The correct option A. -3, is the value of constant 't', for which the equation has no real solutions.
Define the term real solutions?In algebra, a real solution is just an answer to an equation which is a real number. The number of solutions to the provided quadratic equation depends on the discriminant, but can be positive, 0, or negative. A quadratic equation with a positive discriminant has two unique real number solutions.A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.For the stated question-
The quadratic equation is given as-
2x² - 4x = t
2x² - 4x - t = 0
The standard from of quadratic equation is-
ax² + bx + c = 0
For no solution;
Discriminant is less than zero.
D < 0
b² - 4ac < 0
Comparing both equations-
b = -4, a = 2 and c = -t
Put value in D.
(-4)² - 4(2)t < 0
Solve the inequality
16 - 8t < 0
t < -2
Thus, the value of constant 't', for which the equation has no real solutions.
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The correct question is-
2x² - 4x = t,In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?
A. -3
B. -1
C. 1
320 of 562 randomly selected u.s. adults interviewed said they would not be bothered if the national security agency collected records of personal telephone calls they had made. a button hyperlink to the salt program that reads: use salt. is there sufficient evidence to conclude that a majority of u.s. adults feel this way? test the appropriate hypotheses using a 0.01 significance level
There is enough evidence to suggest p>0.5
What is hypothesis in statistics?
A type of statistical analysis called hypothesis testing involves testing your presumptions regarding a population parameter. It is used to estimate the relationship between 2 statistical variables.
Thus, a hypothesis is a set of possible explanations or resolutions applicable to a situation. In other words, the hypotheses pose different scenarios in which the aim is to explain the origin and eventual resolution of the problem.
Let's discuss few examples of statistical hypothesis from real-life -
A teacher assumes that 60% of his college's students come from lower-middle-class families.A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.We are testing :
H0: p <= 0.5
H1: p > 0.5
Test statistic:
Z = [(364/562) - 0.5] / √[0.5(1-0.5)] / 562
= 7.00
P-value = P(Z>7.00) = 0.0000
Hence, there is enough evidence to suggest p>0.5.
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Which function matches the graph?
-5
-2
3/
7
A. f(x) =
(x + 3)(x - 5)(x + 7)²(x - 2)²
B. f(x) = (x - 3)²(x + 5)²(x-7)(x + 2)
C. f(x) = (x - 3)(x + 5)(x - 7)²(x + 2)²
D. f(x) = (x - 3)²(x + 5)(x-7)(x + 2)²
E. f(x) = (x + 3)²(x - 5)(x-7)²(x + 2)
Robert swims a lap in the pool. His coach graphs his distance from the starting block.
A. Determine whether each graph is a function. Justify your answer.
B. Construct Arguments - Which graph must be incorrect. Explain
A) Both the graphs A and B are functions, here the vertical lines can intersect the curve A and B more than once. So, A and B graphs are functions.
B) The incorrect graph is A
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
A) Examine the graph to determine whether any vertical lines generated meet the curve more than once. If such a line exists, the graph does not reflect a function. The graph represents a function if no vertical line intersects the curve more than once.
A and B are functions, according to this.
B) A is the incorrect graph.
Because Robert's acceleration will change
Curved lines have varying slopes; they can begin with a very modest slope and then curve quickly (either upwards or downwards) towards a huge slope. In either case, the curving line with a changing slope indicates fast motion (i.e., changing velocity).
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Jeriel has a smart phone data plan that costs $45 per month that includes 6 GB of data, but will charge an extra $15 per GB over the included amount. How much would Jeriel have to pay in a month where he used 2 GB over the limit? How much would Jeriel have to pay in a month where he used went over by a GB?
Jerial would be responsible for paying $295 if she used more than the allotted 2 GB in a given month.
What is word problem?Word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Using linear equations,
Data plans cost $45 per month.
Additional fee equals $15 per GB
Jerial would be responsible for paying the following in a month if she used 2 GB more than allowed: = $45 + $15(5) = $45 + $ 250 = $ 295
The monthly payment that Jerial will be required to make as her usage exceeded x GB is:
= $45 + $15 (x)
= $45 + $15x
Hence, Jeriel will pay $45 + $15x when he used over a GB in a month.
