Answer:
13 and 15
Step-by-step explanation:
We set up equations.
X=Y-2
2Y=3X-9
We change X=Y-2 into Y=X+2.
Substituting for Y, we get 2Y=2X+4=3X-9
We now solve for x.
2X+4=3X-9 |-2X
4=X-9 |+9
13=X.
X=13
Substituting for Y, we get that Y =15 from the equation Y=X+2.
So, X=13 and Y=15
a line passes through the origin and(5,3). identify two additional points on this line
The equation of the line passes through the origin and (5,3) is y = 3 / 5x and two points are (5 / 3, 1) and (10/3, 2).
What is line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
A line passes through the origin (0, 0) and(5,3),
The equation of the line will be,
y - 0 = 3-0 / 5-0 (x -0)
y = 3 / 5x
Put y = 1 then x = 5 / 3
Put y = 2 then x = 2 × 5 / 3 = 10 / 3
Therefore, the equation of line passes through the origin, and (5,3) is y = 3 / 5x and two points are (5 / 3, 1) and (10/3, 2).
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An athlete eats 0.35 of protein per week while training. How much protein will she eat during 6 weeks of training?
Answer: 0.35
Step-by-step explanation:
Times 7 = 2. 45kg
Alison is going to invest in a stock.
There is a 35% chance that she will make $4000, a
25% chance that she will lose $3000, and a 40%
chance that she will break even (make $0).
What is the expected value for Alison's investment?
Round your answer to the nearest cent if necessary,
but do not include a $ sign or the word "dollars" in
your response.
The expected value for Alison's investment is $650
What is Expected Value in Investment?A projected average value for an investment at some point in the future is known as the expected value (EV).
A anticipated value for an investment is called expected value (EV). It is determined by averaging all conceivable outcomes, multiplied by the likelihood that they will occur. The long-term average of random variables is known as EV. Additionally, it is the probability-weighted average of every potential value.
Given:
There is a 35% chance that she will make $4000.
25% chance that she will lose $3000.
and a 40% chance that she will break even (make $0).
The expected value can be calculated as:
= ∑ (Probability of event happening x Payoff if event happens)
So, The expected value is
= (35% x 4000) + (25% x -(3,000)) + (40% x 0)
= 1400 -750+0
= $650
Hence, the expected value is $2,400.
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You lend out S5500 at 10% compounded monthly. If the debt is repaid in 18 months, what is the total owed at the time of repayment?
Answer:
Step-by-step explanation:
Answer:
$6386.1140
Step-by-step explanation:
Using the compound interest formula :
A = P(1 + r/n) ^nt
P 5500 ; rate, r = 10% = 0.10 ; t = 18 months = 18/12 = 1.5 years,
Compounding times per period = 12 (monthly)
A right triangle has a leg of 5 feet and a hypotenuse of 8 feet. What is the length of the other leg? Round answer to the nearest tenth place. Question 12 options: 2.6 6.2 4.5 5.4
Answer:
6.2 ft
Step-by-step explanation:
a² + b² = c²
a² + 5² = 8²
a² = 64 - 25
a² = 39
a = √39
a = 6.2
Answer: 6.2 ft
The red strip will be cut into
pieces that are 1/2 foot long. How many pieces will there be?
15 pieces will there be.
How many pieces will there be?.5 is the same as 1/2, while 7.5 is the same as 7 1/2. To determine how many strips may be cut, use the following expression:
.5x = 7.5
This is due to the fact that the ribbon length that has to be cut is .5 feet, and we are attempting to determine how many pieces of that length might be cut from a roll of ribbon that is 7.5 feet long.
Divide both sides by 2.5 to separate the variable, and that's all there is to it.
7.5/.5 is 15.
x = 15.
Eli is able to slice a ribbon into three pieces that are each .5 feet long.
The complete question is: The red strips that are 1/2 feet long. The roll of ribbon is 7 1/2 feet long. Which expression could be one of the steps in determining how many strips can be cut?
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If
Draw the missing shape. Then explain how you know your answer is correct.
If Trapezoid + circle = triangle
Then triangle - trapezoid = circle
For the given expression on shapes, if Trapezoid and circle together make a circle , than the difference of triangle and trapezoid equals to a circle.
What is an expression? What is a expression? What is a mathematical equation? A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.Given is that -
Trapezoid + circle = triangle
Triangle - trapezoid = circle
We can write -
t + c = T ..... Eq[1]
T - t = c ...... Eq[2]
We can write -
Eq [2] as-
T = c + t
Then, equation [1] will be -
t + c = c + t
The statements : if trapezoid + circle = triangle, then triangle - trapezoid = circle is proved to be true.
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Which rational Expression Represents x^2 - 9/ 3x^2 * 3x^2 + 9x^2/x-3 when simplified if x ≠ 0 or 3.
