The way in which the given ordered pairs represent a function is: b. For every x value, there is only one y value - a function.
What is a function?A function simply refers to a mathematical expression (equation) which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable (x-value) to an output variable (y-value).
In this context, we can reasonably infer and logically deduce that these ordered pairs represent a function because it has different input variables (x-values) for different or the same output variables (y-values).
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If a bank represents deposits with positive numbers and withdrawals as negative numbers, what could 6+ (-60) represent ?
Given:
A positive number shows a deposit
A negative number shows withdrawals.
Find-: What could $6+
-60 represent
Sol:
+6 represent is:
[tex]6\rightarrow\text{ Deposits}[/tex]-60 represent is:
[tex]60\rightarrow\text{ Withdrawals}[/tex]So the answer is:
$6 deposit followed by a $60 withdrawal
4. CONSTRUCTION A 30-foot ladder
leaning against the side of a house makes
a 70.1 angle with the ground.
70.1
30 ft
a. How far up the side of the house does
the ladder reach?
b. What is the horizontal distance
between the bottom of the ladder
and the house?
The answers to both subparts are with the help of trigonometric functions:
(A) The side of the house to the ladder reach: x = 28.208 ft(B) Horizontal distance: x = 10.211 ftWhat are trigonometric functions?The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others. Sine, Cosine, and Tangent are the three fundamental trigonometrical operations.So, (A) The side of the house to the ladder reach:
Sin70.1 = x/30x = 28.208 ft(B) The horizontal distance between the bottom of the ladder and the house:
Cos70.1 = x/30x = 10.211 ftTherefore, the answers to both subparts are with the help of trigonometric functions:
(A) The side of the house to the ladder reach: x = 28.208 ft(B) Horizontal distance: x = 10.211 ftKnow more about trigonometric functions here:
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Multiply the sum of 4 and 5 by the difference of 14 and 8
We need to know the simple mathematical operations to solve this problem. The final answer on multiplying the sum of 4 and 5 by the difference of 14 and 8 is 54.
We have to use addition, subtraction and multiplication to solve the question. First we need to find the sum which means add 4 and 5. Next we need to find the difference between 14 and 8 which means we need to subtract 8 from 14. Finally we have to multiply both the values to get the final answer.
4+5=9
14-8=6
(4+5) x (14-8)=9 x 6=54
Therefore the final value that we get on multiplying the sum of 4 and 5 by the difference of 14 and 8 is 54.
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Suppose Chris borrows $ 7000 at an interest rate of 8% compounded each year.Assume that no payments are made on the loan.Follow the instructions below. Do not do any rounding.(a) Find the amount owed at the end of 1 year$0(b) Find the amount owed at the end of 2 years.$0Х?
Explanation
The formula for the Amount based on compound interest is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Since the principal is compounded annually, therefore n =1. Also, P = principal = $7000, ratte = r = 8%, t= time
Hence when t = 1 year
[tex]\begin{gathered} A=7000(1+\frac{8}{100})^1 \\ A=7000(1.08) \\ A=7560 \end{gathered}[/tex]
Answer A: $7560
When t = 2 years
[tex]\begin{gathered} A=7000(1+\frac{8}{100})^2 \\ A=7000(1.08)^2 \\ A=8164.8 \end{gathered}[/tex]Answer B: $8164.8
what is 6^9 divided by 6^3
Answer:
Step-by-step explanation:
46656
I need urgent help with this math problem, please help me!
Answer:
See below
Step-by-step explanation:
The MONTHLY payment for each loan is just the interest and principal paid for each month
I just used the first line of each amortization:
First one 26 + 196 = $ 222 per month
Second one 26 + 127 = $ 153 per month
Sorry if the numbers are incorrect....the image is very fuzzy....
but this is the method for the answer .
1. In 2014, the population of Florida was 19,580,000. Write the 2014 population of Florida in scientific notation.
The population of Florida in scientific notation 1.958 x [tex]10^{7}[/tex]
What is Scientific notation?
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.