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Which is the last sentence of the proof? because f + e = 1, a2 + b2 = c2. Because f + e = c, a2 + b2 = c2. Because a2 + b2 = c2, f + e = c. Because a2 + b2 = c2, f + e = 1.
The latest sentence of proof by using the triangle congruence method we can conclude that f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex].
Given that ΔABC and ΔCBD are right triangles
Therefore, one angle of both triangle is of 90°
So, ∠B is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.
Consequently, ∠A is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.
Similarly, When two triangles are similar then their corresponding angles are equal and their corresponding sides are also equal.
Therefore , the two proportions can be rewritten as
a² = cf ( equation 1 )
b² = ce ( equation 2 )
By adding b² on both side of equation 1 then we can write equation 1 as
[tex]a^{2} + b^{2} = b^{2}+cf[/tex]
[tex]a^{2} + b^{2} = ce+cf[/tex]
Because b² and ce are equal and substitute on the right side of equation 1
Using the converse of distributive property in above equation then we get a new equation. That is,
[tex]a^{2} +b^{2} = c(f+e)[/tex]
Because distributive property is a(b+c)=a(b+ac)
a² + b² = c²
Because e + f = c²
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you roll two fair dice. find the probability that the first die is a 6 given that the minimum of the two numbers is a 4.
The probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.
What is the probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Two dice are rolled.
Then the sample space (n) = 36
Possible outcomes = {(6,1), (6, 2), (6, 3), (6, 4)}
Probability = 4/36
= 0.11
Hence, the probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.
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Choose an expression equivalent to 2x2-12x+23
Group of answer choices
2(x+23)2-1
2(x+3)2+14
2(x-3)2+5
2(x-3)2+13
Answer: 2(x-3)2+13
To find the equivalent expression, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers. This property is given by the following equation:
(a-b)2 = a2-2ab+b2
In this case, the expression we are trying to simplify is 2x2-12x+23, which we can rewrite using the property of square roots as follows:
2x2-12x+23 = 2(x2-6x+11)
Then, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers to simplify the expression as follows:
2x2-12x+23 = 2(x2-6x+11) = 2(x2-6x+36-25)
Finally, we can use the commutative property of addition and the associative property of addition to simplify the expression even further:
2x2-12x+23 = 2(x2-6x+36-25) = 2((x-3)2+11) = 2(x-3)2+22
Therefore, the equivalent expression to 2x2-12x+23 is 2(x-3)2+13. This means that the correct answer is 2(x-3)2+13.
a variable is normally distributed with mean 22 and standard deviation 7. use your graphing calculator to find each of the following areas. write your answers in decimal form. round to the nearest thousandth as needed. a) find the area to the left of 25. 0.274 incorrect b) find the area to the left of 17. 0.159 incorrect c) find the area to the right of 22. 0.788 incorrect d) find the area to the right of 27. 0.055 incorrect e) find the area between 17 and 30.
The area to the left of 25 is 0.6664, the area to the left of 17 is 0.2389, the area to the right of 22 is 0.5000, the area to the right of 27 is 0.2389, and the area between 17 and 30 is 0.6340.
How to calculate area from normal distribution?
μ = population mean = 22
σ = standard deviation = 7
The area from normal distribution can be calculated using z test or normal distribution formula.
a) The area to the left of 25 is
P(x ≤ 25) = P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= P(z ≤ [tex]\frac{25-22}{7}[/tex])
= P(z ≤ 0.43)
using z table and we get,
= 0.6664
b) The area to the left of 17 is
P(x ≤ 17) = P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= P(z ≤ [tex]\frac{17-22}{7}[/tex])
= P(z ≤ -0.71)
using z table and we get,
= 0.2389
c) The area to the right of 22 is
P(x > 22) = 1 - P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= 1 - P(z ≤ [tex]\frac{22-22}{7}[/tex])
= 1 - P(z ≤ 0.00)
using z table and we get,
= 1 - 0.5
= 0.5000
d) The area to the right of 27 is
P(x > 22) = 1 - P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= 1 - P(z ≤ [tex]\frac{27-22}{7}[/tex])
= 1 - P(z ≤ 0.71)
using z table and we get,
= 1 - 0.7611
= 0.2389
e) The area between 17 and 30 is
P(17 ≤ x ≤ 22) = P([tex]\frac{x-\mu}{\sigma}[/tex] ≤ z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= P([tex]\frac{17-22}{7}[/tex] ≤ z ≤ [tex]\frac{30-22}{7}[/tex])
= P(-0.71 ≤ z ≤ 1.14)
= P(z ≤ 1.14) - P(z ≤ -0.71)
using z table and we get,
= 0.8729 - 0.2389
= 0.6340
Thus, the area is 0.6664 for area in the left of 25, the area is 0.2389 for area in the left of 17, the area is 0.5 for area in the right of 22, the area is 0.2389 for area in the right of 27, and the area is 0.634 for area between 17 and 30.
