The 80s series of nasal consonants, including /m/, /n/, and /ŋ/, is the best option for testing for hyponasality. These consonants require adequate nasal resonance for accurate articulation, making them effective for identifying individuals with this speech disorder. Option D is correct.
Hyponasality is a speech disorder characterized by reduced nasal resonance during speech production. To test for hyponasality, a series of nasal consonants can be used, as they require appropriate nasal resonance for accurate articulation.
Among the options given, the best series of numbers to use when testing for hyponasality is the 80s. This series includes nasal consonants that are commonly used in the English language, and their production requires adequate nasal resonance. The nasal consonants in the 80s series include /m/, /n/, and /ŋ/, which are produced with varying degrees of nasal airflow.
/m/ is a bilabial nasal consonant, which requires the closure of the lips and the lowering of the velum to allow air to flow through the nasal cavity. /n/ is an alveolar nasal consonant, which requires the tongue to contact the alveolar ridge while the velum is lowered. /ŋ/ is a velar nasal consonant, which requires the back of the tongue to contact the soft palate while the velum is lowered.
Using the 80s series of numbers to test for hyponasality can help identify individuals who have difficulty producing nasal consonants correctly due to reduced nasal resonance. This information can be used to develop appropriate speech therapy interventions to help improve nasal resonance and overall speech production.
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Complete question:
What is the recommended series of numbers to use for testing hyponasality?
a) 50s,
b) 60s,
c) 70s,
d) 80s,
e) 90s
there are two similar triangles: one has sides 3 in, 4 in, and 5 in. if the second triangle has a shortest side of 12 in, what is the length of the longest side?
the length of the longest side in the second triangle is 20 inches.
Hence, the length of the longest side is 20 inches.The two triangles are similar, which means their corresponding sides are in proportion.
In the first triangle, the ratio of the sides is 3:4:5.
Let's use this ratio to find the length of the longest side in the second triangle.
Since the shortest side of the second triangle is 12 in, we can set up the proportion:
3/5 = 12/x
Cross-multiplying, we get:
3x = 60
Dividing both sides by 3, we find:
x = 20
Therefore, the length of the longest side in the second triangle is 20 inches.
Hence, the length of the longest side is 20 inches.
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The height of the cone in figure 2 is
centimeters.
Answer:
4.5
Step-by-step explanation:
3/8=x/12
cross multiply
36=8x
x=4.5
Find the vectors T, N, and B at the given point. r(t) = (t^2, 2/3 t^3, t), (1, -2/3, -1)
The vectors T, N, and B at the given point are: T = (4/3, -2, 0), N = (-2/3, -4/3, 1), and B = (2/3, -4/3, -2).
To find the vectors T, N, and B, we need to find the unit tangent vector T, the unit normal vector N, and the unit binormal vector B at the given point. First, we find the first derivative of the vector function r(t) to get the tangent vector: r'(t) = (2t, 2t^2, 1). Then we evaluate it at t = 1 to get r'(1) = (2, 2/3, 1). To find the unit tangent vector T, we divide r'(1) by its magnitude: T = (2/3, 2/9, 1/3).
Next, we find the second derivative of r(t) to get the curvature vector: r''(t) = (2, 4t, 0). Then we evaluate it at t = 1 to get r''(1) = (2, 4, 0). To find the unit normal vector N, we divide r''(1) by its magnitude and negate it: N = (-2/3, -4/3, 1). Finally, we find the cross product of T and N to get the unit binormal vector B: B = (2/3, -4/3, -2).
Therefore, T = (4/3, -2, 0), N = (-2/3, -4/3, 1), and B = (2/3, -4/3, -2)) is the answer.
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The base of an isosceles triangle is x units. The sum of the lengths of the other two sides is one unit less than the length of the base. If the perimeter of the triangle is 67 units or less, which inequality describes all possible lengths of the
base?
A) x ≤ 34
B) x ≤ 16.5
C) x ≥ 34
D) x ≥ 16 5
The inequality that describes all possible lengths of the base is x ≤ 34 So, the correct option is (A).