The required simplified expression is: x² - 9/ 9x⁴ + 9x² for all x ≠ 0 or 3.
The given expression below is:
x² - 9 / (3x²)(3x²) + 9x²
To simplify the given expression, we must first distribute the terms on the numerator and denominator.
The numerator becomes x² - 9 and the denominator becomes (3x²)(3x²) + 9x².
Next, we must simplify the denominator by combining like terms. The denominator becomes 9x⁴ + 9x².
Finally, we can simplify the entire expression by dividing the numerator by the denominator.
This gives us the simplified expression: x² - 9/ 9x⁴ + 9x².
Note that this expression is not defined when x = 0 or x = 3, as it would result in a division by zero.
Thus, the final simplified expression is x² - 9/ 9x⁴ + 9x² for all x ≠ 0 or 3.
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A rectangular prism has a volume of 960 cubic units. The area of the base is 80 square units.
What is the height of the prism?
Answer:
12 units
Step-by-step explanation:
V = (area of base) × height
height = V/(area of base)
height = 960 units³ / 80 units²
height = 12 units
Assume that each Box object has the properties x, y, width, height and have their origin at their center, and that neither the objects nor the bounding boxes rotate.
As you stated, a convention is as follows: x, y, w, h; likewise, the origin of the picture is from top left, not really the bottom left, as indicated by your drawing. The clusters for top left the box's corner are x, y, and w, h.
The bounding box for object detection may be located in what way?Box Bounding In order to characterize the target position in object recognition, we often utilize a bounding box. Both x and y axis values there at upper-left corner as well as the x and y axes coordinates inside the bottom part of the rectangular define the bounding box, which is a rectangular box.
How can I determine the rectangle's bounding box?The x - axis and y axis values at the upper-left corner as well as the x and y axis values inside the bottom part of a rectangle define the bounding box, which is a rectangular box. Based on the image, we will create the bounding boxes for the dog and cat.
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pair of athletic shoes costs 105$. If the inflation rate remains constant at 7%, write an algebraic rule to determine the cost, c(t), of the shoes after t years.
Answer:
c(t) = 105·1.07^t
Step-by-step explanation:
You want an exponential equation describing the cost of athletic shoes that are $105 now and whose cost is growing at 7% per year for t years.
Exponential equationThe general form of the exponential equation is ...
c(t) = a·b^t
where 'a' is the initial cost (105) and b is the growth factor. The growth factor is related to the given growth rate by ...
b = 1 +r = 1 +7% = 1.07
Then the equation is ...
c(t) = 105·1.07^t
Monty invested $8600 in a savings account with a yearly interest rate of 5% for 12 years. How much sinple interest did he earn.
Answer:
$5160
Step-by-step explanation:
Each year, he earns 5% of 8600 = 0.05 * 8600 = $430
After 12 years, she will earn 12 * 430 = $5160 in interest
The percent error of a measurement tells how close the measurement is to the actual value. The label on a mineral sample kit gave the weight of the sample as 60.5 ounces. The true weight was found to be 62.5 ounces. To find the percent error, first find the absolute value of the difference between the weight on the label and the true weight.
The percentage error when the weight was found to be 62.5 ounces is 3.2%.
What is the percentage error?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Since the the weight of the sample as 60.5 ounces and the true weight was found to be 62.5 ounces.
The percentage error will be:
Error / Initial value × 100
= (62.5 - 60.5) / 62.5 × 100
= 2 / 62.5 × 100
= 3.2%
The percentage error is 3.2%.
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what will be the possible solution of condition that" if the rank of matrix A is less than the rank of its augmented matrix?"
The possible solution to the condition is that if the rank of matrix A is less than the rank of its augmented matrix, the augmented matrix contains a row of the form 0 0…0 | b, where b is nonzero.
What is matrix?A matrix is a rectangular array or table with rows and columns of numbers, symbols, or expressions that are used to represent a mathematical object or an attribute of one.
Since the pivot b must, of course, not be zero, every row entry to the left of the pivot is zero by nature of the row-reduction procedure, which results in a row of the type,
[tex]\left[\begin{array}{ccc}0&0&.......0\ |\ b\end{array}\right][/tex] where b ≠ 0
Therefore, the possible solution to the condition is that if the rank of matrix A is less than the rank of its augmented matrix the augmented matrix contains a row of the form 0 0…0 | b, where b is nonzero.