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Could someone help me with this
Answer:
x >= -3 (third choice)
Step-by-step explanation:
The line is bold and not dotted, meaning that it includes the solution. (or equal to...) This way, we can cross out y>-3 and x>-3.
The line stays on x= -3, and goes right. Meaning that all of the solutions include or are larger than -3.
The answer is x >= -3
suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 6 cubic feet per minute. if the pool has radius 3 feet and height 8 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 6 feet?
The pool's water is changing height at a pace of 0.283 feet per minute.
Given,
Right circular cylinder shaped pool.
The radius of the pool = 3 feet
The height of the pool = 8 feet
Imagine that 6 cubic feet of water per minute is continuously being poured into a swimming pool in the shape of a right circular cylinder.
We have to find the rate of change of the height of the water in the pool when the depth of the water in the pool is 6 feet;
Here,
Due to the swimming pool's right circular cylinder shape, its volume equals;
V(c) = π × r² ×h
Where r is the radius of the base and h the height
We take differentiation on both sides of the equation to get:
dV/dt = π × r² × dh/dt
Since the pool is a right circular cylinder and dV/dt is constant at 6 ft3/min, the rate of change in water height in the pool is independent of water height.
Then:
6 = π × r² × dh/dt
dh/dt = 6 / π × 3²
dh/dt = 8/113,04
dh/dt = 0.283 ft/min
Therefore,
The rate of change of the height of the water in the pool is 0.283 feet/min
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What is the score associated with 1 standard deviation below the mean if a set of scores has a standard deviation of 4 and a mean of 54? a. 62 b. 46 c. 50 d.58
If a set of scores does have a standard deviation of 4 and just a mean of 54, the score that is 1 standard deviation well below mean is 50.
Explain the term standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a large or low standard deviation indicates that the variables are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean.For the given values-
Mean = 54
standard deviation = 4
1 value below the standard deviation is;
54 - 4 = 50
Thus, if a group of scores does have a standard deviation of 4 and just a mean of 54, the score that is 1 standard deviation well below mean is 50.
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IHI Insurance have conducted a multiple linear regression analysis to predict the value of the number of annual claims incurred by a motor insurance policyholder (y)based on the age of the policyholder in years (x1) and the value of the car insured in thousands of dollars (x2). The analysis was based on a random sample of 500 policyholders. The ages in the sample ranged from 16 to 70 and the values of the cars in the sample ranged from $1,100 to $52,000. The multiple linear regression equation corresponding to IHI's analysis is: y^i = 13 + (-0.5)x1i + (0.1)x2i.
Select whether the following statements regarding the multiple linear regression equation are true or false:
True False
a) Holding x2 constant, a one year increase in x1 will result in a decrease of 0.5 in the predicted value of Y. b) A 28 year old policyholder with a car worth $20,000 is predicted to make 29 claims. c) Holding x1 constant, a one thousand dollar increase in x2 will result in an increase of 0.1 in the predicted value of Y.
The statements 1,2,3 are false, true and true respectively.
