Answers
We have the following equation.
[tex]20,000-1.8939m=10,000[/tex]Where m is the number of feet in a mile.
Let us subtract 20,000 from both sides of the equation then simplify
[tex]\begin{gathered} -20,000+20,000-1.8939m=10,000-20,000 \\ -1.8939m=-10,000 \end{gathered}[/tex]The negative sign cancels out and the equation becomes
[tex]\text{1}.8939m=10,000[/tex]Finally, we can apply the Division Property of Equality which states that when we divide both sides of the equation with same number then the equation remains valid.
Let us divide both sides of the equation by 1.8939 then simplify
[tex]\begin{gathered} \frac{1.8939m}{1.8939}=\frac{10,000}{1.8939} \\ m=\frac{10,000}{1.8939} \\ m\approx5280 \end{gathered}[/tex]Therefore, there are 5280 feet in a mile (rounded to nearest whole number)
Related Questions
What is the vertical shift for the absolute value function below?f(x) = 9|x + 11 + 2
Answers
Since the function is shifted 2 units up, the vertical shift is 2
Prove that every differentiable function is continuous
Answers
To prove :
every differentiable function is continuous.
thus, every differentiable function is continuous.
In circle G with m_FGH = 150 and FG = 12 units find area of sector FGH.Round to the nearest hundredth.Fa.
Answers
The formula for the area of sector is,
[tex]A=\frac{\theta}{360}\pi(r)^2[/tex]Substitute the values in the formula to obtain the area of sector FGH.
[tex]\begin{gathered} A=\frac{150}{360}\cdot\pi(12)^2 \\ =188.4955 \\ \approx188.50 \end{gathered}[/tex]So area of sector FGH is 188.50.
I need help with this question... the correct answer choice
Answers
Reflection over the x-axis:
(x,y)--->(x, -y)
and the question is what is not a reflection across the x-axis.
so,
the correct option is D which is:
R'(-9, 4) ----> R'(9, -4)
Because it is a reflection over the y-axis.
A cash register contains only five dollar and ten dollar bills. It contains twice as many fives as tens and the total amount of money in the cash register is 740 dollars. How many tens are in the cash register?
Answers
ANSWER
There are 37 tens in the cash register
EXPLANATION
Given that;
The total amount in the cash register is $740
The cash register contain five dollar and ten dollar
Follow the steps below to find the number of ten dollar in the cash register.
Let x represents the number of $5 and $10 in the cash register.
Recall, that the register contain twice as many $5 as ten dollars and this can be expressed mathematically as
[tex]\text{ 5\lparen2x\rparen+ 10\lparen x\rparen= 740}[/tex]Evaluate x in the above expression
[tex]\begin{gathered} \text{ 10x + 10x = 740} \\ \text{ 20x = 740} \\ \text{ Divide both sides by 20} \\ \text{ }\frac{\text{ 20x}}{\text{ 20 }}\text{ = }\frac{\text{ 740}}{\text{ 20}} \\ \text{ x = 37} \end{gathered}[/tex]Therefore, we have 37 tens in the cash register
Simplify by combining like terms,8t3 + 8y + 7t3 + 6y + 9t2
Answers
The simplification of the expression will be; 15t³ + 9t² + 14y
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions. To derive equivalent expressions of some expressions, we can either make them look more complex or simple.
Given that the expression as 8t³ + 8y + 7t³ + 6y + 9t²
Now combining like terms;
8t³ + 7t³ + 9t² + 8y + 6y
Simplify;
15t³ + 9t² + 14y
It cannot be solved further because of unlike terms in the expression.
Therefore, the simplification of the expression will be; 15t³ + 9t² + 14y
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The perimeter of a rectangle is 36 cm and the length is twice the width. What are the dimensions of this rectangle? What’s the length and width?
Answers
Perimeter = 2x + 2x + x + x = 6x. 6x = 36, so x = 6. The rectangle is 6*12, so area = 72 sq cm.
Determine the reasonableness of a solution to a logarithmic equation
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]\log_3x=7[/tex]STEP 2: State the law of logarithm
[tex]\begin{gathered} If\text{ }\log_ab=c \\ \Rightarrow b=a^c \\ By\text{ substitution,} \\ \therefore\log_aa^c=c \end{gathered}[/tex]STEP 3: Substitute the given values in the question to get the correct answer
[tex]\begin{gathered} \log_3x=7 \\ x=3^7 \\ By\text{ substitution,} \\ \log_3(3^7)=7 \end{gathered}[/tex]Hence, Answer is:
[tex]\log_3(3^7)=7[/tex]OPTION A
When water flows across farmland, some of the soil is washed away, resulting in erosion. Researchers released water
across a test bed at different flow rates and measured the amount of soil washed away. The following table gives the
flow (in liters per second) and the weight (in kilograms) of eroded soil:
Answers
The correlation coefficient between flow rate and amount of eroded soil is:
0.967.
