The most appropriate choice for linear equation will be given by-
[tex]l = 28 - 0.5d[/tex] is the required expression for the length of the bike
path left to build at any point during the construction.
[tex]l[/tex] is the length of the bike path left to build at any point during the construction
[tex]d[/tex] is the number of days
What is Linear equation?
A one degree equation is called a linear equation.
Here,
Let the length of the bike path left to build at any point during the construction be [tex]l[/tex] and the number of days be [tex]d[/tex]
In one day, the crew build 0.5 miles of the path
In d days, the crew can build [tex]0.5 \times d[/tex] miles of the path
Length of path left to construct after [tex]d[/tex] days = [tex]28-0.5d[/tex]
By the problem,
[tex]l = 28 - 0.5d[/tex]
This is the required expression for the length of the bike
path left to build at any point during the construction.
To learn more about linear equation, refer to the link brainly.com/question/2030026
#SPJ9
I need help in this maths problem
By considering the areas of the two rectangles, we have shown that 2x² - 5x - 18 = 0
The value of length AB is 4.5 cm
Calculating Area and lengthFrom the question, we are to show that 2x² - 5x - 18 = 0
From the given information,
The total area of the compound shape ABCDEF is 36 cm²
That is,
Total area = 36 cm² = Area of small rectangle + Area of big rectangle
From the given diagram, we can write that
Area of small rectangle = x(x -4)
Area of small rectangle = x² - 4x
and
Area of big rectangle = (2x + x)(x -2)
Area of big rectangle = 3x(x - 2)
Area of big rectangle = 3x² - 6x
∴ 36 = x² - 4x + 3x² - 6x
36 = 4x² -10x
4x² -10x - 36 = 0
Divide through by 2
2x² - 5x - 18 = 0
Thus, we have shown that 2x² - 5x - 18 = 0
Now, we are to determine the value of length AB
The value of length AB is x cm.
Therefore, we will solve for x
From,
2x² - 5x - 18 = 0
2x² + 4x - 9x - 18 = 0
2x(x + 2) -9(x + 2) = 0
(2x - 9)(x + 2) = 0
2x - 9 = 0 OR x + 2= 0
2x = 9 OR x = -2
x = 9/2 OR x = -2
x = 4.5 OR x = -2
Since x cannot be negative, the value of x is 4.5
Thus,
AB is 4.5 cm
Learn more on Calculating Area and length here: https://brainly.com/question/27844217
#SPJ1
You earn $100 per month and want to save 10% in a savings account. Use the savings
calculator to find out how much your total savings would be in 5 years if your account
has an annual interest rate of 1%. (Do not include the $ sign in your reponse) PLEASE HELPP
With the annual interest of 1%, the total saving after 5 years is $6060.
Interest:
Interest is the amount for a particular principal amount of money at some rate of interest.
Given,
You earn $100 per month and want to save 10% in a savings account.
Here we have to use the savings calculator to find out how much your total savings would be in 5 years if your account has an annual interest rate of 1%.
Through the given details we have identified that,
Monthly earning = $100
Saving per month = 10%
So, in amount it can be
=> 100 x 10/100 = $10
So, for one year the saving without interest is
=> 10 x 12 = 1200
So, When we add the interest of 1% for the year,
Then the interest amount for one year will be,
=> 1200 x 1/100 = 12
So, the total amount including interest for one year,
=> 1200 + 12 = 1212
So, the savings after 5 years will be,
=> 5 x 1212
=> 6060.
Therefore, the total saving amount after 5 years is $6060.
To know more about Interest here.
https://brainly.com/question/13324776
#SPJ1
A trivia contest asks both multiple choice and free response questions. Contestants receive 333 points for each correct multiple choice question and 555 points for each correct free response question, and they must score more than 606060 points to advance to the next round. If Eva advanced to the next round of the contest, which of the following inequalities describes xxx, the number of multiple choice questions, and yyy, the number of free response questions, that she answered correctly?
When Eva advanced to the next round of the contest, the inequality that describes the number of questions will be 3x + 5y > 60
What is an inequality?It should be noted that an inequality will simply used to illustrate the expressions that aren't equal. This is illustrated with the use of greater than, less, than, etc.
