The absolute value equation modelling this situation is presented as follows:
|x - 58.2| = 6.4.
What is the absolute value of a number?The function giving the absolute value of another function is defined by the piece-wise rule presented as follows:
|f(x)| = f(x), f(x) ≥ 0.|f(x)| = -f(x), f(x) < 0.The result is never negative, as the function gives the distance of the function f(x) from the origin, which is the point in which f(x) = 0.
The difference between both the fastest and the slowest time from the average time of 58.2 seconds is of 6.4 seconds, hence the absolute value equation is given as follows:
|x - 58.2| = 6.4.
Which can be solved applying these following rules:
x - 58.2 = -6.4.x - 58.2 = 6.4.To find the fastest and slowest times, respectively.
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joe and matthew plan to visit a bookstore. based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below. a figure is shown with two tables, each with two rows. the top table has a top row that reads number of books joe will buy, 0, 1, 2, and a bottom row that reads probability, 0.50, 0.25, 0.25. the bottom table has a top row that reads number of books matthew will buy, 0, 1, 2, and a bottom row that reads probability, 0.25, 0.50, 0.25. assuming that joe and matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?
The probability that Joe and Mathew would have to purchase no books on this visit to the bookstore is given as 0.125.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We are to find the probability where p(x) = 0 and p(y) = 0
This is where we would have
from the table, p(x) = 0 is 0.5
p(y) = 0 is 0.25
0.25 x 0.5 = 0.125
Hence the probability that no books would be bought is 0.125.
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help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The perfect square trinomial is x² + 10x + [tex] \boxed{\sf 25} [/tex]The factored perfect square trinomial is [tex] \boxed{\sf (x + 5)(x + 5) \ or \ {(x + 5)}^2} [/tex]Step-by-step explanation:
Given:
Binomial: x² + 10x
To Find:
Constant that should be added to the binomial so that it becomes a perfect square trinomial.Factor the trinomial.Solution:
To find the constant we would compare the binomial with (a + b)² i.e. a² + 2ab + b² as it is the formula for perfect square.
By comparing we get:
a² = x²
2ab = 10x
b² = constant (To find out)
From this we can make out:
a = x
[tex] \therefore[/tex]
[tex] \rm \implies 2 \times x \times b = 10x \\ \\ \rm \implies b = \frac{10x}{2x} \\ \\ \rm \implies b = 5 \\ \\ \therefore \\ \\ \rm \implies {b}^{2} = 25[/tex]
So, constant that should be added to the binomial so that it becomes a perfect square trinomial is [tex] \boxed{\rm 25} [/tex].
Perfect square trinomial is x² + 10x + 25
Factorisation of the trinomial:
[tex] \rm \implies {x}^{2} + 10x + 25 \\ \\ \rm \implies {x}^{2} + 10x + {5}^{2} \\ \\ \rm \implies {x}^{2} + 5x + 5x + {5}^{2} \\ \\ \rm \implies x(x + 5) + 5(x + 5) \\ \\ \rm \implies (x + 5)(x + 5) \\ \\ \rm \implies {(x + 5)}^{2} [/tex]
Help needed!!!
a) Convert the length and width of the swimming pool from centimetres to metres.
b) You’re thinking of laying bricks around the outside of the pool. Find the perimeter of the swimming pool, in metres.
c) You want to buy a pool cover. By rounding off your answers in a) to the nearest metre, estimate the area of the pool by multiplying the 2 numbers together.
d) Find the exact area of your new pool, in m2.
e) Was your estimate in d) reasonable?
f) Please explain why it was accurate or not
Answer:
Step-by-step explanation:
a) 100cm 1m so, 320/100=3.2m, 1200/100=12m
b) 3.2+3.2+12+12= 6.4+24=30.4
c) 3*12=36m squared
d) 3.2*12= 3*12+0.2*12=36+2.4=38.4m squared
e) My estimate in d) was reasonable
f) This is because 36 and 38.4 are really close to each other they only have a difference of 2.4 and that is because instead of multiplying the estimate with 3 and a 0.2 I just multiplied it with a 3. 0.2*12=2.4 so the difference is reasonable.
g:x→0.44√3.2x−4.1 i need to make that into a graph in my calculator but im not sure how
The graph of the given functions is (see in attachments).
From the question, we have
g(x) = 0.44√3.2x−4.1
Graph:
A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.
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Donald graphs the distance he walks over time the graph passed through the points (3, 12) and (4, 16)
Using a proportional relationship, it is found that:
A. The slope of the line is of 4.
B. The slope is the same over both segments.
What is a proportional relationship?A proportional relationship is modeled as follows:
y = kx.
Hence a proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
For the presented case, the two variables x and y are direct proportional, and thus the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k.
