[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8 - (-4)]^2 + [7 - (-3)]^2}\implies d=\sqrt{(-8+4)^2 + (7+3)^2} \\\\\\ d=\sqrt{(-4)^2 + 10^2}\implies d=\sqrt{116}\implies d\approx 10.77[/tex]
The slope of a line is -1/5, and the y-intercept is 5. What is the equation of the line written in general form?
Answer:
y= -1/5x+5
STEP BY STEP EXPLAINATION:
m = slope = -1/5
c = y-intercept = 5
equation of a straight line:
y=mx+c
so.
y= -1/5x+5
9. A computer chip manufacturer knows that 72% of the chips produced are defective.
Suppose 3000 chips are produced every hour, what is the probability that exactly 800
chips are acceptable? Compare the results of using the binomial distributions with
those found using the normal approximation.
The probability that exactly 800 chips are acceptable is less than 0.000001
How to determine the probability?The given parameters are:
Sample, n = 3000Percentage acceptable, p = 72%Acceptable chips, x = 800The binomial probability is represented as:
[tex]P(x) = ^nC_x * p^x * (1- p)^{n - x}[/tex]
So, we have:
[tex]P(300) = ^{3000}C_{800} * (72\%)^{800} * (1- 72\%)^{3000 - 800}[/tex]
The data values are large.
So, we use a statistical calculator to evaluate the expression
Using the calculator, we have:
P(300) < 0.000001
Hence, the probability that exactly 800 chips are acceptable is very small i.e. less than 0.000001
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The next model of a sports car will cost 11.8% more than the current model The current model costs 37,000.How much will the price increase in dollars?What will be the price of the next model
$0
$0
?
Answer:
436.6
Step-by-step explanation:
3700×0.118=436.6
What type of function is f(x) = 2x -14?
Exponential
Logarithmic
Polynomial
Rational
The function f(x) = 2x -14 is a polynomial function
How to determine the function type?The equation of the function is given as:
f(x) = 2x -14
A polynomial is represented as:
f(x) =ax^n + bx^(n - 1)....... + c
Where n is at least 1.
The function f(x) = 2x -14 is a polynomial with a degree of 1
Hence, the function f(x) = 2x -14 is a polynomial function
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Select the correct
What is the solution to this system of equations?
3x + y = 17
x + 2y = 49
O A.It has no solution.
OB. It has infinite solutions.
O C. It has a single solution: x = 15, y = 17.
OD. It has a single solution: x = -3, y = 26.
Suppose the scores of seven members of a women’s golf team are 68, 62, 60, 64, 70, 66, and 72. Find the mean, median, and midrange.
a.
Mean = 64, median = 64, midrange = 64
b.
Mean = 65, median = 64, midrange = 66
c.
Mean = 66, median = 77, midrange = 65
d.
Mean = 66, median = 66, midrange = 66
Please select the best answer from the choices provided
A
B
C
D
The mean, median, and midrange of the given that are 66, 66 and 66 respectively.
Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.
What is the mean, median, and midrange?Mean is the sum total of the number divided by number of terms
Median is the middle number when arranged in ascending or descending order.
Midrange is the average of the sum of the maximum number and the minimum number.
Given that;
Data set: 68, 62, 60, 64, 70, 66, and 72n = 7First, we arrange in ascending order.
60, 62. 64, 66, 68, 70, 72
Mean = ( 60 + 62 + 64 + 66 + 68 + 70 + 72 ) / 7
Mean = 462 / 7
Mean = 66
Median = 66
66 is the middle number.
Range = ( Max + Min ) / 2
Range = ( 72 + 60 ) / 2
Range = 132 / 2
Range = 66
Therefore, the mean, median, and midrange of the given that are 66, 66 and 66 respectively.
Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.
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I need to finish this, can someone please help!
Answer:
13
Step-by-step explanation:
a parallelogram has sides that are parallel to the opposite side. This means that y + 7 is going to be parallel to 20.
Two opposing sides of a parallelogram are parallel and equal
You know that the length of both of the sides is equivalent because the other set of opposing lines is also parallel (you can think of it as cutting off the line segment of y+7 and 20 at the same length. )
this means that we can set up the equation to find y as:
y + 7 = 20
then, you can proceed to find y by isolating it:
y + 7 = 20 ; so therefore
y + 7 = 20
- 7 -7
y = 13
y = 13
So, the value of y is 13
El parámetro a de una distribución exponencial cumple que
Pregunta 7 opciones:
a = 0
a < 0
a ≥ 0
a > 0
The parameters of an Exponential Distribution is D. a > 0
What is an Exponential Distribution?This refers to the distribution of probability with respects to time taken in a Poisson point process.