Let the length of each of the other two sides be y. Since the triangle is isosceles, we have y = y. We also know that the sum of the lengths of the other two sides is one unit less than the length of the base, so:
2y = x - 1
Solving for y, we get:
y = (x - 1)/2
The perimeter of the triangle is:
P = x + y + y = x + 2y
Substituting the expression for y we obtained earlier, we get:
P = x + 2[(x - 1)/2] = 2x - 2
We are given that P ≤ 67, so:
2x - 2 ≤ 67
Solving for x, we get:
x ≤ 34.5
Therefore, the inequality that describes all possible lengths of the base is:
x ≤ 34
So, the correct option is (A).
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Sally finds that the correlation between high school gpa and performance ratings at work 5 years later have a correlation ofr = .09, p<.01. She concludes that high school gpa is an excellent and useful predictor of performance ratings at work: Is she right?
Sally's conclusion that high school GPA is an excellent and useful predictor of performance ratings at work is not entirely supported by the correlation coefficient of 0.09 with a significance level of p<.01.
Although a significant correlation suggests a positive association between high school GPA and performance ratings, the strength of the relationship is weak. The practical significance of such a weak correlation may be limited in real-world scenarios where multiple factors can influence job performance.
It is also important to note that correlation does not imply causation.
Therefore, even if high school GPA is significantly correlated with performance ratings at work, it does not necessarily mean that high school GPA is a causative factor in better job performance. Other variables such as work experience, motivation, and personality may also contribute to predicting job performance, and their effects should also be taken into account when assessing the usefulness of high school GPA as a predictor.
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4. What is the measure of arc BC
B
A
98⁰
C
N
80°
70°
D
The measure of arc BC in a circle where the two chords, chord AD and chord AC are equal in measure, is 146°. Therefore, the correct option is option C.
The measure of arc made by parallel chord in a circle are equal in measure.
arc BC=8x-46°
arc AD=5x+26°
arc BC=arc AD
8x-46°=5x+26°
x=24°
arc BC=8x-46°
arc BC=8(24°)-46°
arc BC=192°-46°
arc BC=146°
Therefore, the correct option is option C.
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Your question is incomplete but most probably your full question was,
18r - 3s-r + 4s
1r+s
Answer: 4sr+17r−2s4+17−2
Step-by-step explanation: simplify 18r - 3s-r + 4s1r+s
then multiply by one and get 18r-3s-r+4sr+s.
then combine like terms and get 17r-3s-r+4sr+s.
combine like terms again and end up with 17r-2s+4sr
you then want to rearrange the terms to 4sr+17r-2s
and you have your answer .
Using Pythagoras' theorem, calculate the length of XY. Give your answer in centimetres (cm) to 1 d.p. 16 cm X Z 5 cm
By using Pythagoras' theorem, the length of XY is equal to 14.4 centimeters.
How to calculate the length of XY?In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:
XZ² = ZY² + XY²
16² = 7² + XY²
256 = 49 + XY²
XY² = 256 - 49
XY² = 207
XY = √207
XY = 14.4 centimeters.
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find the first partial derivatives of the function. (sn = x1 2x2 ... xn; i = 1, ..., n. give your answer only in terms of sn and i.) u = sin(x 1 2x2 ⋯ nxn) ∂u ∂xi =
To find the partial derivative of the function u = sin(x1 2x2 ⋯ nxn) with respect to xi, where i is an integer between 1 and n, we need to use the chain rule. The answer can be expressed as follows: ∂u/∂xi = cos(x1 2x2 ⋯ nxn) * 2ixi * x1 2x2 ⋯ xi-1 2xi-1 xi+1 2xi+1 ⋯ xn.
To explain further, we start by applying the chain rule to u = sin(x1 2x2 ⋯ nxn) with respect to xi. We treat all the variables except xi as constants, so we get:
∂u/∂xi = cos(x1 2x2 ⋯ nxn) * ∂(x1 2x2 ⋯ nxn)/∂xi
Next, we use the product rule to differentiate x1 2x2 ⋯ nxn with respect to xi. We treat all the variables except xi as constants, so we get:
∂(x1 2x2 ⋯ nxn)/∂xi = 2ixi * x1 2x2 ⋯ xi-1 2xi-1 xi+1 2xi+1 ⋯ xn
Substituting this result back into our original equation, we get:
∂u/∂xi = cos(x1 2x2 ⋯ nxn) * 2ixi * x1 2x2 ⋯ xi-1 2xi-1 xi+1 2xi+1 ⋯ xn
Therefore, the partial derivative of the function u = sin(x1 2x2 ⋯ nxn) with respect to xi is cos(x1 2x2 ⋯ nxn) multiplied by 2ixi multiplied by the product of all the variables except xi in the original function.