In this problem, the relationship has two points presented as follows:
(3, 12) and (4, 16).
Hence the slope, which is the constant of the relation, is given as follows:
k = 12/3 = 16/4 = 4.
Given two points, the slope is given by the change in y divided by the change in x. Hence, over each segment, the slopes are given as follows:
(1,4) and (3,12): m = (12 - 4)/(3 - 1) = 8/2 = 4.(3, 12) and (4,16): m = (16 - 12)/(4 - 3) = 4.Which are the same slopes.
Missing InformationThe problem is given by the image at the end of the answer.
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S.
The memory card on Melcher's digital camera can hold about 430 pictures. Melcher used 18% of
the memory card while taking pictures at a family reunion. About how many pictares did
Melcher take at the family reunion? Round to the nearest whole number.
Answer:
Step-by-step explanation:
18% of 430 comes out to 77.4 total pictures taken. After rounding it to the nearest whole number because you cant take a fraction of a picture it would be 77 total pictures taken.
solve for x and find each angle measure
(7x-32)
(5x-27)
(9x-8)
equation
x:
please help me !!
it’s for a quiz
Answer:
Step-by-step explanation:
187
Type the correct answer in the box. If necessary, use / for the fraction bar.
Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the pris
expressed as a fraction in simplest form, is
The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.
How to calculate the volume of a pyramid?
The volume of a pyramid can be calculated by using this formula:
Volume = 1/3 × b × h
Where:
h is the height.
b is the base area.
Volume of this prism = 1/2 × b × hHere, both pyramids have the same base area as the prism, their volume is given by:
Volume of a pyramid = (1/3 × b × h) + (1/3 × b × h)
Volume of a pyramid = 2/3 × b × h
Also, the volume of this prism = 1/2 × b × h
Thus, the ratio is given by:
Ratio = (2/3 × b × h)/(1/2 × b × h)
Ratio = 2/3 × 1/2
Ratio = 1/3.
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In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.
Based on the given information, answer the questions below. Round each answer to the nearest tenth.
Part A: How tall is the pole? Show your work.
Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.
Part C: How long is Wire 1? Show your work.
A. Applying the trigonometric ratio, the length of pole = 29.6 ft.
B. 23.1 ft.
C. Length of wire 1 = 45.1 feet.
How to Apply the Trigonometric Ratios?The trigonometric ratios are:
sin ∅ = opposite length/hypotenuse length cos ∅ = adjacent length/hypotenuse lengthtan ∅ = opposite length/adjacent length.Part A: Apply the trigonometric ratio, tan ∅ = opp/adj, to find the length of the pole
∅ = 41°
Opp. = length of pole
Adj. = 34 ft
Substitute
tan 41 = length of pole/34
Length of pole = (tan 41)(34) = 29.6 ft.
Part B:
Let the distance between the base of the pole and wire 2 be represented as x. Therefore, apply tan ∅ = opp/adj.
∅ = 38
Opp. = x
Adj. = 29.6 ft
Therefore:
tan 38 = x/29.6
x = (tan 38)(29.6)
x = 23.1 ft.
Part C: Use the Pythagorean theorem to find the length of wire 1.
Length of wire 1 = √34² + 29.6²)
= 45.1 feet.
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Help me how do I graph this I don’t understand at all?????????
The ones digit is 2 less than the tens digit, and the sum of this number and its reversed number is 154.
Answer:
Step-by-step explanation:
the answer is 86
hope it helps!
(-_-)
help meeeeeeeeeeeeeee pleaseee
The vertex of the curve will be at (-2, -4) and the axis of symmetry is at -2
How to illustrate tye information?From the graph, the roots of the equation are -4 and 0, therefore, (x + 4) is a factor and x is also a a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = + 4x
The x coordinate of the vertex =
will be illustrated as:
-b/2a = axis of symmetry
a and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
Then, substitute x = -2 into y = + 4x to find the y-coordinate of the vertex
y = (-2)² + 4(-2)
y = 4 -8
y = -4
vertex = (-2, -4)
The axis of symmetry is -b/2a which is -2
Therefore, the vertex is at (-2, -4).
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The table shows the probabilities that a biased dice will land on 2, on 3,
on 4, on 5 and on 6.
Number on dice
Probability
1
2
0.1
3
0.17
4
5
6
0.08 0.16 0.14
Paulo rolls the biased dice 300 times.
Work out an estimate for the total number of times the dice will land on 1 or on 5
The total number of times the dice will land on 1 or on 5 is 153.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.All of the probabilities will add up to 1. This gives us the equation.
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
P(1) + 0.17 + 0.08 + 0.16 + 0.14 + 0.1 = 1
P(1) + 0.65 = 1
P(1) = 1 - 0.66
P(1) = 0.35
We now need to find the probability of 1 or 5.