In this case, the contestants receive 3 points for each correct multiple choice question and 5 points for each correct free response question, and they must score more than 60 points to advance to the next round.
Therefore, the inequality that describes the number of questions will be:
= 3(x) + 5(y) > 60
= 3x + 5y > 60
where x = number of multiple choice questions,
y = number of free response questions,
Learn more about inequalities on:
brainly.com/question/11613554
#SPJ1
Help me please with this question
The distance between the two points (2, 6) and (7, -6) will be 13 units.
What is the distance between two points?Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
A right triangle with the two points forming the hypotenuse. The two points are given below.
(2, 6) and (7, -6)
Then the distance between the points (2, 6) and (7, -6) will be given as,
D² = (7 - 2)² + (-6 - 6)²
D² = 5² + (-12)²
D² = 25 + 144
D² = 169
D = 13 units
The distance between the two points (2, 6) and (7, -6) will be 13 units.
Learn more about the distance between two points here:
https://brainly.com/question/18296211
#SPJ1
Solve the following system of equations
-8x -9x = 10
4x -5y = 14
(See picture attached)
Answer:
please trust me.the value of x=10 and the value for y= -10. Try to follow the steps given to you and provide them outHELP IM CONFUSED. NEED HELP ASAP
Answer:
3x+5?
Step-by-step explanation:
Not 100% sure but yh
dr. chang is conducting a research study of undergraduate students at her college. she wants to ensure an equal number of students from each grade level, so she uses the list of all students provided by the registrar’s office. from each list, she randomly selects 50 students from each group. what strategy of sampling is dr. chang using? a. simple random sampling b. accidental sampling c. stratified sampling d. quota sampling e. cluster sampling
The strategy used by Dr. Chang for the research study of undergraduate students is c. stratified sampling.
Stratified sampling can be defined as the type of sampling in which a population is divided into subpopulations and then random samples are taken from these subpopulations. These subpopulations or subgroups are also called strata.
The strategy used by Dr. Chang is stratified sampling because she divided all the undergraduate students into subgroups based on grade level and then from these subgroups she randomly selected 50 students.
Contrastingly, in simple random sampling, no subgroups are involved and the subset of individuals are chosen from a single large population randomly. On the other hand, quota sampling and accidental sampling are not a type of random sampling.
In cluster sampling, the subgroups are internally heterogeneous but in this case, the subgroups are internally homogenous as they are made based on grade level.
To learn more about stratified sampling, click here:
https://brainly.com/question/17354331
#SPJ4
What’s the value of x
In the given angle, the value of x is 18°.
What are angles?In Euclidean geometry, an angle is a shape created by two rays that share an endpoint and are referred to as the angle's sides and vertex, respectively. The plane that contains the rays contains the angles created by two rays. The meeting of two planes can also result in an angle. They are referred to as dihedral angles.So, first label the lines as A, B, C, and D as follows:
Refer to the image attached below.
As we can see that line ADB is a straight line, so ∠ADB will be 180°.Line DC cuts the angle ∠ADB in two parts, so the equation can be:
(6x + 5) + 67 = 180Now, solve for x as follows:
(6x + 5) + 67 = 1806x + 72 = 1806x = 180 - 726x = 108x = 108/6x = 18°Therefore, in the given angle, the value of x is 18°.
Know more about angles here:
https://brainly.com/question/25770607
#SPJ13
1. Situation: There will be a centerpiece on each table. A centerpiece costs $5.50. Represent the relationship between the number of centerpieces and the total cost for the centerpieces. Table: Algebraic rule: Process Graph:
The proportional relationship between the number of centerpieces and the total cost for the centerpieces is graphed at the end of the answer.
Proportional relationships and graphsA graph represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
The constant k is called the slope of the unit rate of the situation, measuring by how much y changes when x changes by 1.
In the context of this problem, the cost of each centerpiece is of $5.50, hence the constant is given as follows:
y = 5.5x.
The number of centerpieces cannot be negative, hence the domain of the relation is given as follows:
x ≥ 0.
Considering this domain, the graph of the relation is given at the end of the answer.
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
Given that all sides are equal for this
triangle, if its height if the triangle is 16
in, and the length of the prims is 33 in.
Solve for the surface area of the
equilateral prism(4 Points)
Type answer in the space provided and attach »
15 in
20 in.
