Answer:
Using the quadratic formula, we find that:
x = 0.555 or x = 89.445
We can ignore the first solution since it doesn't make sense for the speed of a train. Therefore, the speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.
So, the answer is:
The speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.NOT SURE
Step-by-step explanation:
The given equation has been solved in the table.
Answer option for step 2
Addition
Subtraction
multiplication
Division
Answer option for step 4
Addition
Subtraction
multiplication
Division
The operations used here are as follows:
Addition.
Division.
What are operations?The order of operations is a collection of rules that must be followed in a particular order while solving an equation.
The evaluation of any mathematical expression, which includes arithmetic operations like addition, subtraction, multiplication, and division, is what we mean when we say "operations" in mathematics.
Here in the question,
For the 2nd step,
10 was added on both the sides of the equation.
So, addition was the property used.
For the 4th step,
3 was divided from both the sides of the equation.
So, division was the property used.
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find the slope-intercept form of this table
The slope-intercept form of this table is y = 3x - 10.
What is the point-slope form?In Mathematics, the point-slope form of any straight line can be determined by using the following mathematical expression:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex] or y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.At point (25, 65), an equation of this line in slope-intercept form can be calculated by using the point-slope form:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
[tex]y - 65 = \frac{(68- 65)}{(26 - 25)}(x - 25)[/tex]
y - 65 = 3(x - 25)
y = 3x - 75 + 65
y = 3x - 10.
In this context, we can reasonably infer and logically deduce that an equation of the line that represents this table in slope-intercept form is y = 3x - 10.
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In the diagram below, MN is parallel to JK. If ML = 12, LK = 28,
JK 14, and LN 16, find the length of JL. Figures are not necessarily
drawn to scale.
N
M
K
The length of JL can be found by subtracting the length of ML from the sum of LK and LN. Therefore, JL = 28 + 16 - 12 = 32.
To find the length of JL, first we can add the lengths of LK and LN. LK = 28 and LN = 16, so 28 + 16 = 44. Then, we can subtract the length of ML from the sum of LK and LN. ML = 12, so 44 - 12 = 32. Therefore, JL = 32.
This can be done by visualizing the diagram. The length of JL can be found by adding the lengths of LK and LN, which can be seen as the two sides of the right triangle that form the line MN. Then, the length of ML can be subtracted from the sum of LK and LN to get the length of JL. This is because the length of JL is equal to the length of LK plus the length of LN minus the length of ML.
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Satoko has 30 tokens to spend at an arcade. The three lines represent the cost of playing Satoko's three favorite games for various numbers of times. Which game can Satoko play the most number of times with her tokens? Choose 1 answer: (Choice A) KOF (Choice B) DDR (Choice C) Claw
Satoko play the most number of times with her tokens is KOF. The correct answer is A.
A line graph is a type of chart that displays data as a series of points connected by a line. Line graphs show the relationship between two variables. The equation of each line can be obtained from the graph given regarding the game played by satoko.
Let us first derive the equation of first line Claw. This line goes from (0,0) to (5,20) so, the equation is y = 4x. The unit price is 4.
Next, the equation of DDR line. This line is from (0,0) to (5, 10). so, the equation is y = 3x. The unit price is 3.
The equation of line KOF goes from (0,0) to ( 5, 10). The equation of line is y = 2x. So, the unit price is 2.
Here, 4 greater than 3, and 3 is greatter than 2. so the correct answer is choice A, KOF.
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Answer: A
Step-by-step explanation:
i just know because i got it right.
The table shows a function. Is the function linear or nonlinear?
X
3
6
9
y
19
12
2
linear
nonlinear
Below, there is a pattern with its first 5 terms listed. Describe a way to produce each tern from the previous term.
5,8,11,14,17..
Answer:
Add 3
Step-by-step explanation:
The pattern provided can be obtained by adding a constant number to the previous term. The common number is 3 because each term is 3 more than the previous term.
[tex]5^{+3} =8^{+3} =11^{+3} ...[/tex]and so onTherefore, you can add 3 to the previous term to get the next term.