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Jayla is the manager of Super Sandwiches. She recorded the number of sandwiches they sold each day during their Super Sandwich Sale.
The box plot that represents the data on the sandwiches sold by Super Sandwiches is Box Plot 1.
How to find the box plot ?The box plot that shows the data of sandwiches is the one that has the correct measure of the value of Q1 or the lower quartile. This is because the box plots are similar except for the lower quartile.
To find the lower quartile, arrange the numbers;
50, 66, 74, 88, 100, 109, 113, 127, 150
The lower quartile would be the median of the lower half of :
50, 66, 74, 88
The lower quartile is:
= ( 66 + 74 ) / 2
= 70
The first box plot has this Q1 value and so is correct.
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find the exact value of the expression, if it is defined. (if an answer is undefined, enter undefined.) cos−1 cos 11 6
The exact value of the expression cos^-1(cos(11π/6)) is π/ 6 The inverse cosine function (cos^-1) returns the angle whose cosine is a given value.
In this case, we are given the cosine of 11π/6, which is -√3/2 (since cosine is negative in the third quadrant where 11π/6 lies). The value of π/6 is the angle whose cosine is -√3/2. Therefore, the exact value of the expression is π/6.
This means that for any angle θ, the cosine of (θ + 2nπ) is the same as the cosine of θ, where n is any integer. In other words, the cosine function repeats itself every 2π radians.
The inverse cosine function, however, returns a unique angle between 0 and π whose cosine is a given value. In this case, since we are given a negative cosine value, we know that the angle must lie in the second or third quadrant.
By evaluating the cosine function for angles in those quadrants, we can determine which angle has the given cosine value. In this case, we find that the angle is π/6, which is in the third quadrant where cosine is negative.
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Express result in CORRECT Scientific Notation:
In 2011, the number of aluminum cans recycled in the US was 6.1 x 10^10. One empty can weighs .03417 grams. what is the weight of the cans recycled in 2011?
The required scientific notation is written as the weight of cans = 2.07837 x 10⁹ g.
The weight of one empty can is 0.03417 grams. The number of cans recycled in 2011 was 6.1 x 10¹⁰. To find the total weight of the cans recycled in 2011, we need to multiply these two numbers together.
Weight of cans = number of cans * weight of one can
Weight of cans = 6.1 x 10¹⁰* 0.03417
Weight of cans = 2.07837 x 10⁹ grams
The weight of the cans recycled in 2011 is 2.07837 x 10⁹ grams. In scientific notation, this is written as the weight of cans = 2.07837 x 10⁹ g.
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which hypothesis test is most appropriate to determine if there is evidence to support the claim that the proportion of people who smoke is less than 22.5%? correct!
Yes, given explanation is correct.if the calculated test statistic is less than -1.645 then the null hypothesis can be rejected.
For test the claim that the proportion of people who smoke is less than 22.5%.
A one-tailed test of hypothesis can be used. Specifically, a one-sample z-test for a proportion can be used where:
Null hypothesis: p ≥ 0.225 (the proportion of people who smoke is equal to or greater than 22.5%)
Alternative hypothesis: p < 0.225 (the proportion of people who smoke is less than 22.5%)
The test statistic for the one-sample z-test for a proportion is calculated as:
z = (p - P0) / √[(P0 × (1 - P0)) / n]
where p is the sample proportion, P0 = the hypothesized proportion under the null hypothesis and n = The sample size.
If the calculated test statistic falls in the rejection region which is determined by the chosen significance level (e.g., alpha = 0.05) then the null hypothesis can be rejected and it can be concluded that there is evidence to support the claim that the proportion of people who smoke is less than 22.5%.
For a one-tailed test with alpha = 0.05, the critical value is -1.645.
Hence, if the calculated test statistic is less than -1.645 then the null hypothesis can be rejected.