Correlation coefficientsThe correlation coefficient is an index that measures correlation between two variables, assuming values between -1 and 1.
If it is positive, the relation is positive, meaning that the variables are direct proportional. If it is negative, the variables are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the variables is strong.
Given a data-set of two points, the correlation coefficient is found inserting points of the data-set into the calculator. In this problem, the points in the data-set are given as follows:
(0.31, 0.82), (0.85, 1.95), (1.26, 2.18), (2.47, 3.01), (3.75, 6.07).
Using a calculator, the coefficient is given as follows:
0.967.
Hence the last option gives the correct coefficient.
Missing informationThe complete problem is given by the image at the end of the answer.
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Janelle is conducting an experiment to determine whether a new medication is effective in reducing sneezing. She finds 1,000 volunteers with sneezing issues and divides them into two groups. The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of sneezing. What can Janelle conclude from this experiment?
Answers
Answer:
Step-by-step explanation:
When the polynomial mx^3 - 3x^2 +nx +2 is divided by x+3, the remainder is -4. When it is divided by x-2, the remainder is -4. Determine the value of m and n.
Answers
Answer:
[tex]\begin{gathered} m\text{ =-2} \\ n\text{ =11} \end{gathered}[/tex]Explanation:
Here, we want to find the value of m and n
If we substituted a supposed root into the parent polynomial, the value after evaluation is the remainder. If the remainder is zero, then the value substituted is a root.
for x+ 3
x + 3 = 0
x = -3
Substitute this into the first equation as follows:
[tex]\begin{gathered} m(-3)^3-3(-3)^2-3(n)+\text{ 2 = -4} \\ -27m\text{ -27-3n+ 2 = -4} \\ -27m\text{ -3n = -4}+27-2 \\ -27m-3n\text{ = 21} \\ -9m\text{ - n = 7} \end{gathered}[/tex]We do this for the second value as follows:
x-2 = 0
x = 2
Substitute this value into the polynomial:
[tex]\begin{gathered} m(2)^3-3(2)^2+2(n)\text{ + 2 = -4} \\ 8m\text{ - 12 +2n + 2 = -4} \\ 8m\text{ + 2n = -4-2+12} \\ 8m\text{ + 2n = 6} \\ 4m\text{ + n = 3} \end{gathered}[/tex]Now, we have two equations so solve simultaneously:
[tex]\begin{gathered} -9m-n\text{ = 7} \\ 4m\text{ + n = 3} \end{gathered}[/tex]Add both equations:
[tex]\begin{gathered} -5m\text{ = 10} \\ m\text{ =-}\frac{10}{5} \\ m\text{ = -2} \end{gathered}[/tex]To get the value of n, we simply susbstitute the value of m into any of the two equations. Let us use the second one:
[tex]\begin{gathered} 4m\text{ +n = 3} \\ 4(-2)\text{ + n = 3} \\ -8\text{ + n = 3} \\ n\text{ = 8 + 3} \\ n\text{ = 11} \end{gathered}[/tex]Find the volume of the cone.9 cmr= 6 cmV = [?] cm3
Answers
The radius of cone is r = 6 cm.
The height of cone is h = 9 cm.
The formula for the volume of cone is,
[tex]V=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cone.
[tex]\begin{gathered} V=\frac{1}{3}\pi\cdot(6)^2\cdot9 \\ =339.29 \\ \approx339.3 \end{gathered}[/tex]Thus, volume of cone is 339.3 cm^3.
Identify the rate of change and Intial Value in this equationy = 3x +6
Answers
The rate of change is 3.
The initial value is 6.
Step - by - Step Explanation
What to find?
• Rate of change.
,• Initial value.
Given:
y = 3x + 6
The rate of change is also the same as the slope.
To find the slope of the gien equation, compare the equation with y=mx + b.
Where m is the slope (rate of change).
Comparing the two equations, m = 3
Hence, the rate of change is 3.
The initial value also known as the y-intercept, is the value of y at x=0.
y = 3(0) + 6
y = 6
Hence, the initial value is 6.