You have given an exam for which :
μ=85
σ=4.6
What is the probability that a randomly selected faw score will be greater than 96 ? ANSWER: 0.0084
Therefore , the solution of the given problem of probability comes out to be there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.
What is probability exactly?The primary goal of the designs inside a practice known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1 can be used to represent chance, with 1 usually representing a range level of certainty and 0 typically representing possibility. A probability diagram shows the chance that a specific event will occur. Just the digits 0% and approximately 100% make up the decimal 1, 0, and 0.
Here,
To resolve this issue, we can use the conventional normal distribution. First, we must standardise the 96 number using the following equation:
=> z = (x - μ) / σ
where the mean is, the standard deviation is, and x is the number we're interested in. When we enter the numbers, we obtain:
=> z = (96 - 85) / 4.6 = 2.3913
The area to the right of z = 2.3913 can then be determined using a calculator or a conventional normal distribution table.
The area to the right of 2.39, according to a standard normal distribution chart, is 0.0084. (rounded to four decimal places).
As a result, there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.
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In the following term, give the numerical coefficient of the variable.
2b/3
The numerical coefficient of 2b/3 is ____.
The numerical coefficient of [tex]\frac{2b}{3}[/tex] is [tex]\frac{2}{3}[/tex] . So here we know how to find numeric coefficient.
What is Numerical coefficient?A numerical coefficient is defined as a fixed (stable) number that is multiplied to a variable.
When an algebraic expression consists of several (various) parts, each part that is added called a term. The numerical part of a term is called as its numerical coefficient (or coefficient).
Variable, It is a symbol that represents (means) a mathematical object. A variable may represent(mean) a number, a matrix, a function, a vector, the argument of a set, a function, or an element of a set.
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hii, I need help please !
Answer:
∠ 6 = 59°
Step-by-step explanation:
∠ 3 and ∠ 8 are same- side interior angles and sum to 180° , that is
∠ 3 + ∠ 8 = 180°
121° + ∠ 8 = 180° ( subtract 121° from both sides )
∠ 8 = 59°
∠ 8 and ∠ 6 are vertically opposite angles and are congruent , then
∠ 6 = 59°
please guys ano toh answer this
Answer: 15, 18, 21 (next three terms), Rule: Skip counting by 3
What is the rule to finding nth term?First calculate the common difference between the terms, If [tex]a_{1}, a_{2}, a_{3}, a_{4}.....[/tex] are in sequence, the common difference is calculated by [tex](a_{2} -a_{1}), (a_{3} -a_{2}), (a_{4} -a_{3}) .......[/tex]
Since, the common difference are equal so its clear that the given sequence is an Arithmetic Expression.
The nth term of the AP is an = a + (n-1)*d
1. Given: 3, 6, 9, 12, .....
Answer: 15, 18, 21 (next three terms)
Rule: Skip counting by 3
2. Given: 3, 5, 7, 9, .....
Answer: 11, 13, 15 (next three terms)
Rule: Skip counting by 1
3. Given: a, (a+b), (a+2b),.....
Answer: (a+3b), (a+4b), (a+5b) (next three terms)
Rule: nth term = a+(n-1)*b = a+nb-b
if we need 4th term, put n=4 so that 4th term= a+4b-b = (a+3b)
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A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?
prs
StartFraction p Over r s EndFraction
StartFraction r s Over p EndFraction
p + r + s
Answer:
[tex]\boxed{k=\frac{p}{r \ s} }[/tex]
Second option is correct.
Step-by-step explanation:
We have been given that p varies jointly with r and s.
Thus, we can write it mathematically as
[tex]p=krs[/tex]
Here, k is the constant of variation.
Now, we have to find the value of k.
Divide the above equation by rs
[tex]\dfrac{p}{r \ s}=\dfrac{kr\ s}{rs}[/tex]
[tex]k=\dfrac{p}{r s}[/tex]
Hence, the value of k is [tex]k=\dfrac{p}{r s}[/tex]
Second option is correct.
