Given:
The length of the marathon is L= 46,145 yards.
The length covered by terrence is d = 23,561 yrads.
The objective is to find the remaining distance need to cover by terrence.
To calculate the remaining distance, we will use the relation,
[tex]x=L-d[/tex]On plugging the values in the above relation, we get,
[tex]\begin{gathered} x=46145-23561 \\ =22584\text{ yards} \\ \approx23000\text{ yards} \end{gathered}[/tex]Hence, Terrence needs to run about 23000 yards.
2) Theodore inherited two different stocks whose yearly income was $2100. The total appraised value of the stocks was $40,000 and one was paying 4% and one 6% per year. What was the value of each stock? 3) Yi-fei Wang inherited $20,000 which she invested in stocks and bonds. The stocks returned 6% and the bonds 8%. if the return on the
Given data:
The value of the socks are x+y=$40,000.
The total interest is I=$2100.
The interest on first stock is,
i=x(4%)(1)/100
i=0.04x
The interest on second stock is,
i'=y(6%)(1)/100
=0.06x
0.04x+0.06y=2100
Substitute 40,000-x for y in the above expression.
0.04x+0.06(40,000-x)=2100
0.04x-0.06x=-300
-0.02x=-300
x=$15000
The value of second stock is,
y=40,000-15,000
=$25,000
The citizens of a certain community were ask to choose their favorite pet. The pie chart below shows the distribution of the citizens answers. If there are 140.000 citizens in the community, how many chose Cats, Fish, or Dogs
The number of citizens choosing cats, fish and dogs are 3360, 1820 and 3500 respectively.
Given, from the data which is represented by the pie chart, the percentage of citizens of a certain community choosing their favorite pet is listed below:
Fish = 13%
Dogs = 25%
Birds = 21%
Cats = 24%
Hamsters = 9%
Snakes = 8%
Altogether there are 14,000 citizens in the community.
we are asked to determine how many citizens have chosen cats, fish or dogs.
we use the method of percentage over here:
total citizens = 14000
percentage of citizens choosing cats = 24%
hence 24% of 14000 = 24/100 × 14000
= 24×140
= 3360
now, percentage of citizens choosing fish = 13%
hence 13% of 14000 = 13/100 × 14000
= 13×140
= 1820
And, percentage of citizens choosing dogs = 25%
hence 25% of 14000 = 25/100 × 14000
= 25 × 140
= 3500
hence the number of citizens choosing cats, fish and dogs are 3360, 1820 and 3500 respectively.
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The second step in the process for factoring the trinomial x-5x - 36 is to:
There are several ways that you can follow to from two binomials from this trinomial, for example, you can do it by following these steps:
1.write two sets of parenthesis, both with the term x
2. write a list of all the factors of 36
3. find the sum of the factors of 36
4. choose the factors whose sum equals 7 and write them into the two parenthesis
Then, the second step in the process of factoring this trinomial is: option D, to write a list of all the factors of 36
10 State if the two triangles are congruent or not congruent. If they are congruent, state the theorem (one of the five) that proves they are congruent. 1 Show Your Work
By theorem we have that if two sides of a triangle are equal, then the angles opposite to those sides are equal, with this or with knowing that the angle between the known sides are equal we conclude that both triangles are equal [the latter solution is using congruency SAS for the triangles, where S is side and A angle.]
WILL MARK BRAINLIEST IF CORRECT! the verticals of a triangle are A (2, 5), B (1, 2) and C (3, 1). Find the coordinates of the image after a reflection in the y-axis
the coordinates of the image after a reflection in the y- axis are =A (5,2), B (2,1) and C(1,3)
what is coordinates?A pair of number that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x ,y)the x-value and y- value
Firstly, we want to reflect across the x-axis When we reflect a point (x,y) over x-axis, we get (x,-y)
So;
A ( 2,5) becomes (2,-5)
B (1,2) becomes (1,-2)
C ( 3,1) becomes (3,-1)
Then we proceed to rotate 90 degrees counterclockwise about the origin
Here we have;
(x, y) becomes (-y ,x)
(2,-5) becomes (5,2)
(1,-2) becomes (2,1)
(3,-1) becomes (1,3)
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40.3% of consumers Believe that cash will be Obsolete in the next 20 years. Assume that three consumers are randomly selected. Find the probability that fewer than three of the selected consumers believe that cash will be obsolete in the next 20 years.