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what is the probability that the heart rate is under 125 given that its over 100
Given that heart rate before an exam for STA 100 students is normally distributed with mean 100 bpm and standard deviation 20.2 bpm, the probability that a randomly selected student's heart rate is under 125 bpm given that it is over 100 bpm is approximately 0.6306.
We are given that the heart rate before an exam for STA 100 students follows a normal distribution with mean 100 bpm and standard deviation 20.2 bpm.
We want to find the conditional probability that the heart rate is under 125 bpm given that it is over 100 bpm.
Let A be the event that the heart rate is over 100 bpm, and let B be the event that the heart rate is under 125 bpm. Then we want to find P(B | A).
We can use Bayes' theorem to find P(B | A):
P(B | A) = P(A | B) * P(B) / P(A)
We know that P(A) = 1 - P(B), since the two events are complements. We also know that P(B) can be found using the standard normal distribution as follows:
P(B) = P(Z < (125 - 100) / 20.2) = P(Z < 1.2376) = 0.8917,
where Z is a standard normal random variable. To find P(A | B), we need to compute the conditional probability that the heart rate is over 100 bpm given that it is under 125 bpm:
P(A | B) = P(B | A) * P(A) / P(B) = P(B | A) * (1 - P(B)) / P(B).
Since the heart rate follows a normal distribution, we can standardize it by subtracting the mean and dividing by the standard deviation:
P(A | B) = P(Z > (100 - 100) / 20.2 | Z < (125 - 100) / 20.2)
= P(Z > 0 | Z < 1.2376)
= P(Z < 1.2376)
= 0.8917.
Finally, we can plug in the values we have found to obtain the probability we are looking for:
P(B | A) = P(A | B) * P(B) / P(A)
= 0.8917 * 0.8917 / (1 - 0.8917)
= 0.6306 (approximately).
Therefore, the probability that a randomly selected student's heart rate is under 125 bpm given that it is over 100 bpm is approximately 0.6306 or 63.06%.
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Complete Question
6. Assume that heart rate (in beats per minute, or bpm) before an exam for STA 100 students is distributed nor- mal, with a mean of 100 bpm and a standard deviation of 20.2 bpm. Assume all students in the following problem are selected from this population.
If we know a randomly selected students heart rate is over 100 (it is given), what is the probability that it is under 125?
mrs. smith gives a psychology test and finds that the scores form a normal distribution where the mean is 80 and the standard deviation is 12. about what percentage of mrs. smith's students scored at or above a 92%?.
Percentage of Mrs. smith's students scored at or above a 92% for given mean and standard deviation using standard normal distribution is equal to 15.87%.
Mean = 80
Standard deviation = 12
To find the percentage of Mrs. Smith's students who scored at or above a 92%,
Find the area under the normal distribution curve to the right of 92%.
Use a standard normal distribution table or a calculator ,
Find the corresponding z-score for a raw score of 92 in a normal distribution with mean 80 and standard deviation 12.
z = (92 - 80) / 12
= 1
This means that a score of 92 is one standard deviation above the mean.
From a standard normal distribution table,
Attached table.
Find that the area to the right of a z-score of 1 is approximately 0.1587.
This means that approximately 15.87% of Mrs. Smith's students scored at or above a 92%.
Therefore, about 15.87% of Mrs. Smith's students scored at or above a 92% on the psychology test using standard normal distribution .
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imagine that after the birds have been living in the city for many years a second big flock of birds arrive. how will the burd population size change in the 10 -20 years after the extra bird arrive?
it depends on a variety of factors such as the size of the new flock, the availability of resources, and the adaptability of both the existing and new bird populations.
If the new flock is relatively small and the existing population is well-established, the impact may be minimal. However, if the new flock is large and competes for resources such as food, nesting sites, and mates, it could lead to a decrease in the size of the existing population.
Additionally, if the new birds bring new diseases or predators to the area, this could also impact the population size of both groups. On the other hand, if the new birds are able to integrate well and find their own niche within the ecosystem, the population size could potentially increase.
the impact of a new flock of birds on the existing population size can vary depending on a range of factors. It is difficult to predict the exact outcome, but it is important to consider the potential impacts on both the new and existing populations.
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- The midpoint of CD is M(-1,7) and one endpoint of CD is D(4, 5). What are
the coordinates of C?
Answer:
(-6,9)
Step-by-step explanation:
We can use the midpoint formula to find the coordinates of C. The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:
((x1 + x2)/2, (y1 + y2)/2)
In this case, we know that the midpoint of CD is M(-1, 7) and one endpoint of CD is D(4, 5). Let C = (x, y) be the coordinates of the other endpoint of CD. Then we can use the midpoint formula to set up two equations:
(x + 4)/2 = -1
(y + 5)/2 = 7
Solving for x and y, we get:
x + 4 = -2
y + 5 = 14
x = -6
y = 9
Therefore, the coordinates of C are (-6, 9).
Write the equation of the parabola that has its vertex at (-2,7) and passes through (-1,3).
The quadratic equation for the given vertex and point is:
y = -4(x + 2)² + 7
How to write the equation for the parabola?A parabola whose vertex is (h, k) and that has a leading coefficient a, can be written in the vertex form as:
y = a*(x - h)² + k
Here we know that the vertex is (-2, 7), then we can write the equation as:
y = a*(x + 2)² + 7
We also know that the parabola passes through (-1, 3), then we can replace these two values in the equation to get:
3 = a*(-1 + 2)² + 7
3 = a + 7
3 - 7 =a
-4 = a
Then the equation for the parabola is:
y = -4(x + 2)² + 7
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Calculate the area of the figure below.
12 ft.
6 ft.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=12\\ b=6\\ h=9 \end{cases}\implies A=\cfrac{9(12+6)}{2}\implies A=81~ft^2[/tex]
Questions:
1. If the height of the box is 7 inches, what is the volume of the box? (blank)in3
2. If the volume of the box is 123 in3, what is the height of the box? (blank) inches
(Thank you to anyone that answers this!)
1. The volume of the box is 287 cubic inches
2. The height of the box is 3 inches
1. What is the volume of the box?From the question, we have the following parameters that can be used in our computation:
The figure
This figure can be broken down to
TrapezoidRectangleTrapezoidSo, we have
Area = 1/2 * (3 + 7) * 2 * 2 + 7 * 3
Evaluate
Area = 41
The height is 7
So, we have
Volume = 41 * 7
Volume = 284
2. What is the height of the box?In (a), we have
Area = 41
So, we have
Height = Volume/Area
This gives
Height = 123/41
Evaluate
Height = 3
Hence, the height of the box is 3 inches
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identify the similar triangles in the diagram. Complete the similarity statement in the order: Large, medium, small. The order for the statement is established with the large triangle.
Answer: 11.9
Step-by-step explanation:you have to corss multiply
Find d/dx integral from 2^(3 x+1) ln (t+1) dt. show work please
The derivative of the given function can be found using the Fundamental Theorem of Calculus and the chain rule as follows:
d/dx integral from 2^(3 x+1) ln (t+1) dt
= d/dx [integral from a(x) to b(x) f(t) dt] (where a(x) = 1 and b(x) = 2^(3x+1) and f(t) = ln(t+1))
= f(b(x)) * b'(x) - f(a(x)) * a'(x)
= ln(2^(3x+1) + 1) * (2^(3x+1) * ln(2)) - ln(2) * 1
= ln(2) * 2^(3x+1) * (3x + 1) * ln(2^(3x+1) + 1)
Therefore, the derivative of the given function is ln(2) * 2^(3x+1) * (3x + 1) * ln(2^(3x+1) + 1).
The above solution was obtained by applying the Fundamental Theorem of Calculus, which states that the derivative of the definite integral of a function f(t) with respect to x is given by f(b(x)) * b'(x) - f(a(x)) * a'(x), where a(x) and b(x) are functions of x that define the limits of integration. The chain rule was used to compute b'(x), which is the derivative of 2^(3x+1) with respect to x. Finally, the derivative of the integrand ln(t+1) with respect to x was computed using the chain rule.
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Compute the directional derivative of the functionf(x,y)=2xy−3y2,at the point P0=(5,5)in the direction of the vector u = 4i + 3j.
The directional derivative of the function f(x,y) = 2xy - 3y^2 at the point P0 = (5,5) in the direction of the vector u = 4i + 3j is 6√2.