Triangle RST has the coordinates R(0 , 2), S(2 , 9), and T(4 , 2). Which of the following sets of points represents a dilation from the origin of triangle RST? A. R'(0 , 2), S'(8 , 9), T'(16 , 2) B. R'(0 , 2), S'(2 , 36), T'(16 , 2) C. R'(4 , 6), S'(6 , 13), T'(8 , 6) D. R'(0 , 8), S'(8 , 36), T'(16, 8)
Answers
The set of points that represents a dilation from the origin of triangle RST are: D. R'(0 , 8), S'(8 , 36), T'(16, 8).
What is dilation?In Mathematics, dilation is a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
For the given coordinates of triangle RST, the dilation with a scale factor of 4 from the origin (0, 0) or center of dilation should be calculated as follows:
Point R (0, 2) → Point R' (0 × 4, 2 × 4) = Point R' (0, 8).
Point S (2, 9) → Point S' (2 × 4, 9 × 4) = Point S' (8, 36).
Point T (4, 2) → Point T' (4 × 4, 2 × 4) = Point T' (16, 8).
In conclusion, the other sets of points do not represents a dilation from the origin of triangle RST.
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As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
Given that,
Coordinates of the triangle, R(0 , 2), S(2 , 9), and T(4 , 2).
The scale factor for the dilation = 4
The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
According to the question,
The dilated coordinate is given as,
R' = (0×4 , 2×4) = (0, 8)
S' = (2×4, 9×4) = (8, 36)
T' = (4×4, 2×2) = (16, 8)
Thus, As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
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Write the equation of the circle given the following graph.
Answers
Given:
Equation of a circle on a graph with center(3, -2).
To find:
Equation of a circle.
Explanation:
General eqution of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Solution:
From the graph, we can see that center is (3, -2) and radius equal 3.
So, equation of a circle is
[tex](x-3)^2+(y+2)^2=3^2[/tex]Hence, this is the equation of a circle.
In how many ways can 3 students from a class of 23 be chosen for a field trip?aYour answer is:
Answers
SOLUTION:
This is a combination problem.
The number of ways 3 students from a class of 23 be chosen for a field trip is;
[tex]23C_3=\frac{23!}{(23-3)!3!}=1771\text{ }ways[/tex]Find the coordinates of the center, vertices, covertices, foci, length of transverse and conjugate axis and the equation of the asymptotes. Then graph the hyperbola.
Answers
The given equation is,
[tex]\frac{x^2}{36}-\frac{y^2}{16}=1\text{ ---(1)}[/tex]It can be rewritten as,
[tex]\frac{x^2}{6^2}-\frac{y^2}{4^2}=1\text{ ---(2)}[/tex]The above equation is similar to the standard equation of left-right facing a hyperbola given by,
Mr. Santos cycled a total of 16 kilometers by making 4 trips to work. After 5 trips to work, how many kilometers will Mr. Santos have cycled in total? 5 Kilometers
Answers
According to the information given in the exercise, you know that he cycled a total of of 16 kilometers by making 4 trips to work.
Let be "d" the total amount of kilometers Mr. Santos will have cycled after 5 trips to work.
Based on the above, you can set up the following proportion:
[tex]\frac{16}{4}=\frac{d}{5}[/tex]Finally, you must solve for the variable "d" in order to find its value. This is:
[tex]\begin{gathered} 4=\frac{d}{5} \\ \\ (4)(5)=d \\ d=20 \end{gathered}[/tex]Therefore, the answer is:
[tex]20\operatorname{km}[/tex]Find the point that partitions segment AB in a 1:3 ratio (_,_)Find the point that partitions segment AD in 1.1 ratio (_,_)
Answers
AB in 1:3 ratio, Find a pointwhere on one side there is 1/4 of AB and in the other side 3/4 of AB:
Using the conjugate zeros theorem to find all zeros of a polynomial
Answers
We know that 1+i is a root of the polynimial. This also implies that 1-i is also a root of the polynomial. In other words, the term
[tex](x-1+i)(x-1-i)[/tex]is a factor of our polynomial. This last expression can be written as
[tex](x-1+i)(x-1-i)=x^2-2x+2[/tex]so, in order to find the remaining zero, we can compute the following division of polynomials,
which gives
Therefore, the remaining root is x=1.
In summary, the answer is:
[tex]1+i,1-i,1[/tex]
Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of
her collection?