33 M
Enter your maths answer
The equilateral triangular prism has a surface area of 1997.321 square inches
How to determine the surface area of the equilateral triangular prism?From the question, the given parameters are
Side length of the triangle, a = 20 inchesHeight of the equilateral triangular prism, h = 33 inchesThe total surface area of an equilateral triangular prism is calculated using the following formula
Surface area = a(√3/2) + 3(a × h);
Substitute the known values in the above equation
So, we have the following equation
Surface area = 20 * (√3/2) + 3(20 × 33);
Evaluate the product
So, we have the following equation
Surface area = 1997.321
Hence, the surface area of the equilateral triangular prism is 1997.321 square inches
Read more about surface area at
https://brainly.com/question/76387
#SPJ1
HELP FAST!
This is an explain your reasoning question. You will need to show all your work and explain how you arrived at your answer.
Answer:
m∠R = 72°
Step-by-step explanation:
As ΔPQR and ΔUVW are congruent, m∠R = m∠W.
Equate the expressions for the two angles and solve for x:
⇒ m∠R = m∠W
⇒ 10x - 18 = 8x
⇒ 10x - 18 + 18 = 8x + 18
⇒ 10x = 8x + 18
⇒ 10x - 8x = 8x + 18 - 8x
⇒ 2x = 18
⇒ 2x ÷ 2 = 18 ÷ 2
⇒ x = 9
Substitute the found value of x into the expression for m∠R:
⇒ m∠R = 10x - 18
⇒ m∠R = 10(9) - 18
⇒ m∠R = 90 - 18
⇒ m∠R = 72°
Therefore, m∠R = 72°.
A mountain cabin on 1 acre of land costs 30,000 dollars. If the land cost 4 times as much as the cabin, what was the cost of each?
The cost of each land is 120,000 dollars.
How to find the cost of each land?The mountain cabin on 1 acre of land costs 30,000 dollars.
The land cost 4 times as much as the cabin.
Therefore, the cost of each land can be calculated as follows:
cost of each land = 4 (30, 000)
cost of each land = 4 × 30000
cost of each land = 120,000 dollars
Therefore, the land that cost 4 times as much as the cabin cost 120000 dollars for each.
learn more on cost here:https://brainly.com/question/11905065
#SPJ1
which 2 number are distance 8 and -4
Answer: the answer is 6 and 7
Step-by-step explanation:
because never gonna give u up never gonna let u down yessir
Can y’all help me with this math question please
Answer:
[tex]\angle K[/tex]
Step-by-step explanation:
When looking for corresponding angles, compare their order in the names. Since T and K are the first letters in the names of the triangles, they correspond.
The sat exams are scaled so that scores should roughly follow the normal distribution with mean 500 and standard deviation 100.how high must a student score on the sat mathematics exam to fall in the top 25% of all scores?
Answer:
568
Step-by-step explanation:
Using a z-score table, we see the minimum z-score is about 0.68.
Using the formula for the z-score,
[tex]\frac{x-500}{100}=0.68 \\ \\ x-500=68 \\ \\ x=568[/tex]
solve this for me pls
The x-intercepts of the function are 10, and -8.
y-intercept is: -80.
The zeros are: x = 10 and x = -8
f(2) = -80
f(x) = -65 when x = 5 or -3.
What is the Y-intercept and the X-intercept of a Function?The y-intercept of a function is the output (y) when the input value (x) is zero. On the other hand, the x-intercept is the input value (x), when the output value (y) is zero.
What are the Zeros of a Function?The zeros of a function are the x-intercepts of a function.
Given the function, f(x) = x² - 2x - 80, substitute f(x) = 0 to find the value of x, which is the x-intercept:
0 = x² - 2x - 80
x² - 2x - 80 = 0
Factorize
(x - 10)(x + 8)
x = 10 or x = -8
Substitute x = 0 into the function to find the y-intercept:
f(0) = 0² - 2(0) - 80
f(0) = -80
x-intercepts are 10, and -8.
y-intercept is: -80.
