The value 0.00073 feet per millisecond. in scientific notation is 7. 3 × 10⁴ feet per millisecond
What are index forms?Index forms are described as mathematical methods of writing or representing numbers that are too large or two small in more convenient forms.
They are written in the forms of exponents of numbers or variables,
There are other names for index forms which are scientific notation and standard forms.
From the information given, we have that;
The seahorse moves 0.5 miles per hour, or 0.00073 feet per millisecond
In converting 0.00073 feet per millisecond into index forms
count the number of zeros to the first significant number
7. 3 × 10⁴ feet per millisecond
Hence, the value is 7. 3 × 10⁴ feet per millisecond
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a= (6,7) and b= (1,2) if a-b =(x,y) work out values of x and y
The values of x and y are x = 5 and y = 5.
How to calculate vector sums?The subtraction of vectors a and b can be represented as the vector sum of a and the negative of b:
a - b = a + (-b)
To find the negative of b, simply multiply each component by -1:
-b = (-1) × (1, 2) = (-1, -2)
So,
a - b = a + (-b) = (6, 7) + (-1, -2) = (5, 5)
Therefore, the values of x and y are 5 and 5 respectively.
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Your family purchases a new car for $20,000. Its value decreases by 15% each year. During what interval does the car's value exceed $10,000? Round your answer to the nearest hundredth.
From the time it was purchased until about years later.
The value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.
Rounding to the nearest hundredth, the interval is 1 year.
Using the following formula, we can determine the car's value each year:
value = 20000 * [tex](1 - 0.15)^year[/tex]
We're looking for the years where the value exceeds $10,000.
Let's start by determining the car's value after 1 year:
value = 20000 * [tex](1 - 0.15)^1[/tex] = 20000 * 0.85 = 17000
We need to keep lowering the value since it will eventually exceed $10,000 because the value after one year is less than $10,000.
After 2 years:
value = 20000 * (1 - 0.15)² = 20000 * 0.85² = 14525
Still less than $10,000.
After 3 years:
value = 20000 * (1 - 0.15)³ = 20000 * 0.85³ = 12318.75
Since the value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.
Rounding to the nearest hundredth, the interval is 1 year.
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The following times, in seconds, were recorded for a mouse to run through a maze 34, 12, 10, 11, 12, 13, 9
Find the median and the mean
Suppose every piece of data in a set is increased by 20 after treatment. how does this affect the values of the mean and median
The median of the data set is 12.
The mean is 11.29.
Increasing every piece of data by the same value increases the mean and median by the same amount.
How to Find the Median and Mode?The median of the data set is the middle value when the data is arranged in numerical order. To find the median of the data set, we need to arrange the data in increasing order: 9, 10, 11, 12, 12, 13, 34. The median of this data set is 12.
The mean of the data set is the average of all the values. To find the mean, we need to add up all the values and divide by the number of values: (9 + 10 + 11 + 12 + 12 + 13 + 34) / 7 = 11.29.
If every piece of data in the set is increased by 20 after treatment, the new values are 29, 30, 31, 32, 32, 33, 54. The new median is 32 and the new mean is 35.29.
When every piece of data is increased by the same value, the mean and median will increase by the same amount.
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5. A video game store has a 32% markup rate on all video game system. If the game system you wanted cost $399.00,
what would the markup amount be? What would be the total selling price for which the video store would sell to
you?
Answer:
526.68
To find out how much the price went up, you first want to find what 32% of 399 is.
32% of 399 = 127.68
The price will go up $127.68.
Now, just add that to the original price:
127.68 + 399 = 526.68
The price of the game system will now be $526.68
Step-by-step explanation:
Hope it helps! =D
Noah, Preston, and Zach run a broken mechanical pencil disposal service. Noah works 2 hours more than Preston, and Zach works 4 hours less than twice the amount Preston does. If they work 94 hours total, how many hours does each of them work?
Noah, Preston, and Zach work for 26 hours, 24 hours and 44 hours respectively
How to determine how many hours each of them works?
A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Let N, P and Z represent the number of hours Noah, Preston, and Zach work respectively. Thus, we can write:
N = P + 2 ---- (1)
Z = 2P - 4 ---- (2)
N + P + Z = 94 ---- (3)
Put (1) and (2) in (3):
N + P + Z = 94
P+2 + P + 2P-4 = 94
4P -2 = 94
4P = 94 + 2
4P = 96
P = 96/4
P = 24
Since N = P + 2,
N = 24 + 2 = 26
Since Z = 2P - 4,
Z = 2(24) - 4 = 44
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An experiment has 14 possible outcomes, all equally likely. An event can occur in 7 ways. Find the probability that the event occurs.
Probability that the event can happen = 1/2
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes
Given,
Total outcomes of event = 14
Outcomes, event can happen = 7
Probability
= Favorable Outcomes/Total Outcomes
= 7/14 = 1/2
Hence, 1/2 is Probability that the event occurs.