Hence, we can see that from the previous knowledge of exponential distributions, it is stated that λ > 0 is the parameter of the distribution, and is supported on the interval [0, ∞).
Therefore, option D is correct.
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Find the value of x.
4x = 4
Hint! Remember the Multiplicative
Identity Property.
1.a = a
X = = [?]
Enter the number that belongs in the green box.
Enter
Answer:
x=1
Step-by-step explanation:
4x=4
(Linear equation)
Solved:-
Transpose 4 from LHS to RHS:
[tex] \rm = > x = \tt \cfrac{4}{4} [/tex]
[tex] \rm = > x = \tt1 [/tex]
Rani uses a container that can hold 2 liters of water to fill a
fish tank. The fish tank can hold 8 liters of water. How many
times must she fill the smaller container to fill the fish tank?
Answer:
4 times
Step-by-step explanation:
If the smaller container only holds 2 liters, you would have to divide 8 by 2 which is 4.
Answer:
4 times
Step-by-step explanation:
Its 4 times cause 8/2=4
help and thank youu~
Answer:
Perimeter=150cm
Step-by-step explanation:
25cm×6=150cm
Find the quotient and remainder using long division.
x + x - 13
x - 2
The quotient is
The remainder is
Answer:
[tex]\text{The quotient is}~ x^2 +2x +5 \\\\\text{The remainder is}~ -3[/tex]
Step-by-step explanation:
I need this answer as soon as possible! 50 points!
[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]
Answer:
[tex]800\sqrt{5}[/tex]
Step-by-step explanation:
Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]
Properties of Exponents:
Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]
a number raised to a fraction, can be converted to a radical. the numerator becomes the exponent, and the denominator becomes the index of the radical.Product of Powers Property:
when multiplying powers with the same base, add the exponents.1. Convert into a radical:
[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]
2. Simplify the expression:
[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]
3. Evaluate the power:
[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]
4. Multiply:
[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]
What is the greatest common factor of 4xy2 and 20x2y4?
4xy
4
Answer:
4 x y ^2
Step-by-step explanation:
4 x y^2 would be the GFC
30% of the students in a class score an A on the last test. There are 50 students in the class. How many students scores an A on the test?
15
Step-by-step explanation:Percentages represent a proportion of a number. There are 2 ways to find a percent of a whole number.
Multiple of 10
Since 30% is a multiple of 10%, there is a shortcut we can use. We can find 10% and then multiply by 3 in order to find 30%. First, find 10% of 50. Like always, 10% of any number is that number divided by 10 (move the decimal 1 place to the left).
50/5 = 10So, 10% of 50 is 5.0.
Then, to find 30%, multiply 5 by 3.
5*3 = 1530% of 50 is 15.
Multiplication
The more consistent method includes multiplication, this can be used with any percentage. To use this method we need to convert 30% to a decimal. To convert any percentage to a decimal divide by 100 (move the decimal 2 places to the left).
30% / 100 = 0.30Now, we can multiply this decimal by the whole number, 50. This will give us our desired answer.
0.30*50 = 15So, this once again shows that 30% of 50 is 15.
Simplify surd need an answer asap please
What is the value of the next term in the geometric sequence graphed below?
OA. 4
B. 16
C. 8
OD. 32
SUBMIT
The value of the next term in the geometric sequence is 16
How to determine the next term?From the graph, we have the following highlights:
The graph is an exponential functiony multiplies by 2 as x increases by 1The means that:
Next term = Current term * 2
From the graph, we have:
Current term = 8
So, the equation becomes
Next term = 8 * 2
Evaluate
Next term = 16
Hence, the value of the next term in the geometric sequence is 16
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Worth 40 points! Select the correct answer.
