[tex]\huge\red{\mid{\underline{\overline{\textbf{EQUATION AND ANSWER}}}\mid}}[/tex]
_________________
Let's solve this equation using rates,
_________________DefinitionsUnit Rate - A unit rate means a rate for one of something.
Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
_________________
Now that we understand the definition we can further solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Values}}}\mid}}[/tex]
[tex]165[/tex] [tex]km[/tex] ⇒ [tex]1.5[/tex] [tex]hr[/tex]
[tex]x\\[/tex] [tex]km[/tex] ⇒ [tex]2.2[/tex] [tex]hr[/tex]
Now we will use cross-multiplication to solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Equtation}}}\mid}}[/tex]
[tex]165 \cdot 2.2\\x\cdot1.5[/tex]
Once solving this equation we get
[tex]1.5x=363[/tex] [tex]km[/tex]
Divide both sides by [tex]1.5[/tex]
[tex]x=242[/tex] [tex]km[/tex]
[tex]\large\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}[/tex]
A train travels 165 km in 1.5 hours. How far will the train travel in 2.2 hours if it maintains the same speed?The train would've traveled a total of 242 km in 2.2 hours.
Have a good day!what are the mixed decimal fraction and the simplified mixed fraction for 9.875
The given decimal fraction is:
[tex]9.875[/tex]This can be expressed into a fraction as:
[tex]\frac{9875}{1000}[/tex]Hence, the mixed decimal fraction is:
[tex]9\frac{875}{1000}[/tex]Hence, the simplified mixed fraction is:
[tex]9\frac{7}{8}[/tex]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.
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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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]The trip to and from work each day is 5 2/9 kilometers. If gina does this 5 days a week ,how many kilometers does she travel
Answer: Answer is 26.11 Kilometers
Step-by-step explanation:
First, we will convert the mixed fraction into improper fraction for easy calculation. So, the steps to convert mixed fraction to improper fraction are :-
Step 1- Multiply the denominator by the whole number
9 × 5 = 45
Step 2- Add the answer from Step 1 to the numerator
45 + 2 = 47
Step 3 - Write answer from Step 2 over the denominator
47/9
So, Mixed fraction is 47/9.
In other words, she travels 5.22 Kilometers daily.
Now, Gina travels 47/9 km daily to and from for work.
So, Kilometers travelled by her in 5 days are
47/9 * 5 = 26.11 Kilometer
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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.
Describe how to transform into an expression with a rational exponent. Use full sentence
For any numbers x, a and b, we aply the following rules:
[tex]\sqrt[a]{x^b}=x\text{\textasciicircum(b/a)}[/tex]and
[tex](x^a)^b=x^{ab}[/tex]Therefore, we got:
[tex](\sqrt[6]{x^5})^7=x^{(5\cdot7)/6\text{ = 35/6}}[/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]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]Solve each problem by writing an equation that matches the situationthen solve your equation to find the solution.
Question 2:
- Shakira paid $3 to rent shoes for bowling. At this point, she has spent a total of $3.
- Next, she plays bowling games each worth $4.75. This means that:
For her 1st game, she will pay $4.75
For her 2nd game, she will pay 2($4.75)
For her 3rd game, she will pay 3($4.75)
For her 4th game, she will pay 4($4.75)
And so on.
- We can see that her total cost paying for the games follows a pattern and we can therefore generalize. If Shakira plays n games, it means that:
For her nth game, she will pay n($4.75).
- Thus, the total amount that Shakira pays is the amount paid for the shoes plus the amount paid for the games.
- Thus, we can write the equation showing her total cost as follows:
[tex]\begin{gathered} \text{Total cost}=Amt\text{ paid for the shoes }+Amt\text{ paid for the games} \\ \text{Amt paid for the shoes}=3 \\ \text{Amt paid for the shoes}=4.75n \\ \\ \therefore\text{Total Cost}=4.75n+3 \\ \text{where, n is the number of games} \end{gathered}[/tex]- Since Shakira spent a total of $42, we can find the number of games (n) that she played as follows:
[tex]\begin{gathered} 42=4.75n+3 \\ \text{Subtract 3 from both sides} \\ 42-3=4.75n \\ 4.75n=39 \\ \text{Divide both sides by 4.75} \\ \frac{4.75n}{4.75}=\frac{39}{4.75} \\ \\ \therefore n=8.21 \\ \text{ Since she cannot pay a decimal number of games, we should round the number down} \\ \\ \therefore n=8 \end{gathered}[/tex]Question 3:
- In solving this question, we shall convert the information given to a mathematical equation
- Let the number of Field trips taken last year be f.
- Three times as many field trips as last year implies
[tex]3f[/tex]- Two more than three times as many field trips as last year implies
[tex]2+3f[/tex]- Cornell's class takes Two more than three times as many field trips as last year and this number of trips this year is 8.
Thus, we can say:
[tex]2+3f=8[/tex]- This means we can find the number of field trips last year f by solving the above expression.
[tex]\begin{gathered} 2+3f=8 \\ \text{Subtract 2 from both sides} \\ 3f=8-2 \\ 3f=6 \\ \text{Divide both sides by 3} \\ \frac{3f}{3}=\frac{6}{3} \\ \\ \therefore f=2 \end{gathered}[/tex]Final Answer
Question 2:
- The number of games is 8
- The equation is:
[tex]42=4.75n+3[/tex]
Question 3:
- The number of field trips from last year is 2
- The equation is:
[tex]2+3f=8[/tex]
A stone pyramid in Egypt has a square base that measures 158 m on each side. The height is 96 m. What is the volume of the pyramid?
