we have the following:
[tex]\begin{gathered} v(t)=25900\cdot(0.92)^t \\ v(0)=25900\cdot(0.92)^0=25900\cdot1=25900 \\ v(12)=25900\cdot(0.92)^{12}=25900\cdot0.3676=9522.56 \end{gathered}[/tex]therefore, tue intial value is 25900 and value after 12 yeras is 9523
which property of equality should you apply to keep the equation 22*a= 242in balance when solving?
The property of division is apply to keep the equation 22a = 242 in balance.
What is division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Consider, the given equation
22 a = 242
The property of equality should you apply to keep the equation 22*a= 242in balance means we have to use an arithmetic operation (multiplication, addition, and subtraction) and find the value of a.
On the left side, "a" is multiplied to 22.
So, divide both sides by "a", we get
[tex]\frac{22a}{22} = \frac{242}{22}\\ a = 11[/tex]
Hence, we use the division property to keep an equation in balance.
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Answer:
The property of division is apply to keep the equation 22a = 242 in balance.
What is division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Consider, the given equation
22 a = 242
The property of equality should you apply to keep the equation 22*a= 242in balance means we have to use an arithmetic operation (multiplication, addition, and subtraction) and find the value of a.
On the left side, "a" is multiplied to 22.
So, divide both sides by "a", we get
[tex] \frac{22a }{22} = \frac{242}{22 } \\ a = 11[/tex]
Hence, we use the division property to keep an equation in balance.
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10x 10 0 y Match the function with the graph 1 b
To answer this kind of questions, we need to take attention to the original function. In this case, the function is y = 1/x.
We can see from the graph that this function if we multiply this function by -1, the function takes the form of the graph. But we need to add to this function two units in the y-axis direction to obtain the function represented in the graph.
Therefore, the function that matches the one in the graph is y = -1/x +2 (option a).
Is it possible for a standard deviation to be equal to zero ?
Given:
The objective is to explain whether it is possible for a standard deviation to be equal to zero.
Explanation:
A standard deviation can be zero when all the data are equal.
In general the value of standard deviation will decrease while approaching close to the mean value. Similarly, the standard deviation will increase if data points are away from the mean value.
Hence, standard deviation can be zero if all the obtained/provided data contains equal value.
Given the sizes of the three angles for the ∆ABC, please list their sides in order from smallest to largest.
1. m ∠ A=36, m ∠ B=42, m ∠ C= 102
2. m ∠ A = 53, m ∠ B = 72, m ∠ C = 55
Answer:
1. BC, AC, AB2. BC, AB, AC
Step-by-step explanation:
We know smaller side is opposite to smaller angle and the larger side is opposite to larger angle.
Considering this we have the following1. m ∠A = 36, m ∠B = 42, m ∠C = 102
Put in ascending order:
A < B < CSo the opposite sides are:
BC < AC < AB----------------------------------------------------------------------
2. m ∠A = 53, m ∠B = 72, m ∠C = 55
Put in ascending order:
A < C < BSo the opposite sides are:
BC < AB < ACLook at this diagram:If CE and FH are parallel lines and m
If CE and FH are parallel lines and angle EDG is 42 degree, then angle CDB is also 42 degree
If CE and FH are parallel lines and the line BI is the transversal
angle EDG = angle DGF (interior alternate angles)
(when two lines are parallel and is cut by a transversal, the interior alternate angles are equal)
So. angle DGF = 42 degree
angle CDB = angle DGF (corresponding angles)
(when two lines are parallel and is cut by a transversal, the corresponding angles are equal)
angle CDB = 42 degree
Therefore, if CE and FH are parallel lines and angle EDG is 42 degree, then angle CDB is also 42 degree
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The sum of the two numbers is 16. One number is 4 less than 3 times the other. Find the numbers.4, 511, 610, 511, 5
Explanation:
Let the first number be represented as
[tex]=x[/tex]Let the second number be represented as
[tex]=y[/tex]The sum of the two numbers is 16.