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Find the values of x and y
x=_____
y=_____
The value of x is 30 degrees and the value of y = 5
The total figure is divided in to two triangles
Consider the first triangles
All the angles of the triangles is equal that is 60 degrees, This is a equilateral triangles
In equilateral triangles all the sides will be equal
Then the equation will be
8y = 40
y = 40/8
y = 5
Then consider the second triangle
Here, two sides are 40 units and third side is different, therefore it is an isosceles triangle
Then the equation will be
x + x + (180-60) = 180
2x + 120 = 180
2x = 180 - 120
2x = 60
x = 60/2
x = 30 degrees
Therefore, the value of x and y are 30 degrees and 5 respectively
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Question 11 of 25 Imagine that you are given two linear equations in slope-intercept form. You notice that the slopes are different, but the y-intercepts are the same. How many solutions would you expect for this system of equations? O A. infinitely many O B. cannot be determined C. 0 D. 1 SUBMIT
Answer:
D. 1 solution-----------------------------
If the two lines have same y-intercept then this is the point of intersection of the two lines.
Since the slopes are different, the y-intercept is the only point of intersection. So there is one solution.
Correct choice is D.
various studies state that, worldwide, 1% of persons suffer from autism. you believe that this number should be higher. you take an srs of 500 people and find that 8 people have autism. test your claim with 5% significance. Determinan your rejection region.
Out of 500 people, 8 have autism, according to the SRS. The rejection zone is revealed to be at significance() = 5%, or 0.05. This figure need to be higher.
What is autism spectrum ?
Eight people with autism are found out of 500 people in an SRS. Autism, often known as autism spectrum disorder, refers to a wide range of diseases that affect how the brain develops. Therefore, there is a critical need for research on treatment plans that guarantee the best possible outcomes for kids with ASDs. According to several research, autism affects 1% of people globally. You think this number ought to be greater. Using a sample size of 500 persons, you discover 8 cases of autism. 5% significance test for the assertion.
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Find the inequality represented by the graph.
Inequality:
y > 1/3x - 3
If 1/5 of the distance from the x-axis to the point A(2a+3,3a+4) is equal to 6/7 of the distance from the y-axis to the point B(4-a,5-a). What is the value of a, if a>5?
The fraction of the distances of the points A(2·a + 3, 3·a + 4), and B(4 - a, 5 - a) from the x- and y-axis and the value of a > 5, indicates that the value of a is 16.[tex]\overline{4}[/tex]
What is a fraction in mathematics?A fraction is a representation of the amount a part of an item compared to the whole of the item.
The distance from the x-axis to the point A(2·a + 3, 3·a + 4) = 3·a + 4
The distance from the y-axis to the point B(4 - a, 5 - a) = 4 - a
Therefore; 1/5 of the distance from the x-axis to the point A(2·a + 3, 3·a + 4) is (1/5) × (3·a + 4)
6/7 of the distance from the y-axis to the point B(4 - a, 5 - a) is (6/7) × (4 - a)
The details in the question indicates; (1/5) × (3·a + 4) = (6/7) × (4 - a)
However, if a > 5, then 4 - a < 0, while (3·a + 4) > 0, from which we get;
If a > 5, then, (1/5) × (3·a + 4) = (6/7) × (a - 4)
[tex]\dfrac{1}{5} \times (3\cdot a + 4) = \dfrac{6}{7} \times (a -4)[/tex]
7 × (3·a + 4) = 5 × 6 × (a - 4)
21·a + 28 = 30·a - 120
30·a - 21·a = 9·a = 120 + 28 = 148
a = 148/9 = 16.[tex]\overline 4[/tex]
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A researcher in physiology has decided that a good mathematical model for the number of impulses fired after a nerve has been stimulated is given by y=x^2+50x-80, where y is the number of responses per millisecond and x is the number of milliseconds since the nerve was stimulated.
(a)
When will the maximum firing rate be reached?
(b)
What is the maximum firing rate?
The maximum firing rate will be reached after 25 milliseconds and the maximum firing rate is 545 responses per millisecond
How to determine when the maximum firing rate will be reached?From the question, we have the following parameters that can be used in our computation:
y = -x^2 + 50x - 80
Rewrite this function as
y = -x² + 50x - 80
Differentiate the function
So, we have
y = -2x + 50
Set to 0
-2x + 50 = 0
So, we have
2x = 50
Divide by 2
x = 25
How to determine what the maximum firing rate is?Recall that
y = -x² + 50x - 80
Also, we have
x = 25
So, we have
y = -(25)² + 50 x 25 - 80
Evaluate
y = 545
Hence, the maximum is 545 responses per millisecond
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Wanda drove for w hours on a trip. Wanda's husband
drove 3 hours more than she did. Which expression
represents the total time they spent driving?
A. w+6
B. 2w+3
C. w-6
D. 2w -3
By using the concept of addition, it can be calculated that-
The total time they spent driving = 2w + 3
Option b is correct
What is addition?
Suppose there are many numbers, and we need to find the sum total of all those integers, then the operation used in this case is called addition
This is a word problem on addition
Wanda drove for w hours on a trip.