Given:
The base of the pyramid is 158 m.
Height is 96 m
The volume of the Pyramid is given as,
[tex]\begin{gathered} V=\frac{1}{3}\times Area\text{ of the cross- section}\times height \\ V=\frac{1}{3}\times Area\text{ of the square}\times Height \\ V=\frac{1}{3}\times(s^2)\times h \\ V=\frac{1}{3}\times158^2\times96 \\ V=\frac{2396544}{3} \\ V=798848m^3 \end{gathered}[/tex]Answer: The volume of the Pyramid is 798848 cubic meters.
what is the probability thay Noah will score 60 points if the 50 point circle has a radius 0.25 feet?bean bag throw6 feet ling2 feet wide
SOLUTION
Step 1: We need to find the area of the 50 -point circle of radius, 0.25 feet.
Recall that the Area of the Circle =
[tex]\begin{gathered} \pi r^2\text{ where }\pi\text{ =}\frac{22}{7}\text{ , r= 0.25 f}eet \\ =\text{ }\frac{22}{7}\text{ x 0.25 x 0.25 = 0. 1964 f}eet^2 \end{gathered}[/tex]Step 2: We need to find the Area of the Rectangle,
where length =6 feet and Width = 2 feet
[tex]\begin{gathered} \text{Area of the Rectangle = Length X Width} \\ 6\text{ f}eet\text{ x 2 fe}et\text{ = 12 f}eet^2 \end{gathered}[/tex]Step 3 : We need to find the probability that Noah will sc
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
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).
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.
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 < ACthe regular price of a high quality pair of binoculars is $600.00. This week, binoculars are on sale for 12% off. The tax rate is 3.5%. If you hand the cashier twenty-eight $20.00 bills, how much change should you receive ? show your work.
Answer:
$13.52
Explanation:
Regular Price of the binoculars = $600
Discount = 12%
Therefore, the Sale Price of the binocular will be:
[tex]\begin{gathered} (1-12\%)\text{ of 600} \\ =(1-0.12)\times600 \\ =0.88\times600 \\ =\$528 \end{gathered}[/tex]The tax rate is 3.5%.
[tex]\begin{gathered} \text{Tax}=3.5\%\text{ of \$528} \\ =0.035\times528 \\ =18.48 \end{gathered}[/tex]Therefore, the total amount to be paid will be:
[tex]\begin{gathered} =\text{Sales Price+Tax} \\ =528+18.48 \\ =546.48 \end{gathered}[/tex]If you give the cashier twenty-eight $20.00 bills, the change that you would receive will therefore be:
[tex]\begin{gathered} \text{Change}=(28\times20)-546.48 \\ =560-546.48 \\ =\$13.52 \end{gathered}[/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.
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]Find the slope of the line passing through the points (0, 3) and (5, 2).51-1515-51
Given: The points below
[tex]\begin{gathered} Point1:(0,3) \\ Point2:(5,2) \end{gathered}[/tex]To Determine: The slope of the given points
Solution
The slope of two points can be determine using the formula below
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ Slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitute the given points into the formula
[tex]slope=\frac{2-3}{5-0}=-\frac{1}{5}[/tex]Hence, the slope of given line is -1/5
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 streetsPLEASE HELP ASAP 20 POINTS
The simplified form of the algebraic expressions 1, 2, 3, 4 and 5 are -2m-10, 3x + 11, 3²xy + 2z - 16, -7x - 11 and -m + 8 respectively
How to simplify algebraic expressions?An algebraic expression is defined as an expression that is made up of variables and numbers, along with algebraic operations such as addition, subtraction, etc.
Given:
1. -3+ 4m + (-7) -6m = -3 + 4m - 7 - 6m = -2m-10
2. 6x + (-1) - 3x + 12 = 6x - 1 - 3x + 12 = 3x + 11
3. 3xy + 2z - 16 + 6xy = 9xy + 2z - 16 = 3²xy + 2z - 16
4. 4x - 8+ 2x + (-3) - 5x = -4x - 8+ 2x -3 - 5x = -7x - 11
5. 3m² - m + 7 - 3m² + 1 = -m + 8
Therefore, the expressions 1,2,3,4 and 5 simplifies to -2m-10, 3x + 11, 3²xy + 2z - 16, -7x - 11 and -m + 8 respectively
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Which equation represents a line which is parallel to the line 6y-7x=246y−7x=24?
The answer is very simple
First you need to solve the algebraic operations of the line and take it to its minimum expression
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.
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
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
Which answer best describes the shape of this distribution?uniformbell-shapedskewed leftskewed right
To answer this question, we need to understand the difference between uniform, bell-shaped, skewed left and skewed right.
A uniform distribution is a distribution where the data is equally distributed.
A bell-shaped distribution is a symmetric distribution where most of the data are on the center.
If most of the data are on the left side of the distribution but a few larger values are on the right, the data are said to be skewed to the right.
If most of the data are on the right, with a few smaller values showing up on the left side of the histogram, the data are skewed to the left.
Now that we have those definitions, let's analyze our distribution. Since most of the data is located at the right side, we have a skewed left distribution.
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"
Hi I need help with these questions, if you can only answer 1 that’s okay. Thank you!
Each square in the block represents each block of size = 0.1*0.4 = 0.04.
1.
The factor 1.5 is divided into two number because in the figure it is shown that the 1 is up to orange line and 0.5 is up to black line and we want to find only area of divided parts.
That is
1*0.4 + 0.5 * 0.4
= 0.4+0.20
= 0.6
2.
Each square in the block represents each block of size = 0.1*0.4
= 1*4/10*10
= 4/100
= 0.04
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