12-5√13
5 +12√13
12+5√13
-5+12√13
-5 + 12√13
12 +5√13
Using the trigonometric Identities, [tex]tan(A - B) =\frac{-5+12\sqrt{13} }{12+5\sqrt{13} }[/tex]
What are trigonometric identities?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
Given
[tex]sin(A) =\dfrac{5}{13}[/tex]
[tex]\dfrac{\pi }{2} < A < \pi[/tex]
Using the trigonometric identity
[tex]sin^2A+cos^2A=1[/tex]
[tex]cosA =\sqrt{1-sin^2A}[/tex]
[tex]cosA =\sqrt{1-(\dfrac{5}{13})^2 }[/tex]
[tex]cosA =-\dfrac{12}{13}[/tex]
[tex]tanA=\dfrac{sinA}{cosA}[/tex]
[tex]tanA =\dfrac{\frac{5}{13} }{\frac{-12}{13} }[/tex]
[tex]tanA =-\dfrac{5}{12}[/tex]
[tex]tan(A-B) =\dfrac{tanA-tanB}{1+tanAtanB}[/tex]
[tex]=\dfrac{-\frac{5}{12}-(-\sqrt{13}}{1+(-\frac{5}{12})(-\sqrt{3}) }[/tex]
[tex]=\dfrac{5-12\sqrt{13}}{-12-5\sqrt{3} }[/tex]
[tex]=\dfrac{-5+12\sqrt{13} }{12+5\sqrt{13} }[/tex]
Option D is correct.
Hence, [tex]tan(A - B) =\dfrac{-5+12\sqrt{13} }{12+5\sqrt{13} }[/tex]
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Andre studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science, and history.
Answer:
Step-by-step explanation:
it’s a 2 part question
The missing values in the figure is solved using central angle theorem to get
angle FHG = 122 degreesHow to find angle FHGThe measure of an central angle is equal to the measure of the intercepted arc according to the central angle theorem.
From the figure we have that the intercepted arc is FG = 122 degrees. Using the central angle theorem, the central angle is angle FHG
central angle = intercepted arc
angle FHG = arc FG
angle FHG = 122 degrees
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A department store wants to send codes for $15 off a $75 purchase to the subscribers of its email list. The coupon code will have three letters followed by one digit followed by one letter. The letters PQNR will not be used so there are 23 letters and 10 digits that will be used. Assume that the letters can be repeated how many such coupon codes can be generated.
there are 407,230 possible coupon codes that can be generated using the given format.
To find the number of possible coupon codes, we need to count the total number of ways to choose three letters from 23, one digit from 10, and one letter from 23 (since we can repeat letters). Combinations
The number of ways to choose three letters from 23 is:
23[tex]C_{3}[/tex] = (232221)/(321) = 1771
The number of ways to choose one digit from 10 is simply 10.
The number of ways to choose one letter from 23 (allowing repetition) is 23.
Therefore, the total number of possible coupon codes is:
1771 * 10 * 23 = 407,230
So there are 407,230 possible coupon codes that can be generated using the given format.
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increase £142 by 34%
Add £48.28 to £142 so you get £190.28
AnswerAnswerAnswerAnswer:
190.28
Step-by-step explanation:
£142 + 34% = £142 x 1.34 = 190.28
[50 POINTS!!!] I posted a Screen shot of the question down below!
Answer:
C; as x-> infinite, f(x) -> infinite, as x-> neg. infinite, f(x) -> neg. infinite
Step-by-step explanation:
Graphing the equation will help with knowing the end behavior.
X^3 graphs tend to increase infinitely when x is going infinitely positive and decrease infinitely when x is going infinitely negative.
11. The velocity, V of a car moving with a constant acceleration is partly constant and partly
varies as the time taken, t. The velocity of the car after 8s and 12s are 9 m/s and 11
m/s respectively. Find
(i)
(ii)
The relationship between the velocity and the time taken.
The time taken when the velocity is 15 m/s.
Based on the information provided, the relationship between velocity and time taken is V = 4 + 0.5t.
How to find the velocity between the two variables?We can start by using the formula for velocity with constant acceleration:
V = Vo + at
where V is the final velocity, Vo is the initial velocity, a is the constant acceleration, and t is the time taken.
We know that the velocity is partly constant and partly varies with time, so we can write:
V = Vc + Vv
where Vc is the constant part of the velocity and Vv is the part that varies with time.
Using the given information, we can set up a system of equations:
9 = Vc + Vv (when t = 8s)
11 = Vc + Vv (when t = 12s)
Subtracting the first equation from the second, we get:
11 - 9 = (Vc + Vv) - (Vc + Vv)
2 = Vv (when t = 12s) - Vv (when t = 8s)
2 = Vv (12) - Vv (8)
2 = 4Vv
Vv = 0.5 m/s
Now we can use either of the two original equations to find Vc:
9 = Vc + 0.5(8)
Vc = 4 m/s
Therefore, the relationship between the velocity and the time taken is:
V = 4 + 0.5t
where V is the velocity in m/s and t is the time taken in seconds.
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let f(x)=−8(2)3x 3. evaluate f(0) without using a calculator. do not include f(0) in your answer.
For the given function f(x)= [tex]-8(2)^{3x}[/tex] + 3 which contains variable x , whose value on substituting as zero is found to be (calculated without using calculator)
What is variable?