Given that,
Based on the policyholder's age in years (x1) and the insured car's worth in dollars, IHI Insurance performed a multiple linear regression analysis to forecast the value of the number of yearly claims made by a policyholder for motor insurance (y) (X2). 500 policyholders were chosen at random for the analysis. The sample included people ranging in age from 16 to 70, and the cars ranged in price from $1,100 to $52,000. I = 13 + (-0.5)X1i + (0.1)X2i is the multiple linear regression equation that corresponds to IHI's study.
a) y^i = 13 + (-0.5)x1i + (0.1)x2i
Here X 1i = 26 , X zi = 20
y^i = 13 + (-0.5)x1i + (0.1)x2i
y^i = 13 + (-0.5)(26) + (0.1)(20)
y^i = 2 it doesnt make 28 so it is false.
b) As the coefficient of X 1i is negative, it will decrease by 0.5
So, it is true.
c) As the coefficient of X 2i is positive, it will increase by 0.1
So, it is true.
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Are the ratios 10:5 and 20:10 equivalent? yes or no
Answer:
yes
Step-by-step explanation:
They are both equal to 2:1 if you simplify.
The following multiple regression output was generated from a study in which two independent variables are included. The first independent variable (X1) is a quantitative variable measured on a continuous scale. The second variable (X2) is qualitative coded 0 if Yes, 1 if No.Based on this information, which of the following statements is true?If tested at the 0.05 significance level, the overall model would be considered statistically significant.The variable X1 has a slope coefficient that is significantly different from zero if tested at the 0.05 level of significance.The model explains nearly 63 percent of the variation in the dependent variableAll of the above are true.
All of the claims about the multiple regression output are correct. The first independent variable (X1) was a continuous-scale quantitative variable, whereas the second variable (X2) was coded 0 if Yes and 1 if No.
Multiple regression is an effective statistical approach for analyzing the associations between multiple independent variables and a single dependent variable. Multiple regression has numerous uses in the social sciences, and recent research used it to analyze the connection between two independent factors and a single dependent variable.
Finally, the total model is statistically significant, the slope coefficient for variable X1 is considerably different from zero, and the model explains almost 63% of the variance in the dependent variable.
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melissa is using synthetic division to divide 3x3−x2−9x+7 by x−1.
Synthetic division yields the result 3x^2 + 2x - 7 when the equation
3x^3 - x^2 - 9x + 7 is divided by x - 1.
What is synthetic division?
Synthetic division in algebra is a technique that requires less writing and calculation than long division to manually divide polynomials into their Euclidean parts. The method can be applied to division by any polynomial, although it is typically taught for division by linear monic polynomials.
Consider the given polynomial 3x^3 - x^2 - 9x + 7.
We have to divide this polynomial by x - 1 using synthetic division.
3x^2 + 2x - 7
________________________
(x - 1)√(3x^3 - x^2 - 9x + 7)
3x^3 - 3x^2
______________________
2x^2 - 9x + 7
- 2x^2 - 2x
__________________________
-7x + 7
- -7x + 7
_________________________
0 + 0
Hence, Synthetic division yields the result 3x^2 + 2x - 7 when the equation 3x^3 - x^2 - 9x + 7 is divided by x - 1.
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For what value of x is line m parallel to line n?
Answer:
x=20
Step-by-step explanation:
6x+10 and 130 are equal to each other so to solve for x we set them equal
6x+10=130
-10. -10
6x=120
x=20
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A suit is on sale for $475, which is 76% of the regular price.
What is the regular price?
Answer:
The regular price of the suit was $625.
Step-by-step explanation:
First, convert 76% into a decimal by moving the decimal place over twice to get 0.76. Then, set up this equation:
475 ÷ 0.76 = 625
Now, we can check if this is right by setting up this equation:
0.76 x 625 = 475.
Yep! It checks out! Our final answer is $625.
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(7 , -3) : Quadrant 4
(0 , 1) : y-axis
(-3 , -2) : Quadrant 3
(4 , 4) : Quadrant 1
Plot each point on the coordinate grid
Answer:
ur not showing the points u need to plot
Step-by-step explanation:
what number needs to be added to both sides of the equation in order to complete the square? x2+16x=18
In order to complete the square for the given equation x^2+16x=18, the number added to both sides is 64.
Complete the square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial. To complete the square, add or subtract the same value to both sides. In this case, add the square of half the coefficient of the x -term, (b/2)^2 to both sides of the equation. Hence, the number to add would be (16/2)^2 = 64.
Thus,
x^2+16x + 64 =18 + 64
x^2+16x + 64 =82
x^2+ 2*8x + 64 =82
(x + 8)^2 = 82
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The graph shows the number of laps kailee ran around a track over a given number of minutes.