P( 1 or 5) = P(1) + P(5)
= 0.35 + 0.16
= 0.51
We now use the predicting outcomes formula
Expected = P( 1 or 5) * No. of times
= 0.51 * 300
= 153
Hence, the total number of times the dice will land on 1 or on 5 is 153.
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Hayden and Jamie completed 20 math problems together. Jamie completed 2 more than twice the number that Hayden completed. Let p represent the number of math problems Hayden completed.Write an equation that can be used to find the number of math problems that Jamie completed.
Answer:
[tex]p+p+2=20[/tex]
Step-by-step explanation:
This is what my math teacher told us, so I don't know try this.
Step-by-step explanation:
p + j = 20
j = 2p + 2 --> -2p + j = 2
[tex] \binom{1 \: 1}{ - 2 \: 1} \: \binom{20}{2} = \binom{p}{j} [/tex]
Given: 2x+3=4x-5
Prove: x=4
Answer:
Step-by-step explanation:
2x + 3 = 4x - 5
4x - 5 = 2x + 3
Step 1 : Add 5 on both sides.
4x = 2x + 3 + 5
4x = 2x + 8
Step 2 : Subtract 2x on both sides.
4x - 2x = 8
2x = 8
Step 3 : Divide 2 on both sides.
x = 8/2
x = 4
Hence proved.
Answer:
Collect like terms
3+5=4x-2x
(note that when - crosses a line it turns to +
8=2x
8/2=2x/2
x=4
How is this triangle congruent?
Answer:
triangle CBA is congruent to triangle CDA
The triangles are not congruent
what are the coordinates of the image of vertex after a reflection of r x-axias (x,y)
The coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).
To get the coordinates of a point reflected on the x - axis, some important rules be considered here:
1. The x - coordinate of the reflected point is the same as the x - coordinate of the original point.
2. The y - coordinate of reflected point has opposite sign of y-coordinate of original point.
Example:
(1,9) when reflected on the x - axis it will be (1,-9).
Therefore the coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).
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WILL MARK BRAINLIEST! Determine the quadratic function of the form f(x)= a(x - h)² + k whose graph is given on the
right.
Answer:the quadratic function in f(x)= a(x-h)^2+k is f(x) = - (x - 2)² + 2.I think this is false";}
Step-by-step explanation:
What is the mathematical name of the shape
Answer:
Triangular prism
Step-by-step explanation:
If you were to fold all the creases and glue it together you would get a tent shape which is a triangular prism
best ontime airlines: hawaiian airlines topped the list of the most punctual u.s. airlines for full-year 2014, according to data released by the bureau of transportation statistics. the on-time arrival performance was 91.9% another aviation data service believes that this percentage now is even higher. the team of researchers chose 130 randomly selected flights and find that 120 of the flights arrived on time. can a hypothesis test be used to determine whether the proportion of hawaiian airlines flights that arrive on-time is higher than 91.9%? group of answer choices yes, because the sample is random. thus, it is representative of the population of flights for the airlines. yes, because the sample is random and (130)(0.923) and (130)(0.077) are both at least 10. this means the normal model is a good fit for the sampling distribution. yes, because the sample is random and (130)(0.919) and (130)(0.081) are both at least 10. this means the normal model is a good fit for the sampling distribution.
1.because sample is random and (130)
(0.923) and (130)(0.077) are both at least 10.
This means the normal model is a good fit for the sampling distribution.
Consider the provided information.
130 randomly selected flights and find that
120 of the flights arrived on time.
n=130
The on-time arrival performance was 91.9%
p=0.923 and q=1-0.923=0.077
np = 130 x 0.923
np = 120 ≥ 10
nq = 130 × 0.077
nq = 10 = 10
Hence, Yes, because sample is random and
(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.
2.because sample is random and (130)
(0.919) and (130)(0.081) are both at least 10.
This means the normal model is a good fit for the sampling distribution.
Consider the provided information.
130 randomly selected flights and find that
120 of the flights arrived on time.
n=130
The on-time arrival performance was 91.9%
p=0.919 and q=1-0.919=0.081
np = 130 x 0.919
np = 119.5 ≥ 10
nq = 130 × 0.081
nq = 10.5 ≥ 10
Hence, Yes, because sample is random and
(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.
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Ms.emlyn buys a hat and gloves with a coupon for 30% off her entire purchase. the gloves cost $35 before the discount. her bill before tax is $44.80.write an equation to find the original cost of the hat.
The equation to find the original cost of hat is
44.80 = (x + 35) - (x+35)× 10/3
In the given question we have,
Ms. emlyn buys a hat and gloves with coupon for 30% off her entire purchase.
discount on total purchase = 30%
cost of gloves before discount = $35
let the cost of hat be $x before discount . The bill paid by Ms emlyn after discount but without tax = $44.80
total cost ( hat+gloves) before discount= $(x+35)
Now, after sum up all information we get,
$(x+35) - 30%discount on $(x+35) = $44.80
=> x+35 - (x+35)100/30 = 44.80
=> x+35 - (x+35)10/3= 44.80
which is required equation for original cost of hat.