This can be represented below as
[tex]x+y=16----(1)[/tex]One number is 4 less than 3 times the other
This can be represented below as
[tex]y=3x-4----(2)[/tex]Step 1:
Substitute equation (2) in equation (1)
[tex]\begin{gathered} x+y=16 \\ x+3x-4=16 \\ 4x-4=16 \\ add\text{ 4 to both sides} \\ 4x-4+4=16+4 \\ 4x=20 \\ divide\text{ both sides by 4} \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Step 2:
Substitute x=5 in equation (1)
[tex]\begin{gathered} x+y=16 \\ 5+y=16 \\ substract\text{ 5 from both sides} \\ 5-5+y=16-5 \\ y=11 \end{gathered}[/tex]Hence,
The final answers are
[tex]\Rightarrow11,5[/tex]what is the volume of the following rectangular prism?3 1/31 2/5
The volume (V) of the given prism will be equal to the area of the green zone times the lenght of 1 2/5 units, that is,
[tex]\begin{gathered} V=\text{ gre}en\text{ zone area }\times\text{ lenght} \\ V=3\frac{1}{3}\times1\frac{2}{5}units^3 \end{gathered}[/tex]In order to make the product of the mixed fractions, we need to convert them into simple fraction form, that is,
[tex]\begin{gathered} 3\frac{1}{3}=\frac{3\times3+1}{3}=\frac{10}{3} \\ 1\frac{2}{5}=\frac{5\times1+2}{5}=\frac{7}{5} \end{gathered}[/tex]Then, the volume is given as
[tex]\begin{gathered} V=\frac{10}{3}\times\frac{7}{5} \\ V=\frac{10\times7}{3\times5} \\ V=\frac{70}{15} \\ V=\frac{14}{3} \end{gathered}[/tex]Then, the volume expressed in simple fraction form is:
[tex]V=\frac{14}{3}\text{ cubic u nits}[/tex]In order to convert this result into mixed form, we need to find the following division:
Then, the answer in mixed form is:
[tex]V=4\frac{2}{5}\text{ cubic units}[/tex]using demos find the line of best fit to compare fat (x) and the calories(y) from the table pictured. round to the nearest hundredth (2 decimal places if needed
Find line of aproximation to data
the regression data line gives as result
y = ax + b
a= 11.73
b= 193.85
Q13.Neil bought a house for £235 000In the first year the value of the house depreciated by 4%In each of years 2 and 3 the value of the house increased by 6%Work out the value of the house at the end of year 3
Given: Neil bought a house for £235 000
In the first year the value of the house depreciated by 4%
In each of years 2 and 3, the value of the house increased by 6%.
Required: To find out the value of the house at the end of year 3.
Explanation: Since in first year the value of house depreciated by 4%,
[tex]\text{ New price}=235000-\frac{235000\times4\times1}{100}[/tex][tex]undefined[/tex]Determine whether the given statement is true or false b ∈ {a,b,c}
ANSWER:
True
STEP-BY-STEP EXPLANATION:
The statement tells us if b belongs to the set by a, b and c.
Therefore, the statement is true, since it can be seen that b belongs to that set.
x^2 +2= 0I need help with solving this quadratic equation.
The given quadratic equation is:
[tex]x^2+2=0[/tex]Subtract 2 from both sides
[tex]\begin{gathered} x^2+2-2=0-2 \\ x^2=\text{ -2} \end{gathered}[/tex]Find the square root of both sides
[tex]\begin{gathered} \sqrt[]{x^2}=\text{ }\sqrt[]{-2} \\ x=\sqrt[]{-2} \\ x=\pm\sqrt[]{2}\times\sqrt[]{-1} \\ x\text{ =}\pm\text{ }\sqrt[]{2}i \\ x\text{ = }\pm i\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }-i\sqrt[]{2}\text{ or i}\sqrt[]{2} \\ \end{gathered}[/tex]which of the following relate the side of the triangle shown
The angle facing side b is 90 degrees
The angle facing side a is 75 degrees
Since the side facing angle b is greater than the angle facing angle a, therefore side b will be greater than side a.
This makes the correct option to be b>a
The first option is the correct option
I need help with a math question i linked the picture below with the questions the question is also a multiple question but i have to answer one question first to get to the next question
The coefficient is the number in front of a variable
EX: 9x, 3y, -4z
9, 3, and -4 are coefficients
Constant is the numerical term
EX: 3x + 2
3 is a coefficient of x and 2 is the constant
The given expression is
[tex]m+9+6n[/tex]We have 2 variables m and n, and 1 numerical term 9, then
The coefficients are the numbers of m and n
Since the number of m is 1 and the number of n is 6, then
The coefficients are 1 and 6
The constant is the numerical term, then
The constant is 9
The error that Sara made is she did not mention the coefficient of m
Use the law of sines to prove that the sides..............