(a) What is the slope of the line? Use the slope formula and show your work.
(b) How many laps did Kailee run per minute?
(c) If she continued to run at the same rate, how many laps would she run in 30 min?
The slope of the line is 0.4, Kyle runs (2/5)th of a lap in a minute, and In 30 minutes, she would run 12 laps.
As per the given graph, the slope of the line as:
m = (4.4 - 2.2)/(11 - 5.5)
m = 0.4
The equation of line as:
y = 0.4x + 0
y = (2/5)x
So, Kyle runs (2/5)th of a lap in a minute.
In 30 minutes, she would run:
y = (2/5) x 30
y = 12 laps
Therefore, the slope of the line is 0.4, Kyle runs (2/5)th of a lap in a minute, and In 30 minutes, she would run 12 laps.
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The question seems to be incomplete the correct question has been attached
Three consecutive integers have a sum of â€""21. which equation can be used to find the value of the three numbers? x x x = negative 21 x 2 x 3 x = negative 21 x (x 1) (x 2) = negative 21 x (x 2) (x 4) = negative 21
The equation that can be used to find the sum of the three numbers in the given situation is (C) (x) + (x + 1) + (x + 2) = - 21.
What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
So, allow x to be the first number.
Number two: x + 1
Number three: x + 2
Three numbers are added together to provide the sum x + x + 1 + x + 2.
Given that the sum of three consecutive numbers is -21.
So, (x) + (x + 1) + (x + 2) = - 21.
Therefore, the equation that can be used to find the sum of the three numbers in the given situation is (C) (x) + (x + 1) + (x + 2) = - 21.
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Correct question:
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers?
a. x + x + x = - 21
b. x + 2 x + 3 x = - 21
c. x + (x + 1) + (x + 2) = - 21
d. x + (x + 2) + (x + 4) = - 21
what is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
The greatest possible area of the triangle be
Area = 1/2 sq. units.
Given, a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle.
we have to find the greatest possible area of the given triangular region.
Let the height of the triangle be, h and the base of the triangle be b.
using Pythagoras theorem, we get
1² = h² + (b/2)²
1 = h² + b²/4
h² = 1 - b²/4
Now, the area of the triangle be,
A = 1/2×b×h
squaring both the sides,
A² = 1/4×b²×h²
A² = 1/4×b²×(1 - b²/4)
A² = 1/4×b²×(4 - b²)/4
A² = 1/16×b²(4 - b²)
On differentiating, we get
2AA' = 1/16×[2b(4 - b²) -2b³]
2AA' = 1/8×[b(4 - b²) -b³]
2AA' = 1/8×(4b - 2b³)
2AA' = 1/4×(2b - b³)
On equating with zero, we get
b(2 - b²) = 0
b = √2
so, h = 1/√2
Therefore, the greatest possible area of the triangle be
A = 1/2 sq. units.
Hence, the greatest possible area of the triangle be
A = 1/2 sq. units.
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Juan buys 13 bottles of apple juice at the corner store for a total cost of $5.07. Assume
each bottle of juice is the same price. If c represents the total cost in dollars and cents
of the juice for any number, j, of bottles of juice, write a proportional equation for c in
terms of j that matches the context.
The proportional equation for c in terms of j as per the question statement will be equal to c = 0.39(j).
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given information in the question,
Price of 13 bottles = $5.07
Then, the price of each bottle = 5.07/13 = $0.39
As per the statement in the question,
The total cost is represented by c and the number of bottles will be j.
Then, the proportional equation will be,
c = 0.39(j)
As the number of bottles will increase, the total price will also increase with it.
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Water Park A water park charges $12 for admission and $5 to park your vehicle.
Write an inequality that represents the possible number of people that could go for
$50. Solve the inequality. What is the maximum number of people that could go?
There are maximum 3 people could go to the park.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Given:
Water Park A water park charges $12 for admission and $5 to park your vehicle.
Let x be the number of people
y is the cost
The equation becomes,
y=mx + b,
m will be price for each person and
b will be the fixed price for parking;
x, must be of whole numbers only
Here, m = 12, b = 5, y = 50.