Answer:
B
Step-by-step explanation:
edge 23
PLEASE HELPPPPP im struggling
Answer: $2,750
Step-by-step explanation:
I NEED HELP ON THIS QUICKLYYY, WILL GIVE BRAINLIESTT!
The optimal number of TVs to sell in order to achieve the highest profit are 24 and 48, respectively
What is the optimal number of TVs to sell in order to achieve the highest profit?Given the question, the objective function can be stated as follows.
P(n, m) = 175b + 205m
The given values for the constraints and the result of evaluating them are provided as
P(0, 0) =175(0) + 205(0) = 0 P(0, 64) =175(0) + 205(64) =13,120 P(24, 48) =175(24) + 205(48) =14,040 P(72, 0) =175(72) + 205(0) = 12,600After analyzing the above values, we have identified the highest value as
Maximum = 14040
These values are at
b = 24 and m = 48
Hence, the number of TV to be sold are 24 and 48, respectively
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A camera has a listed price of $891. 95 before tax. If the sales tax rate is 9. 5%, find the total cost of the camera with sales tax included
The total cost of the camera with sales tax included is $976.68
The listed price of the camera = $891.95
The sales tax rate = 9.5%
The amount of tax = The listed price of camera × (The sales tax rate / 100)
Substitute the values in the equation
The amount tax = 722.95 × (9.5 / 100)
Divide the terms first
= 891.95 × 0.095
Multiply the terms
= $84.735
The cost of the camera including tax = The listed price of camera + The amount of tax
Substitute the values in the equation
= 891.95 +84.735
= $976.68
Hence, the total cost of the camera with sales tax included is $976.68
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A HORIZONTAL line passes through point (-3, -1) Responses A x = 1x = 1 B x = 3x = 3 C y = -1y = -1 D y = 1
Equation for the line passing through the point (-3, -1) is:
c. y = -1
What is slope intercept?Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.
Now in the question here,
The line passes through the point (-3, -1).
So, the equation that satisfies the point is: y = -1.
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b. What is the probability of the event of getting 2 socks of the same color? The probability is (Type an integer or a simplified fraction.) c. What is the probability of the event of getting two gray
Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.
What is prοbability?The chance that a particular event will οccur is quantified by prοbability. It is a number between 0 and 1, where 0 denοtes that the event is hypοthetical and 1 denοtes that it will undοubtedly οccur. The number οf successful results multiplied by the entire number οf pοssible οutcοmes is used tο calculate an event's prοbability. Tο put it anοther way, prοbability is a way tο express the likelihοοd οf an event οccurring and tο quantify uncertainty.
given:
we can determine the likelihοοd οf receiving twο sοcks οf the same cοlοr.
We can select twο sοcks οf the same hue in any οf the fοllοwing ways:
In ₃C₂ = 3 οptiοns, we can select οur 2 gray sοcks.
There are ₃C₂ = 3 different methοds tο select 2 black sοcks.
Therefοre, there are a tοtal οf 3+3=6 methοds in which we can select 2 sοcks οf the same cοlοr.
There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.
The likelihοοd οf receiving twο sοcks οf the same cοlοr is as fοllοws:
6/15 = 2/5
Thus, the respοnse is c) 2/5.
b) The likelihοοd οf receiving twο pairs οf gray hοsiery is:
There are 3 οptiοns tο chοοse 2 pairs οf gray sοcks (₃C₂ = 3).
There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.
Cοnsequently, the likelihοοd οf receiving twο pairs οf gray hοsiery is:
3/15 = 1/5
Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.
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Si la suma de las razones de una igualdad de 3 razones geométricas continuas es 3/4,
calcule la suma de antecedentes. Considere que la diferencia entre el mayor
y menor consecuente es 120
Note that where the above conditions exists with regard to the geometric ratios, the sum of the antecedents is approximately 445.31.