The zeros are: x = 10 and x = -8
Find f(2):
f(2) = (2²) - 2(2) - 80,
f(2) = 4 - 4 - 80
f(2) = -80
Find x when f(x) = -65:
-65 = x² - 2x - 80
-65 + 80 = x² - 2x
15 = x² - 2x
x² - 2x - 15 = 0
Factorize
(x - 5)(x + 3) = 0
x = 5; x = -3
Therefore, f(x) = -65 when x = 5 or -3.
Learn more about intercepts of functions on:
https://brainly.com/question/15602982
#SPJ1
Do this one please i really need an answer:
Answer: this should be more then 5 coins
Step-by-step explanation:
Answer:
√2 is between the integers 1 and 2.
A mako shark can swim 4 kilometers in 1/10 hour. a blue whale can swim 5 kilometers in 1/4 hour. which animal swims faster at top cruising speed? how much faster?
Answer:
The mako shark swims first
Step-by-step explanation:
mako shark swim's at 40kilometre per hr
ablue whale swim's at 20km per hr
Please help I’m struggling so bad right now
40 squared is between which two positive consecutive integers
first find 40 squared
[tex] {40}^{2} \\ = 1600[/tex]
1598,1599, 1600, 1601,1602
You can see that 1600 is between 1599 and 1601
I am really behind and I need help getting this done if I knew how to make users that answer my questions correctly I would make them brainlest. But I don't know how to do that?
Answer:
[tex]\textsf{3.} \quad \dfrac{5}{6}x+ 10=y[/tex]
4. See below.
[tex]\textsf{5.} \quad \dfrac{10}{3}x-2=y[/tex]
Step-by-step explanation:
Question 3Given equation:
[tex]\dfrac{1}{3}x-\dfrac{2}{5}y=-4[/tex]
[tex]\textsf{Add \;$\dfrac{2}{5}y$ \; to both sides}:[/tex]
[tex]\implies \dfrac{1}{3}x-\dfrac{2}{5}y+\dfrac{2}{5}y=-4+\dfrac{2}{5}y[/tex]
[tex]\implies \dfrac{1}{3}x=\dfrac{2}{5}y-4[/tex]
Add 4 to both sides:
[tex]\implies \dfrac{1}{3}x+4=\dfrac{2}{5}y-4+4[/tex]
[tex]\implies \dfrac{1}{3}x+4=\dfrac{2}{5}y[/tex]
[tex]\textsf{Multiply both sides by \; $\dfrac{5}{2}$}:[/tex]
[tex]\implies \dfrac{5}{2} \cdot \dfrac{1}{3}x+ \dfrac{5}{2} \cdot4=\dfrac{5}{2} \cdot \dfrac{2}{5}y[/tex]
[tex]\implies \dfrac{5}{6}x+ 10=y[/tex]
[tex]\boxed{\begin{minipage}{3cm}$\dfrac{1}{3}x-\dfrac{2}{5}y=-4\\\\\underline{\phantom{\dfrac{1}{3}x}+\dfrac{2}{5}y\phantom{=-4}\dfrac{2}{5}y}\\\\\dfrac{1}{3}x=\dfrac{2}{5}y-4\\\underline{+4 \phantom{)=3y}+4\phantom{)))))}}\\\\\dfrac{1}{3}x+4=\dfrac{2}{5}y\\\\\underline{\phantom{)}\times\dfrac{5}{2}\phantom{))))}\times \dfrac{5}{2}}\\\\\dfrac{5}{6}x+10=y$ \end{minipage}}[/tex]
Question 4See the attachment for the highlighted mistake.
The mistake Mike made is that he did not divide 10x by 3.
Question 5Given equation:
[tex]10x-3y=6[/tex]
Add 3y to both sides:
[tex]\implies 10x-3y+3y=6+3y[/tex]
[tex]\implies 10x=6+3y[/tex]
Subtract 6 from both sides:
[tex]\implies 10x-6=6+3y-6[/tex]
[tex]\implies 10x-6=3y[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{10x}{3}-\dfrac{6}{3}=\dfrac{3y}{3}[/tex]
[tex]\implies \dfrac{10}{3}x-2=y[/tex]
[tex]\boxed{\begin{minipage}{3cm}$10x-3y=6\\\underline{\phantom{10x}+3y\phantom{=6}+3y}\\\\10x=3y+6\\\underline{-6 \phantom{)=3y}-6\phantom{)))))}}\\\\\dfrac{10x-6}{3}=\dfrac{3y}{3}\\\\\dfrac{10}{3}x-2=y$ \end{minipage}}[/tex]
If A = {4, 7, 10, 13, 17) and B = {3, 5, 7, 9), then which of the following statements Is true?