⇒ 12x + 5 = 50
But we want the inequality
⇒ 12x + 5 ≤ 50
Replace x by p
⇒ 12p + 5 ≤ 50
where p is the number of peoples.
Solving inequality,
12p ≤ 50 - 5
12p ≤ 45
p ≤ 45/12
p ≤ 3
Hence, there are maximum 3 people could go to the park.
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What are 7 groups of ten + 2 more groups of 10?
Answer: 90
Step-by-step explanation:
7 * 10 = 70
2 * 10 = 20
70 + 20 = 90
Two parallel lines are crossed by a transversal. Horizontal and parallel lines y and z are cut by transversal x. At the intersection of lines y and x, the top right angle is (2 k + 11) degrees. At the intersection of lines z and x, the bottom left angle is 131 degrees. What is the value of k?.
The number k is equal to 60 when the top right angle at the intersection of the lines y and x is (2 k + 11) degrees and the bottom left angle is 131 degrees.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical expression is a sentence that includes numbers, variables, or both. The equal sign is never used in expressions. A mathematical statement stating the equality of two expressions is known as an equation.
Here,
Those two angles have the same measure. so you have,
2k+11=131
22k=120
k=60
The value of k where at the intersection of lines y and x, the top right angle is (2 k + 11) degrees and at the intersection of lines z and x, the bottom left angle is 131 degrees is 60.
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4) Which function shows a decay rate of 5%?
A) f(x) = 100(-5)
B) f(x) = 105(0.05)
C) f(x) = 100(0.95)
D) f(x) = 100(1.05
E) f(x) = 100(5)
A function is a relationship between inputs where each input is related to exactly one output.
The function with a decay rate of 5% is
f(x) = 100(0.95)
This is with a decay rate of 5%
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Decay rate = 5%
5% = 5/100 = 0.05
The total rate = 100%
100% = 100/100 = 1
The rate to multiply with the function.
= 1 - 0.05
= 0.95
A)
f(x) = 100(-5)
This is not a decay rate of 5%
B)
f(x) = 105(0.05)
This is with a decay rate of 95%.
C)
f(x) = 100(0.95)
This is with a decay rate of 5%
D)
f(x) = 100(1.05)
This is not a decay rate function.
E)
f(x) = 100(5)
This is not a decay rate function.
Thus,
The function with a decay rate of 5% is
f(x) = 100(0.95)
This is with a decay rate of 5%
Option C is the correct answer.
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n a study of the decay theory of memory, three different groups of subjects memorized a list of nonsense syllables and were then tested for their memory of those syllables at different delays. group 1was tested for memory after a delay of one hour. group 2 was tested after a delay of two hours. group 3 was tested after three hours. which statistical test should be used to test whether length of delay affects memory?
The statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.
Given, three different groups of subjects memorized a list of nonsense syllables and were then tested for their memory of those syllables at different delays.
Group 1 was tested for memory after a delay of one hour.
Group 2 was tested after a delay of two hours.
Group 3 was tested after three hours.
we have to find the statistical test that is used to test whether length of delay affects memory.
So, the statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.
Hence, the statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.
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consider the triangle formed by the side of the house, the ladder, and the ground. find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall?
The rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall is [tex]\frac{527}{24}ft^2/sec[/tex].
What is triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.
Given:
dx / dt = 2 feet / sec
We have to find dA/dt when x = 7.
Since,
Area = 1/2 x (xy)
A = 1/2 x (xy)
Differentiating both sides with respect to t
[tex]\frac{dA}{dt} = \frac{1}{2}(\frac{dx}{dt}y+\frac{dy}{dt}x)\\[/tex] ..(1)
We have,
x^2 + y^2 = 25^2
plug x = 7
⇒ y = √(25^2 - 7^2)
y = √(625 - 49)
y = √576
y = 24
Now plug x = 7, y = 24, dx/dt = 2 and dy/dt = -7/12 in equation (1)
[tex]\frac{dA}{dt} = \frac{1}{2} (2(24) + (-\frac{7}{12})(7)) \\ \frac{dA}{dt} = \frac{527}{24} ft^2/sec[/tex]
Hence, the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall is [tex]\frac{527}{24}ft^2/sec[/tex].
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