What is the explanation for the above response?Let the three continuous geometric ratios be a, ar, and ar^2, where a is the first term and r is the common ratio. Then the equality can be written as:
a/ar + ar/ar² + ar² = 3/4
Simplifying this equation, we get:
1/r + r + r² = 3/4
Multiplying both sides by 4r², we get:
4r + 4r³ + 4r⁴ = 3r²
Rearranging, we get:
4r⁴ + 3r² - 4r = 0
We can factor this equation as:
r(4r³ - 4r² + 3) = 0
Since r cannot be zero, we must solve the cubic equation:
4r³ - 4r² + 3 = 0
Using a numerical method or a computer program, we can find that one real root of this equation is approximately 0.8202.
Now that we know the value of r, we can use the difference between the largest and minor consequent to find the value of a. The largest consequent is ar², and the minor consequent is a, so we have:
ar² - a = 120
Substituting r = 0.8202, we get:
a(0.8202)² - a = 120
Simplifying, we get:
a = 120 / (0.6721)
a ≈ 178.63
Finally, we can calculate the sum of the antecedents:
a + ar + ar² = 178.63 + (178.63)(0.8202) + (178.63)(0.8202)²
Summing these terms, we get:
a + ar + ar² ≈ 445.31
Therefore, the sum of the antecedents is approximately 445.31
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Translation:
If the sum of the ratios of an equality of 3 continuous geometric ratios is 3/4, calculate the sum of antecedents. Consider that the difference between the largest and minor consequent is 120
im struggling a lot with this question have good day
well, 2 and 1/2 is just 2 + 1/2 or just 2.5, so 2.5%.
[tex]~~~~~~ \stackrel{ \textit{\LARGE 8 years} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$250\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (250)(0.025)(8) \implies I = 50[/tex]
how about after 1 year? well, we simply set t = 1, so (250)(0.025)(1) = 6.25.
would the interest for t = 2 be the same as for t = 1, if t = 2 is calculated, anyhow, the wording is a bit poor, let me reword it.
after the 1st year, she has an accumulated amount of 250 + 6.25 = 256.25.
now, if for the 2nd year we use the same 2.5% rate BUT we use the accumulated amount of $256.25 to get the interest, instead of the initial $250, will they be the same?
well, hell no, because (250)(0.025)(2) using the inital amount
is not the same as (256.25)(0.025)(2).
bear in mind that simple interest is calculated for each year using the initial amount or deposit, not the accumulated amount thus far.
A pilot flies in a straight path for 90 minutes. She then makes a course correction, heading 20° to the right of her original course, and flies 100 minutes in the new direction. If she maintains a constant speed of 720 miles per hour, how far is she from her starting position? Round your answer to the nearest mile.
"To solve this problem, we can use the Law of Cosines. Let's call the distance the pilot travels before the course correction d1 and the distance she travels after the course correction d2. We want to find the distance between her starting position and ending position, which we can call D.
First, let's find d1:
d1 = (720 mph) * (90 min / 60 min) = 1080 miles
Next, let's find d2:
d2 = (720 mph) * (100 min / 60 min) = 1200 miles
Now we can use the Law of Cosines:
D² = d1² + d2² - 2d1d2*cos(20°)
D² = 1080² + 1200² - 210801200*cos(20°)
D ≈ 1169 miles
Therefore, the pilot is approximately 1169 miles from her starting position." (ChatGPT, 2023)
if anyone could help, would be much appreciated
The numeric value of the expression is given as follows:
[f(x + h) - f(x)]/h = 5h + 10x + 6.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is given as follows:
f(x) = 5x² - 6x + 1.
The numeric value at x = x + h is given as follows:
f(x + h) = 5(x + h)² - 6(x + h) + 1
f(x + h) = 5(x² + 2xh + h²) - 6x + 6h + 1
f(x + h) = 5x² + 10xh + 5h² - 6x + 6h + 1
Hence:
f(x + h) - f(x) = 5x² + 10xh + 5h² - 6x + 6h + 1 - 5x² + 6x + 1
f(x + h) - f(x) = 10xh + 5h² + 6h
f(x + h) - f(x) = h(5h + 10x + 6).