The percent increase of her collection is
Answers
Mr. Rodriguez is preparing photos for an international client. The client has requested a photo that is 20 cm by 15 cm. Mr. Rodriguez knows that the formula c = 2.54n can be used to convert n inches to c centimeters. Which formula can he use to convert centimeters to inches?
Answers
Given:
The formula to convert from inches to centimeters is c = 2.54n
To find:
The formula that can be used to convert from centimeters to inches
To determine the formula, we need to make n the subject of formula:
[tex]\begin{gathered} \text{c = 2.54n} \\ where\text{ c = value in cm} \\ n\text{ = value in inches} \end{gathered}[/tex][tex]\begin{gathered} To\text{ make n, the subject of formula, we will divide both sides by 2.54:} \\ \frac{c}{2.54}=\text{ }\frac{2.54n}{2.54} \\ n\text{ = }\frac{c}{2.54} \\ This\text{ means when we have a value in cm and substitute, the answer will be in inches} \end{gathered}[/tex][tex]n\text{ = }\frac{c}{2.54\text{ }}\text{ \lparen option B\rparen}[/tex]=Given f(x) = -0.4x – 10, what is f(-12)? If it does not exist,enter DNE.
Answers
We have the function:
[tex]f\mleft(x\mright)=-0.4x-10[/tex]And we need to find its value when x = -12. So, replacing x with -12, we obtain:
[tex]f(-12)=-0.4(-12)-10=4.8-10=-5.2[/tex]Notice that the product of two negative numbers is a positive number.
Therefore, the answer is -5.2.
Graph A) -f(x) B) f(x+2) -4Then find the domain and range of each
Answers
a. Graph -f(x):
By the transformations rules for functions, the graph of -f(x) is equal to a reflection over the x-axis, and a change of the y-coordinates:
[tex](x,y)\rightarrow(x,-y)[/tex]Then, given the function:
[tex]f(x)=\sqrt[]{x}[/tex]The graph of -f(x) is:is
The domain of the function is the set of all possible x-values, then it is:
[tex]\lbrack0,+\infty)[/tex]The range is the set of all possible values of the function, then it is:
[tex]\lbrack0,-\infty)[/tex]b. Graph f(x+2)-4:
The transformation f(x+2) is an horizontal translation left 2 units.
And the transformation f(x+2)-4 is a vertical translation down 4 units.
Then, the coordinates of this graph in comparison to the given graph are:
[tex](x,y)\rightarrow(x-2,y-4)[/tex]Then for the point (1,1) the new coordinates are (1-2,1-4)=(-1,-3).
For (4,2): the new coordinates (4-2,2-4)=(2,-2)
For (9,3): the new coordinates (9-2,3-4)=(7,-1)
The graph is:
The domain of this function is:
[tex]\lbrack-2,+\infty)[/tex]And the range is:
[tex]\lbrack-4,+\infty)[/tex]The graph used Is below ill attach a picture of the question and options after
Answers
Using the triangle sum theorem:
[tex]\begin{gathered} m\angle L+m\angle K+20=180 \\ 2m\angle L=180-20 \\ 2m\angle L=160 \\ m\angle L=\frac{160}{2} \\ m\angle L=80 \end{gathered}[/tex]Using the exterior angle theorem:
[tex]\begin{gathered} m\angle E=m\angle L+m\angle J \\ m\angle E=80+20 \\ m\angle E=100 \end{gathered}[/tex]Answer:
100
Which expression represents the area of the rectangle below in square units
Answers
Area of rectangle is given by:-
[tex]\begin{gathered} l\times b \\ =(3x+2)\times2x \\ =6x^2+4x \end{gathered}[/tex]So the correct answer is
[tex]6x^2+4x[/tex]Estimate the difference between 7,472 and 3,827 by rounding each number to the nearest hundred.
Answers
Answer:
The difference is aproximately 3700.
Step-by-step explanation:
First, we'll round each number to the nearest hundred:
[tex]\begin{gathered} 7472\rightarrow7500 \\ 3827\rightarrow3800 \end{gathered}[/tex]Now, we can estimate the difference:
[tex]7500-3800=3700[/tex]This way, we can conlcude that the difference is aproximately 3700.
Hi I have a meeting at my house in about
Answers
The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.
The function is given to be:
[tex]T(t)=Ate^{-kt}[/tex]where A and k are positive constants.