The probability that fewer than three of the selected consumers believe that cash will be obsolete in the next 20 years is 0.538.
How to calculate the probability?The following can be deduced:
p = 40.3% = 0.403
1 - p = 1 - 0.403 = 0.597
n = 6
Therefore X follows the Binomial (6 , 0.403)
The PMF of the Binomial distribution is
P(X = x) = (n C x) * px * (1 - p)n - x ; x = 0 ,1 , 2 , ....., n
Now ,
P(fewer than 3)
= P(X < 3)
= P(X = 0) + P(X = 1) + P(X = 2)
= 0.0453+0.1834+0.3095
= 0.538
The probability is 0.538
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Find the equation of the line:
a) with a gradient of ½ and a y-intercept of -2
b) with a gradient of 3 and passing through the point (-2:2)
c) passing through the points (1; -2) and (-2; 1)
d) parallel to the y-axis cutting the x-axis at -1
Step-by-step explanation:
gradient means slope.
the slope is anyways the factor a of x on the slope-intercept form
y = ax + b
and in the point-slope form
y - y1 = a(x - x1)
"a" is as mentioned the slope. b is the y-intercept (the y- value when x = 0).
(x1, y1) is a point on the line.
a)
y = (1/2)×x - 2
b)
y - 2 = 3(x - -2) = 3(x + 2) = 3x + 6
y = 3x + 8
c)
remember, the slope is defined as ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
so, let's go from (1, -2) to (-2, 1)
x changes by -3 (from 1 to -2)
y charges by +3 (from -2 to 1)
the slope is +3/-3 = -1/1 = -1
so, we pick one point, e.g. (1, -2), and the line is
y - -2 = -(x - 1) = -x + 1
y + 2 = -x + 1
y = -x - 1
d)
x = -1
this is a vertical line (parallel to the y-axis) representing all points on the grid for which x = -1.
the slope is undefined, as it is y/0 (because x never changes at all). and there is no y-intercept, as x can never be 0, and the line is parallel to the y-axis, so, there cannot be any intersection point.
Answer:
[tex]\textsf{a) \quad $y=\dfrac{1}{2}x-2$}[/tex]
[tex]\textsf{b) \quad $y=3x+8$}[/tex]
[tex]\textsf{c) \quad $y=-x-1$}[/tex]
[tex]\textsf{d) \quad $x=-1$}[/tex]
Step-by-step explanation:
Part (a)Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Given values:
Slope = ¹/₂y-intercept = -2Substitute the given values into the formula to create the equation of the line:
[tex]\implies y=\dfrac{1}{2}x-2[/tex]
---------------------------------------------------------------------------
Part (b)Point-slope form of a linear equation:
[tex]y-y_1=m(x-x_1)[/tex]
where:
m is the slope.(x₁, y₁) is a point on the line.Given:
Slope = 3(x₁, y₁) = (-2, 2)Substitute the given values into the formula to create the equation of the line:
[tex]\implies y-2=3(x-(-2))[/tex]
[tex]\implies y-2=3(x+2)[/tex]
[tex]\implies y-2=3x+6[/tex]
[tex]\implies y=3x+8[/tex]
---------------------------------------------------------------------------
Part (c)Slope formula:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are points on the line.
Given points:
(x₁, y₁) = (1, -2)(x₂, y₂) = (-2, 1)Substitute the points into the slope formula to calculate the slope of the line:
[tex]\implies m=\dfrac{1-(-2)}{-2-1}=\dfrac{3}{-3}=-1[/tex]
Substitute the found slope and one of the points into the point-slope formula to create the equation of the line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-2)=-1(x-1)[/tex]
[tex]\implies y+2=-x+1[/tex]
[tex]\implies y=-x-1[/tex]
---------------------------------------------------------------------------
Part (d)If the line is parallel to the y-axis, it is a vertical line.
The equation of a vertical line is x = c.
Therefore, as the line intersects the x-axis at -1, the equation of the line is:
[tex]\implies x=-1[/tex]
The size of a rectangular TV screen is given by the length of its diagnol. What is the width of the 27 TV screen with a height of 16.2 inches?
Given:
The size of a rectangular TV screen is given by the length of its diagnol.