What is the value of x in the triangle? (file of the picture is attached below)
Answer:
Its A
Step-by-step explanation:
This data set represents the widths in yards of pieces of fabric used by a sewing group. What is the mean of this data set? {113, 14, 23, 12, 114}
Answer:
55.2 is the mean
Explanation:
Given data set: {113, 14, 23, 12, 114}
Mean = sum of the terms/number of terms
Mean = (113 + 14 + 23 + 12 + 114)/5
= (276)/5
= 55.2
Answer:
Mean = 55.2
Step-by-step explanation:
Given data set: 113, 14, 23, 12, 114
To find the mean of a data set, divide the sum of all data values by the total number of data values:
[tex]\large \begin{aligned}\sf Mean & = \sf\dfrac{sum\:of\:all\:data\:values}{total\:number\:of\:data\:values} \\\\\implies \sf Mean & = \sf \dfrac{113 + 14 + 23 + 12 + 114}{5}\\\\& = \sf \dfrac{276}{5}\\\\& = \sf 55.2\end{aligned}[/tex]
The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar they notice a submarine is 7,390 miles away from them and north-west of their current position. What angle (off of a north-south line) do they need to travel to sail straight to the submarine?
The angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.
The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar, they notice a submarine is 7,390 miles away from them and north-west of their current position.
Therefore, the angle at which the Carrier needs to move to reach the submarine is,
Cosθ = 4365/7390
θ = Cos⁻¹ (0.59)
θ = 53.843°
Hence, the angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.
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The final exam scores in a statistics class were normally distributed with a mean of
70 and a standard deviation of five. What is the probability that a student scored
more than 65% and less than 75% on the exam?
Answer:
68.27%
Step-by-step explanation:
By the Empirical Rule, as 65% and 75% are both one standard deviation apart from the mean of 70%, then this represents 68.27% of the data.
A patient has been prescribed 1 gram (g) of Drug A. The stock dose is available in 250 milligram (mg) tablets. How many tablets would you administer per dose?
The patient would be administered 4 tablets per dose.
How do we use word problems to solve real-life problems?In mathematics, solving word problems involves a careful understanding of the content of the problem. This will enable the use of appropriate variables and data representation.
From the given information:
A patient has been prescribed = 1 gram of Drug A.A stock dose is available in = 250 mgFrom the standard conversion rate, we know that:
1 g = 1000 mgHere, to determine the number of dose to be administered, we have:
(x) /dose = 1000 mg/250 mg
x = 4 dose.
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4.5% of what number is 46.116?
Answer:
47.1408
Step-by-step explanation:
They gave us the percentage of a number and wants us to find the whole
to do that we will use the following equation:
46.116*100/4.5 = 47.1408 is the number we are looking for.
I need help please
A family purchases a light sphere to be used out on their patio. The diameter of the sphere is 20 in.
What is the volume of the light sphere?
Use 3.14 for pi.
Enter your answer, as a decimal, and round only your final answer to the nearest hundredth.
I have seen two different answers with 5 stars so I am confused on which person solved it correctly
Answer:
4,186.67 in³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3)(3.14)(10 in)³
V = (4/3)(3.14)(1,000 in³)
V = 4,186.666667 in³
A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.
Answer:
33,75 clients(huh?)
Step-by-step explanation:
75 / 100 = 0,75(1% of all clients)
0,75 * 45 = 33,75(number of business clients)
a. Use the product rule to find the derivative of the given function.
b. Find the derivative by expanding the product first.
h(z)= (3-2²) (2³-2z+3)
Answer:
h'(z) = 2
Step-by-step explanation:
(b) First, let's expand everything so our equation is easier to look at.
h(z) = (3-4)(8-2z+3)
(-1)(-2z+11)
2z-11
Now, let's find the derivative:
h'(z) = 2
Factor the polynomial using the greatest common factor.
x^2+3x
x²+3x
= x×x+3×x
= x(x+3)
Solve the system of
equation graphically, by
substitution, and by
elimination.
2x-5y = 34
y=3x-25
Determine the value of x please.
Figure and Answers choice below.
Answer:
B
Step-by-step explanation:
We can either use sine or cosine, I choose cosine but sine works the same. cos(angle) = adj/hyp. adj = cos(angle) x hyp. adj = cos(30)8, cos(30) = √3/2. √3/2 x 8 = 4√3
Suppose that 950 couples each have a baby find the mean and standard deviation for the number of boys in the 950 babies
The mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively
How to determine the mean and the standard deviation?From the complete question, we have:
P(boy)= 0.5
Sample size = 950
The mean is then calculated as:
[tex]\bar x = np[/tex]
This gives
[tex]\bar x = 950 * 0.5[/tex]
Evaluate
[tex]\bar x = 475[/tex]
The standard deviation is calculated as:
[tex]\sigma = \sqrt{np(1 - p)[/tex]
This gives
[tex]\sigma = \sqrt{950 * 0.5(1 - 0.5)[/tex]
Evaluate
[tex]\sigma = 15.41[/tex]
Hence, the mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively
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