Simplifying by h, we have that:
[f(x + h) - f(x)]/h = 5h + 10x + 6.
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Find the gradient of the line passing through (-2, 5) and (5, -5)
The diameter of a circle is 18 millimeters. What is the circle's circumference?
Use 3.14 for .
= millimeters
Answer:
56.52mm
Step-by-step explanation:
If the diameter is 18, the radius is 9.
The formula for circumference is c=2πr
so, 2*3.14*9=56.52
56.52mm
Factorise the following
[tex] {x}^{2} - 5x - 6[/tex]
Answer:
(x+1)(x-6)
Step-by-step explanation:
two number that times to make -6 and add to make-5
these are : -6 and +1
(x+1)(x-6)
when u expand it
x^2-6x+x-6
=x^2-5x-6
What number (a) is 0.4% of 40?
Accοrding the given questiοn 0.16 is 0.4 Percentage οr % οf 40
What is Percentages ?A percentage is a number οr ratiο that can be expressed as a fractiοn οf 100 in mathematics. If we need tο calculate a percentage οf a number, multiply it by 100 and divide it by the tοtal. Sο, a part per hundred is what the percentage refers tο. Percent means fοr every 100. The symbοl "%" is used tο denοte it.
Percentages have nο dimensiοn. Hence it is called a dimensiοnless number. If we say, 50% οf a number, then it means 50 per cent οf its whοle.
0.4% is equivalent tο 0.4/100 = 0.004 as a decimal.
Tο find οut what number (a) is 0.4% οf 40, we can use the fοllοwing fοrmula:
a = 0.004 x 40
a = 0.16
Therefοre, 0.4% οf 40 is 0.16.
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Jalen was repairing the post on his mailbox. He wanted the post to be
perpendicular to the ground, but his protractor showed that the post was at an
82 degree angle with the ground. He incorrectly concluded that he needed to
increase the angle by 12 degrees. What should Jalen have concluded?
A.The angle needs to
be increased by 10
degrees to get a 90
degree angle.
B.The angle needs to
be decreased by 28
degrees to get a 180
degree angle.
C.The angle needs to
be decreased by 98
degrees to get a 180
degree angle.
D.The angle needs to
be increased by 8
degrees to get to a
90 degree angle.
Answer: Jalen wants the post to be perpendicular to the ground, which means the angle between the post and the ground should be 90 degrees. If the protractor showed the angle to be 82 degrees, then the post is leaning towards the ground. To make the post perpendicular, the angle needs to be decreased. Jalen incorrectly concluded that he needed to increase the angle by 12 degrees, which would make the angle 94 degrees, still not perpendicular.
To make the post perpendicular, Jalen needs to decrease the angle by 8 degrees (90 - 82 = 8). Therefore, the correct answer is D: The angle needs to be increased by 8 degrees to get to a 90 degree angle.
Step-by-step explanation:
Determine how many solutions the following systems have
Y=2x-4
-2x+y=-4
Pls answer thiss
give ismple working out
Answer:
add 3
Step-by-step explanation:
adding 3 to each number for next erm
Please help
Graph the inequality
-1
The correct answer is answer choice- A.
Step-by-step explanation:
Answer:
Option A
Step-by-step explanation:
See the attached worksheet. The use of a filled or unfilled circle on a number indicates whether that actual number is included (solid circle) or not included (empty circle) A solid bar between two points telss us these points are all included.
-3<x<3 does not have an equality ("=") for ether +3 nor -3. The the line between those points would be solid (all points are allowed). Either 3 would be an empty circle.
Option A seems to have these features.
brainliest, 100 points, and multiple choice!!!!!!
Answer:
The coordinates are (-2, 4)
The last option
Step-by-step explanation:
When you rotate 90 degrees clockwise, the coordinates change from (x,y) to (y, -x) so you just substitute the numbers to get the answer.
Given the expression
Choose all the equivalent expressions as your answer.
Answer:
(3)(x)(z)
Step-by-step explanation: