The biker needs to travel 65mi in four days and each day he needs to ride 1.5 the distance he did the day before.
In Part A you found that:
Day 1: 8 mi
Day 2: 1.5 (8mi)=12mi
Day 3: 1.5(12mi)=18mi
Day 4: 1.5(18mi)=27mi
This was just a recompilation of our previous results
Regarding part B
So, if x represents the distance traveled during the first day, once we add up each day we obtain the next expression:
[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))[/tex]Notice that the first term corresponds to the distance he bikes on the first day, the second term corresponds to the second day, and so on.
[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))=x+1.5x+2.25x+3.375x=d[/tex]d represents the total distance during the 4 days
And remember, do not combine like terms!
This represents how much distance he will ride during the 4 days given the first-day distance
And, as you found in part A, if x=8, then 8.125(8)=65. So, our result is consistent.
Regarding Part C
Now, as our goal is to ride during 65mi, we only need to do d=65mi, giving us:
[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))=x+1.5x+2.25x+3.375x=65[/tex]Regarding part D:
First, let's remember what 'like terms' mean:
An easy example of like terms is the next set: x, 2x, -7x
Notice that all of them share the term x, so they are 'like terms'
Going back to part C, we have that our final expression is:
[tex]x+1.5x+2.25x+3.375x=65[/tex]As you can see, the left side of the equation contains terms that involve the x-factor, so all the terms on the left side are 'like terms' involving x
[tex]x,1.5x,2.25x,3.375x[/tex]Write the sentence as a proportion. Then determine whether the proportion is a true proportion.six is to three as sixteen is to four------------------------The proportion is (blank) (Type an equation. Do not simplify.)Is the proportion a true proportion?Yes or No
the proportions are:
[tex]\begin{gathered} 6\colon3 \\ 16\colon4 \end{gathered}[/tex]now we can divide the terms to see if they are proportional so:
[tex]\begin{gathered} \frac{6}{3}=2 \\ \frac{16}{4}=4 \end{gathered}[/tex]So they are not proportional
51) Write the equation of the line passing through (-2, 5) and perpendicular x + 3y = 15.
The genral equation of straight line is y=mx+c, where m is the slope of the line and c is the y intercept.
The given line is x+3y=15. Rewrite this equation in the form y=mx+c.
[tex]\begin{gathered} x+3y=15 \\ 3y=-x+15 \\ y=\frac{-1}{3}x+\frac{15}{3} \\ y=\frac{-1}{3}x+5 \end{gathered}[/tex]Comparing above equation with y=mx+c, we can write
[tex]\text{Slope, m=}\frac{-1}{3}[/tex]The slope of a line perpendicular to x+3y=15 is the negative reciprocal of the slope m. Hence, the slope of the perpendicular line can be written as,
[tex]m_1=-\frac{1}{m}=-(\frac{1}{\frac{-1}{3}})=3[/tex]Let (x1,y1)=( -2,5). Now, the equation of the line with slope m1 and passing through (x1,y1) can be written as,
[tex]\begin{gathered} m_1=\frac{y_1-y}{x_1-x} \\ 3=\frac{5-y}{-2-x} \\ 3(-2-x)=5-y \\ -6-3x=5-y \\ y=3x+11 \end{gathered}[/tex]Theefore, the equation of aline passing through (-2,5) and perpendicular to x+3y=15 is y=3x+11.
Which of the lines on the graph represents a proportional relationship with a greater constant of proportionality? and why?
