Answer:
-6
Step-by-step explanation:
-(-3)²+3
-9 + 3
-6
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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Research Study: We want to figure out what characteristics of boys are most attractive to high-school girls. High-school girls were randomly assigned three groups to hear about a guy with trendy clothes, a nice car, or a confident attitude. There were 9 girls in each group. They gave ratings on a scale from 1 to 10, with 1 being "not interested" and 10 being "very interested."
Question: Is there a significant difference between the attractiveness ratings given by the three groups of girls?
What is the factor?
What are the levels of the factor?
Step 1: State Hypotheses
Null:
Research:
Step 2: Determine Comparison Distribution
What is the distribution shape and degrees of freedom for the comparison distribution?
Step 3: Set the Criteria for a Decision
Alpha = .05
dfB =
dfW=
Critical value:
Is the rejection region placed in the upper or lower tail? How do you know?
Step 3: Compute the Test Statistic
Trendy Clothes
Nice Car
Confident Attitude
8
6
10
6
7
9
9
8
10
6
6
10
8
4
8
6
5
9
7
5
10
6
6
9
6
8
8
Step 5: Make a Decision
Reject/Fail to Reject the null?
What does this mean (be sure to talk about significance)?
Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance.
The null hypothesis is accepted.
There is no significant difference between the attractiveness ratings given by the three groups of girls.
Surveyed two random samples of 390 men and 360 women who were tested.
first sample percentage,
p1 = 360 ÷ 390 = 0.9230
second sample percentage,
p2 = 47 ÷ 52 = 0.9030
There is no change, according to the null hypothesis the percentage of males who have positive tests is significantly from the percentage of women who have positive tests.
Different Hypotheses:
There is a discrepancy in the percentage of schoolgirls who heard about a male with stylish clothes, a great automobile, or a confident demeanor across the three groups that were randomly allocated.
Z = (p1 - p2) ÷ √(PQ((1 ÷ n1) + (1 ÷ n2)))
where
p = (n1p1 + n2p2) ÷ n1 + n2
p = 0.920
Z = (0.9230 - 0.9030) ÷ √(0.9230((1 ÷ 390) + (1 ÷ 52)))
Test statistic Z = 0.13008
Level of significance = 0.10
The critical value Z₀.₁₀ = 1.645
Test statistic Z=0.13008 < 1.645 at 0.1 level of significance
The null hypothesis is accepted.
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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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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
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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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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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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at a resturant, diners are given the choice of 4 appetizers, 5 entrees, 3 deserts, and 2 wines. how many different dinners can be assembles?
Total number of ways in which dinner can be assembled will be 120.
What is restaurant?
A restaurant is a place of business where customers can order and receive food and drinks. Meals are typically prepared and consumed on the premises, but many eateries also provide take-out and delivery options.
A commercial space where customers can buy food or drinks.
There are 4 different types of appetizers, so there are 4 ways to choose one of them, which comes out to 4C1 = 4.
Similarly, there are 3 ways to choose desserts and 5 ways to choose an entrees.
2 methods for selecting wines are also included.
As a result, there are
5 x 4 x 3 x 2 = 120 different ways to assemble dinner in total.
Hence, total number of ways in which dinner can be assembled will be 120.
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a stock had returns of 10.00%%.3.00% and -7.00% over the past 3 years.what is the mean ofthe stock's returns over the past 3 years minus the sample standard deviation of the stock'sreturns from the past 3 years?
The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years is -6.54
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
Mean :
Mean = [10+3 + (-7) ] / 3 = 2
sample standard deviation :
subtract the mean from each data element.
10- 2 = 8
3-2 = 1
-7 - 2 = -9
Square those numbers.
8² = 64
1² = 1
(-9)² = 81
Add those
64+1+81 = 146
Divide by (number of elements -1 = 3 -1 = 2)
146/2 = 73
Take square root
8.54
So, the sample standard deviation = 8.54
The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years
= 2 - 8.54
= -6.54
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Please answer number 2 I think I answer is A but please explain how you got your answer.
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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How do I solve this equation 1 3/4÷3
Answer:
1 3/4 * 3
we turn 1 3/4 to improper fraction:
7/4
so,
7/4 * 3 = 21/4 or 5 1/4
Step-by-step explanation:
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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if the speed of the river is s, write an expression for the time it takes to travel 5 kilometers upstream and an expression for the time to travel 10 kilometers downstream
The time taken to travel upstream will be t = 5/(s - r) and the time taken to travel downstream will be equal to t = 10/(s + r).
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
Speed of boat in still water = s
Distance to travel upstream = 5 km and,
Distance to travel downstream = 10 km
Then, the time taken to travel upstream,
t = d/s
t = 5/(s - r)
And, the time is taken to travel downstream.
t = d/s
t = 10/(s + r)
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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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what is the probability you get this question right if you pick a random answer? a.20% b. 80% c. 25% d. 20% e. 50%
Answer: 80%
Step-by-step explanation:
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.
If f(x) = 3x³ + 5x² - 4, then what is the remainder when f(x) is divided by
x-1?
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
Show that (3x + 5)(x - 1)-3 = 3x² + 2x - 8
Answer:
[tex]\tt \left(3x+5\right)\left(x-1\right)-3[/tex]
Distribute:-
[tex]\tt 3x^2+2x-5-3[/tex]
[tex]\tt -5-3=-8[/tex]
[tex]\tt 3x^2+2x-8[/tex]
Hope this help you!
a two-factor anova is conducted and the data are plotted. the chart shows two parallel lines separated by a distance of 9 points. the lines represent factor a and the x axis of the chart represents the levels of factor b. how should you interpret these results?
The correct option is, there is a main effect for Factor A but there is no interaction.
What is two factor anova?
The mean of a quantitative The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the levels of two categorical variables.
Two-way analysis of variance is an extension of one-way analysis of variance in statistics that looks at the impact of two different categorical independent variables on a single continuous dependent variable.
The parallel lines indicates no interaction effect.
For the above problem option 'a' is correct.
There is a main effect for Factor A but there is no interaction
Hence, the correct option is, there is a main effect for Factor A but there is no interaction.
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Complete question:
A two-factor ANOVA is conducted and the data are plotted. The chart shows two parallel lines separated by a distance of 9 points. The lines represent Factor A and the x axis of the chart represents the levels of Factor B. How should you interpret these results?
Select one:
a. There is a main effect for Factor A but there is no interaction
b. There is a main effect for Factor A and there is also an interaction effect
c. There is a main effect for Factor B and there is an interaction effect
d. There is no interaction effect and no main effects
A function has a constant halving time. What type of function does this represent?.
An exponential decay function is one that has a constant time of halving.
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Here,
The function which has a constant halving time is in the following form,
A(t)=A₀(¹/²)^(t/h)
Where: A₀ is the initial amount
h is the half life time or the halving time.
t is the time
A(t) the amount that remains at time t
The previous function represents an Exponential decay function.
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select the most appropriate response. what does it mean when sample results are not statistically significant?
The sample results would be somewhat expected if the null hypothesis were true.
The correct option is (b).
Given,
In the question:
The complete question is this:
Select the most appropriate response.
What does it mean when sample results are not statistically significant?
The null hypothesis is true The sample results would be somewhat expected if the null hypothesis were true.The null hypothesis is wrongThe sample results would be unexpected if the null hypothesis were true.The question is based on MCQ's
Now, According to the question:
What does it mean when sample results are not statistically significant?
It means The sample results would be somewhat expected if the null hypothesis were true.
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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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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.
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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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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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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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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