Given,
19,580,000
We know that,
19580000 = 1.9580000(10000000)
10000000 = [tex]10^{7}[/tex]
Substitute
1.9580000([tex]10^{7}[/tex])
or, 1.958 x [tex]10^{7}[/tex]
Hence, The 2014 population of Florida in scientific notation is equal to 1.958 x [tex]10^{7}[/tex]
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Solve the equation for y.y/a - 16 = h
we have
y/a - 16 = h
solve for y
that means -----> isolate the variable y
so
Adds 16 both sides
y/a=(h+16)
Multiply by a both sides
y=a(h+16)consider the following functions which all have a value of 30 does each equation represent growth or decay
The general equation forms representing growth or decay is;
[tex]\begin{gathered} F=I(1+r)^{t\text{ }}orF=I(1-r)^t \\ F\text{ is future value} \\ I\text{ is initial value} \\ r\text{ is growth rate} \\ t\text{ is time} \\ (1-r)\text{ represents decay} \\ (1+r)\text{ represents growth} \end{gathered}[/tex]So let us consider the equations;
a) f(t) = 30(1.04)^t
f(t) = 30(1+0.04)^t
It is growth as it is greater than 1 and the growth rate is 0.04 = 4/100 = 4%
b) p(x) = 30(0.65)^x
P(x) = 30(1-0.35)^x
it is decay as it is less than 1
Growth rate is 0.35 = 35/100 = 35%
c) A(x) = 30(1.10)^x
A(x) = 30(1 + 0.1)^x
it is growth as it is greater than 1
0.1 = 10/100 = 10%
d) h(t) = 30(0.98)^t
h(t) = 30(1-0.02)^t
It is decay since it is less than 1
growth rate is;
0.02 = 2/100 = 2%
e) s(t) = 30(0.77)^t
s(t) = 30(1-0.23)^t
it is decay as it is less than 1
0.23 is growth rate = 23/100 = 23%
f) B(t) = 30(1.2)^t
B(t) = 30(1+0.2)^t
It is growth since it is greater than 1
0.2 = 20/100 = 20%
The Inn at Fort Lee why
In this problem we have that
the solution is the shaded area above the dashed line
so
Find the equation of the dashed line
x -----> outside temperature
y ----> inside temperature
Find the slope
take the points (0,20) and (10,30)
m=(30-20)/(10-0)
m=10/10
m=1
the equation is
y=x+20
therefore
the inside temperature is always 20 degrees warmer than the outside temperature
answer is option BSolve the given linear system of equations:6serбу9y– 120 +18One solution:O No solutionO Infinite number of solutions
no solution (2nd option)
Explanation:
8x - 6y = 6 .....equation 1
-12x + 9y = 18 .....equation 2
Using elimination method:
we will eliminate y by making both coefficient of y to be the same.
This is done by multiplying equation 1 by 3 and equation 2 by 2
24x - 18y = 18 .....equation 1
-24x + 18y = 36 ....equation 2
Adding both equation:
24x - 24x -18y + 18y = 18 + 36
0 + 0 = 54
[tex]\begin{gathered} 0\ne\text{ 54} \\ \end{gathered}[/tex]Since 0 is not equal to 54, there is no solution (2nd option)
Find the missing length. Round to the nearest tenth if necessary. Find the missing side.
Given:
a = 4
b = 5
c = unknown
Let's find the length of c.
Here, we are given a right triangle, where c is the longest side.
The longest side of a right triangle is called the hypotenuse.
To find the hypotenuse, apply Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]Input values into the equation above:
[tex]\begin{gathered} c^2=4^2+5^2 \\ \\ c^2=16+25 \\ \\ c^2=41 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{41} \\ \\ c=6.4 \end{gathered}[/tex]Therefore, the length of the missing side, c =
If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y = 32 when x = 20
The constant of variation is 1.6, and then the direct variation equation is:
y = 1.6*x
How to find the constant of variation?A direct variation between two variables can be written as:
y = k*x
Where k is called the constant of variation.