From the graph given,
A has a greater constant of proportionality
Reason is that:
In line A, the y values is larger compared to the x value
But in B the y value is not as large as the y value in A and the x-value is larger than tha x-values in B. Also the difference between the x and y-values is not that large as compared to A
How long does it take for $1700 to double if it is invested at 9 % compounded continuously? Round your answer to two decimal places.Answer How to enter your answer (opens in new window) 5 PointsKeypadKeyboard Shortcutsyears
Solution:
Given:
[tex]\begin{gathered} P=\text{ \$}1700 \\ r=9\text{ \%}=\frac{9}{100}=0.09 \\ For\text{ the amount to double,} \\ A=2P \\ A=2\times1700=3400 \\ A=\text{ \$}3400 \end{gathered}[/tex]Using the compound interest formula;
[tex]\begin{gathered} A=P(1+r)^t \\ 3400=1700(1+0.09)^t \\ \frac{3400}{1700}=(1+0.09)^t \\ 2=1.09^t \\ \\ To\text{ solve for the time, take the logarithm of both sides} \end{gathered}[/tex]Taking the logarithm of both sides;
[tex]\begin{gathered} log2=log1.09^t \\ \\ Applying\text{ the law of logarithm,} \\ loga^x=xloga \\ \\ The\text{ equation becomes;} \\ log2=t\text{ }log1.09 \\ Hence, \\ \frac{log2}{log1.09}=t \\ t=8.04\text{ years} \end{gathered}[/tex]Therefore, it will take approximately 8.04 years to double the initial $1700.
Type the missing number to complete the proportion. 8 chairs at 1 table = 16 chairs at tables Submit
One way to solve the exercise is to use the rule of three, like this
[tex]\begin{gathered} 8\text{ chairs}\rightarrow1\text{ table} \\ 16\text{ chairs}\rightarrow x\text{ tables} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{16\text{ chairs }\cdot\text{ 1 table}}{8\text{ chairs}} \\ x=\frac{16}{8}\text{ tables} \\ x=2\text{ tables} \end{gathered}[/tex]Therefore, the missing number to complete the proportion is 2.
congruence - SSS theoremIll send a picture of the question
From the figure,
We need to prove that,
[tex]\Delta\text{MNO}\cong\Delta\text{PQR}[/tex]By SSS theorem,
[tex]\begin{gathered} MN\cong PQ(\text{Given)} \\ NO\cong QR(\text{Given)} \end{gathered}[/tex]So, the third side must be,
[tex]MO\cong PR[/tex]Hence, the correct option is D.
If cos A = 1/3 with A in QIV, then sin A/2=
The question gives us the value of
[tex]\cos A=\frac{1}{3}[/tex]We are then required to find
[tex]\sin (\frac{A}{2})[/tex]In order to find the value of this expression, we need to use the following trigonometric identity:
[tex]\begin{gathered} \cos A=\cos ^2(\frac{A}{2})-\sin ^2(\frac{A}{2}) \\ \\ \cos ^2(\frac{A}{2})=1-\sin ^2(\frac{A}{2}) \\ \\ \therefore\cos A=1-\sin ^2(\frac{A}{2})-\sin ^2(\frac{A}{2}) \\ \cos A=1-2\sin ^2(\frac{A}{2}) \end{gathered}[/tex]With this derived identity for cos A, we can proceed to solve the question.
The identity expresses cos A in terms of sin (A/2). Since we already know the value for cos A, we can proceed to find
the value of sin(A/2)
This is done below:
[tex]\begin{gathered} \cos A=1-2\sin ^2(\frac{A}{2}) \\ \\ \text{Making sin(}\frac{A}{2})\text{ the subject of the formula;} \\ \text{subtract 1 from both sides}S \\ \cos A-1=-2\sin ^2(\frac{A}{2}) \\ \\ \text{Divide both sides by -2} \\ \frac{\cos A-1}{-2}=\sin ^2(\frac{A}{2}) \\ \\ \text{ Find the square root of both sides} \\ \\ \therefore\sin (\frac{A}{2})=\sqrt[]{\frac{\cos A-1}{-2}} \end{gathered}[/tex]Now that we have the final expression for calculating sin(A/2), let us substitute the value of cos A into the expression.
This is done below:
[tex]\begin{gathered} \sin (\frac{A}{2})=\sqrt[]{\frac{\cos A-1}{-2}} \\ \cos A=\frac{1}{3} \\ \\ \sin (\frac{A}{2})=\sqrt[]{\frac{\frac{1}{3}-1}{-2}} \\ \\ \sin (\frac{A}{2})=\sqrt[]{\frac{1}{3}} \\ \\ \end{gathered}[/tex]
How much money would i need to invest for six years at 4 ¼% simple interest to earn 400.00 kina?