THe diagonal length is 27 inches.
The height is 16.2 inches.
Required:
To find the width.
Explanation:
From the given data
Let x be the width.
From the above figure
[tex]\begin{gathered} 27^2=x^2+16.2^2 \\ \\ x^2=27^2-16.2^2 \\ \\ x^2=729-262.44 \\ \\ x^2=466.56 \\ \\ x=\sqrt{466.56} \\ \\ x=21.6 \end{gathered}[/tex]Final Answer:
The width of the TV screen is 21.6 inches.
Out of 250 tickets in a raffle, one ticket will win a $430 prize, one ticket will win a $290 prize, one ticket will win a $190 prize, and one ticket will win a $130 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
The expected value is given by:
[tex]E(x)=\sum ^{}_{}xP(x)[/tex]In this case we have:
[tex]\begin{gathered} E(x)=430(\frac{1}{250})+290(\frac{1}{250})+190(\frac{1}{250})+130(\frac{1}{250}) \\ =4.16 \end{gathered}[/tex]Therefore the expected payoff is $4.16
Today a new Explorer costs $39,900. In 1990, Explorers cost $24,000. What is the price relative?
The price relative of a new Explorer compared to the cost of Explorer in 1990 is 1.66.
What is the price relative?The price relative is the ratio of the price of the Explorer today to the price of the Explorer in 1990. In order to determine the price relative, divide the price of the Explorer today to the price of the Explorer in 1990.
Division is the operation that is used to determine the quotient of two or more numbers. The sign that is used to represent division is ÷.
Price relative = price of the Explorer now / price of the Explorer in 1990
$39,900 / $24,00 = 1.66
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how to find point-slope form off a graph
Solution
For this case we need to remember that the point-slope formula is given by:
y= mx+b
And in order to find the slope we just need to have two points (x1,y1) and (x2,y2) and we can find m like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then if we look at the graph we have two points:
x1= -2, y1= 3
x2= 0, y2= -1
And replacing we got:
[tex]m=\frac{-1-3}{0+2}=-2[/tex]And using the second point we can find the intercept
3= -2(-2)+b
b= 1
Our solution for this case :
y-3=-2(x+2)
identify the vertical asymptotes, horizontal asymtope, domain, range. Sketch the graph
The given function is,
[tex]f(x)=-\frac{4}{x-2}+1[/tex]The domain can be determined as,
[tex]\begin{gathered} x-2\ne0 \\ x\ne2 \\ x\in R-\lbrace2\rbrace \end{gathered}[/tex]Thus, the domain is the set of real numbers excluding the number 2.
The graph can be drawn as,
The vertical asymtotes is x=2 as the fuction attains the value of infinty and negative infinity at x=2.
The horizontal asymtotes is y=1 as at this value of function the value of x is either infinity or negative of infinity.
The range of the function is,
[tex]y\in\in R-\lbrace1\rbrace[/tex]Thus, the required range of the function is set of all real numbers excluding 1.
the cost of 4 Big macs plus $1.07 for fries is $15.07. Write an equation using the variable m to represent the cost of a Big Mac. then solve for your equation
The equation using the variable m to represent the cost of a Big Mac is
m + 1.07 = 15.07.
The cost of a Big mac is $14.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Let the cost of Big macs = m
cost of fries = $1.07
The total cost of Mig macs and fries = $15.07
This can be written as an equation:
m + 1.07 = 15.07
Subtract 1.07 on both sides.
m + 1.07 - 1.07 = 15.07 - 1.07
m = 14
The cost of a Big mac is $14.
Thus,
The equation using the variable m to represent the cost of a Big Mac is
m + 1.07 = 15.07.
The cost of a Big mac is $14.
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use whole numbers and fractions to write 6.32 in expanded form
HELP ASAP
What is the domain of f(x)= log7x-4
May I please get help with this, for I have tried many times to get the correct answers and still could and am confused
We need to determine if the figures are congruent and if one or more of the given transformations map A onto B.
Notice that figure A is a trapezium with bases' lengths 1 and 3.
And figure B is a trapezium with bases' lengths 2 and 4. And both trapeziums have the same height 2.
Thus, the figures are not congruent, not even similar.
Since the listed transformations map to congruent images of A, none of them maps A onto B.
Therefore, they are NOT congruent and NONE of the transformations maps A onto B.