Here we know that when x = 20, the value of y is 32, replacing that in the above equation we get:
32 = k*20
Solving this for k we get:
32/20 = k = 1.6
Then the equation is:
y = 1.6*x
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There are 19 racks of plates in City Restaurant. Each rack has 37 plates. Which choice shows the correct estimate of how many plates are on the plate rack?
A.
400
B.
600
C.
800
D.
1,000
Answer: c.800 that's the answer
The correct estimate of the number of plates on the plate rack is 800.
The number of racks of plates in the City Restaurant is 19.
The number of plates in each rack is 37.
We need to find the estimated number of the total plates on the plate rack in the City Restaurant.
To find the estimate, we will round off the numbers to the nearest ten.
Rounding a number implies simplifying it while retaining its value close to what it was. The end output is less precise but more usable.
The number of racks of plates is rounded off and becomes 20.
The number of plates in each rack is rounded off and becomes 40.
The total number of plates in the rack is given by the multiplication of the two numbers obtained.
The total number of plates on the plate rack is 20x40 = 800.
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Ximena needs to order some new supplies for the restaurant where she works. The restaurant needs at least 333 spoons. There are currently 255 spoons. If each set on sale contains 6 spoons, which inequality can be used to determine
s
s, the minimum number of sets of spoons Ximena should buy?
In linear equation, Joshua should buy is 255 + 6s ≥ 333.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Let the sets of spoons be represented by s
The restaurant needs at least 333 spoons.
Each set on sale contains 8 spoons
There are currently 333 spoons.
At least as an inequality is ≥
Hence:
255 + 6 × s ≥ 333
255 + 6s ≥ 333
Therefore, inequality tha can be used to determine s the minimum number of sets of spoons Joshua should buy is
255 + 6s ≥ 333
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How do u solve 8t-2 I can’t figure out how to solve it
Answer:
2(4t - 1)
Step-by-step explanation:
8t - 2
The common multiple is 2 because 2 will go into both 8 and 2. Move the multiple of 2 outside, and add ():
2(4t - 1)
A real estate agent received $5,880 commission on a sale of an &84,000 home.what is the rate of commission
As given by the question
There are given that the agent received $5880 commission on a sale of $84000.
Now,
The rate of commission is:
[tex]\begin{gathered} \frac{5880}{84000}\times100=0.07\times100 \\ =7\% \end{gathered}[/tex]Hence, the rate of commission is 7%.
help meeeeeeeeee pleaseee
The domain of the line in the graph is x∈R.
What is a domain?The set of all potential inputs for a function is its domain. For instance, the domain of f(x)=x² and g(x)=1/x are all real numbers with the exception of x=0. Additionally, we can define special functions with more constrained domains. Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, the domain the line is:
From the given graph, we know that y = every time.Which means, in the given graph, y = x = 10.
This also means:
y = x = 9y = x = 11y = x = 10The values of x can go to infinity.
Then the domain will be x∈R.Therefore, the domain of the line in the graph is x∈R.
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The formula for the volume of a cone with a base of radius r is . Find the radius to the nearest hundredth centimeter if the volume is 60 cm^3. Branliest to first correct answer
Answer:
not ennough information to answer the question
Step-by-step explanation:
I need help with the multiplication part to find the area
Explanation
Area:
[tex]A=\frac{16.5cm*12.8cm}{2}=\frac{211.2}{2}cm^2=105.6cm^2[/tex]A line passes through the point (−10, 4) and has a slope of 3/2. Write an equation in slope-intercept form for this line.
The equation of the line in slope intercept form is y = 3/2x + 19
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation of the line?The given parameters are
Slope, m = 3/2
Points, (x1, y1) = (-10, 4)
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = m(x - x1) + y1
So, we have
y = 3/2(x + 10) + 4
Expand
y = 3/2x + 15 + 4
Evaluate the like terms
y = 3/2x + 19
Hence. the linear equation is y = 3/2x + 19
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The graph of a function is shown below.Find one value of x for which f(x) = -3 and And /(o).
The graph of a function is given.
When the function of x is -3, that is
[tex]f(x)=-3[/tex]That means the input value which is x, gives us negative 3.
Looking at negative 3 from the graph, the value of x where the graph equals negative 3 (on the vertical axis, or y-axis) is either negative 2 or 1. That is
Also, when the input of the function is zero, then you'll have the output as
[tex]f(0)=1[/tex]This means when the value of x is zero, then the output as shown on the graph is 1 (that is the graph touches the y-axis at 1)
Therefore;
(a) One value of x for which f(x) = -3 is -2 (OR 1)
(b) f(0) = 1
0.51 + 6.1 = 6.61 because 0.51 is precise to the hundredth digit, so theanswer must also be rounded to the nearest hundredth.A. TrueB. False
When two decimal numbers are added, the result is precise to the one that has the least precision.
For example,
0.51 + 6.1
Here 0.51 is precise to the hundredth place and 6.1 is precise to the tenth place.
So, the result will be precise to the tenth place since this was the least precision in the operation.
0.51 + 6.1 = 6.6
You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? The random numbers below represent a simulation with 20 trials. Let 0-7 represent a correct answer and let 8-9 represent an incorrect answer.
0.262144 = 26.2% of getting all the 6 questions correctly.
What is Binomial probability ?
The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes.
This is a binomial distribution problem
Binomial distribution function is represented by :
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 6 multiple choice questions
x = Number of successes required = 6 (we want to get it all right.
p = probability of success = 0.8 (80% chance of getting any individual question right; 0.8 probability of getting each question correctly)
q = probability of failure = 1 - 0.8 = 0.2
P(X = 6) = ⁶C₆ (0.8)⁶ (0.2)⁶⁻⁶
= 1(0.262144)(1)
= 0.262
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The Heights(in inches)and the weight (in pounds)of a simplified women are recorded. round your answer to one decimal place ×=height. y=weight 66. 122 67. 13269. 15368. 13865. 125a) calculate the slope of B1 and the y-intercept Bl0) of the regression line. Write the regression equation.y= _____ x+_____b) Interest interpret the values of B1 and B0. For it each increase of 1 inches the estimate weight increase by_______ pounds. When x=0 inches weight the estimate weight is________ pounds
For the linear regression the dependent and independent variables are:
y: "weight of a woman" (measured in pounds)
x: "height of a woman" (measured in inches)
You have to calculate the estimated linear regression equation:
[tex]y^{}=b_{0\text{ }}+b_1x[/tex]Where
b₀ is the estimate of the y-intercept
b₁ is the estimate of the slope
To calculate both by hand you have to use the following formulas:
[tex]b_1=\frac{\sum ^n_1x_iy_i-\frac{(\sum^n_1x_i)(\sum^n_1y_i)}{n}}{\sum ^n_1x^2_i-\frac{(\sum ^n_1x_i)^2}{n}}[/tex][tex]b_0=y_{\text{bar}}+bx_{\text{bar}}[/tex]y bar and x bar are the sample means for the weight and height
n is the number of women observed, in this case the sample size is
n=5 women
Next calculate the needed summatories, i.e. add each obervation from the corresponding variables
∑xi= 335
∑xi²= 22455
∑yi=670
∑xiyi=44962
ybar=∑yi/n= 670/5=134 pounds
xbar=∑xi/n= 335/5=67 inches
Replace the values in the formulas:
Slope:
[tex]b_1=\frac{44962-\frac{335\cdot670}{5}}{22455-\frac{(335)^2}{5}}=7.20\text{ }\frac{pounds}{In}[/tex]y-intercept
[tex]b_0=134-7.20\cdot67=-348.4\text{pounds}[/tex]The estimated linear equation is:
y=-348.4+7.20x
b)
The y-intercept of the linear regression indicates the value of the estimated mean of the variable y when x equals zero.
The slope of the linear regresion insicates the change of the estimated mean of the variable y when the variable x increases one unit.