ANSWER:
1568.63
STEP-BY-STEP EXPLANATION:
We have that the simple inteters formula is the following:
[tex]I=Prt[/tex]Where I is the interest earned, P is the principal, that is, the amount invested, r the rate and t the time. We substitute and calculate for P, like this:
[tex]\begin{gathered} r=4\frac{1}{4}\text{\%}=4.25\text{\%}=\frac{4.25}{100}=0.0425 \\ t=6 \\ I=400 \\ \text{ replacing} \\ 400=P\cdot0.0425\cdot6 \\ P=\frac{400}{6\cdot0.425} \\ P=1568.63 \end{gathered}[/tex]Therefore, for a profit of 400 under these conditions, 1568.63 must be invested
-Using a ruler and what you know about the Golden Ratio, which image has a length-to-width ratio of about 1.618? Show your measurements below.
1)
a = 3.3
b = 1.1
φ = 3.3/1.1 = 3
2)
a = 3.3
b = 2.1
φ = 3.3/2.1 = 1.5714
3)
a = 3.3
b = 3.1
φ = 3.3/3.1 = 1.06
Question 3 (1 point)Give the algebraic representation of the transformation.Xy)ddf7ec519c24031717c638db9c8e1382.webmBlank 1:Blank 2:
Problem
Solution
For this case we see that A = (-6,-6) and A'= (-2,-2)
then we can find the transformation on this way:
kx = -2/-6 = 1/3
ky = -2/-6= 1/3
Then the correct answer is:
(1/3 x , 1/3y)
The data set lists the number of tickets purchased for a school dance each day for 9 days. {13, 6, 13, 8, 2, 19, 11, 16, 17}If 32 is added to the data set, which statement will be TRUE?
D
1) The median is by nature more consistent and resistant to changes when some value is added to the data set. Let's visualize how that happens:
2) Mean
[tex]\begin{gathered} \left\{13,6,13,8,2,19,11,16,17\right\} \\ \bar{x}=\frac{13+6+13+8+2+19+11+16+17}{9}=11.67 \\ 2)\operatorname{\{}13,\:6,\:13,\:8,\:2,\:19,\:11,\:16,\:17,32\operatorname{\}} \\ \bar{x}=\frac{\sum_{i=1}^na_i=137}{10}=13.7 \end{gathered}[/tex]As we can see, the addition of 32 to the data set changes the mean.
3) Now, let's check the Median. Rewriting that into the ascending order:
[tex]\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19 \\ Median:13 \end{gathered}[/tex]Note that 13 divides the distribution into two halves.
Now, let's add 32 to that dataset and check it:
[tex]\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19,\:32 \\ Md=\frac{13+13}{2}=13 \end{gathered}[/tex]Thus, we can tell that the answer is:
Suppose that $2060 is deposited into an account where the interest is compounded annually. This situationcan be modeled by the function.P(t) = 2060(1.019)where P(t) represent the value (in dollars) of the account at t years afterdepositing the $2060.According to this model, what is the earning interest rate in percent?
Notice that:
[tex]1.019=1+0.019,[/tex]therefore, the interest rate is
[tex]0.019[/tex]which in percent corresponds to:
[tex]0.019\times100=1.9\%.[/tex]Answer:[tex]1.9\%[/tex]The domain of the following relation R {(6, -2), (1, 2), (-3,-4), (-3, 2)} is (1 point) O {-3, -3, 1,6) {-4,-2, 2, 2) O {-4,-2, 2) O {-3, 1,67
The domain of a function are all the input values of a function.
These are the x coordinate values.
In this case;
{(6, -2), (1, 2), (-3,-4), (-3, 2)}
The domain is { -3,-3,1, 6}
Answer
A. {-3, -3, 1 , 6 }
Rewrite in simplest terms: -4(-0.7w – 3w + 0.1) - 0.1w
Step 1: Problem
Rewrite in simplest terms: -4(-0.7w – 3w + 0.1) - 0.1w
Step 2: Concept and method
Use the associative method to open the bracket.
= -4( -0.7w - 3w + 0.1 ) - 0.1w
= -0.7w(-4) -3w(-4) + 0.1(-4) - 0.1w
= - 2.8w + 12w - 0.4 - 0.1w
Collect like terms
= - 2.8w + 12w - 0.1w - 0.4
= 9.1w - 0.4
Step 3: Final answer
= 9.1w - 0.4
I don't know how to order them from greatest to least , could you help?