Explanation:
The directional derivative measures the rate of change of a function in a specific direction. It is denoted by ∇_u f(x,y), where u is the unit vector in the direction of interest. To compute the directional derivative, we need to take the dot product of the gradient of f with the unit vector u.
First, we need to find the gradient of f(x,y).
∇f(x,y) = [2y, 2x - 6y]
Next, we need to normalize the vector u to get the unit vector in the direction of interest.
|u| = √(4^2 + 3^2) = 5
u^ = (4/5)i + (3/5)j
Taking the dot product of the gradient of f with the unit vector u, we get:
∇_u f(x,y) = ∇f(x,y) · u^ = [2y, 2x - 6y] · (4/5)i + (3/5)j
At the point P0 = (5,5), we have:
∇_u f(5,5) = [2(5), 2(5) - 6(5)] · (4/5)i + (3/5)j = 10(4/5) + (-6)(3/5) = 8 - 3.6 = 4.4
Therefore, the directional derivative of f(x,y) at the point P0 = (5,5) in the direction of the vector u = 4i + 3j is:
∇_u f(5,5) = 4.4
Finally, we need to scale the result by the magnitude of the vector u to get the directional derivative in the direction of u.
Directional derivative = ∇_u f(5,5) / |u| = 4.4 / 5 = 0.88 * √(2)
Directional derivative = 6√2.
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HELP SYSTEM OF EQUATIONS WILL GIVE BRAINLIEST
The number of solutions that are there for this system of equation is: C. no solution.
How to solve the given system of equations?In order to solve the given system of equations, we would apply the substitution method. Based on the information provided above, we have the following system of equations:
3x + 6y = 0 .......equation 1.
x + 2y = 0 .......equation 2.
By making x the subject of formula in equation 2, we have the following:
x = -2y .......equation 3.
By using the substitution method to substitute equation 3 into equation 1, we have the following:
3(-2y) + 6y = 0
-6y + 6y = 0 (No solution).
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What is the value of each of these postfix expressions?a) 5 2 1 - - 3 1 4 + + *b) 9 3 / 5 + 7 2 - *c) 3 2 * 2 UP 5 3 - 8 4 / * -
Postfix expressions (a) 5 2 1 - - 3 1 4 + +* is 60. (b) 9 3 / 5 + 7 2 - * is 40. (c) 3 2 * 2 UP 5 3 - 8 4 / * - is 31.25.
a) The value of the postfix expression 5 2 1 - - 3 1 4 + + * is 60.
Starting from the left, 2 is subtracted from 1 and then subtracted from 5, giving 2. Then, 4 and 1 are added, giving 5, and then 3 is added to 2, giving 5. Finally, 2 and 5 are multiplied, giving 10, which is then multiplied by 5 to give 60.
b) The value of the postfix expression 9 3 / 5 + 7 2 - * is 40.
Starting from the left, 3 is divided into 9, giving 3. Then, 5 is added to 3, giving 8. Next, 2 is subtracted from 7, giving 5. Finally, 8 and 5 are multiplied, giving 40.
c) The value of the postfix expression 3 2 * 2 UP 5 3 - 8 4 / * - is -31.25.
Starting from the left, 2 is multiplied by 3, giving 6. Then, 2 is raised to the power of 6, giving 64. Next, 3 is subtracted from 5, giving -2. Then, 4 is divided into 8, giving 2. Finally, -2 and 64 are multiplied, giving -128, which is then subtracted from 2 and multiplied by 2, giving -31.25.
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a computer that costs $4600 new has a book value of $3000 after 2 years. find the value of the computer after 3 years by using the exponential model y
The value of the computer with initial value $4600 after 3 years using the exponential model is equal to $2422.39 (approximately).
Cost of new computer = $4600
Book value after 2 years = $3000
use the exponential model,
y = a × [tex]e^{(-kt)}[/tex]
where y is the value of the computer after t years,
a is the initial value of the computer when t=0,
k is a constant,
and e is the base of the natural logarithm.