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How many solutions are there? 1/2x-1/3y=5 x=2/3y+10
A. There are no solutions.
B. There is one solution.
C. There are infinitely many solutions.
D. It is not possible to determine the number of solutions.
Answer:
Step-by-step explanation:
this is a simultaneous equation type. so there are only 2 solutions. one for X and one for Y
chen's pedometer says he walked 5,600 meters today. how many kilometers has chen walked today?
Answer:
5.6km
Step-by-step explanation:
1km = 1000 meters
5,600 meters = 5.6km
5600 divided by 1000 = 5.6km
So, Chen walked 5.6km today.
Find the perimeter of △XYZ. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
45.0 units is the required perimeter of triangle XYZ
Similar triangle and perimeter of triangle.Triangles are known to be similar if the ratio of the similar sides are equal to a constant. The perimeter is the sum of all the sides of the triangle.
From the given diagram , we need to solve for the value of x first as shown:
9/10 = 14/x
9x = 140
x = 140/9
x = 15.6
Find the required perimeter of XYZ
perimeter = ZY + XY + XZ
perimeter = 15.4 + 14 + 15.6
Perimeter = 45.0 units
Hence the perimeter of triangle XYZ is approximately 45.0 units
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Find the number that makes the ratio equivalent to 4:1.
40:
Answer:
Below
Step-by-step explanation:
You multiplied the '4' by 10 to get 40 .....multiply the '1' by 10 the get the second number = 10 this will keep the ratio correct
Expand and simplify (x - 3)(x + 5)
Answer:X[tex]x^{2} +2x-15[/tex]
Step-by-step explanation: you do it by multiplying out the brackets and then you simplify the result expression by collecting the like terms.
The probability distribution below id for the random variable X= the number of credits taken by a randomly selected first year student at a large state university.
A. is X a discrete or continuous random variable? explain.
B. Show that the probability distribution of X is valid
C. Compute and interpret the expected value of X
D, The standard deviation is 0.829. Interpret this value in the context of the problem
E. Express the event "taking at least 16 credits" in terms of X and find its probability
Answer quickly please
A. X is a discrete random variable
B. The conditions are satisfied.
C. The expected value of X is 15.25
How to determine if X a discrete or continuous random variable?A. X is a discrete random variable because it can only take on specific values (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16) and not any value in an interval.
B. To show that the probability distribution is valid, we need to check if the following conditions are satisfied:
1. P(X=x) ≥ 0 for all x in the set of possible values of X
2. The sum of all probabilities equals 1
From the information given, it appears that these conditions are satisfied.
C. The expected value of X can be calculated as the weighted average of all possible values of X, where the weights are their corresponding probabilities.
E(X) = Σ[x * P(X=x)]
E(X) = (14*0.15) + (15*0.55) + (16*0.20) + (17*0.10) = 15.25
The expected value of X, which is 15.25, represents the mean or average number of credits taken by a randomly selected first-year student at the large state university.
D. The standard deviation measures the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the values are close to the mean (expected value), while a high standard deviation indicates that the values are spread out over a wider range. In this context, a standard deviation of 0.829 means that the number of credits taken by first-year students at the university is spread out over a range of approximately 0.829 units on average.
E. The event "taking at least 16 credits" can be expressed as X ≥ 16. To find its probability, we can sum up the probabilities of all the values that are greater than or equal to 16.
P(X ≥ 16) = ΣP(X = x)
P(X ≥ 16) = 0.20 + 0.10 = 0.30
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Probability: How do I go about this question
The value of k that makes the probability distribution valid is given as follows:
k = 4.
How to obtain the value of k?To obtain the value of k, we must consider that the integral assumes a value of 1 over it's entire domain, that is:
[tex]\int_{-1}^{1} F(x) dx = 1[/tex]
The function F(x) is given as follows:
F(x) = (x + 2)/k.
Considering 1/k as a constant, the integral is given as follows:
1/k[0.5x² + 2x].
At x = 1, the integral is given as follows:
0.5 + 2 = 2.5.
At x = -1, the integral is given as follows:
0.5 - 2 = -1.5.
Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:
1/k[2.5 - (-1.5)] = 4/k.
As the result of the integral must be of one, the value of k is obtained as follows:
4/k = 1
k = 4.
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write down the equation of a line perpendicular to y = 1/2x - 4 which passes through (0,7)
(i got the answer y = 2x + 7, can anyone confirm if this is right/wrong?)
Answer:
y = -2x + 7
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals.
That means that their product is -1.
If the slope of a line is m, then a perpendicular line has slope -1/m.
