Step-by-step explanation:
2x-10x+6=4x-6
2x-10x-4x=-6-6
-12x=-12
x=1
A producer of printed circuit boards (PCBs) wishes to estimate the scoring depth of their circuits. To this end, they have collected 45 samples of measured depths. The mean and standard deviations of these samples is 0.165 mm and 0.022 mm respectively.
1. Create a plot showing the dependence of the size of the confidence interval (ρ) on the confidence level (γ) ranging from 0 to 1. Keep the sample size fixed at 45
2. Create a plot showing the dependence of the size of the confidence interval on the
sample size ranging from 1 to 100. Keep the confidence level fixed at 0.95. (Here you
can assume normality even where N <30)
3. Create a plot showing the pdf of the sample mean and with the area computed above shaded in. Hint: plt.fill between.
The mean and the standard deviations of the samples is 0.165 mm and 0.022 mm.
n = 45
[tex]\overline{X} = 0.165{~}mm[/tex]
s = 0.022 mm
Now, 95% of the confidence interval.
[tex]CI=\overline x {~}\pm t_{\frac{\alpha}{2}, n-1 }\frac{s}{\sqrt{n} }[/tex]
The critical values are:
α = 1 - 0.95 = 0.05
n - 1 = 45 - 1 = 44
[tex]t_{\frac{\alpha}{2} , n-1=t_{0.025,44}=2.0154[/tex]
So, 95% of CI = 0.165 ± 2.0154 × ( 0.022 ÷ √45 )
95% CI = ( 0.158, 0.172 )
1. The plot for the dependence of the size of the confidence interval on the confidence value ranging from 0 to 1.
2. A plot showing the dependence of the size of the confidence interval on the sample size ranging from 1 to 100.
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What are the positive and negative square roots of 256?
Answer:
16 and -16
Hope this helps! :)
what’s the answer????
Domain and range of the graphs are as follows:
1. D: [-4,4] and R: [1,3]
2. D: [-3,5] and R: [0,6]
3. D: [-2 ∝] and R: [-2,4]
Given:
In the first graph:
The graph's domain is its left-to-right travel distance.
Start by examining the leftmost point on this graph.
At the farthest left point, the x-value is at x=-4 Trace the graph once more until you reach the location that is the furthest to the right.
At this point, the x-value is 4. The graph is continuous from -4 to 4 since there are no breaks running from left to right.
Domain is as [-4,4] also written as -4 ≤x≤4
The graph's range is its vertical range from down to up.
Look at the graph's lowest or most distant point. At this point, the y-value is equal to 1. Now examine the graph's top or how high it rises.
This is when x=-4 or x=4, but since we're determining the range right now, we need to take a look at the point's y-value, which is at y=3. Since the graph is continuous from top to bottom, there are no breaks in it.
Range : [1,3] also written as 1 ≤ y ≤ 3
similarly we find the rest of the domain and range of the graphs.
Hence we don't get any line of symmetry in the graph.
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Look at the figure. If <1 = <2 , describe the relationship between lines a and b.
Answer:
Without seeing the picture. I think that the answer might be parallel lines. The two angles pictures might be corresponding angles which means that the lines would be parallel.
Step-by-step explanation:
Two concentric circles are of radii 5 cm and 3 cm. Determine the length of the chord of the larger circle which touches the smaller circle.
The length of the chord of the larger circle which touches the smaller circle.
The chord of the larger circle which is touches the smaller circle having the length of 8cm.
Given that
Two concentric circles are of radii 5 cm and 3 cm.To find
The length of the chord of the larger circle which touches the smaller circle.So, according to the question
we have,
The radius of larger circle = 5cm.The radius of smaller circle = 3cm.From attached figure of that problem,
BC = 5cm
CD = 3cm
AB = ........? (have to find) or from geometry
AB = 2 BD ---------(1)
Now, we have to find BD,
So, from right angle triangle BDC.
BD² = BC²-CD² ( by Pythagoras theorem )
BD = [tex]\sqrt{(BC)^2-(CD)^2}[/tex]
Putting the given values,
BD = [tex]\sqrt{(5)^2-(3)^2}[/tex]
BD = [tex]\sqrt{25-9}[/tex]
BD = [tex]\sqrt{16}[/tex]
BD = 4 (∵[tex]\sqrt{16} = 4[/tex])
Now, putting the value of BD in equation (1)
AB = 2 BD ---------(1)
= 2×4
AB = 8
Answer:
The length of the chord of the larger circle which touches the smaller circle is 8cm.To learn more about Pythagoras theorem, please click on the link:
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4 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids. The
winner offers a bid of $4,000, how much will that bidder need to put into a kitty for the other bidders to
be compensated?
The amount of bidder needs to put into a kitty for the other bidders to be compensated will be $3,000.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
An object may be claimed jointly by 4 persons with the intent to split it using the sealed bid method. The winning price is $4,000.00.
The amount of bidder is given as,
⇒ $4,000 - $4,000/4
⇒ $4,000 - $1,000
⇒ $3,000
The amount of bidder needs to put into a kitty for the other bidders to be compensated will be $3,000.
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help me, i need to learn the Pythagorean theorem. ill pick brainliest!
Answer: The definition/meaning of it is a theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Step-by-step explanation: If you need the equation solved, I can try just type under this.
3× 1,250 in expanded form and use distributive property
Use proportions to solve the following problem.
A 30-pound bag of topsoil will cover a surface area of 9 ft^2.
a) How many pounds of topsoil are needed to cover a surface area of 270 ft^2?
b) How many bags of topsoil must be purchased to cover a surface area of 270 ft^2?
It would take 16 days for the number of magical coins to exceed 50,000.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
30 pound = 1 bag
30 pound = 9 ft²
a) For a surface area of 270 ft²:
Number of pounds = 270 ft² * 30 pound per 9 ft² = 900 pounds
b) For a surface area of 270 ft²:
Number of bags = 900 pounds * 1 bag per 30 pound = 30 bags
900 pounds is needed to cover a surface area of 270 ft² and 30 bags would be needed to be purchased
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Determine ratio of A to B. Round as indicated.
A = 24.7% is the divorce rate in City A
B = 28.7% is the divorce rate in City B
(Round to the nearest hundredth when necessary.)
Select one:
O a. 0.09
O b. 8.61
OC. 0.86
O d. 1.16
Ratio of A to B is option c 0.86
Given,
Divorce rate in City A = 24.7%
Divorce rate in City B = 28.7%
We have to find the ratio of A to B
First we have to change the percentage to fraction form.
That is,
Divorce rate in City A = 24.7% = 24.7/100
Divorce rate in City B = 28.7% = 28.7/100
Now, ratio of A to B
(24.7/100) : (28.7/100)
Equate this into fraction form.
That is, A : B = A/B
Therefore,
(24.7/100) : (28.7/100)
= (24.7/100) / (28.7/100)
= 24.7 × 100 / 28.7 × 100
= 2470 / 2870
= 0.86 approximately.
That is the ratio of A to B is 0.86.
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One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1,240. The next
week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1,027. The following week, they sold
5 7 trumpets, 7 clarinets, and 2 violins for $2,091. Find the cost of a trumpet, clarinet, and
violin
(6,1)+(8,9)
What’s the slope
The slope of the line with the given coordinates (6,1) and (8,9) is 4.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 6,1 )
x₁ = 6y₁ = 1Point 2( 8,9 )
x₂ = 8y₂ = 9Plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 9 - 1 )/( 8 - 6 )
Slope m = ( 8 )/( 2 )
Slope m = 8/2
Slope m = 4
Therefore, the slope of the line with the given coordinates (6,1) and (8,9) is 4.
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How many solutions will each system of linear equations have? Match the systems with the correct number of
solutions.
y=x+6 and 3x-3y=-18
y=-2x+5 and 2x+y = -7
y=-4x+11 and -6x + y = 11
infinitely many solutions
no solution
one solution
The appropriate choices will be as follows in light of the provided information:
There are countless solutions to the equations: y = x + 6 and 3x - 3y = -18.2x + y = -7 and y = -2x + 5: Respectively, no answer.-6x + y = 11 and y = -4x + 11: One answer.What are equations?A mathematical statement known as an equation consists of two expressions joined by an equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.So,
y = -4x + 11 ... (1)-6x + y = 11 ... (2)Add equation I to equation II.
-6x + y = 11-6x + (-4x + 11) = 11-6x - 4x + 11 = 11-6x - 4x = 11 - 11-10x = 0x = 0Consequently, x=0 and y=11 Each variable's solution is provided by this.
y = -2x + 5 ... (1)2x + y = -7 ... (2)Put equation I into equation II.
2x + y = -72x + (-2x + 5) = -72x - 2x = -7 - 50 = -12This means there is no answer.
y = x + 6 ... (1)3x - 3y = -18 ... (2)Put equation I into equation II.
3x - 3y = -183x - 3(x + 6) = -183x - 3x - 18 = -183x - 3x = - 18 + 180 = 0This implies that there are an infinite number of possible answers.
Therefore, the appropriate choices will be as follows in light of the provided information:
There are countless solutions to the equations: y = x + 6 and 3x - 3y = -18.2x + y = -7 and y = -2x + 5: Respectively, no answer.-6x + y = 11 and y = -4x + 11: One answer.Know more about equations here:
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Last time Laura hosted a fancy dinner party for her friends, she spent $108 to feed 9 people. This time, there will be only 7 people at the dinner party. How many dollars should Laura expect to spend this time?
The number of dollars Laura should pay at the dinner party is $84.
Given that, the last time Laura hosted a fancy dinner party for her friends, she spent $108 to feed 9 people. This time, there will be only 7 people at the dinner party.
What is proportion?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of dollars paid by Laura for 7 people be x.
Now, 9:108::7:x
⇒9x=108×7
⇒x=12×7
⇒x=84
Therefore, the number of dollars Laura should pay at the dinner party is $84.
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In the quation below all the asteriks stand for the same number.
What Is the number?
Ivan and Tanya share £150 in the ratio 4:1 work out how much more ivan gets compared to tanya
Ivan and Tanya share £150 in the ratio 4:1 workout. lvan gets more compared to Tanya. = $ 90
Ratio :
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.
Total Ivan and Tanya share = £150
Ivan and Tanya share in the ratio of 4:1 respectively.
Let 4x be the money got by Ivan and x be the money got by Tanya.
Then, according to the question, we have
4x+x= 150
5x = 150
x= 150/5
x= 30
∴ Ivan has Money = 4x
= 4*30
= $ 120
Tanya has Money = x
= $ 30
Difference = 120-30 = $ 90
Hence, Ivan gets more compared to Tanya. = $ 90
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Tanya and Ivan split £150 in the 4:1 workout. Tanya receives less compared to Ivan. = $ 90
Ratio:
A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.
Ivan and Tanya's combined portion is £150.
Tanya and Ivan each share in a ratio of 4:1.
Let x and 4x represent Tanya's and Ivan's respective earnings.
Then, according to the question, we have
4x+x= 150
5x = 150
x= 150/5
x= 30
∴ Ivan has Money = 4x
= 4*30
= $ 120
Tanya has Money = x
= $ 30
Difference = 120-30 = $ 90
Hence, Ivan gets more compared to Tanya. = $ 90
Please help!!
Create a polynomial with 3 terms, written in standard form.
how do you know it’s in standard form?
if you can explain it as well that would be great :)
In mathematics, a polynomial is a mathematical expression that is the sum of a number of terms that contain the same variable raised to different powers. These come up all the time in the study of mathematics, so it is important to be familiar with them and the different forms we can write them in.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To write a polynomial in standard form, we make sure that any like terms are combined, and then we arrange the terms so that the exponents of each term go in descending order.
For example, consider the following polynomial:
8x - x⁵ + 2x + 3x² - 7x⁴ + 3To write this polynomial in standard form, we first look for any like terms that need to be combined, where like terms are terms that have the same variable raised to the same power. We see that 8x and 2x are like terms, so we add these together to turn our polynomial into the following:
10x - x⁵+ 3x² - 7x⁴ + 3Now, we just rearrange the polynomial so that the term with the highest degree goes first, the term with the second highest degree goes second, and so on until the polynomial is arranged so that the exponents go in descending order from highest to lowest.
-x⁵ - 7x⁴+ 3x² + 10x + 3This gives us our polynomial in standard form.
A polynomial with 3 terms : x² + 3x³ + 27 - x
___________________________________________
HELP FAST AGAIN PLEASE I BEG U
Answer:
[tex]\frac{72}9[/tex]
Step-by-step explanation:
We're asked to find out how many pages we will need to use if each paper can hold up to 9 cards. To find this, we would have to divide our total amount of cards by 9.
A dotplot of the distribution of height for Mrs. Navard’s class is shown, along with some numerical summaries of the data. Suppose that Mrs. Navard has the entire class stand on a 6-inch high platform and then asks the students to measure the distance from the top of their heads to the ground.
What are the mean and median of the new distribution of distance?
The new mean after adding a 6-inch high platform is 73 inches, while the median changes from 66 inches to 72 inches.
What are the mean and the median?The mean refers to the average of a data set and is the result of the sum of the values of the data set divided by the number of items.
The median is the middle value in the data set when arranged in an ascending or descending order.
For instance, the number of the data set is 25. The median value is the number 13, whose value is 66 inches in the old distribution or 72 inches in the new distribution.
Old Distribution of Heights:Height (in.) Number of Students Cumulative Total
60 1 60 (60 x 1)
61 0 60 (60 + 61 x 0)
62 2 184
63 4 436
64 2 564
65 1 629
66 3 Median 827
67 1 894
68 3 1,098
69 2 1,236
70 0 1,236
71 1 1,307
72 2 1,451
73 0 1,451
74 1 1,525
75 2 1,675
Mean = 67 (1,675/25)
New Distribution of Heights:Height (in.) Number of Students Cumulative Total
66 1 66 (66 x 1)
67 0 66 (66 + 67 x 0)
68 2 202
69 4 478
70 2 618
71 1 689
72 3 Median 905
73 1 978
74 3 1,200
75 2 1,350
76 0 1,350
77 1 1,427
78 2 1,583
79 0 1,583
80 1 1,663
81 2 1,825
Mean = 73 (1,825/25)
Thus, the new mean is 73 inches and the new median is 72 inches.
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help me with this
pls help
i love you <3
Answer:
Step by step evaluation
Formula
T = 4B + 10C
Sharlene purchased a new truck, whose value over time depreciates. Sharlene's truck depreciates according to the function y = 45,529(0.78)x, where x represents the number of months since the truck was purchased. What is the range of the exponential function y based on its equation and the context of the problem?
ℝ
y ≥ 0
y < 45529
0 < y ≤ 45529
The range of the exponential function y based on its equation and the context of the problem is; 0 < y ≤ 45529
What is the range of a function?The range of a function is the set that contains all possible output values for the function.
In this question, the function is given as: y = 45,529(0.78)^x.
It is an exponential function with initial value 45,529 and rate of change of 0.78.
Now, it should be noted that exponential functions that are not shifted down, such as this one, are never negative nor zero. Thus, the range also has the restriction y > 0, and is given by:
D. 0 < y ≤ 45529
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1. The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
27 30 41 27 20 22 36 37 44 45 29 29
(a) What is the five-number summary of the data set? Show your work.
(b) What is the range of the data set? Show your work.
(c) What is the interquartile range (IQR) of the data set? Show your work
1. The five-number summary of the data set is: 20, 27, 29.5, 39, 45.
b. Range = 25
c. Interquartile range (IQR) = 12
How to Find the Five-Number Summary?Given the data set for fuel efficiencies for vehicles featured in a car-buying guide as: 27, 30, 41, 27, 20, 22, 36, 37, 44, 45, 29, 29, we have five-number summary solved as shown below.
a. Minimum: 20 (smallest data point.)
First Quartile: 27 (center of the first part/half of the data set when ordered)
Median: 29.5 (center of the data set when ordered)
Third Quartile: 39 (center of the 2nd half of the data set when ordered)
Maximum: 45 (largest data point.)
Thus, the five-number summary of the data set is: 20, 27, 29.5, 39, 45.
b. Range = max - min
Range = 45 - 20
Range = 25
c. Interquartile range (IQR) = Third Quartile - First Quartile
Interquartile range (IQR) = 39 - 27
Interquartile range (IQR) = 12
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graph the function 2x +3y = -21
Answer:
check below
Step-by-step explanation:
2x + 3y = -21
3y = -21 - 2x
3y = - 2x -21
divide both sides by 3
y = -[tex]\frac{2}{3}[/tex]x - 7
Select the correct numeral form of this number written in scientific notation. 4.1 × 10 2
0.41
41,000
4,100
410
The longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m find the longer diagonal and the area.
If the longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m. The longer diagonal is 10m and the area is 30m².
Longer diagonalThe longer diagonal is calculated as:
Longer diagonal=6+4
Longer diagonal=10m
The area is calculated as:
Area of kite=5m×6m
Area of kite=30m²
Therefore If the longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m. The longer diagonal is 10m and the area is 30m².
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{ x − 10 ≤ x ≤ 15 }
it also needs to be graphed please help its due in 20 minutes
The graph is attached below:
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given:
x − 10 ≤ x ≤ 15
as, the given inequality we have to break the inequality is
x − 10 ≤ x and x ≤ 15
The graph to the inequality is attached below.
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Need help with this one.
Answer:
x ≠ 8, 5
Step-by-step explanation:
We only care about the denominator:
x² - 13x + 40
--------------------
-8 × -5 = 40
-8 + -5 = -13
--------------------
(x - 8) (x - 5) = 0
x - 8 = 0. x - 5 = 0
x = 8. x = 5
I hope this helps!
During Hurricane Matthew, Fayetteville received 14 ½ inches of rain in 21 %4 hours. What is the rainfall rate in inches per hour?
OA. inches per hour
OB. 1 inch per hour
O C. 1 ½ inches per hour
OD: 2 inches per hour
The rainfall rate in inches per hour is 2/3 inches per hour.
What is rate?A rate is a special ratio in which the two terms are in different units. a fixed ratio between two things2: a number, amount, or degree measured in relation to another quantity; examples include the heartbeat, metabolic rate, pulse, and sedimentation rate.
Given that,
The inches of the rain is 14×1/2is 29/2
The direction of the rain is 21×3/4 is 87/4
Rate is 29/2 /87/4
is29/2×4/87 is 2/3
Therefore, rate of rain is 2/3.
The rainfall rate in inches per hour is 2/3 inches per hour.
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Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,4) and (-7,6).
The standard form of the equation is(x + 2)² +(y - 5)² = 26
The equation of a circle in standard form is
(x - a)² + (y - b)² = r²
where (a , b) are the coordinates of the centre and r the radius
The centre is at the midpoint of the endpoints of the diameter and r is the distance from the centre to either of the 2 endpoints
Find centre using the ' midpoint formula'
(a , b) = [ (3 - 7), (4 + 6) ] = (-2 , 5)
to find r use the ' distance formula '
with (-2 ,5) and (3 , 4)
r = √(3 + 2)² + (4 - 5)² = √(25 + 1 ) = √26 ⇒ r² = (√26)² = 26
(x + 2)^² + (y - 5)² = 26 it is the equation in standard form'
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.
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What's 9+10
Please don't be stoopid
Answer: 19
Step-by-step explanation: 10
+ 9
19
Answer:
9+10=19
Step-by-step explanation:
Remember treat others as you want to be treated. That being said we are not stoopid.