BCA
AUB=(7)
BCB
math.uh.edu what effect does increasing the sample size have on a distribution of sample means? a) it will not make any difference b) it will have less variation c) it will have more variation
By using Distribution of the sample mean, “It will have less variation”. So option B is correct.
With Large numbers of successive random samples, the mean of the sampling distribution is equal to the mean population (µ). The variability of each sampling distribution decreases in increase of sample size..
so that they become increasingly more Leptokurtic distribution .
As a sample size increases, sample variance (variation between observations) increases but the variance of the standard error decreases.
The mean of the sample means would be equal to μ (approx.), the mean from which the samples were drawn. However, the sample means will depend on the size of the samples, since big samples are more likely to give estimated means that are equal to the true mean of the population(Approx. )
To learn more about Distribution of the sample mean.
https://brainly.com/question/4292260
#SPJ4
I need help with this
please help meeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!
Answer:
3 x 3 x 3 or 3 to the 3rd power :)
Step-by-step explanation:
Lets solve! :)
3 x 3 x 3
9 x 3
27
The volume of the tank would be 27s :)
Have an amazing day!!
Please rate and mark brainliest!
Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions MC)
Rewrite 1/6x³y + 5/6xy² using a common factor.
xy(x² +5y)
xy(3x² +15y)
xy(x² +5y)
x³y²(y+5x)
Answer:
xy(x² +5y)
Step-by-step explanation:
Rewrite 1/6x³y + 5/6xy² using a common factor.
To simplify, multiple each term by 6:
6 × (1/6x³y) + 6 × (5/6xy²)
= [tex]x^{3} y+5xy^{2} \\[/tex]
take the common term xy and
= [tex]xy(x^{2} +5y)[/tex]
Order four and seven tenths repeating, negative four and eight ninths, 490%, and −4.9 from least to greatest.
Answer:
-4.9, negative four and eight ninths, four and seven tenths, 490%
Step-by-step explanation:
4 7/10 =approx. 4.7
-4 8/9 = -4.888889
490% = 4.9
-4.9
Temperature Suppose there is a 14°F drop in temperature for every thousand feet that an alplane climbs into the sky If the temperature on the ground is 616, what
will be the temperature when the plane reaches an altitude of 4,000 ?
The temperature will be (Type an integer or a decimal)
The temperature when the plane reaches an altitude of 4,000 will be 560°F.
What is temperature?It should be noted that temperature simply means the degree of hotness and coldness of a body.
In this case, there is a 14°F drop in temperature for every thousand feet that an alplane climbs into the sky.
Since the the temperature on the ground is 616, the temperature when the plane reaches an altitude of 4,000 will be:
= 616 - 14(4000/1000)
= 616 - 14(4)
= 616 - 56
= 560°F
Learn more about temperature on:
brainly.com/question/24746268
#SPJ1
while on vacation Francisco sent postcards and letters to his friends. he spent $3.18 on postage. a stamp for a letter costs 39 cents. How many postcards and letters did he send.
Answer: 8
Step-by-step explanation: 3.18 divided by 0.39 is 8 (without the decimals)
Find the equation of the line that passes through (1,2) and is perpendicular to
y
=
2
x
+
3
.
Leave your answer in the form
a
x
+
b
y
=
c
Where
a
,
b
and
c
are integers.
Answer:
x + 2y = 5
Step-by-step explanation:
y = mx + b the m is the slope or gradient.
y=2x+3 The slope is 2.
When lines are perpendicular, the slopes are opposite inverses of each other. So, the perpendicular slope to 2 is -1/2. I would write the answer in the point slope of the line and then change the equation to the stand form
y -2 = -1/2(x -1) Distribute the -1/2
y - 2 = -1/2x + 1/2 Add 1/2 x to both sides
1/2x + y -2 = 1/2 Add 2 to both sides
1/2x +y = 5/2 Multiply by 2 to clear the decimal
x + 2y = 5