According to the given data, we have the following numbers to order:
3, 1.5%, π, √4, -1 3/4, -157%
To order them from greatest to least, we use logic and common sense as follows:
Number 3 is in this case no problem.
1.5%. This number is express as a percentage, hence, when you have a percentage you have to divide the coefficient to 100, therefore in this case would be 1.5/100 and this is equal to 0.015
π. The number pi is equal mathematically to 3.14159 26535
√4=2
-1 3/4= -1 * 0.75=-0.75
-157%=-157/100=-1.57
Therefore, given the results calculated above, the order from greatest to least would be:
π, 3, √4, 1.5%, -1 3/4, -157%
a triangle has side lengths of 6 8 and 10 . Is it a right triangle? explain
For a triangle to be right angled triangle, it muist satisfy the pythagoras theorem,
[tex]\begin{gathered} H^2=P^2+B^2 \\ 10^2=6^2+8^2 \\ 100=36+64 \\ 100=100 \\ \text{left hand side = right hand side} \end{gathered}[/tex]Hence, It is a right angle.
Select all the expressions that equivalent to 5(f + 7)
Answer
Options A and B are correct.
5 (f + 7)
= (f + 7) 5
= 5f + 35
Explanation
5 (f + 7)
This expression can be rewritten as
5 (f + 7)
= (f + 7) 5
Since multiplication is commutative, that is a × b = b × a
And it can be further simplified by opening the bracket
5 (f + 7)
= 5f + 35
Hope this Helps!!!
If an item that originally cost $19 is decreased to $16, what is the percentage of decrease in the item?
Round your answer to 3 decimal places.
15.789% is the percentage decrease of the item with an originally cost of $19 and decreasing to $16
What is the percentage decrease of the item?Percentage decrease is simply the amount of decrease from the original value to the new value in terms of 100 parts of the original value.
The formula for percentage decrease is expressed as;
D = ((x₁ - x₂) / x₁)100%
Given the data in the question;
original value x₁ = $19New value x₂ = $16Percentage decrease D = ?To determine the percentage decrease, plug the given values into the percentage decrease formula above.
D = ((x₁ - x₂) / x₁)100%
D = (( 19 - 16 ) / 19 )100%
D = (( 3 ) / 19 )100%
D = ( 0.1578947 )100%
D = 15.789%
Therefore, the percentage decrease of the item is 15.789%.
Learn more about Percentages here: brainly.com/question/24159063
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Consider the sets, A={x€N:P(x)} and B={x€N:O(x)} 1. Examine A and B with respect to the subset relation. What can you conclude? Justify your answer. 2. Are A and B equal? Justify your answer
Solution:
Consider the set A and set B;
[tex]A=\mleft\lbrace x\in N\colon P(x\mright)\},B=\mleft\lbrace x\in N\colon O(x)\mright\rbrace[/tex]Let P be the property "is a prime number" and O be the property "is an odd integer".
[tex]\begin{gathered} A=\mleft\lbrace2,3,5,7,11,\ldots\mright\rbrace,B=\mleft\lbrace1,3,5,7,9,11,\ldots\mright\rbrace \\ A\text{ is not a subset of set B} \end{gathered}[/tex]Also;
[tex]undefined[/tex]Please help: write the equation in logarithmic form 1/64 = (1/4)^3
Recall the equation,
x = a^y
This is an exponential equation. To write it as a logarithmic function, it becomes
y = loga x
where
a is the base of the logarithm
The given exponential equation is
1/64 = (1/4)^3
By comparing both equations, we have
a = 1/4, y = 3, x = 1/64
Thus, in logarithmic form, the equation is
3 = log(1/4) 1/64
where
1/4 is the base of the logarithm
how to know the number of solutions in a linear equation (1 solution, infinite solutions or no solutions)
The first one:
[tex]-40x+40=20x-20[/tex]Solving for x:
[tex]-40x-20x=-40-20=>\text{ -60x=-60, so x=1}[/tex]The second one:
[tex]20x+40=40x+20[/tex][tex]20x-40x=20-40->\text{ -20x=-20= x=1}[/tex]The third one:
[tex]-20x+40=-20x+20[/tex][tex]-20x+20x=20-40->\text{ 0=-20}[/tex]This one don´t have
And the last one
[tex]40x+40=40x+20[/tex][tex]40x-40x=20-40=>\text{ 0=-20}[/tex]It doesn't have solution
Solve for y.3y² +2=−7y
We need to solve for y:
[tex]3y²+2=−7y[/tex]We have the form a
How do I solve inequalities and graph their solutions afterwards
Solve for x, by dividing both sides by 6
[tex]\begin{gathered} 6x<-11 \\ \frac{6x}{6}<\frac{-11}{6} \\ x<-\frac{11}{6} \end{gathered}[/tex]Now that we know that the solution is x < -11/6, to graph it, create a number line, and then locate -11/6, which is approximately -1.833, which is between -2, and -1, but closer to -2.