Given the triangle:
We could use the law of sines to prove that sides b and c have the same length.
Find and simplify the difference quotient for the following function
Therefore:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-8xh-h^2+7x+7h+4-(-4x^2+7x+4)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{7h-8xh-h^2}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(7-8x-h)}{h} \\ \frac{f(x+h)-f(x)}{h}=7-8x-h \end{gathered}[/tex]Find the volume of a cube if an edge has length 2r st units.Volume =cubic unitsQuestion Help: Message instructorCheck Answer
You have a cube with side 2 rst units.
In order to calculate the volume of the given cube, you use the following formula:
V = a³
where a is the length of cube sides.
By replacing the value of a into V formula you obtain:
V = (2 srt)³ units³
V = 8 r³s³t³
where you have used tha fact 2³=8 and that variables r,s and t power to 3 are equal to r³s³t³.
Hence, the volume of the given cube is V = 8 r³s³t³ units³
A national trivia tournament starts with 262,144 teams. With each round, there are half as many teams as before. The number of teams after any number of rounds, x, can be modeled with the following function.f(x)=262144(1/2)^xWhich statement compares the mathematical range and reasonable range of the function?1. Both the mathematical and reasonable ranges are limited to real numbers greater than 0 and less than or equal to 262,144.2. Both the mathematical and reasonable ranges are limited to whole numbers greater than 0 and less than or equal to 262,144.3. The mathematical range is all real numbers greater than 0. The reasonable range is all real numbers greater than 0 and less than or equal to 262,144.4. The mathematical range is all real numbers greater than 0. The reasonable range is all whole numbers greater than 0 and less than or equal to 262,144
The given function is
[tex]f(x)=262,144(\frac{1}{2})^x[/tex]This is a decreasing exponential function, due to the base is less than 1. When the base is less than one, the function is decreasing and 1/2 is less than 1.
The range of this exponential function is "all numbers greater than zero" because a power can't result in a null result (nor negative), that is, we can't get zero (or negative number) from a power, no matter what base it has, this applies for every exponential function.
However, the reasonable range refers to those values that make sense to the problem, because not all of the values from the function are valid as a reasonable solution.
Therefore, the reasonable range
[tex](0,262144\rbrack[/tex]Notice that the limit is 262,144, since that's the maximum number of teams possible.
The right choice is the "The mathematical range is all real numbers greater than 0. The reasonable range is all whole numbers greater than 0 and less than or equal to 262,144"
Two common names for streets are Fourth Street and Main Street, with 14,593 streets bearing one of these names.There are 443 more streets named Fourth Street than Main Street. How many streets bear each name?
Let
x ----> number of streets that bear Fourth Street
y ----> number of streets that bear Main Street
we know that
x+y =14,593 --------> x=14,593-y -----> equation 1
and
x=y+443 ------> equation 2
Solve the system of equations
Equate both equations
14,593-y=y+443
solve for y
2y=14,593-443
2y=14,150
y=7,075
Find out the value of x
x=y+443 ---------> x=7,075+443=7,518
therefore
Fourth Street: 7,518 streetsMain Street: 7,075 streetsCan you help me answer a, b and c please?
Answer:
Explanation:
Using the rule of significant figures!*Please help this one is tricky
Answer: 2
Step-by-step explanation:
223.4: 4 significant figures
7.5: 2 significant figures
when we multiply numbers with sifnificant figures, the answer will have the same number of significant figures as the measurement with the lowest number of significant figure.
In this exercise, since we have a measurent with 2 significant figures and another measurement with 4 significant figures, the result will have 2 significant figures.
20. Find the volume of the following figure.a. 448.4 cm3b. 149.5 cmC. 896.7 cm3d. 21.4 cm3
Volume of an hexagonal prism (v ): (3√3/2)a^2h
Where:
a = side base = 7cm
h= height = 7 cm
Replacing:
V = (3√3/2)7^2(7) = 891.14 cm3
The following summarizes the number of fiction read last summers by a sample of 28 students.
SOLUTION:
The mean is given by the formula;
[tex]\frac{\sum_^fx}{\sum_^x}[/tex]We calculate this as;
[tex]\frac{2(3)+3(10)+4(15)}{3+10+15}=3.4[/tex]Therefore, the mean is 3.4
f(x) = 2x - 1 g(x) = 3x h(x) = x^2 + 1Find f(g(x))
Given the following functions:
f(x) = 2x - 1
g(x) = 3x
h(x) = x2 + 1
f(g(x)) means that we will be substituting the function of g(x) as x of the f(x) function.