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I GIVE you 20 points if you answer ASP PLS
The function graphed shows the total cost of a gym membership for x months.
Select from the drop-down menus to correctly identify the gym membership information provided by the graph.
The Slope is
The Slope Represents
Answer: Y=mx+b
Step-by-step explanation:
If you use the formula you can figure it out.
Answer:
the slope is 10
The slope represents the cost of gym membership per month.
for g(x)=x to the power of 2 minus x, find g(x) when x=-2
The value of the function g(x) when x = -2 is 6
How to evaluate the function?The definition of the function is given as
g(x)=x to the power of 2 minus x
Rewrite the above function properly
So, we have the following representation
g(x) = x² - x
To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2
This is represented by
Calculate g(x), when x = -2
Substitute -2 for x in the equation g(x) = x² - x
So, we have the following equation
g(-2) = (-2)² - (-2)
Evaluate the exponents
This gives
g(-2) = 4 - (-2)
Evaluate the sum
g(-2) = 6
Hence, the value of the function is 6
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How to solve for x step by step 3x-1=20
Answer:
x = 7
Step-by-step explanation:
Given equation,
→ 3x - 1 = 20
Now the value of x will be,
→ 3x - 1 = 20
→ 3x = 20 + 1
→ x = 21/3
→ [ x = 7 ]
Hence, the value of x is 7.
HELP MEEE PLEASEEEEEE
Answer:
Length YZ is about 16.2 cm (to the first decimal place)
Step-by-step explanation:
In order to find the lenth YZ we need to know the the Pythagorean theorem which is a²+b²=c² (or leg² + leg² = hypothnose)
For this problem let a = line segment XY, let b = YZ and let your hypothnose (c) to be ZX
Substitute your known values in the equation so we know a = 5 cm and c = 17 cm so we can apply it in our equation 5²+ b² = 17² Square your known values in this case 5² and 17² which is 25 and 289 respectively. The equation is now 25+b²=289 Do the inverse operation to Isolate you unknown variable which is b. We do this by subtracting 25 on both sides after doing so the equation is now b²= 264 Square root both sides of the equation the point is to get rid of the squared part of b². After doing so your answer is b = 16.2480768093Round to the first decimal place the two remains the same so the final answer is 16.2 cmhelp me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Answer: love
Step-by-step explanation: love
LOTS OF POINTS coordinate proof explaining how the midsegment of a triangle forms a triangle with 1/4 of area
The coordinate geometry, the midsegment theorem shows that the midsegment of a triangle is 1/4 area of the triangle.
How to show that the midsegment of a triangle is 1/4 area?
The midsegment if a triangle is defined as a line that joins two midpoints of two opposite sides of a triangle.
The midsegment theory of a triangle states that in a triangle, the midsegments of 2 sides is parallel to, and half the length of the 3rd side.
The 3 midsegments of a triangle forms a small triangle within the larger triangle.
This therefore, forms 4 triangles.
Area of a triangle =base x height
Hence 4 triangles are formed,
The area of the larger triangle is [tex]\frac{bh}{4}[/tex] =1/4(bh)
Therefore; Area =1/4 of area.
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0.1 times n equals 89.5
Answer: n=895
Step-by-step explanation:
Answer:
n = 895
Step-by-step explanation:
Here we want to find n , 1st form the Equation then solve it for n
0.1 times n = 0.1n
0.1 times n equal 89.5
Then 0.1n = 89.5
Solve for n , b dividing both sides by 0.1
n = 89.5 / 0.1 = 895
-13x + x = 8x – 20x help me pls
The solution of the equation given as -13x + x = 8x - 20x is infinite many solutions
How to evaluate the equation?From the question, the equation is given as
-13x + x = 8x - 20x
To start with, we need to rewrite the expression
So, we have the following representation
x - 13x = 8x - 20x
Solving further, we need to evaluate the like terms
So, we have the following equation
-12x = 8x - 20x
Evaluate the like terms again
So, the equation becomes
-12x = -12x
Both sides of the above equation are the same
i.e. -12x is on both sides of the equation
When we have a solution that all sides of the equation have the same value, then the solution is that the equation has infinite many solutions
Hence, -13x + x = 8x - 20x has infinite solutions
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(d)
After one year, the value of Annie's car had reduced by 20%.
At the end of the second year, the value of Annie's car had reduced by a further 15% of its value at the
end of the first year.
07
(i) Calculate the overall percentage reduction after the two years.
20