Explain why the products (x - 3)^2 and (x + 3)(x - 3)have a different number of terms.
the expression (x - 3)², has one term
the expression (x + 3)(x - 3), has two terms (x- 3) and (x + 3)
8000 is Shared between Oku and Ojo
In the ratio of 4:5 what is olu’s share and ojo’s
4444 is ratio of ojo’s share and 355.2 is the ratio of olu’s share .
What does a math ratio mean?
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.the ratio of olu’s share and ojo’s = 4:5
total Shared = 8000
the ratio of olu’s share = 8000 * 4/9
= 888.8 * 4 = 355.2
the ratio of ojo’s share = 8000 * 5/9
= 888.8 * 5 = 4444
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18. The area of the Great Lakes is about
9.5 x 104 square miles. About how many
square miles is the area of the Great Lakes?
The area of the Great Lakes is 988 square miles.
According to the question,
We have the following information:
The area of the Great Lakes is about 9.5 x 104 square miles.
Now, the area of the Great Lakes can simply be found by multiplying the given two numbers.
Now, in the multiplication involving numbers with decimal points, we know that the numbers are multiplied first as if there is no decimal point but in the result obtained we put the decimal point to exactly counting the digits where the decimal point was placed in the input. We move the decimal point to the left hand side according to the number of digits.
In this case, point is after 1 digit.
9.5*104 square miles
988.0 square miles
988 square miles
Hence, the area of the Great Lakes is 988 square miles.
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During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 15% per month. State whether this increase was linear or exponential. If your food bill was $130 in one month during this period, what was it three months later?What was the monthly food bill after three months?$ enter your response here
Given:
Increased rate = 15%
One month bill = $130
Find-:
What was the monthly food bill after three months?
Explanation-:
Formula:
[tex]A=P(1+\frac{r}{100})^n[/tex]Where,
[tex]\begin{gathered} A=\text{ Amount after time} \\ \\ P=\text{ Initial amount} \\ \\ r=\text{ Rate} \\ \\ n=\text{ Time period } \end{gathered}[/tex]The given value is:
[tex]\begin{gathered} P=130 \\ \\ r=15 \\ \\ n=3 \end{gathered}[/tex]Amount after 3 months.
[tex]A=P(1+\frac{r}{100})^n[/tex][tex]\begin{gathered} A=130(1+\frac{15}{100})^3 \\ \\ A=130(1+0.15)^3 \\ \\ A=130(1.15)^3 \\ \\ A=130\times1.521 \\ \\ A=197.714 \end{gathered}[/tex]So, the food bill after three months is $197.714
PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 MATH HW
Answer: a. the weight of a burger with 0 patties is not 0 ounces because
the burger has to have weight, it cannot just be 0 ounces because you will not feel anything in your hand.
b. For patty 0 the weight is 0 oz, For patty 1 the weight is 6.6 oz, For patty 2 the weight is 22.2 oz, For patty 3 the weight is 46.8 oz.
Im sorry but I do not know what to do for C, I hope this helps. Sorry that I couldn't help you with c, but good luck!!
:)
Step-by-step explanation:
Julia's text messaging plan charges 15 cents for each messages over 650 in addition to a $15 base charges. If she owes $49.50 for text messaging in the month of May, how many test messages did she send for that month?
Julia sent 880 text messages in the moth of May .
In the question ,
it is given that
Cost for first 650 messages = $15
additional text message charge = $0.15
Amount owed by Julia for the month of May = $49.50
Let the number of Additional messages be x.
So, according to the question
15 + 0.15x = 49.50
0.15x = 49.50 - 15
0.15x = 34.5
x = 34.5/0.15
x = 230
number of extra messages = 230
total messages = first 650 messages + extra messages
= 650+230
= 880
Therefore , Julia sent 880 text messages in the month of May .