Wanda's husband drove 3 hours more than she did.
Time for which Wanda's husband drove = w + 3
The total time they spent driving = w + w + 3
= 2w + 3
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It is estimated that a driver takes, on average, 1.5 seconds from seeing an obstacle to reacting by applying the brake or swerving.
How far will a car, traveling at 65 miles per hour, travel in feet before the driver reacts to an obstacle? Round answer to the ones place.
HELP DUE TONIGHT
Answer: We know that 60 mph = 88 feet per sec (this can be shown easily enough).
Then we have a proportion:
60%2F88+=+85%2Fx
and we cross-multiply to get
60x = 7480
x = 124.7 feet per sec
Now multiply that by 1.5 sec and get
187 feet
(This is not realistic...the average alert driver reacts in about 0.15 seconds, not 1.5)
So answer 187 feet
Step-by-step explanation:
Callie and her friend Elena are reading through different novels they checked out from their school library last Tuesday. Callie's progress
Calculator:
Neutral
through her novel can be modeled by the function p(d) = -25d. +
318, where p(d) represents the number of pages remaining to be read and dis the number of days since receiving the book. Elena's progress through her novel is modeled by the graph below.I
Answer: 69
Step-by-step explanation: jamal
What is the common monomial factor of the expression 16m^2n^2 − 12mn^5?
Answer:
[tex]4mn^{2}[/tex] is their common factor.
Step-by-step explanation:
It is the common factor of both as it is a number they are both easily divisible by.
Answer:
4mn^2
Step-by-step explanation:
You want the common factor of the terms in 16m^2n^2 -12mn^5.
FactorsThe terms can be factored as ...
16m^2n^2 = (4)(4)(m)(m)(n^2)
-12 mn^5 = (-3)(4)(m)(n^2)(n^3)
The factors that are in both lists are ...
(4)(m)(n^2)
The common monomial factor of the expression is 4mn^2.
__
Additional comment
Factoring out that common factor gives ...
= 4mn^2(4m -3n^3)
Write the equation of the line described below in slope-intercept form.
Find the equation of the line that is perpendicular to the line y=2 x and passes through the point (10,2).
Equation of the line passes through (10,2) and is perpendicular to the line y = 2x is given by y = -x / 2 + 7.
As given in the question,
Given equation of the line :
y = 2x
Line passes through the point (x₁ , y₁ ) = (10, 2)
Standard form of slope intercept form
y = mx + c
'm' is the slope
slope of the given line 'm₁' = 2
let 'm₂' be the slope of the required line
Multiplication of the Slope of two perpendicular lines is given by :
m₁ × m₂ = -1
⇒2 × m₂ = -1
⇒m₂ = -1/2
Equation of the line perpendicular to the given line and passes through
(x₁ , y₁ ) = (10, 2)
y - y₁ = m₂ ( x - x₁ )
⇒ y - 2 = (-1/2) ( x - 10 )
⇒ y = -x / 2 + 7
Therefore, the required equation of the line in slope intercept form is given by y = -x / 2 + 7 .
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a pineapple which was bought for $1.00 was sold at $1.30. calculate the profit percent
Answer: 30%
Step-by-step explanation:
First, calculate the difference between the original number and the new number:
1.30 - 1.00 = 0.30
Second, divide the difference by the original number.
0.30/1.00 = 0.3
Third, multiply the answer by 100 to get the percentage. (Remember cent means 100!)
0.3 * 100 = 30
Therefore, the profit per cent was 30%.
Hoped this helped!
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
i think the answer is something like maybe if the artist is really good at doing something well and looking good
this question is hard
Graph line with slope -5 and y-intercept 6
Answer:
y=-5x+6
Step-by-step explanation:
y=mx+b
y=-5x+6
What is 2+2?
A. 4
B. 2
C. 1
D. 0
Answer:
A. 4
Step-by-step explanation:
2+2=4
Adding
Write the model for g (a), whose graph represents the indicated transformations of
f (x).
f(x) = x²
2 Units Left, then 3 Units Down, followed by a reflection in the x-axis
NO SPACES and use ^2 to represent the 2 in ²
g(x) =
The function of g is -3x+6
How to calculate function of g?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The g function can be obtained from the graph using two points, the first (0,6) and the second (2,0).
Remember, a line has the following equation:
Since x=0 and y=6, y=mx=b, where'm' denotes the slope and 'b' the interception.
Now to find the slope, lets use the following equation:
m=y2 - y1/x2 - x1
With the previously obtained point.
We have m=-3
g=-3x+6
Therefore the function of g is -3x+6
The complete question is : Write a function g whose graph represents the indicated transformation of the graph of f(x)=6-x.
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