We get,
[tex]f\mleft(g\mleft(x\mright)\mright)\text{ }\rightarrow\text{ f(x) = 2x - 1 }\rightarrow\text{ }f(g(x))=\text{ 2(3x) - 1}[/tex][tex]f(g(x))=\text{ 6x - 1}[/tex]1. (01.01 )At a local restaurant, Enrique is paid $4.55 per hour and earns an average of $19 tips on all food sales. Identify the algebraic expression that could be used to represent Enrique's gross pey (4 points)O 455() +1.90455() +0.19004550) - 1.900O 455-0.1960
Data
• $4.55 per hour
,• Earns an average of 19 tips (assuming that the tips are in dollars).
Procedure
To identify the algebraic expression, we have to identify the variable earn (the quantity that depends on something) and the fixed (the one that is mostly constant).
Based on the information given, we can assume that the variable quantity is $4.55, as it depends on the time, and the fixed is $19. Thus, the algebraic expression can be written as follows:
[tex]E=4.55t+19[/tex]where E represents the earnings and t represents the time.
Answer:
[tex]E=4.55t+19[/tex]Let’s work with some actual data this time. Go online to research and find a set of real-world data in two variables. The data can be in tabular form or in a scatter plot. Choose data that has a reasonable number of data points so you’re able to uncover trends. For the purposes of this activity, the data must not show a linear association. Describe the data you’ve identified in a sentence or two, and include a link to the data.
Here, we can observe how the human population is growing through time.
In approximately 100 years the population is twice the original population.
In a isosceles triangle one angle is 57° greater than each of the other two equal angles. find a measure of all three angles
An Isosceles triangle has two sides and two angles to be congruent or equal.
Let the two congruent angles be x° degrees, then the third side which is 57° greater than the congruent angles would measure (x+57°).
SKETCH
The sum of angles in a triangle is 180°. Hence,
[tex]\begin{gathered} x+x+(x+57)=180^0 \\ 3x+57=180^0 \\ 3x=180-57 \\ 3x=123 \\ x=\frac{123}{3} \\ x=41^0 \\ \therefore(x+57)=41^0+57^0=98^0 \end{gathered}[/tex]Therefore, the measure of all three angles are: 41,⁰ 41⁰, and 98⁰
how do we know that 1+1=2?
Method 1
By observation
1 cat and another 1 cat makes 2 cats
Method 1
1 boo
3/4 + 7/10Write your answer as a fraction in simplest form.
action
Given
[tex]\frac{3}{4}+\frac{7}{10}[/tex]Solution
First, find the LCM which is 20 and write as common denominator
[tex]\frac{15}{20}+\frac{14}{20}[/tex]Add the fraction
[tex]\frac{15}{20}+\frac{14}{20}=\frac{29}{20}[/tex]Now to the simplest form
[tex]\frac{29}{20}=1\frac{9}{20}[/tex]The final answer
[tex]1\frac{9}{20}[/tex]11> _ <49 how do I solve this?
The question is asking for a number less or equal than 11 and less or equal to 49, then by the options we have, the number would be:
[tex]11\ge8\leq49[/tex]This Venn diagram shows sports played by 10 students.PLAYSBASKETBALLMaiPLAYSSOCCERMickeyMarcusFranEllalanKarlJadaGabbyJuanLet event A = The student plays basketball.Let event B = The student plays soccer.What is PAB)?O A.A. «0.17B. 1=0.1010
ANSWER
[tex]P(A|B)=\frac{1}{3}\approx0.333[/tex]EXPLANATION
We want to find the probability P(A|B).
This is a conditional probability and its formula is:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]where P(A n B) is the probability that the student plays basketball and soccer and P(B) is the probability that the student plays soccer.
We have that:
[tex]P(A\cap B)=\frac{1}{10}[/tex]and
[tex]P(B)=\frac{3}{10}[/tex]Therefore, we have that:
[tex]\begin{gathered} P(A|B)=\frac{1}{10}\div\frac{3}{10} \\ P(A|B)=\frac{1}{10}\cdot\frac{10}{3} \\ P(A|B)=\frac{1}{3}\approx0.333 \end{gathered}[/tex]That is the answer.