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|5-2x|+1≤10 absolute value equations or inequalities and graph the solution set on the number line
The given inequality is
[tex]|5-2x|+1\leq10[/tex]First, we subtract 1 on each side
[tex]\begin{gathered} |5-2x|+1-1\leq10-1 \\ |5-2x|\leq9 \end{gathered}[/tex]Now we use the property of inequalities with absolute values, which states
[tex]|x|\leq a\rightarrow-a\leq x\leq a[/tex]Using this property, we have
[tex]|5-2x|\leq9\rightarrow-9\leq5-2x\leq9[/tex]We solve the compound inequality now
[tex]\begin{gathered} -9\leq5-2x\leq9 \\ -9-5\leq-2x\leq9-5 \\ -14\leq-2x\leq4 \\ \frac{-14}{-2}\ge\frac{-2x}{-2}\ge\frac{4}{-2} \\ 7\ge x\ge-2 \\ -2\leq x\leq7 \end{gathered}[/tex]Therefore, the solution is the interval [-2,7], and the graph of it would be
If f(x)=x²+5 and g(x)=3x, find (f . g)(x) and (g . f)(x).
(f . g)(x)= _____ (Simplify your answer.)
The value of the functions are given as;
(f. g)(x) = 9x² + 5
(g . f)(x) = 3x² + 15
What is a function?A function can simply be described as an expression, law, or rule showing or explaining relationship between two variables in an equation.
The variables are namely;
The dependent variableThe independent variableGiven the functions;
fx)=x²+5g(x)=3xTo determine ( f. g)(x), we have to substitute the value of g(x) as x in the function, we get;
(f. g)(x) = (3x)² + 5
expand the bracket
(f. g)(x) = 9x² + 5
To determine (g . f )(x), we have to substitute the value of x in the function
(g . f(x) = 3(x² + 5)
expand the bracket
(g . f)(x) = 3x² + 15
Hence, the values are 9x² + 5 and 3x² + 15
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help meeeeee pleaseee !!!!!!!!!
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
there is a number that is eight less than the sum of 20 + 12. find the number let n = the number
The number is given to be n.
[tex]n=(20+12)-8[/tex]Mr. barber used 5/6 yard of wire to put up a ceiling fan. he used 1/2 yard of wire to fix a switch pt 1 out of 2 complete the calculations below to write equivalent fraction with the least common denominator
Least common denominator is the smallest number that can be divided by both given denominators.
From the problem, we have :
[tex]\frac{5}{6}\quad \text{and}\quad \frac{1}{2}[/tex]The denominators are 6 and 2.
The smallest number that can be divided by 6 and 2 is 6.
6/6 = 1 and 6/2 = 3
So we need an equivalent fraction with a denominator of 6.
For 5/6, multiply this by 1/1 since the denominator is already 6.
[tex]\frac{5}{6}=\frac{5\times1}{6\times1}=\frac{5}{6}[/tex]For 1/2, multiply this by 3/3 to make the denominator equal to 6.
[tex]\frac{1}{2}=\frac{1\times3}{2\times3}=\frac{3}{6}[/tex]4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2
Answer: 268435456
Step-by-step explanation:
please mark brainliest if this helped :)
Answer:
Use order of operations,
1. 4^5 = 1024
2. 4^3 = 64
3. 4^2 = 16
4. 1024 * 64 = 65,476
5. 65,476 * 16 = 696,616
6. 16 * 4 = 64
7. 64 * 16 = 1,024
8. 696,616 / 1,024 = 680.2890625
y=x^2+20
determine if symmetric on the..
x axysis
y axysis
both
The graph of the equation defined by; y = f(x) = x² + 20 as represented in the task content is symmetrical about the y-axis.
To which axis is the graph of the equation given symmetrical about?It follows from the task content that the axis about which the given graph is symmetrical be determined as follows.
Since it follows that for a function to be symmetric about the y-axis;
f(-x) = f(x).
Therefore, we have;
f(-x) = (-x)² + 20.
f(-x) = x² + 20 = f(x).
Hence, the graph is symmetrical about the y-axis.
Also; Since; f(-x) = x² + 20 ≠ - f(x).
It follows that the graph is not symmetrical about the origin and hence, the graph is only symmetrical about the y-axis.
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Pls help me answer these 2 questions
Answer:
Step-by-step explanation:
A = 1 plus negatives out be minusing positive
B= -8 minus negatives would be nega tive plus negatives
rules
If you love to love your a lover
if you hate to hate your a lover
if you love to have ur a hater
if you hate to love ur a hater
this all relates to positive and negative addition and subtraction
Answer:
4+(-3) = 1
-6-2= -8
Step-by-step explanation:
Same sign add
Different sign subtract
Keep the sign of the bigger number