Given line slope: 1/2
Perpendicular slope: -2
Perpendicular line:
y = -2x + b
Point on new line: (0, 7)
7 = -2(0) + b
b = 7
Perpendicular line:
y = -2x + 7
Perpendicular lines have slopes that are negative reciprocals of each other.
Solving the QuestionWe're given:
Perpendicular to [tex]y =\dfrac{1}{2}x - 4[/tex]Passes through (0,7)First, we must find the slope.
The negative reciprocal of [tex]\dfrac{1}{2}[/tex] is -2.Plug this into [tex]y=mx+b[/tex]:[tex]y=-2x+b[/tex]The y-intercept occurs when x=0. Therefore, given the point (0,7), we know that the y-intercept is 7:
[tex]y=-2x+7[/tex]Answer[tex]y=-2x+7[/tex]
Just wanted to ask if anyone has any advice on what maths textbooks to buy/things I can use to improve maths etc. I’m a grade 2 in maths and I find very difficult.
Answer: Young gentleman. Here are some things you can use.
Step-by-step explanation: Calculator, Desmos (this was a website) ruler, protractor, math dictionary.
Find a possible formula for the trigonometric function whose values are in the following table .
The trigonometric function for the values in the table is defined as follows:
y = 3sin(π/4(x - π/2)) + 3.
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function has a maximum value of 6 and a minimum value of 0, for a difference of 6 units, hence the amplitude is obtained as follows:
2A = 6
A = 3.
Without vertical shift, a function with amplitude of 3 would oscillate between -3 and 3, while this one oscillates between 0 and 6, hence the vertical shift is given as follows:
D = 3.
The shortest distance between repetitions can be given by 8 - 0, hence the period is of 8 units and the coefficient B is given as follows:
2π/B = 8
B = 2π/8.
B = π/4.
The function is at's minimum value at x = 0, meaning that the sine function has a phase shift of π/2 units right, thus the coefficient C is given as follows:
C = π/2.
Then the function is defined as follows:
y = 3sin(π/4(x - π/2)) + 3.
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math assignment help
Since the abs. val. graph points down, there has to be a -1 outside the abs val symbol.
Since it's also going through (1,-3) and (-1,-3) instead of (1,-1) and (-1,-1), it's been stretched by a factor of 3.
So y = -3•|x| works.
Help! View picture!!
The ratios of the line segments are given below.
Determine the coordinates of point B and point D.
(5,0)
(-1,0)
(-1,-4)
(1,2)
(-4,6)
(-2,-6)
Therefore , the solution of the given problem of ratio comes out to be
CD:DE = 1:2. and AB:BC = 2:1 .
Describe ratio.Use the simple formula "a / b" to create a group of linked variables "a" and "b," where "b" may also be higher than zero. One ratio is created by combining two equation ratios. If there were only one man and three ladies, the ratio would be 1:1. There are 1/4 males and 3/4 girls in the group. A division between two or more objects, a number, or even a portion of a component's volume are all examples of parts.
Here,
Ratio 1: AB:BC = 2:1
Let's use the midpoint formula to find the coordinates of point C, which is the midpoint of line segment AB:
C = ((5+x)/2, (0+y)/2) = ((5+x)/2, y/2)
Since AB:BC = 2:1, we know that the distance from A to B is twice the distance from B to C. Using the distance formula, we can write:
2 * BC = AB
2 * √((x+1)² + y²) = √((x-5)^2 + y^2)
Simplifying this equation, we get:
4 * (x+1)² + 4y² = x² - 10x + 25 + y²
Simplifying further, we get:
3x²+ 8x - 16y² - 75 = 0
Ratio 2: CD:DE = 1:2
Let's use the midpoint formula to find the coordinates of point E, which is the midpoint of line segment CD:
E = ((p-1)/2, (q-4)/2)
Since CD:DE = 1:2.
Therefore , the solution of the given problem of ratio comes out to be
CD:DE = 1:2. and AB:BC = 2:1 .
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Answer:
(-4, 6) (-1, 0)
Source:
Took test. ✌
Which equation represents the graft function (0,3) (1,1)
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ -2 }{ 1 } \implies - 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=-2x+3 \end{array}}[/tex]
1. What number am I?
I have four digits.
My tens and tenths are the same value.
My hundredths is the difference of 5 and 1.
My tens is double my hundredths.
My ones is the other factor of 4 besides 1 and itself.
the height h of the triangle is 8cm greater than its corresponding base
Dante is working at Pizza Hut and trying to impress his boss for a promotion. His boss has been trying to figure which of these pizzas has an area closest to 450 square inches, and he came to Dante for help finding the answer because Dante is really good at math. Which one of these pizzas did he determine has an area closest to 450 square inches? (Use 3. 14 for pi)
Pizza 4 has the area closest to 450 square inches.
What is an area?