Find the value of k using the information given,
y(2) = 3000
⇒3000 = a × [tex]e^{(-2k)}[/tex]
y(0) = 4600
⇒ 4600 = a × e⁰
⇒ 4600 = a
Dividing the two equations, we get,
⇒3000/4600 = [tex]e^{(-2k)}[/tex]
⇒0.6522 = [tex]e^{(-2k)}[/tex]
Taking the natural logarithm of both sides, we get,
⇒ -2k = ln (0.6522 )
Solving for k, we get,
⇒ k = -0.4276 /2
⇒ k = - 0.2138
So the exponential model for the value of the computer is,
y = 4600 × [tex]e^{(-0.2138 \times t)}[/tex]
To find the value of the computer after 3 years, we can plug in t=3,
y(3) = 4600 × [tex]e^{(-0.2138 \times 3)}[/tex]
= 4600 × [tex]e^{(-0.6413)}[/tex]
= 4600 × 0.5266
= 2422.39
Therefore, the value of the computer after 3 years using the exponential model is approximately $2422.39.
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one variable increases, then the other increases, as well.which term would best describe this scenario?
This scenario where one variable increases, then the other increases, as well describes a positive correlation between two variables. So, correct option is A.
Positive correlation occurs when two variables increase or decrease together, meaning that as the value of one variable increases, the value of the other variable also increases.
For example, if we consider the relationship between the amount of time spent studying and the grade achieved on a test, a positive correlation would exist if students who study more tend to get higher grades.
Positive correlation is often represented by a scatter plot, where the points are clustered around a straight line sloping upwards from left to right.
The correlation coefficient, also known as Pearson's r, can be used to quantify the strength and direction of the relationship between two variables, with a value of +1 indicating a perfect positive correlation and a value of 0 indicating no correlation.
In summary, a positive correlation describes a scenario where two variables increase or decrease together, and is represented by a scatter plot with points clustered around a line sloping upwards from left to right.
So, correct option is A.
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Complete question is:
One variable increases, then the other increases, as well.
Which term would best describe this scenario?
A) positive correlation
B) hypothesis
C) transitional form
D) causation
Find a set of parametric equations for the rectangular equation that satisfies the given condition. (Enter your answers as a comma-separated list.) y = 3x - 4, t = 0 at the point (4, 8)
To find the set of parametric equations for the rectangular equation y = 3x - 4, we need to express x and y in terms of a parameter, say t. Let us assume that t = 0 at the point (4, 8).
First, we can write x in terms of t as x = 4 + at, where a is some constant. To find the value of a, we can use the fact that y = 3x - 4. Substituting x = 4 + at in this equation, we get y = 3(4 + at) - 4 = 12 + 3at. So, the set of parametric equations for y and x are:
x = 4 + at
y = 12 + 3at
Note that these parametric equations are not unique. We could have chosen a different parameterization, say t = 1 at the point (4,8), and obtained a different set of parametric equations. However, the given condition specifies the starting point and therefore determines the parameterization.
In summary, we can find a set of parametric equations for a rectangular equation by expressing x and y in terms of a parameter, using the given condition to determine the starting point, and choosing a suitable parameterization.
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please help i have no idea how to do this
The geometric sequence is -6, 1, -1/6, 1/36.......
Given is a geometric sequence, -6, ?, ?, 1/36 we need to find the missing terms,
So, we know that the ratios between the terms of a geometric sequence are common,
Let the 2nd term be x and the 3rd term be y, so,
-x/6 = 1/36 / y
-x/6 = 1/36y
6 = -36xy
x·y = -1/6
So, we get x·y = -1/6,
Now if we see the options, the third option gives 1 × -1/6 = -1/6,
Therefore, the terms can be written as,
-6, 1, -1/6, 1/36.......
If we see the common ratio we get,
-1/6
-1/6/1 = -1/6
1/36 / (-1/6) = -1/6
Hence the geometric sequence is -6, 1, -1/6, 1/36.......
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please help, i have a C in my math class and i really need help on this. please help!
1. The image shows translation
2. It is a translated image because there is no change in the size from the pre-image
3. Point A from the pre-image corresponds with point D
What is the type of transformation?In mathematics, there are four different types of transformation. They are listed as;
TranslationDilationReflectionRotationNow, it is important to note that for translation, we have that;
A 2-d shape causes sliding of that shapeThere is no change in size or shape; Changes only the direction of the shape The shape is horizontally (left/right) or vertically (up/down)Learn more about translation at: https://brainly.com/question/1574635
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