We can find the derivative of the function as follows:
[tex]T^{\prime}(t)=\frac{d}{dt}(Ate^{-kt})[/tex]Step 1: Pull out the constant factor
[tex]T^{\prime}(t)=A\cdot\frac{d}{dt}(te^{-kt})[/tex]Step 2: Apply the product rule
[tex]\frac{d(uv)}{dx}=u \frac{dv}{dx}+v \frac{du}{dx}[/tex]Let
[tex]\begin{gathered} u=t \\ v=e^{-kt} \\ \therefore \\ \frac{du}{dt}=1 \\ \frac{dv}{dt}=-ke^{-kt} \end{gathered}[/tex]Therefore, we have:
[tex]T^{\prime}(t)=A(t\cdot(-ke^{-kt})+e^{-kt}\cdot1)[/tex]Step 3: Simplify
[tex]T^{\prime}(t)=A(-kte^{-kt}+e^{-kt})[/tex]QUESTION A
At t = 0, the instantaneous rate of change is calculated to be:
[tex]\begin{gathered} t=0 \\ \therefore \\ T^{\prime}(0)=A(-k(0)e^{-k(0)}+e^{-k(0)}) \\ T^{\prime}(0)=A(0+e^0) \\ Recall \\ e^0=1 \\ \therefore \\ T^{\prime}(0)=A \end{gathered}[/tex]The rate of change is:
[tex]rate\text{ }of\text{ }change=A[/tex]QUESTION B
At t = 30, the instantaneous rate of change is calculated to be:
[tex]\begin{gathered} t=30 \\ \therefore \\ T(30)=A(-k(30)e^{-k(30)}+e^{-k(30)}) \\ T(30)=A(-30ke^{-30k}+e^{-30k}) \\ Collecting\text{ }common\text{ }factors \\ T(30)=Ae^{-30k}(-30k+1) \end{gathered}[/tex]The rate of change is:
[tex]rate\text{ }of\text{ }change=Ae^{-30k}(-30k+1)[/tex]QUESTION C
When the rate of change is equal to 0, we have:
[tex]0=A(-kte^{-kt}+e^{-kt})[/tex]We can make t the subject of the formula using the following steps:
Step 1: Apply the Zero Factor principle
[tex]\begin{gathered} If \\ ab=0 \\ a=0,b=0 \\ \therefore \\ -kte^{-kt}+e^{-kt}=0 \end{gathered}[/tex]Step 2: Collect common terms
[tex]e^{-kt}(-kt+1)=0[/tex]Step 3: Apply the Zero Factor Principle:
[tex]\begin{gathered} e^{-kt}=0 \\ \ln e^{-kt}=\ln0 \\ -kt=\infty \\ t=\infty \end{gathered}[/tex]or
[tex]\begin{gathered} -kt+1=0 \\ -kt=-1 \\ t=\frac{-1}{-k} \\ t=\frac{1}{k} \end{gathered}[/tex]The time will be:
[tex]t=\frac{1}{k}[/tex]can you please help me on e. f. and g.
Answers
His temperature was 100.1 degree farad initially which is around 6 pm. At 7 pm it became 101 degree farad.
[tex]\begin{gathered} \text{slope = }\frac{y_2-y_1}{x_2-x_1}=\frac{101-100.1}{7-6}=\frac{0.9}{1}=0.9 \\ m=0.9 \end{gathered}[/tex]y = mx + b
where
m = slope
b = y - intercept
let find the y intercept
[tex]\begin{gathered} 101=0.9(7)+b \\ 101-6.3=b \\ b=94.7 \end{gathered}[/tex]Therefore, the equation is
[tex]y=0.9x+94.7[/tex]e. let us draw a graph
His temperature will be critical above 22 minutes past 9 pm.
f . He should go to emergency room.
g.
[tex]\begin{gathered} y=0.9x+94.7 \\ 98.6=0.9x+94.7 \\ 98.6-94.7=0.9x \\ 3.9=0.9x \\ x=\frac{3.9}{0.9} \\ x=4.33333333333 \end{gathered}[/tex]His temperature will be normal around past 4 pm which is 98.6 degree farad.
(G.lla, 1 point) Use the circle shown to answer the question. ♡ If MAC = 64. and m 2 ABC 16) find the value of x. A. 12 B 36 C. 25 D. 24
Answers
12
1) In this case, we have two chords within that circle. And since the arc = 64º and the m ∠ABC = 4x -16
2) Applying one Theorem that states that
3) So we can write:
[tex]\begin{gathered} (4x-16)\text{ =}\frac{64}{2} \\ 4x-16\text{ =32} \\ 4x\text{ =32+16} \\ 4x\text{ = 48} \\ x=12 \end{gathered}[/tex]So the value of x = 12