The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
To determine the pizza with the area closest to 450 square inches, Dante needs to calculate the area of each pizza. The formula for the area of a circle is A = πr², where r is the radius of the pizza.
Here are the areas of the four pizzas:
Pizza 1: A = π * 10² = 314 square inches
Pizza 2: A = π * 9² = 254.34 square inches
Pizza 3: A = π * 11² = 379.94 square inches
Pizza 4: A = π * 12² = 452.16 square inches
Out of the four pizzas, Pizza 4 has the area closest to 450 square inches. The area of Pizza 4 is 452.16 square inches, which is only 2.16 square inches greater than 450.
So, Pizza 4 has the area closest to 450 square inches.
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Demonstrate/explain how you can use the formula that partitions any segment into a given ratio to derive the specific formula for a midpoint. (Hint: Think of the ratio that is formed by a midpoint.)
let's say we have two points A(a , b) and B(c , d) partitioned by a point C, since we're dealing with the MidPoint, C is partitioning AB into two equal halves, so in the ratio of 1 : 1.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(a,b)\qquad B(c,d)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:1} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{1}\implies \cfrac{A}{B} = \cfrac{1}{1}\implies 1A=1B \\\\\\ 1(a,b)=1(c,d) \implies (a~~,~~ b)=(c~~,~~ d) \\\\\\ C=\left( \cfrac{a+c}{1+1}~~,~~\cfrac{b+d}{1+1} \right)\implies \stackrel{ \textit{MidPoint Formula} }{C=\left( \cfrac{a+c}{2}~~,~~\cfrac{b+d}{2} \right)}[/tex]
a sports uniform costs 160 dollars. For Christmas is sold at a discount of 35%.The cost of the sports uniform with the discount is??
Answer: 104
Step-by-step explanation:
To put it simply, let's say 100% is 160 dollars. When Christmas arrived, it was sold with a discount of 35%. This means we deduct 35% from 100% which is 65%. We then find 65% of 160 dollars, which is 104.
Hope that helps, if not, then please reply back :)
Consider parallelogram ABCD below.
Use the information given in the figure to find m ZB, x, and mBCA.
The values in the parallelogram figure are as follows
angle B = 74 degrees
x = 4
angle BCA = 49 degrees
How to find angle BRemembering that opposite angels of a parallelogram are equal will help us know that angel B is equal to angel D which is 74 degrees
The property that the two opposite sides of parallelogram is used to find x
4x = 16
x = 4
Applying alternate interior angles postulate, we can see that
angle BCA = angle DAC = 49 degrees
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Anna compra helado y naranjas en la tienda.
• Ella paga un total de $59.53.
• Ella paga un total de $6.49 por el helado.
• Ella compra 8 bolsas de naranjas que cuestan la misma cantidad cada una.
Escribe y resuelve una ecuación que se pueda usar para determinar X, cuánto cuesta
cada bolsa de naranjas.
Ecuación:
Respuesta: X=
Answer:
Ecuación: 59.53 - 6.49 = 53.04
53.04 / 8 = X
X = 6.63
Respuesta: X=6.63
Slope -2.5 and pass through (2,1.5) in slope intercept form
Answer:
y = -2.5x + 6.5
Step-by-step explanation:
The equation of the line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.
With a slope of -2.5 and a point (2,1.5) on the line, we can use the point-slope formula to find the equation of the line:
y - 1.5 = -2.5 (x - 2)
Expanding the right-hand side, we get:
y - 1.5 = -2.5x + 5
Adding 1.5 to both sides, we get:
y = -2.5x + 6.5
So the equation of the line in slope-intercept form is y = -2.5x + 6.5.
Which is the better value: $285 for 150 ft square of carpet or $252 for 120 ft square of carpet
Answer: $252 for 120 ft
Step-by-step explanation: Divide the money by the feet value in order to find dollars per foot. Since 252/120 = 2.1 $/ft and 285/150 = 1.9 $/ft, it would be better value to go with the 1.9 $/ft option.
50 POINTS
Which linear graph represents a proportional relationship?
a graph of a line that passes through the points 0 comma 0 and 0.5 comma negative 3
a graph of a line that passes through the points 0 comma 2 and 1 comma 5
a graph of a line that passes through the points 0 comma 4 and 1 comma 4
a graph of a line that passes through the points 0 comma negative 0.5 and negative 1 comma 0
The linear graph represents a proportional relationship, a graph of a line that passes through the points (0, 0) and (0.5, -3).
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given the coordinates to find the linear graph represents a proportional relationship,
we know the equation of a line given by,
y = mx + c
where m is the slope and c is the y-intercept,
to prove the graph the proportional value of the y-intercept should be zero, (0, 0)
when c = 0, y = mx
the equation will proportional,
When the line passes from the origin the equation will be proportional.
Hence option A is correct.
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Its A because if the line passes through the middle of the square is a proportional relationship.