Variable is a term used in algebra or algebraic expressions and equations to represent the unknown values or whose value is not fixed. variables and constants are combined to form algebraic expressions or equations. The difference between expression and an equation is that expressions do not contain 'equal to' sign and equations shows balance between left hand side and the right side using 'equal to' sign.
Here the function is f(x)= [tex]-8(2)^{3x}[/tex] + 3
To find the value of given function at x= 0 , we need to substititute zero in place of x.
f(x) at x=0 will be [tex]-8(2)^{3(0)}[/tex] + 3
= [tex]-8(2)^{0}[/tex] + 3
= [tex]-8(1)[/tex] + 3 { we know that [tex]m^{0} = 1[/tex] }
= - 8 + 3
= -5
∴The value of function at x=0 is found to be -5
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Refer to the attachment for complete question
use composition of functions to determine whether f(x) and g(x) are inverse of each other. show all work for full credit.
f(x)=4/5 x=1
g(x)=5x-5/4
After computing the composition of f(g(x)) and g(f(x)), it is clear that f(x) and g(x) are not inverse functions of each other.
To determine whether f(x) and g(x) are inverse functions of each other, we need to check whether the composition of the two functions f(g(x)) and g(f(x)) result in the identity function, which is equal to x.
First, let's find f(g(x)):
f(g(x)) = f(5x - 5/4) (substituting g(x) into f(x))
f(g(x)) = 4/5(5x - 5/4) + 1 (substituting the expression for f(x))
f(g(x)) = 4x - 1 + 1
f(g(x)) = 4x
Now let's find g(f(x)):
g(f(x)) = g(4/5x + 1) (substituting f(x) into g(x))
g(f(x)) = 5(4/5x + 1) - 5/4 (substituting the expression for g(x))
g(f(x)) = 4x + 5 - 5/4
g(f(x)) = 4x + 20/4 - 5/4
g(f(x)) = 4x + 15/4
Since f(g(x)) = 4x and g(f(x)) = 4x + 15/4, we can see that the two compositions are not equal to x, which means that f(x) and g(x) are not inverse functions of each other.
Therefore, we can conclude that f(x) and g(x) are not inverse functions of each other.
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Select the correct answer. Suppose x varies indirectly as y, and x = 5 when y = 24. What is the value of x when y = 8? A. 15 B. 1. 67 C. 960 D. 38. 40 Re
The value of x is 15 when y =8
If x varies indirectly as y, then we can write:
x = k/y
where k is the constant of variation. To find the value of k, we can use the given information that x = 5 when y = 24:
5 = k/24
Multiplying both sides by 24, we get:
k = 120
Now we can use this value of k to find x when y = 8:
x = 120/8 = 15
Therefore, the answer is A. 15.
A ratio that depicts the association between the independent variable (x) and the dependent variable is known as a constant of variation (k) (y). In the event that both of those variables have known values, it can be calculated by dividing y by x.
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the top face of a portable digital device measures 3.01 inches by 1.23 inches. find the area of the face of the device
The area of the face of the portable digital device is approximately 3.7033 square inches.
Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is expressed in square units and can be calculated by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms.
The area of the face of the portable digital device can be found by multiplying the length by the width
Area = Length x Width
Area = 3.01 inches x 1.23 inches
Area = 3.7033 square inches (rounded to four decimal places)
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What is the product of 3a + 5 and 2a2 + 4a – 2?
A. 6a3 + 22a2 + 14a – 10
B. 6a3 + 22a2 + 26a –10
C. 18a3 + 10a2 + 14a – 10
D. 28a3 + 14a – 10
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Answer: Option A, [tex]\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a - 10}[/tex]
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Given: [tex]\textsf{3a + 5 and 2a}^2\textsf{ + 4a - 2}[/tex]
Find: [tex]\textsf{The product of the two given equations}[/tex]
Solution: The first step toward solving this problem would be to distribute the 3a and 5 to each of the values in the second equation.
[tex]\textsf{(3a + 5)(2a}^2\textsf{ + 4a - 2)}[/tex][tex]\textsf{(2a}^2\textsf{ * 3a) + (2a}^2\textsf{ * 5) + (4a * 3a) + (4a * 5) + (-2 * 3a) + (-2 * 5)}[/tex]After doing so, we can simplify each of the expressions until we have one equation. This can be done by both some simple algebra and combining of like terms.
[tex]\textsf{(6a}^3\textsf{) + (10a}^2\textsf{) + (12a}^2\textsf{) + (20a) + (-6a) + (-10)}[/tex][tex]\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a + -10}[/tex]Therefore, the correct answer to this question is Option A, [tex]\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a - 10}[/tex].
find f0.05 where v1=8 and v2=11
a) 2.95
b) 2.30
c) 4.74
d) 3.66
The correct answer for F-distribution f0.05 is d) 3.66
How to find F-distribution f0.05?To find f0.05 with v1=8 and v2=11, you can use an F-distribution table or an online calculator.
Here's a step-by-step explanation:
1. Locate the row in the F-distribution table corresponding to the degrees of freedom for the numerator (v1), which is 8 in this case.
2. Locate the column corresponding to the degrees of freedom for the denominator (v2), which is 11 in this case.
3. Find the intersection of the row and column to get the critical value for f0.05.
Using an F-distribution table or calculator, you will find that the f0.05 value for v1=8 and v2=11 is approximately 3.66.
So, the correct answer is:
d) 3.66
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