Since the inequality is less than ( < ), draw a hole at the starting point -1.833, and then draw an arrow towards the left. Notice that the direction of the inequality sign less than ( < ), is the same direction of the arrow ( <=== ) that we also drew on the number line.
use one unit multiplier to change 840 inches to feet
Recall that
12 inch = 1 foot
Hence
840 inches = 840/12
= 70 feet
3 expression equivalent to: 10(2+3)-8 × 3
We want to know about 3 expression equivalent to
[tex]10\mleft(2+3\mright)-8\times3\text{ }[/tex]you have to do the parenthesis operations first, that is: (2+ 3) = 5
Now:
10 (2+3) = 10 (5)= 50
the we apply the following operations to the previous equation
50 - 8 x 3 = 50- (8x3) = 50 - (24) = 50-24 = 26.
the first equivalent equation is
1. 10(5) - (8 x3)
the second equivalent equation is
2. 50 - 24
the third equation is
3. 10(5) - (24)
Avenue B makes a 70 degree angle with Center Street what are the measures of the angles at South Street makes with Avenue B
1.- They are also perpendicular.
2.- It is also 70° .
i need help with my homewrok PLEASE CHECK WORK number 1
Answer
D
[tex]C(t)=84(1.02)^{t}[/tex]Step-by-step explanation
Given that the price of the tickets each year is 2% more than the previous year, then the function that represents the price is an exponential growth function.
Exponential growth formula
[tex]C(t)=a(1+r)^t[/tex]where
• C(t): ticket's price after t years
,• a: initial price
,• r: growth rate, as a decimal
,• t: time in years
Substituting a = $84, r = 0.02 (= 2/100):
[tex]\begin{gathered} C(t)=84(1+0.02)^t \\ C(t)=84(1.02)^t \end{gathered}[/tex]What is the difference in high temperatures between the coldest day and the warmest day?
The temperature of the coldest day is -2.1 degree celcius
and the temperature of the warmest day is 3.4-degree celcius
so the difference in the temperature is
3.4-(-2.1)
3.4+2.1=5.5
so the answer is 5.5 degrees celsius.
here the warmest day is Saturday with 3.4 degree celcius
based on a survey of random samples from Saint Joseph citizens the proportion of citizens interested in creating a Riverfront tourist area is 71 with a margin of error of .04 what interval contains the margin of error of 95% of the sample proportions?
In order to find the interval for 95% of the sample proportions, we need to find the z-scores for the interval of 95% in the normal distribution.
To do so, we can find the z value for 2.5% and 97.5% (this way, we can subtract then and find the interval of 95%).
Looking at the table, we have that z1 = -1.96 for 0.025 and z2 = 1.96 for 0.975.
Now, finding the interval, we have that:
[tex]\begin{gathered} \text{interval}=\lbrack\mu+\sigma\cdot z1,\mu+\sigma\cdot z2\rbrack \\ \text{interval}=\lbrack71+0.04\cdot(-1.96),71+0.04\cdot1.96\rbrack \\ \text{interval}=\lbrack71-0.0784,71+0.0784\rbrack \\ \text{interval}=\lbrack70.9216,71.0784\rbrack \end{gathered}[/tex]So the interval is from 70.9216 to 71.0784.
Question 3 of 5 Which math expression means "the sum of 270 and 180"? O A. 270 + 180 B. 270 : 180 O C. 270 = 180 O D. 270 - 180
Sum of 270 and 180
270+180 (option A)