So in terms of this exercise you can interpret the y-intercept as:
-348.4pounds is the estimated average weight of women when their height is zero inches.
→ Note that this interpretation has no logical meaning, at least not one applicable in real life, but for the regression is a valid mathematical result and interpretation.
And the slope can be interpreted as:
7.2pounds/inches is the modification of the estimated average weight of weomen when their height increases 1 inch.
my teacher was teaching us this earlier but she didn't actually explain because she focuses on the class but I'm on virtual
________________________________
x= red titles
two times = 2x
50
2x= 0.5x + 75
2x - 0.5x = 75
(2- 0.5) x = 75
1.5 x = 75
x= 75/ 1.5
x= 50
_______________________
Can you see the updates?
_________________________
Answer
Option D = 50
____________________
Do you have any questions regarding the solution?
What is the value of y^2-x^4y
2
−x
4
y, squared, minus, x, start superscript, 4, end superscript when y=8y=8y, equals, 8 and x=2x=2x, equals, 2?
The value of the given expression is -64.
what is value?
Any specific mathematical thing can, in general, have one mathematical meaning. The numeral or other mathematical object assigned to a vector, constant, or other mathematical object is its value. When the expression's variables and constants are given b, the formula stated in this expression yields the result of the mathematical equation.The number that a function assumes for each given value assigned toward its argument(s) is known as the function's value. Real-value variables, expressions, and functions simply assume real values. A complex-valued variables, expression, or function simply assumes complex values in the same way.Given expression:
y^2-x^4y
=y^2-x^4y
=y(y-x^4)
Putting value x=2, y=8
8(8-2^4)
=-64
The value of the given expression is -64.
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Stella measured a line to be 12.4 inches long. If the actual length of the line is 9.6 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
measured 12.4 inches but it is 9.6, the error is 12.4 - 9.6 = 2.8 inches
2.8 inches in percentage with tespect to 9.6:
100 (2.8/9.6) = 280/9.6 = 29.2 %
Answer:
Error is 29.2% of the actual lenght (9.6)
Please help me with this sample question.The sample questions only allow me to test each country once before moving to the next. I need all countries.
Let be "a" the number of medals that Country A won, "b" the number of medals that Country B won, and "c" the number of medals that Country C won.
You can set up the following System of equations using the information given in the exercise:
[tex]\begin{cases}a+b+c=119 \\ b=c+7 \\ a=b+c+33\end{cases}[/tex]In order to solve the System of equations, you can follow these steps:
1. Substitute the second equation into the third equation:
[tex]\begin{gathered} a=b+c+33 \\ a=(c+7)+c+33 \\ a=2c+40 \end{gathered}[/tex]2. Substitute this new equation and the second original equation, into the first original equation:
[tex](2c+40)+(c+7)+c=119[/tex]3. Solve for "c":
[tex]\begin{gathered} 4c+47=119 \\ 4c=119-47 \\ \\ c=\frac{72}{4} \\ \\ c=18 \end{gathered}[/tex]4. Knowing the value of "c", you can substitute it into the second original equation and then evaluate, in order to find the value of "b":
[tex]\begin{gathered} b=(18)+7 \\ b=25 \end{gathered}[/tex]5. Knowing the value of "b" and "c", you can substitute them into the third original equation and then evaluate, in order to find the value of "a":
[tex]\begin{gathered} a=b+c+33 \\ a=(25)+(18)+33 \\ a=76 \end{gathered}[/tex]Therefore, the answer is:
- Country A won 76 medals.
- Country B won 25 medals.
- Country C won 18 medals.
Check each answer to see whether the student evaluated the expression correctly. If the answer is incorrect, cross out the answer and write the correct answer. Algebraic expressions 7p+5 when p=12Student answer7(12) +5 = 7(17) =119
Given the expression:
[tex]7p+5[/tex]We will find the value of the expression when p = 12
so, substitute with p = 12
[tex]7(12)+5=84+5=89[/tex]So, the student answer is incorrect
The correct answer will be 89
